Finite Group Databasebeta

← #34055585

Subgroups — #34055585

Order 19072.

378 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750201C211yesmaximal, characteristic
2#23750198C211yesmaximal, characteristic
3#23749969C211yesmaximal, characteristic, complemented
4#23749968C211yesmaximal, characteristic, complemented
5#23749966C211yesmaximal, characteristic, complemented
6#23749884C211yesmaximal, characteristic, complemented
7#23749882C211yesmaximal, characteristic, complemented
8#23749867C211yesmaximal, characteristic, complemented
9#23749865C211yesmaximal, characteristic, complemented
10#23749783C211yesmaximal, characteristic, complemented
11#23749782C211yesmaximal, characteristic, complemented
12#23749782C211yesmaximal, characteristic, complemented
13#23749780C211yesmaximal, characteristic, complemented
14#23749590C211yesmaximal, characteristic
15#485×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×Dic298C2211yescharacteristic
18C2×Q8×D149C2211yescharacteristic
19C2×Dic596C2211yescharacteristic
20C2×Dic596C2211yescharacteristic
21C2×#14558726C2211yescharacteristic
22C2×#14558726C2211yescharacteristic
23C2×#14558719C2211yescharacteristic
24C2×C8×D149C2211yescharacteristic
25#18011911—21no—
26#18011910—21no—
27#18011899—21no—
28#18011897—21no—
29#18011896—21no—
30#18011895—21no—
31#18011895—21no—
32#18011893—21no—
33#18011891C2211yescharacteristic
34#18011891C2211yescharacteristic
35#18011891C2211yescharacteristic
36#18011891C2211yescharacteristic
37#18011891C2211yescharacteristic
38#18011890C2211yescharacteristic
39#18011887C2211yescharacteristic
40#18011869C2211yescharacteristic
41#18011844C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011834C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C22⋊Q8×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558736—41no—
60#14558736—41no—
61C2×Dic298—21no—
62C2×Dic298—21no—
63C2×Dic298—41no—
64C2×Dic298—41no—
65C2×Dic298D411yescharacteristic
66C2×Dic298C2311yescharacteristic
67C2×Dic298C2311yescharacteristic
68C2×Dic298C2311yescharacteristic
69Q8×D149—41no—
70Q8×D149—41no—
71C2×D596D411yescharacteristic
72C2×C22⋊D149D411yescharacteristic
73C2×C22⋊D149D411yescharacteristic
74C22×Dic149—21no—
75C2×C4×D149—21no—
76C2×C4×D149C2311yescharacteristic
77C2×C4×D149C2311yescharacteristic
78Dic596—41no—
79Dic596—41no—
80#14558726—41no—
81#14558726—41no—
82#14558719—41no—
83C2×#11924746C2311yescharacteristic
84C2×#11924746C2311yescharacteristic
85C8×D149—41no—
86C4⋊Dic149—21no—
87C4⋊Dic149—21no—
88C4⋊Dic149—21no—
89C4⋊Dic149—21no—
90C4⋊Dic149—21no—
91C4⋊Dic149C2311yescharacteristic
92#14558715—21no—
93#14558715—21no—
94C22⋊Dic149—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713—21no—
101#14558713—21no—
102C4×Dic149—21no—
103C2×Q8×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149—21no—
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C22⋊C4×C149—21no—
112C22⋊C4×C149—21no—
113C42×C149—21no—
114C22×D149C2×D411yescharacteristic
115C22×D149C2×D411yescharacteristic
116Dic298—21no—
117Dic298—21no—
118Dic298—21no—
119Dic298—21no—
120Dic298—21no—
121Dic298—21no—
122Dic298—41no—
123Dic298—42no—
124Dic298—42no—
125D596—41no—
126C22⋊D149—41no—
127C22⋊D149—41no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—42no—
133C2×Dic149C2×D411yescharacteristic
134C2×Dic149C2×D411yescharacteristic
135C4×D149—21no—
136C4×D149—21no—
137C4×D149—21no—
138C4×D149—21no—
139C4×D149—42no—
140#11924746—21no—
141#11924746—21no—
142C23×C149C2×D411yescharacteristic
143Q8×C149—21no—
144Q8×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149C2×D411yescharacteristic
152C2×C4×C149C2411yescharacteristic
153C8×C149—21no—
154C8×C149—21no—
155C22×C149—21no—
156C22×C149—21no—
157C22×C149—21no—
158C22×C149C22×D411yescharacteristic
159C2×D149—21no—
160C2×D149—21no—
161C2×D149—21no—
162C2×D149—21no—
163C2×D149—21no—
164C2×D149—21no—
165C4×C149—21no—
166C4×C149—41no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149—41no—
170C4×C149H(5,𝔽2)11yescharacteristic
171C4×C149H(5,𝔽2)11yescharacteristic
172Dic149—21no—
173Dic149—21no—
174Dic149—41no—
175Dic149—41no—
176Dic149—41no—
177Dic149—41no—
178C2×C149—41no—
179C2×C149#53411yescharacteristic
180C2×C149#57811yescharacteristic
181C2×C149#57811yescharacteristic
182D149—41no—
183D149—41no—
184C149#320211yescharacteristic, complemented, Sylow
185#3202—1491nomaximal, Sylow
186#536—1491no—
187#536—1491no—
188#485—1491no—
189#485—1491no—
190#485—1491no—
191#485D14911yescharacteristic, complemented
192#470—1491no—
193#470—1491no—
194#467—1491no—
195#467—1491no—
196#451—1491no—
197#451—1491no—
198#451—1491no—
199#451—1491no—
200#408—1491no—
201C2×#41—1491no—
202C22×Q8—1491no—
203C22×Q8—1491no—
204C2×Q16—1491no—
205C2×Q16—1491no—
206C2×Q16—1491no—
207C2×Q16—1491no—
208C2×M16—1491no—
209C22×C8—1491no—
210C4⋊Q8—2981no—
211C4⋊Q8—2981no—
212#124—2981no—
213#124—2981no—
214#123—2981no—
215#123—2981no—
216#123—2981no—
217#123—2981no—
218C22⋊Q8—1491no—
219C22⋊Q8—1491no—
220C22⋊Q8—1491no—
221C22⋊Q8—1491no—
222C22⋊Q8—1491no—
223C22⋊Q8—1491no—
224C22⋊Q8—1491no—
225C22⋊Q8C2×D14911yescharacteristic
226#117—1491no—
227#117C2×D14911yescharacteristic
228#107—1491no—
229#107C2×D14911yescharacteristic
230#106—1491no—
231#106C2×D14911yescharacteristic
232#103—1491no—
233#103—1491no—
234#103—1491no—
235#103—1491no—
236#103—1491no—
237#103—1491no—
238#103C2×D14911yescharacteristic
239#103C2×D14911yescharacteristic
240C22⋊C8—1491no—
241C22⋊C8—1491no—
242C22⋊C8—1491no—
243C22⋊C8C2×D14911yescharacteristic
244#41—5961no—
245#41—5961no—
246C2×Q8—2981no—
247C2×Q8—2981no—
248C2×Q8—5961no—
249C2×Q8—5961no—
250C2×Q8—5961no—
251C2×Q8—5961no—
252C2×Q8—1491no—
253C2×Q8—1491no—
254C2×Q8—1491no—
255C2×Q8—1491no—
256C2×Q8C22×D14911yescharacteristic
257C2×D4—1491no—
258C2×D4—1491no—
259C2×D4—1491no—
260C22×C4—2981no—
261C22×C4—2981no—
262C22×C4—1491no—
263C22×C4—1491no—
264C22×C4C22×D14911yescharacteristic
265Q16—5961no—
266Q16—5961no—
267Q16—5961no—
268Q16—5961no—
269M16—5961no—
270C2×C8—5961no—
271C2×C8—1491no—
272C2×C8—1491no—
273C2×C8C22×D14911yescharacteristic
274C2×C8C22×D14911yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—2981no—
277C4⋊C4—2981no—
278C4⋊C4—2981no—
279C4⋊C4—2981no—
280C4⋊C4—2981no—
281C4⋊C4—2981no—
282C4⋊C4—2981no—
283C4⋊C4—1491no—
284C4⋊C4C22×D14911yescharacteristic
285C4⋊C4C22×D14911yescharacteristic
286C4⋊C4C22×D14911yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C42—21no—
298C42—2981no—
299C23—1491no—
300C23—1491no—
301C23D4×D14911yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—2981no—
305Q8—2981no—
306Q8—2981no—
307Q8—2981no—
308Q8—2981no—
309Q8—2981no—
310Q8—5961no—
311Q8—5962no—
312Q8—5962no—
313D4—5961no—
314D4—5961no—
315D4—5961no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—2981no—
325C2×C4—2981no—
326C2×C4—2981no—
327C2×C4—2981no—
328C2×C4—2981no—
329C2×C4—2981no—
330C2×C4—5962no—
331C2×C4—5962no—
332C2×C4—1491no—
333C2×C4—1491no—
334C2×C4D4×D14911yescharacteristic
335C2×C4C23×D14911yescharacteristic
336C8—21no—
337C8—21no—
338C8—2981no—
339C8—2981no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—2981no—
344C22—2981no—
345C22—2981no—
346C22—2981no—
347C22—2981no—
348C22—2981no—
349C22C2×D4×D14911yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—2981no—
356C4—2981no—
357C4—5961no—
358C4—5961no—
359C4—5961no—
360C4—5961no—
361C4#1801195711yescharacteristic
362C4#1801195711yescharacteristic
363C2—41no—
364C2—5961no—
365C2—5961no—
366C2#2375018611yescharacteristic
367C2#2375043911yescharacteristic
368C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#485×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558736C22
hypercenter#485D149
hypocenterC149#3202
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #23749969C2semidirect
4. #23749968C2semidirect
5. #23749966C2semidirect
6. #23749884C2semidirect
7. #23749882C2semidirect
8. #23749867C2semidirect
9. #23749865C2semidirect
10. #23749783C2semidirect
11. #23749782C2semidirect
12. #23749782C2semidirect
13. #23749780C2semidirect
15. #485×C149C2semidirect
184. C149#3202semidirect
191. #485D149semidirect

Maximal subgroups

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

subgroupindex
#237502012
#237501982
#237499692
#237499682
#237499662
#237498842
#237498822
#237498672
#237498652
#237497832
#237497822
#237497802
#237495902
#485×C1492
#3202149