Finite Group Databasebeta

← #49168609

Subgroups — #49168609

Order 37504.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036756C211yesmaximal, characteristic, complemented
2#34036601C211yesmaximal, characteristic
3#34036432C211yesmaximal, characteristic, complemented
4#34036430C211yesmaximal, characteristic, complemented
5#34036429C211yesmaximal, characteristic, complemented
6#34036427C211yesmaximal, characteristic, complemented
7#34036417C211yesmaximal, characteristic, complemented
8#34036416C211yesmaximal, characteristic, complemented
9#34036408C211yesmaximal, characteristic, complemented
10#34036170C211yesmaximal, characteristic, complemented
11#34036166C211yesmaximal, characteristic, complemented
12#34036154C211yesmaximal, characteristic, complemented
13#34036132C211yesmaximal, characteristic
14#102×D293C211yesmaximal, characteristic
15#474×C293C211yesmaximal, characteristic, complemented
16C2×D4×D293C2211yescharacteristic
17C2×#17989785C2211yescharacteristic
18C2×C8×D293C2211yescharacteristic
19#22627623C2211yescharacteristic, complemented
20#22627622—21no—
21#22627616C2211yescharacteristic, complemented
22#22627615C2211yescharacteristic, complemented
23#22627614—21no—
24#22627602—21no—
25#22627600—21no—
26C4×D1172C2211yescharacteristic
27D4×Dic293C2211yescharacteristic
28#22627586C2211yescharacteristic
29C4×C22⋊D293—21no—
30#22627584—21no—
31#22627582C2211yescharacteristic
32#22627582C2211yescharacteristic
33#22627581C2211yescharacteristic
34C4⋊C4×D293C2211yescharacteristic
35C2×#17989779—21no—
36C22⋊C4×D293—21no—
37#22627558C2211yescharacteristic, complemented
38#22627557C2211yescharacteristic, complemented
39#22627556C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41#22627555C2211yescharacteristic, complemented
42#22627555C2211yescharacteristic, complemented
43C4⋊#14556873C2211yescharacteristic, complemented
44#22627553C2211yescharacteristic, complemented
45#22627553C2211yescharacteristic, complemented
46#22627546C2211yescharacteristic
47#22627546C2211yescharacteristic
48#22627545C2211yescharacteristic
49#22627545C2211yescharacteristic
50#22627544C2211yescharacteristic
51#22627544C2211yescharacteristic
52C4⋊Q8×C293C2211yescharacteristic, complemented
53C4×D4×C293C2211yescharacteristic
54#107×C293C2211yescharacteristic, complemented
55#107×C293C2211yescharacteristic, complemented
56C4⋊C8×C293C2211yescharacteristic, complemented
57#102×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59C23×D293—21no—
60C2×Dic586—21no—
61C2×D1172C2311yescharacteristic
62C2×C22⋊D293—21no—
63D4×D293—22no—
64D4×D293Q814yescomplemented
65C22×Dic293—21no—
66C2×C4×D293—21no—
67C2×C4×D293—21no—
68C2×C4×D293—21no—
69C2×C4×D293C2311yescharacteristic
70#17989785—22no—
71C2×#14556873C2311yescharacteristic
72C2×#14556873C2311yescharacteristic
73C8×D293—22no—
74C4⋊Dic293—21no—
75C4⋊Dic293C2311yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77C4⋊Dic293C2311yescharacteristic
78#17989781—21no—
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781D411yescharacteristic
84#17989781D411yescharacteristic
85C22⋊Dic293—21no—
86#17989779—21no—
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779D411yescharacteristic
91#17989779D411yescharacteristic
92C4×Dic293—21no—
93C4×Dic293—21no—
94C4×Dic293C2311yescharacteristic
95C2×Q8×C293—21no—
96C2×D4×C293C2311yescharacteristic
97C22×C4×C293—21no—
98C2×C8×C293C2311yescharacteristic
99C2×C8×C293C2311yescharacteristic
100C4⋊C4×C293—21no—
101C4⋊C4×C293C2311yescharacteristic
102C4⋊C4×C293C2311yescharacteristic
103C4⋊C4×C293C2311yescharacteristic
104C22⋊C4×C293—21no—
105C42×C293C2311yescharacteristic
106C22×D293—21no—
107C22×D293—24no—
108C22×D293—81no—
109C22×D293—81no—
110C22×D293C2×D411yescharacteristic
111Dic586—81no—
112D1172—21no—
113D1172C2×Q812yes—
114C22⋊D293—24no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—21no—
118C2×Dic293—81no—
119C2×Dic293C2×D411yescharacteristic
120C2×Dic293C2×D411yescharacteristic
121C2×Dic293C2×D411yescharacteristic
122C4×D293—81no—
123C4×D293—81no—
124C4×D293—81no—
125C4×D293C2×Q812yes—
126C4×D293#4112yes—
127#14556873—21no—
128#14556873—21no—
129C23×C293—21no—
130Q8×C293—81no—
131D4×C293—21no—
132D4×C293C2×Q812yes—
133C2×C4×C293—21no—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—81no—
137C2×C4×C293C2×D411yescharacteristic
138C2×C4×C293C2×D411yescharacteristic
139C2×C4×C293C2411yescharacteristic
140C8×C293—21no—
141C8×C293—21no—
142C22×C293—22no—
143C22×C293—41no—
144C22×C293—41no—
145C22×C293C22×D411yescharacteristic
146C2×D293—21no—
147C2×D293—21no—
148C2×D293—22no—
149C2×D293—41no—
150C2×D293—41no—
151C2×D293—84no—
152C2×D293C22⋊Q812yes—
153C4×C293—21no—
154C4×C293—21no—
155C4×C293—41no—
156C4×C293—41no—
157C4×C293—41no—
158C4×C293C22×Q811yescharacteristic
159C4×C293C2×#4111yescharacteristic
160Dic293—21no—
161Dic293—21no—
162Dic293—41no—
163Dic293—41no—
164Dic293—41no—
165Dic293C22⋊Q812yes—
166C2×C293—42no—
167C2×C293C2×C22⋊Q811yescharacteristic
168C2×C293#57611yescharacteristic
169C2×C293#57711yescharacteristic
170D293—22no—
171D293—42no—
172C293#308111yescharacteristic, complemented, Sylow
173#3081—2931nomaximal, Sylow
174#544—2931no—
175#518—2931no—
176#478—2931no—
177#478—2931no—
178#478—2931no—
179#478—2931no—
180#476—2931no—
181#476—2931no—
182#474—2931no—
183#474D29311yescharacteristic, complemented
184#428—2931no—
185#427—2931no—
186#424—2931no—
187#418—2931no—
188C2×#102—2931no—
189C22×D4—2931no—
190C2×M16—2931no—
191C22×C8—2931no—
192C4⋊Q8—2931no—
193C4⋊Q8—5861no—
194C4⋊Q8C2×D29311yescharacteristic, complemented
195#125—2931no—
196#125—2931no—
197#125—5861no—
198C22⋊Q8—5861no—
199C22⋊Q8—5861no—
200C4×D4—2931no—
201C4×D4—2931no—
202C4×D4—2931no—
203C4×D4—5861no—
204C4×D4—5861no—
205C4×D4C2×D29311yescharacteristic
206#117—2931no—
207#117—2931no—
208#117—2931no—
209C2×C4⋊C4—2931no—
210C2×C22⋊C4—5861no—
211C2×C22⋊C4—5861no—
212#107—2931no—
213#107—2931no—
214#107C2×D29311yescharacteristic, complemented
215#107C2×D29311yescharacteristic, complemented
216#106—2931no—
217#106—2931no—
218#106—2931no—
219#106—2931no—
220C4⋊C8—2931no—
221C4⋊C8—2931no—
222C4⋊C8—2931no—
223C4⋊C8C2×D29311yescharacteristic, complemented
224#102—2931no—
225#102—2931no—
226#102—2931no—
227#102—2931no—
228#102—2931no—
229#102—2931no—
230#102C2×D29311yescharacteristic
231#102C2×D29311yescharacteristic
232C24—5861no—
233C2×Q8—21no—
234C2×Q8—5861no—
235C2×D4—2934no—
236C2×D4—2931no—
237C2×D4—5862no—
238C2×D4—5861no—
239C2×D4C22×D29311yescharacteristic
240C22×C4—21no—
241C22×C4—2931no—
242C22×C4—5861no—
243C22×C4—5861no—
244C22×C4—5861no—
245C22×C4—5861no—
246M16—5862no—
247C2×C8—2931no—
248C2×C8—2931no—
249C2×C8—5862no—
250C2×C8C22×D29311yescharacteristic
251C2×C8C22×D29311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—2931no—
254C4⋊C4—2931no—
255C4⋊C4—2931no—
256C4⋊C4—2931no—
257C4⋊C4—2931no—
258C4⋊C4—5861no—
259C4⋊C4—5861no—
260C4⋊C4—5861no—
261C4⋊C4—5861no—
262C4⋊C4—5861no—
263C4⋊C4—5861no—
264C4⋊C4C22×D29311yescharacteristic
265C4⋊C4C22×D29311yescharacteristic
266C4⋊C4C22×D29311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—2931no—
269C22⋊C4—2931no—
270C22⋊C4—5861no—
271C22⋊C4—5861no—
272C22⋊C4—5861no—
273C22⋊C4—5861no—
274C22⋊C4—5861no—
275C42—2931no—
276C42—5861no—
277C42—5861no—
278C42C22×D29311yescharacteristic
279C23—21no—
280C23—2931no—
281C23—23441no—
282C23—23441no—
283C23—5864no—
284C23—5861no—
285Q8—81no—
286Q8—23441no—
287D4—21no—
288D4—2932no—
289D4—5864no—
290D4—5861no—
291D4Q8×D29312yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—2931no—
297C2×C4—2932no—
298C2×C4—2932no—
299C2×C4—2931no—
300C2×C4—2931no—
301C2×C4—23441no—
302C2×C4—23441no—
303C2×C4—23441no—
304C2×C4—23441no—
305C2×C4—5861no—
306C2×C4—5861no—
307C2×C4—5861no—
308C2×C4D4×D29311yescharacteristic
309C2×C4D4×D29311yescharacteristic
310C2×C4C23×D29311yescharacteristic
311C8—21no—
312C8—21no—
313C8—5861no—
314C8—5861no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—2932no—
319C22—23444no—
320C22—5861no—
321C22—5861no—
322C22—5862no—
323C22—11721no—
324C22—11721no—
325C22C2×D4×D29311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—2932no—
332C4—5861no—
333C4—5861no—
334C4—11721no—
335C4—11721no—
336C4—11721no—
337C4C2×Q8×D29311yescharacteristic
338C4#41×D29311yescharacteristic
339C2—42no—
340C2—5862no—
341C2—11722no—
342C2C22⋊Q8×D29311yescharacteristic
343C2#3403693011yescharacteristic
344C2#3403693811yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#474×C293C2
socleC22×C293C22×D4
prime radicalC2×D4×D293C22
hypercenter#474D293
hypocenterC293#3081
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #34036756C2semidirect
3. #34036432C2semidirect
4. #34036430C2semidirect
5. #34036429C2semidirect
6. #34036427C2semidirect
7. #34036417C2semidirect
8. #34036416C2semidirect
9. #34036408C2semidirect
10. #34036170C2semidirect
11. #34036166C2semidirect
12. #34036154C2semidirect
15. #474×C293C2semidirect
19. #22627623C22semidirect
21. #22627616C22semidirect
22. #22627615C22semidirect
37. #22627558C22semidirect
38. #22627557C22semidirect
39. #22627556C22semidirect
40. #22627555C22semidirect
41. #22627555C22semidirect
42. #22627555C22semidirect
43. C4⋊#14556873C22semidirect
44. #22627553C22semidirect
45. #22627553C22semidirect
52. C4⋊Q8×C293C22semidirect
54. #107×C293C22semidirect
55. #107×C293C22semidirect
56. C4⋊C8×C293C22semidirect
64. D4×D293Q8semidirect
172. C293#3081semidirect
183. #474D293semidirect
194. C4⋊Q8C2×D293semidirect
214. #107C2×D293semidirect
215. #107C2×D293semidirect
223. C4⋊C8C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340367562
#340366012
#340364322
#340364302
#340364292
#340364272
#340364172
#340364162
#340364082
#340361702
#340361662
#340361542
#340361322
#102×D2932
#474×C2932
#3081293