Finite Group Databasebeta

← #49169396

Subgroups — #49169396

Order 37504.

362 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#34036750C211yesmaximal, characteristic, complemented
2#34036525C211yesmaximal, characteristic, complemented
3#34036511C211yesmaximal, characteristic, complemented
4#34036491C211yesmaximal, characteristic, complemented
5#34036488C211yesmaximal, characteristic, complemented
6#34036385C211yesmaximal, characteristic, complemented
7#34036380C211yesmaximal, characteristic
8#34036360C211yesmaximal, characteristic, complemented
9#34036356C211yesmaximal, characteristic, complemented
10#34036239C211yesmaximal, characteristic, complemented
11#34036234C211yesmaximal, characteristic, complemented
12C4×#17989789C211yesmaximal, characteristic, complemented
13C4×#17989790C211yesmaximal, characteristic, complemented
14#34036085C211yesmaximal, characteristic, complemented
15#542×C293C211yesmaximal, characteristic, complemented
16C2×#17989792C2211yescharacteristic
17C2×#17989790C2211yescharacteristic
18C2×#17989789C2211yescharacteristic
19C2×#17989787C2211yescharacteristic
20C2×#17989786C2211yescharacteristic
21C22×#14556873C2211yescharacteristic
22#22627624C2211yescharacteristic
23#22627619—21no—
24#22627612C2211yescharacteristic
25#22627610—21no—
26#22627606—21no—
27#22627603C2211yescharacteristic
28#22627602—21no—
29#22627598C2211yescharacteristic
30C4×Dic586C2211yescharacteristic
31C4×D1172C2211yescharacteristic
32#22627555C2211yescharacteristic
33#22627555C2211yescharacteristic
34#22627555C2211yescharacteristic
35#22627555C2211yescharacteristic
36#22627548C2211yescharacteristic
37#22627548C2211yescharacteristic
38#22627547C2211yescharacteristic
39#22627547C2211yescharacteristic
40#22627545C2211yescharacteristic
41#22627545C2211yescharacteristic
42#22627544C2211yescharacteristic
43#22627544C2211yescharacteristic
44#22627535C2211yescharacteristic
45#22627535C2211yescharacteristic
46C4×#14556873C2211yescharacteristic
47C4×#14556873C2211yescharacteristic
48C4⋊Q8×C293C2211yescharacteristic
49#126×C293—21no—
50#124×C293—21no—
51#124×C293C2211yescharacteristic
52#123×C293—21no—
53C22⋊Q8×C293—21no—
54C22⋊Q8×C293C2211yescharacteristic
55#121×C293C2211yescharacteristic
56C4×Q8×C293C2211yescharacteristic
57C4×D4×C293C2211yescharacteristic
58#117×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586C2311yescharacteristic
61C2×D1172C2311yescharacteristic
62C2×C22⋊D293—21no—
63C2×C4×D293—21no—
64#17989792—22no—
65#17989790—22no—
66#17989789—22no—
67#17989787—22no—
68#17989786—22no—
69C2×#14556873—22no—
70C2×#14556873C2311yescharacteristic
71C2×#14556873C2311yescharacteristic
72C2×#14556873C2311yescharacteristic
73C2×#14556873C2311yescharacteristic
74C4⋊Dic293—21no—
75C4⋊Dic293C2311yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77#17989781—21no—
78#17989781—21no—
79C22⋊Dic293—21no—
80#17989779—21no—
81#17989779—21no—
82#17989779—21no—
83#17989779—21no—
84C4×Dic293—21no—
85C2×Q8×C293—21no—
86C2×Q8×C293C2311yescharacteristic
87C2×D4×C293—21no—
88C2×D4×C293C2311yescharacteristic
89C22×C4×C293—21no—
90C22×C4×C293C2311yescharacteristic
91C4⋊C4×C293—21no—
92C4⋊C4×C293—21no—
93C4⋊C4×C293—21no—
94C4⋊C4×C293D411yescharacteristic
95C4⋊C4×C293D411yescharacteristic
96C4⋊C4×C293C2311yescharacteristic
97C4⋊C4×C293C2311yescharacteristic
98C22⋊C4×C293—21no—
99C22⋊C4×C293—21no—
100C22⋊C4×C293—21no—
101C22⋊C4×C293—21no—
102C22⋊C4×C293—21no—
103C22⋊C4×C293D411yescharacteristic
104C22⋊C4×C293D411yescharacteristic
105C42×C293—21no—
106C42×C293C2311yescharacteristic
107C42×C293C2311yescharacteristic
108C22×D293—21no—
109Dic586—21no—
110Dic586—21no—
111Dic586—81no—
112D1172—21no—
113D1172—21no—
114C22⋊D293—81no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—21no—
118C4×D293—81no—
119#14556873—21no—
120#14556873—21no—
121#14556873#4112yes—
122#14556873#4112yes—
123C23×C293—21no—
124C23×C293C2×D411yescharacteristic
125Q8×C293—21no—
126Q8×C293—21no—
127Q8×C293—81no—
128D4×C293—21no—
129D4×C293—21no—
130D4×C293—81no—
131C2×C4×C293—21no—
132C2×C4×C293—21no—
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×C293C2×D411yescharacteristic
140C2×C4×C293C2×D411yescharacteristic
141C2×C4×C293C2×D411yescharacteristic
142C2×C4×C293C2411yescharacteristic
143C22×C293—21no—
144C22×C293—21no—
145C22×C293—21no—
146C22×C293—41no—
147C22×C293—41no—
148C22×C293—41no—
149C22×C293C22×D411yescharacteristic
150C2×D293—41no—
151C2×D293—41no—
152C2×D293—41no—
153C4×C293—21no—
154C4×C293—21no—
155C4×C293—21no—
156C4×C293—21no—
157C4×C293—21no—
158C4×C293—41no—
159C4×C293—41no—
160C4×C293—41no—
161C4×C293C2×#4111yescharacteristic
162C4×C293C2×#4111yescharacteristic
163Dic293—41no—
164Dic293—41no—
165Dic293—41no—
166C2×C293—41no—
167C2×C293—81no—
168C2×C293#53211yescharacteristic
169C2×C293#57711yescharacteristic
170C2×C293#57711yescharacteristic
171D293—81no—
172C293#317311yescharacteristic, complemented, Sylow
173#3173—2931nomaximal, Sylow
174#542—2931no—
175#542D29311yescharacteristic, complemented
176#498—2931no—
177#495—2931no—
178#489—2931no—
179#489—2931no—
180#470—2931no—
181#469—2931no—
182#465—2931no—
183#465—2931no—
184#442—2931no—
185#441—2931no—
186C4×SD16—2931no—
187C4×SD16—2931no—
188#405—2931no—
189C2×Q16—2931no—
190C2×SD16—2931no—
191C2×SD16—2931no—
192C2×D8—2931no—
193C2×M16—2931no—
194C22×C8—2931no—
195C4⋊Q8—2931no—
196C4⋊Q8C2×D29311yescharacteristic
197#126—21no—
198#126—5861no—
199#124—21no—
200#124—2931no—
201#124—5861no—
202#124C2×D29311yescharacteristic
203#123—21no—
204#123—5861no—
205C22⋊Q8—21no—
206C22⋊Q8—2931no—
207C22⋊Q8—5861no—
208C22⋊Q8C2×D29311yescharacteristic
209#121—2931no—
210#121C2×D29311yescharacteristic
211C4×Q8—2931no—
212C4×Q8C2×D29311yescharacteristic
213C4×D4—2931no—
214C4×D4C2×D29311yescharacteristic
215#117C2×D29311yescharacteristic
216#106—2931no—
217#106—2931no—
218#106—2931no—
219#106—2931no—
220#103—2931no—
221#103—2931no—
222#103—2931no—
223#103—2931no—
224#102—2931no—
225#102—2931no—
226#102—2931no—
227#102—2931no—
228#97—2931no—
229#97—2931no—
230C4×C8—2931no—
231C4×C8—2931no—
232C2×Q8—21no—
233C2×Q8—2931no—
234C2×Q8—5861no—
235C2×Q8C22×D29311yescharacteristic
236C2×D4—21no—
237C2×D4—2931no—
238C2×D4—5861no—
239C2×D4C22×D29311yescharacteristic
240C22×C4—21no—
241C22×C4—5861no—
242C22×C4C22×D29311yescharacteristic
243Q16—5862no—
244SD16—5862no—
245SD16—5862no—
246D8—5862no—
247M16—5862no—
248C2×C8—2931no—
249C2×C8—2931no—
250C2×C8—2931no—
251C2×C8—2931no—
252C2×C8—5862no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—2931no—
257C4⋊C4—2931no—
258C4⋊C4—5861no—
259C4⋊C4—5861no—
260C4⋊C4—5861no—
261C4⋊C4C22⋊D29311yescharacteristic
262C4⋊C4C22⋊D29311yescharacteristic
263C4⋊C4C22×D29311yescharacteristic
264C4⋊C4C22×D29311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—5861no—
271C22⋊C4—5861no—
272C22⋊C4—5861no—
273C22⋊C4—5861no—
274C22⋊C4—5861no—
275C22⋊C4C22⋊D29311yescharacteristic
276C22⋊C4C22⋊D29311yescharacteristic
277C42—21no—
278C42—5861no—
279C42C22×D29311yescharacteristic
280C42C22×D29311yescharacteristic
281C23—21no—
282C23—5861no—
283C23C2×C22⋊D29311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—23441no—
288Q8—5861no—
289Q8—5861no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—23441no—
294D4—5861no—
295D4—5861no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—23441no—
303C2×C4—5861no—
304C2×C4—5861no—
305C2×C4—5861no—
306C2×C4C2×C22⋊D29311yescharacteristic
307C2×C4C2×C22⋊D29311yescharacteristic
308C2×C4C2×C22⋊D29311yescharacteristic
309C2×C4C2×C22⋊D29311yescharacteristic
310C2×C4C2×C22⋊D29311yescharacteristic
311C2×C4C23×D29311yescharacteristic
312C8—2932no—
313C8—2932no—
314C8—5861no—
315C8—5861no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—11721no—
323C22—11721no—
324C22—11721no—
325C22C22×C22⋊D29311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—11721no—
335C4—11721no—
336C4—11721no—
337C4#41×D29311yescharacteristic
338C4#41×D29311yescharacteristic
339C2—41no—
340C2—81no—
341C2—23441no—
342C2#3403667511yescharacteristic
343C2#3403693711yescharacteristic
344C2#3403694011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#542×C293C2
socleC22×C293C22×D4
prime radical#34036380C2
hypercenter#542D293
hypocenterC293#3173
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #34036750C2semidirect
2. #34036525C2semidirect
3. #34036511C2semidirect
4. #34036491C2semidirect
5. #34036488C2semidirect
6. #34036385C2semidirect
8. #34036360C2semidirect
9. #34036356C2semidirect
10. #34036239C2semidirect
11. #34036234C2semidirect
12. C4×#17989789C2semidirect
13. C4×#17989790C2semidirect
14. #34036085C2semidirect
15. #542×C293C2semidirect
172. C293#3173semidirect
175. #542D293semidirect

Maximal subgroups

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

subgroupindex
#340367502
#340365252
#340365112
#340364912
#340364882
#340363852
#340363802
#340363602
#340363562
#340362392
#340362342
C4×#179897892
C4×#179897902
#340360852
#542×C2932
#3173293