Finite Group Databasebeta

← #34054899

Subgroups — #34054899

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#23750105C211yesmaximal, characteristic
2#23749958C211yesmaximal, characteristic, complemented
3#23749953C211yesmaximal, characteristic, complemented
4#23749929C211yesmaximal, characteristic, complemented
5#23749922C211yesmaximal, characteristic, complemented
6#23749832C211yesmaximal, characteristic, complemented
7#23749827C211yesmaximal, characteristic, complemented
8#23749785C211yesmaximal, characteristic
9#23749785C211yesmaximal, characteristic
10#23749730C211yesmaximal, characteristic, complemented
11#23749723C211yesmaximal, characteristic, complemented
12C4×#14558726C211yesmaximal, characteristic, complemented
13C4×#14558723C211yesmaximal, characteristic, complemented
14#23749686C211yesmaximal, characteristic, complemented
15#541×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558726C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21C4×Dic298C2211yescharacteristic
22C4×Dic298C2211yescharacteristic
23C4×D596C2211yescharacteristic
24C4×D596C2211yescharacteristic
25#18011871—21no—
26#18011871—21no—
27#18011869—21no—
28C2×C4⋊Dic149C2211yescharacteristic
29C4⋊C4×D149—21no—
30#18011844C2211yescharacteristic
31#18011844C2211yescharacteristic
32#18011842C2211yescharacteristic
33#18011842C2211yescharacteristic
34C4⋊#11924746C2211yescharacteristic
35C4⋊#11924746C2211yescharacteristic
36#18011835C2211yescharacteristic
37#18011835C2211yescharacteristic
38#18011835C2211yescharacteristic
39#18011835C2211yescharacteristic
40#18011834C2211yescharacteristic
41#18011834C2211yescharacteristic
42#18011831C2211yescharacteristic
43#18011831C2211yescharacteristic
44C22⋊#11924746C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46#18011822C2211yescharacteristic
47C4×#11924746C2211yescharacteristic
48C4⋊Q8×C149C2211yescharacteristic
49#126×C149—21no—
50#126×C149—21no—
51#125×C149—21no—
52#125×C149—21no—
53#125×C149C2211yescharacteristic
54C22⋊Q8×C149C2211yescharacteristic
55C22⋊Q8×C149C2211yescharacteristic
56C4×Q8×C149C2211yescharacteristic
57C4×Q8×C149C2211yescharacteristic
58#117×C149C2211yescharacteristic
59#14558736—22no—
60#14558736—22no—
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C22×Dic149—21no—
65C2×C4×D149—21no—
66C2×C4×D149—21no—
67C2×C4×D149—21no—
68#14558726—22no—
69#14558726—22no—
70#14558723—22no—
71#14558723—22no—
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C2×#11924746C2311yescharacteristic
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81#14558713—21no—
82#14558713—21no—
83C4×Dic149—21no—
84C4×Dic149—21no—
85C2×Q8×C149C2311yescharacteristic
86C2×Q8×C149C2311yescharacteristic
87C22×C4×C149C2311yescharacteristic
88C4⋊C4×C149—21no—
89C4⋊C4×C149—21no—
90C4⋊C4×C149—21no—
91C4⋊C4×C149—21no—
92C4⋊C4×C149—21no—
93C4⋊C4×C149—21no—
94C4⋊C4×C149—21no—
95C4⋊C4×C149—21no—
96C4⋊C4×C149D411yescharacteristic
97C4⋊C4×C149D411yescharacteristic
98C4⋊C4×C149C2311yescharacteristic
99C4⋊C4×C149C2311yescharacteristic
100C22⋊C4×C149—21no—
101C22⋊C4×C149—21no—
102C22⋊C4×C149D411yescharacteristic
103C22⋊C4×C149D411yescharacteristic
104C42×C149—21no—
105C42×C149—21no—
106C42×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109Dic298—21no—
110Dic298#4112yes—
111D596—21no—
112D596#4112yes—
113C22⋊D149—24no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—81no—
118C4×D149—24no—
119C4×D149—81no—
120C4×D149—81no—
121#11924746—21no—
122#11924746—21no—
123#11924746—21no—
124#11924746—21no—
125C23×C149C2×D411yescharacteristic
126Q8×C149—21no—
127Q8×C149—21no—
128Q8×C149—21no—
129Q8×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149C2×D411yescharacteristic
137C2×C4×C149C2×D411yescharacteristic
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2411yescharacteristic
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×C149—41no—
155C4×C149—41no—
156C4×C149—41no—
157C4×C149—41no—
158C4×C149C2×#4111yescharacteristic
159C4×C149C2×#4111yescharacteristic
160Dic149—22no—
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#541D14911yescharacteristic, complemented
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#433—1491no—
185C2×#41—1491no—
186C2×Q16—1491no—
187C2×Q16—1491no—
188C2×SD16—1491no—
189C2×SD16—1491no—
190C4⋊Q8C2×D14911yescharacteristic
191#126—21no—
192#126—21no—
193#125—21no—
194#125—21no—
195#125C2×D14911yescharacteristic
196C22⋊Q8C2×D14911yescharacteristic
197C22⋊Q8C2×D14911yescharacteristic
198C4×Q8—1491no—
199C4×Q8—1491no—
200C4×Q8C2×D14911yescharacteristic
201C4×Q8C2×D14911yescharacteristic
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⋊C8—1491no—
215C4⋊C8—1491no—
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⋊C8—1491no—
225C22⋊C8—1491no—
226#97—1491no—
227C4×C8—1491no—
228#41—2982no—
229#41—2982no—
230C2×Q8—1491no—
231C2×Q8C22×D14911yescharacteristic
232C2×Q8C22×D14911yescharacteristic
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×C8—1491no—
245C2×C8—1491no—
246C2×C8—1491no—
247C2×C8—1491no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—2981no—
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—1491no—
260C4⋊C4—1491no—
261C4⋊C4C22⋊D14911yescharacteristic
262C4⋊C4C22⋊D14911yescharacteristic
263C4⋊C4C22×D14911yescharacteristic
264C4⋊C4C22×D14911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—2981no—
268C22⋊C4—2981no—
269C22⋊C4C22⋊D14911yescharacteristic
270C22⋊C4C22⋊D14911yescharacteristic
271C42—21no—
272C42—21no—
273C42—2981no—
274C42—2981no—
275C42C22×D14911yescharacteristic
276C42C22×D14911yescharacteristic
277C23—2981no—
278C23C2×C22⋊D14911yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—2981no—
284Q8—1492no—
285D4—2984no—
286D4—2981no—
287D4—1492no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—2984no—
295C2×C4—2981no—
296C2×C4—2981no—
297C2×C4—2981no—
298C2×C4—11921no—
299C2×C4—11921no—
300C2×C4—11921no—
301C2×C4C2×C22⋊D14911yescharacteristic
302C2×C4C2×C22⋊D14911yescharacteristic
303C2×C4C2×C22⋊D14911yescharacteristic
304C2×C4C2×C22⋊D14911yescharacteristic
305C2×C4C2×C22⋊D14911yescharacteristic
306C2×C4C23×D14911yescharacteristic
307C8—2981no—
308C8—2981no—
309C8—2981no—
310C8—2981no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—2982no—
315C22—5961no—
316C22—5961no—
317C22C22×C22⋊D14911yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—2982no—
328C4—5961no—
329C4—5961no—
330C4#41×D14911yescharacteristic
331C4#41×D14911yescharacteristic
332C2—41no—
333C2—5962no—
334C2#2375013211yescharacteristic
335C2#2375043311yescharacteristic
336C2#2375044011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#541×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558736C22
hypercenter#541D149
hypocenterC149#3120
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #23749958C2semidirect
3. #23749953C2semidirect
4. #23749929C2semidirect
5. #23749922C2semidirect
6. #23749832C2semidirect
7. #23749827C2semidirect
10. #23749730C2semidirect
11. #23749723C2semidirect
12. C4×#14558726C2semidirect
13. C4×#14558723C2semidirect
14. #23749686C2semidirect
15. #541×C149C2semidirect
168. C149#3120semidirect
170. #541D149semidirect

Maximal subgroups

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

subgroupindex
#237501052
#237499582
#237499532
#237499292
#237499222
#237498322
#237498272
#237497852
#237497302
#237497232
C4×#145587262
C4×#145587232
#237496862
#541×C1492
#3120149