Finite Group Databasebeta

← #49170640

Subgroups — #49170640

Order 37504.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036829C211yesmaximal, characteristic, complemented
2#34036774C211yesmaximal, characteristic, complemented
3#34036484C211yesmaximal, characteristic, complemented
4#34036466C211yesmaximal, characteristic, complemented
5#34036456C211yesmaximal, characteristic, complemented
6#34036429C211yesmaximal, characteristic, complemented
7#34036364C211yesmaximal, characteristic, complemented
8#34036357C211yesmaximal, characteristic, complemented
9#34036344C211yesmaximal, characteristic, complemented
10#34036271C211yesmaximal, characteristic, complemented
11#34036261C211yesmaximal, characteristic, complemented
12C8×D1172C211yesmaximal, characteristic, complemented
13#34036122C211yesmaximal, characteristic, complemented
14#102×D293C211yesmaximal, characteristic, complemented
15C4×D8×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic
17C2×D4×D293C2211yescharacteristic
18C2×#17989790C2211yescharacteristic, complemented
19C2×#17989787C2211yescharacteristic
20C2×C8×D293C2211yescharacteristic
21C2×C8×D293C2211yescharacteristic, complemented
22#22627617—21no—
23#22627616C2211yescharacteristic, complemented
24#22627612C2211yescharacteristic
25#22627608—21no—
26#22627607—21no—
27#22627604C2211yescharacteristic
28#22627599C2211yescharacteristic
29#22627598—21no—
30#22627597—21no—
31#22627595C2211yescharacteristic
32#22627595C2211yescharacteristic, complemented
33#22627594—21no—
34C4×D1172C2211yescharacteristic
35C4×C22⋊D293—21no—
36#22627582C2211yescharacteristic, complemented
37C4⋊C4×D293C2211yescharacteristic
38C2×#17989779—21no—
39#22627557C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41C4⋊#14556873C2211yescharacteristic, complemented
42#22627549C2211yescharacteristic, complemented
43#22627549C2211yescharacteristic, complemented
44#22627547C2211yescharacteristic, complemented
45#22627546C2211yescharacteristic
46#22627546C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627545C2211yescharacteristic
49#22627544C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627536C2211yescharacteristic, complemented
52C2×D8×C293C2211yescharacteristic
53C4×D4×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic, complemented
55#107×C293C2211yescharacteristic, complemented
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic, complemented
58C4×C8×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60#17989801—22no—
61#17989801—41no—
62C2×Dic586C2311yescharacteristic
63C2×D1172—21no—
64C2×D1172D411yescharacteristic
65C2×D1172C2311yescharacteristic
66C2×C22⋊D293—21no—
67C2×C22⋊D293—21no—
68C2×C22⋊D293—21no—
69C2×C22⋊D293—21no—
70D4×D293—22no—
71D4×D293—41no—
72C22×Dic293—21no—
73C2×C4×D293—21no—
74C2×C4×D293C2311yescharacteristic
75C2×C4×D293C2311yescharacteristic
76#17989790—41no—
77#17989787—41no—
78C2×#14556873C2311yescharacteristic
79C2×#14556873C2311yescharacteristic
80C8×D293—41no—
81C8×D293—41no—
82C4⋊Dic293—21no—
83C4⋊Dic293D411yescharacteristic
84C4⋊Dic293C2311yescharacteristic
85C4⋊Dic293C2311yescharacteristic
86#17989781—21no—
87#17989781—21no—
88#17989781—21no—
89C22⋊Dic293—21no—
90C22⋊Dic293—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779—21no—
95#17989779—21no—
96#17989779D411yescharacteristic
97#17989779D411yescharacteristic
98C4×Dic293—21no—
99C2×D4×C293C2311yescharacteristic
100C2×D4×C293C2311yescharacteristic
101C22×C4×C293—21no—
102C22×C4×C293—21no—
103D8×C293—22no—
104C2×C8×C293C2311yescharacteristic
105C2×C8×C293C2311yescharacteristic
106C4⋊C4×C293C2311yescharacteristic
107C4⋊C4×C293C2311yescharacteristic
108C22⋊C4×C293—21no—
109C22⋊C4×C293—21no—
110C42×C293C2311yescharacteristic
111C22×D293—21no—
112C22×D293—42no—
113C22×D293—42no—
114C22×D293—81no—
115C22×D293C2×D411yescharacteristic
116C22×D293C2×D411yescharacteristic
117Dic586—21no—
118Dic586—21no—
119D1172—22no—
120D1172—21no—
121D1172—21no—
122D1172—81no—
123C22⋊D293—42no—
124C22⋊D293—42no—
125C22⋊D293—42no—
126C22⋊D293—81no—
127C2×Dic293—21no—
128C2×Dic293—21no—
129C2×Dic293—21no—
130C2×Dic293—42no—
131C2×Dic293C2×D411yescharacteristic
132C2×Dic293C2×D411yescharacteristic
133C4×D293—21no—
134C4×D293—21no—
135C4×D293—21no—
136C4×D293—21no—
137C4×D293—81no—
138#14556873—21no—
139#14556873—21no—
140C23×C293—21no—
141C23×C293—21no—
142D4×C293—21no—
143D4×C293—21no—
144D4×C293—21no—
145D4×C293#4112yes—
146C2×C4×C293—21no—
147C2×C4×C293—21no—
148C2×C4×C293—81no—
149C2×C4×C293—81no—
150C2×C4×C293C2×D411yescharacteristic
151C2×C4×C293C2×D411yescharacteristic
152C2×C4×C293C2411yescharacteristic
153C8×C293—21no—
154C8×C293—21no—
155C22×C293—22no—
156C22×C293—41no—
157C22×C293—41no—
158C22×C293—41no—
159C22×C293—41no—
160C22×C293—41no—
161C22×C293C22×D411yescharacteristic
162C2×D293—21no—
163C2×D293—21no—
164C2×D293—21no—
165C2×D293—21no—
166C2×D293—21no—
167C2×D293—41no—
168C2×D293—41no—
169C2×D293—41no—
170C2×D293—84no—
171C2×D293#13512yes—
172C4×C293—21no—
173C4×C293—21no—
174C4×C293—41no—
175C4×C293—41no—
176C4×C293C2×#4111yescharacteristic
177C4×C293H(5,𝔽2)11yescharacteristic
178Dic293—21no—
179Dic293—21no—
180Dic293—41no—
181Dic293—41no—
182Dic293—41no—
183C2×C293—42no—
184C2×C293—81no—
185C2×C293#54611yescharacteristic
186C2×C293C2×#13511yescharacteristic
187C2×C293#57611yescharacteristic
188D293—22no—
189D293—41no—
190D293—81no—
191C293#329711yescharacteristic, complemented, Sylow
192#3297—2931nomaximal, Sylow
193#553—2931no—
194#546—2931no—
195#488—2931no—
196#484—2931no—
197#482—2931no—
198#478—2931no—
199#466—2931no—
200#465—2931no—
201#463—2931no—
202#449—2931no—
203#447—2931no—
204C4×D8D29311yescharacteristic, complemented
205C8×D4—2931no—
206#416—2931no—
207C2×#102—2931no—
208C2×#41—2931no—
209C22×D4—2931no—
210C2×SD16—2931no—
211C2×D8—2931no—
212C2×D8C2×D29311yescharacteristic
213C22×C8—2931no—
214C22×C8—2931no—
215#126—5861no—
216#125—2931no—
217#124—2931no—
218#123—5861no—
219#123—5861no—
220C22⋊Q8—2931no—
221#121—2931no—
222#121—2931no—
223#121—2931no—
224#121—5861no—
225#121—5861no—
226#120—5861no—
227C4×D4—2931no—
228C4×D4—5861no—
229C4×D4C2×D29311yescharacteristic
230C4×D4C2×D29311yescharacteristic, complemented
231#117—2931no—
232C2×C4⋊C4—2931no—
233C2×C22⋊C4—5861no—
234#107—2931no—
235#107C2×D29311yescharacteristic, complemented
236#106—2931no—
237C4⋊C8—2931no—
238#103—2931no—
239#103—2931no—
240#103—2931no—
241#102—2931no—
242#102—2931no—
243#102—2931no—
244#102—2931no—
245#102—2931no—
246#102C2×D29311yescharacteristic
247#102C2×D29311yescharacteristic, complemented
248C22⋊C8—2931no—
249C22⋊C8—2931no—
250C4×C8C2×D29311yescharacteristic, complemented
251C24—5861no—
252#41—5862no—
253#41—11721no—
254C2×Q8—2931no—
255C2×D4—2931no—
256C2×D4—2931no—
257C2×D4—5861no—
258C2×D4—5861no—
259C2×D4—5861no—
260C2×D4—5862no—
261C2×D4—5861no—
262C2×D4—5861no—
263C2×D4—11721no—
264C2×D4C22×D29311yescharacteristic
265C2×D4C22×D29311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—2931no—
269C22×C4—2931no—
270C22×C4—5861no—
271C22×C4—5861no—
272SD16—11721no—
273D8—22no—
274D8—11721no—
275C2×C8—2931no—
276C2×C8—2931no—
277C2×C8—11721no—
278C2×C8—11721no—
279C2×C8C22×D29311yescharacteristic
280C2×C8C22×D29311yescharacteristic
281C4⋊C4—2931no—
282C4⋊C4—2931no—
283C4⋊C4—2931no—
284C4⋊C4—5861no—
285C4⋊C4—5861no—
286C4⋊C4—5861no—
287C4⋊C4—5861no—
288C4⋊C4C22×D29311yescharacteristic
289C4⋊C4C22×D29311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—2931no—
293C22⋊C4—2931no—
294C22⋊C4—5861no—
295C22⋊C4—5861no—
296C22⋊C4—5861no—
297C22⋊C4—5861no—
298C22⋊C4—5861no—
299C22⋊C4—5861no—
300C22⋊C4—5861no—
301C42—5861no—
302C42C22×D29311yescharacteristic
303C23—21no—
304C23—21no—
305C23—2931no—
306C23—2931no—
307C23—23441no—
308C23—5861no—
309C23—11722no—
310C23—11722no—
311Q8—5861no—
312Q8—5861no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—23441no—
317D4—23441no—
318D4—5862no—
319D4—5861no—
320D4—5861no—
321D4—11722no—
322D4—11722no—
323D4—11722no—
324D4#1798980212yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—2931no—
330C2×C4—2931no—
331C2×C4—23441no—
332C2×C4—5861no—
333C2×C4—5861no—
334C2×C4—5861no—
335C2×C4—5861no—
336C2×C4—5861no—
337C2×C4—5861no—
338C2×C4—5861no—
339C2×C4—11722no—
340C2×C4D4×D29311yescharacteristic
341C2×C4D4×D29311yescharacteristic
342C2×C4C23×D29311yescharacteristic
343C8—21no—
344C8—21no—
345C8—5861no—
346C8—5861no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—2932no—
354C22—23444no—
355C22—5861no—
356C22—5861no—
357C22—5861no—
358C22—5861no—
359C22—5861no—
360C22—11721no—
361C22—11721no—
362C22—11721no—
363C22C2×D4×D29311yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—5861no—
369C4—5861no—
370C4—11721no—
371C4—11721no—
372C4—11721no—
373C4C2×#1798980211yescharacteristic
374C4#2262767011yescharacteristic
375C2—42no—
376C2—81no—
377C2—23441no—
378C2—5862no—
379C2—11721no—
380C2#3403677511yescharacteristic
381C2#135×D29311yescharacteristic
382C2#3403693011yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC4×D8×C293C2
socleC22×C293C22×D4
hypercenterC4×D8D293
hypocenterC293#3297
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #34036829C2semidirect
2. #34036774C2semidirect
3. #34036484C2semidirect
4. #34036466C2semidirect
5. #34036456C2semidirect
6. #34036429C2semidirect
7. #34036364C2semidirect
8. #34036357C2semidirect
9. #34036344C2semidirect
10. #34036271C2semidirect
11. #34036261C2semidirect
12. C8×D1172C2semidirect
13. #34036122C2semidirect
14. #102×D293C2semidirect
15. C4×D8×C293C2semidirect
18. C2×#17989790C22semidirect
21. C2×C8×D293C22semidirect
23. #22627616C22semidirect
32. #22627595C22semidirect
36. #22627582C22semidirect
39. #22627557C22semidirect
40. #22627555C22semidirect
41. C4⋊#14556873C22semidirect
42. #22627549C22semidirect
43. #22627549C22semidirect
44. #22627547C22semidirect
51. #22627536C22semidirect
54. C4×D4×C293C22semidirect
55. #107×C293C22semidirect
57. #102×C293C22semidirect
58. C4×C8×C293C22semidirect
191. C293#3297semidirect
204. C4×D8D293semidirect
230. C4×D4C2×D293semidirect
235. #107C2×D293semidirect
247. #102C2×D293semidirect
250. C4×C8C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340368292
#340367742
#340364842
#340364662
#340364562
#340364292
#340363642
#340363572
#340363442
#340362712
#340362612
C8×D11722
#340361222
#102×D2932
C4×D8×C2932
#3297293