Finite Group Databasebeta

← #49170742

Subgroups — #49170742

Order 37504.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036780C211yesmaximal, characteristic, complemented
2#34036773C211yesmaximal, characteristic, complemented
3#34036487C211yesmaximal, characteristic, complemented
4#34036459C211yesmaximal, characteristic, complemented
5#34036446C211yesmaximal, characteristic, complemented
6#34036417C211yesmaximal, characteristic, complemented
7#34036381C211yesmaximal, characteristic, complemented
8#34036358C211yesmaximal, characteristic, complemented
9#34036343C211yesmaximal, characteristic, complemented
10#34036275C211yesmaximal, characteristic, complemented
11#34036263C211yesmaximal, characteristic, complemented
12#34036238C211yesmaximal, characteristic, complemented
13#34036200C211yesmaximal, characteristic, complemented
14#34036127C211yesmaximal, characteristic, complemented
15C2×#102×C293C211yesmaximal, characteristic, complemented
16C2×#17989802—21no—
17C2×#17989801C2211yescharacteristic
18C2×#17989791C2211yescharacteristic, complemented
19C2×#17989787C2211yescharacteristic
20C2×#17989787C2211yescharacteristic
21C2×#17989785C2211yescharacteristic, complemented
22#22627623C2211yescharacteristic, complemented
23#22627611C2211yescharacteristic
24#22627609—21no—
25#22627607—21no—
26#22627605—21no—
27#22627603C2211yescharacteristic
28#22627602—21no—
29#22627599C2211yescharacteristic, complemented
30#22627598C2211yescharacteristic
31#22627596—21no—
32#22627595C2211yescharacteristic
33#22627593—21no—
34D4×Dic293C2211yescharacteristic
35#22627586C2211yescharacteristic, complemented
36C4×C22⋊D293C2211yescharacteristic
37C4⋊C4×D293C2211yescharacteristic, complemented
38C2×C22⋊Dic293—21no—
39#22627556C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41#22627555C2211yescharacteristic, complemented
42#22627553C2211yescharacteristic, complemented
43#22627549C2211yescharacteristic, complemented
44#22627547C2211yescharacteristic, complemented
45#22627547C2211yescharacteristic, complemented
46#22627546C2211yescharacteristic, complemented
47#22627545C2211yescharacteristic
48#22627545C2211yescharacteristic
49C22⋊#14556873C2211yescharacteristic
50#22627536C2211yescharacteristic, complemented
51#22627534C2211yescharacteristic, complemented
52C22×D4×C293C2211yescharacteristic
53C22×C8×C293C2211yescharacteristic
54C2×C4⋊C4×C293C2211yescharacteristic
55#102×C293C2211yescharacteristic
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59#17989802—44no—
60#17989801—22no—
61#17989801—41no—
62C2×Dic586—21no—
63C2×Dic586C2311yescharacteristic
64C2×D1172—21no—
65C2×D1172C2311yescharacteristic
66C2×C22⋊D293—21no—
67C2×C22⋊D293—21no—
68C2×C22⋊D293—21no—
69C2×C22⋊D293D411yescharacteristic
70C22×Dic293—21no—
71C22×Dic293—21no—
72C2×C4×D293—21no—
73C2×C4×D293—21no—
74C2×C4×D293C2311yescharacteristic
75#17989791—41no—
76#17989787—22no—
77#17989787—41no—
78#17989785—41no—
79C2×#14556873C2311yescharacteristic
80C2×#14556873C2311yescharacteristic
81C4⋊Dic293C2311yescharacteristic
82C4⋊Dic293C2311yescharacteristic
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86#17989781D411yescharacteristic
87C22⋊Dic293—21no—
88C22⋊Dic293—21no—
89C22⋊Dic293—21no—
90C22⋊Dic293—21no—
91C22⋊Dic293—21no—
92C22⋊Dic293D411yescharacteristic
93#17989779—21no—
94#17989779—21no—
95#17989779—21no—
96#17989779D411yescharacteristic
97C4×Dic293C2311yescharacteristic
98C24×C293—21no—
99C2×D4×C293—22no—
100C2×D4×C293—21no—
101C2×D4×C293—41no—
102C2×D4×C293C2311yescharacteristic
103C2×D4×C293C2311yescharacteristic
104C22×C4×C293—21no—
105C22×C4×C293C2311yescharacteristic
106C2×C8×C293—41no—
107C2×C8×C293C2311yescharacteristic
108C2×C8×C293C2311yescharacteristic
109C4⋊C4×C293—21no—
110C4⋊C4×C293C2311yescharacteristic
111C4⋊C4×C293C2311yescharacteristic
112C22×D293—21no—
113C22×D293C2×D411yescharacteristic
114Dic586—21no—
115Dic586—21no—
116Dic586—42no—
117D1172—21no—
118D1172—21no—
119D1172—42no—
120C22⋊D293—22no—
121C22⋊D293—42no—
122C22⋊D293—42no—
123C22⋊D293—81no—
124C2×Dic293—21no—
125C2×Dic293—21no—
126C2×Dic293—21no—
127C2×Dic293—42no—
128C2×Dic293—81no—
129C2×Dic293C2×D411yescharacteristic
130C2×Dic293C2×D411yescharacteristic
131C2×Dic293C2×D411yescharacteristic
132C4×D293—21no—
133C4×D293—21no—
134C4×D293—42no—
135C4×D293—42no—
136#14556873—21no—
137#14556873—21no—
138C23×C293—21no—
139C23×C293—21no—
140C23×C293—42no—
141C23×C293—42no—
142C23×C293—81no—
143C23×C293C2×D411yescharacteristic
144D4×C293—21no—
145D4×C293—21no—
146D4×C293—21no—
147D4×C293—42no—
148D4×C293#4112yescomplemented
149C2×C4×C293—21no—
150C2×C4×C293—21no—
151C2×C4×C293—21no—
152C2×C4×C293—21no—
153C2×C4×C293—42no—
154C2×C4×C293C2×D411yescharacteristic
155C2×C4×C293C2411yescharacteristic
156C8×C293—21no—
157C8×C293—21no—
158C22×C293—21no—
159C22×C293—21no—
160C22×C293—22no—
161C22×C293—41no—
162C22×C293—41no—
163C22×C293—41no—
164C22×C293—41no—
165C22×C293—41no—
166C22×C293—84no—
167C22×C293AGL(1,ℤ/8)12yes—
168C22×C293C22×D411yescharacteristic
169C2×D293—21no—
170C2×D293—21no—
171C2×D293—21no—
172C2×D293—41no—
173C2×D293—41no—
174C2×D293—41no—
175C4×C293—21no—
176C4×C293—41no—
177C4×C293—41no—
178C4×C293C2×#4111yescharacteristic
179C4×C293H(5,𝔽2)11yescharacteristic
180Dic293—21no—
181Dic293—21no—
182Dic293—21no—
183Dic293—41no—
184Dic293—41no—
185Dic293—41no—
186C2×C293—22no—
187C2×C293—42no—
188C2×C293—81no—
189C2×C293#54611yescharacteristic
190C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C293#57711yescharacteristic
192D293—41no—
193D293—81no—
194C293#330611yescharacteristic, complemented, Sylow
195#3306—2931nomaximal, Sylow
196#547—2931no—
197#546—2931no—
198#489—2931no—
199#483—2931no—
200#481—2931no—
201#476—2931no—
202#469—2931no—
203#465—2931no—
204#463—2931no—
205#449—2931no—
206#447—2931no—
207#442—2931no—
208#435—2931no—
209#417—2931no—
210C2×#102D29311yescharacteristic, complemented
211C2×#41—2931no—
212C2×#41—5861no—
213C22×D4C2×D29311yescharacteristic
214C2×SD16—2931no—
215C2×D8—2931no—
216C2×D8—2931no—
217C2×M16—2931no—
218C22×C8C2×D29311yescharacteristic
219C4⋊Q8—2931no—
220#124—2931no—
221#123—5861no—
222#123—5861no—
223#123—5861no—
224C22⋊Q8—2931no—
225C22⋊Q8—5861no—
226#121—2931no—
227#121—2931no—
228#121—2931no—
229#121—5861no—
230#120—5861no—
231C4×D4—2931no—
232C4×D4—2931no—
233C4×D4—2931no—
234C2×C4⋊C4—2931no—
235C2×C4⋊C4C2×D29311yescharacteristic
236C2×C22⋊C4—5861no—
237#106—2931no—
238#106—2931no—
239#106—2931no—
240C4⋊C8—2931no—
241#103—2931no—
242#103—2931no—
243#103—2931no—
244#102—2931no—
245#102—2931no—
246#102—2931no—
247#102C2×D29311yescharacteristic
248#102C2×D29311yescharacteristic
249#102C2×D29311yescharacteristic
250#102C2×D29311yescharacteristic
251C22⋊C8—2931no—
252C22⋊C8—2931no—
253#97—2931no—
254C24—21no—
255#41—5862no—
256#41—11724no—
257#41—11721no—
258C2×Q8—2931no—
259C2×Q8—5861no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—2931no—
264C2×D4—2931no—
265C2×D4—5861no—
266C2×D4—5861no—
267C2×D4—5861no—
268C2×D4—5861no—
269C2×D4C22×D29311yescharacteristic
270C2×D4C22×D29311yescharacteristic
271C22×C4—21no—
272C22×C4—2931no—
273C22×C4—5861no—
274C22×C4—5861no—
275C22×C4—5861no—
276C22×C4—5861no—
277C22×C4C22×D29311yescharacteristic
278SD16—11721no—
279D8—5862no—
280D8—11721no—
281M16—11721no—
282C2×C8—41no—
283C2×C8—2931no—
284C2×C8—2931no—
285C2×C8C22×D29311yescharacteristic
286C2×C8C22×D29311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—2931no—
289C4⋊C4—2931no—
290C4⋊C4—2931no—
291C4⋊C4—5861no—
292C4⋊C4—5861no—
293C4⋊C4—5861no—
294C4⋊C4C22×D29311yescharacteristic
295C4⋊C4C22×D29311yescharacteristic
296C22⋊C4—2931no—
297C22⋊C4—2931no—
298C22⋊C4—5861no—
299C22⋊C4—5861no—
300C22⋊C4—5861no—
301C22⋊C4—5861no—
302C22⋊C4—5861no—
303C22⋊C4—5861no—
304C22⋊C4—5861no—
305C22⋊C4—5861no—
306C42—2931no—
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—2931no—
313C23—5861no—
314C23D4×D29311yescharacteristic
315Q8—5861no—
316Q8—5861no—
317Q8—11722no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—23441no—
323D4—5862no—
324D4—5861no—
325D4—5861no—
326D4—11722no—
327D4—11722no—
328D4—11722no—
329D4#1798980212yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—2931no—
336C2×C4—2931no—
337C2×C4—2931no—
338C2×C4—23441no—
339C2×C4—5861no—
340C2×C4—5861no—
341C2×C4—5861no—
342C2×C4—5861no—
343C2×C4—5861no—
344C2×C4—11722no—
345C2×C4—11722no—
346C2×C4—11722no—
347C2×C4D4×D29311yescharacteristic
348C2×C4C23×D29311yescharacteristic
349C8—21no—
350C8—21no—
351C8—5861no—
352C8—5861no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—84no—
362C22—5861no—
363C22—5861no—
364C22—5861no—
365C22—11721no—
366C22—11721no—
367C22—11721no—
368C22#2262764812yes—
369C22C2×D4×D29311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—5861no—
374C4—5861no—
375C4—5861no—
376C4—11721no—
377C4—11721no—
378C4—11721no—
379C4C2×#1798980211yescharacteristic
380C4#2262766911yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—23441no—
385C2—11721no—
386C2#3403676911yescharacteristic
387C2C2×#2262764811yescharacteristic
388C2#3403693511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC2×#102×C293C2
socleC22×C293C22×D4
hypercenterC2×#102D293
hypocenterC293#3306
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #34036780C2semidirect
2. #34036773C2semidirect
3. #34036487C2semidirect
4. #34036459C2semidirect
5. #34036446C2semidirect
6. #34036417C2semidirect
7. #34036381C2semidirect
8. #34036358C2semidirect
9. #34036343C2semidirect
10. #34036275C2semidirect
11. #34036263C2semidirect
12. #34036238C2semidirect
13. #34036200C2semidirect
14. #34036127C2semidirect
15. C2×#102×C293C2semidirect
18. C2×#17989791C22semidirect
21. C2×#17989785C22semidirect
22. #22627623C22semidirect
29. #22627599C22semidirect
35. #22627586C22semidirect
37. C4⋊C4×D293C22semidirect
39. #22627556C22semidirect
40. #22627555C22semidirect
41. #22627555C22semidirect
42. #22627553C22semidirect
43. #22627549C22semidirect
44. #22627547C22semidirect
45. #22627547C22semidirect
46. #22627546C22semidirect
50. #22627536C22semidirect
51. #22627534C22semidirect
148. D4×C293#41semidirect
194. C293#3306semidirect
210. C2×#102D293semidirect
329. D4#17989802semidirect

Maximal subgroups

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

subgroupindex
#340367802
#340367732
#340364872
#340364592
#340364462
#340364172
#340363812
#340363582
#340363432
#340362752
#340362632
#340362382
#340362002
#340361272
C2×#102×C2932
#3306293