Finite Group Databasebeta

← #28340069

Subgroups — #28340069

Order 13696.

914 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133817C211yesmaximal, characteristic, complemented
2C2×#16812093C211yesmaximal, characteristic, complemented
3C2×#16812083C211yesmaximal, characteristic, complemented
4C2×#16812081C211yesmaximal, characteristic, complemented
5#20292548C211yesmaximal, characteristic, complemented
6#20292543C211yesmaximal, characteristic, complemented
7#20292540C211yesmaximal, characteristic, complemented
8#20292536C211yesmaximal, characteristic, complemented
9#20292505C211yesmaximal, characteristic, complemented
10#20292504C211yesmaximal, characteristic, complemented
11#20292504C211yesmaximal, characteristic, complemented
12#20292502C211yesmaximal, characteristic, complemented
13#20292501C211yesmaximal, characteristic, complemented
14C2×C107⋊#95C211yesmaximal, characteristic, complemented
15#386×C107C211yesmaximal, characteristic, complemented
16C2×#13133817—24no—
17C2×#13133817—24no—
18C2×#13133817—24no—
19C22×Dic214C2211yescharacteristic
20C22×D428C2211yescharacteristic
21C22×C22⋊D107C2211yescharacteristic
22C22×C22⋊D107C2211yescharacteristic
23C22×C22⋊D107C2211yescharacteristic
24C22×C22⋊D107C2211yescharacteristic
25C23×Dic107C2211yescharacteristic
26C23×Dic107C2211yescharacteristic
27C23×Dic107C2211yescharacteristic
28C22×C4×D107C2211yescharacteristic
29#16812093—24no—
30#16812083—24no—
31#16812081—24no—
32C2×C4⋊Dic107C2211yescharacteristic
33C2×C4⋊Dic107C2211yescharacteristic
34C2×C4⋊Dic107C2211yescharacteristic
35C2×Dic107⋊C4C2211yescharacteristic
36C2×C22⋊Dic107C2211yescharacteristic
37C2×(C2×D107)⋊C4C2211yescharacteristic
38C2×(C2×D107)⋊C4C2211yescharacteristic
39C2×(C2×D107)⋊C4C2211yescharacteristic
40C2×(C2×D107)⋊C4C2211yescharacteristic
41C2×(C2×D107)⋊C4C2211yescharacteristic
42C2×(C2×D107)⋊C4C2211yescharacteristic
43C2×(C2×D107)⋊C4C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C107⋊#95C2211yescharacteristic
46C107⋊#95C2211yescharacteristic
47C107⋊#95C2211yescharacteristic
48C107⋊#95C2211yescharacteristic
49C107⋊#95C2211yescharacteristic
50C22×D4×C107C2211yescharacteristic
51C23×C4×C107C2211yescharacteristic
52C2×C22⋊C4×C107C2211yescharacteristic
53C2×C22⋊C4×C107C2211yescharacteristic
54C2×C22⋊C4×C107C2211yescharacteristic
55#95×C107C2211yescharacteristic
56#95×C107C2211yescharacteristic
57C23×D107C2311yescharacteristic
58C23×D107C2311yescharacteristic
59#13133817—232no—
60C2×Dic214—22no—
61C2×Dic214—22no—
62C2×Dic214—22no—
63C2×D428—22no—
64C2×D428—22no—
65C2×D428—41no—
66C2×C22⋊D107—22no—
67C2×C22⋊D107—22no—
68C2×C22⋊D107—22no—
69C2×C22⋊D107—22no—
70C2×C22⋊D107—22no—
71C2×C22⋊D107—22no—
72C2×C22⋊D107—22no—
73C2×C22⋊D107—22no—
74C2×C22⋊D107—22no—
75C2×C22⋊D107—22no—
76C2×C22⋊D107—41no—
77C2×C22⋊D107D414yescomplemented
78C22×Dic107—22no—
79C22×Dic107—22no—
80C22×Dic107—22no—
81C22×Dic107—22no—
82C22×Dic107—22no—
83C22×Dic107—22no—
84C22×Dic107—22no—
85C22×Dic107—41no—
86C22×Dic107D414yescomplemented
87C22×Dic107C2311yescharacteristic
88C22×Dic107C2311yescharacteristic
89C22×Dic107C2311yescharacteristic
90C22×Dic107C2311yescharacteristic
91C22×Dic107C2311yescharacteristic
92C22×Dic107C2311yescharacteristic
93C2×C4×D107—22no—
94C2×C4×D107—22no—
95C2×C4×D107—22no—
96C4⋊Dic107—22no—
97C4⋊Dic107—22no—
98C4⋊Dic107—22no—
99Dic107⋊C4—22no—
100C22⋊Dic107—22no—
101(C2×D107)⋊C4—22no—
102(C2×D107)⋊C4—22no—
103(C2×D107)⋊C4—22no—
104(C2×D107)⋊C4—22no—
105(C2×D107)⋊C4—22no—
106(C2×D107)⋊C4—22no—
107(C2×D107)⋊C4—41no—
108C24×C107C2311yescharacteristic
109C24×C107C2311yescharacteristic
110C2×D4×C107—22no—
111C2×D4×C107—22no—
112C2×D4×C107D414yescomplemented
113C22×C4×C107—22no—
114C22×C4×C107—22no—
115C22×C4×C107—41no—
116C22×C4×C107C2311yescharacteristic
117C22×C4×C107C2311yescharacteristic
118C22×C4×C107C2311yescharacteristic
119C22×C4×C107C2311yescharacteristic
120C22×C4×C107C2311yescharacteristic
121C22⋊C4×C107—22no—
122C22⋊C4×C107—22no—
123C22⋊C4×C107—41no—
124C23×C107—21no—
125C23×C107—21no—
126C23×C107—21no—
127C23×C107—21no—
128C23×C107—21no—
129C23×C107—21no—
130C23×C107—21no—
131C23×C107—21no—
132C23×C107—21no—
133C23×C107—21no—
134C23×C107C2×D412yes—
135C23×C107C2×D412yes—
136C23×C107C2×D412yes—
137C23×C107C2×D412yes—
138C23×C107C2411yescharacteristic
139C22×D107—21no—
140C22×D107—21no—
141C22×D107—21no—
142C22×D107—21no—
143C22×D107—21no—
144C22×D107—21no—
145C22×D107—21no—
146C22×D107—21no—
147C22×D107—21no—
148C22×D107—21no—
149C22×D107—21no—
150C22×D107—21no—
151C22×D107—21no—
152C22×D107C2×D412yes—
153D4×C107—28no—
154C2×C4×C107—21no—
155C2×C4×C107—21no—
156C2×C4×C107—21no—
157C2×C4×C107—21no—
158C2×C4×C107—21no—
159C2×C4×C107—21no—
160C2×C4×C107—21no—
161C2×C4×C107—21no—
162C2×C4×C107—21no—
163C2×C4×C107—21no—
164C2×C4×C107—21no—
165C2×C4×C107—21no—
166C2×C4×C107—21no—
167C2×C4×C107—44no—
168C2×C4×C107C2×D412yes—
169C2×C4×C107#4112yescomplemented
170C22⋊D107—28no—
171C22⋊D107—28no—
172C22⋊D107—44no—
173C22⋊D107—44no—
174C2×Dic107—28no—
175C2×Dic107—28no—
176C2×Dic107—21no—
177C2×Dic107—21no—
178C2×Dic107—21no—
179C2×Dic107—21no—
180C2×Dic107—21no—
181C2×Dic107—21no—
182C2×Dic107—21no—
183C2×Dic107—21no—
184C2×Dic107—21no—
185C2×Dic107—21no—
186C2×Dic107—21no—
187C2×Dic107—21no—
188C2×Dic107—21no—
189C2×Dic107—21no—
190C2×Dic107—44no—
191C2×Dic107C2×D412yes—
192C2×Dic107C2×D412yes—
193C2×Dic107C2×D412yes—
194C2×Dic107#4112yescomplemented
195D428—44no—
196C4×D107—28no—
197Dic214—28no—
198C22×C107—22no—
199C22×C107—22no—
200C22×C107—22no—
201C22×C107—22no—
202C22×C107—22no—
203C22×C107—22no—
204C22×C107—22no—
205C22×C107—22no—
206C22×C107—22no—
207C22×C107—41no—
208C22×C107—41no—
209C22×C107—41no—
210C22×C107—41no—
211C22×C107#12014yes—
212C22×C107C22×D411yescharacteristic
213C22×C107C22×D411yescharacteristic
214C22×C107C22×D411yescharacteristic
215C22×C107C2×#4111yescharacteristic
216C22×C107C2×#4111yescharacteristic
217C22×C107H(5,𝔽2)11yescharacteristic
218C22×C1072−1+411yescharacteristic
219C2×D107—22no—
220C2×D107—22no—
221C2×D107—22no—
222C2×D107—41no—
223C2×D107—41no—
224C2×D107—41no—
225C2×D107—41no—
226C2×D107—41no—
227C2×D107—41no—
228C2×D107—41no—
229C2×D107—41no—
230C2×D107—41no—
231C2×D107—41no—
232C2×D107—41no—
233C4×C107—22no—
234C4×C107—22no—
235C4×C107—41no—
236C4×C107—41no—
237C4×C107—41no—
238Dic107—22no—
239Dic107—22no—
240Dic107—22no—
241Dic107—22no—
242Dic107—41no—
243Dic107—41no—
244C2×C107—24no—
245C2×C107—42no—
246C2×C107C2×#12011yescharacteristic
247C2×C107#53211yescharacteristic
248C2×C107#53711yescharacteristic
249C2×C107#54611yescharacteristic
250C2×C107#54611yescharacteristic
251C2×C107#54711yescharacteristic
252C2×C107#54711yescharacteristic
253D107—42no—
254D107—81no—
255#2430—1071nomaximal, Sylow
256C107#243011yescharacteristic, complemented, Sylow
257C22×#41—1071no—
258C2×#123—1071no—
259C2×#121—1071no—
260C2×#121—1071no—
261#395—1071no—
262#394—1071no—
263#393—1071no—
264#392—1071no—
265#386—1071no—
266#386—1071no—
267#386—1071no—
268#386D10711yescharacteristic, complemented
269#385—1071no—
270#385—1071no—
271C2×#95—1071no—
272C2×#41—2144no—
273C2×#41—2144no—
274C2×#41—2144no—
275C22×Q8—1071no—
276C22×D4—1071no—
277C22×D4—1071no—
278C22×D4—1071no—
279C22×D4—1071no—
280C22×D4—1071no—
281C22×D4C2×D10711yescharacteristic
282C23×C4—1071no—
283C23×C4—1071no—
284C23×C4—1071no—
285C23×C4—1071no—
286C23×C4C2×D10711yescharacteristic
287#123—2144no—
288#121—2144no—
289#121—2144no—
290C2×C4⋊C4—1071no—
291C2×C4⋊C4—1071no—
292C2×C4⋊C4—1071no—
293C2×C4⋊C4—1071no—
294C2×C22⋊C4—1071no—
295C2×C22⋊C4—1071no—
296C2×C22⋊C4—1071no—
297C2×C22⋊C4—1071no—
298C2×C22⋊C4—1071no—
299C2×C22⋊C4—1071no—
300C2×C22⋊C4—1071no—
301C2×C22⋊C4—1071no—
302C2×C22⋊C4C2×D10711yescharacteristic
303C2×C22⋊C4C2×D10711yescharacteristic
304C2×C22⋊C4C2×D10711yescharacteristic
305#95—1071no—
306#95—1071no—
307#95—1071no—
308#95—1071no—
309#95—1071no—
310#95—1071no—
311#95C2×D10711yescharacteristic
312#95C2×D10711yescharacteristic
313C24—1071no—
314C24—1071no—
315C24C22×D10711yescharacteristic
316C24C22×D10711yescharacteristic
317#41—21432no—
318C2×Q8—2142no—
319C2×Q8—2142no—
320C2×Q8—2142no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—1074no—
324C2×D4—4281no—
325C2×D4—4281no—
326C2×D4—2142no—
327C2×D4—2142no—
328C2×D4—2142no—
329C2×D4—2142no—
330C2×D4—2142no—
331C2×D4—2142no—
332C2×D4—2142no—
333C2×D4—2142no—
334C2×D4—2142no—
335C2×D4—2142no—
336C2×D4—2142no—
337C2×D4—2142no—
338C2×D4D42814yescomplemented
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—41no—
342C22×C4—1074no—
343C22×C4—1071no—
344C22×C4—1071no—
345C22×C4—1071no—
346C22×C4—1071no—
347C22×C4—1071no—
348C22×C4—1071no—
349C22×C4—4281no—
350C22×C4—2142no—
351C22×C4—2142no—
352C22×C4—2142no—
353C22×C4—2142no—
354C22×C4—2142no—
355C22×C4—2142no—
356C22×C4—2142no—
357C22×C4—2142no—
358C22×C4—2142no—
359C22×C4—2142no—
360C22×C4C22×D10711yescharacteristic
361C22×C4C22×D10711yescharacteristic
362C22×C4C22×D10711yescharacteristic
363C22×C4C22×D10711yescharacteristic
364C22×C4C22×D10711yescharacteristic
365C4⋊C4—2142no—
366C4⋊C4—2142no—
367C4⋊C4—2142no—
368C4⋊C4—2142no—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C22⋊C4—41no—
372C22⋊C4—4281no—
373C22⋊C4—2142no—
374C22⋊C4—2142no—
375C22⋊C4—2142no—
376C22⋊C4—2142no—
377C22⋊C4—2142no—
378C22⋊C4—2142no—
379C22⋊C4—2142no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—1072no—
391C23—2141no—
392C23—2141no—
393C23—2141no—
394C23—2141no—
395C23—2141no—
396C23—2141no—
397C23—2141no—
398C23—2141no—
399C23—2141no—
400C23—2141no—
401C23—2141no—
402C23—2141no—
403C23—2141no—
404C23D4×D10712yes—
405C23D4×D10712yes—
406C23C2×D42812yes—
407C23C2×D42812yes—
408C23C23×D10711yescharacteristic
409Q8—2148no—
410D4—28no—
411D4—4284no—
412D4—4284no—
413D4—4284no—
414D4—2148no—
415D4—2148no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—44no—
430C2×C4—1072no—
431C2×C4—1072no—
432C2×C4—1072no—
433C2×C4—1072no—
434C2×C4—4284no—
435C2×C4—2148no—
436C2×C4—2141no—
437C2×C4—2141no—
438C2×C4—2141no—
439C2×C4—2141no—
440C2×C4—2141no—
441C2×C4—2141no—
442C2×C4—2148no—
443C2×C4—2148no—
444C2×C4—2141no—
445C2×C4—2141no—
446C2×C4—2141no—
447C2×C4—2141no—
448C2×C4—2141no—
449C2×C4—2141no—
450C2×C4—2141no—
451C2×C4—2141no—
452C2×C4C2×D42812yes—
453C2×C4#1313381712yescomplemented
454C22—22no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—4281no—
468C22—4281no—
469C22—4281no—
470C22—4281no—
471C22—4281no—
472C22—4281no—
473C22—4281no—
474C22—4281no—
475C22—4281no—
476C22—4281no—
477C22—4281no—
478C22—2142no—
479C22—2142no—
480C22—2142no—
481C22#1681207914yes—
482C22C2×D4×D10711yescharacteristic
483C22C2×D4×D10711yescharacteristic
484C22C22×D42811yescharacteristic
485C22#41×D10711yescharacteristic
486C22C2×#1313381711yescharacteristic
487C22#1681215411yescharacteristic
488C22#1681215611yescharacteristic
489C4—22no—
490C4—22no—
491C4—41no—
492C4—41no—
493C4—41no—
494C4—4281no—
495C4—4281no—
496C4—2142no—
497C4—2142no—
498C4—2142no—
499C4—2142no—
500C2—24no—
501C2—42no—
502C2—8561no—
503C2—4282no—
504C2C2×#1681207911yescharacteristic
505C2#2029317211yescharacteristic
506C2#2029320411yescharacteristic
507C2#2029326411yescharacteristic
508C2#2029327211yescharacteristic
509C2#2029327511yescharacteristic
510C2#2029328111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#386×C107C2
hypercenter#386D107
hypocenterC107#2430
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×#13133817C2semidirect
2. C2×#16812093C2semidirect
3. C2×#16812083C2semidirect
4. C2×#16812081C2semidirect
5. #20292548C2semidirect
6. #20292543C2semidirect
7. #20292540C2semidirect
8. #20292536C2semidirect
9. #20292505C2semidirect
10. #20292504C2semidirect
11. #20292504C2semidirect
12. #20292502C2semidirect
13. #20292501C2semidirect
14. C2×C107⋊#95C2semidirect
15. #386×C107C2semidirect
77. C2×C22⋊D107D4semidirect
86. C22×Dic107D4semidirect
112. C2×D4×C107D4semidirect
169. C2×C4×C107#41semidirect
194. C2×Dic107#41semidirect
256. C107#2430semidirect
268. #386D107semidirect
338. C2×D4D428semidirect
453. C2×C4#13133817semidirect

Maximal subgroups

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

subgroupindex
C22×#131338172
C2×#168120932
C2×#168120832
C2×#168120812
#202925482
#202925432
#202925402
#202925362
#202925052
#202925042
#202925022
#202925012
C2×C107⋊#952
#386×C1072
#2430107