Finite Group Databasebeta

← #34053737

Subgroups — #34053737

Order 19072.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750137C211yesmaximal, characteristic
2#23749704C211yesmaximal, characteristic, complemented
3#23749702C211yesmaximal, characteristic, complemented
4#23749698C211yesmaximal, characteristic, complemented
5#23749698C211yesmaximal, characteristic, complemented
6#23749695C211yesmaximal, characteristic, complemented
7#23749695C211yesmaximal, characteristic, complemented
8C8×D596C211yesmaximal, characteristic, complemented
9#23749690C211yesmaximal, characteristic, complemented
10#23749686C211yesmaximal, characteristic, complemented
11#23749590C211yesmaximal, characteristic, complemented
12#23749590C211yesmaximal, characteristic, complemented
13#23749587C211yesmaximal, characteristic, complemented
14C22⋊C8×D149C211yesmaximal, characteristic, complemented
15#433×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18C2×#14558719C2211yescharacteristic
19C2×#14558719C2211yescharacteristic
20C2×#14558719C2211yescharacteristic, complemented
21C2×#14558719C2211yescharacteristic, complemented
22C2×C8×D149C2211yescharacteristic
23C2×C8×D149C2211yescharacteristic
24C2×C8×D149C2211yescharacteristic, complemented
25C2×C8×D149C2211yescharacteristic, complemented
26#18011895C411yescharacteristic
27#18011895C411yescharacteristic
28#18011891C411yescharacteristic
29#18011891C411yescharacteristic
30#18011886C411yescharacteristic
31#18011886C411yescharacteristic
32#18011881C411yescharacteristic
33#18011881C411yescharacteristic
34C4×D596C2211yescharacteristic
35C4×D596C2211yescharacteristic
36C4×D596C2211yescharacteristic
37C4×D596C2211yescharacteristic
38C4⋊#11924746C2211yescharacteristic, complemented
39C4⋊#11924746C2211yescharacteristic, complemented
40C22⋊#11924746C2211yescharacteristic
41C22⋊#11924746C2211yescharacteristic
42#18011823C2211yescharacteristic
43#18011823C2211yescharacteristic
44#18011823C2211yescharacteristic
45#18011823C2211yescharacteristic
46#18011823C2211yescharacteristic, complemented
47#18011823C2211yescharacteristic, complemented
48#18011823C2211yescharacteristic, complemented
49#18011823C2211yescharacteristic, complemented
50#18011822C2211yescharacteristic, complemented
51C4×#11924746C2211yescharacteristic, complemented
52#117×C149C2211yescharacteristic
53C4⋊C8×C149C2211yescharacteristic, complemented
54C4⋊C8×C149C2211yescharacteristic, complemented
55C22⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57#97×C149C2211yescharacteristic, complemented
58C4×C8×C149C2211yescharacteristic, complemented
59C23×D149C2×C411yescharacteristic
60#14558736—41no—
61#14558736—41no—
62C2×Dic298C2×C411yescharacteristic
63C2×D596C2×C411yescharacteristic
64C2×D596C2×C411yescharacteristic
65C2×D596C2×C411yescharacteristic
66C2×D596C2×C411yescharacteristic
67C2×D596C2×C411yescharacteristic
68C2×C22⋊D149C2×C411yescharacteristic
69C2×C22⋊D149C2×C411yescharacteristic
70C22×Dic149C2×C411yescharacteristic
71C2×C4×D149—41no—
72C2×C4×D149—41no—
73C2×C4×D149C2×C411yescharacteristic
74C2×C4×D149C2×C411yescharacteristic
75C2×C4×D149C2311yescharacteristic
76C2×C4×D149C2311yescharacteristic
77C2×C4×D149C2311yescharacteristic
78C2×C4×D149C2311yescharacteristic
79#14558719—41no—
80#14558719—41no—
81#14558719—41no—
82#14558719—41no—
83C2×#11924746C2311yescharacteristic
84C2×#11924746C2311yescharacteristic
85C2×#11924746C2311yescharacteristic
86C2×#11924746C2311yescharacteristic
87C8×D149—41no—
88C8×D149—41no—
89C8×D149—41no—
90C8×D149—41no—
91C4⋊Dic149C2×C411yescharacteristic
92C4⋊Dic149C2×C411yescharacteristic
93C4⋊Dic149C2×C411yescharacteristic
94C4⋊Dic149C2×C411yescharacteristic
95#14558713C2×C411yescharacteristic
96#14558713C2×C411yescharacteristic
97#14558713C2×C411yescharacteristic
98#14558713C2×C411yescharacteristic
99#14558713C2×C411yescharacteristic
100#14558713C2×C411yescharacteristic
101#14558713C2×C411yescharacteristic
102#14558713C2×C411yescharacteristic
103C22×C4×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C4⋊C4×C149C2×C411yescharacteristic
109C4⋊C4×C149C2×C411yescharacteristic
110C22⋊C4×C149C2×C411yescharacteristic
111C22⋊C4×C149C2×C411yescharacteristic
112C42×C149C2311yescharacteristic
113C42×C149C2311yescharacteristic
114C22×D149—22no—
115C22×D149—41no—
116C22×D149—41no—
117C22×D149C22×C411yescharacteristic
118C22×D149C22×C411yescharacteristic
119C22×D149C22×C411yescharacteristic
120C22×D149C22×C411yescharacteristic
121Dic298—41no—
122D596—22no—
123D596—22no—
124D596—41no—
125D596—41no—
126D596—41no—
127C22⋊D149—41no—
128C22⋊D149—41no—
129C2×Dic149—41no—
130C2×Dic149C22×C411yescharacteristic
131C2×Dic149C22×C411yescharacteristic
132C2×Dic149C22×C411yescharacteristic
133C2×Dic149C22×C411yescharacteristic
134C4×D149—21no—
135C4×D149—21no—
136C4×D149—21no—
137C4×D149—21no—
138C4×D149—21no—
139C4×D149—21no—
140C4×D149—21no—
141C4×D149—21no—
142C4×D149—41no—
143C4×D149—41no—
144#11924746—21no—
145#11924746—21no—
146#11924746—21no—
147#11924746—21no—
148C23×C149C22×C411yescharacteristic
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149C22×C411yescharacteristic
152C2×C4×C149C22×C411yescharacteristic
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×C149C23×C411yescharacteristic
165C2×D149—21no—
166C2×D149—21no—
167C2×D149—21no—
168C2×D149—21no—
169C2×D149—21no—
170C2×D149—21no—
171C2×D149—21no—
172C2×D149—21no—
173C2×D149—21no—
174C2×D149—21no—
175C2×D149—21no—
176C2×D149—44no—
177C2×D149#13112yes—
178C4×C149—21no—
179C4×C149—21no—
180C4×C149—21no—
181C4×C149—21no—
182C4×C149—21no—
183C4×C149H(5,𝔽2)11yescharacteristic
184C4×C149H(5,𝔽2)11yescharacteristic
185Dic149—21no—
186Dic149—21no—
187Dic149—21no—
188Dic149—21no—
189C2×C149—41no—
190C2×C149#51811yescharacteristic
191C2×C149C2×#13111yescharacteristic
192C2×C149#56811yescharacteristic
193D149—22no—
194D149—41no—
195D149—41no—
196D149—41no—
197C149#297611yescharacteristic, complemented, Sylow
198#2976—1491nomaximal, Sylow
199#525—1491no—
200#436—1491no—
201#436—1491no—
202#435—1491no—
203#435—1491no—
204#435—1491no—
205#435—1491no—
206C8×D4—1491no—
207C8×D4—1491no—
208#433—1491no—
209#433D14911yescharacteristic, complemented
210#408—1491no—
211#408—1491no—
212#407—1491no—
213C2×C22⋊C8—1491no—
214C2×#41—1491no—
215C23×C4—1491no—
216C2×M16—1491no—
217C2×M16—1491no—
218C2×M16—1491no—
219C2×M16—1491no—
220C22×C8—1491no—
221C22×C8—1491no—
222C22×C8—1491no—
223C22×C8—1491no—
224#123—1491no—
225#123—1491no—
226C22⋊Q8—1491no—
227C22⋊Q8—1491no—
228#121—1491no—
229#121—1491no—
230#120—1491no—
231#120—1491no—
232C4×D4—1491no—
233C4×D4—1491no—
234C4×D4—1491no—
235C4×D4—1491no—
236#117C2×D14911yescharacteristic
237C4⋊C8—1491no—
238C4⋊C8—1491no—
239C4⋊C8C2×D14911yescharacteristic, complemented
240C4⋊C8C2×D14911yescharacteristic, complemented
241C22⋊C8—1491no—
242C22⋊C8—1491no—
243C22⋊C8—1491no—
244C22⋊C8—1491no—
245C22⋊C8—1491no—
246C22⋊C8—1491no—
247C22⋊C8—1491no—
248C22⋊C8—1491no—
249C22⋊C8—1491no—
250C22⋊C8—1491no—
251C22⋊C8C2×D14911yescharacteristic
252C22⋊C8C2×D14911yescharacteristic
253#97—1491no—
254#97C2×D14911yescharacteristic, complemented
255C4×C8—1491no—
256C4×C8C2×D14911yescharacteristic, complemented
257C24—1491no—
258#41—5961no—
259#41—5961no—
260C2×Q8—1491no—
261C2×D4—1491no—
262C2×D4—1491no—
263C2×D4—1491no—
264C2×D4—1491no—
265C2×D4—1491no—
266C2×D4—1491no—
267C2×D4—1491no—
268C22×C4—5961no—
269C22×C4—5961no—
270C22×C4—1491no—
271C22×C4—1491no—
272C22×C4—1491no—
273C22×C4—1491no—
274C22×C4—1491no—
275C22×C4—1491no—
276C22×C4—1491no—
277C22×C4C22×D14911yescharacteristic
278M16—5961no—
279M16—5961no—
280M16—5961no—
281M16—5961no—
282C2×C8—5961no—
283C2×C8—5961no—
284C2×C8—5961no—
285C2×C8—5961no—
286C2×C8—1491no—
287C2×C8—1491no—
288C2×C8—1491no—
289C2×C8—1491no—
290C2×C8C22×D14911yescharacteristic
291C2×C8C22×D14911yescharacteristic
292C2×C8C22×D14911yescharacteristic
293C2×C8C22×D14911yescharacteristic
294C4⋊C4—1491no—
295C4⋊C4—1491no—
296C4⋊C4—1491no—
297C4⋊C4—1491no—
298C4⋊C4C4×D14911yescharacteristic
299C4⋊C4C4×D14911yescharacteristic
300C22⋊C4—1491no—
301C22⋊C4—1491no—
302C22⋊C4—1491no—
303C22⋊C4—1491no—
304C22⋊C4—1491no—
305C22⋊C4—1491no—
306C22⋊C4—1491no—
307C22⋊C4—1491no—
308C22⋊C4C4×D14911yescharacteristic
309C22⋊C4C4×D14911yescharacteristic
310C42C22×D14911yescharacteristic
311C42C22×D14911yescharacteristic
312C23—2982no—
313C23—5961no—
314C23—5961no—
315C23—1491no—
316C23—1491no—
317C23—1491no—
318C23—1491no—
319C23C2×C4×D14911yescharacteristic
320Q8—5961no—
321D4—2982no—
322D4—2982no—
323D4—5961no—
324D4—5961no—
325D4—5961no—
326D4—5961no—
327D4—5961no—
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—5961no—
339C2×C4—5961no—
340C2×C4—5961no—
341C2×C4—1491no—
342C2×C4—1491no—
343C2×C4—1491no—
344C2×C4—1491no—
345C2×C4C2×C4×D14911yescharacteristic
346C2×C4C2×C4×D14911yescharacteristic
347C2×C4C2×C4×D14911yescharacteristic
348C2×C4C2×C4×D14911yescharacteristic
349C2×C4C2×C4×D14911yescharacteristic
350C2×C4C23×D14911yescharacteristic
351C8—21no—
352C8—21no—
353C8—21no—
354C8—21no—
355C8—2981no—
356C8—2981no—
357C8—2981no—
358C8—2981no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—2981no—
363C22—2981no—
364C22—2981no—
365C22—2981no—
366C22—2981no—
367C22—2981no—
368C22—2981no—
369C22—2981no—
370C22—2981no—
371C22—2981no—
372C22—2981no—
373C22—5964no—
374C22—1492no—
375C22C22×C4×D14911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—2981no—
382C4—2981no—
383C4—2981no—
384C4—2981no—
385C4#1801195711yescharacteristic
386C4#1801195711yescharacteristic
387C2—41no—
388C2—2982no—
389C2—5961no—
390C2—5961no—
391C2—5961no—
392C2#2375009911yescharacteristic
393C2#131×D14911yescharacteristic
394C2#2375039011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D149
commutator, socleC22×C149C23×C4
Fitting#433×C149C2
prime radical#23750137C2
cosocleC2×C4×C149C24
hypercenter#433D149
hypocenterC149#2976
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #23749704C2semidirect
3. #23749702C2semidirect
4. #23749698C2semidirect
5. #23749698C2semidirect
6. #23749695C2semidirect
7. #23749695C2semidirect
8. C8×D596C2semidirect
9. #23749690C2semidirect
10. #23749686C2semidirect
11. #23749590C2semidirect
12. #23749590C2semidirect
13. #23749587C2semidirect
14. C22⋊C8×D149C2semidirect
15. #433×C149C2semidirect
20. C2×#14558719C22semidirect
21. C2×#14558719C22semidirect
24. C2×C8×D149C22semidirect
25. C2×C8×D149C22semidirect
38. C4⋊#11924746C22semidirect
39. C4⋊#11924746C22semidirect
46. #18011823C22semidirect
47. #18011823C22semidirect
48. #18011823C22semidirect
49. #18011823C22semidirect
50. #18011822C22semidirect
51. C4×#11924746C22semidirect
53. C4⋊C8×C149C22semidirect
54. C4⋊C8×C149C22semidirect
57. #97×C149C22semidirect
58. C4×C8×C149C22semidirect
197. C149#2976semidirect
209. #433D149semidirect
239. C4⋊C8C2×D149semidirect
240. C4⋊C8C2×D149semidirect
254. #97C2×D149semidirect
256. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501372
#237497042
#237497022
#237496982
#237496952
C8×D5962
#237496902
#237496862
#237495902
#237495872
C22⋊C8×D1492
#433×C1492
#2976149