Finite Group Databasebeta

← #49169036

Subgroups — #49169036

Order 37504.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036737C211yesmaximal, characteristic, complemented
2#34036601C211yesmaximal, characteristic
3#34036472C211yesmaximal, characteristic, complemented
4#34036469C211yesmaximal, characteristic, complemented
5#34036432C211yesmaximal, characteristic, complemented
6#34036427C211yesmaximal, characteristic, complemented
7#34036333C211yesmaximal, characteristic, complemented
8#34036332C211yesmaximal, characteristic, complemented
9#34036281C211yesmaximal, characteristic
10#34036278C211yesmaximal, characteristic
11#34036231C211yesmaximal, characteristic, complemented
12C4×#17989789C211yesmaximal, characteristic, complemented
13C4×#17989790C211yesmaximal, characteristic, complemented
14#34036191C211yesmaximal, characteristic, complemented
15#440×C293C211yesmaximal, characteristic, complemented
16C2×D4×D293C2211yescharacteristic
17C2×#17989791C2211yescharacteristic
18C2×#17989790C2211yescharacteristic
19C2×#17989789C2211yescharacteristic
20#22627622C2211yescharacteristic, complemented
21#22627619—21no—
22#22627618—21no—
23#22627616—21no—
24#22627615C2211yescharacteristic, complemented
25#22627614—21no—
26#22627604C2211yescharacteristic
27#22627600C2211yescharacteristic
28C4×Dic586C2211yescharacteristic, complemented
29C4×D1172C2211yescharacteristic
30D4×Dic293C2211yescharacteristic
31#22627586C2211yescharacteristic
32C4×C22⋊D293—21no—
33#22627584—21no—
34#22627582C2211yescharacteristic
35#22627581C2211yescharacteristic
36C2×#17989779—21no—
37C22⋊C4×D293—21no—
38#22627558C2211yescharacteristic, complemented
39#22627555C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41#22627553C2211yescharacteristic, complemented
42#22627553C2211yescharacteristic, complemented
43#22627549C2211yescharacteristic, complemented
44#22627548C2211yescharacteristic, complemented
45#22627547C2211yescharacteristic, complemented
46#22627546C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627544C2211yescharacteristic
49#22627536C2211yescharacteristic
50#22627536C2211yescharacteristic
51C4×#14556873C2211yescharacteristic, complemented
52C2×SD16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic, complemented
54C4×D4×C293C2211yescharacteristic
55#107×C293C2211yescharacteristic, complemented
56#103×C293C2211yescharacteristic, complemented
57#102×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60C2×Dic586C2311yescharacteristic
61C2×D1172C2311yescharacteristic
62C2×C22⋊D293—21no—
63D4×D293—22no—
64D4×D293—22no—
65C22×Dic293—21no—
66C2×C4×D293—21no—
67C2×C4×D293—21no—
68C2×C4×D293C2311yescharacteristic
69#17989791—22no—
70#17989790—22no—
71#17989789—22no—
72C2×#14556873C2311yescharacteristic
73C2×#14556873C2311yescharacteristic
74C4⋊Dic293—21no—
75C4⋊Dic293—21no—
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#17989779—21no—
91#17989779D411yescharacteristic
92#17989779D411yescharacteristic
93C4×Dic293—21no—
94C4×Dic293—21no—
95C4×Dic293C2311yescharacteristic
96C2×Q8×C293C2311yescharacteristic
97C2×D4×C293C2311yescharacteristic
98C22×C4×C293—21no—
99SD16×C293—22no—
100C2×C8×C293C2311yescharacteristic
101C2×C8×C293C2311yescharacteristic
102C4⋊C4×C293—21no—
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C22⋊C4×C293—21no—
106C42×C293—21no—
107C42×C293C2311yescharacteristic
108C22×D293—21no—
109C22×D293—24no—
110C22×D293—81no—
111C22×D293—81no—
112C22×D293C2×D411yescharacteristic
113Dic586—21no—
114Dic586—21no—
115D1172—21no—
116D1172#4112yes—
117C22⋊D293—24no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293—21no—
121C2×Dic293—81no—
122C2×Dic293C2×D411yescharacteristic
123C2×Dic293C2×D411yescharacteristic
124C2×Dic293C2×D411yescharacteristic
125C4×D293—21no—
126C4×D293—21no—
127C4×D293—81no—
128C4×D293—81no—
129#14556873—21no—
130#14556873—21no—
131C23×C293—21no—
132Q8×C293—21no—
133Q8×C293—21no—
134D4×C293—21no—
135D4×C293#4112yes—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293—21no—
139C2×C4×C293—81no—
140C2×C4×C293C2×D411yescharacteristic
141C2×C4×C293C2×D411yescharacteristic
142C2×C4×C293C2411yescharacteristic
143C8×C293—21no—
144C8×C293—21no—
145C22×C293—22no—
146C22×C293—41no—
147C22×C293—41no—
148C22×C293C22×D411yescharacteristic
149C2×D293—21no—
150C2×D293—22no—
151C2×D293—21no—
152C2×D293—21no—
153C2×D293—41no—
154C2×D293—41no—
155C2×D293—84no—
156C4×C293—21no—
157C4×C293—21no—
158C4×C293—41no—
159C4×C293—41no—
160C4×C293—41no—
161C4×C293C2×#4111yescharacteristic
162C4×C293C2×#4111yescharacteristic
163Dic293—21no—
164Dic293—21no—
165Dic293—21no—
166Dic293—41no—
167Dic293—41no—
168Dic293—41no—
169C2×C293—42no—
170C2×C293#52511yescharacteristic
171C2×C293#57711yescharacteristic
172C2×C293#57711yescharacteristic
173D293—41no—
174D293—42no—
175C293#312311yescharacteristic, complemented, Sylow
176#3123—2931nomaximal, Sylow
177#541—2931no—
178#518—2931no—
179#485—2931no—
180#485—2931no—
181#478—2931no—
182#478—2931no—
183#461—2931no—
184#461—2931no—
185#450—2931no—
186#450—2931no—
187#440—2931no—
188#440D29311yescharacteristic, complemented
189C4×SD16—2931no—
190C4×SD16—2931no—
191#433—2931no—
192C22×D4—2931no—
193C2×SD16—2931no—
194C2×SD16—2931no—
195C2×SD16—2931no—
196C2×SD16C2×D29311yescharacteristic
197C4⋊Q8—2931no—
198#126—5861no—
199#126—5861no—
200#125—2931no—
201#125—5861no—
202#125—5861no—
203C22⋊Q8—2931no—
204C22⋊Q8—2931no—
205C4×Q8—2931no—
206C4×Q8C2×D29311yescharacteristic, complemented
207C4×D4—2931no—
208C4×D4—2931no—
209C4×D4—2931no—
210C4×D4—5861no—
211C4×D4—5861no—
212C4×D4C2×D29311yescharacteristic
213#117—2931no—
214#117—2931no—
215C2×C22⋊C4—5861no—
216C2×C22⋊C4—5861no—
217#107—2931no—
218#107C2×D29311yescharacteristic, complemented
219#106—2931no—
220#106—2931no—
221C4⋊C8—2931no—
222C4⋊C8—2931no—
223#103—2931no—
224#103—2931no—
225#103—2931no—
226#103C2×D29311yescharacteristic, complemented
227#102—2931no—
228#102—2931no—
229#102—2931no—
230#102C2×D29311yescharacteristic
231C22⋊C8—2931no—
232C22⋊C8—2931no—
233#97C2×D29311yescharacteristic, complemented
234C4×C8—2931no—
235C24—5861no—
236C2×Q8—2931no—
237C2×Q8C22×D29311yescharacteristic
238C2×D4—2931no—
239C2×D4—5861no—
240C2×D4—5862no—
241C2×D4—5862no—
242C2×D4C22×D29311yescharacteristic
243C22×C4—21no—
244C22×C4—2931no—
245C22×C4—5861no—
246C22×C4—5861no—
247C22×C4—5861no—
248SD16—22no—
249SD16—5862no—
250SD16—5862no—
251SD16—5862no—
252C2×C8—2931no—
253C2×C8—2931no—
254C2×C8C22×D29311yescharacteristic
255C2×C8C22×D29311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—2931no—
258C4⋊C4—2931no—
259C4⋊C4—2931no—
260C4⋊C4—2931no—
261C4⋊C4—5861no—
262C4⋊C4—5861no—
263C4⋊C4—5861no—
264C4⋊C4—5861no—
265C4⋊C4—5861no—
266C4⋊C4—5861no—
267C4⋊C4—5861no—
268C4⋊C4C22×D29311yescharacteristic
269C4⋊C4C22×D29311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—2931no—
272C22⋊C4—2931no—
273C22⋊C4—5861no—
274C22⋊C4—5861no—
275C22⋊C4—5861no—
276C22⋊C4—5861no—
277C22⋊C4—5861no—
278C22⋊C4—5861no—
279C42—21no—
280C42—2931no—
281C42—5861no—
282C42—5861no—
283C42C22×D29311yescharacteristic
284C23—21no—
285C23—2931no—
286C23—23441no—
287C23—23441no—
288C23—5864no—
289C23—5861no—
290Q8—21no—
291Q8—21no—
292Q8—5861no—
293Q8—5861no—
294D4—21no—
295D4—2932no—
296D4—5864no—
297D4—5861no—
298D4#1798980212yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—2931no—
304C2×C4—2931no—
305C2×C4—2931no—
306C2×C4—23441no—
307C2×C4—23441no—
308C2×C4—23441no—
309C2×C4—5861no—
310C2×C4—5861no—
311C2×C4—5861no—
312C2×C4—5861no—
313C2×C4—5861no—
314C2×C4D4×D29311yescharacteristic
315C2×C4D4×D29311yescharacteristic
316C2×C4C23×D29311yescharacteristic
317C8—21no—
318C8—21no—
319C8—5861no—
320C8—5861no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—23444no—
325C22—5861no—
326C22—5862no—
327C22—5861no—
328C22—5861no—
329C22—11721no—
330C22—11721no—
331C22C2×D4×D29311yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—5861no—
338C4—5861no—
339C4—5861no—
340C4—11721no—
341C4—11721no—
342C4—11721no—
343C4#41×D29311yescharacteristic
344C4C2×#1798980211yescharacteristic
345C2—42no—
346C2—11721no—
347C2—11722no—
348C2#3403663811yescharacteristic
349C2#3403693811yescharacteristic
350C2#3403693911yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#440×C293C2
socleC22×C293C22×D4
prime radicalC2×D4×D293C22
hypercenter#440D293
hypocenterC293#3123
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. #34036737C2semidirect
3. #34036472C2semidirect
4. #34036469C2semidirect
5. #34036432C2semidirect
6. #34036427C2semidirect
7. #34036333C2semidirect
8. #34036332C2semidirect
11. #34036231C2semidirect
12. C4×#17989789C2semidirect
13. C4×#17989790C2semidirect
14. #34036191C2semidirect
15. #440×C293C2semidirect
20. #22627622C22semidirect
24. #22627615C22semidirect
28. C4×Dic586C22semidirect
38. #22627558C22semidirect
39. #22627555C22semidirect
40. #22627555C22semidirect
41. #22627553C22semidirect
42. #22627553C22semidirect
43. #22627549C22semidirect
44. #22627548C22semidirect
45. #22627547C22semidirect
51. C4×#14556873C22semidirect
53. C4×Q8×C293C22semidirect
55. #107×C293C22semidirect
56. #103×C293C22semidirect
58. #97×C293C22semidirect
175. C293#3123semidirect
188. #440D293semidirect
206. C4×Q8C2×D293semidirect
218. #107C2×D293semidirect
226. #103C2×D293semidirect
233. #97C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340367372
#340366012
#340364722
#340364692
#340364322
#340364272
#340363332
#340363322
#340362812
#340362782
#340362312
C4×#179897892
C4×#179897902
#340361912
#440×C2932
#3123293