Finite Group Databasebeta

← #34055575

Subgroups — #34055575

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#23750203C211yesmaximal, characteristic
2#23750196C211yesmaximal, characteristic, complemented
3#23749967C211yesmaximal, characteristic, complemented
4#23749961C211yesmaximal, characteristic, complemented
5#23749956C211yesmaximal, characteristic, complemented
6#23749950C211yesmaximal, characteristic, complemented
7#23749883C211yesmaximal, characteristic, complemented
8#23749871C211yesmaximal, characteristic, complemented
9#23749866C211yesmaximal, characteristic, complemented
10#23749854C211yesmaximal, characteristic, complemented
11#23749789C211yesmaximal, characteristic, complemented
12#23749789C211yesmaximal, characteristic, complemented
13#23749783C211yesmaximal, characteristic, complemented
14#23749766C211yesmaximal, characteristic, complemented
15#408×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×Dic298C2211yescharacteristic
18C2×Dic596C2211yescharacteristic
19C2×Dic596C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21C2×#14558725C2211yescharacteristic
22#18011909—21no—
23#18011898—21no—
24#18011892—21no—
25#18011892—21no—
26#18011890C2211yescharacteristic
27#18011890C2211yescharacteristic
28#18011890C2211yescharacteristic
29#18011890C2211yescharacteristic
30#18011890C2211yescharacteristic
31#18011890C2211yescharacteristic
32#18011887—21no—
33#18011885C2211yescharacteristic
34#18011885C2211yescharacteristic
35#18011883—21no—
36#18011883—21no—
37#18011882—21no—
38#18011870C2211yescharacteristic
39C2×C4⋊Dic149C2211yescharacteristic
40#18011845C2211yescharacteristic
41#18011845C2211yescharacteristic
42#18011843C2211yescharacteristic
43#18011843C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011836C2211yescharacteristic
48#18011836C2211yescharacteristic
49#18011836C2211yescharacteristic
50#18011833C2211yescharacteristic
51#18011833C2211yescharacteristic
52C2×#41×C149C2211yescharacteristic
53C2×M16×C149C2211yescharacteristic
54C22×C8×C149C2211yescharacteristic
55C22⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57C22⋊C8×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558736—41no—
60#14558736—41no—
61C2×Dic298—21no—
62C2×Dic298—41no—
63C2×Dic298—41no—
64C2×Dic298C2311yescharacteristic
65C2×Dic298C2311yescharacteristic
66C2×Dic298C2311yescharacteristic
67C2×D596C2311yescharacteristic
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C22×Dic149—21no—
72C22×Dic149—21no—
73C2×C4×D149—21no—
74Dic596—41no—
75Dic596—41no—
76#14558725—41no—
77#14558725—41no—
78C4⋊Dic149—21no—
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92C22⋊Dic149—21no—
93C22⋊Dic149—21no—
94C22⋊Dic149—21no—
95C22⋊Dic149—21no—
96#14558713—21no—
97#14558713—21no—
98C4×Dic149—21no—
99#41×C149—41no—
100#41×C149—41no—
101C2×Q8×C149D411yescharacteristic
102C2×D4×C149D411yescharacteristic
103C2×D4×C149D411yescharacteristic
104C2×D4×C149D411yescharacteristic
105C22×C4×C149C2311yescharacteristic
106C22×C4×C149C2311yescharacteristic
107C22×C4×C149C2311yescharacteristic
108M16×C149—41no—
109C2×C8×C149—41no—
110C2×C8×C149C2311yescharacteristic
111C2×C8×C149C2311yescharacteristic
112C2×C8×C149C2311yescharacteristic
113C2×C8×C149C2311yescharacteristic
114C22×D149—21no—
115Dic298—21no—
116Dic298—21no—
117Dic298—21no—
118Dic298—21no—
119Dic298—21no—
120Dic298—21no—
121Dic298—42no—
122D596—21no—
123D596—21no—
124C22⋊D149—42no—
125C22⋊D149—81no—
126C22⋊D149—81no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—21no—
133C2×Dic149—21no—
134C2×Dic149—42no—
135C2×Dic149—81no—
136C4×D149—42no—
137C23×C149C2×D411yescharacteristic
138C23×C149C2×D411yescharacteristic
139C23×C149C2×D411yescharacteristic
140Q8×C149—41no—
141D4×C149—41no—
142D4×C149—41no—
143D4×C149—41no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149C2×D411yescharacteristic
151C2×C4×C149C2×D411yescharacteristic
152C2×C4×C149C2×D411yescharacteristic
153C2×C4×C149C2411yescharacteristic
154C8×C149—21no—
155C8×C149—21no—
156C8×C149—21no—
157C8×C149—21no—
158C22×C149—21no—
159C22×C149—21no—
160C22×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149—21no—
165C22×C149—21no—
166C22×C149—21no—
167C22×C149C22×D411yescharacteristic
168C2×D149—41no—
169C2×D149—41no—
170C2×D149—41no—
171C4×C149—21no—
172C4×C149—21no—
173C4×C149—21no—
174C4×C149H(5,𝔽2)11yescharacteristic
175C4×C149H(5,𝔽2)11yescharacteristic
176Dic149—41no—
177Dic149—41no—
178Dic149—41no—
179Dic149—41no—
180Dic149—41no—
181Dic149—41no—
182Dic149—41no—
183C2×C149—41no—
184C2×C149—41no—
185C2×C149—41no—
186C2×C149#53411yescharacteristic
187C2×C149#57711yescharacteristic
188C2×C149#57811yescharacteristic
189D149—81no—
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#468—1491no—
200#467—1491no—
201#465—1491no—
202#452—1491no—
203#452—1491no—
204#451—1491no—
205#448—1491no—
206#408D14911yescharacteristic, complemented
207C2×#41—1491no—
208C2×#41C2×D14911yescharacteristic
209C22×Q8—1491no—
210C2×Q16—1491no—
211C2×Q16—1491no—
212C2×SD16—1491no—
213C2×SD16—1491no—
214C2×M16C2×D14911yescharacteristic
215C22×C8C2×D14911yescharacteristic
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⋊Q8—1491no—
227#121—2981no—
228#121—2981no—
229#121—2981no—
230#121—1491no—
231#121—1491no—
232#117—1491no—
233C2×C4⋊C4—1491no—
234#107—1491no—
235#107—1491no—
236#106—1491no—
237#106—1491no—
238#103—1491no—
239#103—1491no—
240#103—1491no—
241#103—1491no—
242#103—1491no—
243#103—1491no—
244#102—1491no—
245#102—1491no—
246C22⋊C8C2×D14911yescharacteristic
247C22⋊C8C2×D14911yescharacteristic
248C22⋊C8C2×D14911yescharacteristic
249C22⋊C8C2×D14911yescharacteristic
250#41—41no—
251#41—41no—
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×Q8D59611yescharacteristic
261C2×D4—2981no—
262C2×D4—2981no—
263C2×D4—2981no—
264C2×D4—1491no—
265C2×D4D59611yescharacteristic
266C2×D4D59611yescharacteristic
267C2×D4D59611yescharacteristic
268C22×C4—2981no—
269C22×C4—2981no—
270C22×C4—2981no—
271C22×C4C22×D14911yescharacteristic
272C22×C4C22×D14911yescharacteristic
273C22×C4C22×D14911yescharacteristic
274Q16—5961no—
275Q16—5961no—
276SD16—5961no—
277SD16—5961no—
278M16—41no—
279C2×C8—41no—
280C2×C8C22×D14911yescharacteristic
281C2×C8C22×D14911yescharacteristic
282C2×C8C22×D14911yescharacteristic
283C2×C8C22×D14911yescharacteristic
284C4⋊C4—2981no—
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⋊C4—1491no—
294C4⋊C4—1491no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C22⋊C4—2981no—
300C22⋊C4—2981no—
301C22⋊C4—2981no—
302C22⋊C4—2981no—
303C22⋊C4—2981no—
304C42—2981no—
305C23—2981no—
306C23C2×D59611yescharacteristic
307C23C2×D59611yescharacteristic
308C23C2×D59611yescharacteristic
309Q8—41no—
310Q8—2981no—
311Q8—2981no—
312Q8—2981no—
313Q8—2981no—
314Q8—2981no—
315Q8—2981no—
316Q8—5962no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—2981no—
321D4—2981no—
322D4—5962no—
323D4—11921no—
324D4—11921no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
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—11921no—
341C2×C4C2×D59611yescharacteristic
342C2×C4C2×D59611yescharacteristic
343C2×C4C2×D59611yescharacteristic
344C2×C4C23×D14911yescharacteristic
345C8—21no—
346C8—21no—
347C8—21no—
348C8—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—5961no—
359C22—5961no—
360C22—5961no—
361C22C22×D59611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—5961no—
366C4—5961no—
367C4—5961no—
368C4—5961no—
369C4—5961no—
370C4—5961no—
371C4—5961no—
372C4#1801195611yescharacteristic
373C4#1801195611yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—11921no—
378C2#2375018711yescharacteristic
379C2#2375043711yescharacteristic
380C2#2375044211yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#408×C149C2
socleC22×C149C22×D4
prime radical#23750203C2
hypercenter#408D149
hypocenterC149#3201
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #23750196C2semidirect
3. #23749967C2semidirect
4. #23749961C2semidirect
5. #23749956C2semidirect
6. #23749950C2semidirect
7. #23749883C2semidirect
8. #23749871C2semidirect
9. #23749866C2semidirect
10. #23749854C2semidirect
11. #23749789C2semidirect
12. #23749789C2semidirect
13. #23749783C2semidirect
14. #23749766C2semidirect
15. #408×C149C2semidirect
190. C149#3201semidirect
206. #408D149semidirect

Maximal subgroups

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

subgroupindex
#237502032
#237501962
#237499672
#237499612
#237499562
#237499502
#237498832
#237498712
#237498662
#237498542
#237497892
#237497832
#237497662
#408×C1492
#3201149