Finite Group Databasebeta

← #26386252

Subgroups — #26386252

Order 12032.

1778 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#20247934C211yesmaximal, characteristic, complemented
2#20247932C211yesmaximal, characteristic, complemented
3#20247923C211yesmaximal, characteristic, complemented
4#20247921C211yesmaximal, characteristic, complemented
5#20247914C211yesmaximal, characteristic, complemented
6#20247908C211yesmaximal, characteristic, complemented
7#20247903C211yesmaximal, characteristic, complemented
8#20247897C211yesmaximal, characteristic, complemented
9#20247893C211yesmaximal, characteristic
10#20247891C211yesmaximal, characteristic
11#20247885C211yesmaximal, characteristic
12#20247883C211yesmaximal, characteristic
13#20247528C211yesmaximal, characteristic
14#20247526C211yesmaximal, characteristic
15#20247523C211yesmaximal, characteristic
16#20246694C211yesmaximal, characteristic, complemented
17#20246692C211yesmaximal, characteristic, complemented
18#20246692C211yesmaximal, characteristic, complemented
19#20246692C211yesmaximal, characteristic, complemented
20#125×Dic47C211yesmaximal, characteristic, complemented
21#20245947C211yesmaximal, characteristic, complemented
22#20245945C211yesmaximal, characteristic, complemented
23#20245945C211yesmaximal, characteristic, complemented
24#20245867C211yesmaximal, characteristic
25#20245867C211yesmaximal, characteristic
26#20245867C211yesmaximal, characteristic
27#20245867C211yesmaximal, characteristic
28#20245790C211yesmaximal, characteristic
29C4×#13093980C211yesmaximal, characteristic
30C2×C4⋊C4×Dic47C211yesmaximal, characteristic
31C47×#2473C211yesmaximal, characteristic
32C2×#13094015C2211yescharacteristic
33C2×#13094014C2211yescharacteristic
34C2×#13094014C2211yescharacteristic
35C2×#13093980C2211yescharacteristic
36C2×#13093980C2211yescharacteristic
37C2×#13093980C2211yescharacteristic
38C2×#13093980C2211yescharacteristic
39C22×C4⋊Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43#15689065C2211yescharacteristic
44#15689065C2211yescharacteristic
45#15689065C2211yescharacteristic
46#15689065C2211yescharacteristic
47#15689064C2211yescharacteristic
48#15689064C2211yescharacteristic
49#15689063C2211yescharacteristic
50#15689063C2211yescharacteristic
51#15689063C2211yescharacteristic
52#15689062C2211yescharacteristic
53#15689062C2211yescharacteristic
54#15689062C2211yescharacteristic
55#15689061C2211yescharacteristic
56#15689061C2211yescharacteristic
57#15689061C2211yescharacteristic
58#15689057C2211yescharacteristic
59#15689057C2211yescharacteristic
60#15689056C2211yescharacteristic
61#15689056C2211yescharacteristic
62#15689056C2211yescharacteristic
63#15689056C2211yescharacteristic
64#15689055C2211yescharacteristic
65#15689055C2211yescharacteristic
66#15689055C2211yescharacteristic
67#15689054C2211yescharacteristic
68#15689053C2211yescharacteristic
69#15689053C2211yescharacteristic
70#15689053C2211yescharacteristic
71#15689022C2211yescharacteristic
72#15689022C2211yescharacteristic
73#15689021C2211yescharacteristic
74#15689020C2211yescharacteristic
75#15689020C2211yescharacteristic
76#15689020C2211yescharacteristic
77#15689020C2211yescharacteristic
78#15689020C2211yescharacteristic
79#15689020C2211yescharacteristic
80#15689020C2211yescharacteristic
81#15689020C2211yescharacteristic
82#15689020C2211yescharacteristic
83#15689020C2211yescharacteristic
84#15689018C2211yescharacteristic
85#15689018C2211yescharacteristic
86#15689018C2211yescharacteristic
87#15689018C2211yescharacteristic
88#15689018C2211yescharacteristic
89#15689018C2211yescharacteristic
90#15689018C2211yescharacteristic
91#15689018C2211yescharacteristic
92#15689018C2211yescharacteristic
93#15689018C2211yescharacteristic
94#15689010C2211yescharacteristic
95#15689010C2211yescharacteristic
96#15689009C2211yescharacteristic
97#15689009C2211yescharacteristic
98#15689009C2211yescharacteristic
99#15689009C2211yescharacteristic
100#15689008C2211yescharacteristic
101#15689008C2211yescharacteristic
102#15689007C2211yescharacteristic
103#15689007C2211yescharacteristic
104#15689006C2211yescharacteristic
105#15689006C2211yescharacteristic
106#15689004C2211yescharacteristic
107#15689004C2211yescharacteristic
108#15688998C2211yescharacteristic
109#15688998C2211yescharacteristic
110#15688998C2211yescharacteristic
111#15688998C2211yescharacteristic
112#15688996C2211yescharacteristic
113#15688996C2211yescharacteristic
114#15688996C2211yescharacteristic
115#15688996C2211yescharacteristic
116#15688995C2211yescharacteristic
117#15688995C2211yescharacteristic
118#15688995C2211yescharacteristic
119#15688995C2211yescharacteristic
120#15688992C2211yescharacteristic
121#15688992C2211yescharacteristic
122#15688989C2211yescharacteristic
123#15688988C2211yescharacteristic
124#15688987C2211yescharacteristic
125#15688987C2211yescharacteristic
126#15688987C2211yescharacteristic
127#15688987C2211yescharacteristic
128#15688983C2211yescharacteristic
129#15688981C2211yescharacteristic
130#15688981C2211yescharacteristic
131C4⋊C4×Dic47C2211yescharacteristic
132C4⋊C4×Dic47C2211yescharacteristic
133C4⋊C4×Dic47C2211yescharacteristic
134C4⋊C4×Dic47C2211yescharacteristic
135C4⋊C4×Dic47C2211yescharacteristic
136C4⋊C4×Dic47C2211yescharacteristic
137C4⋊C4×Dic47C2211yescharacteristic
138C4⋊C4×Dic47C2211yescharacteristic
139C4⋊C4×Dic47C2211yescharacteristic
140C4⋊C4×Dic47C2211yescharacteristic
141C4⋊C4×Dic47C2211yescharacteristic
142C4⋊C4×Dic47C2211yescharacteristic
143C4⋊C4×Dic47C2211yescharacteristic
144C4⋊C4×Dic47C2211yescharacteristic
145C4⋊C4×Dic47C2211yescharacteristic
146C4⋊C4×Dic47C2211yescharacteristic
147C4⋊C4×Dic47C2211yescharacteristic
148C4⋊C4×Dic47C2211yescharacteristic
149C4×Dic47⋊C4C2211yescharacteristic
150C4×Dic47⋊C4C2211yescharacteristic
151#15688974C2211yescharacteristic
152#15688974C2211yescharacteristic
153#15688974C2211yescharacteristic
154#15688974C2211yescharacteristic
155#15688974C2211yescharacteristic
156#15688974C2211yescharacteristic
157#15688974C2211yescharacteristic
158#15688974C2211yescharacteristic
159#15688974C2211yescharacteristic
160#15688974C2211yescharacteristic
161#15688974C2211yescharacteristic
162#15688974C2211yescharacteristic
163C22⋊C4×Dic47C2211yescharacteristic
164C22⋊C4×Dic47C2211yescharacteristic
165C4×C22⋊Dic47C2211yescharacteristic
166#15688968C2211yescharacteristic
167#15688968C2211yescharacteristic
168C2×C47⋊#95C2211yescharacteristic
169C2×C47⋊#95C2211yescharacteristic
170C42×Dic47C2211yescharacteristic
171C42×Dic47C2211yescharacteristic
172C2×#125×C47C2211yescharacteristic
173C22×C4⋊C4×C47C2211yescharacteristic
174C47×#400C2211yescharacteristic
175C47×#398C2211yescharacteristic
176C47×#398C2211yescharacteristic
177C47×#398C2211yescharacteristic
178C47×#389C2211yescharacteristic
179C47×#387C2211yescharacteristic
180C47×#387C2211yescharacteristic
181C47×#385C2211yescharacteristic
182C47×#385C2211yescharacteristic
183C47×#385C2211yescharacteristic
184C47×#385C2211yescharacteristic
185C47×#380C2211yescharacteristic
186C4×C22⋊C4×C47C2211yescharacteristic
187C23×Dic47C2311yescharacteristic
188C23×Dic47C2311yescharacteristic
189C23×Dic47C2311yescharacteristic
190C23×Dic47C2311yescharacteristic
191#13094015—24no—
192#13094014—24no—
193#13094014—24no—
194#13093980—24no—
195#13093980—24no—
196#13093980—24no—
197#13093980Q818yes—
198C2×C4⋊Dic47—24no—
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×C4⋊Dic47C2311yescharacteristic
209C2×C4⋊Dic47C2311yescharacteristic
210C2×C4⋊Dic47C2311yescharacteristic
211C2×C4⋊Dic47C2311yescharacteristic
212C2×C4⋊Dic47C2311yescharacteristic
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×Dic47⋊C4C2311yescharacteristic
234C2×Dic47⋊C4C2311yescharacteristic
235C2×Dic47⋊C4C2311yescharacteristic
236C2×Dic47⋊C4C2311yescharacteristic
237C2×Dic47⋊C4C2311yescharacteristic
238C2×Dic47⋊C4C2311yescharacteristic
239C2×Dic47⋊C4C2311yescharacteristic
240C2×Dic47⋊C4C2311yescharacteristic
241C2×C22⋊Dic47C2311yescharacteristic
242C2×C22⋊Dic47C2311yescharacteristic
243C2×C22⋊Dic47C2311yescharacteristic
244C2×C22⋊Dic47C2311yescharacteristic
245C2×C4×Dic47—24no—
246C2×C4×Dic47—24no—
247C2×C4×Dic47—24no—
248C2×C4×Dic47C2311yescharacteristic
249C2×C4×Dic47C2311yescharacteristic
250C2×C4×Dic47C2311yescharacteristic
251C2×C4×Dic47C2311yescharacteristic
252C2×C4×Dic47C2311yescharacteristic
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
264C2×C4×Dic47C2311yescharacteristic
265C2×C4×Dic47C2311yescharacteristic
266C2×C4×Dic47C2311yescharacteristic
267C2×C4×Dic47C2311yescharacteristic
268C2×C4×Dic47C2311yescharacteristic
269C2×C4×Dic47C2311yescharacteristic
270C2×C4×Dic47C2311yescharacteristic
271C2×C4×Dic47C2311yescharacteristic
272C2×C4×Dic47C2311yescharacteristic
273C2×C4×Dic47C2311yescharacteristic
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
314C47⋊#95C2311yescharacteristic
315C47⋊#95C2311yescharacteristic
316C47⋊#95C2311yescharacteristic
317C47⋊#95C2311yescharacteristic
318C23×C4×C47C2311yescharacteristic
319C23×C4×C47C2311yescharacteristic
320C23×C4×C47C2311yescharacteristic
321#125×C47—24no—
322C2×C4⋊C4×C47—24no—
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×C4⋊C4×C47C2311yescharacteristic
330C2×C4⋊C4×C47C2311yescharacteristic
331C2×C4⋊C4×C47C2311yescharacteristic
332C2×C4⋊C4×C47C2311yescharacteristic
333C2×C4⋊C4×C47C2311yescharacteristic
334C2×C4⋊C4×C47C2311yescharacteristic
335C2×C4⋊C4×C47C2311yescharacteristic
336C2×C4⋊C4×C47C2311yescharacteristic
337C2×C22⋊C4×C47C2311yescharacteristic
338C2×C22⋊C4×C47C2311yescharacteristic
339C2×C22⋊C4×C47C2311yescharacteristic
340C2×C22⋊C4×C47C2311yescharacteristic
341C2×C42×C47C2311yescharacteristic
342C2×C42×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
351#95×C47C2311yescharacteristic
352#95×C47C2311yescharacteristic
353#95×C47C2311yescharacteristic
354#95×C47C2311yescharacteristic
355C24×C47C2411yescharacteristic
356C22×C4×C47—22no—
357C22×C4×C47—22no—
358C22×C4×C47—22no—
359C22×C4×C47—22no—
360C22×C4×C47—22no—
361C22×C4×C47—22no—
362C22×C4×C47—22no—
363C22×C4×C47—41no—
364C22×C4×C47—41no—
365C22×C4×C47C2411yescharacteristic
366C22×C4×C47C2411yescharacteristic
367C22×C4×C47C2411yescharacteristic
368C22×C4×C47C2411yescharacteristic
369C22×C4×C47C2411yescharacteristic
370C22×C4×C47C2411yescharacteristic
371C22×C4×C47C2411yescharacteristic
372C22×C4×C47C2411yescharacteristic
373C22×C4×C47C2411yescharacteristic
374C22×C4×C47C2411yescharacteristic
375C22×C4×C47C2411yescharacteristic
376C22×C4×C47C2411yescharacteristic
377C22×C4×C47C2411yescharacteristic
378C22×C4×C47C2411yescharacteristic
379C22×Dic47—22no—
380C22×Dic47—22no—
381C22×Dic47—22no—
382C22×Dic47—22no—
383C22×Dic47—22no—
384C22×Dic47—41no—
385C22×Dic47—41no—
386C22×Dic47—41no—
387C22×Dic47—41no—
388C22×Dic47C2×Q814yes—
389C22×Dic47#4114yes—
390C22×Dic47#4114yes—
391C22×Dic47C2411yescharacteristic
392C22×Dic47C2411yescharacteristic
393C22×Dic47C2411yescharacteristic
394C22×Dic47C2411yescharacteristic
395C22×Dic47C2411yescharacteristic
396C22×Dic47C2411yescharacteristic
397C22×Dic47C2411yescharacteristic
398C22×Dic47C2411yescharacteristic
399C22×Dic47C2411yescharacteristic
400C22×Dic47C2411yescharacteristic
401C22×Dic47C2411yescharacteristic
402C22×Dic47C2411yescharacteristic
403C22×Dic47C2411yescharacteristic
404C22×Dic47C2411yescharacteristic
405C22×Dic47C2411yescharacteristic
406C22×Dic47C2411yescharacteristic
407C4⋊C4×C47—22no—
408C4⋊C4×C47—22no—
409C4⋊C4×C47—22no—
410C4⋊C4×C47—22no—
411C4⋊C4×C47—22no—
412C4⋊C4×C47—22no—
413C4⋊C4×C47—22no—
414C4⋊C4×C47—22no—
415C4⋊C4×C47—22no—
416C4⋊C4×C47—22no—
417C4⋊C4×C47—41no—
418C4⋊C4×C47—41no—
419C4⋊C4×C47—41no—
420C4⋊C4×C47#4114yes—
421C22⋊C4×C47—22no—
422C22⋊C4×C47—22no—
423C22⋊C4×C47—22no—
424C22⋊C4×C47C2×Q814yes—
425C42×C47—22no—
426C42×C47—41no—
427C22⋊Dic47—22no—
428C22⋊Dic47—22no—
429C22⋊Dic47—22no—
430C22⋊Dic47C2×Q814yes—
431C4⋊Dic47—22no—
432C4⋊Dic47—22no—
433C4⋊Dic47—22no—
434C4⋊Dic47—22no—
435C4⋊Dic47—22no—
436C4⋊Dic47—22no—
437C4⋊Dic47—41no—
438C4⋊Dic47—41no—
439C4⋊Dic47—41no—
440C4⋊Dic47—41no—
441C4⋊Dic47—41no—
442C4⋊Dic47—41no—
443C4⋊Dic47—41no—
444C4⋊Dic47#4114yes—
445Dic47⋊C4—22no—
446Dic47⋊C4—22no—
447Dic47⋊C4—22no—
448Dic47⋊C4—22no—
449Dic47⋊C4—22no—
450Dic47⋊C4—22no—
451Dic47⋊C4—22no—
452Dic47⋊C4—22no—
453Dic47⋊C4—22no—
454Dic47⋊C4—22no—
455Dic47⋊C4—22no—
456Dic47⋊C4—22no—
457Dic47⋊C4—22no—
458Dic47⋊C4—22no—
459Dic47⋊C4—22no—
460Dic47⋊C4—22no—
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⋊C4C2×Q814yes—
472Dic47⋊C4C2×Q814yes—
473C4×Dic47—22no—
474C4×Dic47—22no—
475C4×Dic47—22no—
476C4×Dic47—22no—
477C4×Dic47—22no—
478C4×Dic47—22no—
479C4×Dic47—22no—
480C4×Dic47—22no—
481C4×Dic47—22no—
482C4×Dic47—22no—
483C4×Dic47—22no—
484C4×Dic47—22no—
485C4×Dic47—22no—
486C4×Dic47—22no—
487C4×Dic47—22no—
488C4×Dic47—22no—
489C4×Dic47—22no—
490C4×Dic47—22no—
491C4×Dic47—22no—
492C4×Dic47—22no—
493C4×Dic47—22no—
494C4×Dic47—41no—
495C4×Dic47—41no—
496C4×Dic47—41no—
497C4×Dic47C2×Q814yes—
498C4×Dic47C2×Q814yes—
499C23×C47—21no—
500C23×C47—21no—
501C23×C47—21no—
502C23×C47—21no—
503C23×C47C22×Q812yes—
504C23×C47C2×#4112yes—
505C23×C47C2×#4112yes—
506C23×C47C2511yescharacteristic
507C2×C4×C47—28no—
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—21no—
544C2×C4×C47—44no—
545C2×C4×C47—44no—
546C2×C4×C47C22×Q812yes—
547C2×C4×C47C22×Q812yes—
548C2×C4×C47C2×#4112yes—
549C2×C4×C47C2×#4112yes—
550C2×C4×C47C2×#4112yes—
551C2×C4×C47C2×#4112yes—
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—44no—
591C2×Dic47—44no—
592C2×Dic47—44no—
593C2×Dic47#125116yescomplemented
594C2×Dic47C22×Q812yes—
595C2×Dic47C22×Q812yes—
596C2×Dic47C22×Q812yes—
597C2×Dic47C22×Q812yes—
598C2×Dic47C2×#4112yes—
599C2×Dic47C2×#4112yes—
600C2×Dic47C2×#4112yes—
601C2×Dic47C2×#4112yes—
602C2×Dic47C2×#4112yes—
603C2×Dic47C2×#4112yes—
604#34815—471nomaximal, Sylow
605C22×C47—22no—
606C22×C47—22no—
607C22×C47—22no—
608C22×C47—22no—
609C22×C47—22no—
610C22×C47—22no—
611C22×C47C2×#12514yes—
612C22×C47C23×Q811yescharacteristic
613C22×C47C22×#4111yescharacteristic
614C22×C47C22×#4111yescharacteristic
615C22×C47C22×#4111yescharacteristic
616C22×C47C22×#4111yescharacteristic
617C22×C47#58511yescharacteristic
618C22×C47#58511yescharacteristic
619C4×C47—22no—
620C4×C47—22no—
621C4×C47—22no—
622C4×C47—22no—
623C4×C47—22no—
624C4×C47—22no—
625C4×C47—41no—
626C4×C47—41no—
627C4×C47—41no—
628C4×C47—41no—
629C4×C47—41no—
630C4×C47—41no—
631C4×C47—41no—
632C4×C47—41no—
633Dic47—22no—
634Dic47—22no—
635Dic47—22no—
636Dic47—22no—
637Dic47—41no—
638Dic47—41no—
639Dic47—41no—
640Dic47—41no—
641Dic47—41no—
642Dic47—41no—
643Dic47—41no—
644Dic47—41no—
645Dic47—41no—
646Dic47—41no—
647Dic47C2×#12514yes—
648Dic47C2×#12514yes—
649#2509—471no—
650#2509—471no—
651#2508—471no—
652#2508—471no—
653#2507—471no—
654#2507—471no—
655#2506—471no—
656#2506—471no—
657#2505—471no—
658#2505—471no—
659#2505—471no—
660#2505—471no—
661#2473—471no—
662#2473—471no—
663#2473—471no—
664#2473D4711yescharacteristic
665#2402—471no—
666#2402—471no—
667#2402—471no—
668#2402—471no—
669C4×#125—471no—
670C4×#125—471no—
671C4×#125—471no—
672C4×#125—471no—
673#2296—471no—
674#2296—471no—
675#2296—471no—
676#2296—471no—
677#2285—471no—
678C4×#117—471no—
679C2×C4×C4⋊C4—471no—
680C2×C47—24no—
681C2×C47C22×#12511yescharacteristic
682C2×C47#344411yescharacteristic
683C2×C47#345511yescharacteristic
684C2×C47#347511yescharacteristic
685C2×C47#347511yescharacteristic
686C2×C47Q8×#4111yescharacteristic
687C2×C47Q8×#4111yescharacteristic
688C2×#125—471no—
689C2×#125—471no—
690C2×#125—471no—
691C2×#125C2×D4711yescharacteristic
692C2×#117—471no—
693C2×#117—471no—
694C2×#117—471no—
695C2×#117—471no—
696C22×C4⋊C4—471no—
697C22×C4⋊C4C2×D4711yescharacteristic
698C22×C42—471no—
699C22×C42—471no—
700C22×C42—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#400C2×D4711yescharacteristic
717#398—471no—
718#398—471no—
719#398—471no—
720#398—471no—
721#398—471no—
722#398—471no—
723#398—471no—
724#398—471no—
725#398—471no—
726#398—471no—
727#398—471no—
728#398—471no—
729#398—471no—
730#398C2×D4711yescharacteristic
731#398C2×D4711yescharacteristic
732#398C2×D4711yescharacteristic
733#389—471no—
734#389—471no—
735#389—471no—
736#389—471no—
737#389—471no—
738#389—471no—
739#389—471no—
740#389—471no—
741#389—471no—
742#389—471no—
743#389—471no—
744#389—471no—
745#389—471no—
746#389—471no—
747#389—471no—
748#389—471no—
749#389—471no—
750#389—471no—
751#389—471no—
752#389—471no—
753#389—471no—
754#389—471no—
755#389—471no—
756#389C2×D4711yescharacteristic
757#387—471no—
758#387—471no—
759#387—471no—
760#387—471no—
761#387—471no—
762#387—471no—
763#387—471no—
764#387—471no—
765#387—471no—
766#387—471no—
767#387—471no—
768#387—471no—
769#387—471no—
770#387—471no—
771#387C2×D4711yescharacteristic
772#387C2×D4711yescharacteristic
773#385—471no—
774#385—471no—
775#385—471no—
776#385—471no—
777#385—471no—
778#385—471no—
779#385—471no—
780#385—471no—
781#385—471no—
782#385—471no—
783#385—471no—
784#385—471no—
785#385C2×D4711yescharacteristic
786#385C2×D4711yescharacteristic
787#385C2×D4711yescharacteristic
788#385C2×D4711yescharacteristic
789#384—471no—
790#384—471no—
791#382—471no—
792#382—471no—
793#382—471no—
794#382—471no—
795#382—471no—
796#382—471no—
797#380—471no—
798#380—471no—
799#380—471no—
800#380C2×D4711yescharacteristic
801C4×C4⋊C4—471no—
802C4×C4⋊C4—471no—
803C4×C4⋊C4—471no—
804C4×C4⋊C4—471no—
805C4×C4⋊C4—471no—
806C4×C4⋊C4—471no—
807C4×C4⋊C4—471no—
808C4×C4⋊C4—471no—
809C4×C4⋊C4—471no—
810C4×C4⋊C4—471no—
811C4×C4⋊C4—471no—
812C4×C4⋊C4—471no—
813C4×C4⋊C4—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⋊C4—471no—
828C4×C4⋊C4—471no—
829C4×C4⋊C4—471no—
830C4×C4⋊C4—471no—
831C4×C4⋊C4—471no—
832C4×C4⋊C4—471no—
833C4×C22⋊C4—471no—
834C4×C22⋊C4—471no—
835C4×C22⋊C4—471no—
836C4×C22⋊C4C2×D4711yescharacteristic
837#376—471no—
838#376—471no—
839C2×#95—471no—
840C2×#95—471no—
841C43—471no—
842C43—471no—
843C47#3481511yescharacteristic, complemented, Sylow
844C23×C4—471no—
845C23×C4—471no—
846C23×C4—471no—
847C23×C4—471no—
848C23×C4C22×D4711yescharacteristic
849C23×C4C22×D4711yescharacteristic
850C23×C4C22×D4711yescharacteristic
851#125—24no—
852#125—944no—
853#125—944no—
854#125—944no—
855#117—478no—
856#117—944no—
857#117—944no—
858#117—944no—
859C2×C4⋊C4—24no—
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⋊C4—471no—
895C2×C4⋊C4—471no—
896C2×C4⋊C4—471no—
897C2×C4⋊C4—471no—
898C2×C4⋊C4—471no—
899C2×C4⋊C4—471no—
900C2×C4⋊C4—471no—
901C2×C4⋊C4—471no—
902C2×C4⋊C4—944no—
903C2×C4⋊C4C22×D4711yescharacteristic
904C2×C4⋊C4C22×D4711yescharacteristic
905C2×C4⋊C4C22×D4711yescharacteristic
906C2×C4⋊C4C22×D4711yescharacteristic
907C2×C4⋊C4C22×D4711yescharacteristic
908C2×C4⋊C4C22×D4711yescharacteristic
909C2×C4⋊C4C22×D4711yescharacteristic
910C2×C4⋊C4C22×D4711yescharacteristic
911C2×C4⋊C4C22×D4711yescharacteristic
912C2×C4⋊C4C22×D4711yescharacteristic
913C2×C4⋊C4C22×D4711yescharacteristic
914C2×C4⋊C4C22×D4711yescharacteristic
915C2×C4⋊C4C22×D4711yescharacteristic
916C2×C4⋊C4C22×D4711yescharacteristic
917C2×C22⋊C4—471no—
918C2×C22⋊C4—471no—
919C2×C22⋊C4—471no—
920C2×C22⋊C4—471no—
921C2×C22⋊C4C22×D4711yescharacteristic
922C2×C22⋊C4C22×D4711yescharacteristic
923C2×C22⋊C4C22×D4711yescharacteristic
924C2×C22⋊C4C22×D4711yescharacteristic
925C2×C42—471no—
926C2×C42—471no—
927C2×C42—471no—
928C2×C42—471no—
929C2×C42—471no—
930C2×C42—471no—
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×C42—471no—
943C2×C42—471no—
944C2×C42—471no—
945C2×C42—471no—
946C2×C42—471no—
947C2×C42—471no—
948C2×C42—471no—
949C2×C42—471no—
950C2×C42—471no—
951C2×C42—944no—
952C2×C42—944no—
953C2×C42—944no—
954C2×C42C22×D4711yescharacteristic
955C2×C42C22×D4711yescharacteristic
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#95—471no—
999#95—471no—
1000#95C22×D4711yescharacteristic
1001#95C22×D4711yescharacteristic
1002#95C22×D4711yescharacteristic
1003#95C22×D4711yescharacteristic
1004#95C22×D4711yescharacteristic
1005#95C22×D4711yescharacteristic
1006#95C22×D4711yescharacteristic
1007#95C22×D4711yescharacteristic
1008#95C22×D4711yescharacteristic
1009#95C22×D4711yescharacteristic
1010#95C22×D4711yescharacteristic
1011#95C22×D4711yescharacteristic
1012C24C23×D4711yescharacteristic
1013C22×C4—22no—
1014C22×C4—22no—
1015C22×C4—22no—
1016C22×C4—22no—
1017C22×C4—22no—
1018C22×C4—22no—
1019C22×C4—22no—
1020C22×C4—41no—
1021C22×C4—41no—
1022C22×C4—474no—
1023C22×C4—474no—
1024C22×C4—474no—
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—471no—
1041C22×C4—942no—
1042C22×C4—942no—
1043C22×C4—942no—
1044C22×C4—942no—
1045C22×C4—942no—
1046C22×C4—1881no—
1047C22×C4—1881no—
1048C22×C4—1881no—
1049C22×C4—1881no—
1050C22×C4C23×D4711yescharacteristic
1051C22×C4C23×D4711yescharacteristic
1052C22×C4C23×D4711yescharacteristic
1053C22×C4C23×D4711yescharacteristic
1054C22×C4C23×D4711yescharacteristic
1055C22×C4C23×D4711yescharacteristic
1056C22×C4C23×D4711yescharacteristic
1057C22×C4C23×D4711yescharacteristic
1058C22×C4C23×D4711yescharacteristic
1059C22×C4C23×D4711yescharacteristic
1060C22×C4C23×D4711yescharacteristic
1061C22×C4C23×D4711yescharacteristic
1062C22×C4C23×D4711yescharacteristic
1063C22×C4C23×D4711yescharacteristic
1064C4⋊C4—22no—
1065C4⋊C4—22no—
1066C4⋊C4—22no—
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—22no—
1070C4⋊C4—22no—
1071C4⋊C4—22no—
1072C4⋊C4—22no—
1073C4⋊C4—22no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—474no—
1078C4⋊C4—474no—
1079C4⋊C4—474no—
1080C4⋊C4—942no—
1081C4⋊C4—942no—
1082C4⋊C4—942no—
1083C4⋊C4—942no—
1084C4⋊C4—942no—
1085C4⋊C4—942no—
1086C4⋊C4—942no—
1087C4⋊C4—942no—
1088C4⋊C4—942no—
1089C4⋊C4—942no—
1090C4⋊C4—942no—
1091C4⋊C4—942no—
1092C4⋊C4—942no—
1093C4⋊C4—942no—
1094C4⋊C4—942no—
1095C4⋊C4—942no—
1096C4⋊C4—942no—
1097C4⋊C4—942no—
1098C4⋊C4—942no—
1099C4⋊C4—942no—
1100C4⋊C4—942no—
1101C4⋊C4—942no—
1102C4⋊C4—1881no—
1103C4⋊C4—1881no—
1104C4⋊C4—1881no—
1105C4⋊C4—1881no—
1106C4⋊C4—1881no—
1107C4⋊C4—1881no—
1108C4⋊C4—1881no—
1109C4⋊C4—1881no—
1110C4⋊C4—1881no—
1111C4⋊C4—1881no—
1112C4⋊C4—1881no—
1113C4⋊C4—1881no—
1114C4⋊C4—1881no—
1115C4⋊C4—1881no—
1116C4⋊C4—1881no—
1117C4⋊C4—1881no—
1118C4⋊C4—1881no—
1119C4⋊C4#1062535214yes—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—22no—
1123C22⋊C4—474no—
1124C22⋊C4—942no—
1125C22⋊C4—942no—
1126C22⋊C4—942no—
1127C22⋊C4Q8×D4714yes—
1128C42—22no—
1129C42—41no—
1130C42—474no—
1131C42—474no—
1132C42—942no—
1133C42—942no—
1134C42—942no—
1135C42—942no—
1136C42—942no—
1137C42—942no—
1138C42—942no—
1139C42—942no—
1140C42—942no—
1141C42—942no—
1142C42—942no—
1143C42—942no—
1144C42—942no—
1145C42—942no—
1146C42—942no—
1147C42—942no—
1148C42—942no—
1149C42—942no—
1150C42—942no—
1151C42—942no—
1152C42—942no—
1153C42—1881no—
1154C42—1881no—
1155C42—1881no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23C2×Q8×D4712yes—
1161C23#41×D4712yes—
1162C23#41×D4712yes—
1163C23C24×D4711yescharacteristic
1164C2×C4—28no—
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—44no—
1202C2×C4—44no—
1203C2×C4—4716no—
1204C2×C4—472no—
1205C2×C4—472no—
1206C2×C4—472no—
1207C2×C4—472no—
1208C2×C4—472no—
1209C2×C4—472no—
1210C2×C4—472no—
1211C2×C4—472no—
1212C2×C4—472no—
1213C2×C4—472no—
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—941no—
1250C2×C4—941no—
1251C2×C4—941no—
1252C2×C4—1884no—
1253C2×C4—1884no—
1254C2×C4—1884no—
1255C2×C4C2×Q8×D4712yes—
1256C2×C4C2×Q8×D4712yes—
1257C2×C4#41×D4712yes—
1258C2×C4C2×#1062535212yes—
1259C2×C4C2×#1062535212yes—
1260C2×C4C2×#1062535212yes—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22#125×D4714yes—
1268C22C22×Q8×D4711yescharacteristic
1269C22C2×#41×D4711yescharacteristic
1270C22C2×#41×D4711yescharacteristic
1271C22C2×#41×D4711yescharacteristic
1272C22C22×#1062535211yescharacteristic
1273C22#1568995811yescharacteristic
1274C22#1568996011yescharacteristic
1275C4—22no—
1276C4—22no—
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—474no—
1290C4—474no—
1291C4—942no—
1292C4—942no—
1293C4—942no—
1294C4—942no—
1295C4—1881no—
1296C4—1881no—
1297C4—1881no—
1298C4—1881no—
1299C4—1881no—
1300C4—1881no—
1301C4—1881no—
1302C4—1881no—
1303C4—1881no—
1304C4—1881no—
1305C2—24no—
1306C2C2×#125×D4711yescharacteristic
1307C2#2025668011yescharacteristic
1308C2#2025677411yescharacteristic
1309C2#2025693911yescharacteristic
1310C2#2025695311yescharacteristic
1311C2Q8×#1062535211yescharacteristic
1312C2#2025696711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2473C2
prime radicalC24×C47C24
hypercenter#2473D47
hypocenterC47#34815
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2473

Complements

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

NH ≅ G/Ntype
1. #20247934C2semidirect
2. #20247932C2semidirect
3. #20247923C2semidirect
4. #20247921C2semidirect
5. #20247914C2semidirect
6. #20247908C2semidirect
7. #20247903C2semidirect
8. #20247897C2semidirect
16. #20246694C2semidirect
17. #20246692C2semidirect
18. #20246692C2semidirect
19. #20246692C2semidirect
20. #125×Dic47C2semidirect
21. #20245947C2semidirect
22. #20245945C2semidirect
23. #20245945C2semidirect
593. C2×Dic47#125semidirect
843. C47#34815semidirect

Maximal subgroups

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

subgroupindex
#202479342
#202479322
#202479232
#202479212
#202479142
#202479082
#202479032
#202478972
#202478932
#202478912
#202478852
#202478832
#202475282
#202475262
#202475232
#202466942
#202466922
#125×Dic472
#202459472
#202459452
#202458672
#202457902
C4×#130939802
C2×C4⋊C4×Dic472
C47×#24732
#3481547