Finite Group Databasebeta

← #28339994

Subgroups — #28339994

Order 13696.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812080C211yesmaximal, characteristic, complemented
2C2×#16812077C211yesmaximal, characteristic, complemented
3C2×#16812077C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D107C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D107C211yesmaximal, characteristic, complemented
6#20292549C211yesmaximal, characteristic, complemented
7#20292541C211yesmaximal, characteristic, complemented
8#20292541C211yesmaximal, characteristic, complemented
9#20292535C211yesmaximal, characteristic, complemented
10#20292527C211yesmaximal, characteristic, complemented
11#20292520C211yesmaximal, characteristic, complemented
12#20292506C211yesmaximal, characteristic, complemented
13#20292503C211yesmaximal, characteristic, complemented
14#20292498C211yesmaximal, characteristic, complemented
15C2×#121×C107C211yesmaximal, characteristic, complemented
16C24×D107C2211yescharacteristic
17C22×C22⋊D107C2211yescharacteristic
18C22×C22⋊D107C2211yescharacteristic
19C22×C22⋊D107C2211yescharacteristic
20C22×C22⋊D107C2211yescharacteristic
21C22×C4×D107C2211yescharacteristic
22C22×C4×D107C2211yescharacteristic
23#16812080—24no—
24#16812077—24no—
25#16812077—24no—
26C4×C22⋊D107—24no—
27C2×C4⋊Dic107C2211yescharacteristic, complemented
28C2×Dic107⋊C4C2211yescharacteristic, complemented
29C2×Dic107⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic107C2211yescharacteristic
31C2×C22⋊Dic107C2211yescharacteristic
32C2×C22⋊Dic107C2211yescharacteristic
33C2×C22⋊Dic107C2211yescharacteristic, complemented
34C2×C22⋊Dic107C2211yescharacteristic, complemented
35C2×C22⋊Dic107C2211yescharacteristic, complemented
36C2×C22⋊Dic107C2211yescharacteristic, complemented
37C2×(C2×D107)⋊C4C2211yescharacteristic
38C2×(C2×D107)⋊C4C2211yescharacteristic
39C2×(C2×D107)⋊C4C2211yescharacteristic
40C2×(C2×D107)⋊C4C2211yescharacteristic
41C2×(C2×D107)⋊C4C2211yescharacteristic
42C2×(C2×D107)⋊C4C2211yescharacteristic
43C22⋊C4×D107—24no—
44C2×C4×Dic107C2211yescharacteristic, complemented
45C107⋊#95C2211yescharacteristic, complemented
46C107⋊#95C2211yescharacteristic, complemented
47C107⋊#95C2211yescharacteristic, complemented
48C107⋊#95C2211yescharacteristic, complemented
49C22×D4×C107C2211yescharacteristic
50C22×D4×C107C2211yescharacteristic
51C22×D4×C107C2211yescharacteristic, complemented
52C23×C4×C107C2211yescharacteristic, complemented
53#121×C107—24no—
54C2×C4⋊C4×C107C2211yescharacteristic, complemented
55C2×C22⋊C4×C107C2211yescharacteristic
56C2×C22⋊C4×C107C2211yescharacteristic, complemented
57C23×D107—22no—
58C23×D107—22no—
59C23×D107—22no—
60C23×D107—22no—
61C23×D107—22no—
62C23×D107—41no—
63C23×D107—41no—
64C23×D107C2311yescharacteristic
65C23×D107C2311yescharacteristic
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—41no—
76C2×C22⋊D107—41no—
77C2×C22⋊D107D414yescomplemented
78C22×Dic107C2311yescharacteristic
79C22×Dic107C2311yescharacteristic
80C22×Dic107C2311yescharacteristic
81C22×Dic107C2311yescharacteristic
82C22×Dic107C2311yescharacteristic
83C22×Dic107C2311yescharacteristic
84C2×C4×D107—22no—
85C2×C4×D107—22no—
86C2×C4×D107—22no—
87C2×C4×D107—22no—
88C2×C4×D107—41no—
89C2×C4×D107—41no—
90C4⋊Dic107—22no—
91Dic107⋊C4—22no—
92Dic107⋊C4—41no—
93C22⋊Dic107—22no—
94C22⋊Dic107—22no—
95C22⋊Dic107—22no—
96C22⋊Dic107—22no—
97C22⋊Dic107—22no—
98C22⋊Dic107—22no—
99C22⋊Dic107—41no—
100(C2×D107)⋊C4—22no—
101(C2×D107)⋊C4—22no—
102(C2×D107)⋊C4—22no—
103(C2×D107)⋊C4—22no—
104(C2×D107)⋊C4—22no—
105(C2×D107)⋊C4D414yescomplemented
106C4×Dic107—22no—
107C24×C107C2311yescharacteristic
108C24×C107C2311yescharacteristic
109C24×C107C2311yescharacteristic
110C2×D4×C107—22no—
111C2×D4×C107—22no—
112C2×D4×C107—22no—
113C2×D4×C107—22no—
114C2×D4×C107—22no—
115C2×D4×C107—22no—
116C2×D4×C107—41no—
117C2×D4×C107—41no—
118C2×D4×C107—41no—
119C22×C4×C107—22no—
120C22×C4×C107—22no—
121C22×C4×C107—41no—
122C22×C4×C107C2311yescharacteristic
123C22×C4×C107C2311yescharacteristic
124C22×C4×C107C2311yescharacteristic
125C22×C4×C107C2311yescharacteristic
126C4⋊C4×C107—22no—
127C22⋊C4×C107—22no—
128C22⋊C4×C107D414yescomplemented
129C23×C107—21no—
130C23×C107—21no—
131C23×C107—21no—
132C23×C107—21no—
133C23×C107—21no—
134C23×C107—21no—
135C23×C107—21no—
136C23×C107—21no—
137C23×C107—21no—
138C23×C107—21no—
139C23×C107—21no—
140C23×C107—21no—
141C23×C107—21no—
142C23×C107—21no—
143C23×C107—21no—
144C23×C107—21no—
145C23×C107—21no—
146C23×C107—21no—
147C23×C107—21no—
148C23×C107C2×D412yes—
149C23×C107C2×D412yes—
150C23×C107C2411yescharacteristic
151C22×D107—21no—
152C22×D107—21no—
153C22×D107—21no—
154C22×D107—21no—
155C22×D107—28no—
156C22×D107—21no—
157C22×D107—21no—
158C22×D107—21no—
159C22×D107—21no—
160C22×D107—21no—
161C22×D107—21no—
162C22×D107—44no—
163C22×D107—44no—
164C22×D107—44no—
165C22×D107—44no—
166C22×D107—44no—
167C22×D107—44no—
168C22×D107C2×D412yes—
169C22×D107C2×D412yes—
170C22×D107#4112yes—
171C22×D107#4112yes—
172D4×C107—44no—
173D4×C107—44no—
174D4×C107—44no—
175C2×C4×C107—21no—
176C2×C4×C107—21no—
177C2×C4×C107—21no—
178C2×C4×C107—21no—
179C2×C4×C107—21no—
180C2×C4×C107—21no—
181C2×C4×C107—21no—
182C2×C4×C107—21no—
183C2×C4×C107—21no—
184C2×C4×C107—44no—
185C2×C4×C107C2×D412yes—
186C2×C4×C107C2×D412yes—
187C2×C4×C107C2×D412yes—
188C22⋊D107—28no—
189C22⋊D107—44no—
190C22⋊D107—44no—
191C22⋊D107—44no—
192C2×Dic107—21no—
193C2×Dic107—21no—
194C2×Dic107—21no—
195C2×Dic107—21no—
196C2×Dic107—21no—
197C2×Dic107—21no—
198C2×Dic107—21no—
199C2×Dic107—21no—
200C2×Dic107—21no—
201C2×Dic107—21no—
202C2×Dic107—21no—
203C2×Dic107—21no—
204C2×Dic107—21no—
205C2×Dic107—21no—
206C2×Dic107—21no—
207C2×Dic107—21no—
208C2×Dic107C2×D412yes—
209C2×Dic107C2×D412yes—
210C4×D107—44no—
211C4×D107—44no—
212C22×C107—22no—
213C22×C107—22no—
214C22×C107—22no—
215C22×C107—22no—
216C22×C107—22no—
217C22×C107—22no—
218C22×C107—41no—
219C22×C107—41no—
220C22×C107—41no—
221C22×C107—41no—
222C22×C107—41no—
223C22×C107—41no—
224C22×C107—41no—
225C22×C107—41no—
226C22×C107—41no—
227C22×C107—41no—
228C22×C107—41no—
229C22×C107—41no—
230C22×C107—41no—
231C22×C107—41no—
232C22×C107—41no—
233C22×C107C22×D411yescharacteristic
234C22×C107C22×D411yescharacteristic
235C22×C107C22×D411yescharacteristic
236C22×C107C2×#4111yescharacteristic
237C22×C107C2×#4111yescharacteristic
238C22×C107H(5,𝔽2)11yescharacteristic
239C22×C107H(5,𝔽2)11yescharacteristic
240C2×D107—22no—
241C2×D107—22no—
242C2×D107—22no—
243C2×D107—22no—
244C2×D107—22no—
245C2×D107—22no—
246C2×D107—22no—
247C2×D107—22no—
248C2×D107—22no—
249C2×D107—416no—
250C2×D107—41no—
251C2×D107—41no—
252C2×D107—41no—
253C2×D107—41no—
254C2×D107#12114yescomplemented
255C4×C107—22no—
256C4×C107—22no—
257C4×C107—22no—
258C4×C107—41no—
259Dic107—22no—
260Dic107—22no—
261Dic107—41no—
262Dic107—41no—
263Dic107—41no—
264Dic107—41no—
265C2×C107—42no—
266C2×C107—42no—
267C2×C107—81no—
268C2×C107C2×#12111yescharacteristic
269C2×C107#52511yescharacteristic
270C2×C107#53811yescharacteristic
271C2×C107D4211yescharacteristic
272C2×C107D4211yescharacteristic
273C2×C107#54611yescharacteristic
274C2×C107#54611yescharacteristic
275D107—24no—
276D107—42no—
277#2424—1071nomaximal, Sylow
278C107#242411yescharacteristic, complemented, Sylow
279C2×#121—1071no—
280C2×#121D10711yescharacteristic, complemented
281C2×#120—1071no—
282C2×#120—1071no—
283C2×C4×D4—1071no—
284C22×C22⋊C4—1071no—
285#396—1071no—
286#394—1071no—
287#394—1071no—
288#392—1071no—
289#390—1071no—
290#388—1071no—
291#386—1071no—
292#386—1071no—
293#385—1071no—
294C25—1071no—
295C22×D4—1071no—
296C22×D4—1071no—
297C22×D4—1071no—
298C22×D4—1071no—
299C22×D4C2×D10711yescharacteristic
300C22×D4C2×D10711yescharacteristic
301C22×D4C2×D10711yescharacteristic, complemented
302C23×C4—1071no—
303C23×C4—1071no—
304C23×C4C2×D10711yescharacteristic, complemented
305#121—24no—
306#121—2144no—
307#120—2144no—
308#120—2144no—
309C4×D4—2144no—
310C2×C4⋊C4—1071no—
311C2×C4⋊C4—1071no—
312C2×C4⋊C4—1071no—
313C2×C4⋊C4C2×D10711yescharacteristic, complemented
314C2×C22⋊C4—1071no—
315C2×C22⋊C4—1071no—
316C2×C22⋊C4—1071no—
317C2×C22⋊C4—1071no—
318C2×C22⋊C4—1071no—
319C2×C22⋊C4—1071no—
320C2×C22⋊C4—1071no—
321C2×C22⋊C4—1071no—
322C2×C22⋊C4—1071no—
323C2×C22⋊C4—1071no—
324C2×C22⋊C4—1071no—
325C2×C22⋊C4—1071no—
326C2×C22⋊C4—1071no—
327C2×C22⋊C4—2144no—
328C2×C22⋊C4C2×D10711yescharacteristic
329C2×C22⋊C4C2×D10711yescharacteristic, complemented
330C2×C42—1071no—
331#95—1071no—
332#95—1071no—
333#95—1071no—
334#95—1071no—
335C24—1071no—
336C24—1071no—
337C24—4281no—
338C24—4281no—
339C24—2142no—
340C24—2142no—
341C24—2142no—
342C24—2142no—
343C24—2142no—
344C24C22×D10711yescharacteristic
345C24C22×D10711yescharacteristic
346C24C22×D10711yescharacteristic
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—1074no—
357C2×D4—4281no—
358C2×D4—4281no—
359C2×D4—2142no—
360C2×D4—2142no—
361C2×D4—2142no—
362C2×D4—2142no—
363C2×D4—2142no—
364C2×D4—2142no—
365C2×D4—2142no—
366C2×D4—2142no—
367C2×D4—2142no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—41no—
371C22×C4—1071no—
372C22×C4—1071no—
373C22×C4—1071no—
374C22×C4—1071no—
375C22×C4—1071no—
376C22×C4—1071no—
377C22×C4—4281no—
378C22×C4—4281no—
379C22×C4—2142no—
380C22×C4—2142no—
381C22×C4—2142no—
382C22×C4—2142no—
383C22×C4C22×D10711yescharacteristic
384C22×C4C22×D10711yescharacteristic
385C22×C4C22×D10711yescharacteristic
386C22×C4C22×D10711yescharacteristic
387C4⋊C4—22no—
388C4⋊C4—4281no—
389C4⋊C4—2142no—
390C4⋊C4—2142no—
391C22⋊C4—22no—
392C22⋊C4—1074no—
393C22⋊C4—4281no—
394C22⋊C4—2142no—
395C22⋊C4—2142no—
396C22⋊C4—2142no—
397C22⋊C4—2142no—
398C22⋊C4—2142no—
399C22⋊C4—2142no—
400C22⋊C4—2142no—
401C22⋊C4—2142no—
402C22⋊C4—2142no—
403C22⋊C4—2142no—
404C22⋊C4—2142no—
405C22⋊C4C22⋊D10714yescomplemented
406C42—2142no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—1072no—
427C23—1072no—
428C23—1072no—
429C23—1072no—
430C23—4284no—
431C23—4284no—
432C23—4284no—
433C23—4284no—
434C23—4284no—
435C23—4284no—
436C23—2148no—
437C23—2141no—
438C23—2141no—
439C23—2141no—
440C23—2141no—
441C23—2141no—
442C23—2141no—
443C23—2141no—
444C23—2141no—
445C23—2141no—
446C23—2141no—
447C23D4×D10712yes—
448C23C2×C22⋊D10712yes—
449C23C23×D10711yescharacteristic
450D4—44no—
451D4—44no—
452D4—44no—
453D4—4284no—
454D4—4284no—
455D4—4284no—
456D4—2148no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—44no—
467C2×C4—1072no—
468C2×C4—1072no—
469C2×C4—4284no—
470C2×C4—4284no—
471C2×C4—2141no—
472C2×C4—2141no—
473C2×C4—2141no—
474C2×C4—2141no—
475C2×C4—2141no—
476C2×C4—2141no—
477C2×C4—2141no—
478C2×C4—2141no—
479C2×C4—2141no—
480C2×C4—2141no—
481C2×C4—2141no—
482C2×C4—2141no—
483C2×C4—2141no—
484C2×C4—2141no—
485C2×C4—2141no—
486C2×C4—2141no—
487C2×C4D4×D10712yes—
488C2×C4C2×C22⋊D10712yes—
489C2×C4C2×C22⋊D10712yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—1074no—
512C22—42816no—
513C22—4281no—
514C22—4281no—
515C22—4281no—
516C22—4281no—
517C22—2142no—
518C22—2142no—
519C22—2142no—
520C22—2142no—
521C22—2142no—
522C22—2142no—
523C22—2142no—
524C22—2142no—
525C22—2142no—
526C22C2×D4×D10711yescharacteristic
527C22C2×D4×D10711yescharacteristic
528C22C22×C22⋊D10711yescharacteristic
529C22#41×D10711yescharacteristic
530C22#41×D10711yescharacteristic
531C22#1681215411yescharacteristic
532C22#1681215411yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—41no—
537C4—4281no—
538C4—4281no—
539C4—4281no—
540C4—4281no—
541C4—2142no—
542C4—2142no—
543C2—42no—
544C2—42no—
545C2—81no—
546C2—4282no—
547C2—2144no—
548C2#121×D10711yescharacteristic
549C2#2029313411yescharacteristic
550C2#2029320911yescharacteristic
551C2D4×C22⋊D10711yescharacteristic
552C2D4×C22⋊D10711yescharacteristic
553C2#2029326611yescharacteristic
554C2#2029327411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
FittingC2×#121×C107C2
hypercenterC2×#121D107
hypocenterC107#2424
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16812080C2semidirect
2. C2×#16812077C2semidirect
3. C2×#16812077C2semidirect
4. C2×C4×C22⋊D107C2semidirect
5. C2×C22⋊C4×D107C2semidirect
6. #20292549C2semidirect
7. #20292541C2semidirect
8. #20292541C2semidirect
9. #20292535C2semidirect
10. #20292527C2semidirect
11. #20292520C2semidirect
12. #20292506C2semidirect
13. #20292503C2semidirect
14. #20292498C2semidirect
15. C2×#121×C107C2semidirect
27. C2×C4⋊Dic107C22semidirect
28. C2×Dic107⋊C4C22semidirect
29. C2×Dic107⋊C4C22semidirect
33. C2×C22⋊Dic107C22semidirect
34. C2×C22⋊Dic107C22semidirect
35. C2×C22⋊Dic107C22semidirect
36. C2×C22⋊Dic107C22semidirect
44. C2×C4×Dic107C22semidirect
45. C107⋊#95C22semidirect
46. C107⋊#95C22semidirect
47. C107⋊#95C22semidirect
48. C107⋊#95C22semidirect
51. C22×D4×C107C22semidirect
52. C23×C4×C107C22semidirect
54. C2×C4⋊C4×C107C22semidirect
56. C2×C22⋊C4×C107C22semidirect
77. C2×C22⋊D107D4semidirect
105. (C2×D107)⋊C4D4semidirect
128. C22⋊C4×C107D4semidirect
254. C2×D107#121semidirect
278. C107#2424semidirect
280. C2×#121D107semidirect
301. C22×D4C2×D107semidirect
304. C23×C4C2×D107semidirect
313. C2×C4⋊C4C2×D107semidirect
329. C2×C22⋊C4C2×D107semidirect
405. C22⋊C4C22⋊D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168120802
C2×#168120772
C2×C4×C22⋊D1072
C2×C22⋊C4×D1072
#202925492
#202925412
#202925352
#202925272
#202925202
#202925062
#202925032
#202924982
C2×#121×C1072
#2424107