Finite Group Databasebeta

← #49170327

Subgroups — #49170327

Order 37504.

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×#22627651C211yesmaximal, characteristic, complemented
2C2×#22627645C211yesmaximal, characteristic, complemented
3#34036801C211yesmaximal, characteristic, complemented
4#34036774C211yesmaximal, characteristic, complemented
5#34036518C211yesmaximal, characteristic, complemented
6#34036376C211yesmaximal, characteristic, complemented
7#34036366C211yesmaximal, characteristic, complemented
8#34036351C211yesmaximal, characteristic, complemented
9#34036324C211yesmaximal, characteristic, complemented
10#34036294C211yesmaximal, characteristic, complemented
11#34036277C211yesmaximal, characteristic, complemented
12#34036275C211yesmaximal, characteristic, complemented
13#34036264C211yesmaximal, characteristic, complemented
14#34036202C211yesmaximal, characteristic, complemented
15#440×C293C211yesmaximal, characteristic, complemented
16C2×#17989803C2211yescharacteristic
17C2×#17989803C2211yescharacteristic, complemented
18C2×#17989801C2211yescharacteristic
19C2×D4×D293C2211yescharacteristic
20#22627651—24no—
21#22627645—24no—
22C2×#17989792C2211yescharacteristic, complemented
23C2×#17989791C2211yescharacteristic, complemented
24C2×#17989791C2211yescharacteristic, complemented
25C2×#17989789C2211yescharacteristic
26C2×D2344C2211yescharacteristic
27C2×D2344C2211yescharacteristic
28C2×#17989787C2211yescharacteristic
29C2×#17989787C2211yescharacteristic
30C2×#17989785C2211yescharacteristic
31C2×C8×D293C2211yescharacteristic, complemented
32#22627621—21no—
33#22627621C2211yescharacteristic, complemented
34#22627612C2211yescharacteristic
35#22627608—21no—
36#22627604C2211yescharacteristic
37#22627599—21no—
38#22627599—21no—
39#22627599C2211yescharacteristic
40#22627599C2211yescharacteristic
41#22627599C2211yescharacteristic, complemented
42#22627598—21no—
43#22627594—21no—
44C4×D1172—21no—
45C4×D1172C2211yescharacteristic
46C2×#17989779—21no—
47C4⋊#14556873C2211yescharacteristic, complemented
48#22627547C2211yescharacteristic, complemented
49#22627544C2211yescharacteristic
50#22627544C2211yescharacteristic, complemented
51#22627544C2211yescharacteristic, complemented
52#22627536C2211yescharacteristic
53#22627536C2211yescharacteristic, complemented
54C2×SD16×C293C2211yescharacteristic
55C4×Q8×C293C2211yescharacteristic, complemented
56C4×D4×C293C2211yescharacteristic
57#107×C293C2211yescharacteristic, complemented
58#103×C293C2211yescharacteristic, complemented
59#102×C293C2211yescharacteristic
60#97×C293C2211yescharacteristic, complemented
61C23×D293—21no—
62#17989803—22no—
63#17989803—22no—
64#17989803—41no—
65#17989803—41no—
66#17989801—22no—
67#17989801—41no—
68C2×Dic586C2311yescharacteristic
69C2×D1172—21no—
70C2×D1172—21no—
71C2×D1172—21no—
72C2×D1172—21no—
73C2×D1172—21no—
74C2×D1172—21no—
75C2×D1172—21no—
76C2×D1172D411yescharacteristic
77C2×D1172C2311yescharacteristic
78C2×D1172C2311yescharacteristic
79C2×D1172C2311yescharacteristic
80C2×C22⋊D293—21no—
81C2×C22⋊D293—21no—
82D4×D293—22no—
83D4×D293—41no—
84C22×Dic293—21no—
85C2×C4×D293—21no—
86C2×C4×D293—21no—
87C2×C4×D293C2311yescharacteristic
88C2×C4×D293C2311yescharacteristic
89#17989792—22no—
90#17989791—22no—
91#17989791—41no—
92#17989789—22no—
93D2344—22no—
94D2344—41no—
95#17989787—22no—
96#17989787—22no—
97#17989785—22no—
98C2×#14556873C2311yescharacteristic
99C2×#14556873C2311yescharacteristic
100C8×D293—22no—
101C4⋊Dic293—21no—
102C4⋊Dic293D411yescharacteristic
103#17989779—21no—
104#17989779—21no—
105#17989779—21no—
106#17989779—21no—
107#17989779—21no—
108#17989779—21no—
109#17989779D411yescharacteristic
110#17989779D411yescharacteristic
111C2×Q8×C293C2311yescharacteristic
112C2×D4×C293C2311yescharacteristic
113C22×C4×C293—21no—
114SD16×C293D414yescomplemented
115C2×C8×C293C2311yescharacteristic
116C2×C8×C293C2311yescharacteristic
117C4⋊C4×C293—21no—
118C4⋊C4×C293C2311yescharacteristic
119C4⋊C4×C293C2311yescharacteristic
120C22⋊C4×C293—21no—
121C42×C293—21no—
122C42×C293C2311yescharacteristic
123C22×D293—21no—
124C22×D293—21no—
125C22×D293—21no—
126C22×D293—42no—
127C22×D293—42no—
128C22×D293—81no—
129C22×D293C2×D411yescharacteristic
130C22×D293C2×D411yescharacteristic
131Dic586—21no—
132Dic586—21no—
133D1172—21no—
134D1172—21no—
135D1172—21no—
136D1172—21no—
137D1172—21no—
138D1172—21no—
139D1172—41no—
140D1172—42no—
141D1172—42no—
142D1172—42no—
143D1172—81no—
144D1172—81no—
145D1172—81no—
146D1172—81no—
147C22⋊D293—42no—
148C22⋊D293—42no—
149C2×Dic293—21no—
150C2×Dic293—42no—
151C2×Dic293C2×D411yescharacteristic
152C2×Dic293C2×D411yescharacteristic
153C4×D293—21no—
154C4×D293—21no—
155C4×D293—21no—
156C4×D293—21no—
157C4×D293—42no—
158C4×D293—42no—
159#14556873—21no—
160#14556873—21no—
161C23×C293—21no—
162Q8×C293—21no—
163Q8×C293C2×D412yes—
164D4×C293—21no—
165D4×C293C2×D412yes—
166C2×C4×C293—21no—
167C2×C4×C293—21no—
168C2×C4×C293—21no—
169C2×C4×C293—81no—
170C2×C4×C293C2×D411yescharacteristic
171C2×C4×C293C2×D411yescharacteristic
172C2×C4×C293C2411yescharacteristic
173C8×C293—21no—
174C8×C293C2×D412yes—
175C22×C293—22no—
176C22×C293—41no—
177C22×C293—41no—
178C22×C293C22×D411yescharacteristic
179C2×D293—21no—
180C2×D293—21no—
181C2×D293—21no—
182C2×D293—21no—
183C2×D293—21no—
184C2×D293—21no—
185C2×D293—41no—
186C2×D293—41no—
187C2×D293—41no—
188C2×D293—41no—
189C2×D293—41no—
190C2×D293—41no—
191C2×D293—41no—
192C2×D293—41no—
193C2×D293—41no—
194C2×D293—84no—
195C4×C293—22no—
196C4×C293—21no—
197C4×C293—21no—
198C4×C293—41no—
199C4×C293—41no—
200C4×C293C22×D411yescharacteristic
201C4×C293H(5,𝔽2)11yescharacteristic
202Dic293—21no—
203Dic293—21no—
204Dic293—41no—
205C2×C293—42no—
206C2×C293D4211yescharacteristic
207C2×C293#57511yescharacteristic
208C2×C293#57611yescharacteristic
209D293—41no—
210D293—41no—
211D293—81no—
212D293—81no—
213D293—81no—
214C293#326811yescharacteristic, complemented, Sylow
215#3268—2931nomaximal, Sylow
216C2×AGL(1,ℤ/8)—2931no—
217C2×#135—2931no—
218#550—2931no—
219#546—2931no—
220#496—2931no—
221#468—2931no—
222#466—2931no—
223#464—2931no—
224#459—2931no—
225#452—2931no—
226#449—2931no—
227#449—2931no—
228#447—2931no—
229#440D29311yescharacteristic, complemented
230#435—2931no—
231C2×#41—2931no—
232C2×#41—2931no—
233C2×#41—2931no—
234C22×D4—2931no—
235AGL(1,ℤ/8)—5864no—
236#135—5864no—
237C2×Q16—2931no—
238C2×SD16—2931no—
239C2×SD16—2931no—
240C2×SD16—2931no—
241C2×SD16C2×D29311yescharacteristic
242C2×D8—2931no—
243C2×D8—2931no—
244C2×D8—2931no—
245C2×D8—2931no—
246C2×M16—2931no—
247C22×C8—2931no—
248#127—2931no—
249#127—5861no—
250#124—2931no—
251#123—5861no—
252C22⋊Q8—2931no—
253#121—2931no—
254#121—2931no—
255#121—2931no—
256#121—5861no—
257#121—5861no—
258#121—5861no—
259#120—5861no—
260C4×Q8C2×D29311yescharacteristic, complemented
261C4×D4—2931no—
262C4×D4—5861no—
263C4×D4C2×D29311yescharacteristic
264C2×C22⋊C4—5861no—
265#107C2×D29311yescharacteristic, complemented
266C4⋊C8—2931no—
267#103—2931no—
268#103C2×D29311yescharacteristic, complemented
269#102—2931no—
270#102—2931no—
271#102—2931no—
272#102C2×D29311yescharacteristic
273C22⋊C8—2931no—
274C22⋊C8—2931no—
275#97C2×D29311yescharacteristic, complemented
276C24—5861no—
277#41—5862no—
278#41—5862no—
279#41—5862no—
280#41—11721no—
281#41—11721no—
282#41—11721no—
283C2×Q8—2931no—
284C2×Q8C22×D29311yescharacteristic
285C2×D4—2931no—
286C2×D4—2931no—
287C2×D4—2931no—
288C2×D4—2931no—
289C2×D4—5861no—
290C2×D4—5861no—
291C2×D4—5861no—
292C2×D4—5861no—
293C2×D4—5861no—
294C2×D4—5861no—
295C2×D4—5862no—
296C2×D4—5861no—
297C2×D4—5861no—
298C2×D4—5861no—
299C2×D4—11721no—
300C2×D4C22×D29311yescharacteristic
301C22×C4—21no—
302C22×C4—2931no—
303C22×C4—2931no—
304C22×C4—5861no—
305C22×C4—5861no—
306C22×C4—5861no—
307Q16—5862no—
308SD16—5862no—
309SD16—5862no—
310SD16—11721no—
311SD16D117214yescomplemented
312D8—5862no—
313D8—5862no—
314D8—5862no—
315D8—11721no—
316M16—5862no—
317C2×C8—2931no—
318C2×C8—2931no—
319C2×C8—5862no—
320C2×C8C22×D29311yescharacteristic
321C2×C8C22×D29311yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—2931no—
324C4⋊C4—5861no—
325C4⋊C4C22×D29311yescharacteristic
326C4⋊C4C22×D29311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—2931no—
329C22⋊C4—2931no—
330C22⋊C4—5861no—
331C22⋊C4—5861no—
332C22⋊C4—5861no—
333C22⋊C4—5861no—
334C22⋊C4—5861no—
335C22⋊C4—5861no—
336C42—21no—
337C42C22×D29311yescharacteristic
338C23—21no—
339C23—2931no—
340C23—2931no—
341C23—23441no—
342C23—5861no—
343C23—5861no—
344C23—5861no—
345C23—11722no—
346C23—11722no—
347Q8—21no—
348Q8—5861no—
349Q8—5861no—
350Q8C2×D117212yes—
351D4—21no—
352D4—23441no—
353D4—23441no—
354D4—23441no—
355D4—23441no—
356D4—5861no—
357D4—5861no—
358D4—5861no—
359D4—5861no—
360D4—5861no—
361D4—5861no—
362D4—11721no—
363D4—11722no—
364D4—11722no—
365D4—11722no—
366D4—11722no—
367D4—11722no—
368D4C2×D117212yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—2931no—
374C2×C4—2931no—
375C2×C4—5861no—
376C2×C4—5861no—
377C2×C4—5861no—
378C2×C4—5861no—
379C2×C4—5861no—
380C2×C4—11722no—
381C2×C4—11722no—
382C2×C4—11722no—
383C2×C4D4×D29311yescharacteristic
384C2×C4D4×D29311yescharacteristic
385C2×C4C23×D29311yescharacteristic
386C8—21no—
387C8—5861no—
388C8—5861no—
389C8C2×D117212yes—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—23444no—
394C22—5861no—
395C22—5861no—
396C22—5861no—
397C22—5861no—
398C22—5861no—
399C22—5861no—
400C22—11721no—
401C22—11721no—
402C22—11721no—
403C22—11721no—
404C22—11721no—
405C22—11721no—
406C22—11721no—
407C22—11721no—
408C22—11721no—
409C22C2×D4×D29311yescharacteristic
410C4—22no—
411C4—21no—
412C4—21no—
413C4—41no—
414C4—41no—
415C4—5861no—
416C4—5861no—
417C4—11721no—
418C4C22×D117211yescharacteristic
419C4#2262767011yescharacteristic
420C2—42no—
421C2—23441no—
422C2—23441no—
423C2—23441no—
424C2—11721no—
425C2—11721no—
426C2D4×D117211yescharacteristic
427C2#3403692811yescharacteristic
428C2#3403693311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#440×C293C2
socleC22×C293C22×D4
hypercenter#440D293
hypocenterC293#3268
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#22627651C2semidirect
2. C2×#22627645C2semidirect
3. #34036801C2semidirect
4. #34036774C2semidirect
5. #34036518C2semidirect
6. #34036376C2semidirect
7. #34036366C2semidirect
8. #34036351C2semidirect
9. #34036324C2semidirect
10. #34036294C2semidirect
11. #34036277C2semidirect
12. #34036275C2semidirect
13. #34036264C2semidirect
14. #34036202C2semidirect
15. #440×C293C2semidirect
17. C2×#17989803C22semidirect
22. C2×#17989792C22semidirect
23. C2×#17989791C22semidirect
24. C2×#17989791C22semidirect
31. C2×C8×D293C22semidirect
33. #22627621C22semidirect
41. #22627599C22semidirect
47. C4⋊#14556873C22semidirect
48. #22627547C22semidirect
50. #22627544C22semidirect
51. #22627544C22semidirect
53. #22627536C22semidirect
55. C4×Q8×C293C22semidirect
57. #107×C293C22semidirect
58. #103×C293C22semidirect
60. #97×C293C22semidirect
114. SD16×C293D4semidirect
214. C293#3268semidirect
229. #440D293semidirect
260. C4×Q8C2×D293semidirect
265. #107C2×D293semidirect
268. #103C2×D293semidirect
275. #97C2×D293semidirect
311. SD16D1172semidirect

Maximal subgroups

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

subgroupindex
C2×#226276512
C2×#226276452
#340368012
#340367742
#340365182
#340363762
#340363662
#340363512
#340363242
#340362942
#340362772
#340362752
#340362642
#340362022
#440×C2932
#3268293