Finite Group Databasebeta

← #34055596

Subgroups — #34055596

Order 19072.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750205C211yesmaximal, characteristic, complemented
2#23750204C211yesmaximal, characteristic, complemented
3#23749957C211yesmaximal, characteristic, complemented
4#23749954C211yesmaximal, characteristic, complemented
5#23749945C211yesmaximal, characteristic, complemented
6#23749942C211yesmaximal, characteristic, complemented
7#23749881C211yesmaximal, characteristic, complemented
8#23749876C211yesmaximal, characteristic, complemented
9#23749854C211yesmaximal, characteristic, complemented
10#23749790C211yesmaximal, characteristic, complemented
11#23749784C211yesmaximal, characteristic, complemented
12#23749771C211yesmaximal, characteristic, complemented
13#23749769C211yesmaximal, characteristic, complemented
14#23749591C211yesmaximal, characteristic, complemented
15#465×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558736C2211yescharacteristic
18C2×#14558735C2211yescharacteristic
19C2×#14558726C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21C2×#14558721C2211yescharacteristic
22C2×#14558720C2211yescharacteristic
23#18011891C2211yescharacteristic
24#18011890C2211yescharacteristic
25#18011889—21no—
26#18011888—21no—
27#18011887C2211yescharacteristic
28#18011886—21no—
29#18011886C2211yescharacteristic
30#18011885C2211yescharacteristic
31#18011884—21no—
32#18011884—21no—
33#18011884—21no—
34#18011883—21no—
35#18011882—21no—
36#18011882C2211yescharacteristic
37C4⋊C4×D149C2211yescharacteristic
38C4⋊C4×D149C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C22×C8×C149C2211yescharacteristic
54C22⋊Q8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558737—41no—
60#14558737—41no—
61#14558736—41no—
62#14558736—41no—
63#14558735—41no—
64#14558735—41no—
65C2×Dic298D411yescharacteristic
66C2×Dic298C2311yescharacteristic
67C2×D596—21no—
68C2×D596—21no—
69C2×D596D411yescharacteristic
70C2×D596C2311yescharacteristic
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73C2×C22⋊D149—21no—
74C2×C22⋊D149D411yescharacteristic
75C2×C22⋊D149D411yescharacteristic
76C22×Dic149—21no—
77C2×C4×D149—21no—
78C2×C4×D149—21no—
79C2×C4×D149—21no—
80C2×C4×D149C2311yescharacteristic
81C2×C4×D149C2311yescharacteristic
82#14558726—41no—
83#14558725—41no—
84#14558721—41no—
85#14558720—41no—
86C2×#11924746C2311yescharacteristic
87C2×#11924746C2311yescharacteristic
88C4⋊Dic149—21no—
89C4⋊Dic149C2311yescharacteristic
90C4⋊Dic149C2311yescharacteristic
91#14558715—21no—
92#14558715—21no—
93#14558715—21no—
94#14558715—21no—
95C22⋊Dic149—21no—
96C22⋊Dic149—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713—21no—
101C2×Q8×C149C2311yescharacteristic
102C2×D4×C149—21no—
103C2×D4×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105SD16×C149—41no—
106C2×C8×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×D149—21no—
115C22×D149C2×D411yescharacteristic
116C22×D149C2×D411yescharacteristic
117Dic298—21no—
118Dic298—21no—
119Dic298—41no—
120D596—21no—
121D596—21no—
122D596—41no—
123D596—42no—
124D596—81no—
125C22⋊D149—41no—
126C22⋊D149—41no—
127C22⋊D149—42no—
128C22⋊D149—81no—
129C22⋊D149—81no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—21no—
133C2×Dic149—42no—
134C2×Dic149C2×D411yescharacteristic
135C2×Dic149C2×D411yescharacteristic
136C4×D149—21no—
137C4×D149—21no—
138C4×D149—21no—
139C4×D149—21no—
140C4×D149—42no—
141C4×D149—81no—
142C4×D149—81no—
143#11924746—21no—
144#11924746—21no—
145C23×C149—21no—
146C23×C149C2×D411yescharacteristic
147Q8×C149—21no—
148Q8×C149—21no—
149D4×C149—21no—
150D4×C149—21no—
151D4×C149—81no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149C2×D411yescharacteristic
158C2×C4×C149C2411yescharacteristic
159C8×C149—21no—
160C8×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149C22×D411yescharacteristic
168C2×D149—21no—
169C2×D149—21no—
170C2×D149—21no—
171C2×D149—21no—
172C2×D149—21no—
173C2×D149—21no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C4×C149—21no—
178C4×C149—41no—
179C4×C149—41no—
180C4×C149—41no—
181C4×C149H(5,𝔽2)11yescharacteristic
182C4×C149H(5,𝔽2)11yescharacteristic
183Dic149—21no—
184Dic149—21no—
185Dic149—41no—
186Dic149—41no—
187Dic149—41no—
188C2×C149—41no—
189C2×C149—81no—
190C2×C149#53411yescharacteristic
191C2×C149#57711yescharacteristic
192C2×C149#57711yescharacteristic
193D149—41no—
194D149—41no—
195D149—81no—
196C149#320411yescharacteristic, complemented, Sylow
197#3204—1491nomaximal, Sylow
198#537—1491no—
199#537—1491no—
200#483—1491no—
201#483—1491no—
202#481—1491no—
203#481—1491no—
204#470—1491no—
205#469—1491no—
206#465—1491no—
207#465D14911yescharacteristic, complemented
208#452—1491no—
209#452—1491no—
210#449—1491no—
211#449—1491no—
212#408—1491no—
213C2×#41—1491no—
214C2×#41—1491no—
215C2×#41—1491no—
216C2×Q16—1491no—
217C2×SD16—1491no—
218C2×SD16C2×D14911yescharacteristic
219C2×D8—1491no—
220C2×M16—1491no—
221C22×C8C2×D14911yescharacteristic
222C22⋊Q8—2981no—
223C22⋊Q8—2981no—
224C22⋊Q8—1491no—
225C22⋊Q8—1491no—
226C22⋊Q8—1491no—
227C22⋊Q8C2×D14911yescharacteristic
228#121—2981no—
229#121—2981no—
230#121—2981no—
231#121—2981no—
232#121—2981no—
233#121—2981no—
234#121—1491no—
235#121—1491no—
236#121—1491no—
237#121C2×D14911yescharacteristic
238C2×C4⋊C4—1491no—
239C2×C4⋊C4—1491no—
240#106—1491no—
241#106—1491no—
242#106—1491no—
243#106C2×D14911yescharacteristic
244#103—1491no—
245#103—1491no—
246#103—1491no—
247#103C2×D14911yescharacteristic
248#102—1491no—
249#102—1491no—
250#102—1491no—
251#102C2×D14911yescharacteristic
252C22⋊C8—1491no—
253C22⋊C8—1491no—
254C22⋊C8—1491no—
255C22⋊C8—1491no—
256#41—5961no—
257#41—5961no—
258#41—5961no—
259#41—5961no—
260#41—5961no—
261#41—5961no—
262C2×Q8—1491no—
263C2×Q8—1491no—
264C2×Q8C22×D14911yescharacteristic
265C2×D4—21no—
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—2981no—
270C2×D4—2981no—
271C2×D4—1491no—
272C2×D4—1491no—
273C2×D4—1491no—
274C2×D4—1491no—
275C2×D4C22×D14911yescharacteristic
276C22×C4—2981no—
277C22×C4—2981no—
278C22×C4—2981no—
279C22×C4—2981no—
280C22×C4—1491no—
281C22×C4—1491no—
282C22×C4C22×D14911yescharacteristic
283Q16—5961no—
284SD16—41no—
285SD16—5961no—
286D8—5961no—
287M16—5961no—
288C2×C8—41no—
289C2×C8—1491no—
290C2×C8—1491no—
291C2×C8C22×D14911yescharacteristic
292C2×C8C22×D14911yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—2981no—
295C4⋊C4—2981no—
296C4⋊C4—2981no—
297C4⋊C4—2981no—
298C4⋊C4—2981no—
299C4⋊C4—1491no—
300C4⋊C4—1491no—
301C4⋊C4C22×D14911yescharacteristic
302C4⋊C4C22×D14911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—2981no—
306C22⋊C4—2981no—
307C22⋊C4—2981no—
308C22⋊C4—2981no—
309C22⋊C4—2981no—
310C22⋊C4—2981no—
311C23—21no—
312C23—2981no—
313C23—1491no—
314C23—1491no—
315C23D4×D14911yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—2981no—
319Q8—2981no—
320Q8—5961no—
321D4—21no—
322D4—21no—
323D4—81no—
324D4—2981no—
325D4—2981no—
326D4—5961no—
327D4—5962no—
328D4—5961no—
329D4—5961no—
330D4—5962no—
331D4—11921no—
332D4—11921no—
333D4—11921no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—2981no—
340C2×C4—2981no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—5962no—
347C2×C4—5962no—
348C2×C4—1491no—
349C2×C4—1491no—
350C2×C4—11921no—
351C2×C4—11921no—
352C2×C4D4×D14911yescharacteristic
353C2×C4C23×D14911yescharacteristic
354C8—21no—
355C8—21no—
356C8—2981no—
357C8—2981no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—2981no—
365C22—2981no—
366C22—2981no—
367C22—2981no—
368C22—2981no—
369C22—2981no—
370C22—5961no—
371C22—5961no—
372C22—5961no—
373C22C2×D4×D14911yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—2981no—
379C4—2981no—
380C4—5961no—
381C4—5961no—
382C4—5961no—
383C4#1801195611yescharacteristic
384C4#1801195711yescharacteristic
385C2—41no—
386C2—81no—
387C2—5961no—
388C2—5961no—
389C2—11921no—
390C2#2375018311yescharacteristic
391C2#2375043111yescharacteristic
392C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#465×C149C2
socleC22×C149C22×D4
hypercenter#465D149
hypocenterC149#3204
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #23750205C2semidirect
2. #23750204C2semidirect
3. #23749957C2semidirect
4. #23749954C2semidirect
5. #23749945C2semidirect
6. #23749942C2semidirect
7. #23749881C2semidirect
8. #23749876C2semidirect
9. #23749854C2semidirect
10. #23749790C2semidirect
11. #23749784C2semidirect
12. #23749771C2semidirect
13. #23749769C2semidirect
14. #23749591C2semidirect
15. #465×C149C2semidirect
196. C149#3204semidirect
207. #465D149semidirect

Maximal subgroups

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

subgroupindex
#237502052
#237502042
#237499572
#237499542
#237499452
#237499422
#237498812
#237498762
#237498542
#237497902
#237497842
#237497712
#237497692
#237495912
#465×C1492
#3204149