Finite Group Databasebeta

← #34053759

Subgroups — #34053759

Order 19072.

394 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#23750172C211yesmaximal, characteristic
2#23749699C211yesmaximal, characteristic, complemented
3#23749698C211yesmaximal, characteristic, complemented
4#23749697C211yesmaximal, characteristic, complemented
5#23749696C211yesmaximal, characteristic, complemented
6#23749695C211yesmaximal, characteristic, complemented
7#23749694C211yesmaximal, characteristic, complemented
8#23749693C211yesmaximal, characteristic, complemented
9#23749681C211yesmaximal, characteristic, complemented
10#23749680C211yesmaximal, characteristic, complemented
11#23749593C211yesmaximal, characteristic, complemented
12#23749591C211yesmaximal, characteristic, complemented
13#23749590C211yesmaximal, characteristic, complemented
14#23749590C211yesmaximal, characteristic, complemented
15#435×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558736C2211yescharacteristic
18C2×#14558720C2211yescharacteristic
19C2×#14558719C2211yescharacteristic
20C2×#14558719C2211yescharacteristic
21C22×#11924746C2211yescharacteristic
22C2×C8×D149C2211yescharacteristic
23C2×C8×D149C2211yescharacteristic
24#18011910C411yescharacteristic
25#18011907C411yescharacteristic
26#18011897C411yescharacteristic
27#18011897C411yescharacteristic
28#18011886C411yescharacteristic
29#18011884C411yescharacteristic
30#18011884C411yescharacteristic
31#18011882C411yescharacteristic
32C4×D596C2211yescharacteristic
33C4×C22⋊D149C2211yescharacteristic
34C4×C22⋊D149C2211yescharacteristic
35C42×D149C2211yescharacteristic
36C4⋊#11924746C2211yescharacteristic
37#18011840C2211yescharacteristic
38#18011840C2211yescharacteristic
39C22⋊#11924746C2211yescharacteristic
40C22⋊#11924746C2211yescharacteristic
41#18011823C2211yescharacteristic
42#18011823C2211yescharacteristic
43#18011823C2211yescharacteristic
44#18011823C2211yescharacteristic
45#18011823C2211yescharacteristic
46#18011823C2211yescharacteristic
47#18011823C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011822C2211yescharacteristic
50#18011821C2211yescharacteristic
51#18011821C2211yescharacteristic
52C2×M16×C149C2211yescharacteristic
53C22×C8×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55C4⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57C22⋊C8×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59#14558736—41no—
60#14558736—41no—
61#14558736—41no—
62#14558736—41no—
63C2×Dic298C2×C411yescharacteristic
64C2×Dic298C2×C411yescharacteristic
65C2×D596C2×C411yescharacteristic
66C2×D596C2×C411yescharacteristic
67C2×D596C2×C411yescharacteristic
68C2×C22⋊D149C2×C411yescharacteristic
69C2×C22⋊D149C2×C411yescharacteristic
70C2×C22⋊D149C2×C411yescharacteristic
71C2×C22⋊D149C2×C411yescharacteristic
72C2×C22⋊D149C2×C411yescharacteristic
73C2×C22⋊D149C2×C411yescharacteristic
74C2×C4×D149C2×C411yescharacteristic
75C2×C4×D149C2×C411yescharacteristic
76C2×C4×D149C2311yescharacteristic
77C2×C4×D149C2311yescharacteristic
78C2×C4×D149C2311yescharacteristic
79#14558720—41no—
80#14558719—41no—
81#14558719—41no—
82C2×#11924746—41no—
83C2×#11924746C2311yescharacteristic
84C2×#11924746C2311yescharacteristic
85C2×#11924746C2311yescharacteristic
86C2×#11924746C2311yescharacteristic
87C8×D149—41no—
88C8×D149—41no—
89C4⋊Dic149C2×C411yescharacteristic
90#14558715C2×C411yescharacteristic
91#14558715C2×C411yescharacteristic
92C22⋊Dic149C2×C411yescharacteristic
93C22⋊Dic149C2×C411yescharacteristic
94#14558713C2×C411yescharacteristic
95#14558713C2×C411yescharacteristic
96#14558713C2×C411yescharacteristic
97#14558713C2×C411yescharacteristic
98C4×Dic149C2×C411yescharacteristic
99C4×Dic149C2×C411yescharacteristic
100C4×Dic149C2311yescharacteristic
101C2×D4×C149C2×C411yescharacteristic
102C22×C4×C149C2311yescharacteristic
103C22×C4×C149C2311yescharacteristic
104M16×C149—41no—
105C2×C8×C149—41no—
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C2×C8×C149C2311yescharacteristic
109C2×C8×C149C2311yescharacteristic
110C4⋊C4×C149C2×C411yescharacteristic
111C22⋊C4×C149C2×C411yescharacteristic
112C22⋊C4×C149C2×C411yescharacteristic
113C42×C149C2311yescharacteristic
114C22×D149C22×C411yescharacteristic
115C22×D149C22×C411yescharacteristic
116C22×D149C22×C411yescharacteristic
117Dic298—41no—
118Dic298—41no—
119D596—41no—
120D596—41no—
121D596—41no—
122C22⋊D149—41no—
123C22⋊D149—41no—
124C22⋊D149—41no—
125C22⋊D149—41no—
126C22⋊D149—41no—
127C22⋊D149—41no—
128C2×Dic149C22×C411yescharacteristic
129C2×Dic149C22×C411yescharacteristic
130C2×Dic149C22×C411yescharacteristic
131C2×Dic149C22×C411yescharacteristic
132C2×Dic149C22×C411yescharacteristic
133C4×D149—21no—
134C4×D149—21no—
135C4×D149—21no—
136C4×D149—21no—
137C4×D149—21no—
138C4×D149—21no—
139C4×D149—41no—
140C4×D149—41no—
141#11924746—21no—
142#11924746—21no—
143#11924746—21no—
144#11924746—21no—
145C23×C149C22×C411yescharacteristic
146C23×C149C22×C411yescharacteristic
147D4×C149—41no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
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×C149—21no—
165C22×C149—21no—
166C22×C149—21no—
167C22×C149C23×C411yescharacteristic
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—21no—
177C4×C149—21no—
178C4×C149—21no—
179C4×C149—21no—
180C4×C149—21no—
181C4×C149H(5,𝔽2)11yescharacteristic
182C4×C149H(5,𝔽2)11yescharacteristic
183Dic149—21no—
184Dic149—21no—
185Dic149—21no—
186Dic149—21no—
187Dic149—21no—
188C2×C149—41no—
189C2×C149—41no—
190C2×C149#51811yescharacteristic
191C2×C149#56811yescharacteristic
192C2×C149#56811yescharacteristic
193D149—41no—
194D149—41no—
195D149—41no—
196C149#298011yescharacteristic, complemented, Sylow
197#2980—1491nomaximal, Sylow
198#532—1491no—
199#435—1491no—
200#435—1491no—
201#435—1491no—
202#435—1491no—
203#435—1491no—
204#435—1491no—
205#435—1491no—
206#435D14911yescharacteristic, complemented
207#432—1491no—
208#432—1491no—
209#408—1491no—
210#408—1491no—
211#408—1491no—
212#408—1491no—
213C2×#41—1491no—
214C2×#41—1491no—
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×D4C2×D14911yescharacteristic
235C2×C42—1491no—
236C4⋊C8—1491no—
237C4⋊C8—1491no—
238C4⋊C8—1491no—
239C4⋊C8C2×D14911yescharacteristic
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⋊C8—1491no—
249C22⋊C8—1491no—
250C22⋊C8C2×D14911yescharacteristic
251C22⋊C8C2×D14911yescharacteristic
252#97—1491no—
253#97—1491no—
254#97—1491no—
255#97C2×D14911yescharacteristic
256#41—5961no—
257#41—5961no—
258#41—5961no—
259#41—5961no—
260C2×Q8—1491no—
261C2×Q8—1491no—
262C2×D4—1491no—
263C2×D4—1491no—
264C2×D4—1491no—
265C2×D4—1491no—
266C2×D4—1491no—
267C2×D4—1491no—
268C2×D4—1491no—
269C2×D4—1491no—
270C2×D4—1491no—
271C2×D4C4×D14911yescharacteristic
272C22×C4—1491no—
273C22×C4—1491no—
274C22×C4—1491no—
275C22×C4—1491no—
276C22×C4—1491no—
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⋊C4C4×D14911yescharacteristic
299C22⋊C4—1491no—
300C22⋊C4—1491no—
301C22⋊C4—1491no—
302C22⋊C4—1491no—
303C22⋊C4—1491no—
304C22⋊C4—1491no—
305C22⋊C4C4×D14911yescharacteristic
306C22⋊C4C4×D14911yescharacteristic
307C42—1491no—
308C42—1491no—
309C42—1491no—
310C42C22×D14911yescharacteristic
311C23—1491no—
312C23—1491no—
313C23—1491no—
314C23C2×C4×D14911yescharacteristic
315C23C2×C4×D14911yescharacteristic
316Q8—5961no—
317Q8—5961no—
318D4—41no—
319D4—5961no—
320D4—5961no—
321D4—5961no—
322D4—5961no—
323D4—5961no—
324D4—5961no—
325D4—5961no—
326D4—5961no—
327D4—5961no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
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—1491no—
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×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—2981no—
365C22—2981no—
366C22—2981no—
367C22—2981no—
368C22—2981no—
369C22—2981no—
370C22—2981no—
371C22—2981no—
372C22—2981no—
373C22C22×C4×D14911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—2981no—
379C4—2981no—
380C4—2981no—
381C4—2981no—
382C4—2981no—
383C4#1801195611yescharacteristic
384C4#1801195711yescharacteristic
385C2—41no—
386C2—41no—
387C2—5961no—
388C2—5961no—
389C2—5961no—
390C2#2375009711yescharacteristic
391C2#2375039011yescharacteristic
392C2#2375039111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D149
commutator, socleC22×C149C23×C4
Fitting#435×C149C2
prime radical#23750172C2
cosocleC2×C4×C149C24
hypercenter#435D149
hypocenterC149#2980
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #23749699C2semidirect
3. #23749698C2semidirect
4. #23749697C2semidirect
5. #23749696C2semidirect
6. #23749695C2semidirect
7. #23749694C2semidirect
8. #23749693C2semidirect
9. #23749681C2semidirect
10. #23749680C2semidirect
11. #23749593C2semidirect
12. #23749591C2semidirect
13. #23749590C2semidirect
14. #23749590C2semidirect
15. #435×C149C2semidirect
196. C149#2980semidirect
206. #435D149semidirect

Maximal subgroups

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

subgroupindex
#237501722
#237496992
#237496982
#237496972
#237496962
#237496952
#237496942
#237496932
#237496812
#237496802
#237495932
#237495912
#237495902
#435×C1492
#2980149