Finite Group Databasebeta

← #26422962

Subgroups — #26422962

Order 12032.

1484 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251659C211yesmaximal, characteristic, complemented
2#20251624C211yesmaximal, characteristic, complemented
3#20251623C211yesmaximal, characteristic, complemented
4#20251622C211yesmaximal, characteristic, complemented
5#20251619C211yesmaximal, characteristic, complemented
6#20251591C211yesmaximal, characteristic, complemented
7#20251587C211yesmaximal, characteristic, complemented
8#20251584C211yesmaximal, characteristic, complemented
9#20251582C211yesmaximal, characteristic, complemented
10#20251565C211yesmaximal, characteristic, complemented
11#20251563C211yesmaximal, characteristic, complemented
12#20251532C211yesmaximal, characteristic
13#20251530C211yesmaximal, characteristic
14#20251458C211yesmaximal, characteristic, complemented
15#20251442C211yesmaximal, characteristic
16#20251437C211yesmaximal, characteristic
17#20246689C211yesmaximal, characteristic, complemented
18#20246689C211yesmaximal, characteristic, complemented
19#20246688C211yesmaximal, characteristic, complemented
20#20246688C211yesmaximal, characteristic, complemented
21#20246682C211yesmaximal, characteristic, complemented
22#20246679C211yesmaximal, characteristic, complemented
23#20246664C211yesmaximal, characteristic, complemented
24#20246658C211yesmaximal, characteristic, complemented
25#20246656C211yesmaximal, characteristic, complemented
26#20246649C211yesmaximal, characteristic
27#20246645C211yesmaximal, characteristic
28C4×#13094015C211yesmaximal, characteristic, complemented
29C4×#13094014C211yesmaximal, characteristic, complemented
30C4×#13094010C211yesmaximal, characteristic
31C47×#2396C211yesmaximal, characteristic, complemented
32C2×#13094015C2211yescharacteristic
33C2×#13094014C2211yescharacteristic
34C2×#13094010C2211yescharacteristic
35C2×C4×Dic94C2211yescharacteristic
36C2×C4×Dic94C2211yescharacteristic
37C2×C4×C22⋊D47C2211yescharacteristic
38C2×#13093981C2211yescharacteristic
39C47⋊#401C2211yescharacteristic
40C47⋊#401C2211yescharacteristic
41C47⋊#401C2211yescharacteristic
42C47⋊#401C2211yescharacteristic
43#15689065C2211yescharacteristic
44#15689065C2211yescharacteristic
45#15689065C2211yescharacteristic
46#15689065C2211yescharacteristic
47#15689064C2211yescharacteristic
48#15689064C2211yescharacteristic
49#15689064C2211yescharacteristic
50#15689064C2211yescharacteristic
51#15689063C2211yescharacteristic
52#15689063C2211yescharacteristic
53#15689062C2211yescharacteristic
54#15689062C2211yescharacteristic
55#15689062C2211yescharacteristic
56#15689061C2211yescharacteristic
57#15689061C2211yescharacteristic
58#15689061C2211yescharacteristic
59#15689061C2211yescharacteristic
60#15689059C2211yescharacteristic
61#15689059C2211yescharacteristic
62#15689058C2211yescharacteristic
63#15689058C2211yescharacteristic
64#15689058C2211yescharacteristic
65#15689057C2211yescharacteristic
66#15689057C2211yescharacteristic
67#15689057C2211yescharacteristic
68#15689057C2211yescharacteristic
69#15689056C2211yescharacteristic
70#15689056C2211yescharacteristic
71#15689056C2211yescharacteristic
72#15689056C2211yescharacteristic
73#15689056C2211yescharacteristic
74#15689056C2211yescharacteristic
75#15689054C2211yescharacteristic
76#15689054C2211yescharacteristic
77#15689054C2211yescharacteristic
78#15689054C2211yescharacteristic
79#15689053C2211yescharacteristic
80#15689053C2211yescharacteristic
81#15689052C2211yescharacteristic
82#15689052C2211yescharacteristic
83#15689052C2211yescharacteristic
84#15689051C2211yescharacteristic
85#15689051C2211yescharacteristic
86#15689051C2211yescharacteristic
87#15689051C2211yescharacteristic
88#15689051C2211yescharacteristic
89#15689051C2211yescharacteristic
90#15689051C2211yescharacteristic
91#15689050C2211yescharacteristic
92#15689050C2211yescharacteristic
93#15689050C2211yescharacteristic
94#15689049C2211yescharacteristic
95#15689049C2211yescharacteristic
96#15689049C2211yescharacteristic
97#15689048C2211yescharacteristic
98#15689048C2211yescharacteristic
99#15689047C2211yescharacteristic
100#15689046C2211yescharacteristic
101#15689046C2211yescharacteristic
102#15689046C2211yescharacteristic
103#15689046C2211yescharacteristic
104#15689045C2211yescharacteristic
105#15689045C2211yescharacteristic
106#15689045C2211yescharacteristic
107#15689045C2211yescharacteristic
108#15689045C2211yescharacteristic
109#15689044C2211yescharacteristic
110#15689044C2211yescharacteristic
111#15689043C2211yescharacteristic
112#15689043C2211yescharacteristic
113#15689043C2211yescharacteristic
114#15689043C2211yescharacteristic
115#15689043C2211yescharacteristic
116#15689043C2211yescharacteristic
117#15689042C2211yescharacteristic
118#15689042C2211yescharacteristic
119#15689042C2211yescharacteristic
120#15689039C2211yescharacteristic
121#15689038C2211yescharacteristic
122#15689038C2211yescharacteristic
123#15689038C2211yescharacteristic
124#15689036C2211yescharacteristic
125#15689035C2211yescharacteristic
126#15689034C2211yescharacteristic
127#15689027C2211yescharacteristic
128#15689023C2211yescharacteristic
129#15689022C2211yescharacteristic
130#15689020C2211yescharacteristic
131#15689019C2211yescharacteristic
132#15689018C2211yescharacteristic
133#15689016C2211yescharacteristic
134#15689015C2211yescharacteristic
135#15689012C2211yescharacteristic
136#15689011C2211yescharacteristic
137#15689010C2211yescharacteristic
138#15689010C2211yescharacteristic
139#15689009C2211yescharacteristic
140#15689008C2211yescharacteristic
141#15689006C2211yescharacteristic
142#15689006C2211yescharacteristic
143#15689005C2211yescharacteristic
144#15689004C2211yescharacteristic
145#15688988C2211yescharacteristic
146#15688987C2211yescharacteristic
147#15688987C2211yescharacteristic
148C4×Dic47⋊C4C2211yescharacteristic
149C4×Dic47⋊C4C2211yescharacteristic
150C4×Dic47⋊C4C2211yescharacteristic
151C4×Dic47⋊C4C2211yescharacteristic
152C4×Dic47⋊C4C2211yescharacteristic
153C4×Dic47⋊C4C2211yescharacteristic
154C4×Dic47⋊C4C2211yescharacteristic
155C4×Dic47⋊C4C2211yescharacteristic
156C4×Dic47⋊C4C2211yescharacteristic
157C4×C4⋊Dic47C2211yescharacteristic
158C4×C4⋊Dic47C2211yescharacteristic
159C4×C4⋊Dic47C2211yescharacteristic
160C4×C4⋊Dic47C2211yescharacteristic
161C4×(C2×D47)⋊C4C2211yescharacteristic
162C4×(C2×D47)⋊C4C2211yescharacteristic
163C4×(C2×D47)⋊C4C2211yescharacteristic
164C4×(C2×D47)⋊C4C2211yescharacteristic
165C4×(C2×D47)⋊C4C2211yescharacteristic
166C4×C22⋊Dic47C2211yescharacteristic
167C4×C22⋊Dic47C2211yescharacteristic
168C4×C22⋊Dic47C2211yescharacteristic
169#15688969C2211yescharacteristic
170#15688969C2211yescharacteristic
171C42×Dic47C2211yescharacteristic
172C2×C4×Q8×C47C2211yescharacteristic
173C2×#117×C47C2211yescharacteristic
174C47×#400C2211yescharacteristic
175C47×#399C2211yescharacteristic
176C47×#398C2211yescharacteristic
177C47×#398C2211yescharacteristic
178C47×#396C2211yescharacteristic
179C47×#396C2211yescharacteristic
180C47×#395C2211yescharacteristic
181C47×#393C2211yescharacteristic
182C4×C4⋊C4×C47C2211yescharacteristic
183C4×C4⋊C4×C47C2211yescharacteristic
184C4×C4⋊C4×C47C2211yescharacteristic
185C4×C22⋊C4×C47C2211yescharacteristic
186C4×C22⋊C4×C47C2211yescharacteristic
187C22×Dic94C2311yescharacteristic
188C22×Dic94C2311yescharacteristic
189C22×C22⋊D47C2311yescharacteristic
190C22×C4×D47C2311yescharacteristic
191#13094015—24no—
192#13094014—24no—
193#13094010—24no—
194C4×Dic94—42no—
195C4×Dic94—42no—
196C4×C22⋊D47—42no—
197#13093981—42no—
198C2×C4⋊Dic47C2311yescharacteristic
199C2×C4⋊Dic47C2311yescharacteristic
200C2×C4⋊Dic47C2311yescharacteristic
201C2×C4⋊Dic47C2311yescharacteristic
202C2×C4⋊Dic47C2311yescharacteristic
203C2×C4⋊Dic47C2311yescharacteristic
204C2×C4⋊Dic47C2311yescharacteristic
205C2×C4⋊Dic47C2311yescharacteristic
206C2×C4⋊Dic47C2311yescharacteristic
207C2×C4⋊Dic47C2311yescharacteristic
208C2×Dic47⋊C4C2311yescharacteristic
209C2×Dic47⋊C4C2311yescharacteristic
210C2×Dic47⋊C4C2311yescharacteristic
211C2×Dic47⋊C4C2311yescharacteristic
212C2×Dic47⋊C4C2311yescharacteristic
213C2×Dic47⋊C4C2311yescharacteristic
214C2×Dic47⋊C4C2311yescharacteristic
215C2×Dic47⋊C4C2311yescharacteristic
216C2×Dic47⋊C4C2311yescharacteristic
217C2×Dic47⋊C4C2311yescharacteristic
218C2×Dic47⋊C4C2311yescharacteristic
219C2×Dic47⋊C4C2311yescharacteristic
220C2×Dic47⋊C4C2311yescharacteristic
221C2×Dic47⋊C4C2311yescharacteristic
222C2×Dic47⋊C4C2311yescharacteristic
223C2×Dic47⋊C4C2311yescharacteristic
224C2×Dic47⋊C4C2311yescharacteristic
225C2×Dic47⋊C4C2311yescharacteristic
226C2×Dic47⋊C4C2311yescharacteristic
227C2×Dic47⋊C4C2311yescharacteristic
228C2×Dic47⋊C4C2311yescharacteristic
229C2×Dic47⋊C4C2311yescharacteristic
230C2×Dic47⋊C4C2311yescharacteristic
231C2×Dic47⋊C4C2311yescharacteristic
232C2×Dic47⋊C4C2311yescharacteristic
233C2×C22⋊Dic47C2311yescharacteristic
234C2×C22⋊Dic47C2311yescharacteristic
235C2×C22⋊Dic47C2311yescharacteristic
236C2×C22⋊Dic47C2311yescharacteristic
237C2×C22⋊Dic47C2311yescharacteristic
238C2×C22⋊Dic47C2311yescharacteristic
239C2×C22⋊Dic47C2311yescharacteristic
240C2×(C2×D47)⋊C4C2311yescharacteristic
241C2×(C2×D47)⋊C4C2311yescharacteristic
242C2×(C2×D47)⋊C4C2311yescharacteristic
243C2×(C2×D47)⋊C4C2311yescharacteristic
244C2×(C2×D47)⋊C4C2311yescharacteristic
245C2×(C2×D47)⋊C4C2311yescharacteristic
246C2×(C2×D47)⋊C4C2311yescharacteristic
247C2×(C2×D47)⋊C4C2311yescharacteristic
248C2×(C2×D47)⋊C4C2311yescharacteristic
249C2×(C2×D47)⋊C4C2311yescharacteristic
250C2×(C2×D47)⋊C4C2311yescharacteristic
251C2×(C2×D47)⋊C4C2311yescharacteristic
252C2×(C2×D47)⋊C4C2311yescharacteristic
253C2×C4×Dic47C2311yescharacteristic
254C2×C4×Dic47C2311yescharacteristic
255C2×C4×Dic47C2311yescharacteristic
256C2×C4×Dic47C2311yescharacteristic
257C2×C4×Dic47C2311yescharacteristic
258C2×C4×Dic47C2311yescharacteristic
259C2×C4×Dic47C2311yescharacteristic
260C2×C4×Dic47C2311yescharacteristic
261C2×C4×Dic47C2311yescharacteristic
262C2×C4×Dic47C2311yescharacteristic
263C2×C4×Dic47C2311yescharacteristic
264C47⋊#95C2311yescharacteristic
265C47⋊#95C2311yescharacteristic
266C47⋊#95C2311yescharacteristic
267C47⋊#95C2311yescharacteristic
268C47⋊#95C2311yescharacteristic
269C47⋊#95C2311yescharacteristic
270C47⋊#95C2311yescharacteristic
271C47⋊#95C2311yescharacteristic
272C47⋊#95C2311yescharacteristic
273C47⋊#95C2311yescharacteristic
274C47⋊#95C2311yescharacteristic
275C47⋊#95C2311yescharacteristic
276C47⋊#95C2311yescharacteristic
277C47⋊#95C2311yescharacteristic
278C47⋊#95C2311yescharacteristic
279C47⋊#95C2311yescharacteristic
280C47⋊#95C2311yescharacteristic
281C47⋊#95C2311yescharacteristic
282C47⋊#95C2311yescharacteristic
283C47⋊#95C2311yescharacteristic
284C47⋊#95C2311yescharacteristic
285C47⋊#95C2311yescharacteristic
286C47⋊#95C2311yescharacteristic
287C47⋊#95C2311yescharacteristic
288C47⋊#95C2311yescharacteristic
289C47⋊#95C2311yescharacteristic
290C47⋊#95C2311yescharacteristic
291C47⋊#95C2311yescharacteristic
292C47⋊#95C2311yescharacteristic
293C47⋊#95C2311yescharacteristic
294C47⋊#95C2311yescharacteristic
295C47⋊#95C2311yescharacteristic
296C47⋊#95C2311yescharacteristic
297C47⋊#95C2311yescharacteristic
298C47⋊#95C2311yescharacteristic
299C47⋊#95C2311yescharacteristic
300C47⋊#95C2311yescharacteristic
301C47⋊#95C2311yescharacteristic
302C47⋊#95C2311yescharacteristic
303C47⋊#95C2311yescharacteristic
304C47⋊#95C2311yescharacteristic
305C47⋊#95C2311yescharacteristic
306C47⋊#95C2311yescharacteristic
307C47⋊#95C2311yescharacteristic
308C47⋊#95C2311yescharacteristic
309C47⋊#95C2311yescharacteristic
310C47⋊#95C2311yescharacteristic
311C47⋊#95C2311yescharacteristic
312C47⋊#95C2311yescharacteristic
313C47⋊#95C2311yescharacteristic
314C22×Q8×C47C2311yescharacteristic
315C23×C4×C47C2311yescharacteristic
316C4×Q8×C47—42no—
317#117×C47—42no—
318C2×C4⋊C4×C47C2311yescharacteristic
319C2×C4⋊C4×C47C2311yescharacteristic
320C2×C4⋊C4×C47C2311yescharacteristic
321C2×C4⋊C4×C47C2311yescharacteristic
322C2×C4⋊C4×C47C2311yescharacteristic
323C2×C4⋊C4×C47C2311yescharacteristic
324C2×C4⋊C4×C47C2311yescharacteristic
325C2×C4⋊C4×C47C2311yescharacteristic
326C2×C4⋊C4×C47C2311yescharacteristic
327C2×C4⋊C4×C47C2311yescharacteristic
328C2×C4⋊C4×C47C2311yescharacteristic
329C2×C22⋊C4×C47C2311yescharacteristic
330C2×C22⋊C4×C47C2311yescharacteristic
331C2×C22⋊C4×C47C2311yescharacteristic
332C2×C22⋊C4×C47C2311yescharacteristic
333C2×C22⋊C4×C47C2311yescharacteristic
334C2×C22⋊C4×C47C2311yescharacteristic
335C2×C42×C47C2311yescharacteristic
336C2×C42×C47C2311yescharacteristic
337C2×C42×C47C2311yescharacteristic
338C2×C42×C47C2311yescharacteristic
339C2×C42×C47C2311yescharacteristic
340C2×C42×C47C2311yescharacteristic
341#95×C47C2311yescharacteristic
342#95×C47C2311yescharacteristic
343#95×C47C2311yescharacteristic
344#95×C47C2311yescharacteristic
345#95×C47C2311yescharacteristic
346#95×C47C2311yescharacteristic
347#95×C47C2311yescharacteristic
348#95×C47C2311yescharacteristic
349#95×C47C2311yescharacteristic
350#95×C47C2311yescharacteristic
351C24×C47C2411yescharacteristic
352C23×D47C2411yescharacteristic
353C2×Q8×C47—41no—
354C2×Q8×C47—41no—
355C2×Q8×C47—41no—
356C22×C4×C47—22no—
357C22×C4×C47—22no—
358C22×C4×C47—22no—
359C22×C4×C47C2411yescharacteristic
360C22×C4×C47C2411yescharacteristic
361C22×C4×C47C2411yescharacteristic
362C22×C4×C47C2411yescharacteristic
363C22×C4×C47C2411yescharacteristic
364C22×C4×C47C2411yescharacteristic
365C22×C4×C47C2411yescharacteristic
366C22×C4×C47C2411yescharacteristic
367C22×C4×C47C2411yescharacteristic
368C22×C4×C47C2411yescharacteristic
369C22×C4×C47C2411yescharacteristic
370C22×C4×C47C2411yescharacteristic
371C22×C4×C47C2411yescharacteristic
372C22×C4×C47C2411yescharacteristic
373C2×C22⋊D47—22no—
374C2×C22⋊D47—41no—
375C2×C22⋊D47—41no—
376C22×Dic47C2411yescharacteristic
377C22×Dic47C2411yescharacteristic
378C22×Dic47C2411yescharacteristic
379C22×Dic47C2411yescharacteristic
380C22×Dic47C2411yescharacteristic
381C22×Dic47C2411yescharacteristic
382C22×Dic47C2411yescharacteristic
383C22×Dic47C2411yescharacteristic
384C22×Dic47C2411yescharacteristic
385C22×Dic47C2411yescharacteristic
386C22×Dic47C2411yescharacteristic
387C22×Dic47C2411yescharacteristic
388C22×Dic47C2411yescharacteristic
389C22×Dic47C2411yescharacteristic
390C22×Dic47C2411yescharacteristic
391C2×C4×D47—22no—
392C2×C4×D47—22no—
393C2×C4×D47—22no—
394C2×Dic94—22no—
395C2×Dic94—41no—
396C2×Dic94—41no—
397C2×Dic94—41no—
398C2×Dic94—41no—
399C2×Dic94—41no—
400C4⋊C4×C47—22no—
401C4⋊C4×C47—22no—
402C4⋊C4×C47—41no—
403C4⋊C4×C47—41no—
404C4⋊C4×C47—41no—
405C4⋊C4×C47—41no—
406C4⋊C4×C47—41no—
407C4⋊C4×C47—41no—
408C4⋊C4×C47—41no—
409C4⋊C4×C47—41no—
410C4⋊C4×C47—41no—
411C22⋊C4×C47—22no—
412C22⋊C4×C47—41no—
413C22⋊C4×C47—41no—
414C22⋊C4×C47—41no—
415C22⋊C4×C47—41no—
416C22⋊C4×C47—41no—
417C42×C47—22no—
418C42×C47—22no—
419C42×C47—22no—
420C42×C47—22no—
421C42×C47—22no—
422C42×C47—22no—
423C22⋊Dic47—22no—
424C22⋊Dic47—41no—
425C22⋊Dic47—41no—
426C22⋊Dic47—41no—
427C22⋊Dic47—41no—
428C22⋊Dic47—41no—
429C22⋊Dic47—41no—
430(C2×D47)⋊C4—22no—
431(C2×D47)⋊C4—22no—
432(C2×D47)⋊C4—41no—
433(C2×D47)⋊C4—41no—
434(C2×D47)⋊C4—41no—
435(C2×D47)⋊C4—41no—
436(C2×D47)⋊C4—41no—
437(C2×D47)⋊C4—41no—
438(C2×D47)⋊C4—41no—
439(C2×D47)⋊C4—41no—
440(C2×D47)⋊C4—41no—
441(C2×D47)⋊C4—41no—
442(C2×D47)⋊C4—41no—
443C4⋊Dic47—22no—
444C4⋊Dic47—22no—
445C4⋊Dic47—22no—
446C4⋊Dic47—22no—
447C4⋊Dic47—41no—
448C4⋊Dic47—41no—
449C4⋊Dic47—41no—
450C4⋊Dic47—41no—
451C4⋊Dic47—41no—
452C4⋊Dic47—41no—
453Dic47⋊C4—22no—
454Dic47⋊C4—22no—
455Dic47⋊C4—22no—
456Dic47⋊C4—22no—
457Dic47⋊C4—22no—
458Dic47⋊C4—22no—
459Dic47⋊C4—41no—
460Dic47⋊C4—41no—
461Dic47⋊C4—41no—
462Dic47⋊C4—41no—
463Dic47⋊C4—41no—
464Dic47⋊C4—41no—
465Dic47⋊C4—41no—
466Dic47⋊C4—41no—
467Dic47⋊C4—41no—
468Dic47⋊C4—41no—
469Dic47⋊C4—41no—
470Dic47⋊C4—41no—
471Dic47⋊C4—41no—
472Dic47⋊C4—41no—
473Dic47⋊C4—41no—
474Dic47⋊C4—41no—
475Dic47⋊C4—41no—
476Dic47⋊C4—41no—
477Dic47⋊C4—41no—
478C4×Dic47—22no—
479C4×Dic47—22no—
480C4×Dic47—22no—
481C4×Dic47—22no—
482C4×Dic47—22no—
483C4×Dic47—22no—
484C4×Dic47—22no—
485C4×Dic47—41no—
486C4×Dic47—41no—
487C4×Dic47—41no—
488C4×Dic47#4114yes—
489C23×C47—21no—
490C23×C47—21no—
491C23×C47—21no—
492C23×C47—21no—
493C23×C47—21no—
494C23×C47—21no—
495C23×C47—21no—
496C23×C47C2511yescharacteristic
497C22×D47—21no—
498C22×D47—21no—
499C22×D47—21no—
500C22×D47—21no—
501C22×D47—21no—
502C22×D47—21no—
503C22×D47—21no—
504Q8×C47—44no—
505C2×C4×C47—21no—
506C2×C4×C47—21no—
507C2×C4×C47—21no—
508C2×C4×C47—21no—
509C2×C4×C47—21no—
510C2×C4×C47—21no—
511C2×C4×C47—21no—
512C2×C4×C47—21no—
513C2×C4×C47—21no—
514C2×C4×C47—21no—
515C2×C4×C47—21no—
516C2×C4×C47—21no—
517C2×C4×C47—21no—
518C2×C4×C47—21no—
519C2×C4×C47—21no—
520C2×C4×C47—21no—
521C2×C4×C47—21no—
522C2×C4×C47—21no—
523C2×C4×C47—21no—
524C2×C4×C47—21no—
525C2×C4×C47—21no—
526C2×C4×C47—21no—
527C2×C4×C47—21no—
528C2×C4×C47—21no—
529C2×C4×C47—21no—
530C2×C4×C47—21no—
531C2×C4×C47—21no—
532C2×C4×C47—21no—
533C2×C4×C47—21no—
534C2×C4×C47—21no—
535C2×C4×C47—21no—
536C2×C4×C47—21no—
537C2×C4×C47—21no—
538C2×C4×C47—21no—
539C2×C4×C47—21no—
540C2×C4×C47—21no—
541C2×C4×C47—21no—
542C2×C4×C47—21no—
543C2×C4×C47—44no—
544C2×C4×C47C2×#4112yes—
545C2×C4×C47H(5,𝔽2)12yes—
546C2×C4×C472−1+412yes—
547C2×C4×C472−1+412yes—
548C22⋊D47—44no—
549C2×Dic47—21no—
550C2×Dic47—21no—
551C2×Dic47—21no—
552C2×Dic47—21no—
553C2×Dic47—21no—
554C2×Dic47—21no—
555C2×Dic47—21no—
556C2×Dic47—21no—
557C2×Dic47—21no—
558C2×Dic47—21no—
559C2×Dic47—21no—
560C2×Dic47—21no—
561C2×Dic47—21no—
562C2×Dic47—21no—
563C2×Dic47—21no—
564C2×Dic47—21no—
565C2×Dic47—21no—
566C2×Dic47—21no—
567C2×Dic47—21no—
568C2×Dic47—21no—
569C2×Dic47—21no—
570C2×Dic47—21no—
571C2×Dic47—21no—
572C2×Dic47—21no—
573C2×Dic47—21no—
574C2×Dic47—21no—
575C2×Dic47—21no—
576C2×Dic47—21no—
577C2×Dic47—21no—
578C2×Dic47—21no—
579C2×Dic47—21no—
580C2×Dic47—21no—
581C2×Dic47—21no—
582C2×Dic47—21no—
583C2×Dic47—21no—
584C2×Dic47—21no—
585C2×Dic47—21no—
586C2×Dic47—21no—
587C2×Dic47—21no—
588C2×Dic47—21no—
589C2×Dic47—21no—
590C2×Dic47—21no—
591C2×Dic47—21no—
592C2×Dic47C2×#4112yes—
593C2×Dic47C2×#4112yes—
594C4×D47—44no—
595Dic94—44no—
596Dic94—44no—
597#36698—471nomaximal, Sylow
598C22×C47—41no—
599C22×C47—41no—
600C22×C47—41no—
601C22×C47—41no—
602C22×C47—41no—
603C22×C47—41no—
604C22×C47—41no—
605C22×C47C22×#4111yescharacteristic
606C22×C47C2×H(5,𝔽2)11yescharacteristic
607C22×C47C2×2−1+411yescharacteristic
608C22×C47C2×2−1+411yescharacteristic
609C22×C47#58511yescharacteristic
610C22×C47#58511yescharacteristic
611C22×C47#58511yescharacteristic
612C2×D47—41no—
613C2×D47—41no—
614C2×D47—41no—
615C2×D47—41no—
616C2×D47—41no—
617C2×D47—41no—
618C2×D47—41no—
619C4×C47—22no—
620C4×C47—41no—
621C4×C47—41no—
622C4×C47—41no—
623C4×C47—41no—
624C4×C47—41no—
625C4×C47—41no—
626C4×C47—41no—
627C4×C47—41no—
628C4×C47—41no—
629C4×C47—41no—
630C4×C47—41no—
631C4×C47—41no—
632C4×C47#56314yes—
633Dic47—22no—
634Dic47—22no—
635Dic47—41no—
636Dic47—41no—
637Dic47—41no—
638Dic47—41no—
639Dic47—41no—
640Dic47—41no—
641Dic47—41no—
642Dic47—41no—
643Dic47—41no—
644Dic47—41no—
645Dic47—41no—
646Dic47—41no—
647Dic47—41no—
648#2844—471no—
649#2838—471no—
650#2838—471no—
651#2838—471no—
652#2838—471no—
653#2836—471no—
654#2836—471no—
655#2836—471no—
656#2836—471no—
657#2833—471no—
658#2833—471no—
659#2830—471no—
660#2830—471no—
661#2822—471no—
662#2820—471no—
663#2820—471no—
664#2401—471no—
665#2401—471no—
666#2401—471no—
667#2401—471no—
668#2399—471no—
669#2399—471no—
670#2396—471no—
671#2396—471no—
672#2396—471no—
673#2396D4711yescharacteristic, complemented
674#2395—471no—
675#2395—471no—
676C4×#125—471no—
677C4×#125—471no—
678C4×#124—471no—
679C2×C47—81no—
680C2×C47#346011yescharacteristic
681C2×C47#346111yescharacteristic
682C2×C47#346111yescharacteristic
683C2×C47C2×#56311yescharacteristic
684C2×C47#352911yescharacteristic
685C2×C47#353111yescharacteristic
686C2×C47#353111yescharacteristic
687D47—81no—
688C2×#125—471no—
689C2×#125—471no—
690C2×#124—471no—
691C2×C4×Q8—471no—
692C2×C4×Q8—471no—
693C2×C4×Q8C2×D4711yescharacteristic
694C2×C4×D4—471no—
695C2×#117—471no—
696C2×#117C2×D4711yescharacteristic
697#401—471no—
698#401—471no—
699#401—471no—
700#401—471no—
701#400—471no—
702#400—471no—
703#400—471no—
704#400—471no—
705#400—471no—
706#400—471no—
707#400—471no—
708#400—471no—
709#400—471no—
710#400—471no—
711#400—471no—
712#400—471no—
713#400—471no—
714#400—471no—
715#400—471no—
716#400—471no—
717#400—471no—
718#400C2×D4711yescharacteristic
719#399—471no—
720#399—471no—
721#399—471no—
722#399—471no—
723#399—471no—
724#399C2×D4711yescharacteristic
725#398—471no—
726#398—471no—
727#398—471no—
728#398—471no—
729#398—471no—
730#398—471no—
731#398—471no—
732#398—471no—
733#398—471no—
734#398—471no—
735#398—471no—
736#398—471no—
737#398—471no—
738#398—471no—
739#398—471no—
740#398—471no—
741#398C2×D4711yescharacteristic
742#398C2×D4711yescharacteristic
743#397—471no—
744#397—471no—
745#397—471no—
746#397—471no—
747#397—471no—
748#397—471no—
749#397—471no—
750#397—471no—
751#397—471no—
752#397—471no—
753#397—471no—
754#397—471no—
755#397—471no—
756#397—471no—
757#397—471no—
758#397—471no—
759#397—471no—
760#397—471no—
761#396—471no—
762#396—471no—
763#396—471no—
764#396—471no—
765#396—471no—
766#396—471no—
767#396—471no—
768#396—471no—
769#396—471no—
770#396—471no—
771#396C2×D4711yescharacteristic
772#396C2×D4711yescharacteristic
773#395—471no—
774#395—471no—
775#395—471no—
776#395—471no—
777#395—471no—
778#395—471no—
779#395—471no—
780#395—471no—
781#395—471no—
782#395—471no—
783#395—471no—
784#395C2×D4711yescharacteristic
785#394—471no—
786#394—471no—
787#394—471no—
788#394—471no—
789#393—471no—
790#393—471no—
791#393—471no—
792#393C2×D4711yescharacteristic
793#391—471no—
794#390—471no—
795#389—471no—
796#389—471no—
797#389—471no—
798#389—471no—
799#388—471no—
800#388—471no—
801#388—471no—
802#388—471no—
803#387—471no—
804#387—471no—
805#387—471no—
806#387—471no—
807#387—471no—
808#387—471no—
809#387—471no—
810#387—471no—
811#382—471no—
812#382—471no—
813#382—471no—
814C4×C4⋊C4—471no—
815C4×C4⋊C4—471no—
816C4×C4⋊C4—471no—
817C4×C4⋊C4—471no—
818C4×C4⋊C4—471no—
819C4×C4⋊C4—471no—
820C4×C4⋊C4—471no—
821C4×C4⋊C4—471no—
822C4×C4⋊C4—471no—
823C4×C4⋊C4—471no—
824C4×C4⋊C4—471no—
825C4×C4⋊C4—471no—
826C4×C4⋊C4—471no—
827C4×C4⋊C4C2×D4711yescharacteristic
828C4×C4⋊C4C2×D4711yescharacteristic
829C4×C4⋊C4C2×D4711yescharacteristic
830C4×C22⋊C4—471no—
831C4×C22⋊C4—471no—
832C4×C22⋊C4—471no—
833C4×C22⋊C4—471no—
834C4×C22⋊C4—471no—
835C4×C22⋊C4—471no—
836C4×C22⋊C4—471no—
837C4×C22⋊C4—471no—
838C4×C22⋊C4C2×D4711yescharacteristic
839C4×C22⋊C4C2×D4711yescharacteristic
840#376—471no—
841#376—471no—
842C43—471no—
843C47#3669811yescharacteristic, complemented, Sylow
844C22×Q8—471no—
845C22×Q8—471no—
846C22×Q8C22×D4711yescharacteristic
847C22×D4—471no—
848C23×C4—471no—
849C23×C4C22×D4711yescharacteristic
850#125—944no—
851#125—944no—
852#124—944no—
853C4×Q8—42no—
854C4×Q8—1882no—
855C4×Q8—1882no—
856C4×D4—1882no—
857#117—42no—
858#117—1882no—
859C2×C4⋊C4—471no—
860C2×C4⋊C4—471no—
861C2×C4⋊C4—471no—
862C2×C4⋊C4—471no—
863C2×C4⋊C4—471no—
864C2×C4⋊C4—471no—
865C2×C4⋊C4—471no—
866C2×C4⋊C4—471no—
867C2×C4⋊C4—471no—
868C2×C4⋊C4—471no—
869C2×C4⋊C4—471no—
870C2×C4⋊C4—471no—
871C2×C4⋊C4—471no—
872C2×C4⋊C4—471no—
873C2×C4⋊C4—471no—
874C2×C4⋊C4—471no—
875C2×C4⋊C4—471no—
876C2×C4⋊C4—471no—
877C2×C4⋊C4—471no—
878C2×C4⋊C4—471no—
879C2×C4⋊C4—471no—
880C2×C4⋊C4—471no—
881C2×C4⋊C4—471no—
882C2×C4⋊C4—471no—
883C2×C4⋊C4—471no—
884C2×C4⋊C4—471no—
885C2×C4⋊C4—471no—
886C2×C4⋊C4—471no—
887C2×C4⋊C4—471no—
888C2×C4⋊C4—471no—
889C2×C4⋊C4—471no—
890C2×C4⋊C4—471no—
891C2×C4⋊C4—471no—
892C2×C4⋊C4—471no—
893C2×C4⋊C4—471no—
894C2×C4⋊C4C22×D4711yescharacteristic
895C2×C4⋊C4C22×D4711yescharacteristic
896C2×C4⋊C4C22×D4711yescharacteristic
897C2×C4⋊C4C22×D4711yescharacteristic
898C2×C4⋊C4C22×D4711yescharacteristic
899C2×C4⋊C4C22×D4711yescharacteristic
900C2×C4⋊C4C22×D4711yescharacteristic
901C2×C4⋊C4C22×D4711yescharacteristic
902C2×C4⋊C4C22×D4711yescharacteristic
903C2×C4⋊C4C22×D4711yescharacteristic
904C2×C4⋊C4C22×D4711yescharacteristic
905C2×C22⋊C4—471no—
906C2×C22⋊C4—471no—
907C2×C22⋊C4—471no—
908C2×C22⋊C4—471no—
909C2×C22⋊C4—471no—
910C2×C22⋊C4—471no—
911C2×C22⋊C4—471no—
912C2×C22⋊C4—471no—
913C2×C22⋊C4—471no—
914C2×C22⋊C4—471no—
915C2×C22⋊C4—471no—
916C2×C22⋊C4—471no—
917C2×C22⋊C4—471no—
918C2×C22⋊C4—471no—
919C2×C22⋊C4—471no—
920C2×C22⋊C4—471no—
921C2×C22⋊C4—471no—
922C2×C22⋊C4—471no—
923C2×C22⋊C4—471no—
924C2×C22⋊C4—471no—
925C2×C22⋊C4C22×D4711yescharacteristic
926C2×C22⋊C4C22×D4711yescharacteristic
927C2×C22⋊C4C22×D4711yescharacteristic
928C2×C22⋊C4C22×D4711yescharacteristic
929C2×C22⋊C4C22×D4711yescharacteristic
930C2×C22⋊C4C22×D4711yescharacteristic
931C2×C42—471no—
932C2×C42—471no—
933C2×C42—471no—
934C2×C42—471no—
935C2×C42—471no—
936C2×C42—471no—
937C2×C42—471no—
938C2×C42—471no—
939C2×C42—471no—
940C2×C42—471no—
941C2×C42—471no—
942C2×C42C22×D4711yescharacteristic
943C2×C42C22×D4711yescharacteristic
944C2×C42C22×D4711yescharacteristic
945C2×C42C22×D4711yescharacteristic
946C2×C42C22×D4711yescharacteristic
947C2×C42C22×D4711yescharacteristic
948#95—471no—
949#95—471no—
950#95—471no—
951#95—471no—
952#95—471no—
953#95—471no—
954#95—471no—
955#95—471no—
956#95—471no—
957#95—471no—
958#95—471no—
959#95—471no—
960#95—471no—
961#95—471no—
962#95—471no—
963#95—471no—
964#95—471no—
965#95—471no—
966#95—471no—
967#95—471no—
968#95—471no—
969#95—471no—
970#95—471no—
971#95—471no—
972#95—471no—
973#95—471no—
974#95—471no—
975#95—471no—
976#95—471no—
977#95—471no—
978#95—471no—
979#95—471no—
980#95—471no—
981#95—471no—
982#95—471no—
983#95—471no—
984#95—471no—
985#95—471no—
986#95—471no—
987#95—471no—
988#95—471no—
989#95—471no—
990#95—471no—
991#95—471no—
992#95—471no—
993#95—471no—
994#95—471no—
995#95—471no—
996#95—471no—
997#95—471no—
998#95C22×D4711yescharacteristic
999#95C22×D4711yescharacteristic
1000#95C22×D4711yescharacteristic
1001#95C22×D4711yescharacteristic
1002#95C22×D4711yescharacteristic
1003#95C22×D4711yescharacteristic
1004#95C22×D4711yescharacteristic
1005#95C22×D4711yescharacteristic
1006#95C22×D4711yescharacteristic
1007#95C22×D4711yescharacteristic
1008C24—471no—
1009C24C23×D4711yescharacteristic
1010C2×Q8—41no—
1011C2×Q8—41no—
1012C2×Q8—41no—
1013C2×Q8—942no—
1014C2×Q8—1881no—
1015C2×Q8—1881no—
1016C2×Q8—1881no—
1017C2×Q8—1881no—
1018C2×Q8—1881no—
1019C2×D4—942no—
1020C2×D4—1881no—
1021C2×D4—1881no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—471no—
1026C22×C4—471no—
1027C22×C4—471no—
1028C22×C4—471no—
1029C22×C4—471no—
1030C22×C4—471no—
1031C22×C4—471no—
1032C22×C4—471no—
1033C22×C4—471no—
1034C22×C4—471no—
1035C22×C4—471no—
1036C22×C4—471no—
1037C22×C4—471no—
1038C22×C4—471no—
1039C22×C4—471no—
1040C22×C4—942no—
1041C22×C4—942no—
1042C22×C4—942no—
1043C22×C4C23×D4711yescharacteristic
1044C22×C4C23×D4711yescharacteristic
1045C22×C4C23×D4711yescharacteristic
1046C22×C4C23×D4711yescharacteristic
1047C22×C4C23×D4711yescharacteristic
1048C22×C4C23×D4711yescharacteristic
1049C22×C4C23×D4711yescharacteristic
1050C22×C4C23×D4711yescharacteristic
1051C22×C4C23×D4711yescharacteristic
1052C22×C4C23×D4711yescharacteristic
1053C22×C4C23×D4711yescharacteristic
1054C22×C4C23×D4711yescharacteristic
1055C22×C4C23×D4711yescharacteristic
1056C22×C4C23×D4711yescharacteristic
1057C4⋊C4—22no—
1058C4⋊C4—22no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—942no—
1069C4⋊C4—942no—
1070C4⋊C4—942no—
1071C4⋊C4—942no—
1072C4⋊C4—942no—
1073C4⋊C4—942no—
1074C4⋊C4—942no—
1075C4⋊C4—942no—
1076C4⋊C4—942no—
1077C4⋊C4—942no—
1078C4⋊C4—1881no—
1079C4⋊C4—1881no—
1080C4⋊C4—1881no—
1081C4⋊C4—1881no—
1082C4⋊C4—1881no—
1083C4⋊C4—1881no—
1084C4⋊C4—1881no—
1085C4⋊C4—1881no—
1086C4⋊C4—1881no—
1087C4⋊C4—1881no—
1088C4⋊C4—1881no—
1089C4⋊C4—1881no—
1090C4⋊C4—1881no—
1091C4⋊C4—1881no—
1092C4⋊C4—1881no—
1093C4⋊C4—1881no—
1094C4⋊C4—1881no—
1095C4⋊C4—1881no—
1096C4⋊C4—1881no—
1097C4⋊C4—1881no—
1098C4⋊C4—1881no—
1099C4⋊C4—1881no—
1100C4⋊C4—1881no—
1101C4⋊C4—1881no—
1102C4⋊C4—1881no—
1103C22⋊C4—22no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—41no—
1107C22⋊C4—41no—
1108C22⋊C4—41no—
1109C22⋊C4—942no—
1110C22⋊C4—942no—
1111C22⋊C4—942no—
1112C22⋊C4—1881no—
1113C22⋊C4—1881no—
1114C22⋊C4—1881no—
1115C22⋊C4—1881no—
1116C22⋊C4—1881no—
1117C22⋊C4—1881no—
1118C22⋊C4—1881no—
1119C22⋊C4—1881no—
1120C22⋊C4—1881no—
1121C22⋊C4—1881no—
1122C22⋊C4—1881no—
1123C22⋊C4—1881no—
1124C22⋊C4—1881no—
1125C22⋊C4—1881no—
1126C22⋊C4—1881no—
1127C22⋊C4—1881no—
1128C22⋊C4—1881no—
1129C42—22no—
1130C42—22no—
1131C42—22no—
1132C42—22no—
1133C42—22no—
1134C42—22no—
1135C42—474no—
1136C42—942no—
1137C42—942no—
1138C42—942no—
1139C42—942no—
1140C42—942no—
1141C42—942no—
1142C42—942no—
1143C42—1881no—
1144C42—1881no—
1145C42—1881no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—941no—
1154C23—941no—
1155C23—941no—
1156C23—941no—
1157C23—941no—
1158C23—941no—
1159C23—941no—
1160C23C24×D4711yescharacteristic
1161Q8—44no—
1162Q8—1884no—
1163Q8—1884no—
1164D4—1884no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—44no—
1204C2×C4—472no—
1205C2×C4—472no—
1206C2×C4—941no—
1207C2×C4—941no—
1208C2×C4—941no—
1209C2×C4—941no—
1210C2×C4—941no—
1211C2×C4—941no—
1212C2×C4—941no—
1213C2×C4—941no—
1214C2×C4—941no—
1215C2×C4—941no—
1216C2×C4—941no—
1217C2×C4—941no—
1218C2×C4—941no—
1219C2×C4—941no—
1220C2×C4—941no—
1221C2×C4—941no—
1222C2×C4—941no—
1223C2×C4—941no—
1224C2×C4—941no—
1225C2×C4—941no—
1226C2×C4—941no—
1227C2×C4—941no—
1228C2×C4—941no—
1229C2×C4—941no—
1230C2×C4—941no—
1231C2×C4—941no—
1232C2×C4—941no—
1233C2×C4—941no—
1234C2×C4—941no—
1235C2×C4—941no—
1236C2×C4—941no—
1237C2×C4—941no—
1238C2×C4—941no—
1239C2×C4—941no—
1240C2×C4—941no—
1241C2×C4—941no—
1242C2×C4—941no—
1243C2×C4—941no—
1244C2×C4—941no—
1245C2×C4—941no—
1246C2×C4—941no—
1247C2×C4—941no—
1248C2×C4—941no—
1249C2×C4—1884no—
1250C2×C4#41×D4712yes—
1251C2×C4#1309406912yes—
1252C2×C4#1309407112yes—
1253C2×C4#1309407212yes—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—1881no—
1262C22—1881no—
1263C22—1881no—
1264C22—1881no—
1265C22—1881no—
1266C22—1881no—
1267C22—1881no—
1268C22C2×#41×D4711yescharacteristic
1269C22C2×#1309406911yescharacteristic
1270C22C2×#1309407111yescharacteristic
1271C22C2×#1309407211yescharacteristic
1272C22#1568995911yescharacteristic
1273C22#1568995911yescharacteristic
1274C22#1568995911yescharacteristic
1275C4—22no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—942no—
1289C4—942no—
1290C4—1881no—
1291C4—1881no—
1292C4—1881no—
1293C4—1881no—
1294C4—1881no—
1295C4—1881no—
1296C4—1881no—
1297C4—1881no—
1298C4—1881no—
1299C4—1881no—
1300C4—1881no—
1301C4—1881no—
1302C4—1881no—
1303C4#1568987414yes—
1304C2—81no—
1305C2—3761no—
1306C2#2025680211yescharacteristic
1307C2#2025681711yescharacteristic
1308C2#2025681911yescharacteristic
1309C2C2×#1568987411yescharacteristic
1310C2#2025752611yescharacteristic
1311C2#2025753311yescharacteristic
1312C2#2025753511yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutator, socle, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC47×#2396C2
prime radicalC22×C22⋊D47C23
hypercenter#2396D47
hypocenterC47#36698
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2396

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20251659C2semidirect
2. #20251624C2semidirect
3. #20251623C2semidirect
4. #20251622C2semidirect
5. #20251619C2semidirect
6. #20251591C2semidirect
7. #20251587C2semidirect
8. #20251584C2semidirect
9. #20251582C2semidirect
10. #20251565C2semidirect
11. #20251563C2semidirect
14. #20251458C2semidirect
17. #20246689C2semidirect
18. #20246689C2semidirect
19. #20246688C2semidirect
20. #20246688C2semidirect
21. #20246682C2semidirect
22. #20246679C2semidirect
23. #20246664C2semidirect
24. #20246658C2semidirect
25. #20246656C2semidirect
28. C4×#13094015C2semidirect
29. C4×#13094014C2semidirect
31. C47×#2396C2semidirect
673. #2396D47semidirect
843. C47#36698semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202516592
#202516242
#202516232
#202516222
#202516192
#202515912
#202515872
#202515842
#202515822
#202515652
#202515632
#202515322
#202515302
#202514582
#202514422
#202514372
#202466892
#202466882
#202466822
#202466792
#202466642
#202466582
#202466562
#202466492
#202466452
C4×#130940152
C4×#130940142
C4×#130940102
C47×#23962
#3669847