Finite Group Databasebeta

← #16831038

Subgroups — #16831038

Order 3712.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745273C211yesmaximal, characteristic, complemented
2C2×#11745274C211yesmaximal, characteristic, complemented
3#14271833C211yesmaximal, characteristic, complemented
4#14271808C211yesmaximal, characteristic, complemented
5#14271550C211yesmaximal, characteristic, complemented
6#14271408C211yesmaximal, characteristic, complemented
7#14271398C211yesmaximal, characteristic, complemented
8#14271386C211yesmaximal, characteristic, complemented
9#14271326C211yesmaximal, characteristic, complemented
10#14271309C211yesmaximal, characteristic, complemented
11#14271305C211yesmaximal, characteristic, complemented
12#14271295C211yesmaximal, characteristic, complemented
13#14271263C211yesmaximal, characteristic, complemented
14#14271233C211yesmaximal, characteristic, complemented
15C29×#459C211yesmaximal, characteristic, complemented
16C2×#90807C2211yescharacteristic
17C2×#90807C2211yescharacteristic
18C2×#90807C2211yescharacteristic, complemented
19C2×D4×D29C2211yescharacteristic
20C2×D8×C29C2211yescharacteristic
21C2×D8×C29C2211yescharacteristic
22C29×#127C2211yescharacteristic, complemented
23C4×D4×C29C2211yescharacteristic
24#11745302—21no—
25#11745301—21no—
26#11745301—21no—
27#11745300C2211yescharacteristic
28#11745300C2211yescharacteristic, complemented
29D4×Dic29—21no—
30C2×#90783C2211yescharacteristic
31C2×#90783C2211yescharacteristic, complemented
32C2×#90783C2211yescharacteristic, complemented
33C2×#90782C2211yescharacteristic
34C2×#90782C2211yescharacteristic
35#11745292—21no—
36C2×#90781—21no—
37#11745274—24no—
38#11745273—24no—
39C2×Dic116C2211yescharacteristic, complemented
40C2×#90773C2211yescharacteristic
41C2×#90772C2211yescharacteristic
42C2×C8×D29C2211yescharacteristic, complemented
43#11745259C2211yescharacteristic
44#11745257C2211yescharacteristic
45#11745248—21no—
46#11745244—21no—
47#11745237C2211yescharacteristic
48C4×D116C2211yescharacteristic
49C4×Dic58C2211yescharacteristic, complemented
50C29×C4⋊C8C2211yescharacteristic, complemented
51C29×#102C2211yescharacteristic, complemented
52C29×#102C2211yescharacteristic, complemented
53#11745180C2211yescharacteristic
54#11745169C2211yescharacteristic
55#11745168C2211yescharacteristic
56#11745168C2211yescharacteristic, complemented
57#11745164C2211yescharacteristic, complemented
58#11745158C2211yescharacteristic, complemented
59#11745155C2211yescharacteristic, complemented
60#11745151C2211yescharacteristic, complemented
61C23×D29—21no—
62C2×D4×C29—21no—
63C2×D4×C29—21no—
64C2×D4×C29C2311yescharacteristic
65C2×D4×C29C2311yescharacteristic
66C2×D4×C29C2311yescharacteristic
67C22×C4×C29—21no—
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72C2×C22⋊D29—21no—
73C2×C22⋊D29—21no—
74C22×Dic29—21no—
75C22×Dic29—21no—
76C22×Dic29—21no—
77#90807—22no—
78#90807—22no—
79#90807—22no—
80#90807—41no—
81#90807—41no—
82#90807—41no—
83D4×D29—22no—
84D4×D29—41no—
85C2×D116—21no—
86C2×D116D411yescharacteristic
87C2×D116C2311yescharacteristic
88C2×C4×D29C2311yescharacteristic
89C2×C4×D29C2311yescharacteristic
90C2×Dic58C2311yescharacteristic
91C2×Dic58C2311yescharacteristic
92D8×C29—22no—
93D8×C29—22no—
94C2×C8×C29C2311yescharacteristic
95C2×C8×C29C2311yescharacteristic
96C4⋊C4×C29C2311yescharacteristic
97C22⋊C4×C29—21no—
98C42×C29C2311yescharacteristic
99C22⋊Dic29—21no—
100C22⋊Dic29—21no—
101#90783—22no—
102#90783—41no—
103#90783D414yescomplemented
104#90782—22no—
105#90782—41no—
106#90781—21no—
107#90781—21no—
108#90781—21no—
109#90781—21no—
110#90781D411yescharacteristic
111#90781D411yescharacteristic
112C4⋊Dic29—21no—
113C4⋊Dic29D411yescharacteristic
114C4⋊Dic29C2311yescharacteristic
115#90779—21no—
116C4×Dic29—21no—
117C2×#6597C2311yescharacteristic
118C2×#6597C2311yescharacteristic
119Dic116—22no—
120#90773—22no—
121#90772—22no—
122C8×D29—22no—
123C23×C29—21no—
124C23×C29—21no—
125C23×C29—21no—
126C22×D29—21no—
127C22×D29—42no—
128C22×D29—42no—
129C22×D29—81no—
130C22×D29C2×D411yescharacteristic
131C22×D29C2×D411yescharacteristic
132D4×C29—21no—
133D4×C29—21no—
134D4×C29—21no—
135D4×C29—21no—
136D4×C29—21no—
137D4×C29—42no—
138D4×C29—81no—
139D4×C29C2×D412yes—
140C2×C4×C29—21no—
141C2×C4×C29—81no—
142C2×C4×C29C2×D411yescharacteristic
143C2×C4×C29C2×D411yescharacteristic
144C2×C4×C29C2411yescharacteristic
145C22⋊D29—42no—
146C22⋊D29—42no—
147C22⋊D29—42no—
148C22⋊D29—42no—
149C22⋊D29—81no—
150C22⋊D29—81no—
151C2×Dic29—21no—
152C2×Dic29—21no—
153C2×Dic29—21no—
154C2×Dic29—42no—
155C2×Dic29—42no—
156C2×Dic29—42no—
157C2×Dic29C2×D411yescharacteristic
158C2×Dic29C2×D411yescharacteristic
159D116—21no—
160D116—21no—
161D116—41no—
162D116—81no—
163C4×D29—21no—
164C4×D29—21no—
165C4×D29—21no—
166C4×D29—21no—
167Dic58—21no—
168Dic58—21no—
169Dic58—21no—
170Dic58C2×D412yes—
171C8×C29—21no—
172C8×C29—21no—
173#6597—21no—
174#6597C2×D412yes—
175#3268—291nomaximal, Sylow
176C22×C29—22no—
177C22×C29—41no—
178C22×C29—41no—
179C22×C29—41no—
180C22×C29—41no—
181C22×C29—41no—
182C22×C29—41no—
183C22×C29—41no—
184C22×C29—41no—
185C22×C29C22×D411yescharacteristic
186C2×D29—21no—
187C2×D29—21no—
188C2×D29—21no—
189C2×D29—21no—
190C2×D29—21no—
191C2×D29—21no—
192C2×D29—41no—
193C2×D29—41no—
194C2×D29—41no—
195C2×D29—84no—
196C4×C29—21no—
197C4×C29—21no—
198C4×C29—41no—
199C4×C29C22×D411yescharacteristic
200C4×C29H(5,𝔽2)11yescharacteristic
201Dic29—22no—
202Dic29—21no—
203Dic29—21no—
204Dic29—41no—
205Dic29—41no—
206C2×AGL(1,ℤ/8)—291no—
207C2×#135—291no—
208#550—291no—
209#546—291no—
210#496—291no—
211#468—291no—
212#466—291no—
213#464—291no—
214#459D2911yescharacteristic, complemented
215#452—291no—
216#449—291no—
217#449—291no—
218#447—291no—
219#440—291no—
220#435—291no—
221C2×C29—42no—
222C2×C29—81no—
223C2×C29—81no—
224C2×C29D4211yescharacteristic
225C2×C29#57511yescharacteristic
226C2×C29#57611yescharacteristic
227D29—41no—
228D29—41no—
229D29—81no—
230C2×#41—291no—
231C2×#41—291no—
232C2×#41—291no—
233C22×D4—291no—
234AGL(1,ℤ/8)—584no—
235#135—584no—
236C2×Q16—291no—
237C2×SD16—291no—
238C2×SD16—291no—
239C2×SD16—291no—
240C2×SD16—291no—
241C2×D8—291no—
242C2×D8—291no—
243C2×D8C2×D2911yescharacteristic
244C2×D8C2×D2911yescharacteristic
245C2×M16—291no—
246C22×C8—291no—
247#127—581no—
248#127C2×D2911yescharacteristic, complemented
249#124—291no—
250#123—581no—
251C22⋊Q8—291no—
252#121—291no—
253#121—291no—
254#121—291no—
255#121—581no—
256#121—581no—
257#121—581no—
258#120—581no—
259C4×Q8—291no—
260C4×D4—291no—
261C4×D4—581no—
262C4×D4C2×D2911yescharacteristic
263C2×C22⋊C4—581no—
264#107—291no—
265C4⋊C8C2×D2911yescharacteristic, complemented
266#103—291no—
267#103—291no—
268#102—291no—
269#102—291no—
270#102C2×D2911yescharacteristic, complemented
271#102C2×D2911yescharacteristic, complemented
272C22⋊C8—291no—
273C22⋊C8—291no—
274#97—291no—
275C29#326811yescharacteristic, complemented, Sylow
276C24—581no—
277#41—582no—
278#41—582no—
279#41—582no—
280#41—1161no—
281#41—1161no—
282#41—1161no—
283C2×Q8—291no—
284C2×Q8—291no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—291no—
288C2×D4—291no—
289C2×D4—581no—
290C2×D4—581no—
291C2×D4—582no—
292C2×D4—581no—
293C2×D4—581no—
294C2×D4—581no—
295C2×D4—581no—
296C2×D4—581no—
297C2×D4—1161no—
298C2×D4C22×D2911yescharacteristic
299C2×D4C22×D2911yescharacteristic
300C2×D4C22×D2911yescharacteristic
301C22×C4—21no—
302C22×C4—291no—
303C22×C4—291no—
304C22×C4—581no—
305C22×C4—581no—
306C22×C4—581no—
307Q16—582no—
308SD16—294no—
309SD16—582no—
310SD16—582no—
311SD16—1161no—
312D8—22no—
313D8—22no—
314D8—582no—
315D8—1161no—
316M16—582no—
317C2×C8—291no—
318C2×C8—291no—
319C2×C8—582no—
320C2×C8C22×D2911yescharacteristic
321C2×C8C22×D2911yescharacteristic
322C4⋊C4—291no—
323C4⋊C4—291no—
324C4⋊C4—581no—
325C4⋊C4—581no—
326C4⋊C4C22×D2911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—291no—
329C22⋊C4—291no—
330C22⋊C4—581no—
331C22⋊C4—581no—
332C22⋊C4—581no—
333C22⋊C4—581no—
334C22⋊C4—581no—
335C22⋊C4—581no—
336C42—581no—
337C42C22×D2911yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—291no—
342C23—291no—
343C23—581no—
344C23—1162no—
345C23—1162no—
346C23—2321no—
347Q8—292no—
348Q8—581no—
349Q8—581no—
350Q8—581no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—581no—
359D4—581no—
360D4—1161no—
361D4—1162no—
362D4—1162no—
363D4—1162no—
364D4—1162no—
365D4—2321no—
366D4—2321no—
367D4—2321no—
368D4D4×D2912yes—
369C2×C4—21no—
370C2×C4—81no—
371C2×C4—291no—
372C2×C4—291no—
373C2×C4—581no—
374C2×C4—581no—
375C2×C4—581no—
376C2×C4—581no—
377C2×C4—581no—
378C2×C4—581no—
379C2×C4—581no—
380C2×C4—1162no—
381C2×C4—1162no—
382C2×C4—1162no—
383C2×C4D4×D2911yescharacteristic
384C2×C4D4×D2911yescharacteristic
385C2×C4C23×D2911yescharacteristic
386C8—21no—
387C8—21no—
388C8—292no—
389C8—581no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—581no—
400C22—581no—
401C22—581no—
402C22—581no—
403C22—581no—
404C22—581no—
405C22—1161no—
406C22—1161no—
407C22—1161no—
408C22—2324no—
409C22C2×D4×D2911yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—581no—
414C4—581no—
415C4—582no—
416C4—1161no—
417C4—1161no—
418C4C2×D4×D2911yescharacteristic
419C4#1174536411yescharacteristic
420C2—42no—
421C2—81no—
422C2—81no—
423C2—1161no—
424C2—1161no—
425C2—2321no—
426C2#1427179711yescharacteristic
427C2#1427195911yescharacteristic
428C2#1427196411yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#459C2
socleC22×C29C22×D4
hypercenter#459D29
hypocenterC29#3268
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#11745273C2semidirect
2. C2×#11745274C2semidirect
3. #14271833C2semidirect
4. #14271808C2semidirect
5. #14271550C2semidirect
6. #14271408C2semidirect
7. #14271398C2semidirect
8. #14271386C2semidirect
9. #14271326C2semidirect
10. #14271309C2semidirect
11. #14271305C2semidirect
12. #14271295C2semidirect
13. #14271263C2semidirect
14. #14271233C2semidirect
15. C29×#459C2semidirect
18. C2×#90807C22semidirect
22. C29×#127C22semidirect
28. #11745300C22semidirect
31. C2×#90783C22semidirect
32. C2×#90783C22semidirect
39. C2×Dic116C22semidirect
42. C2×C8×D29C22semidirect
49. C4×Dic58C22semidirect
50. C29×C4⋊C8C22semidirect
51. C29×#102C22semidirect
52. C29×#102C22semidirect
56. #11745168C22semidirect
57. #11745164C22semidirect
58. #11745158C22semidirect
59. #11745155C22semidirect
60. #11745151C22semidirect
103. #90783D4semidirect
214. #459D29semidirect
248. #127C2×D29semidirect
265. C4⋊C8C2×D29semidirect
270. #102C2×D29semidirect
271. #102C2×D29semidirect
275. C29#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#117452732
C2×#117452742
#142718332
#142718082
#142715502
#142714082
#142713982
#142713862
#142713262
#142713092
#142713052
#142712952
#142712632
#142712332
C29×#4592
#326829