Finite Group Databasebeta

← #34054848

Subgroups — #34054848

Order 19072.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750177C211yesmaximal, characteristic, complemented
2#23750093C211yesmaximal, characteristic
3#23749966C211yesmaximal, characteristic, complemented
4#23749919C211yesmaximal, characteristic, complemented
5#23749914C211yesmaximal, characteristic, complemented
6#23749834C211yesmaximal, characteristic, complemented
7#23749829C211yesmaximal, characteristic, complemented
8#23749789C211yesmaximal, characteristic
9#23749785C211yesmaximal, characteristic
10#23749731C211yesmaximal, characteristic, complemented
11#23749729C211yesmaximal, characteristic, complemented
12#23749728C211yesmaximal, characteristic, complemented
13#23749724C211yesmaximal, characteristic, complemented
14#23749679C211yesmaximal, characteristic, complemented
15#485×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011909C2211yescharacteristic
23#18011901—21no—
24#18011890C2211yescharacteristic
25#18011888—21no—
26Q8×Dic149C2211yescharacteristic
27#18011876—21no—
28#18011876C2211yescharacteristic
29#18011876C2211yescharacteristic
30#18011876C2211yescharacteristic
31#18011873C2211yescharacteristic
32#18011873C2211yescharacteristic
33#18011871—21no—
34#18011871—21no—
35#18011868—21no—
36#18011867—21no—
37C2×C4×Dic149C2211yescharacteristic
38C42×D149—21no—
39#18011844C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic
51#18011821C2211yescharacteristic
52C22⋊Q8×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558736—22no—
60#14558736—22no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C2×Dic298C2311yescharacteristic
64C2×D596C2311yescharacteristic
65C2×C22⋊D149—21no—
66C22×Dic149D411yescharacteristic
67C22×Dic149D411yescharacteristic
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71Dic596—22no—
72#14558726—22no—
73#14558725—22no—
74#14558723—22no—
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C4⋊Dic149—21no—
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149—21no—
87#14558713—21no—
88#14558713—21no—
89C4×Dic149—21no—
90C4×Dic149—21no—
91C4×Dic149—21no—
92C4×Dic149—21no—
93C4×Dic149D411yescharacteristic
94C4×Dic149D411yescharacteristic
95C4×Dic149C2311yescharacteristic
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149C2311yescharacteristic
98C22×C4×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C4⋊C4×C149—21no—
102C4⋊C4×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C22⋊C4×C149—21no—
106C22⋊C4×C149—21no—
107C42×C149—21no—
108C22×D149—21no—
109Dic298—21no—
110Dic298—21no—
111Dic298—21no—
112Dic298—42no—
113Dic298#4112yes—
114D596—21no—
115D596#4112yes—
116C22⋊D149—24no—
117C2×Dic149—21no—
118C2×Dic149—22no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—41no—
122C2×Dic149C2×D411yescharacteristic
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C4×D149—24no—
127C4×D149—42no—
128C4×D149—42no—
129#11924746—21no—
130#11924746—21no—
131C23×C149C2×D411yescharacteristic
132Q8×C149—21no—
133Q8×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2411yescharacteristic
142C8×C149—21no—
143C8×C149—21no—
144C22×C149—21no—
145C22×C149—21no—
146C22×C149—21no—
147C22×C149C22×D411yescharacteristic
148C2×D149—22no—
149C2×D149—41no—
150C2×D149—41no—
151C4×C149—21no—
152C4×C149—41no—
153C4×C149—41no—
154C4×C149—41no—
155C4×C149—41no—
156C4×C149C2×#4111yescharacteristic
157C4×C149C2×#4111yescharacteristic
158Dic149—22no—
159Dic149—21no—
160Dic149—21no—
161Dic149—21no—
162Dic149—41no—
163Dic149—41no—
164Dic149#13712yes—
165C2×C149—41no—
166C2×C149#52511yescharacteristic
167C2×C149C2×#13711yescharacteristic
168C2×C149#57511yescharacteristic
169D149—42no—
170C149#311611yescharacteristic, complemented, Sylow
171#3116—1491nomaximal, Sylow
172#533—1491no—
173C4×#41—1491no—
174#485—1491no—
175#485D14911yescharacteristic, complemented
176#477—1491no—
177#476—1491no—
178#462—1491no—
179#461—1491no—
180#452—1491no—
181#452—1491no—
182#441—1491no—
183#441—1491no—
184#440—1491no—
185#440—1491no—
186#432—1491no—
187C2×#41—1491no—
188C2×Q16—1491no—
189C2×Q16—1491no—
190C2×SD16—1491no—
191C2×SD16—1491no—
192C4⋊Q8—1491no—
193C4⋊Q8—1491no—
194#125—2981no—
195C22⋊Q8—2981no—
196C22⋊Q8—1491no—
197C22⋊Q8C2×D14911yescharacteristic
198C4×Q8—2981no—
199C4×Q8—1491no—
200C4×Q8—1491no—
201C4×Q8—1491no—
202C4×Q8—1491no—
203C4×D4—2981no—
204C4×D4—2981no—
205C4×D4—1491no—
206C4×D4—1491no—
207#117—2981no—
208#117—2981no—
209#117C2×D14911yescharacteristic
210C2×C42—2981no—
211C2×C42—1491no—
212#107—1491no—
213#107C2×D14911yescharacteristic
214#106—1491no—
215#106C2×D14911yescharacteristic
216C4⋊C8—1491no—
217C4⋊C8—1491no—
218#103—1491no—
219#103—1491no—
220#103—1491no—
221#103—1491no—
222#103C2×D14911yescharacteristic
223#103C2×D14911yescharacteristic
224#102—1491no—
225#102—1491no—
226C22⋊C8—1491no—
227C22⋊C8C2×D14911yescharacteristic
228#97—1491no—
229#97—1491no—
230#41—2982no—
231#41—2982no—
232C2×Q8—2981no—
233C2×Q8—1491no—
234C2×Q8—1491no—
235C2×Q8C22×D14911yescharacteristic
236C2×D4—2981no—
237C2×D4—1491no—
238C22×C4—2981no—
239C22×C4—2981no—
240C22×C4—2981no—
241C22×C4—1491no—
242C22×C4—1491no—
243C22×C4C22×D14911yescharacteristic
244Q16—2982no—
245Q16—2982no—
246SD16—2982no—
247SD16—2982no—
248C2×C8—1491no—
249C2×C8—1491no—
250C2×C8C22×D14911yescharacteristic
251C2×C8C22×D14911yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—2981no—
254C4⋊C4—2981no—
255C4⋊C4—2981no—
256C4⋊C4—2981no—
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—2981no—
260C4⋊C4—2981no—
261C4⋊C4—1491no—
262C4⋊C4C22×D14911yescharacteristic
263C4⋊C4C22×D14911yescharacteristic
264C4⋊C4C22×D14911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—2981no—
268C22⋊C4—2981no—
269C22⋊C4—2981no—
270C42—21no—
271C42—2981no—
272C42—2981no—
273C42—2981no—
274C42—2981no—
275C42—1491no—
276C42—1491no—
277C42—1491no—
278C42—1491no—
279C23—2981no—
280C23D4×D14911yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—2981no—
284Q8—2981no—
285Q8—2981no—
286Q8—5962no—
287Q8—1492no—
288D4—2984no—
289D4—2981no—
290D4—1492no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—2984no—
298C2×C4—2981no—
299C2×C4—2982no—
300C2×C4—2981no—
301C2×C4—2981no—
302C2×C4—5962no—
303C2×C4—5962no—
304C2×C4—5961no—
305C2×C4—1491no—
306C2×C4—1491no—
307C2×C4—1491no—
308C2×C4—1491no—
309C2×C4D4×D14911yescharacteristic
310C2×C4C23×D14911yescharacteristic
311C8—21no—
312C8—21no—
313C8—2981no—
314C8—2981no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—2982no—
319C22—5961no—
320C22—5961no—
321C22C2×D4×D14911yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—2981no—
328C4—2981no—
329C4—2981no—
330C4—2982no—
331C4—5961no—
332C4—5961no—
333C4—1492no—
334C4#41×D14911yescharacteristic
335C4#41×D14911yescharacteristic
336C2—41no—
337C2—5962no—
338C2#2375013311yescharacteristic
339C2#137×D14911yescharacteristic
340C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#485×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558736C22
hypercenter#485D149
hypocenterC149#3116
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #23750177C2semidirect
3. #23749966C2semidirect
4. #23749919C2semidirect
5. #23749914C2semidirect
6. #23749834C2semidirect
7. #23749829C2semidirect
10. #23749731C2semidirect
11. #23749729C2semidirect
12. #23749728C2semidirect
13. #23749724C2semidirect
14. #23749679C2semidirect
15. #485×C149C2semidirect
170. C149#3116semidirect
175. #485D149semidirect

Maximal subgroups

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

subgroupindex
#237501772
#237500932
#237499662
#237499192
#237499142
#237498342
#237498292
#237497892
#237497852
#237497312
#237497292
#237497282
#237497242
#237496792
#485×C1492
#3116149