Finite Group Databasebeta

← #34057284

Subgroups — #34057284

Order 19072.

386 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750338C211yesmaximal, characteristic, complemented
2#23750275C211yesmaximal, characteristic, complemented
3#23750022C211yesmaximal, characteristic, complemented
4#23749948C211yesmaximal, characteristic, complemented
5#23749945C211yesmaximal, characteristic, complemented
6#23749944C211yesmaximal, characteristic, complemented
7#23749913C211yesmaximal, characteristic, complemented
8#23749904C211yesmaximal, characteristic, complemented
9#23749877C211yesmaximal, characteristic, complemented
10#23749876C211yesmaximal, characteristic, complemented
11#23749705C211yesmaximal, characteristic, complemented
12#23749700C211yesmaximal, characteristic, complemented
13#23749668C211yesmaximal, characteristic, complemented
14#23749666C211yesmaximal, characteristic, complemented
15#482×C149C211yesmaximal, characteristic, complemented
16C2×#14558735—21no—
17C2×#14558721C2211yescharacteristic
18C2×#14558720C2211yescharacteristic
19C2×#14558719C2211yescharacteristic
20#18011910C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011899—21no—
23#18011897—21no—
24#18011893—21no—
25#18011892—21no—
26#18011888—21no—
27#18011886C2211yescharacteristic
28#18011885C2211yescharacteristic
29#18011884—21no—
30#18011882C2211yescharacteristic
31D4×Dic149C2211yescharacteristic
32#18011873C2211yescharacteristic
33C4×C22⋊D149C2211yescharacteristic
34#18011869C2211yescharacteristic
35#18011868—21no—
36C2×C4⋊Dic149C2211yescharacteristic
37C4⋊C4×D149C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011842C2211yescharacteristic
44#18011842C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52#121×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558735—44no—
60C2×Dic298—21no—
61C2×Dic298—21no—
62C2×D596—21no—
63C2×D596C2311yescharacteristic
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149D411yescharacteristic
67C22×Dic149—21no—
68C22×Dic149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149C2311yescharacteristic
72#14558721—22no—
73#14558720—22no—
74#14558719—22no—
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C4⋊Dic149—21no—
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715D411yescharacteristic
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149D411yescharacteristic
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713D411yescharacteristic
93C4×Dic149—21no—
94C4×Dic149C2311yescharacteristic
95C2×D4×C149—21no—
96C2×D4×C149C2311yescharacteristic
97C22×C4×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C22⋊C4×C149—21no—
104C22⋊C4×C149—21no—
105C42×C149—21no—
106C22×D149—21no—
107C22×D149C2×D411yescharacteristic
108Dic298—42no—
109Dic298—81no—
110D596—21no—
111D596—21no—
112D596—81no—
113C22⋊D149—22no—
114C22⋊D149—42no—
115C22⋊D149—81no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—42no—
120C2×Dic149—42no—
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C2×Dic149C2×D411yescharacteristic
124C4×D149—21no—
125C4×D149—21no—
126C4×D149—42no—
127C4×D149—42no—
128#11924746—21no—
129#11924746#4112yescomplemented
130C23×C149—21no—
131C23×C149C2×D411yescharacteristic
132D4×C149—21no—
133D4×C149—21no—
134D4×C149—42no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2411yescharacteristic
142C8×C149—21no—
143C8×C149—21no—
144C22×C149—21no—
145C22×C149—21no—
146C22×C149—21no—
147C22×C149—41no—
148C22×C149—41no—
149C22×C149—41no—
150C22×C149C22×D411yescharacteristic
151C2×D149—21no—
152C2×D149—21no—
153C2×D149—21no—
154C2×D149—41no—
155C2×D149—41no—
156C2×D149—41no—
157C4×C149—21no—
158C4×C149—41no—
159C4×C149—41no—
160C4×C149—41no—
161C4×C149C2×#4111yescharacteristic
162C4×C1492−1+411yescharacteristic
163Dic149—21no—
164Dic149—21no—
165Dic149—41no—
166Dic149—41no—
167Dic149—41no—
168Dic149AGL(1,ℤ/8)12yes—
169C2×C149—41no—
170C2×C149—81no—
171C2×C149#54711yescharacteristic
172C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C149#57711yescharacteristic
174D149—41no—
175D149—81no—
176C149#335411yescharacteristic, complemented, Sylow
177#3354—1491nomaximal, Sylow
178#555—1491no—
179#547—1491no—
180#498—1491no—
181#482—1491no—
182#482D14911yescharacteristic, complemented
183#481—1491no—
184#481—1491no—
185#476—1491no—
186#474—1491no—
187#469—1491no—
188#469—1491no—
189C4×D8—1491no—
190#436—1491no—
191#428—1491no—
192#428—1491no—
193C2×#41—2981no—
194C2×D8—1491no—
195C2×M16—1491no—
196C2×M16—1491no—
197C4⋊Q8—1491no—
198C4⋊Q8—1491no—
199#124—2981no—
200#124—2981no—
201#123—2981no—
202#123—2981no—
203C22⋊Q8—2981no—
204#121—2981no—
205#121—1491no—
206#121—1491no—
207#121—1491no—
208#121C2×D14911yescharacteristic
209C4×D4—1491no—
210C4×D4—1491no—
211C4×D4—1491no—
212#117—2981no—
213#117—1491no—
214#117C2×D14911yescharacteristic
215C2×C4⋊C4—1491no—
216C2×C4⋊C4—1491no—
217#107—1491no—
218#107—1491no—
219#107C2×D14911yescharacteristic
220#106—1491no—
221#106—1491no—
222#106—1491no—
223#106—1491no—
224#106—1491no—
225#106C2×D14911yescharacteristic
226C4⋊C8—1491no—
227#102—1491no—
228#102—1491no—
229#102—1491no—
230#102—1491no—
231#102C2×D14911yescharacteristic
232#102C2×D14911yescharacteristic
233C22⋊C8—1491no—
234C22⋊C8C2×D14911yescharacteristic
235C4×C8—1491no—
236#41—5964no—
237C2×Q8—2981no—
238C2×Q8—2981no—
239C2×D4—21no—
240C2×D4—2981no—
241C2×D4—2981no—
242C2×D4—2981no—
243C2×D4—1491no—
244C2×D4—1491no—
245C2×D4C22×D14911yescharacteristic
246C22×C4—2981no—
247C22×C4—2981no—
248C22×C4—2981no—
249C22×C4—2981no—
250C22×C4—1491no—
251C22×C4C22×D14911yescharacteristic
252D8—2982no—
253M16—2982no—
254M16—2982no—
255C2×C8—1491no—
256C2×C8—1491no—
257C2×C8C22×D14911yescharacteristic
258C2×C8C22×D14911yescharacteristic
259C4⋊C4—2981no—
260C4⋊C4—2981no—
261C4⋊C4—2981no—
262C4⋊C4—2981no—
263C4⋊C4—1491no—
264C4⋊C4—1491no—
265C4⋊C4—1491no—
266C4⋊C4—1491no—
267C4⋊C4C22×D14911yescharacteristic
268C4⋊C4C22×D14911yescharacteristic
269C4⋊C4C22×D14911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—1491no—
279C22⋊C4—1491no—
280C42—21no—
281C42—2981no—
282C42—1491no—
283C23—21no—
284C23—2981no—
285C23—1491no—
286C23D4×D14911yescharacteristic
287Q8—5962no—
288Q8—11921no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—2982no—
293D4—2981no—
294D4—2981no—
295D4—5962no—
296D4—11921no—
297D4—11921no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—2981no—
306C2×C4—2981no—
307C2×C4—2981no—
308C2×C4—5962no—
309C2×C4—5962no—
310C2×C4—5962no—
311C2×C4—5962no—
312C2×C4—1491no—
313C2×C4—1491no—
314C2×C4—1491no—
315C2×C4D4×D14911yescharacteristic
316C2×C4C23×D14911yescharacteristic
317C8—21no—
318C8—21no—
319C8—2981no—
320C8—1492no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—2981no—
328C22—2981no—
329C22—2981no—
330C22—5961no—
331C22—5961no—
332C22—5961no—
333C22C2×D4×D14911yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—2981no—
339C4—2981no—
340C4—5961no—
341C4—5961no—
342C4—5961no—
343C4—1492no—
344C4#41×D14911yescharacteristic
345C4#1801195811yescharacteristic
346C2—41no—
347C2—81no—
348C2—5961no—
349C2—11921no—
350C2#2375027311yescharacteristic
351C2AGL(1,ℤ/8)×D14911yescharacteristic
352C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#482×C149C2
socleC22×C149C22×D4
hypercenter#482D149
hypocenterC149#3354
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #23750338C2semidirect
2. #23750275C2semidirect
3. #23750022C2semidirect
4. #23749948C2semidirect
5. #23749945C2semidirect
6. #23749944C2semidirect
7. #23749913C2semidirect
8. #23749904C2semidirect
9. #23749877C2semidirect
10. #23749876C2semidirect
11. #23749705C2semidirect
12. #23749700C2semidirect
13. #23749668C2semidirect
14. #23749666C2semidirect
15. #482×C149C2semidirect
129. #11924746#41semidirect
176. C149#3354semidirect
182. #482D149semidirect

Maximal subgroups

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

subgroupindex
#237503382
#237502752
#237500222
#237499482
#237499452
#237499442
#237499132
#237499042
#237498772
#237498762
#237497052
#237497002
#237496682
#237496662
#482×C1492
#3354149