Finite Group Databasebeta

← #28339308

Subgroups — #28339308

Order 13696.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812067C211yesmaximal, characteristic, complemented
2C22×(C2×D107)⋊C4C211yesmaximal, characteristic
3C2×C22⋊C4×D107C211yesmaximal, characteristic
4#20292519C211yesmaximal, characteristic, complemented
5#20292519C211yesmaximal, characteristic, complemented
6#20292517C211yesmaximal, characteristic, complemented
7#20292517C211yesmaximal, characteristic, complemented
8#20292502C211yesmaximal, characteristic, complemented
9#20292489C211yesmaximal, characteristic, complemented
10#20292484C211yesmaximal, characteristic, complemented
11#20292482C211yesmaximal, characteristic
12C22⋊C4×Dic107C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic107C211yesmaximal, characteristic, complemented
14#20292474C211yesmaximal, characteristic, complemented
15#385×C107C211yesmaximal, characteristic, complemented
16C24×D107C2211yescharacteristic
17C23×Dic107C2211yescharacteristic
18C22×C4×D107C2211yescharacteristic
19C22×C4×D107C2211yescharacteristic
20#16812067—24no—
21C2×C4⋊Dic107C2211yescharacteristic, complemented
22C2×C4⋊Dic107C2211yescharacteristic, complemented
23C2×C22⋊Dic107C2211yescharacteristic
24C2×C22⋊Dic107C2211yescharacteristic
25C2×(C2×D107)⋊C4—24no—
26C2×(C2×D107)⋊C4C2211yescharacteristic
27C2×(C2×D107)⋊C4C2211yescharacteristic
28C2×(C2×D107)⋊C4C2211yescharacteristic
29C2×(C2×D107)⋊C4C2211yescharacteristic
30C2×(C2×D107)⋊C4C2211yescharacteristic
31C2×(C2×D107)⋊C4C2211yescharacteristic
32C2×(C2×D107)⋊C4C2211yescharacteristic
33C2×(C2×D107)⋊C4C2211yescharacteristic
34C2×(C2×D107)⋊C4C2211yescharacteristic
35C2×(C2×D107)⋊C4C2211yescharacteristic
36C22⋊C4×D107C418yescomplemented
37C2×C4×Dic107C2211yescharacteristic, complemented
38C2×C4×Dic107C2211yescharacteristic, complemented
39C2×C4×Dic107C2211yescharacteristic, complemented
40C2×C4×Dic107C2211yescharacteristic, complemented
41C107⋊#95C2211yescharacteristic, complemented
42C107⋊#95C2211yescharacteristic, complemented
43C107⋊#95C2211yescharacteristic, complemented
44C107⋊#95C2211yescharacteristic, complemented
45C107⋊#95C2211yescharacteristic, complemented
46C107⋊#95C2211yescharacteristic, complemented
47C23×C4×C107C2211yescharacteristic
48C2×C4⋊C4×C107C2211yescharacteristic, complemented
49C2×C4⋊C4×C107C2211yescharacteristic, complemented
50C2×C22⋊C4×C107C2211yescharacteristic
51C2×C22⋊C4×C107C2211yescharacteristic
52#95×C107C2211yescharacteristic, complemented
53#95×C107C2211yescharacteristic, complemented
54C23×D107—22no—
55C23×D107—22no—
56C23×D107—22no—
57C23×D107—22no—
58C23×D107—41no—
59C23×D107—41no—
60C23×D107C2×C414yes—
61C23×D107C2311yescharacteristic
62C23×D107C2311yescharacteristic
63C22×Dic107—22no—
64C22×Dic107—22no—
65C22×Dic107—41no—
66C22×Dic107C2311yescharacteristic
67C22×Dic107C2311yescharacteristic
68C22×Dic107C2311yescharacteristic
69C22×Dic107C2311yescharacteristic
70C22×Dic107C2311yescharacteristic
71C22×Dic107C2311yescharacteristic
72C2×C4×D107—22no—
73C2×C4×D107—22no—
74C2×C4×D107—41no—
75C2×C4×D107—41no—
76C2×C4×D107C2×C414yescomplemented
77C2×C4×D107C2×C414yescomplemented
78C4⋊Dic107—22no—
79C4⋊Dic107—41no—
80C22⋊Dic107—22no—
81C22⋊Dic107C2×C414yes—
82(C2×D107)⋊C4—22no—
83(C2×D107)⋊C4—22no—
84(C2×D107)⋊C4—22no—
85(C2×D107)⋊C4—22no—
86(C2×D107)⋊C4—22no—
87(C2×D107)⋊C4—41no—
88(C2×D107)⋊C4—41no—
89(C2×D107)⋊C4C2×C414yescomplemented
90(C2×D107)⋊C4C2×C414yescomplemented
91(C2×D107)⋊C4D414yes—
92C4×Dic107—22no—
93C4×Dic107—22no—
94C4×Dic107—41no—
95C4×Dic107—41no—
96C24×C107C2311yescharacteristic
97C22×C4×C107—22no—
98C22×C4×C107—22no—
99C22×C4×C107—41no—
100C22×C4×C107C2311yescharacteristic
101C22×C4×C107C2311yescharacteristic
102C22×C4×C107C2311yescharacteristic
103C22×C4×C107C2311yescharacteristic
104C22×C4×C107C2311yescharacteristic
105C22×C4×C107C2311yescharacteristic
106C4⋊C4×C107—22no—
107C4⋊C4×C107—41no—
108C22⋊C4×C107—22no—
109C22⋊C4×C107C2×C414yes—
110C23×C107—21no—
111C23×C107—21no—
112C23×C107—21no—
113C23×C107—21no—
114C23×C107C22×C412yes—
115C23×C107#4112yes—
116C23×C107#4112yes—
117C23×C107C2411yescharacteristic
118C22×D107—21no—
119C22×D107—21no—
120C22×D107—21no—
121C22×D107—21no—
122C22×D107—28no—
123C22×D107—21no—
124C22×D107—21no—
125C22×D107—21no—
126C22×D107—21no—
127C22×D107—21no—
128C22×D107—21no—
129C22×D107—28no—
130C22×D107—44no—
131C22×D107—44no—
132C22×D107—44no—
133C22×D107—44no—
134C22×D107—44no—
135C22×D107C22×C412yes—
136C22×D107C22×C412yes—
137C22×D107C2×D412yes—
138C22×D107#4112yes—
139C2×C4×C107—21no—
140C2×C4×C107—21no—
141C2×C4×C107—21no—
142C2×C4×C107—21no—
143C2×C4×C107—21no—
144C2×C4×C107—21no—
145C2×C4×C107—21no—
146C2×C4×C107—21no—
147C2×C4×C107—21no—
148C2×C4×C107—21no—
149C2×C4×C107—21no—
150C2×C4×C107—21no—
151C2×C4×C107—21no—
152C2×C4×C107—21no—
153C2×C4×C107—21no—
154C2×C4×C107—44no—
155C2×C4×C107C22×C412yes—
156C2×C4×C107C22×C412yes—
157C2×C4×C107C2×D412yes—
158C2×Dic107—21no—
159C2×Dic107—21no—
160C2×Dic107—21no—
161C2×Dic107—21no—
162C2×Dic107—21no—
163C2×Dic107—21no—
164C2×Dic107—21no—
165C2×Dic107—21no—
166C2×Dic107—21no—
167C2×Dic107—21no—
168C2×Dic107—21no—
169C2×Dic107—21no—
170C2×Dic107—21no—
171C2×Dic107—21no—
172C2×Dic107—21no—
173C2×Dic107—44no—
174C2×Dic107C22×C412yes—
175C2×Dic107C22×C412yes—
176C2×Dic107C2×D412yes—
177C4×D107—28no—
178C4×D107—44no—
179C22×C107—22no—
180C22×C107—22no—
181C22×C107—22no—
182C22×C107—22no—
183C22×C107—22no—
184C22×C107—22no—
185C22×C107#11714yescomplemented
186C22×C107C23×C411yescharacteristic
187C22×C107C22×D411yescharacteristic
188C22×C107C2×#4111yescharacteristic
189C22×C107C2×#4111yescharacteristic
190C22×C107C2×#4111yescharacteristic
191C22×C107H(5,𝔽2)11yescharacteristic
192C22×C107H(5,𝔽2)11yescharacteristic
193C2×D107—22no—
194C2×D107—22no—
195C2×D107—22no—
196C2×D107—22no—
197C2×D107—22no—
198C2×D107—22no—
199C2×D107—22no—
200C2×D107—22no—
201C2×D107—22no—
202C2×D107—416no—
203C2×D107—41no—
204C2×D107—41no—
205C2×D107—41no—
206C2×D107—41no—
207C2×D107C4×D414yes—
208C4×C107—22no—
209C4×C107—22no—
210C4×C107—22no—
211C4×C107—41no—
212C4×C107—41no—
213C4×C107—41no—
214Dic107—22no—
215Dic107—22no—
216Dic107—22no—
217Dic107—41no—
218Dic107—41no—
219Dic107—41no—
220C2×C107—24no—
221C2×C107C2×#11711yescharacteristic
222C2×C107C2×C4×D411yescharacteristic
223C2×C107#51811yescharacteristic
224C2×C107#54611yescharacteristic
225C2×C107#54611yescharacteristic
226C2×C107#55111yescharacteristic
227C2×C107#55111yescharacteristic
228D107—24no—
229D107—42no—
230#2342—1071nomaximal, Sylow
231C107#234211yescharacteristic, complemented, Sylow
232C2×#117—1071no—
233C22×C22⋊C4—1071no—
234C22×C22⋊C4—1071no—
235#388—1071no—
236#388—1071no—
237#388—1071no—
238#388—1071no—
239#385—1071no—
240#385D10711yescharacteristic, complemented
241#381—1071no—
242#380—1071no—
243#379—1071no—
244C4×C22⋊C4—1071no—
245C4×C22⋊C4—1071no—
246C4×C22⋊C4—1071no—
247C25—1071no—
248C23×C4—1071no—
249C23×C4—1071no—
250C23×C4—1071no—
251C23×C4C2×D10711yescharacteristic
252#117—2144no—
253C2×C4⋊C4—1071no—
254C2×C4⋊C4—1071no—
255C2×C4⋊C4C2×D10711yescharacteristic, complemented
256C2×C4⋊C4C2×D10711yescharacteristic, complemented
257C2×C22⋊C4—1071no—
258C2×C22⋊C4—1071no—
259C2×C22⋊C4—1071no—
260C2×C22⋊C4—1071no—
261C2×C22⋊C4—1078no—
262C2×C22⋊C4—1071no—
263C2×C22⋊C4—1071no—
264C2×C22⋊C4—1071no—
265C2×C22⋊C4—1071no—
266C2×C22⋊C4—1071no—
267C2×C22⋊C4—1071no—
268C2×C22⋊C4—1071no—
269C2×C22⋊C4—1071no—
270C2×C22⋊C4—2144no—
271C2×C22⋊C4C2×D10711yescharacteristic
272C2×C22⋊C4C2×D10711yescharacteristic
273C2×C42—1071no—
274C2×C42—1071no—
275C2×C42—1071no—
276C2×C42—1071no—
277#95—1071no—
278#95—1071no—
279#95—1071no—
280#95—1071no—
281#95—1071no—
282#95—1071no—
283#95C2×D10711yescharacteristic, complemented
284#95C2×D10711yescharacteristic, complemented
285C24—1071no—
286C24—1074no—
287C24—1071no—
288C24—4281no—
289C24—4281no—
290C24—2142no—
291C24—2142no—
292C24—2142no—
293C24—2142no—
294C24C22×D10711yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—41no—
298C22×C4—1071no—
299C22×C4—1071no—
300C22×C4—1071no—
301C22×C4—1074no—
302C22×C4—1074no—
303C22×C4—1071no—
304C22×C4—1071no—
305C22×C4—1071no—
306C22×C4—4281no—
307C22×C4—4281no—
308C22×C4—4281no—
309C22×C4—2142no—
310C22×C4—2142no—
311C22×C4—2142no—
312C22×C4—2142no—
313C22×C4C22×D10711yescharacteristic
314C22×C4C22×D10711yescharacteristic
315C22×C4C22×D10711yescharacteristic
316C22×C4C22×D10711yescharacteristic
317C22×C4C22×D10711yescharacteristic
318C22×C4C22×D10711yescharacteristic
319C4⋊C4—22no—
320C4⋊C4—41no—
321C4⋊C4—4281no—
322C4⋊C4—2142no—
323C22⋊C4—22no—
324C22⋊C4—1074no—
325C22⋊C4—1074no—
326C22⋊C4—1074no—
327C22⋊C4—1074no—
328C22⋊C4—4281no—
329C22⋊C4—4281no—
330C22⋊C4—2142no—
331C22⋊C4—2142no—
332C22⋊C4—2142no—
333C22⋊C4—2142no—
334C22⋊C4—2142no—
335C22⋊C4—2142no—
336C22⋊C4C4×D10714yes—
337C42—4281no—
338C42—4281no—
339C42—2142no—
340C42—2142no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—1072no—
346C23—1072no—
347C23—1072no—
348C23—1072no—
349C23—4284no—
350C23—4284no—
351C23—4284no—
352C23—4284no—
353C23—4284no—
354C23—2148no—
355C23—2148no—
356C23—2141no—
357C23—2141no—
358C23—2141no—
359C23—2141no—
360C23—2141no—
361C23—2141no—
362C23—2141no—
363C23—2141no—
364C23—2141no—
365C23—2141no—
366C23C2×C4×D10712yes—
367C23#1313381712yes—
368C23#1313381912yes—
369C23C23×D10711yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—44no—
386C2×C4—1072no—
387C2×C4—1072no—
388C2×C4—1072no—
389C2×C4—4284no—
390C2×C4—4284no—
391C2×C4—2148no—
392C2×C4—2141no—
393C2×C4—2141no—
394C2×C4—2141no—
395C2×C4—2141no—
396C2×C4—2141no—
397C2×C4—2141no—
398C2×C4—2141no—
399C2×C4—2141no—
400C2×C4—2141no—
401C2×C4—2141no—
402C2×C4—2141no—
403C2×C4—2141no—
404C2×C4—2141no—
405C2×C4—2141no—
406C2×C4—2141no—
407C2×C4C2×C4×D10712yes—
408C2×C4C2×C4×D10712yes—
409C2×C4D4×D10712yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—1074no—
417C22—42816no—
418C22—4281no—
419C22—4281no—
420C22—4281no—
421C22—4281no—
422C22—2142no—
423C22—2142no—
424C22—2142no—
425C22—2142no—
426C22—2142no—
427C22—2142no—
428C22—2142no—
429C22—2142no—
430C22—2142no—
431C22#1681206714yescomplemented
432C22C22×C4×D10711yescharacteristic
433C22C2×D4×D10711yescharacteristic
434C22#41×D10711yescharacteristic
435C22C2×#1313381711yescharacteristic
436C22C2×#1313381911yescharacteristic
437C22#1681215411yescharacteristic
438C22#1681215511yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—4281no—
446C4—4281no—
447C4—4281no—
448C4—2142no—
449C4—2142no—
450C4—2142no—
451C2—24no—
452C2—4282no—
453C2—2144no—
454C2C2×#1681206711yescharacteristic
455C2C4×D4×D10711yescharacteristic
456C2#2029309911yescharacteristic
457C2#2029326411yescharacteristic
458C2#2029326811yescharacteristic
459C2#2029330011yescharacteristic
460C2#2029330411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutatorC22×C107C23×C4
Fitting#385×C107C2
socle, cosocleC23×C107C24
prime radicalC24×D107C22
hypercenter#385D107
hypocenterC107#2342
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#16812067C2semidirect
4. #20292519C2semidirect
5. #20292519C2semidirect
6. #20292517C2semidirect
7. #20292517C2semidirect
8. #20292502C2semidirect
9. #20292489C2semidirect
10. #20292484C2semidirect
12. C22⋊C4×Dic107C2semidirect
13. C4×C22⋊Dic107C2semidirect
14. #20292474C2semidirect
15. #385×C107C2semidirect
21. C2×C4⋊Dic107C22semidirect
22. C2×C4⋊Dic107C22semidirect
36. C22⋊C4×D107C4semidirect
37. C2×C4×Dic107C22semidirect
38. C2×C4×Dic107C22semidirect
39. C2×C4×Dic107C22semidirect
40. C2×C4×Dic107C22semidirect
41. C107⋊#95C22semidirect
42. C107⋊#95C22semidirect
43. C107⋊#95C22semidirect
44. C107⋊#95C22semidirect
45. C107⋊#95C22semidirect
46. C107⋊#95C22semidirect
48. C2×C4⋊C4×C107C22semidirect
49. C2×C4⋊C4×C107C22semidirect
52. #95×C107C22semidirect
53. #95×C107C22semidirect
76. C2×C4×D107C2×C4semidirect
77. C2×C4×D107C2×C4semidirect
89. (C2×D107)⋊C4C2×C4semidirect
90. (C2×D107)⋊C4C2×C4semidirect
185. C22×C107#117semidirect
231. C107#2342semidirect
240. #385D107semidirect
255. C2×C4⋊C4C2×D107semidirect
256. C2×C4⋊C4C2×D107semidirect
283. #95C2×D107semidirect
284. #95C2×D107semidirect
431. C22#16812067semidirect

Maximal subgroups

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

subgroupindex
C2×#168120672
C22×(C2×D107)⋊C42
C2×C22⋊C4×D1072
#202925192
#202925172
#202925022
#202924892
#202924842
#202924822
C22⋊C4×Dic1072
C4×C22⋊Dic1072
#202924742
#385×C1072
#2342107