Finite Group Databasebeta

← #28339439

Subgroups — #28339439

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×#16812079C211yesmaximal, characteristic
2C2×C4×D428C211yesmaximal, characteristic, complemented
3C2×#16812071C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D107C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D107C211yesmaximal, characteristic, complemented
6#20292527C211yesmaximal, characteristic, complemented
7#20292520C211yesmaximal, characteristic, complemented
8#20292505C211yesmaximal, characteristic, complemented
9#20292505C211yesmaximal, characteristic, complemented
10#20292503C211yesmaximal, characteristic, complemented
11#20292501C211yesmaximal, characteristic, complemented
12#20292498C211yesmaximal, characteristic, complemented
13C4×(C2×D107)⋊C4C211yesmaximal, characteristic, complemented
14#20292474C211yesmaximal, characteristic, complemented
15#388×C107C211yesmaximal, characteristic, complemented
16C24×D107C2211yescharacteristic
17C22×D428C2211yescharacteristic
18C22×D428C2211yescharacteristic
19C22×C22⋊D107C2211yescharacteristic
20C22×C4×D107C2211yescharacteristic
21C22×C4×D107C2211yescharacteristic
22C22×C4×D107C2211yescharacteristic
23C22×C4×D107C2211yescharacteristic
24C22×C4×D107C2211yescharacteristic, complemented
25#16812079C418yescomplemented
26C4×D428—24no—
27#16812071—24no—
28C2×C4⋊Dic107C2211yescharacteristic, complemented
29C2×Dic107⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic107C2211yescharacteristic
31C2×C22⋊Dic107C2211yescharacteristic
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, complemented
39C2×(C2×D107)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D107)⋊C4C2211yescharacteristic, complemented
41C22⋊C4×D107—24no—
42C22⋊C4×D107—24no—
43C2×C4×Dic107C2211yescharacteristic, complemented
44C2×C4×Dic107C2211yescharacteristic, complemented
45C107⋊#95C2211yescharacteristic, complemented
46C107⋊#95C2211yescharacteristic, complemented
47C107⋊#95C2211yescharacteristic, complemented
48C107⋊#95C2211yescharacteristic, complemented
49C2×C4⋊C4×C107C2211yescharacteristic, complemented
50C2×C22⋊C4×C107C2211yescharacteristic
51C2×C22⋊C4×C107C2211yescharacteristic
52C2×C22⋊C4×C107C2211yescharacteristic
53C2×C42×C107C2211yescharacteristic, complemented
54#95×C107C2211yescharacteristic, complemented
55#95×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
65C23×D107C2311yescharacteristic
66C2×D428—22no—
67C2×D428—22no—
68C2×D428—22no—
69C2×D428—22no—
70C2×D428C2×C414yescomplemented
71C2×D428C2×C414yescomplemented
72C2×C22⋊D107—41no—
73C2×C22⋊D107—41no—
74C2×C22⋊D107C2×C414yescomplemented
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—22no—
85C2×C4×D107—22no—
86C2×C4×D107—22no—
87C2×C4×D107—22no—
88C2×C4×D107—22no—
89C2×C4×D107—22no—
90C2×C4×D107—41no—
91C2×C4×D107—41no—
92C2×C4×D107—41no—
93C2×C4×D107—41no—
94C2×C4×D107—41no—
95C4⋊Dic107—22no—
96Dic107⋊C4—41no—
97C22⋊Dic107—22no—
98C22⋊Dic107—22no—
99(C2×D107)⋊C4—22no—
100(C2×D107)⋊C4—22no—
101(C2×D107)⋊C4—22no—
102(C2×D107)⋊C4—22no—
103(C2×D107)⋊C4—41no—
104(C2×D107)⋊C4C2×C414yescomplemented
105(C2×D107)⋊C4C2×C414yescomplemented
106(C2×D107)⋊C4D414yescomplemented
107(C2×D107)⋊C4D414yescomplemented
108C4×Dic107—22no—
109C4×Dic107—41no—
110C24×C107C2311yescharacteristic
111C22×C4×C107C2311yescharacteristic
112C22×C4×C107C2311yescharacteristic
113C22×C4×C107C2311yescharacteristic
114C22×C4×C107C2311yescharacteristic
115C22×C4×C107C2311yescharacteristic
116C22×C4×C107C2311yescharacteristic
117C4⋊C4×C107—22no—
118C22⋊C4×C107—22no—
119C22⋊C4×C107—22no—
120C22⋊C4×C107C2×C414yescomplemented
121C42×C107—22no—
122C23×C107—21no—
123C23×C107—21no—
124C23×C107—21no—
125C23×C107—21no—
126C23×C107—21no—
127C23×C107—21no—
128C23×C107C22×C412yes—
129C23×C107C2411yescharacteristic
130C22×D107—21no—
131C22×D107—21no—
132C22×D107—21no—
133C22×D107—21no—
134C22×D107—21no—
135C22×D107—21no—
136C22×D107—21no—
137C22×D107—21no—
138C22×D107—21no—
139C22×D107—21no—
140C22×D107—21no—
141C22×D107—21no—
142C22×D107—21no—
143C22×D107—21no—
144C22×D107—28no—
145C22×D107—28no—
146C22×D107—44no—
147C22×D107—44no—
148C22×D107—44no—
149C22×D107—44no—
150C22×D107—44no—
151C22×D107C22×C412yes—
152C22×D107C22×C412yes—
153C22×D107C22×C412yes—
154C22×D107C2×D412yes—
155C22×D107C2×D412yes—
156C22×D107#4112yes—
157C22×D107#4112yes—
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—21no—
168C2×C4×C107—21no—
169C2×C4×C107—21no—
170C2×C4×C107—21no—
171C2×C4×C107—21no—
172C2×C4×C107C22×C412yes—
173C2×C4×C107C22×C412yes—
174C2×C4×C107C2×D412yes—
175C2×C4×C107C2×D412yes—
176C22⋊D107—44no—
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×Dic107C22×C412yes—
190C2×Dic107C2×D412yes—
191C2×Dic107C2×D412yes—
192D428—28no—
193D428—28no—
194C4×D107—44no—
195C4×D107—44no—
196C4×D107—44no—
197C4×D107—44no—
198C4×D107—44no—
199C22×C107—22no—
200C22×C107—22no—
201C22×C107—22no—
202C22×C107—41no—
203C22×C107—41no—
204C22×C107—41no—
205C22×C107—41no—
206C22×C107C23×C411yescharacteristic
207C22×C107C22×D411yescharacteristic
208C22×C107C22×D411yescharacteristic
209C22×C107C2×#4111yescharacteristic
210C22×C107C2×#4111yescharacteristic
211C22×C107H(5,𝔽2)11yescharacteristic
212C22×C107H(5,𝔽2)11yescharacteristic
213C2×D107—22no—
214C2×D107—22no—
215C2×D107—22no—
216C2×D107—22no—
217C2×D107—22no—
218C2×D107—22no—
219C2×D107—22no—
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—416no—
229C2×D107—41no—
230C2×D107—41no—
231C2×D107—41no—
232C2×D107—41no—
233C2×D107C4×D414yescomplemented
234C2×D107C4×D414yescomplemented
235C4×C107—22no—
236C4×C107—22no—
237C4×C107—22no—
238C4×C107—22no—
239C4×C107—41no—
240C4×C107—41no—
241Dic107—22no—
242Dic107—22no—
243Dic107—22no—
244Dic107—41no—
245Dic107—41no—
246C2×C107—42no—
247C2×C107C2×C4×D411yescharacteristic
248C2×C107C2×C4×D411yescharacteristic
249C2×C107#51811yescharacteristic
250C2×C107D4211yescharacteristic
251C2×C107#54611yescharacteristic
252C2×C107#54611yescharacteristic
253C2×C107#55111yescharacteristic
254D107—24no—
255D107—24no—
256D107—42no—
257#2358—1071nomaximal, Sylow
258C107#235811yescharacteristic, complemented, Sylow
259C2×#120—1071no—
260C2×C4×D4—1071no—
261C2×C4×D4—1071no—
262C22×C22⋊C4—1071no—
263C22×C22⋊C4—1071no—
264#390—1071no—
265#388—1071no—
266#388D10711yescharacteristic, complemented
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×D4—1071no—
278C23×C4—1071no—
279C23×C4—1071no—
280C23×C4—1071no—
281C23×C4—1071no—
282C23×C4—1071no—
283#120—1078no—
284C4×D4—2144no—
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—2144no—
301C2×C22⋊C4—2144no—
302C2×C22⋊C4C2×D10711yescharacteristic
303C2×C22⋊C4C2×D10711yescharacteristic
304C2×C22⋊C4C2×D10711yescharacteristic
305C2×C42—1071no—
306C2×C42—1071no—
307C2×C42C2×D10711yescharacteristic, complemented
308#95—1071no—
309#95—1071no—
310#95—1071no—
311#95—1071no—
312#95C2×D10711yescharacteristic, complemented
313#95C2×D10711yescharacteristic, complemented
314C24—1071no—
315C24—1071no—
316C24—1074no—
317C24—1071no—
318C24—4281no—
319C24—4281no—
320C24—2142no—
321C24—2142no—
322C24—2142no—
323C24—2142no—
324C24C22×D10711yescharacteristic
325C2×D4—1074no—
326C2×D4—1074no—
327C2×D4—1074no—
328C2×D4—4281no—
329C2×D4—4281no—
330C2×D4—2142no—
331C2×D4—2142no—
332C2×D4—2142no—
333C2×D4—2142no—
334C22×C4—1071no—
335C22×C4—1071no—
336C22×C4—1071no—
337C22×C4—1071no—
338C22×C4—1071no—
339C22×C4—4281no—
340C22×C4—4281no—
341C22×C4—4281no—
342C22×C4—4281no—
343C22×C4—4281no—
344C22×C4—2142no—
345C22×C4—2142no—
346C22×C4—2142no—
347C22×C4—2142no—
348C22×C4—2142no—
349C22×C4—2142no—
350C22×C4—2142no—
351C22×C4—2142no—
352C22×C4—2142no—
353C22×C4—2142no—
354C22×C4C22×D10711yescharacteristic
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—22no—
365C22⋊C4—1074no—
366C22⋊C4—1074no—
367C22⋊C4—1074no—
368C22⋊C4—1074no—
369C22⋊C4—4281no—
370C22⋊C4—2142no—
371C22⋊C4—2142no—
372C22⋊C4—2142no—
373C22⋊C4—2142no—
374C22⋊C4—2142no—
375C22⋊C4—2142no—
376C22⋊C4C4×D10714yescomplemented
377C42—22no—
378C42—4281no—
379C42—2142no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—1072no—
387C23—1072no—
388C23—1072no—
389C23—1072no—
390C23—1072no—
391C23—1072no—
392C23—1072no—
393C23—4284no—
394C23—4284no—
395C23—4284no—
396C23—4284no—
397C23—4284no—
398C23—2148no—
399C23—2148no—
400C23—2141no—
401C23—2141no—
402C23—2141no—
403C23—2141no—
404C23—2141no—
405C23—2141no—
406C23—2141no—
407C23—2141no—
408C23—2141no—
409C23—2141no—
410C23—2141no—
411C23—2141no—
412C23—2141no—
413C23—2141no—
414C23C2×C4×D10712yes—
415C23C23×D10711yescharacteristic
416D4—4284no—
417D4—2148no—
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—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—1072no—
434C2×C4—1072no—
435C2×C4—1072no—
436C2×C4—4284no—
437C2×C4—4284no—
438C2×C4—4284no—
439C2×C4—4284no—
440C2×C4—4284no—
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×C4C2×C4×D10712yes—
455C2×C4D4×D10712yes—
456C2×C4D4×D10712yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—1074no—
465C22—1074no—
466C22—42816no—
467C22—4281no—
468C22—4281no—
469C22—4281no—
470C22—4281no—
471C22—2142no—
472C22—2142no—
473C22—2142no—
474C22—2142no—
475C22—2142no—
476C22—2142no—
477C22—2142no—
478C22—2142no—
479C22—2142no—
480C22—2142no—
481C22—2142no—
482C22—2142no—
483C22—2142no—
484C22—2142no—
485C22—2142no—
486C22C22×C4×D10711yescharacteristic
487C22C2×D4×D10711yescharacteristic
488C22C2×D4×D10711yescharacteristic
489C22#41×D10711yescharacteristic
490C22#41×D10711yescharacteristic
491C22#1681215511yescharacteristic
492C22#1681215511yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—41no—
499C4—4281no—
500C4—4281no—
501C4—2142no—
502C4—2142no—
503C4—2142no—
504C2—42no—
505C2—4282no—
506C2—2144no—
507C2—2144no—
508C2C4×D4×D10711yescharacteristic
509C2C4×D4×D10711yescharacteristic
510C2#2029310111yescharacteristic
511C2#2029326111yescharacteristic
512C2#2029326911yescharacteristic
513C2#2029327011yescharacteristic
514C2#2029330211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutatorC22×C107C23×C4
Fitting#388×C107C2
socle, cosocleC23×C107C24
prime radicalC2×#16812079C2
hypercenter#388D107
hypocenterC107#2358
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×D428C2semidirect
3. C2×#16812071C2semidirect
4. C2×C22⋊C4×D107C2semidirect
5. C2×C22⋊C4×D107C2semidirect
6. #20292527C2semidirect
7. #20292520C2semidirect
8. #20292505C2semidirect
9. #20292505C2semidirect
10. #20292503C2semidirect
11. #20292501C2semidirect
12. #20292498C2semidirect
13. C4×(C2×D107)⋊C4C2semidirect
14. #20292474C2semidirect
15. #388×C107C2semidirect
24. C22×C4×D107C22semidirect
25. #16812079C4semidirect
28. C2×C4⋊Dic107C22semidirect
29. C2×Dic107⋊C4C22semidirect
38. C2×(C2×D107)⋊C4C22semidirect
39. C2×(C2×D107)⋊C4C22semidirect
40. C2×(C2×D107)⋊C4C22semidirect
43. C2×C4×Dic107C22semidirect
44. C2×C4×Dic107C22semidirect
45. C107⋊#95C22semidirect
46. C107⋊#95C22semidirect
47. C107⋊#95C22semidirect
48. C107⋊#95C22semidirect
49. C2×C4⋊C4×C107C22semidirect
53. C2×C42×C107C22semidirect
54. #95×C107C22semidirect
55. #95×C107C22semidirect
62. C23×D107C2×C4semidirect
70. C2×D428C2×C4semidirect
71. C2×D428C2×C4semidirect
74. C2×C22⋊D107C2×C4semidirect
104. (C2×D107)⋊C4C2×C4semidirect
105. (C2×D107)⋊C4C2×C4semidirect
106. (C2×D107)⋊C4D4semidirect
107. (C2×D107)⋊C4D4semidirect
120. C22⋊C4×C107C2×C4semidirect
233. C2×D107C4×D4semidirect
234. C2×D107C4×D4semidirect
258. C107#2358semidirect
266. #388D107semidirect
288. C2×C4⋊C4C2×D107semidirect
307. C2×C42C2×D107semidirect
312. #95C2×D107semidirect
313. #95C2×D107semidirect
376. C22⋊C4C4×D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168120792
C2×C4×D4282
C2×#168120712
C2×C22⋊C4×D1072
#202925272
#202925202
#202925052
#202925032
#202925012
#202924982
C4×(C2×D107)⋊C42
#202924742
#388×C1072
#2358107