Finite Group Databasebeta

← #34053764

Subgroups — #34053764

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#23750171C211yesmaximal, characteristic
2#23749701C211yesmaximal, characteristic, complemented
3#23749700C211yesmaximal, characteristic, complemented
4#23749699C211yesmaximal, characteristic, complemented
5#23749696C211yesmaximal, characteristic, complemented
6#23749694C211yesmaximal, characteristic, complemented
7#23749693C211yesmaximal, characteristic, complemented
8C8×C22⋊D149C211yesmaximal, characteristic, complemented
9#23749688C211yesmaximal, characteristic, complemented
10#23749679C211yesmaximal, characteristic, complemented
11#23749675C211yesmaximal, characteristic, complemented
12#23749592C211yesmaximal, characteristic, complemented
13#23749590C211yesmaximal, characteristic, complemented
14#23749590C211yesmaximal, characteristic, complemented
15#408×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558720C2211yescharacteristic
18C2×#14558719C2211yescharacteristic
19C2×#14558719C2211yescharacteristic
20C22×#11924746C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic
22C2×C8×D149C2211yescharacteristic
23#18011909C411yescharacteristic
24#18011907C411yescharacteristic
25#18011900C411yescharacteristic
26#18011898C411yescharacteristic
27#18011883C411yescharacteristic
28#18011883C411yescharacteristic
29#18011883C411yescharacteristic
30#18011883C411yescharacteristic
31C4×C22⋊D149C2211yescharacteristic
32C4×C22⋊D149C2211yescharacteristic
33C4×C22⋊D149C2211yescharacteristic
34C4×C22⋊D149C2211yescharacteristic
35C2×C4×Dic149C2211yescharacteristic
36#18011840C2211yescharacteristic
37#18011840C2211yescharacteristic
38#18011840C2211yescharacteristic
39#18011840C2211yescharacteristic
40C22⋊#11924746C2211yescharacteristic
41C22⋊#11924746C2211yescharacteristic
42C22⋊#11924746C2211yescharacteristic
43C22⋊#11924746C2211yescharacteristic
44#18011823C2211yescharacteristic
45#18011823C2211yescharacteristic
46#18011823C2211yescharacteristic
47#18011823C2211yescharacteristic
48#18011821C2211yescharacteristic
49#18011821C2211yescharacteristic
50C8×Dic149C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
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×Dic298C2×C411yescharacteristic
62C2×D596C2×C411yescharacteristic
63C2×C22⋊D149C2×C411yescharacteristic
64C2×C22⋊D149C2×C411yescharacteristic
65C2×C22⋊D149C2×C411yescharacteristic
66C2×C22⋊D149C2×C411yescharacteristic
67C2×C22⋊D149C2×C411yescharacteristic
68C2×C22⋊D149C2×C411yescharacteristic
69C22×Dic149C2×C411yescharacteristic
70C22×Dic149C2×C411yescharacteristic
71C2×C4×D149C2311yescharacteristic
72C2×C4×D149C2311yescharacteristic
73#14558720—41no—
74#14558719—41no—
75#14558719—41no—
76C2×#11924746—41no—
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C2×#11924746C2311yescharacteristic
80C2×#11924746C2311yescharacteristic
81C8×D149—41no—
82C8×D149—41no—
83#14558715C2×C411yescharacteristic
84#14558715C2×C411yescharacteristic
85#14558715C2×C411yescharacteristic
86#14558715C2×C411yescharacteristic
87C22⋊Dic149C2×C411yescharacteristic
88C22⋊Dic149C2×C411yescharacteristic
89C22⋊Dic149C2×C411yescharacteristic
90C22⋊Dic149C2×C411yescharacteristic
91#14558713C2×C411yescharacteristic
92#14558713C2×C411yescharacteristic
93#14558713C2×C411yescharacteristic
94#14558713C2×C411yescharacteristic
95C4×Dic149C2×C411yescharacteristic
96C4×Dic149C2×C411yescharacteristic
97C4×Dic149C2311yescharacteristic
98C4×Dic149C2311yescharacteristic
99#41×C149—41no—
100#41×C149—41no—
101C2×Q8×C149C2×C411yescharacteristic
102C2×D4×C149C2×C411yescharacteristic
103C2×D4×C149C2×C411yescharacteristic
104C2×D4×C149C2×C411yescharacteristic
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×D149C22×C411yescharacteristic
115C22×D149C22×C411yescharacteristic
116Dic298—41no—
117D596—41no—
118C22⋊D149—22no—
119C22⋊D149—22no—
120C22⋊D149—41no—
121C22⋊D149—41no—
122C22⋊D149—41no—
123C22⋊D149—41no—
124C2×Dic149—22no—
125C2×Dic149—41no—
126C2×Dic149C22×C411yescharacteristic
127C2×Dic149C22×C411yescharacteristic
128C2×Dic149C22×C411yescharacteristic
129C2×Dic149C22×C411yescharacteristic
130C2×Dic149C22×C411yescharacteristic
131C2×Dic149C22×C411yescharacteristic
132C4×D149—21no—
133C4×D149—21no—
134C4×D149—21no—
135C4×D149—21no—
136#11924746—21no—
137#11924746—21no—
138#11924746—21no—
139#11924746—21no—
140C23×C149C22×C411yescharacteristic
141C23×C149C22×C411yescharacteristic
142C23×C149C22×C411yescharacteristic
143Q8×C149—41no—
144D4×C149—41no—
145D4×C149—41no—
146D4×C149—41no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149C22×C411yescharacteristic
154C2×C4×C149C22×C411yescharacteristic
155C2×C4×C149C22×C411yescharacteristic
156C2×C4×C149C2411yescharacteristic
157C8×C149—21no—
158C8×C149—21no—
159C8×C149—21no—
160C8×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149—21no—
165C22×C149—21no—
166C22×C149—21no—
167C22×C149—21no—
168C22×C149—21no—
169C22×C149—21no—
170C22×C149C23×C411yescharacteristic
171C2×D149—21no—
172C2×D149—21no—
173C2×D149—21no—
174C2×D149—21no—
175C2×D149—21no—
176C2×D149—21no—
177C4×C149—21no—
178C4×C149—21no—
179C4×C149—21no—
180C4×C149H(5,𝔽2)11yescharacteristic
181C4×C149H(5,𝔽2)11yescharacteristic
182Dic149—21no—
183Dic149—21no—
184Dic149—21no—
185Dic149—21no—
186Dic149—21no—
187Dic149#13112yes—
188C2×C149—41no—
189C2×C149—41no—
190C2×C149—41no—
191C2×C149#51811yescharacteristic
192C2×C149C2×#13111yescharacteristic
193C2×C149#56811yescharacteristic
194D149—41no—
195D149—41no—
196C149#298111yescharacteristic, complemented, Sylow
197#2981—1491nomaximal, Sylow
198#532—1491no—
199#436—1491no—
200#436—1491no—
201#435—1491no—
202#435—1491no—
203#435—1491no—
204#435—1491no—
205C8×D4—1491no—
206C8×D4—1491no—
207#432—1491no—
208#431—1491no—
209#408—1491no—
210#408—1491no—
211#408—1491no—
212#408D14911yescharacteristic, complemented
213C2×#41—1491no—
214C2×#41C2×D14911yescharacteristic
215C2×M16—1491no—
216C2×M16—1491no—
217C2×M16—1491no—
218C2×M16C2×D14911yescharacteristic
219C22×C8—1491no—
220C22×C8—1491no—
221C22×C8—1491no—
222C22×C8C2×D14911yescharacteristic
223C4⋊Q8—1491no—
224#127—1491no—
225#124—1491no—
226#124—1491no—
227#121—1491no—
228#121—1491no—
229#121—1491no—
230#121—1491no—
231C4×D4—1491no—
232C4×D4—1491no—
233C4×D4—1491no—
234C4×D4—1491no—
235C2×C42—1491no—
236C4⋊C8—1491no—
237C4⋊C8—1491no—
238C4⋊C8—1491no—
239C4⋊C8—1491no—
240C22⋊C8—1491no—
241C22⋊C8—1491no—
242C22⋊C8—1491no—
243C22⋊C8—1491no—
244C22⋊C8—1491no—
245C22⋊C8—1491no—
246C22⋊C8—1491no—
247C22⋊C8—1491no—
248C22⋊C8C2×D14911yescharacteristic
249C22⋊C8C2×D14911yescharacteristic
250C22⋊C8C2×D14911yescharacteristic
251C22⋊C8C2×D14911yescharacteristic
252#97—1491no—
253#97—1491no—
254C4×C8—1491no—
255C4×C8—1491no—
256#41—41no—
257#41—41no—
258#41—5961no—
259#41—5961no—
260C2×Q8—1491no—
261C2×Q8C4×D14911yescharacteristic
262C2×D4—1491no—
263C2×D4—1491no—
264C2×D4—1491no—
265C2×D4—1491no—
266C2×D4—1491no—
267C2×D4—1491no—
268C2×D4—1491no—
269C2×D4C4×D14911yescharacteristic
270C2×D4C4×D14911yescharacteristic
271C2×D4C4×D14911yescharacteristic
272C22×C4—1491no—
273C22×C4—1491no—
274C22×C4—1491no—
275C22×C4—1491no—
276C22×C4C22×D14911yescharacteristic
277C22×C4C22×D14911yescharacteristic
278C22×C4C22×D14911yescharacteristic
279M16—41no—
280M16—5961no—
281M16—5961no—
282M16—5961no—
283C2×C8—41no—
284C2×C8—5961no—
285C2×C8—5961no—
286C2×C8—5961no—
287C2×C8—1491no—
288C2×C8—1491no—
289C2×C8—1491no—
290C2×C8—1491no—
291C2×C8C22×D14911yescharacteristic
292C2×C8C22×D14911yescharacteristic
293C2×C8C22×D14911yescharacteristic
294C2×C8C22×D14911yescharacteristic
295C4⋊C4—1491no—
296C4⋊C4—1491no—
297C4⋊C4—1491no—
298C4⋊C4—1491no—
299C22⋊C4—1491no—
300C22⋊C4—1491no—
301C22⋊C4—1491no—
302C22⋊C4—1491no—
303C22⋊C4—1491no—
304C22⋊C4—1491no—
305C22⋊C4—1491no—
306C22⋊C4—1491no—
307C42—1491no—
308C42—1491no—
309C42—1491no—
310C42—1491no—
311C23—1491no—
312C23—1491no—
313C23C2×C4×D14911yescharacteristic
314C23C2×C4×D14911yescharacteristic
315C23C2×C4×D14911yescharacteristic
316Q8—41no—
317Q8—5961no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—2982no—
322D4—2982no—
323D4—5961no—
324D4—5961no—
325D4—5961no—
326D4—5961no—
327D4—5961no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—2982no—
335C2×C4—2981no—
336C2×C4—2981no—
337C2×C4—2981no—
338C2×C4—2981no—
339C2×C4—5961no—
340C2×C4—1491no—
341C2×C4—1491no—
342C2×C4—1491no—
343C2×C4—1491no—
344C2×C4—1491no—
345C2×C4—1491no—
346C2×C4C2×C4×D14911yescharacteristic
347C2×C4C2×C4×D14911yescharacteristic
348C2×C4C2×C4×D14911yescharacteristic
349C2×C4C23×D14911yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C8—2981no—
355C8—2981no—
356C8—2981no—
357C8—2981no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—2981no—
368C22—2981no—
369C22—2981no—
370C22—2981no—
371C22—2981no—
372C22—2981no—
373C22C22×C4×D14911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—2981no—
378C4—2981no—
379C4—2981no—
380C4—2981no—
381C4—2981no—
382C4—1492no—
383C4#1801195611yescharacteristic
384C4#1801195611yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—5961no—
389C2—5961no—
390C2#2375009811yescharacteristic
391C2#131×D14911yescharacteristic
392C2#2375039011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D149
commutator, socleC22×C149C23×C4
Fitting#408×C149C2
prime radical#23750171C2
cosocleC2×C4×C149C24
hypercenter#408D149
hypocenterC149#2981
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #23749701C2semidirect
3. #23749700C2semidirect
4. #23749699C2semidirect
5. #23749696C2semidirect
6. #23749694C2semidirect
7. #23749693C2semidirect
8. C8×C22⋊D149C2semidirect
9. #23749688C2semidirect
10. #23749679C2semidirect
11. #23749675C2semidirect
12. #23749592C2semidirect
13. #23749590C2semidirect
14. #23749590C2semidirect
15. #408×C149C2semidirect
196. C149#2981semidirect
212. #408D149semidirect

Maximal subgroups

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

subgroupindex
#237501712
#237497012
#237497002
#237496992
#237496962
#237496942
#237496932
C8×C22⋊D1492
#237496882
#237496792
#237496752
#237495922
#237495902
#408×C1492
#2981149