Finite Group Databasebeta

← #34054907

Subgroups — #34054907

Order 19072.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750237C211yesmaximal, characteristic, complemented
2#23750105C211yesmaximal, characteristic
3#23749961C211yesmaximal, characteristic, complemented
4#23749956C211yesmaximal, characteristic, complemented
5#23749933C211yesmaximal, characteristic, complemented
6#23749926C211yesmaximal, characteristic, complemented
7#23749836C211yesmaximal, characteristic, complemented
8#23749831C211yesmaximal, characteristic, complemented
9#23749789C211yesmaximal, characteristic
10#23749789C211yesmaximal, characteristic
11#23749733C211yesmaximal, characteristic, complemented
12#23749727C211yesmaximal, characteristic, complemented
13C4×Dic596C211yesmaximal, characteristic, complemented
14C4×#14558725C211yesmaximal, characteristic, complemented
15#433×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×Dic596C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21#18011911C2211yescharacteristic
22#18011904—21no—
23#18011904—21no—
24#18011903C2211yescharacteristic
25#18011901—21no—
26#18011901—21no—
27#18011890C2211yescharacteristic
28#18011890C2211yescharacteristic
29C4×Dic298C2211yescharacteristic
30C4×Dic298C2211yescharacteristic
31C4×Dic298C2211yescharacteristic
32C4×Dic298C2211yescharacteristic
33C4×D596C2211yescharacteristic
34C4×D596C2211yescharacteristic
35#18011871—21no—
36#18011871—21no—
37#18011869—21no—
38C2×C4⋊Dic149C2211yescharacteristic
39C4⋊C4×D149—21no—
40#18011845C2211yescharacteristic
41#18011845C2211yescharacteristic
42#18011843C2211yescharacteristic
43#18011843C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011836C2211yescharacteristic
48#18011836C2211yescharacteristic
49#18011836C2211yescharacteristic
50#18011833C2211yescharacteristic
51#18011833C2211yescharacteristic
52#117×C149C2211yescharacteristic
53C4⋊C8×C149C2211yescharacteristic
54C4⋊C8×C149C2211yescharacteristic
55C22⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57#97×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59#14558736—22no—
60#14558736—22no—
61C2×Dic298C2311yescharacteristic
62C2×Dic298C2311yescharacteristic
63C2×Dic298C2311yescharacteristic
64C2×D596C2311yescharacteristic
65C2×C22⋊D149—21no—
66C22×Dic149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70Dic596—22no—
71Dic596—22no—
72#14558725—22no—
73#14558725—22no—
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91#14558713—21no—
92#14558713—21no—
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149—21no—
97C22×C4×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C4⋊C4×C149D411yescharacteristic
103C4⋊C4×C149D411yescharacteristic
104C22⋊C4×C149D411yescharacteristic
105C22⋊C4×C149D411yescharacteristic
106C42×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109Dic298—21no—
110Dic298—21no—
111Dic298—21no—
112Dic298—21no—
113Dic298—21no—
114Dic298#4112yes—
115D596—21no—
116D596#4112yes—
117C22⋊D149—24no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—81no—
126C4×D149—24no—
127C4×D149—81no—
128C4×D149—81no—
129C23×C149C2×D411yescharacteristic
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149C2×D411yescharacteristic
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2×D411yescharacteristic
135C2×C4×C149C2×D411yescharacteristic
136C2×C4×C149C2×D411yescharacteristic
137C2×C4×C149C2411yescharacteristic
138C8×C149—21no—
139C8×C149—21no—
140C8×C149—21no—
141C8×C149—21no—
142C22×C149—21no—
143C22×C149—21no—
144C22×C149—21no—
145C22×C149C22×D411yescharacteristic
146C2×D149—22no—
147C2×D149—41no—
148C2×D149—41no—
149C4×C149—21no—
150C4×C149—21no—
151C4×C149—21no—
152C4×C149—21no—
153C4×C149—21no—
154C4×C149C2×#4111yescharacteristic
155C4×C149C2×#4111yescharacteristic
156Dic149—22no—
157Dic149—41no—
158Dic149—41no—
159Dic149—41no—
160Dic149—41no—
161Dic149—41no—
162Dic149—41no—
163C2×C149—41no—
164C2×C149#52511yescharacteristic
165C2×C149#57711yescharacteristic
166C2×C149#57811yescharacteristic
167D149—42no—
168C149#312011yescharacteristic, complemented, Sylow
169#3120—1491nomaximal, Sylow
170#541—1491no—
171#520—1491no—
172#484—1491no—
173#483—1491no—
174#479—1491no—
175#478—1491no—
176#462—1491no—
177#461—1491no—
178#452—1491no—
179#452—1491no—
180#441—1491no—
181#440—1491no—
182C4×Q16—1491no—
183C4×SD16—1491no—
184#433D14911yescharacteristic, complemented
185C2×#41—1491no—
186C2×Q16—1491no—
187C2×Q16—1491no—
188C2×SD16—1491no—
189C2×SD16—1491no—
190C4⋊Q8—1491no—
191#126—2981no—
192#126—2981no—
193#125—2981no—
194#125—2981no—
195#125—1491no—
196C22⋊Q8—1491no—
197C22⋊Q8—1491no—
198C4×Q8—1491no—
199C4×Q8—1491no—
200C4×Q8—1491no—
201C4×Q8—1491no—
202C4×D4—2981no—
203C4×D4—2981no—
204C4×D4—1491no—
205C4×D4—1491no—
206#117—2981no—
207#117C2×D14911yescharacteristic
208C2×C4⋊C4—2981no—
209C2×C4⋊C4—1491no—
210#107—1491no—
211#107—1491no—
212#106—1491no—
213#106—1491no—
214C4⋊C8C2×D14911yescharacteristic
215C4⋊C8C2×D14911yescharacteristic
216#103—1491no—
217#103—1491no—
218#103—1491no—
219#103—1491no—
220#103—1491no—
221#103—1491no—
222#102—1491no—
223#102—1491no—
224C22⋊C8C2×D14911yescharacteristic
225C22⋊C8C2×D14911yescharacteristic
226#97C2×D14911yescharacteristic
227C4×C8C2×D14911yescharacteristic
228#41—2982no—
229#41—2982no—
230C2×Q8—1491no—
231C2×Q8—1491no—
232C2×Q8—1491no—
233C2×D4—2981no—
234C2×D4—1491no—
235C22×C4—2981no—
236C22×C4—2981no—
237C22×C4—2981no—
238C22×C4—2981no—
239C22×C4C22×D14911yescharacteristic
240Q16—2982no—
241Q16—2982no—
242SD16—2982no—
243SD16—2982no—
244C2×C8C22×D14911yescharacteristic
245C2×C8C22×D14911yescharacteristic
246C2×C8C22×D14911yescharacteristic
247C2×C8C22×D14911yescharacteristic
248C4⋊C4—2981no—
249C4⋊C4—2981no—
250C4⋊C4—2981no—
251C4⋊C4—2981no—
252C4⋊C4—2981no—
253C4⋊C4—2981no—
254C4⋊C4—2981no—
255C4⋊C4—2981no—
256C4⋊C4—2981no—
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—1491no—
260C4⋊C4—1491no—
261C4⋊C4—1491no—
262C4⋊C4—1491no—
263C4⋊C4D59611yescharacteristic
264C4⋊C4D59611yescharacteristic
265C22⋊C4—2981no—
266C22⋊C4—2981no—
267C22⋊C4—2981no—
268C22⋊C4—2981no—
269C22⋊C4D59611yescharacteristic
270C22⋊C4D59611yescharacteristic
271C42—2981no—
272C42—2981no—
273C42—2981no—
274C42—2981no—
275C42C22×D14911yescharacteristic
276C42C22×D14911yescharacteristic
277C23—2981no—
278C23C2×D59611yescharacteristic
279Q8—2981no—
280Q8—2981no—
281Q8—2981no—
282Q8—2981no—
283Q8—2981no—
284Q8—1492no—
285D4—2984no—
286D4—2981no—
287D4—1492no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—2984no—
291C2×C4—2981no—
292C2×C4—2981no—
293C2×C4—2981no—
294C2×C4—2981no—
295C2×C4—2981no—
296C2×C4—2981no—
297C2×C4—2981no—
298C2×C4—11921no—
299C2×C4—11921no—
300C2×C4—11921no—
301C2×C4C2×D59611yescharacteristic
302C2×C4C2×D59611yescharacteristic
303C2×C4C2×D59611yescharacteristic
304C2×C4C2×D59611yescharacteristic
305C2×C4C2×D59611yescharacteristic
306C2×C4C23×D14911yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—2982no—
315C22—5961no—
316C22—5961no—
317C22C22×D59611yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—2982no—
324C4—5961no—
325C4—5961no—
326C4—5961no—
327C4—5961no—
328C4—5961no—
329C4—5961no—
330C4#41×D14911yescharacteristic
331C4#41×D14911yescharacteristic
332C2—41no—
333C2—5962no—
334C2#2375013711yescharacteristic
335C2#2375043711yescharacteristic
336C2#2375044211yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#433×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558736C22
hypercenter#433D149
hypocenterC149#3120
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23750237C2semidirect
3. #23749961C2semidirect
4. #23749956C2semidirect
5. #23749933C2semidirect
6. #23749926C2semidirect
7. #23749836C2semidirect
8. #23749831C2semidirect
11. #23749733C2semidirect
12. #23749727C2semidirect
13. C4×Dic596C2semidirect
14. C4×#14558725C2semidirect
15. #433×C149C2semidirect
168. C149#3120semidirect
184. #433D149semidirect

Maximal subgroups

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

subgroupindex
#237502372
#237501052
#237499612
#237499562
#237499332
#237499262
#237498362
#237498312
#237497892
#237497332
#237497272
C4×Dic5962
C4×#145587252
#433×C1492
#3120149