Finite Group Databasebeta

← #26423000

Subgroups — #26423000

Order 12032.

1304 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251662C211yesmaximal, characteristic
2#20251639C211yesmaximal, characteristic
3#20251638C211yesmaximal, characteristic
4#20251637C211yesmaximal, characteristic
5#20251636C211yesmaximal, characteristic
6#20251635C211yesmaximal, characteristic
7#20251634C211yesmaximal, characteristic
8#20251633C211yesmaximal, characteristic
9#20251632C211yesmaximal, characteristic
10#20251631C211yesmaximal, characteristic
11#20251629C211yesmaximal, characteristic
12#20251627C211yesmaximal, characteristic
13#20251625C211yesmaximal, characteristic
14#20251458C211yesmaximal, characteristic
15#20251457C211yesmaximal, characteristic
16#20251454C211yesmaximal, characteristic
17#20246696C211yesmaximal, characteristic
18#20246696C211yesmaximal, characteristic
19#20246696C211yesmaximal, characteristic
20#20246695C211yesmaximal, characteristic
21#20246695C211yesmaximal, characteristic
22#20246695C211yesmaximal, characteristic
23#20246695C211yesmaximal, characteristic
24#20246695C211yesmaximal, characteristic
25#20246695C211yesmaximal, characteristic
26#20246693C211yesmaximal, characteristic
27#20246693C211yesmaximal, characteristic
28C4×#13094015C211yesmaximal, characteristic
29C4×#13094014C211yesmaximal, characteristic
30C4×#13094014C211yesmaximal, characteristic
31C47×#2402C211yesmaximal, characteristic
32C2×#13094015C2211yescharacteristic
33C2×#13094014C2211yescharacteristic
34C2×#13094014C2211yescharacteristic
35#15689065C2211yescharacteristic
36#15689065C2211yescharacteristic
37#15689065C2211yescharacteristic
38#15689065C2211yescharacteristic
39#15689065C2211yescharacteristic
40#15689065C2211yescharacteristic
41#15689065C2211yescharacteristic
42#15689065C2211yescharacteristic
43#15689065C2211yescharacteristic
44#15689065C2211yescharacteristic
45#15689065C2211yescharacteristic
46#15689065C2211yescharacteristic
47#15689065C2211yescharacteristic
48#15689065C2211yescharacteristic
49#15689064C2211yescharacteristic
50#15689064C2211yescharacteristic
51#15689064C2211yescharacteristic
52#15689064C2211yescharacteristic
53#15689064C2211yescharacteristic
54#15689064C2211yescharacteristic
55#15689064C2211yescharacteristic
56#15689064C2211yescharacteristic
57#15689064C2211yescharacteristic
58#15689064C2211yescharacteristic
59#15689064C2211yescharacteristic
60#15689064C2211yescharacteristic
61#15689063C2211yescharacteristic
62#15689063C2211yescharacteristic
63#15689063C2211yescharacteristic
64#15689063C2211yescharacteristic
65#15689063C2211yescharacteristic
66#15689063C2211yescharacteristic
67#15689062C2211yescharacteristic
68#15689062C2211yescharacteristic
69#15689062C2211yescharacteristic
70#15689062C2211yescharacteristic
71#15689062C2211yescharacteristic
72#15689062C2211yescharacteristic
73#15689061C2211yescharacteristic
74#15689061C2211yescharacteristic
75#15689061C2211yescharacteristic
76#15689061C2211yescharacteristic
77#15689061C2211yescharacteristic
78#15689061C2211yescharacteristic
79#15689057C2211yescharacteristic
80#15689057C2211yescharacteristic
81#15689057C2211yescharacteristic
82#15689057C2211yescharacteristic
83#15689057C2211yescharacteristic
84#15689057C2211yescharacteristic
85#15689057C2211yescharacteristic
86#15689057C2211yescharacteristic
87#15689057C2211yescharacteristic
88#15689057C2211yescharacteristic
89#15689057C2211yescharacteristic
90#15689057C2211yescharacteristic
91#15689057C2211yescharacteristic
92#15689057C2211yescharacteristic
93#15689056C2211yescharacteristic
94#15689056C2211yescharacteristic
95#15689056C2211yescharacteristic
96#15689056C2211yescharacteristic
97#15689056C2211yescharacteristic
98#15689056C2211yescharacteristic
99#15689056C2211yescharacteristic
100#15689056C2211yescharacteristic
101#15689056C2211yescharacteristic
102#15689056C2211yescharacteristic
103#15689056C2211yescharacteristic
104#15689056C2211yescharacteristic
105#15689055C2211yescharacteristic
106#15689055C2211yescharacteristic
107#15689055C2211yescharacteristic
108#15689055C2211yescharacteristic
109#15689055C2211yescharacteristic
110#15689055C2211yescharacteristic
111#15689054C2211yescharacteristic
112#15689054C2211yescharacteristic
113#15689054C2211yescharacteristic
114#15689054C2211yescharacteristic
115#15689054C2211yescharacteristic
116#15689054C2211yescharacteristic
117#15689053C2211yescharacteristic
118#15689053C2211yescharacteristic
119#15689053C2211yescharacteristic
120#15689053C2211yescharacteristic
121#15689053C2211yescharacteristic
122#15689053C2211yescharacteristic
123#15689022C2211yescharacteristic
124#15689020C2211yescharacteristic
125#15689020C2211yescharacteristic
126#15689019C2211yescharacteristic
127#15689018C2211yescharacteristic
128#15689018C2211yescharacteristic
129#15689010C2211yescharacteristic
130#15689010C2211yescharacteristic
131#15689009C2211yescharacteristic
132#15689009C2211yescharacteristic
133#15689008C2211yescharacteristic
134#15689008C2211yescharacteristic
135#15689006C2211yescharacteristic
136#15689006C2211yescharacteristic
137#15689005C2211yescharacteristic
138#15689005C2211yescharacteristic
139#15689004C2211yescharacteristic
140#15689004C2211yescharacteristic
141#15688988C2211yescharacteristic
142#15688987C2211yescharacteristic
143#15688987C2211yescharacteristic
144C4×Dic47⋊C4C2211yescharacteristic
145C4×Dic47⋊C4C2211yescharacteristic
146C4×Dic47⋊C4C2211yescharacteristic
147C4×Dic47⋊C4C2211yescharacteristic
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×Dic47⋊C4C2211yescharacteristic
158C4×Dic47⋊C4C2211yescharacteristic
159C4×Dic47⋊C4C2211yescharacteristic
160C4×C4⋊Dic47C2211yescharacteristic
161C4×C4⋊Dic47C2211yescharacteristic
162C4×C4⋊Dic47C2211yescharacteristic
163C4×C4⋊Dic47C2211yescharacteristic
164C4×C4⋊Dic47C2211yescharacteristic
165C4×C4⋊Dic47C2211yescharacteristic
166C4×C4⋊Dic47C2211yescharacteristic
167C4×C4⋊Dic47C2211yescharacteristic
168#15688969C2211yescharacteristic
169#15688969C2211yescharacteristic
170#15688969C2211yescharacteristic
171C42×Dic47C2211yescharacteristic
172C47×#400C2211yescharacteristic
173C47×#400C2211yescharacteristic
174C47×#400C2211yescharacteristic
175C47×#400C2211yescharacteristic
176C47×#398C2211yescharacteristic
177C47×#398C2211yescharacteristic
178C47×#398C2211yescharacteristic
179C47×#398C2211yescharacteristic
180C4×C4⋊C4×C47C2211yescharacteristic
181C4×C4⋊C4×C47C2211yescharacteristic
182C4×C4⋊C4×C47C2211yescharacteristic
183C4×C4⋊C4×C47C2211yescharacteristic
184C4×C4⋊C4×C47C2211yescharacteristic
185C4×C4⋊C4×C47C2211yescharacteristic
186C47×#376C2211yescharacteristic
187#13094015—24no—
188#13094014—24no—
189#13094014—24no—
190C2×C4⋊Dic47C2311yescharacteristic
191C2×C4⋊Dic47C2311yescharacteristic
192C2×C4⋊Dic47C2311yescharacteristic
193C2×C4⋊Dic47C2311yescharacteristic
194C2×C4⋊Dic47C2311yescharacteristic
195C2×C4⋊Dic47C2311yescharacteristic
196C2×C4⋊Dic47C2311yescharacteristic
197C2×C4⋊Dic47C2311yescharacteristic
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×Dic47⋊C4C2311yescharacteristic
207C2×Dic47⋊C4C2311yescharacteristic
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×Dic47⋊C4C2311yescharacteristic
234C2×Dic47⋊C4C2311yescharacteristic
235C2×Dic47⋊C4C2311yescharacteristic
236C2×Dic47⋊C4C2311yescharacteristic
237C2×Dic47⋊C4C2311yescharacteristic
238C2×C4×Dic47C2311yescharacteristic
239C2×C4×Dic47C2311yescharacteristic
240C2×C4×Dic47C2311yescharacteristic
241C2×C4×Dic47C2311yescharacteristic
242C2×C4×Dic47C2311yescharacteristic
243C2×C4×Dic47C2311yescharacteristic
244C2×C4×Dic47C2311yescharacteristic
245C2×C4×Dic47C2311yescharacteristic
246C2×C4×Dic47C2311yescharacteristic
247C2×C4×Dic47C2311yescharacteristic
248C2×C4×Dic47C2311yescharacteristic
249C2×C4×Dic47C2311yescharacteristic
250C47⋊#95C2311yescharacteristic
251C47⋊#95C2311yescharacteristic
252C47⋊#95C2311yescharacteristic
253C47⋊#95C2311yescharacteristic
254C47⋊#95C2311yescharacteristic
255C47⋊#95C2311yescharacteristic
256C47⋊#95C2311yescharacteristic
257C47⋊#95C2311yescharacteristic
258C47⋊#95C2311yescharacteristic
259C47⋊#95C2311yescharacteristic
260C47⋊#95C2311yescharacteristic
261C47⋊#95C2311yescharacteristic
262C47⋊#95C2311yescharacteristic
263C47⋊#95C2311yescharacteristic
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
310C2×C4⋊C4×C47C2311yescharacteristic
311C2×C4⋊C4×C47C2311yescharacteristic
312C2×C4⋊C4×C47C2311yescharacteristic
313C2×C4⋊C4×C47C2311yescharacteristic
314C2×C4⋊C4×C47C2311yescharacteristic
315C2×C4⋊C4×C47C2311yescharacteristic
316C2×C4⋊C4×C47C2311yescharacteristic
317C2×C4⋊C4×C47C2311yescharacteristic
318C2×C4⋊C4×C47C2311yescharacteristic
319C2×C4⋊C4×C47C2311yescharacteristic
320C2×C4⋊C4×C47C2311yescharacteristic
321C2×C4⋊C4×C47C2311yescharacteristic
322C2×C42×C47C2311yescharacteristic
323C2×C42×C47C2311yescharacteristic
324C2×C42×C47C2311yescharacteristic
325C2×C42×C47C2311yescharacteristic
326C2×C42×C47C2311yescharacteristic
327C2×C42×C47C2311yescharacteristic
328C2×C42×C47C2311yescharacteristic
329#95×C47C2311yescharacteristic
330#95×C47C2311yescharacteristic
331#95×C47C2311yescharacteristic
332#95×C47C2311yescharacteristic
333#95×C47C2311yescharacteristic
334#95×C47C2311yescharacteristic
335#95×C47C2311yescharacteristic
336#95×C47C2311yescharacteristic
337#95×C47C2311yescharacteristic
338#95×C47C2311yescharacteristic
339#95×C47C2311yescharacteristic
340#95×C47C2311yescharacteristic
341#95×C47C2311yescharacteristic
342#95×C47C2311yescharacteristic
343#95×C47C2311yescharacteristic
344#95×C47C2311yescharacteristic
345C22×C4×C47C2411yescharacteristic
346C22×C4×C47C2411yescharacteristic
347C22×C4×C47C2411yescharacteristic
348C22×C4×C47C2411yescharacteristic
349C22×C4×C47C2411yescharacteristic
350C22×C4×C47C2411yescharacteristic
351C22×C4×C47C2411yescharacteristic
352C22×C4×C47C2411yescharacteristic
353C22×C4×C47C2411yescharacteristic
354C22×C4×C47C2411yescharacteristic
355C22×C4×C47C2411yescharacteristic
356C22×C4×C47C2411yescharacteristic
357C22×C4×C47C2411yescharacteristic
358C22×C4×C47C2411yescharacteristic
359C22×C4×C47C2411yescharacteristic
360C22×Dic47C2411yescharacteristic
361C22×Dic47C2411yescharacteristic
362C22×Dic47C2411yescharacteristic
363C22×Dic47C2411yescharacteristic
364C22×Dic47C2411yescharacteristic
365C22×Dic47C2411yescharacteristic
366C22×Dic47C2411yescharacteristic
367C22×Dic47C2411yescharacteristic
368C22×Dic47C2411yescharacteristic
369C22×Dic47C2411yescharacteristic
370C22×Dic47C2411yescharacteristic
371C22×Dic47C2411yescharacteristic
372C22×Dic47C2411yescharacteristic
373C22×Dic47C2411yescharacteristic
374C22×Dic47C2411yescharacteristic
375C22×Dic47C2411yescharacteristic
376C4⋊C4×C47—22no—
377C4⋊C4×C47—22no—
378C4⋊C4×C47—22no—
379C4⋊C4×C47—41no—
380C4⋊C4×C47—41no—
381C4⋊C4×C47—41no—
382C4⋊C4×C47—41no—
383C4⋊C4×C47—41no—
384C4⋊C4×C47—41no—
385C4⋊C4×C47—41no—
386C4⋊C4×C47—41no—
387C4⋊C4×C47—41no—
388C42×C47—22no—
389C42×C47—22no—
390C42×C47—22no—
391C42×C47—22no—
392C42×C47—22no—
393C42×C47—22no—
394C42×C47—22no—
395C4⋊Dic47—22no—
396C4⋊Dic47—22no—
397C4⋊Dic47—22no—
398C4⋊Dic47—22no—
399C4⋊Dic47—22no—
400C4⋊Dic47—41no—
401C4⋊Dic47—41no—
402C4⋊Dic47—41no—
403C4⋊Dic47—41no—
404C4⋊Dic47—41no—
405C4⋊Dic47—41no—
406C4⋊Dic47—41no—
407C4⋊Dic47—41no—
408C4⋊Dic47—41no—
409C4⋊Dic47—41no—
410C4⋊Dic47—41no—
411Dic47⋊C4—22no—
412Dic47⋊C4—22no—
413Dic47⋊C4—22no—
414Dic47⋊C4—22no—
415Dic47⋊C4—22no—
416Dic47⋊C4—22no—
417Dic47⋊C4—22no—
418Dic47⋊C4—22no—
419Dic47⋊C4—22no—
420Dic47⋊C4—22no—
421Dic47⋊C4—41no—
422Dic47⋊C4—41no—
423Dic47⋊C4—41no—
424Dic47⋊C4—41no—
425Dic47⋊C4—41no—
426Dic47⋊C4—41no—
427Dic47⋊C4—41no—
428Dic47⋊C4—41no—
429Dic47⋊C4—41no—
430Dic47⋊C4—41no—
431Dic47⋊C4—41no—
432Dic47⋊C4—41no—
433Dic47⋊C4—41no—
434Dic47⋊C4—41no—
435Dic47⋊C4—41no—
436Dic47⋊C4—41no—
437Dic47⋊C4—41no—
438Dic47⋊C4—41no—
439Dic47⋊C4—41no—
440Dic47⋊C4—41no—
441Dic47⋊C4—41no—
442Dic47⋊C4—41no—
443C4×Dic47—22no—
444C4×Dic47—22no—
445C4×Dic47—22no—
446C4×Dic47—22no—
447C4×Dic47—22no—
448C4×Dic47—22no—
449C4×Dic47—22no—
450C4×Dic47—22no—
451C4×Dic47—41no—
452C4×Dic47—41no—
453C4×Dic47—41no—
454C4×Dic47#4114yes—
455C23×C47C2511yescharacteristic
456C2×C4×C47—21no—
457C2×C4×C47—21no—
458C2×C4×C47—21no—
459C2×C4×C47—21no—
460C2×C4×C47—21no—
461C2×C4×C47—21no—
462C2×C4×C47—21no—
463C2×C4×C47—21no—
464C2×C4×C47—21no—
465C2×C4×C47—21no—
466C2×C4×C47—21no—
467C2×C4×C47—21no—
468C2×C4×C47—21no—
469C2×C4×C47—21no—
470C2×C4×C47—21no—
471C2×C4×C47—21no—
472C2×C4×C47—21no—
473C2×C4×C47—21no—
474C2×C4×C47—21no—
475C2×C4×C47—21no—
476C2×C4×C47—21no—
477C2×C4×C47—21no—
478C2×C4×C47—21no—
479C2×C4×C47—21no—
480C2×C4×C47—21no—
481C2×C4×C47—21no—
482C2×C4×C47—21no—
483C2×C4×C47—21no—
484C2×C4×C47—21no—
485C2×C4×C47—21no—
486C2×C4×C47—21no—
487C2×C4×C47—21no—
488C2×C4×C47—21no—
489C2×C4×C47—21no—
490C2×C4×C47—21no—
491C2×C4×C47—21no—
492C2×C4×C47—21no—
493C2×C4×C47—21no—
494C2×C4×C47—21no—
495C2×C4×C47—21no—
496C2×C4×C47—21no—
497C2×C4×C47C2×#4112yes—
498C2×C4×C472−1+412yes—
499C2×C4×C472−1+412yes—
500C2×C4×C472−1+412yes—
501C2×Dic47—21no—
502C2×Dic47—21no—
503C2×Dic47—21no—
504C2×Dic47—21no—
505C2×Dic47—21no—
506C2×Dic47—21no—
507C2×Dic47—21no—
508C2×Dic47—21no—
509C2×Dic47—21no—
510C2×Dic47—21no—
511C2×Dic47—21no—
512C2×Dic47—21no—
513C2×Dic47—21no—
514C2×Dic47—21no—
515C2×Dic47—21no—
516C2×Dic47—21no—
517C2×Dic47—21no—
518C2×Dic47—21no—
519C2×Dic47—21no—
520C2×Dic47—21no—
521C2×Dic47—21no—
522C2×Dic47—21no—
523C2×Dic47—21no—
524C2×Dic47—21no—
525C2×Dic47—21no—
526C2×Dic47—21no—
527C2×Dic47—21no—
528C2×Dic47—21no—
529C2×Dic47—21no—
530C2×Dic47—21no—
531C2×Dic47—21no—
532C2×Dic47—21no—
533C2×Dic47—21no—
534C2×Dic47—21no—
535C2×Dic47—21no—
536C2×Dic47—21no—
537C2×Dic47—21no—
538C2×Dic47—21no—
539C2×Dic47—21no—
540C2×Dic47—21no—
541C2×Dic47—21no—
542C2×Dic47—21no—
543C2×Dic47—21no—
544C2×Dic47—21no—
545C2×Dic47—21no—
546C2×Dic47—21no—
547C2×Dic47C2×#4112yes—
548C2×Dic47C2×#4112yes—
549#36701—471nomaximal, Sylow
550C22×C47C22×#4111yescharacteristic
551C22×C47C2×2−1+411yescharacteristic
552C22×C47C2×2−1+411yescharacteristic
553C22×C47C2×2−1+411yescharacteristic
554C22×C47#58511yescharacteristic
555C22×C47#58511yescharacteristic
556C22×C47#58511yescharacteristic
557C4×C47—22no—
558C4×C47—41no—
559C4×C47—41no—
560C4×C47—41no—
561C4×C47—41no—
562C4×C47—41no—
563C4×C47—41no—
564C4×C47—41no—
565C4×C47—41no—
566C4×C47—41no—
567C4×C47—41no—
568C4×C47—41no—
569C4×C47—41no—
570C4×C47—41no—
571C4×C47#56414yes—
572Dic47—22no—
573Dic47—22no—
574Dic47—41no—
575Dic47—41no—
576Dic47—41no—
577Dic47—41no—
578Dic47—41no—
579Dic47—41no—
580Dic47—41no—
581Dic47—41no—
582Dic47—41no—
583Dic47—41no—
584Dic47—41no—
585Dic47—41no—
586Dic47—41no—
587Dic47—41no—
588#2845—471no—
589#2839—471no—
590#2839—471no—
591#2839—471no—
592#2839—471no—
593#2839—471no—
594#2839—471no—
595#2839—471no—
596#2839—471no—
597#2839—471no—
598#2839—471no—
599#2839—471no—
600#2839—471no—
601#2822—471no—
602#2822—471no—
603#2822—471no—
604#2402—471no—
605#2402—471no—
606#2402—471no—
607#2402—471no—
608#2402—471no—
609#2402—471no—
610#2402—471no—
611#2402—471no—
612#2402—471no—
613#2402—471no—
614#2402—471no—
615#2402D4711yescharacteristic
616C4×#125—471no—
617C4×#125—471no—
618C4×#125—471no—
619C2×C47#346111yescharacteristic
620C2×C47#346111yescharacteristic
621C2×C47#346111yescharacteristic
622C2×C47C2×#56411yescharacteristic
623C2×C47#353111yescharacteristic
624C2×C47#353111yescharacteristic
625C2×C47#353111yescharacteristic
626C2×#125—471no—
627C2×#125—471no—
628C2×#125—471no—
629#400—471no—
630#400—471no—
631#400—471no—
632#400—471no—
633#400—471no—
634#400—471no—
635#400—471no—
636#400—471no—
637#400—471no—
638#400—471no—
639#400—471no—
640#400—471no—
641#400—471no—
642#400—471no—
643#400—471no—
644#400—471no—
645#400—471no—
646#400—471no—
647#400—471no—
648#400—471no—
649#400—471no—
650#400—471no—
651#400—471no—
652#400—471no—
653#400—471no—
654#400—471no—
655#400—471no—
656#400—471no—
657#400—471no—
658#400—471no—
659#400—471no—
660#400—471no—
661#400—471no—
662#400—471no—
663#400—471no—
664#400—471no—
665#400—471no—
666#400—471no—
667#400—471no—
668#400—471no—
669#400—471no—
670#400—471no—
671#400—471no—
672#400—471no—
673#400C2×D4711yescharacteristic
674#400C2×D4711yescharacteristic
675#400C2×D4711yescharacteristic
676#400C2×D4711yescharacteristic
677#398—471no—
678#398—471no—
679#398—471no—
680#398—471no—
681#398—471no—
682#398—471no—
683#398—471no—
684#398—471no—
685#398—471no—
686#398—471no—
687#398—471no—
688#398—471no—
689#398—471no—
690#398—471no—
691#398—471no—
692#398—471no—
693#398—471no—
694#398—471no—
695#398—471no—
696#398—471no—
697#398—471no—
698#398—471no—
699#398—471no—
700#398—471no—
701#398—471no—
702#398—471no—
703#398—471no—
704#398—471no—
705#398—471no—
706#398—471no—
707#398—471no—
708#398—471no—
709#398—471no—
710#398—471no—
711#398—471no—
712#398—471no—
713#398—471no—
714#398—471no—
715#398—471no—
716#398—471no—
717#398—471no—
718#398—471no—
719#398—471no—
720#398—471no—
721#398C2×D4711yescharacteristic
722#398C2×D4711yescharacteristic
723#398C2×D4711yescharacteristic
724#398C2×D4711yescharacteristic
725#389—471no—
726#389—471no—
727#389—471no—
728#389—471no—
729#389—471no—
730#389—471no—
731#387—471no—
732#387—471no—
733#387—471no—
734#387—471no—
735#387—471no—
736#387—471no—
737#387—471no—
738#387—471no—
739#387—471no—
740#387—471no—
741#387—471no—
742#387—471no—
743#382—471no—
744#382—471no—
745#382—471no—
746C4×C4⋊C4—471no—
747C4×C4⋊C4—471no—
748C4×C4⋊C4—471no—
749C4×C4⋊C4—471no—
750C4×C4⋊C4—471no—
751C4×C4⋊C4—471no—
752C4×C4⋊C4—471no—
753C4×C4⋊C4—471no—
754C4×C4⋊C4—471no—
755C4×C4⋊C4—471no—
756C4×C4⋊C4—471no—
757C4×C4⋊C4—471no—
758C4×C4⋊C4—471no—
759C4×C4⋊C4—471no—
760C4×C4⋊C4—471no—
761C4×C4⋊C4—471no—
762C4×C4⋊C4—471no—
763C4×C4⋊C4—471no—
764C4×C4⋊C4—471no—
765C4×C4⋊C4—471no—
766C4×C4⋊C4—471no—
767C4×C4⋊C4—471no—
768C4×C4⋊C4—471no—
769C4×C4⋊C4—471no—
770C4×C4⋊C4C2×D4711yescharacteristic
771C4×C4⋊C4C2×D4711yescharacteristic
772C4×C4⋊C4C2×D4711yescharacteristic
773C4×C4⋊C4C2×D4711yescharacteristic
774C4×C4⋊C4C2×D4711yescharacteristic
775C4×C4⋊C4C2×D4711yescharacteristic
776#376—471no—
777#376—471no—
778#376—471no—
779#376C2×D4711yescharacteristic
780C43—471no—
781C47#3670111yescharacteristic, complemented, Sylow
782#125—944no—
783#125—944no—
784#125—944no—
785C2×C4⋊C4—471no—
786C2×C4⋊C4—471no—
787C2×C4⋊C4—471no—
788C2×C4⋊C4—471no—
789C2×C4⋊C4—471no—
790C2×C4⋊C4—471no—
791C2×C4⋊C4—471no—
792C2×C4⋊C4—471no—
793C2×C4⋊C4—471no—
794C2×C4⋊C4—471no—
795C2×C4⋊C4—471no—
796C2×C4⋊C4—471no—
797C2×C4⋊C4—471no—
798C2×C4⋊C4—471no—
799C2×C4⋊C4—471no—
800C2×C4⋊C4—471no—
801C2×C4⋊C4—471no—
802C2×C4⋊C4—471no—
803C2×C4⋊C4—471no—
804C2×C4⋊C4—471no—
805C2×C4⋊C4—471no—
806C2×C4⋊C4—471no—
807C2×C4⋊C4—471no—
808C2×C4⋊C4—471no—
809C2×C4⋊C4—471no—
810C2×C4⋊C4—471no—
811C2×C4⋊C4—471no—
812C2×C4⋊C4—471no—
813C2×C4⋊C4—471no—
814C2×C4⋊C4—471no—
815C2×C4⋊C4—471no—
816C2×C4⋊C4—471no—
817C2×C4⋊C4—471no—
818C2×C4⋊C4—471no—
819C2×C4⋊C4—471no—
820C2×C4⋊C4—471no—
821C2×C4⋊C4—471no—
822C2×C4⋊C4—471no—
823C2×C4⋊C4—471no—
824C2×C4⋊C4—471no—
825C2×C4⋊C4—471no—
826C2×C4⋊C4—471no—
827C2×C4⋊C4—471no—
828C2×C4⋊C4—471no—
829C2×C4⋊C4—471no—
830C2×C4⋊C4—471no—
831C2×C4⋊C4—471no—
832C2×C4⋊C4—471no—
833C2×C4⋊C4C22×D4711yescharacteristic
834C2×C4⋊C4C22×D4711yescharacteristic
835C2×C4⋊C4C22×D4711yescharacteristic
836C2×C4⋊C4C22×D4711yescharacteristic
837C2×C4⋊C4C22×D4711yescharacteristic
838C2×C4⋊C4C22×D4711yescharacteristic
839C2×C4⋊C4C22×D4711yescharacteristic
840C2×C4⋊C4C22×D4711yescharacteristic
841C2×C4⋊C4C22×D4711yescharacteristic
842C2×C4⋊C4C22×D4711yescharacteristic
843C2×C4⋊C4C22×D4711yescharacteristic
844C2×C4⋊C4C22×D4711yescharacteristic
845C2×C42—471no—
846C2×C42—471no—
847C2×C42—471no—
848C2×C42—471no—
849C2×C42—471no—
850C2×C42—471no—
851C2×C42—471no—
852C2×C42—471no—
853C2×C42—471no—
854C2×C42—471no—
855C2×C42—471no—
856C2×C42—471no—
857C2×C42C22×D4711yescharacteristic
858C2×C42C22×D4711yescharacteristic
859C2×C42C22×D4711yescharacteristic
860C2×C42C22×D4711yescharacteristic
861C2×C42C22×D4711yescharacteristic
862C2×C42C22×D4711yescharacteristic
863C2×C42C22×D4711yescharacteristic
864#95—471no—
865#95—471no—
866#95—471no—
867#95—471no—
868#95—471no—
869#95—471no—
870#95—471no—
871#95—471no—
872#95—471no—
873#95—471no—
874#95—471no—
875#95—471no—
876#95—471no—
877#95—471no—
878#95—471no—
879#95—471no—
880#95—471no—
881#95—471no—
882#95—471no—
883#95—471no—
884#95—471no—
885#95—471no—
886#95—471no—
887#95—471no—
888#95—471no—
889#95—471no—
890#95—471no—
891#95—471no—
892#95—471no—
893#95—471no—
894#95—471no—
895#95—471no—
896#95—471no—
897#95—471no—
898#95—471no—
899#95—471no—
900#95—471no—
901#95—471no—
902#95—471no—
903#95—471no—
904#95—471no—
905#95—471no—
906#95—471no—
907#95—471no—
908#95—471no—
909#95—471no—
910#95—471no—
911#95—471no—
912#95—471no—
913#95—471no—
914#95—471no—
915#95—471no—
916#95—471no—
917#95—471no—
918#95—471no—
919#95—471no—
920#95—471no—
921#95—471no—
922#95—471no—
923#95—471no—
924#95C22×D4711yescharacteristic
925#95C22×D4711yescharacteristic
926#95C22×D4711yescharacteristic
927#95C22×D4711yescharacteristic
928#95C22×D4711yescharacteristic
929#95C22×D4711yescharacteristic
930#95C22×D4711yescharacteristic
931#95C22×D4711yescharacteristic
932#95C22×D4711yescharacteristic
933#95C22×D4711yescharacteristic
934#95C22×D4711yescharacteristic
935#95C22×D4711yescharacteristic
936#95C22×D4711yescharacteristic
937#95C22×D4711yescharacteristic
938#95C22×D4711yescharacteristic
939#95C22×D4711yescharacteristic
940C22×C4—471no—
941C22×C4—471no—
942C22×C4—471no—
943C22×C4—471no—
944C22×C4—471no—
945C22×C4—471no—
946C22×C4—471no—
947C22×C4—471no—
948C22×C4—471no—
949C22×C4—471no—
950C22×C4—471no—
951C22×C4—471no—
952C22×C4—471no—
953C22×C4—471no—
954C22×C4—471no—
955C22×C4—471no—
956C22×C4C23×D4711yescharacteristic
957C22×C4C23×D4711yescharacteristic
958C22×C4C23×D4711yescharacteristic
959C22×C4C23×D4711yescharacteristic
960C22×C4C23×D4711yescharacteristic
961C22×C4C23×D4711yescharacteristic
962C22×C4C23×D4711yescharacteristic
963C22×C4C23×D4711yescharacteristic
964C22×C4C23×D4711yescharacteristic
965C22×C4C23×D4711yescharacteristic
966C22×C4C23×D4711yescharacteristic
967C22×C4C23×D4711yescharacteristic
968C22×C4C23×D4711yescharacteristic
969C22×C4C23×D4711yescharacteristic
970C22×C4C23×D4711yescharacteristic
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—942no—
984C4⋊C4—942no—
985C4⋊C4—942no—
986C4⋊C4—942no—
987C4⋊C4—942no—
988C4⋊C4—942no—
989C4⋊C4—942no—
990C4⋊C4—942no—
991C4⋊C4—942no—
992C4⋊C4—942no—
993C4⋊C4—942no—
994C4⋊C4—942no—
995C4⋊C4—942no—
996C4⋊C4—942no—
997C4⋊C4—942no—
998C4⋊C4—1881no—
999C4⋊C4—1881no—
1000C4⋊C4—1881no—
1001C4⋊C4—1881no—
1002C4⋊C4—1881no—
1003C4⋊C4—1881no—
1004C4⋊C4—1881no—
1005C4⋊C4—1881no—
1006C4⋊C4—1881no—
1007C4⋊C4—1881no—
1008C4⋊C4—1881no—
1009C4⋊C4—1881no—
1010C4⋊C4—1881no—
1011C4⋊C4—1881no—
1012C4⋊C4—1881no—
1013C4⋊C4—1881no—
1014C4⋊C4—1881no—
1015C4⋊C4—1881no—
1016C4⋊C4—1881no—
1017C4⋊C4—1881no—
1018C4⋊C4—1881no—
1019C4⋊C4—1881no—
1020C4⋊C4—1881no—
1021C4⋊C4—1881no—
1022C4⋊C4—1881no—
1023C4⋊C4—1881no—
1024C4⋊C4—1881no—
1025C4⋊C4—1881no—
1026C4⋊C4—1881no—
1027C4⋊C4—1881no—
1028C4⋊C4—1881no—
1029C4⋊C4—1881no—
1030C4⋊C4—1881no—
1031C42—22no—
1032C42—22no—
1033C42—22no—
1034C42—22no—
1035C42—22no—
1036C42—22no—
1037C42—22no—
1038C42—474no—
1039C42—942no—
1040C42—942no—
1041C42—942no—
1042C42—942no—
1043C42—942no—
1044C42—942no—
1045C42—942no—
1046C42—942no—
1047C42—1881no—
1048C42—1881no—
1049C42—1881no—
1050C23C24×D4711yescharacteristic
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—472no—
1093C2×C4—472no—
1094C2×C4—941no—
1095C2×C4—941no—
1096C2×C4—941no—
1097C2×C4—941no—
1098C2×C4—941no—
1099C2×C4—941no—
1100C2×C4—941no—
1101C2×C4—941no—
1102C2×C4—941no—
1103C2×C4—941no—
1104C2×C4—941no—
1105C2×C4—941no—
1106C2×C4—941no—
1107C2×C4—941no—
1108C2×C4—941no—
1109C2×C4—941no—
1110C2×C4—941no—
1111C2×C4—941no—
1112C2×C4—941no—
1113C2×C4—941no—
1114C2×C4—941no—
1115C2×C4—941no—
1116C2×C4—941no—
1117C2×C4—941no—
1118C2×C4—941no—
1119C2×C4—941no—
1120C2×C4—941no—
1121C2×C4—941no—
1122C2×C4—941no—
1123C2×C4—941no—
1124C2×C4—941no—
1125C2×C4—941no—
1126C2×C4—941no—
1127C2×C4—941no—
1128C2×C4—941no—
1129C2×C4—941no—
1130C2×C4—941no—
1131C2×C4—941no—
1132C2×C4—941no—
1133C2×C4—941no—
1134C2×C4—941no—
1135C2×C4—941no—
1136C2×C4—941no—
1137C2×C4—941no—
1138C2×C4—941no—
1139C2×C4—941no—
1140C2×C4#41×D4712yes—
1141C2×C4#1309407112yes—
1142C2×C4#1309407112yes—
1143C2×C4#1309407212yes—
1144C22C2×#41×D4711yescharacteristic
1145C22C2×#1309407111yescharacteristic
1146C22C2×#1309407111yescharacteristic
1147C22C2×#1309407211yescharacteristic
1148C22#1568995911yescharacteristic
1149C22#1568995911yescharacteristic
1150C22#1568995911yescharacteristic
1151C4—22no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—942no—
1166C4—942no—
1167C4—1881no—
1168C4—1881no—
1169C4—1881no—
1170C4—1881no—
1171C4—1881no—
1172C4—1881no—
1173C4—1881no—
1174C4—1881no—
1175C4—1881no—
1176C4—1881no—
1177C4—1881no—
1178C4—1881no—
1179C4—1881no—
1180C4—1881no—
1181C4C47⋊#56414yes—
1182C2#2025681311yescharacteristic
1183C2#2025681711yescharacteristic
1184C2#2025681911yescharacteristic
1185C2C2×C47⋊#56411yescharacteristic
1186C2#2025753311yescharacteristic
1187C2#2025753311yescharacteristic
1188C2#2025753511yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutator, socle, prime radical, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC47×#2402C2
hypercenter#2402D47
hypocenterC47#36701
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2402

Complements

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

NH ≅ G/Ntype
781. C47#36701semidirect

Maximal subgroups

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

subgroupindex
#202516622
#202516392
#202516382
#202516372
#202516362
#202516352
#202516342
#202516332
#202516322
#202516312
#202516292
#202516272
#202516252
#202514582
#202514572
#202514542
#202466962
#202466952
#202466932
C4×#130940152
C4×#130940142
C47×#24022
#3670147