Finite Group Databasebeta

← #34055771

Subgroups — #34055771

Order 19072.

364 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750233C211yesmaximal, characteristic, complemented
2#23750195C211yesmaximal, characteristic
3#23750016C211yesmaximal, characteristic, complemented
4#23750003C211yesmaximal, characteristic, complemented
5#23749992C211yesmaximal, characteristic, complemented
6#23749978C211yesmaximal, characteristic, complemented
7#23749844C211yesmaximal, characteristic, complemented
8#23749836C211yesmaximal, characteristic, complemented
9#23749835C211yesmaximal, characteristic, complemented
10#23749788C211yesmaximal, characteristic
11#23749784C211yesmaximal, characteristic
12#23749782C211yesmaximal, characteristic, complemented
13#23749779C211yesmaximal, characteristic, complemented
14#23749685C211yesmaximal, characteristic, complemented
15#464×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic
18C2×Dic596C2211yescharacteristic
19C2×Dic596C2211yescharacteristic
20C2×#14558726C2211yescharacteristic
21C2×#14558726C2211yescharacteristic
22C2×#14558726C2211yescharacteristic
23C2×#14558724C2211yescharacteristic
24#18011911C2211yescharacteristic
25#18011909C2211yescharacteristic
26#18011909C2211yescharacteristic
27#18011906—21no—
28#18011905—21no—
29#18011903—21no—
30#18011902C2211yescharacteristic
31#18011901—21no—
32#18011898C2211yescharacteristic
33#18011893—21no—
34#18011893—21no—
35#18011891C2211yescharacteristic
36#18011888—21no—
37#18011888—21no—
38#18011887C2211yescharacteristic
39C4×Dic298C2211yescharacteristic
40#18011868C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×Q16×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54#124×C149C2211yescharacteristic
55C4×Q8×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558735—41no—
60#14558735—41no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C2×Dic298C2311yescharacteristic
64C2×Dic298C2311yescharacteristic
65Q8×D149—41no—
66Q8×D149—41no—
67C2×C22⋊D149—21no—
68C22×Dic149—21no—
69C2×C4×D149—21no—
70C2×C4×D149C2311yescharacteristic
71Dic596—41no—
72Dic596—41no—
73#14558726—41no—
74#14558726—41no—
75#14558726—41no—
76#14558724—41no—
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C4⋊Dic149—21no—
80C4⋊Dic149—21no—
81C4⋊Dic149—21no—
82C4⋊Dic149—21no—
83C4⋊Dic149C2311yescharacteristic
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89#14558715—21no—
90#14558715—21no—
91#14558715D411yescharacteristic
92#14558715D411yescharacteristic
93C22⋊Dic149—21no—
94C22⋊Dic149—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713D411yescharacteristic
98#14558713D411yescharacteristic
99C4×Dic149—21no—
100C4×Dic149C2311yescharacteristic
101C2×Q8×C149C2311yescharacteristic
102C2×Q8×C149C2311yescharacteristic
103C2×D4×C149C2311yescharacteristic
104Q16×C149—41no—
105SD16×C149—41no—
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C4⋊C4×C149—21no—
109C4⋊C4×C149C2311yescharacteristic
110C22⋊C4×C149—21no—
111C22⋊C4×C149—21no—
112C42×C149—21no—
113C42×C149C2311yescharacteristic
114C22×D149C2×D411yescharacteristic
115Dic298—21no—
116Dic298—21no—
117Dic298—21no—
118Dic298—21no—
119Dic298—21no—
120Dic298—21no—
121Dic298—42no—
122C22⋊D149—42no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—42no—
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C2×Dic149C2×D411yescharacteristic
131C4×D149—21no—
132C4×D149—21no—
133C4×D149—42no—
134#11924746—21no—
135#11924746—21no—
136C23×C149—21no—
137Q8×C149—21no—
138Q8×C149—21no—
139Q8×C149—21no—
140Q8×C149—21no—
141D4×C149—21no—
142D4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2411yescharacteristic
149C8×C149—21no—
150C8×C149—21no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149C22×D411yescharacteristic
155C2×D149—21no—
156C2×D149—21no—
157C2×D149—21no—
158C4×C149—21no—
159C4×C149—21no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149H(5,𝔽2)11yescharacteristic
164C4×C149H(5,𝔽2)11yescharacteristic
165Dic149—21no—
166Dic149—21no—
167Dic149—21no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171Dic149—41no—
172C2×C149—81no—
173C2×C149#53511yescharacteristic
174C2×C149#57811yescharacteristic
175C2×C149#57811yescharacteristic
176D149—41no—
177C149#322311yescharacteristic, complemented, Sylow
178#3223—1491nomaximal, Sylow
179#541—1491no—
180#536—1491no—
181#497—1491no—
182#494—1491no—
183#491—1491no—
184#488—1491no—
185#464—1491no—
186#464D14911yescharacteristic, complemented
187#462—1491no—
188#462—1491no—
189#452—1491no—
190#452—1491no—
191#451—1491no—
192#451—1491no—
193#433—1491no—
194C2×#41—1491no—
195C22×Q8—1491no—
196C2×Q16—1491no—
197C2×Q16—1491no—
198C2×Q16—1491no—
199C2×Q16—1491no—
200C2×Q16—1491no—
201C2×Q16C2×D14911yescharacteristic
202C2×SD16—1491no—
203C2×SD16C2×D14911yescharacteristic
204C4⋊Q8—1491no—
205C4⋊Q8—1491no—
206C4⋊Q8—1491no—
207#126—2981no—
208#126—2981no—
209#125—2981no—
210#125—2981no—
211#125—1491no—
212#124—1491no—
213#124C2×D14911yescharacteristic
214#123—2981no—
215#123—2981no—
216C22⋊Q8—2981no—
217C22⋊Q8—2981no—
218C22⋊Q8—1491no—
219C22⋊Q8—1491no—
220C4×Q8—1491no—
221C4×Q8C2×D14911yescharacteristic
222#117—1491no—
223C4⋊C8—1491no—
224C4⋊C8C2×D14911yescharacteristic
225#103—1491no—
226#103—1491no—
227#103—1491no—
228#103—1491no—
229#103—1491no—
230#103C2×D14911yescharacteristic
231#102—1491no—
232#102C2×D14911yescharacteristic
233C22⋊C8—1491no—
234C22⋊C8—1491no—
235#97—1491no—
236C4×C8—1491no—
237#41—5961no—
238#41—5961no—
239C2×Q8—2981no—
240C2×Q8—5961no—
241C2×Q8—5961no—
242C2×Q8—1491no—
243C2×Q8—1491no—
244C2×Q8—1491no—
245C2×Q8C22×D14911yescharacteristic
246C2×Q8C22×D14911yescharacteristic
247C2×D4—2981no—
248C2×D4C22×D14911yescharacteristic
249C22×C4—2981no—
250C22×C4—2981no—
251C22×C4—1491no—
252Q16—41no—
253Q16—5961no—
254Q16—5961no—
255Q16—5961no—
256Q16—5961no—
257Q16—5961no—
258SD16—41no—
259SD16—5961no—
260C2×C8—1491no—
261C2×C8—1491no—
262C2×C8C22×D14911yescharacteristic
263C2×C8C22×D14911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—2981no—
272C4⋊C4—2981no—
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—1491no—
277C4⋊C4—1491no—
278C4⋊C4—1491no—
279C4⋊C4C22×D14911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—1491no—
287C22⋊C4—1491no—
288C42—21no—
289C42—2981no—
290C42—1491no—
291C42C22×D14911yescharacteristic
292C23—21no—
293C23—1491no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—2981no—
299Q8—2981no—
300Q8—2981no—
301Q8—2981no—
302Q8—2981no—
303Q8—2981no—
304Q8—5962no—
305D4—21no—
306D4—21no—
307D4—5962no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—5962no—
318C2×C4—5962no—
319C2×C4—1491no—
320C2×C4—1491no—
321C2×C4—1491no—
322C2×C4D4×D14911yescharacteristic
323C2×C4D4×D14911yescharacteristic
324C2×C4C23×D14911yescharacteristic
325C8—21no—
326C8—21no—
327C8—2981no—
328C8—2981no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—2981no—
333C22—2981no—
334C22—2981no—
335C22C2×D4×D14911yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—2981no—
342C4—2981no—
343C4—2981no—
344C4—5961no—
345C4—5961no—
346C4—5961no—
347C4—5961no—
348C4#1801195611yescharacteristic
349C4#1801195711yescharacteristic
350C2—81no—
351C2—5961no—
352C2#2375019111yescharacteristic
353C2#2375043911yescharacteristic
354C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#464×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558735C22
hypercenter#464D149
hypocenterC149#3223
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #23750233C2semidirect
3. #23750016C2semidirect
4. #23750003C2semidirect
5. #23749992C2semidirect
6. #23749978C2semidirect
7. #23749844C2semidirect
8. #23749836C2semidirect
9. #23749835C2semidirect
12. #23749782C2semidirect
13. #23749779C2semidirect
14. #23749685C2semidirect
15. #464×C149C2semidirect
177. C149#3223semidirect
186. #464D149semidirect

Maximal subgroups

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

subgroupindex
#237502332
#237501952
#237500162
#237500032
#237499922
#237499782
#237498442
#237498362
#237498352
#237497882
#237497842
#237497822
#237497792
#237496852
#464×C1492
#3223149