Finite Group Databasebeta

← #28339438

Subgroups — #28339438

Order 13696.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812077C211yesmaximal, characteristic
2C2×C4×C22⋊D107C211yesmaximal, characteristic, complemented
3C22×(C2×D107)⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D107C211yesmaximal, characteristic, complemented
5#20292527C211yesmaximal, characteristic, complemented
6#20292518C211yesmaximal, characteristic, complemented
7#20292517C211yesmaximal, characteristic, complemented
8#20292507C211yesmaximal, characteristic, complemented
9#20292506C211yesmaximal, characteristic, complemented
10#20292503C211yesmaximal, characteristic, complemented
11#20292500C211yesmaximal, characteristic, complemented
12#20292498C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic107C211yesmaximal, characteristic, complemented
14C4×(C2×D107)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×D4×C107C211yesmaximal, characteristic, complemented
16C24×D107C2211yescharacteristic
17C22×C22⋊D107C2211yescharacteristic
18C22×C22⋊D107C2211yescharacteristic
19C23×Dic107C2211yescharacteristic
20C22×C4×D107C2211yescharacteristic
21C22×C4×D107C2211yescharacteristic
22#16812077C418yescomplemented
23C4×C22⋊D107—24no—
24C2×Dic107⋊C4C2211yescharacteristic, complemented
25C2×Dic107⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic107C2211yescharacteristic
27C2×C22⋊Dic107C2211yescharacteristic
28C2×C22⋊Dic107C2211yescharacteristic, complemented
29C2×C22⋊Dic107C2211yescharacteristic, complemented
30C2×(C2×D107)⋊C4—24no—
31C2×(C2×D107)⋊C4C2211yescharacteristic
32C2×(C2×D107)⋊C4C2211yescharacteristic
33C2×(C2×D107)⋊C4C2211yescharacteristic
34C2×(C2×D107)⋊C4C2211yescharacteristic
35C2×(C2×D107)⋊C4C2211yescharacteristic
36C2×(C2×D107)⋊C4C2211yescharacteristic
37C2×(C2×D107)⋊C4C2211yescharacteristic
38C2×(C2×D107)⋊C4C2211yescharacteristic
39C22⋊C4×D107—24no—
40C2×C4×Dic107C2211yescharacteristic, complemented
41C2×C4×Dic107C2211yescharacteristic, complemented
42C107⋊#95C2211yescharacteristic, complemented
43C107⋊#95C2211yescharacteristic, complemented
44C107⋊#95C2211yescharacteristic, complemented
45C107⋊#95C2211yescharacteristic, complemented
46C107⋊#95C2211yescharacteristic, complemented
47C107⋊#95C2211yescharacteristic, complemented
48C22×D4×C107C2211yescharacteristic
49C23×C4×C107C2211yescharacteristic
50C23×C4×C107C2211yescharacteristic, complemented
51C4×D4×C107—24no—
52C2×C4⋊C4×C107C2211yescharacteristic, complemented
53C2×C22⋊C4×C107C2211yescharacteristic
54C2×C22⋊C4×C107C2211yescharacteristic, complemented
55C2×C42×C107C2211yescharacteristic, complemented
56C23×D107—22no—
57C23×D107—22no—
58C23×D107—22no—
59C23×D107—22no—
60C23×D107—41no—
61C23×D107—41no—
62C23×D107C2×C414yescomplemented
63C23×D107C2311yescharacteristic
64C23×D107C2311yescharacteristic
65C2×C22⋊D107—22no—
66C2×C22⋊D107—22no—
67C2×C22⋊D107—41no—
68C2×C22⋊D107—41no—
69C2×C22⋊D107C2×C414yescomplemented
70C2×C22⋊D107C2×C414yescomplemented
71C22×Dic107—22no—
72C22×Dic107—22no—
73C22×Dic107—41no—
74C22×Dic107C2311yescharacteristic
75C22×Dic107C2311yescharacteristic
76C22×Dic107C2311yescharacteristic
77C22×Dic107C2311yescharacteristic
78C22×Dic107C2311yescharacteristic
79C22×Dic107C2311yescharacteristic
80C2×C4×D107—22no—
81C2×C4×D107—22no—
82C2×C4×D107—22no—
83C2×C4×D107—22no—
84C2×C4×D107—41no—
85C2×C4×D107—41no—
86Dic107⋊C4—22no—
87Dic107⋊C4—41no—
88C22⋊Dic107—22no—
89C22⋊Dic107—22no—
90C22⋊Dic107—41no—
91C22⋊Dic107C2×C414yescomplemented
92(C2×D107)⋊C4—22no—
93(C2×D107)⋊C4—22no—
94(C2×D107)⋊C4—22no—
95(C2×D107)⋊C4—22no—
96(C2×D107)⋊C4—22no—
97(C2×D107)⋊C4C2×C414yescomplemented
98(C2×D107)⋊C4C2×C414yescomplemented
99(C2×D107)⋊C4D414yescomplemented
100C4×Dic107—22no—
101C4×Dic107—41no—
102C24×C107C2311yescharacteristic
103C24×C107C2311yescharacteristic
104C2×D4×C107—22no—
105C2×D4×C107—22no—
106C2×D4×C107C2×C414yescomplemented
107C22×C4×C107—22no—
108C22×C4×C107—22no—
109C22×C4×C107—22no—
110C22×C4×C107—22no—
111C22×C4×C107—41no—
112C22×C4×C107—41no—
113C22×C4×C107C2311yescharacteristic
114C22×C4×C107C2311yescharacteristic
115C22×C4×C107C2311yescharacteristic
116C22×C4×C107C2311yescharacteristic
117C22×C4×C107C2311yescharacteristic
118C4⋊C4×C107—22no—
119C22⋊C4×C107—22no—
120C22⋊C4×C107D414yescomplemented
121C42×C107—22no—
122C23×C107—21no—
123C23×C107—21no—
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×C107C22×C412yes—
133C23×C107C22×C412yes—
134C23×C107C2×D412yes—
135C23×C107#4112yes—
136C23×C107C2411yescharacteristic
137C22×D107—21no—
138C22×D107—21no—
139C22×D107—21no—
140C22×D107—21no—
141C22×D107—28no—
142C22×D107—21no—
143C22×D107—21no—
144C22×D107—21no—
145C22×D107—21no—
146C22×D107—21no—
147C22×D107—21no—
148C22×D107—28no—
149C22×D107—44no—
150C22×D107—44no—
151C22×D107—44no—
152C22×D107—44no—
153C22×D107—44no—
154C22×D107C22×C412yes—
155C22×D107C22×C412yes—
156C22×D107C2×D412yes—
157C22×D107#4112yes—
158D4×C107—28no—
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—21no—
168C2×C4×C107—21no—
169C2×C4×C107—21no—
170C2×C4×C107—44no—
171C2×C4×C107—44no—
172C2×C4×C107C22×C412yes—
173C2×C4×C107C2×D412yes—
174C2×C4×C107C2×D412yes—
175C2×C4×C107C2×D412yes—
176C22⋊D107—28no—
177C22⋊D107—44no—
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—21no—
191C2×Dic107—21no—
192C2×Dic107—21no—
193C2×Dic107—44no—
194C2×Dic107C22×C412yes—
195C2×Dic107C22×C412yes—
196C2×Dic107C2×D412yes—
197C4×D107—44no—
198C4×D107—44no—
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—22no—
208C22×C107—41no—
209C22×C107—41no—
210C22×C107—41no—
211C22×C107—41no—
212C22×C107C4×D414yescomplemented
213C22×C107C23×C411yescharacteristic
214C22×C107C22×D411yescharacteristic
215C22×C107C22×D411yescharacteristic
216C22×C107C2×#4111yescharacteristic
217C22×C107C2×#4111yescharacteristic
218C22×C107H(5,𝔽2)11yescharacteristic
219C22×C107H(5,𝔽2)11yescharacteristic
220C2×D107—22no—
221C2×D107—22no—
222C2×D107—22no—
223C2×D107—22no—
224C2×D107—22no—
225C2×D107—22no—
226C2×D107—22no—
227C2×D107—22no—
228C2×D107—22no—
229C2×D107—416no—
230C2×D107—41no—
231C2×D107—41no—
232C2×D107—41no—
233C2×D107—41no—
234C2×D107C4×D414yescomplemented
235C4×C107—22no—
236C4×C107—22no—
237C4×C107—22no—
238C4×C107—22no—
239C4×C107—41no—
240Dic107—22no—
241Dic107—22no—
242Dic107—22no—
243Dic107—41no—
244Dic107—41no—
245Dic107—41no—
246C2×C107—24no—
247C2×C107—42no—
248C2×C107C2×C4×D411yescharacteristic
249C2×C107C2×C4×D411yescharacteristic
250C2×C107#51811yescharacteristic
251C2×C107D4211yescharacteristic
252C2×C107#54611yescharacteristic
253C2×C107#54611yescharacteristic
254C2×C107#55111yescharacteristic
255D107—24no—
256D107—42no—
257#2358—1071nomaximal, Sylow
258C107#235811yescharacteristic, complemented, Sylow
259C2×#120—1071no—
260C2×C4×D4—1071no—
261C2×C4×D4D10711yescharacteristic, complemented
262C22×C22⋊C4—1071no—
263C22×C22⋊C4—1071no—
264#390—1071no—
265#388—1071no—
266#388—1071no—
267#386—1071no—
268#386—1071no—
269#386—1071no—
270#385—1071no—
271#385—1071no—
272C4×C22⋊C4—1071no—
273C4×C22⋊C4—1071no—
274C25—1071no—
275C22×D4—1071no—
276C22×D4—1071no—
277C22×D4C2×D10711yescharacteristic
278C23×C4—1071no—
279C23×C4—1071no—
280C23×C4—1071no—
281C23×C4C2×D10711yescharacteristic
282C23×C4C2×D10711yescharacteristic, complemented
283#120—1078no—
284C4×D4—24no—
285C4×D4—2144no—
286C2×C4⋊C4—1071no—
287C2×C4⋊C4—1071no—
288C2×C4⋊C4C2×D10711yescharacteristic, complemented
289C2×C22⋊C4—1071no—
290C2×C22⋊C4—1071no—
291C2×C22⋊C4—1071no—
292C2×C22⋊C4—1071no—
293C2×C22⋊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—2144no—
302C2×C22⋊C4—2144no—
303C2×C22⋊C4C2×D10711yescharacteristic
304C2×C22⋊C4C2×D10711yescharacteristic, complemented
305C2×C42—1071no—
306C2×C42—1071no—
307C2×C42C2×D10711yescharacteristic, complemented
308#95—1071no—
309#95—1071no—
310#95—1071no—
311#95—1071no—
312#95—1071no—
313#95—1071no—
314C24—1071no—
315C24—1074no—
316C24—1071no—
317C24—4281no—
318C24—4281no—
319C24—2142no—
320C24—2142no—
321C24—2142no—
322C24—2142no—
323C24C22×D10711yescharacteristic
324C24C22×D10711yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—1074no—
328C2×D4—1074no—
329C2×D4—4281no—
330C2×D4—4281no—
331C2×D4—2142no—
332C2×D4—2142no—
333C2×D4C4×D10714yescomplemented
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—1071no—
341C22×C4—1071no—
342C22×C4—1071no—
343C22×C4—1071no—
344C22×C4—1071no—
345C22×C4—1071no—
346C22×C4—4281no—
347C22×C4—4281no—
348C22×C4—4281no—
349C22×C4—2142no—
350C22×C4—2142no—
351C22×C4—2142no—
352C22×C4—2142no—
353C22×C4—2142no—
354C22×C4—2142no—
355C22×C4C22×D10711yescharacteristic
356C22×C4C22×D10711yescharacteristic
357C22×C4C22×D10711yescharacteristic
358C22×C4C22×D10711yescharacteristic
359C22×C4C22×D10711yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—4281no—
362C4⋊C4—2142no—
363C22⋊C4—22no—
364C22⋊C4—1074no—
365C22⋊C4—1074no—
366C22⋊C4—1074no—
367C22⋊C4—1074no—
368C22⋊C4—4281no—
369C22⋊C4—2142no—
370C22⋊C4—2142no—
371C22⋊C4—2142no—
372C22⋊C4—2142no—
373C22⋊C4—2142no—
374C22⋊C4—2142no—
375C22⋊C4—2142no—
376C22⋊C4C22⋊D10714yescomplemented
377C42—22no—
378C42—4281no—
379C42—2142no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—1072no—
391C23—1072no—
392C23—1072no—
393C23—1072no—
394C23—4284no—
395C23—4284no—
396C23—4284no—
397C23—4284no—
398C23—4284no—
399C23—2148no—
400C23—2148no—
401C23—2141no—
402C23—2141no—
403C23—2141no—
404C23—2141no—
405C23—2141no—
406C23—2141no—
407C23—2141no—
408C23—2141no—
409C23—2141no—
410C23—2141no—
411C23C2×C4×D10712yes—
412C23C2×C4×D10712yes—
413C23C2×C22⋊D10712yes—
414C23#1313381812yes—
415C23C23×D10711yescharacteristic
416D4—28no—
417D4—4284no—
418D4—2148no—
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—21no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—1072no—
433C2×C4—1072no—
434C2×C4—1072no—
435C2×C4—4284no—
436C2×C4—4284no—
437C2×C4—4284no—
438C2×C4—2141no—
439C2×C4—2141no—
440C2×C4—2141no—
441C2×C4—2141no—
442C2×C4—2141no—
443C2×C4—2141no—
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×C4—2141no—
453C2×C4C2×C4×D10712yes—
454C2×C4D4×D10712yes—
455C2×C4C2×C22⋊D10712yes—
456C2×C4C2×C22⋊D10712yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—1074no—
471C22—42816no—
472C22—4281no—
473C22—4281no—
474C22—4281no—
475C22—4281no—
476C22—2142no—
477C22—2142no—
478C22—2142no—
479C22—2142no—
480C22—2142no—
481C22—2142no—
482C22—2142no—
483C22—2142no—
484C22—2142no—
485C22C4×C22⋊D10714yescomplemented
486C22C22×C4×D10711yescharacteristic
487C22C2×D4×D10711yescharacteristic
488C22C22×C22⋊D10711yescharacteristic
489C22#41×D10711yescharacteristic
490C22C2×#1313381811yescharacteristic
491C22#1681215411yescharacteristic
492C22#1681215511yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—4281no—
499C4—4281no—
500C4—4281no—
501C4—2142no—
502C4—2142no—
503C4—2142no—
504C2—24no—
505C2—42no—
506C2—4282no—
507C2—2144no—
508C2C4×D4×D10711yescharacteristic
509C2C2×C4×C22⋊D10711yescharacteristic
510C2#2029309911yescharacteristic
511C2D4×C22⋊D10711yescharacteristic
512C2#2029326511yescharacteristic
513C2#2029327311yescharacteristic
514C2#2029330611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutatorC22×C107C23×C4
FittingC2×C4×D4×C107C2
socle, cosocleC23×C107C24
prime radicalC2×#16812077C2
hypercenterC2×C4×D4D107
hypocenterC107#2358
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D107C2semidirect
3. C22×(C2×D107)⋊C4C2semidirect
4. C2×C22⋊C4×D107C2semidirect
5. #20292527C2semidirect
6. #20292518C2semidirect
7. #20292517C2semidirect
8. #20292507C2semidirect
9. #20292506C2semidirect
10. #20292503C2semidirect
11. #20292500C2semidirect
12. #20292498C2semidirect
13. C22⋊C4×Dic107C2semidirect
14. C4×(C2×D107)⋊C4C2semidirect
15. C2×C4×D4×C107C2semidirect
22. #16812077C4semidirect
24. C2×Dic107⋊C4C22semidirect
25. C2×Dic107⋊C4C22semidirect
28. C2×C22⋊Dic107C22semidirect
29. C2×C22⋊Dic107C22semidirect
40. C2×C4×Dic107C22semidirect
41. C2×C4×Dic107C22semidirect
42. C107⋊#95C22semidirect
43. C107⋊#95C22semidirect
44. C107⋊#95C22semidirect
45. C107⋊#95C22semidirect
46. C107⋊#95C22semidirect
47. C107⋊#95C22semidirect
50. C23×C4×C107C22semidirect
52. C2×C4⋊C4×C107C22semidirect
54. C2×C22⋊C4×C107C22semidirect
55. C2×C42×C107C22semidirect
62. C23×D107C2×C4semidirect
69. C2×C22⋊D107C2×C4semidirect
70. C2×C22⋊D107C2×C4semidirect
91. C22⋊Dic107C2×C4semidirect
97. (C2×D107)⋊C4C2×C4semidirect
98. (C2×D107)⋊C4C2×C4semidirect
99. (C2×D107)⋊C4D4semidirect
106. C2×D4×C107C2×C4semidirect
120. C22⋊C4×C107D4semidirect
212. C22×C107C4×D4semidirect
234. C2×D107C4×D4semidirect
258. C107#2358semidirect
261. C2×C4×D4D107semidirect
282. C23×C4C2×D107semidirect
288. C2×C4⋊C4C2×D107semidirect
304. C2×C22⋊C4C2×D107semidirect
307. C2×C42C2×D107semidirect
333. C2×D4C4×D107semidirect
376. C22⋊C4C22⋊D107semidirect
485. C22C4×C22⋊D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168120772
C2×C4×C22⋊D1072
C22×(C2×D107)⋊C42
C2×C22⋊C4×D1072
#202925272
#202925182
#202925172
#202925072
#202925062
#202925032
#202925002
#202924982
C22⋊C4×Dic1072
C4×(C2×D107)⋊C42
C2×C4×D4×C1072
#2358107