Finite Group Databasebeta

← #28339927

Subgroups — #28339927

Order 13696.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812091C211yesmaximal, characteristic, complemented
2C2×#16812078C211yesmaximal, characteristic
3C2×(C22⋊D107)⋊C4C211yesmaximal, characteristic, complemented
4C22×C22⋊Dic107C211yesmaximal, characteristic, complemented
5#20292563C211yesmaximal, characteristic, complemented
6#20292555C211yesmaximal, characteristic, complemented
7#20292543C211yesmaximal, characteristic, complemented
8#20292542C211yesmaximal, characteristic, complemented
9#20292521C211yesmaximal, characteristic, complemented
10#20292520C211yesmaximal, characteristic, complemented
11#20292504C211yesmaximal, characteristic, complemented
12#20292503C211yesmaximal, characteristic, complemented
13#20292502C211yesmaximal, characteristic, complemented
14#20292485C211yesmaximal, characteristic, complemented
15#379×C107C211yesmaximal, characteristic, complemented
16C22×C22⋊D107C2211yescharacteristic
17C22×C22⋊D107C2211yescharacteristic
18C22×C22⋊D107C2211yescharacteristic
19C23×Dic107C2211yescharacteristic
20C23×Dic107C2211yescharacteristic
21C22×C4×D107C2211yescharacteristic, complemented
22#16812091—24no—
23#16812078—24no—
24(C22⋊D107)⋊C4—24no—
25C2×C4⋊Dic107C2211yescharacteristic, complemented
26C2×C4⋊Dic107C2211yescharacteristic, complemented
27C2×Dic107⋊C4C2211yescharacteristic, complemented
28C2×Dic107⋊C4C2211yescharacteristic, complemented
29C2×Dic107⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic107—24no—
31C2×C22⋊Dic107C2211yescharacteristic
32C2×C22⋊Dic107C2211yescharacteristic
33C2×C22⋊Dic107C2211yescharacteristic
34C2×C22⋊Dic107C2211yescharacteristic
35C2×C22⋊Dic107C2211yescharacteristic
36C2×C22⋊Dic107C2211yescharacteristic
37C2×C22⋊Dic107C2211yescharacteristic
38C2×(C2×D107)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D107)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D107)⋊C4C2211yescharacteristic, complemented
41C2×C4×Dic107C2211yescharacteristic, complemented
42C107⋊#95C2211yescharacteristic, complemented
43C107⋊#95C2211yescharacteristic, complemented
44C107⋊#95C2211yescharacteristic, complemented
45C107⋊#95C2211yescharacteristic, complemented
46C107⋊#95C2211yescharacteristic, complemented
47C107⋊#95C2211yescharacteristic, complemented
48C25×C107C2211yescharacteristic
49C2×C22⋊C4×C107C2211yescharacteristic
50C2×C22⋊C4×C107C2211yescharacteristic
51C2×C22⋊C4×C107C2211yescharacteristic
52C2×C22⋊C4×C107C2211yescharacteristic
53C2×C22⋊C4×C107C2211yescharacteristic
54C2×C22⋊C4×C107C2211yescharacteristic
55C23×D107C2311yescharacteristic
56C2×C22⋊D107—22no—
57C2×C22⋊D107—22no—
58C2×C22⋊D107—22no—
59C2×C22⋊D107—22no—
60C2×C22⋊D107—22no—
61C2×C22⋊D107—22no—
62C2×C22⋊D107—41no—
63C2×C22⋊D107—41no—
64C2×C22⋊D107D414yes—
65C22×Dic107—22no—
66C22×Dic107—22no—
67C22×Dic107—22no—
68C22×Dic107—22no—
69C22×Dic107—41no—
70C22×Dic107—41no—
71C22×Dic107C2311yescharacteristic
72C22×Dic107C2311yescharacteristic
73C22×Dic107C2311yescharacteristic
74C22×Dic107C2311yescharacteristic
75C22×Dic107C2311yescharacteristic
76C22×Dic107C2311yescharacteristic
77C22×Dic107C2311yescharacteristic
78C2×C4×D107—22no—
79C2×C4×D107—22no—
80C2×C4×D107—41no—
81C4⋊Dic107—22no—
82C4⋊Dic107—41no—
83Dic107⋊C4—22no—
84Dic107⋊C4—22no—
85Dic107⋊C4—41no—
86C22⋊Dic107—22no—
87C22⋊Dic107—22no—
88C22⋊Dic107—22no—
89C22⋊Dic107—22no—
90C22⋊Dic107—22no—
91C22⋊Dic107—22no—
92C22⋊Dic107D414yescomplemented
93(C2×D107)⋊C4—22no—
94(C2×D107)⋊C4—22no—
95(C2×D107)⋊C4—41no—
96C4×Dic107—22no—
97C24×C107—22no—
98C24×C107—22no—
99C24×C107—22no—
100C24×C107—22no—
101C24×C107—22no—
102C24×C107—41no—
103C24×C107—41no—
104C24×C107C2311yescharacteristic
105C24×C107C2311yescharacteristic
106C24×C107C2311yescharacteristic
107C22×C4×C107C2311yescharacteristic
108C22×C4×C107C2311yescharacteristic
109C22×C4×C107C2311yescharacteristic
110C22×C4×C107C2311yescharacteristic
111C22⋊C4×C107—22no—
112C22⋊C4×C107—22no—
113C22⋊C4×C107—22no—
114C22⋊C4×C107—22no—
115C22⋊C4×C107—41no—
116C22⋊C4×C107—41no—
117C23×C107—21no—
118C23×C107—21no—
119C23×C107—21no—
120C23×C107—21no—
121C23×C107—28no—
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×C107—21no—
133C23×C107—21no—
134C23×C107—44no—
135C23×C107—44no—
136C23×C107—44no—
137C23×C107—44no—
138C23×C107—44no—
139C23×C107—44no—
140C23×C107C2×D412yes—
141C23×C107C2×D412yes—
142C23×C107#4112yes—
143C23×C107#4112yes—
144C23×C107#4112yes—
145C23×C107C2411yescharacteristic
146C22×D107—21no—
147C22×D107—21no—
148C22×D107—21no—
149C22×D107—21no—
150C22×D107—21no—
151C22×D107—21no—
152C22×D107C2×D412yes—
153C2×C4×C107—21no—
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—
165C22⋊D107—28no—
166C22⋊D107—44no—
167C22⋊D107—44no—
168C2×Dic107—21no—
169C2×Dic107—21no—
170C2×Dic107—21no—
171C2×Dic107—21no—
172C2×Dic107—21no—
173C2×Dic107—21no—
174C2×Dic107—21no—
175C2×Dic107—21no—
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—44no—
187C2×Dic107—44no—
188C2×Dic107C2×D412yes—
189C2×Dic107C2×D412yes—
190C2×Dic107C2×D412yes—
191C4×D107—44no—
192C22×C107—22no—
193C22×C107—22no—
194C22×C107—22no—
195C22×C107—22no—
196C22×C107—22no—
197C22×C107—22no—
198C22×C107—22no—
199C22×C107—22no—
200C22×C107—22no—
201C22×C107—22no—
202C22×C107—22no—
203C22×C107—22no—
204C22×C107—416no—
205C22×C107—41no—
206C22×C107—41no—
207C22×C107—41no—
208C22×C107—41no—
209C22×C107—41no—
210C22×C107—41no—
211C22×C107—41no—
212C22×C107—41no—
213C22×C107#12314yescomplemented
214C22×C107C22×D411yescharacteristic
215C22×C107C22×D411yescharacteristic
216C22×C107C2×#4111yescharacteristic
217C22×C107C2×#4111yescharacteristic
218C22×C107C2×#4111yescharacteristic
219C22×C107H(5,𝔽2)11yescharacteristic
220C22×C107H(5,𝔽2)11yescharacteristic
221C2×D107—22no—
222C2×D107—22no—
223C2×D107—22no—
224C2×D107—41no—
225C2×D107—41no—
226C2×D107—41no—
227C2×D107—41no—
228C4×C107—41no—
229C4×C107—41no—
230C4×C107—41no—
231C4×C107—41no—
232Dic107—22no—
233Dic107—22no—
234Dic107—22no—
235Dic107—41no—
236Dic107—41no—
237Dic107—41no—
238Dic107—41no—
239C2×C107—24no—
240C2×C107—42no—
241C2×C107—42no—
242C2×C107C2×#12311yescharacteristic
243C2×C107#52511yescharacteristic
244C2×C107#53811yescharacteristic
245C2×C107D4211yescharacteristic
246C2×C107#54611yescharacteristic
247C2×C107#54611yescharacteristic
248C2×C107#55111yescharacteristic
249D107—42no—
250#2418—1071nomaximal, Sylow
251C107#241811yescharacteristic, complemented, Sylow
252C2×#123—1071no—
253C2×#120—1071no—
254C2×C4×D4—1071no—
255C22×C22⋊C4—1071no—
256#399—1071no—
257#397—1071no—
258#394—1071no—
259#394—1071no—
260#388—1071no—
261#388—1071no—
262#386—1071no—
263#386—1071no—
264#385—1071no—
265#380—1071no—
266#379D10711yescharacteristic, complemented
267C25C2×D10711yescharacteristic
268C22×D4—1071no—
269C22×D4—1071no—
270C22×D4—1071no—
271C23×C4—1071no—
272C23×C4—1071no—
273C23×C4—1071no—
274#123—2144no—
275#120—2144no—
276C4×D4—2144no—
277C2×C4⋊C4—1071no—
278C2×C4⋊C4—1071no—
279C2×C4⋊C4—1071no—
280C2×C4⋊C4—1071no—
281C2×C4⋊C4—1071no—
282C2×C22⋊C4—1071no—
283C2×C22⋊C4—1071no—
284C2×C22⋊C4—1071no—
285C2×C22⋊C4—1071no—
286C2×C22⋊C4—1071no—
287C2×C22⋊C4—1071no—
288C2×C22⋊C4—1071no—
289C2×C22⋊C4—1071no—
290C2×C22⋊C4—1071no—
291C2×C22⋊C4—1071no—
292C2×C22⋊C4—2144no—
293C2×C22⋊C4C2×D10711yescharacteristic
294C2×C22⋊C4C2×D10711yescharacteristic
295C2×C22⋊C4C2×D10711yescharacteristic
296C2×C22⋊C4C2×D10711yescharacteristic
297C2×C22⋊C4C2×D10711yescharacteristic
298C2×C22⋊C4C2×D10711yescharacteristic
299C2×C42—1071no—
300#95—1071no—
301#95—1071no—
302#95—1071no—
303#95—1071no—
304#95—1071no—
305#95—1071no—
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—22no—
311C24—41no—
312C24—41no—
313C24—1071no—
314C24C22×D10711yescharacteristic
315C24C22×D10711yescharacteristic
316C24C22×D10711yescharacteristic
317C2×D4—1074no—
318C2×D4—4281no—
319C2×D4—4281no—
320C2×D4—2142no—
321C2×D4—2142no—
322C2×D4—2142no—
323C2×D4—2142no—
324C2×D4—2142no—
325C2×D4—2142no—
326C22×C4—1071no—
327C22×C4—1071no—
328C22×C4—1071no—
329C22×C4—1071no—
330C22×C4—1071no—
331C22×C4—1071no—
332C22×C4—1071no—
333C22×C4—4281no—
334C22×C4—4281no—
335C22×C4—4281no—
336C22×C4—2142no—
337C22×C4—2142no—
338C22×C4—2142no—
339C22×C4—2142no—
340C22×C4—2142no—
341C22×C4—2142no—
342C22×C4C22×D10711yescharacteristic
343C22×C4C22×D10711yescharacteristic
344C22×C4C22×D10711yescharacteristic
345C22×C4C22×D10711yescharacteristic
346C4⋊C4—4281no—
347C4⋊C4—4281no—
348C4⋊C4—2142no—
349C4⋊C4—2142no—
350C4⋊C4—2142no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—1074no—
358C22⋊C4—4281no—
359C22⋊C4—2142no—
360C22⋊C4—2142no—
361C22⋊C4—2142no—
362C22⋊C4—2142no—
363C22⋊C4—2142no—
364C22⋊C4—2142no—
365C22⋊C4—2142no—
366C22⋊C4—2142no—
367C42—2142no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—44no—
386C23—44no—
387C23—44no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—1072no—
392C23—2141no—
393C23—2141no—
394C23—2141no—
395C23—2141no—
396C23—2141no—
397C23—2141no—
398C23D4×D10712yes—
399C23D4×D10712yes—
400C23#1313381712yes—
401C23#1313381712yes—
402C23#1313381812yes—
403C23C23×D10711yescharacteristic
404D4—4284no—
405D4—4284no—
406D4—2148no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—1072no—
420C2×C4—1072no—
421C2×C4—1072no—
422C2×C4—4284no—
423C2×C4—4284no—
424C2×C4—4284no—
425C2×C4—2141no—
426C2×C4—2141no—
427C2×C4—2141no—
428C2×C4—2141no—
429C2×C4—2141no—
430C2×C4—2141no—
431C2×C4—2141no—
432C2×C4—2141no—
433C2×C4—2141no—
434C2×C4—2141no—
435C2×C4—2141no—
436C2×C4—2141no—
437C2×C4—2141no—
438C2×C4—2141no—
439C2×C4—2141no—
440C2×C4—2141no—
441C2×C4—2141no—
442C2×C4—2141no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—416no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—4281no—
465C22—4281no—
466C22—4281no—
467C22—4281no—
468C22—2142no—
469C22—2142no—
470C22—2142no—
471C22#1681209114yescomplemented
472C22C2×D4×D10711yescharacteristic
473C22C2×D4×D10711yescharacteristic
474C22C2×#1313381711yescharacteristic
475C22C2×#1313381711yescharacteristic
476C22C2×#1313381811yescharacteristic
477C22#1681215411yescharacteristic
478C22#1681215411yescharacteristic
479C4—41no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—4281no—
484C4—4281no—
485C4—4281no—
486C4—4281no—
487C4—2142no—
488C4—2142no—
489C4—2142no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—4282no—
494C2C2×#1681209111yescharacteristic
495C2#2029313311yescharacteristic
496C2#2029321211yescharacteristic
497C2#2029325911yescharacteristic
498C2#2029326411yescharacteristic
499C2#2029326711yescharacteristic
500C2#2029330311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#379×C107C2
prime radicalC2×#16812078C2
hypercenter#379D107
hypocenterC107#2418
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#16812091C2semidirect
3. C2×(C22⋊D107)⋊C4C2semidirect
4. C22×C22⋊Dic107C2semidirect
5. #20292563C2semidirect
6. #20292555C2semidirect
7. #20292543C2semidirect
8. #20292542C2semidirect
9. #20292521C2semidirect
10. #20292520C2semidirect
11. #20292504C2semidirect
12. #20292503C2semidirect
13. #20292502C2semidirect
14. #20292485C2semidirect
15. #379×C107C2semidirect
21. C22×C4×D107C22semidirect
25. C2×C4⋊Dic107C22semidirect
26. C2×C4⋊Dic107C22semidirect
27. C2×Dic107⋊C4C22semidirect
28. C2×Dic107⋊C4C22semidirect
29. C2×Dic107⋊C4C22semidirect
38. C2×(C2×D107)⋊C4C22semidirect
39. C2×(C2×D107)⋊C4C22semidirect
40. C2×(C2×D107)⋊C4C22semidirect
41. C2×C4×Dic107C22semidirect
42. C107⋊#95C22semidirect
43. C107⋊#95C22semidirect
44. C107⋊#95C22semidirect
45. C107⋊#95C22semidirect
46. C107⋊#95C22semidirect
47. C107⋊#95C22semidirect
92. C22⋊Dic107D4semidirect
213. C22×C107#123semidirect
251. C107#2418semidirect
266. #379D107semidirect
471. C22#16812091semidirect

Maximal subgroups

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

subgroupindex
C2×#168120912
C2×#168120782
C2×(C22⋊D107)⋊C42
C22×C22⋊Dic1072
#202925632
#202925552
#202925432
#202925422
#202925212
#202925202
#202925042
#202925032
#202925022
#202924852
#379×C1072
#2418107