Finite Group Databasebeta

← #16831031

Subgroups — #16831031

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×#11745278C211yesmaximal, characteristic, complemented
3#14271833C211yesmaximal, characteristic, complemented
4#14271806C211yesmaximal, characteristic, complemented
5#14271406C211yesmaximal, characteristic, complemented
6#14271396C211yesmaximal, characteristic, complemented
7#14271382C211yesmaximal, characteristic, complemented
8#14271355C211yesmaximal, characteristic, complemented
9#14271322C211yesmaximal, characteristic, complemented
10#14271307C211yesmaximal, characteristic, complemented
11#14271305C211yesmaximal, characteristic, complemented
12#14271295C211yesmaximal, characteristic, complemented
13#14271265C211yesmaximal, characteristic, complemented
14#14271236C211yesmaximal, characteristic, complemented
15C29×#496C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×#90807C2211yescharacteristic
18C2×#90807C2211yescharacteristic, complemented
19C2×D4×D29C2211yescharacteristic
20C2×SD16×C29C2211yescharacteristic, complemented
21C2×SD16×C29C2211yescharacteristic, complemented
22C2×D8×C29C2211yescharacteristic
23C2×D8×C29C2211yescharacteristic
24C29×#127C2211yescharacteristic, complemented
25C29×#124C2211yescharacteristic
26#11745308C2211yescharacteristic
27C2×#90785C2211yescharacteristic, complemented
28#11745302—21no—
29#11745301—21no—
30#11745301—21no—
31#11745300C2211yescharacteristic
32#11745300C2211yescharacteristic
33#11745300C2211yescharacteristic, complemented
34D4×Dic29—21no—
35C2×#90783C2211yescharacteristic
36C2×#90782C2211yescharacteristic
37C2×#90782C2211yescharacteristic
38#11745278—24no—
39#11745273—24no—
40C2×#90773C2211yescharacteristic
41C2×#90772C2211yescharacteristic
42C2×C8×D29C2211yescharacteristic, complemented
43#11745246—21no—
44#11745245—21no—
45#11745244—21no—
46C22⋊C4×D29—21no—
47C4×D116C2211yescharacteristic
48C4×D116C2211yescharacteristic
49C4×Dic58C2211yescharacteristic, complemented
50C29×#97C2211yescharacteristic, complemented
51#11745183C2211yescharacteristic, complemented
52#11745180C2211yescharacteristic
53#11745180C2211yescharacteristic, complemented
54#11745180C2211yescharacteristic, complemented
55#11745169C2211yescharacteristic
56#11745168C2211yescharacteristic
57#11745168C2211yescharacteristic, complemented
58#11745166C2211yescharacteristic, complemented
59#11745164C2211yescharacteristic, complemented
60C4⋊#6597C2211yescharacteristic, complemented
61C23×D29—21no—
62C2×Q8×C29C2311yescharacteristic
63C2×D4×C29—21no—
64C2×D4×C29—21no—
65C2×D4×C29C2311yescharacteristic
66C2×D4×C29C2311yescharacteristic
67C2×D4×C29C2311yescharacteristic
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—
76#90809—22no—
77#90809—41no—
78#90807—22no—
79#90807—22no—
80#90807—41no—
81#90807—41no—
82D4×D29—22no—
83D4×D29—41no—
84C2×D116—21no—
85C2×D116D411yescharacteristic
86C2×D116C2311yescharacteristic
87C2×C4×D29—21no—
88C2×C4×D29—21no—
89C2×C4×D29C2311yescharacteristic
90C2×C4×D29C2311yescharacteristic
91C2×Dic58C2311yescharacteristic
92SD16×C29—22no—
93SD16×C29—41no—
94D8×C29—22no—
95D8×C29—41no—
96C2×C8×C29C2311yescharacteristic
97C2×C8×C29C2311yescharacteristic
98C22⋊C4×C29—21no—
99C22⋊C4×C29—21no—
100C42×C29C2311yescharacteristic
101C22⋊Dic29—21no—
102C22⋊Dic29—21no—
103C22⋊Dic29—21no—
104#90785—22no—
105#90783—22no—
106#90782—22no—
107#90782—22no—
108#90781—21no—
109#90781—21no—
110#90781D411yescharacteristic
111#90781D411yescharacteristic
112C4⋊Dic29D411yescharacteristic
113C4⋊Dic29C2311yescharacteristic
114C4⋊Dic29C2311yescharacteristic
115#90779—21no—
116#90779—21no—
117C4×Dic29—21no—
118C2×#6597C2311yescharacteristic
119C2×#6597C2311yescharacteristic
120#90773D414yescomplemented
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
132Q8×C29—21no—
133Q8×C29—21no—
134D4×C29—21no—
135D4×C29—21no—
136D4×C29—21no—
137D4×C29—21no—
138D4×C29—21no—
139D4×C29—21no—
140D4×C29—42no—
141D4×C29—81no—
142C2×C4×C29—21no—
143C2×C4×C29C2×D411yescharacteristic
144C2×C4×C29C2×D411yescharacteristic
145C2×C4×C29C2411yescharacteristic
146C22⋊D29—42no—
147C22⋊D29—42no—
148C22⋊D29—42no—
149C22⋊D29—81no—
150C22⋊D29—81no—
151C22⋊D29—81no—
152C2×Dic29—21no—
153C2×Dic29—21no—
154C2×Dic29—21no—
155C2×Dic29—42no—
156C2×Dic29—42no—
157C2×Dic29C2×D411yescharacteristic
158C2×Dic29C2×D411yescharacteristic
159D116—21no—
160D116—41no—
161D116—42no—
162D116C2×D412yes—
163C4×D29—21no—
164C4×D29—21no—
165C4×D29—21no—
166C4×D29—21no—
167C4×D29—42no—
168C4×D29—81no—
169Dic58—21no—
170Dic58C2×D412yes—
171C8×C29—21no—
172C8×C29C2×D412yes—
173#6597—21no—
174#6597—21no—
175#3268—291nomaximal, Sylow
176C22×C29—41no—
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—22no—
189C2×D29—21no—
190C2×D29—21no—
191C2×D29—21no—
192C2×D29—21no—
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#496D2911yescharacteristic, complemented
211#468—291no—
212#466—291no—
213#464—291no—
214#459—291no—
215#452—291no—
216#449—291no—
217#449—291no—
218#447—291no—
219#440—291no—
220#435—291no—
221C2×C29—81no—
222C2×C29—81no—
223C2×C29—81no—
224C2×C29D4211yescharacteristic
225C2×C29#57511yescharacteristic
226C2×C29#57611yescharacteristic
227D29—41no—
228D29—41no—
229D29—42no—
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×SD16C2×D2911yescharacteristic, complemented
240C2×SD16C2×D2911yescharacteristic, complemented
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#124C2×D2911yescharacteristic
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—291no—
262C4×D4—581no—
263C2×C22⋊C4—581no—
264#107—291no—
265C4⋊C8—291no—
266#103—291no—
267#103—291no—
268#102—291no—
269#102—291no—
270#102—291no—
271#102—291no—
272C22⋊C8—291no—
273C22⋊C8—291no—
274#97C2×D2911yescharacteristic, complemented
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×Q8C22×D2911yescharacteristic
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—291no—
302C22×C4—291no—
303C22×C4—581no—
304C22×C4—581no—
305C22×C4—581no—
306C22×C4—581no—
307Q16—582no—
308SD16—22no—
309SD16—41no—
310SD16—294no—
311SD16—582no—
312D8—22no—
313D8—41no—
314D8—582no—
315D8—582no—
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—291no—
325C4⋊C4—581no—
326C4⋊C4—581no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—291no—
330C22⋊C4—291no—
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—21no—
348Q8—21no—
349Q8—292no—
350Q8—581no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—21no—
357D4—42no—
358D4—81no—
359D4—292no—
360D4—581no—
361D4—1161no—
362D4—1162no—
363D4—1162no—
364D4—1162no—
365D4—1162no—
366D4—2321no—
367D4—2321no—
368D4—2321no—
369C2×C4—21no—
370C2×C4—291no—
371C2×C4—291no—
372C2×C4—581no—
373C2×C4—581no—
374C2×C4—581no—
375C2×C4—581no—
376C2×C4—581no—
377C2×C4—581no—
378C2×C4—581no—
379C2×C4—1162no—
380C2×C4—1162no—
381C2×C4—1162no—
382C2×C4—2321no—
383C2×C4D4×D2911yescharacteristic
384C2×C4D4×D2911yescharacteristic
385C2×C4C23×D2911yescharacteristic
386C8—21no—
387C8—581no—
388C8—581no—
389C8D4×D2912yes—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—581no—
400C22—581no—
401C22—582no—
402C22—581no—
403C22—581no—
404C22—581no—
405C22—581no—
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#1174535911yescharacteristic
420C2—81no—
421C2—81no—
422C2—81no—
423C2—1161no—
424C2—1161no—
425C2—1162no—
426C2#1427179811yescharacteristic
427C2#1427195911yescharacteristic
428C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#496C2
socleC22×C29C22×D4
hypercenter#496D29
hypocenterC29#3268
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#11745273C2semidirect
2. C2×#11745278C2semidirect
3. #14271833C2semidirect
4. #14271806C2semidirect
5. #14271406C2semidirect
6. #14271396C2semidirect
7. #14271382C2semidirect
8. #14271355C2semidirect
9. #14271322C2semidirect
10. #14271307C2semidirect
11. #14271305C2semidirect
12. #14271295C2semidirect
13. #14271265C2semidirect
14. #14271236C2semidirect
15. C29×#496C2semidirect
18. C2×#90807C22semidirect
20. C2×SD16×C29C22semidirect
21. C2×SD16×C29C22semidirect
24. C29×#127C22semidirect
27. C2×#90785C22semidirect
33. #11745300C22semidirect
42. C2×C8×D29C22semidirect
49. C4×Dic58C22semidirect
50. C29×#97C22semidirect
51. #11745183C22semidirect
53. #11745180C22semidirect
54. #11745180C22semidirect
57. #11745168C22semidirect
58. #11745166C22semidirect
59. #11745164C22semidirect
60. C4⋊#6597C22semidirect
120. #90773D4semidirect
210. #496D29semidirect
239. C2×SD16C2×D29semidirect
240. C2×SD16C2×D29semidirect
248. #127C2×D29semidirect
274. #97C2×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×#117452782
#142718332
#142718062
#142714062
#142713962
#142713822
#142713552
#142713222
#142713072
#142713052
#142712952
#142712652
#142712362
C29×#4962
#326829