Finite Group Databasebeta

← #34055568

Subgroups — #34055568

Order 19072.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750204C211yesmaximal, characteristic
2#23750198C211yesmaximal, characteristic, complemented
3#23749968C211yesmaximal, characteristic, complemented
4#23749962C211yesmaximal, characteristic, complemented
5#23749954C211yesmaximal, characteristic, complemented
6#23749948C211yesmaximal, characteristic, complemented
7#23749883C211yesmaximal, characteristic, complemented
8#23749864C211yesmaximal, characteristic, complemented
9#23749852C211yesmaximal, characteristic, complemented
10#23749788C211yesmaximal, characteristic, complemented
11#23749784C211yesmaximal, characteristic, complemented
12#23749782C211yesmaximal, characteristic, complemented
13#23749762C211yesmaximal, characteristic, complemented
14#23749593C211yesmaximal, characteristic, complemented
15#468×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C2×Q8×D149C2211yescharacteristic
19C2×Dic596C2211yescharacteristic
20C2×#14558726C2211yescharacteristic
21C2×#14558724C2211yescharacteristic
22C22×#11924746C2211yescharacteristic
23#18011910—21no—
24#18011897—21no—
25#18011896—21no—
26#18011893—21no—
27#18011891C2211yescharacteristic
28#18011891C2211yescharacteristic
29#18011890C2211yescharacteristic
30#18011890C2211yescharacteristic
31#18011888—21no—
32#18011887C2211yescharacteristic
33#18011884—21no—
34#18011883—21no—
35#18011882—21no—
36#18011882C2211yescharacteristic
37#18011869C2211yescharacteristic
38C4⋊C4×D149C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C2×M16×C149C2211yescharacteristic
54C22⋊Q8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56#107×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558736—41no—
60#14558736—41no—
61#14558735—41no—
62#14558735—41no—
63C2×Dic298—21no—
64C2×Dic298D411yescharacteristic
65C2×Dic298C2311yescharacteristic
66C2×Dic298C2311yescharacteristic
67Q8×D149—41no—
68Q8×D149—41no—
69C2×D596D411yescharacteristic
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149D411yescharacteristic
73C2×C22⋊D149D411yescharacteristic
74C22×Dic149—21no—
75C2×C4×D149—21no—
76C2×C4×D149—21no—
77C2×C4×D149C2311yescharacteristic
78C2×C4×D149C2311yescharacteristic
79Dic596—41no—
80#14558726—41no—
81#14558724—41no—
82C2×#11924746—41no—
83C2×#11924746C2311yescharacteristic
84C2×#11924746C2311yescharacteristic
85C4⋊Dic149—21no—
86C4⋊Dic149—21no—
87C4⋊Dic149C2311yescharacteristic
88C4⋊Dic149C2311yescharacteristic
89#14558715—21no—
90#14558715—21no—
91#14558715—21no—
92#14558715—21no—
93C22⋊Dic149—21no—
94C22⋊Dic149—21no—
95C22⋊Dic149—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713—21no—
100C4×Dic149—21no—
101C2×Q8×C149C2311yescharacteristic
102C2×D4×C149—21no—
103C2×D4×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105SD16×C149—41no—
106M16×C149—41no—
107C2×C8×C149C2311yescharacteristic
108C2×C8×C149C2311yescharacteristic
109C4⋊C4×C149—21no—
110C4⋊C4×C149C2311yescharacteristic
111C4⋊C4×C149C2311yescharacteristic
112C22⋊C4×C149—21no—
113C22⋊C4×C149—21no—
114C22×D149C2×D411yescharacteristic
115C22×D149C2×D411yescharacteristic
116Dic298—21no—
117Dic298—21no—
118Dic298—21no—
119Dic298—21no—
120Dic298—41no—
121Dic298—42no—
122D596—41no—
123C22⋊D149—41no—
124C22⋊D149—41no—
125C22⋊D149—42no—
126C22⋊D149—81no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—42no—
132C2×Dic149C2×D411yescharacteristic
133C2×Dic149C2×D411yescharacteristic
134C4×D149—21no—
135C4×D149—21no—
136C4×D149—21no—
137C4×D149—21no—
138C4×D149—42no—
139C4×D149—81no—
140#11924746—21no—
141#11924746—21no—
142C23×C149—21no—
143C23×C149C2×D411yescharacteristic
144Q8×C149—21no—
145Q8×C149—21no—
146D4×C149—21no—
147D4×C149—21no—
148D4×C149—81no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149C2×D411yescharacteristic
155C2×C4×C149C2411yescharacteristic
156C8×C149—21no—
157C8×C149—21no—
158C22×C149—21no—
159C22×C149—21no—
160C22×C149—21no—
161C22×C149—41no—
162C22×C149—41no—
163C22×C149—41no—
164C22×C149C22×D411yescharacteristic
165C2×D149—21no—
166C2×D149—21no—
167C2×D149—21no—
168C2×D149—21no—
169C2×D149—21no—
170C2×D149—21no—
171C4×C149—21no—
172C4×C149—41no—
173C4×C149—41no—
174C4×C149—41no—
175C4×C149H(5,𝔽2)11yescharacteristic
176C4×C149H(5,𝔽2)11yescharacteristic
177Dic149—21no—
178Dic149—21no—
179Dic149—41no—
180Dic149—41no—
181Dic149—41no—
182Dic149—41no—
183C2×C149—41no—
184C2×C149—81no—
185C2×C149#53411yescharacteristic
186C2×C149#57711yescharacteristic
187C2×C149#57811yescharacteristic
188D149—41no—
189D149—41no—
190C149#320111yescharacteristic, complemented, Sylow
191#3201—1491nomaximal, Sylow
192#537—1491no—
193#536—1491no—
194#485—1491no—
195#484—1491no—
196#483—1491no—
197#482—1491no—
198#470—1491no—
199#468D14911yescharacteristic, complemented
200#467—1491no—
201#465—1491no—
202#452—1491no—
203#452—1491no—
204#451—1491no—
205#448—1491no—
206#408—1491no—
207C2×#41—1491no—
208C2×#41—1491no—
209C22×Q8—1491no—
210C2×Q16—1491no—
211C2×Q16—1491no—
212C2×SD16—1491no—
213C2×SD16C2×D14911yescharacteristic
214C2×M16C2×D14911yescharacteristic
215C22×C8—1491no—
216C4⋊Q8—2981no—
217#124—2981no—
218#123—2981no—
219#123—2981no—
220C22⋊Q8—2981no—
221C22⋊Q8—1491no—
222C22⋊Q8—1491no—
223C22⋊Q8—1491no—
224C22⋊Q8—1491no—
225C22⋊Q8—1491no—
226C22⋊Q8C2×D14911yescharacteristic
227#121—2981no—
228#121—2981no—
229#121—2981no—
230#121—1491no—
231#121C2×D14911yescharacteristic
232#117—1491no—
233C2×C4⋊C4—1491no—
234#107—1491no—
235#107C2×D14911yescharacteristic
236#106—1491no—
237#106—1491no—
238#103—1491no—
239#103—1491no—
240#103—1491no—
241#103—1491no—
242#103—1491no—
243#103C2×D14911yescharacteristic
244#102—1491no—
245#102C2×D14911yescharacteristic
246C22⋊C8—1491no—
247C22⋊C8—1491no—
248C22⋊C8—1491no—
249C22⋊C8—1491no—
250#41—5961no—
251#41—5961no—
252#41—5961no—
253#41—5961no—
254C2×Q8—2981no—
255C2×Q8—5961no—
256C2×Q8—5961no—
257C2×Q8—1491no—
258C2×Q8—1491no—
259C2×Q8—1491no—
260C2×Q8C22×D14911yescharacteristic
261C2×D4—21no—
262C2×D4—2981no—
263C2×D4—2981no—
264C2×D4—1491no—
265C2×D4—1491no—
266C2×D4—1491no—
267C2×D4C22×D14911yescharacteristic
268C22×C4—2981no—
269C22×C4—2981no—
270C22×C4—2981no—
271C22×C4—1491no—
272C22×C4—1491no—
273C22×C4C22×D14911yescharacteristic
274Q16—5961no—
275Q16—5961no—
276SD16—41no—
277SD16—5961no—
278M16—41no—
279C2×C8—5961no—
280C2×C8—1491no—
281C2×C8—1491no—
282C2×C8C22×D14911yescharacteristic
283C2×C8C22×D14911yescharacteristic
284C4⋊C4—21no—
285C4⋊C4—2981no—
286C4⋊C4—2981no—
287C4⋊C4—2981no—
288C4⋊C4—2981no—
289C4⋊C4—2981no—
290C4⋊C4—2981no—
291C4⋊C4—1491no—
292C4⋊C4—1491no—
293C4⋊C4C22×D14911yescharacteristic
294C4⋊C4C22×D14911yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C22⋊C4—2981no—
300C22⋊C4—2981no—
301C22⋊C4—2981no—
302C22⋊C4—2981no—
303C22⋊C4—2981no—
304C42—2981no—
305C23—21no—
306C23—1491no—
307C23—1491no—
308C23D4×D14911yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—2981no—
312Q8—2981no—
313Q8—2981no—
314Q8—2981no—
315Q8—5961no—
316Q8—5962no—
317D4—21no—
318D4—21no—
319D4—81no—
320D4—5961no—
321D4—5961no—
322D4—5961no—
323D4—5962no—
324D4—11921no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—2981no—
336C2×C4—2981no—
337C2×C4—2981no—
338C2×C4—5962no—
339C2×C4—5962no—
340C2×C4—1491no—
341C2×C4—1491no—
342C2×C4—11921no—
343C2×C4D4×D14911yescharacteristic
344C2×C4C23×D14911yescharacteristic
345C8—21no—
346C8—21no—
347C8—2981no—
348C8—2981no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—2981no—
356C22—2981no—
357C22—2981no—
358C22—2981no—
359C22—2981no—
360C22—2981no—
361C22C2×D4×D14911yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—2981no—
367C4—2981no—
368C4—5961no—
369C4—5961no—
370C4—5961no—
371C4—5961no—
372C4#1801195611yescharacteristic
373C4#1801195711yescharacteristic
374C2—41no—
375C2—81no—
376C2—5961no—
377C2—5961no—
378C2#2375018311yescharacteristic
379C2#2375043511yescharacteristic
380C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#468×C149C2
socleC22×C149C22×D4
prime radical#23750204C2
hypercenter#468D149
hypocenterC149#3201
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. #23750198C2semidirect
3. #23749968C2semidirect
4. #23749962C2semidirect
5. #23749954C2semidirect
6. #23749948C2semidirect
7. #23749883C2semidirect
8. #23749864C2semidirect
9. #23749852C2semidirect
10. #23749788C2semidirect
11. #23749784C2semidirect
12. #23749782C2semidirect
13. #23749762C2semidirect
14. #23749593C2semidirect
15. #468×C149C2semidirect
190. C149#3201semidirect
199. #468D149semidirect

Maximal subgroups

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

subgroupindex
#237502042
#237501982
#237499682
#237499622
#237499542
#237499482
#237498832
#237498642
#237498522
#237497882
#237497842
#237497822
#237497622
#237495932
#468×C1492
#3201149