Finite Group Databasebeta

← #49167448

Subgroups — #49167448

Order 37504.

392 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036597C211yesmaximal, characteristic
2#34036190C211yesmaximal, characteristic, complemented
3#34036189C211yesmaximal, characteristic, complemented
4#34036189C211yesmaximal, characteristic, complemented
5#34036184C211yesmaximal, characteristic, complemented
6#34036183C211yesmaximal, characteristic, complemented
7#34036180C211yesmaximal, characteristic, complemented
8#34036179C211yesmaximal, characteristic, complemented
9#34036151C211yesmaximal, characteristic, complemented
10C4⋊C8×D293C211yesmaximal, characteristic, complemented
11#34036094C211yesmaximal, characteristic
12#34036094C211yesmaximal, characteristic
13#34036086C211yesmaximal, characteristic, complemented
14#34036083C211yesmaximal, characteristic, complemented
15#433×C293C211yesmaximal, characteristic, complemented
16C2×#17989802C2211yescharacteristic
17C2×#17989785C2211yescharacteristic
18C2×#17989785C2211yescharacteristic
19C2×C8×D293C2211yescharacteristic
20C2×C8×D293C2211yescharacteristic
21#22627589C411yescharacteristic
22#22627589C411yescharacteristic
23#22627586C411yescharacteristic
24#22627586C411yescharacteristic
25#22627584C411yescharacteristic
26#22627584C411yescharacteristic
27#22627584C411yescharacteristic
28#22627584C411yescharacteristic
29#22627581C2211yescharacteristic
30#22627581C2211yescharacteristic
31C2×C4×Dic293C2211yescharacteristic
32C42×D293C2211yescharacteristic
33C42×D293C2211yescharacteristic
34C4⋊#14556873C2211yescharacteristic
35C4⋊#14556873C2211yescharacteristic
36#22627553C2211yescharacteristic
37#22627553C2211yescharacteristic
38#22627553C2211yescharacteristic
39#22627553C2211yescharacteristic
40C22⋊#14556873C2211yescharacteristic
41C22⋊#14556873C2211yescharacteristic
42#22627536C2211yescharacteristic
43#22627536C2211yescharacteristic
44#22627536C2211yescharacteristic
45#22627536C2211yescharacteristic
46#22627535C2211yescharacteristic
47#22627534C2211yescharacteristic
48#22627534C2211yescharacteristic
49C4×#14556873C2211yescharacteristic
50C8×Dic293C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52#117×C293C2211yescharacteristic
53C4⋊C8×C293C2211yescharacteristic
54C4⋊C8×C293C2211yescharacteristic
55C22⋊C8×C293C2211yescharacteristic
56C22⋊C8×C293C2211yescharacteristic
57#97×C293C2211yescharacteristic
58C4×C8×C293C2211yescharacteristic
59#17989802—22no—
60#17989802—22no—
61C2×Dic586C2×C411yescharacteristic
62C2×D1172C2×C411yescharacteristic
63C2×C22⋊D293C2×C411yescharacteristic
64C2×C22⋊D293C2×C411yescharacteristic
65C22×Dic293C2×C411yescharacteristic
66C22×Dic293C2×C411yescharacteristic
67C2×C4×D293C2×C411yescharacteristic
68C2×C4×D293C2×C411yescharacteristic
69C2×C4×D293C2×C411yescharacteristic
70C2×C4×D293C2×C411yescharacteristic
71C2×C4×D293C2311yescharacteristic
72C2×C4×D293C2311yescharacteristic
73#17989785—22no—
74#17989785—22no—
75C2×#14556873C2311yescharacteristic
76C2×#14556873C2311yescharacteristic
77C2×#14556873C2311yescharacteristic
78C2×#14556873C2311yescharacteristic
79C8×D293—22no—
80C8×D293—22no—
81#17989781C2×C411yescharacteristic
82#17989781C2×C411yescharacteristic
83#17989781C2×C411yescharacteristic
84#17989781C2×C411yescharacteristic
85#17989779C2×C411yescharacteristic
86#17989779C2×C411yescharacteristic
87#17989779C2×C411yescharacteristic
88#17989779C2×C411yescharacteristic
89C4×Dic293C2×C411yescharacteristic
90C4×Dic293C2×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×D293C22×C411yescharacteristic
109C22×D293C22×C411yescharacteristic
110Dic586—22no—
111D1172—22no—
112C22⋊D293—22no—
113C22⋊D293—22no—
114C2×Dic293—22no—
115C2×Dic293—41no—
116C2×Dic293C22×C411yescharacteristic
117C2×Dic293C22×C411yescharacteristic
118C2×Dic293C22×C411yescharacteristic
119C2×Dic293C22×C411yescharacteristic
120C2×Dic293C22×C411yescharacteristic
121C2×Dic293C22×C411yescharacteristic
122C4×D293—21no—
123C4×D293—21no—
124C4×D293—22no—
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—21no—
156C2×D293#11712yes—
157C4×C293—21no—
158C4×C293—21no—
159C4×C293—21no—
160C4×C293—21no—
161C4×C293—21no—
162C4×C293C2×#4111yescharacteristic
163C4×C293C2×#4111yescharacteristic
164Dic293—21no—
165Dic293—21no—
166Dic293—21no—
167Dic293—21no—
168Dic293#11712yes—
169Dic293#13112yes—
170C2×C293—41no—
171C2×C293C2×#11711yescharacteristic
172C2×C293C2×#13111yescharacteristic
173C2×C293#56811yescharacteristic
174D293—22no—
175D293—41no—
176C293#292511yescharacteristic, complemented, Sylow
177#2925—2931nomaximal, Sylow
178C4×#41—2931no—
179#433—2931no—
180#433—2931no—
181#433—2931no—
182#433D29311yescharacteristic, complemented
183#432—2931no—
184#432—2931no—
185#431—2931no—
186#431—2931no—
187#423—2931no—
188C2×C4⋊C8—2931no—
189#408—2931no—
190#408—2931no—
191#405—2931no—
192#405—2931no—
193C2×#41—2931no—
194C2×M16—2931no—
195C2×M16—2931no—
196C22×C8—2931no—
197C22×C8—2931no—
198C4×Q8—2931no—
199C4×Q8—2931no—
200C4×D4—2931no—
201C4×D4—2931no—
202C4×D4—2931no—
203C4×D4—2931no—
204C4×D4—2931no—
205C4×D4—2931no—
206#117—2931no—
207#117—2931no—
208#117C2×D29311yescharacteristic
209C2×C42—2931no—
210C2×C42—2931no—
211C2×C42—2931no—
212C4⋊C8—2931no—
213C4⋊C8—2931no—
214C4⋊C8—2931no—
215C4⋊C8—2931no—
216C4⋊C8—2931no—
217C4⋊C8—2931no—
218C4⋊C8C2×D29311yescharacteristic
219C4⋊C8C2×D29311yescharacteristic
220C22⋊C8—2931no—
221C22⋊C8—2931no—
222C22⋊C8—2931no—
223C22⋊C8—2931no—
224C22⋊C8—2931no—
225C22⋊C8—2931no—
226C22⋊C8C2×D29311yescharacteristic
227C22⋊C8C2×D29311yescharacteristic
228#97—2931no—
229#97—2931no—
230#97—2931no—
231#97C2×D29311yescharacteristic
232C4×C8—2931no—
233C4×C8—2931no—
234C4×C8—2931no—
235C4×C8C2×D29311yescharacteristic
236#41—5862no—
237#41—5862no—
238C2×Q8—2931no—
239C2×D4—2931no—
240C2×D4—2931no—
241C2×D4—2931no—
242C22×C4—2931no—
243C22×C4—2931no—
244C22×C4—2931no—
245C22×C4—2931no—
246C22×C4—2931no—
247C22×C4—2931no—
248C22×C4—2931no—
249C22×C4—2931no—
250C22×C4C22×D29311yescharacteristic
251M16—5862no—
252M16—5862no—
253C2×C8—2931no—
254C2×C8—2931no—
255C2×C8—2931no—
256C2×C8—2931no—
257C2×C8—5862no—
258C2×C8—5862no—
259C2×C8C22×D29311yescharacteristic
260C2×C8C22×D29311yescharacteristic
261C2×C8C22×D29311yescharacteristic
262C2×C8C22×D29311yescharacteristic
263C4⋊C4—2931no—
264C4⋊C4—2931no—
265C4⋊C4—2931no—
266C4⋊C4—2931no—
267C4⋊C4C4×D29311yescharacteristic
268C4⋊C4C4×D29311yescharacteristic
269C22⋊C4—2931no—
270C22⋊C4—2931no—
271C22⋊C4—2931no—
272C22⋊C4—2931no—
273C22⋊C4C4×D29311yescharacteristic
274C22⋊C4C4×D29311yescharacteristic
275C42—2931no—
276C42—2931no—
277C42—2931no—
278C42—2931no—
279C42—2931no—
280C42—2931no—
281C42—2931no—
282C42—2931no—
283C42C22×D29311yescharacteristic
284C42C22×D29311yescharacteristic
285C23—2931no—
286C23—2931no—
287C23C2×C4×D29311yescharacteristic
288Q8—5862no—
289D4—5862no—
290D4—5862no—
291D4—5862no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—2931no—
295C2×C4—2931no—
296C2×C4—2932no—
297C2×C4—2932no—
298C2×C4—2931no—
299C2×C4—2931no—
300C2×C4—2931no—
301C2×C4—2931no—
302C2×C4—5862no—
303C2×C4—5862no—
304C2×C4—5862no—
305C2×C4—5861no—
306C2×C4—5861no—
307C2×C4—11721no—
308C2×C4—11721no—
309C2×C4—11721no—
310C2×C4C2×C4×D29311yescharacteristic
311C2×C4C2×C4×D29311yescharacteristic
312C2×C4C2×C4×D29311yescharacteristic
313C2×C4C2×C4×D29311yescharacteristic
314C2×C4C2×C4×D29311yescharacteristic
315C2×C4C23×D29311yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C8—5861no—
321C8—5861no—
322C8—5861no—
323C8—5861no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—2932no—
328C22—5861no—
329C22—5861no—
330C22—5861no—
331C22—5861no—
332C22—5861no—
333C22C22×C4×D29311yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—2932no—
340C4—2932no—
341C4—5861no—
342C4—5861no—
343C4—5861no—
344C4—5861no—
345C4#41×D29311yescharacteristic
346C4#41×D29311yescharacteristic
347C2—41no—
348C2—5862no—
349C2—11721no—
350C2#117×D29311yescharacteristic
351C2#131×D29311yescharacteristic
352C2#3403689411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D293
commutator, socleC22×C293C23×C4
Fitting#433×C293C2
prime radicalC2×#17989802C22
cosocleC2×C4×C293C24
hypercenter#433D293
hypocenterC293#2925
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. #34036189C2semidirect
4. #34036189C2semidirect
5. #34036184C2semidirect
6. #34036183C2semidirect
7. #34036180C2semidirect
8. #34036179C2semidirect
9. #34036151C2semidirect
10. C4⋊C8×D293C2semidirect
13. #34036086C2semidirect
14. #34036083C2semidirect
15. #433×C293C2semidirect
176. C293#2925semidirect
182. #433D293semidirect

Maximal subgroups

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

subgroupindex
#340365972
#340361902
#340361892
#340361842
#340361832
#340361802
#340361792
#340361512
C4⋊C8×D2932
#340360942
#340360862
#340360832
#433×C2932
#2925293