Finite Group Databasebeta

← #49170706

Subgroups — #49170706

Order 37504.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036843C211yesmaximal, characteristic, complemented
2#34036778C211yesmaximal, characteristic, complemented
3#34036478C211yesmaximal, characteristic, complemented
4#34036471C211yesmaximal, characteristic, complemented
5#34036469C211yesmaximal, characteristic, complemented
6#34036417C211yesmaximal, characteristic, complemented
7#34036356C211yesmaximal, characteristic, complemented
8#34036355C211yesmaximal, characteristic, complemented
9#34036332C211yesmaximal, characteristic, complemented
10#34036271C211yesmaximal, characteristic, complemented
11D8×Dic293C211yesmaximal, characteristic, complemented
12#34036192C211yesmaximal, characteristic, complemented
13#34036125C211yesmaximal, characteristic, complemented
14#34036122C211yesmaximal, characteristic, complemented
15#449×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic
17C2×#17989790C2211yescharacteristic
18C22×#14556873C2211yescharacteristic
19C2×C8×D293C2211yescharacteristic
20#22627623C2211yescharacteristic
21#22627622C2211yescharacteristic
22#22627611—21no—
23#22627610—21no—
24#22627607—21no—
25#22627605—21no—
26#22627603C2211yescharacteristic
27#22627600C2211yescharacteristic
28#22627596—21no—
29#22627596—21no—
30#22627595C2211yescharacteristic
31D4×Dic293C2211yescharacteristic
32D4×Dic293C2211yescharacteristic
33C4×C22⋊D293C2211yescharacteristic
34#22627583C2211yescharacteristic
35#22627582C2211yescharacteristic
36#22627580—21no—
37C2×#17989781—21no—
38#22627558C2211yescharacteristic
39#22627556C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627548C2211yescharacteristic
45#22627548C2211yescharacteristic
46#22627547C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627545C2211yescharacteristic
49#22627545C2211yescharacteristic
50#22627536C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C2×#41×C293C2211yescharacteristic
53C2×SD16×C293C2211yescharacteristic
54C2×D8×C293C2211yescharacteristic
55#121×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C22⋊C8×C293C2211yescharacteristic
59#17989801—22no—
60#17989801—41no—
61C2×Dic586—21no—
62C2×Dic586C2311yescharacteristic
63C2×C22⋊D293—21no—
64C2×C22⋊D293—21no—
65C2×C22⋊D293D411yescharacteristic
66C22×Dic293—21no—
67C22×Dic293—21no—
68C22×Dic293—21no—
69C2×C4×D293C2311yescharacteristic
70#17989790—41no—
71C2×#14556873—41no—
72C2×#14556873C2311yescharacteristic
73C2×#14556873C2311yescharacteristic
74C8×D293—41no—
75C4⋊Dic293C2311yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77C4⋊Dic293C2311yescharacteristic
78#17989781—21no—
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781D411yescharacteristic
84C22⋊Dic293—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88C22⋊Dic293—21no—
89C22⋊Dic293D411yescharacteristic
90#17989779—21no—
91#17989779—21no—
92#17989779D411yescharacteristic
93C4×Dic293—21no—
94C4×Dic293—21no—
95C4×Dic293C2311yescharacteristic
96#41×C293—22no—
97#41×C293—41no—
98C2×Q8×C293C2311yescharacteristic
99C2×D4×C293—21no—
100C2×D4×C293—21no—
101C2×D4×C293C2311yescharacteristic
102C2×D4×C293C2311yescharacteristic
103C22×C4×C293—21no—
104C22×C4×C293C2311yescharacteristic
105SD16×C293—41no—
106D8×C293—22no—
107C2×C8×C293C2311yescharacteristic
108C2×C8×C293C2311yescharacteristic
109C4⋊C4×C293C2311yescharacteristic
110C22⋊C4×C293—21no—
111C22×D293C2×D411yescharacteristic
112Dic586—21no—
113Dic586—21no—
114Dic586—81no—
115C22⋊D293—22no—
116C22⋊D293—42no—
117C22⋊D293—81no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293—21no—
121C2×Dic293—21no—
122C2×Dic293—42no—
123C2×Dic293—42no—
124C2×Dic293—42no—
125C2×Dic293C2×D411yescharacteristic
126C2×Dic293C2×D411yescharacteristic
127C2×Dic293C2×D411yescharacteristic
128C4×D293—21no—
129C4×D293—21no—
130#14556873—21no—
131#14556873—21no—
132C23×C293—21no—
133C23×C293—21no—
134C23×C293C2×D411yescharacteristic
135Q8×C293—21no—
136Q8×C293—21no—
137D4×C293—21no—
138D4×C293—21no—
139D4×C293—21no—
140D4×C293—42no—
141D4×C293—81no—
142D4×C293#4112yes—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293—21no—
146C2×C4×C293—21no—
147C2×C4×C293—42no—
148C2×C4×C293C2×D411yescharacteristic
149C2×C4×C293C2411yescharacteristic
150C8×C293—21no—
151C8×C293—21no—
152C22×C293—21no—
153C22×C293—22no—
154C22×C293—21no—
155C22×C293—21no—
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—
165C4×C293—21no—
166C4×C293—41no—
167C4×C293—41no—
168C4×C293C2×#4111yescharacteristic
169C4×C293H(5,𝔽2)11yescharacteristic
170Dic293—21no—
171Dic293—21no—
172Dic293—41no—
173Dic293—41no—
174Dic293—41no—
175Dic293—41no—
176Dic293#13512yes—
177C2×C293—41no—
178C2×C293—42no—
179C2×C293—81no—
180C2×C293#54611yescharacteristic
181C2×C293C2×#13511yescharacteristic
182C2×C293#57711yescharacteristic
183D293—41no—
184C293#330311yescharacteristic, complemented, Sylow
185#3303—2931nomaximal, Sylow
186#555—2931no—
187#547—2931no—
188#487—2931no—
189#485—2931no—
190#485—2931no—
191#476—2931no—
192#465—2931no—
193#465—2931no—
194#461—2931no—
195#449—2931no—
196#449D29311yescharacteristic, complemented
197C4×D8—2931no—
198C8×D4—2931no—
199#416—2931no—
200#416—2931no—
201C2×#41—2931no—
202C2×#41C2×D29311yescharacteristic
203C2×SD16—2931no—
204C2×SD16C2×D29311yescharacteristic
205C2×D8C2×D29311yescharacteristic
206C22×C8—2931no—
207C22×C8—2931no—
208C4⋊Q8—2931no—
209C4⋊Q8—2931no—
210#124—5861no—
211#124—5861no—
212#123—5861no—
213#123—5861no—
214C22⋊Q8—2931no—
215C22⋊Q8—2931no—
216#121—2931no—
217#121—5861no—
218#121—5861no—
219#121C2×D29311yescharacteristic
220C4×D4—2931no—
221C4×D4—2931no—
222C4×D4—2931no—
223#117—2931no—
224#117—2931no—
225#117—5861no—
226C2×C4⋊C4—5861no—
227#107—2931no—
228#106—2931no—
229#106—2931no—
230C4⋊C8—2931no—
231#103—2931no—
232#103—2931no—
233#103—2931no—
234#103—2931no—
235#103—2931no—
236#103C2×D29311yescharacteristic
237#102—2931no—
238#102—2931no—
239#102—2931no—
240#102C2×D29311yescharacteristic
241C22⋊C8—2931no—
242C22⋊C8C2×D29311yescharacteristic
243C4×C8—2931no—
244#41—22no—
245#41—41no—
246#41—5862no—
247#41—11721no—
248C2×Q8—2931no—
249C2×Q8—5861no—
250C2×Q8C22×D29311yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—2931no—
254C2×D4—5861no—
255C2×D4—5861no—
256C2×D4C22×D29311yescharacteristic
257C2×D4C22×D29311yescharacteristic
258C22×C4—21no—
259C22×C4—2931no—
260C22×C4—5861no—
261C22×C4—5861no—
262C22×C4—5861no—
263C22×C4C22×D29311yescharacteristic
264SD16—41no—
265SD16—11721no—
266D8—22no—
267C2×C8—2931no—
268C2×C8—2931no—
269C2×C8—11721no—
270C2×C8—11721no—
271C2×C8C22×D29311yescharacteristic
272C2×C8C22×D29311yescharacteristic
273C4⋊C4—2931no—
274C4⋊C4—2931no—
275C4⋊C4—2931no—
276C4⋊C4—2931no—
277C4⋊C4—5861no—
278C4⋊C4—5861no—
279C4⋊C4—5861no—
280C4⋊C4—5861no—
281C4⋊C4—5861no—
282C4⋊C4C22×D29311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—2931no—
285C22⋊C4—2931no—
286C22⋊C4—5861no—
287C22⋊C4—5861no—
288C22⋊C4—5861no—
289C22⋊C4—5861no—
290C22⋊C4—5861no—
291C22⋊C4—5861no—
292C22⋊C4—5861no—
293C42—2931no—
294C42—5861no—
295C42—5861no—
296C23—21no—
297C23—21no—
298C23—2931no—
299C23D4×D29311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—23441no—
303Q8—5861no—
304Q8—5861no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—23441no—
311D4—5862no—
312D4—11722no—
313D4#1798980112yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—2931no—
320C2×C4—2931no—
321C2×C4—2931no—
322C2×C4—5861no—
323C2×C4—5861no—
324C2×C4—5861no—
325C2×C4—5861no—
326C2×C4—5861no—
327C2×C4—5861no—
328C2×C4—11722no—
329C2×C4—11722no—
330C2×C4—11722no—
331C2×C4D4×D29311yescharacteristic
332C2×C4C23×D29311yescharacteristic
333C8—21no—
334C8—21no—
335C8—5861no—
336C8—5861no—
337C22—21no—
338C22—22no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—5861no—
347C22—5861no—
348C22—5861no—
349C22C2×D4×D29311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—2932no—
354C4—5861no—
355C4—5861no—
356C4—11721no—
357C4—11721no—
358C4—11721no—
359C4—11721no—
360C4C2×#1798980111yescharacteristic
361C4#2262766911yescharacteristic
362C2—41no—
363C2—42no—
364C2—81no—
365C2—11721no—
366C2#3403676611yescharacteristic
367C2#135×D29311yescharacteristic
368C2#3403693911yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#449×C293C2
socleC22×C293C22×D4
hypercenter#449D293
hypocenterC293#3303
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #34036843C2semidirect
2. #34036778C2semidirect
3. #34036478C2semidirect
4. #34036471C2semidirect
5. #34036469C2semidirect
6. #34036417C2semidirect
7. #34036356C2semidirect
8. #34036355C2semidirect
9. #34036332C2semidirect
10. #34036271C2semidirect
11. D8×Dic293C2semidirect
12. #34036192C2semidirect
13. #34036125C2semidirect
14. #34036122C2semidirect
15. #449×C293C2semidirect
184. C293#3303semidirect
196. #449D293semidirect

Maximal subgroups

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

subgroupindex
#340368432
#340367782
#340364782
#340364712
#340364692
#340364172
#340363562
#340363552
#340363322
#340362712
D8×Dic2932
#340361922
#340361252
#340361222
#449×C2932
#3303293