Finite Group Databasebeta

← #49167441

Subgroups — #49167441

Order 37504.

402 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#117×D293C211yesmaximal, characteristic
2#34036190C211yesmaximal, characteristic, complemented
3#34036187C211yesmaximal, characteristic, complemented
4#34036187C211yesmaximal, characteristic, complemented
5#34036185C211yesmaximal, characteristic, complemented
6#34036184C211yesmaximal, characteristic, complemented
7#34036181C211yesmaximal, characteristic, complemented
8#34036180C211yesmaximal, characteristic, complemented
9#34036154C211yesmaximal, characteristic, complemented
10#34036154C211yesmaximal, characteristic, complemented
11#34036091C211yesmaximal, characteristic
12C22⋊C8×D293C211yesmaximal, characteristic
13#34036086C211yesmaximal, characteristic, complemented
14#34036083C211yesmaximal, characteristic, complemented
15#433×C293C211yesmaximal, characteristic, complemented
16C22×C4×D293C2211yescharacteristic
17C2×#17989785C2211yescharacteristic
18C2×#17989785C2211yescharacteristic
19C2×C8×D293C2211yescharacteristic
20C2×C8×D293C2211yescharacteristic
21#22627583C2211yescharacteristic
22#22627582C411yescharacteristic
23#22627582C411yescharacteristic
24#22627581C2211yescharacteristic
25#22627581C2211yescharacteristic
26#22627580C411yescharacteristic
27#22627580C411yescharacteristic
28C4⋊C4×D293C411yescharacteristic
29C4⋊C4×D293C411yescharacteristic
30C22⋊C4×D293C411yescharacteristic
31C22⋊C4×D293C411yescharacteristic
32C42×D293C2211yescharacteristic
33C42×D293C2211yescharacteristic
34C4⋊#14556873C2211yescharacteristic, complemented
35C4⋊#14556873C2211yescharacteristic, complemented
36#22627553C2211yescharacteristic, complemented
37#22627553C2211yescharacteristic, complemented
38#22627553C2211yescharacteristic, complemented
39#22627553C2211yescharacteristic, complemented
40C22⋊#14556873C2211yescharacteristic
41C22⋊#14556873C2211yescharacteristic
42#22627536C2211yescharacteristic
43#22627536C2211yescharacteristic
44#22627536C2211yescharacteristic
45#22627536C2211yescharacteristic
46#22627535C2211yescharacteristic, complemented
47#22627534C2211yescharacteristic, complemented
48#22627534C2211yescharacteristic, complemented
49C4×#14556873C2211yescharacteristic, complemented
50C8×Dic293C2211yescharacteristic, complemented
51C8×Dic293C2211yescharacteristic, complemented
52#117×C293C2211yescharacteristic
53C4⋊C8×C293C2211yescharacteristic, complemented
54C4⋊C8×C293C2211yescharacteristic, complemented
55C22⋊C8×C293C2211yescharacteristic
56C22⋊C8×C293C2211yescharacteristic
57#97×C293C2211yescharacteristic, complemented
58C4×C8×C293C2211yescharacteristic, complemented
59C23×D293C2×C411yescharacteristic
60C22×Dic293C2×C411yescharacteristic
61C2×C4×D293—22no—
62C2×C4×D293—22no—
63C2×C4×D293C2×C411yescharacteristic
64C2×C4×D293C2×C411yescharacteristic
65C2×C4×D293C2×C411yescharacteristic
66C2×C4×D293C2×C411yescharacteristic
67C2×C4×D293C2×C411yescharacteristic
68C2×C4×D293C2×C411yescharacteristic
69C2×C4×D293C2311yescharacteristic
70C2×C4×D293C2311yescharacteristic
71#17989785—22no—
72#17989785—22no—
73C2×#14556873C2311yescharacteristic
74C2×#14556873C2311yescharacteristic
75C2×#14556873C2311yescharacteristic
76C2×#14556873C2311yescharacteristic
77C8×D293—22no—
78C8×D293—22no—
79C4⋊Dic293C2×C411yescharacteristic
80C4⋊Dic293C2×C411yescharacteristic
81#17989781C2×C411yescharacteristic
82#17989781C2×C411yescharacteristic
83#17989781C2×C411yescharacteristic
84#17989781C2×C411yescharacteristic
85C22⋊Dic293C2×C411yescharacteristic
86C22⋊Dic293C2×C411yescharacteristic
87#17989779C2×C411yescharacteristic
88#17989779C2×C411yescharacteristic
89#17989779C2×C411yescharacteristic
90#17989779C2×C411yescharacteristic
91C4×Dic293C2×C411yescharacteristic
92C4×Dic293C2×C411yescharacteristic
93C4×Dic293C2×C411yescharacteristic
94C4×Dic293C2×C411yescharacteristic
95C4×Dic293C2311yescharacteristic
96C4×Dic293C2311yescharacteristic
97C22×C4×C293C2311yescharacteristic
98C2×C8×C293C2311yescharacteristic
99C2×C8×C293C2311yescharacteristic
100C2×C8×C293C2311yescharacteristic
101C2×C8×C293C2311yescharacteristic
102C4⋊C4×C293C2×C411yescharacteristic
103C4⋊C4×C293C2×C411yescharacteristic
104C22⋊C4×C293C2×C411yescharacteristic
105C22⋊C4×C293C2×C411yescharacteristic
106C42×C293C2311yescharacteristic
107C42×C293C2311yescharacteristic
108C22×D293—22no—
109C22×D293—22no—
110C22×D293—41no—
111C22×D293C22×C411yescharacteristic
112C22×D293C22×C411yescharacteristic
113C2×Dic293—22no—
114C2×Dic293C22×C411yescharacteristic
115C2×Dic293C22×C411yescharacteristic
116C2×Dic293C22×C411yescharacteristic
117C2×Dic293C22×C411yescharacteristic
118C2×Dic293C22×C411yescharacteristic
119C2×Dic293C22×C411yescharacteristic
120C4×D293—22no—
121C4×D293—22no—
122C4×D293—22no—
123C4×D293—21no—
124C4×D293—21no—
125C4×D293—22no—
126C4×D293—41no—
127C4×D293—41no—
128C4×D293#4112yes—
129C4×D293#4112yes—
130#14556873—21no—
131#14556873—21no—
132#14556873—21no—
133#14556873—21no—
134C23×C293C22×C411yescharacteristic
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293C22×C411yescharacteristic
138C2×C4×C293C22×C411yescharacteristic
139C2×C4×C293C22×C411yescharacteristic
140C2×C4×C293C22×C411yescharacteristic
141C2×C4×C293C22×C411yescharacteristic
142C2×C4×C293C2411yescharacteristic
143C8×C293—21no—
144C8×C293—21no—
145C8×C293—21no—
146C8×C293—21no—
147C22×C293—21no—
148C22×C293—21no—
149C22×C293—21no—
150C22×C293C23×C411yescharacteristic
151C2×D293—21no—
152C2×D293—21no—
153C2×D293—21no—
154C2×D293—21no—
155C2×D293—44no—
156C2×D293#11712yes—
157C2×D293#13112yes—
158C4×C293—21no—
159C4×C293—21no—
160C4×C293—21no—
161C4×C293—21no—
162C4×C293—21no—
163C4×C293C2×#4111yescharacteristic
164C4×C293C2×#4111yescharacteristic
165Dic293—21no—
166Dic293—21no—
167Dic293—21no—
168Dic293—21no—
169Dic293—21no—
170Dic293#11712yes—
171C2×C293—41no—
172C2×C293C2×#11711yescharacteristic
173C2×C293C2×#13111yescharacteristic
174C2×C293#56811yescharacteristic
175D293—22no—
176D293—22no—
177C293#292411yescharacteristic, complemented, Sylow
178#2924—2931nomaximal, Sylow
179C2×#117—2931no—
180#433—2931no—
181#433—2931no—
182#433—2931no—
183#433D29311yescharacteristic, complemented
184#432—2931no—
185#432—2931no—
186#431—2931no—
187#431—2931no—
188#424—2931no—
189#424—2931no—
190#407—2931no—
191C2×C22⋊C8—2931no—
192#405—2931no—
193#405—2931no—
194C23×C4—2931no—
195C2×M16—2931no—
196C2×M16—2931no—
197C22×C8—2931no—
198C22×C8—2931no—
199#117—2931no—
200#117—2931no—
201#117—2931no—
202#117—2931no—
203#117—2931no—
204#117—2931no—
205#117—2931no—
206#117C2×D29311yescharacteristic
207C2×C4⋊C4—2931no—
208C2×C4⋊C4—2931no—
209C2×C22⋊C4—2931no—
210C2×C22⋊C4—2931no—
211C2×C42—2931no—
212C2×C42—2931no—
213C4⋊C8—2931no—
214C4⋊C8—2931no—
215C4⋊C8—2931no—
216C4⋊C8—2931no—
217C4⋊C8—2931no—
218C4⋊C8—2931no—
219C4⋊C8C2×D29311yescharacteristic, complemented
220C4⋊C8C2×D29311yescharacteristic, complemented
221C22⋊C8—2931no—
222C22⋊C8—2931no—
223C22⋊C8—2931no—
224C22⋊C8—2931no—
225C22⋊C8—2931no—
226C22⋊C8—2931no—
227C22⋊C8C2×D29311yescharacteristic
228C22⋊C8C2×D29311yescharacteristic
229#97—2931no—
230#97—2931no—
231#97—2931no—
232#97C2×D29311yescharacteristic, complemented
233C4×C8—2931no—
234C4×C8—2931no—
235C4×C8—2931no—
236C4×C8C2×D29311yescharacteristic, complemented
237C24—2931no—
238C22×C4—2931no—
239C22×C4—2931no—
240C22×C4—2931no—
241C22×C4—2931no—
242C22×C4—2931no—
243C22×C4—2931no—
244C22×C4—2931no—
245C22×C4—2931no—
246C22×C4—2931no—
247C22×C4—5862no—
248C22×C4—5862no—
249C22×C4C22×D29311yescharacteristic
250M16—5862no—
251M16—5862no—
252C2×C8—2931no—
253C2×C8—2931no—
254C2×C8—2931no—
255C2×C8—2931no—
256C2×C8—5862no—
257C2×C8—5862no—
258C2×C8C22×D29311yescharacteristic
259C2×C8C22×D29311yescharacteristic
260C2×C8C22×D29311yescharacteristic
261C2×C8C22×D29311yescharacteristic
262C4⋊C4—2931no—
263C4⋊C4—2931no—
264C4⋊C4—2931no—
265C4⋊C4—2931no—
266C4⋊C4—2931no—
267C4⋊C4—2931no—
268C4⋊C4C4×D29311yescharacteristic
269C4⋊C4C4×D29311yescharacteristic
270C22⋊C4—2931no—
271C22⋊C4—2931no—
272C22⋊C4—2931no—
273C22⋊C4—2931no—
274C22⋊C4—2931no—
275C22⋊C4—2931no—
276C22⋊C4C4×D29311yescharacteristic
277C22⋊C4C4×D29311yescharacteristic
278C42—2931no—
279C42—2931no—
280C42—2931no—
281C42—2931no—
282C42—2931no—
283C42—2931no—
284C42C22×D29311yescharacteristic
285C42C22×D29311yescharacteristic
286C23—2931no—
287C23—2931no—
288C23—5862no—
289C23—5862no—
290C23—11721no—
291C23C2×C4×D29311yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—2931no—
295C2×C4—2932no—
296C2×C4—2932no—
297C2×C4—2931no—
298C2×C4—2931no—
299C2×C4—2931no—
300C2×C4—2931no—
301C2×C4—2931no—
302C2×C4—5862no—
303C2×C4—5862no—
304C2×C4—5862no—
305C2×C4—5862no—
306C2×C4—5862no—
307C2×C4—5861no—
308C2×C4—5861no—
309C2×C4—11721no—
310C2×C4—11721no—
311C2×C4C2×C4×D29311yescharacteristic
312C2×C4C2×C4×D29311yescharacteristic
313C2×C4C2×C4×D29311yescharacteristic
314C2×C4C2×C4×D29311yescharacteristic
315C2×C4C2×C4×D29311yescharacteristic
316C2×C4C23×D29311yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8—21no—
321C8—5861no—
322C8—5861no—
323C8—5861no—
324C8—5861no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—2932no—
329C22—2932no—
330C22—5861no—
331C22—5861no—
332C22—5861no—
333C22—5861no—
334C22—11724no—
335C22C22×C4×D29311yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—2932no—
342C4—5861no—
343C4—5861no—
344C4—5861no—
345C4—5861no—
346C4—5861no—
347C4#41×D29311yescharacteristic
348C4#41×D29311yescharacteristic
349C2—41no—
350C2—5862no—
351C2—5862no—
352C2#117×D29311yescharacteristic
353C2#131×D29311yescharacteristic
354C2#3403689411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D293
commutator, socleC22×C293C23×C4
Fitting#433×C293C2
prime radicalC23×D293C2×C4
cosocleC2×C4×C293C24
hypercenter#433D293
hypocenterC293#2924
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C2×C4 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #34036190C2semidirect
3. #34036187C2semidirect
4. #34036187C2semidirect
5. #34036185C2semidirect
6. #34036184C2semidirect
7. #34036181C2semidirect
8. #34036180C2semidirect
9. #34036154C2semidirect
10. #34036154C2semidirect
13. #34036086C2semidirect
14. #34036083C2semidirect
15. #433×C293C2semidirect
34. C4⋊#14556873C22semidirect
35. C4⋊#14556873C22semidirect
36. #22627553C22semidirect
37. #22627553C22semidirect
38. #22627553C22semidirect
39. #22627553C22semidirect
46. #22627535C22semidirect
47. #22627534C22semidirect
48. #22627534C22semidirect
49. C4×#14556873C22semidirect
50. C8×Dic293C22semidirect
51. C8×Dic293C22semidirect
53. C4⋊C8×C293C22semidirect
54. C4⋊C8×C293C22semidirect
57. #97×C293C22semidirect
58. C4×C8×C293C22semidirect
177. C293#2924semidirect
183. #433D293semidirect
219. C4⋊C8C2×D293semidirect
220. C4⋊C8C2×D293semidirect
232. #97C2×D293semidirect
236. C4×C8C2×D293semidirect

Maximal subgroups

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

subgroupindex
#117×D2932
#340361902
#340361872
#340361852
#340361842
#340361812
#340361802
#340361542
#340360912
C22⋊C8×D2932
#340360862
#340360832
#433×C2932
#2924293