Finite Group Databasebeta

← #34057033

Subgroups — #34057033

Order 19072.

420 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750276C211yesmaximal, characteristic, complemented
2#23750275C211yesmaximal, characteristic, complemented
3#23750029C211yesmaximal, characteristic, complemented
4#23749940C211yesmaximal, characteristic, complemented
5#23749939C211yesmaximal, characteristic, complemented
6#23749937C211yesmaximal, characteristic, complemented
7#23749904C211yesmaximal, characteristic, complemented
8#23749903C211yesmaximal, characteristic, complemented
9#23749860C211yesmaximal, characteristic, complemented
10#23749859C211yesmaximal, characteristic, complemented
11#23749705C211yesmaximal, characteristic, complemented
12#23749688C211yesmaximal, characteristic, complemented
13C2×#18011844C211yesmaximal, characteristic, complemented
14#107×D149C211yesmaximal, characteristic, complemented
15#480×C149C211yesmaximal, characteristic, complemented
16C2×#14558736—21no—
17C2×#14558735—21no—
18C2×#14558721C2211yescharacteristic
19C22×#11924746C2211yescharacteristic
20C2×C8×D149C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011910C2211yescharacteristic
23#18011896—21no—
24#18011894—21no—
25#18011893—21no—
26#18011892—21no—
27#18011889—21no—
28#18011888—21no—
29#18011886C2211yescharacteristic
30#18011885C2211yescharacteristic
31#18011882C2211yescharacteristic
32D4×Dic149C2211yescharacteristic
33#18011873C2211yescharacteristic
34C4×C22⋊D149C2211yescharacteristic
35C2×C4⋊Dic149C2211yescharacteristic
36C4⋊C4×D149C2211yescharacteristic
37C4⋊C4×D149C2211yescharacteristic
38#18011845C2211yescharacteristic
39#18011845C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011844C2211yescharacteristic
42#18011844C2211yescharacteristic
43#18011844C2211yescharacteristic
44#18011844C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52#121×C149C2211yescharacteristic
53C2×C4⋊C4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558736—44no—
60#14558735—44no—
61C2×Dic298—21no—
62C2×Dic298—21no—
63C2×D596—21no—
64C2×D596C2311yescharacteristic
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149D411yescharacteristic
68C22×Dic149—21no—
69C22×Dic149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73C2×C4×D149C2311yescharacteristic
74#14558721—22no—
75C2×#11924746—22no—
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C8×D149—22no—
79C4⋊Dic149—21no—
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715D411yescharacteristic
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149D411yescharacteristic
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713D411yescharacteristic
95C4×Dic149C2311yescharacteristic
96C2×D4×C149—21no—
97C2×D4×C149C2311yescharacteristic
98C22×C4×C149—21no—
99C22×C4×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C22×D149—21no—
108C22×D149C2×D411yescharacteristic
109Dic298—42no—
110Dic298—42no—
111D596—21no—
112D596—21no—
113D596—42no—
114C22⋊D149—42no—
115C22⋊D149—42no—
116C22⋊D149D814yescomplemented
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149—42no—
121C2×Dic149—42no—
122C2×Dic149C2×D411yescharacteristic
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C4×D149—21no—
126C4×D149—21no—
127C4×D149—42no—
128C4×D149—42no—
129C4×D149—42no—
130#11924746—21no—
131#11924746#4112yescomplemented
132C23×C149—21no—
133C23×C149C2×D411yescharacteristic
134D4×C149—21no—
135D4×C149—21no—
136D4×C149—42no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—42no—
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2411yescharacteristic
145C8×C149—21no—
146C8×C149—21no—
147C22×C149—21no—
148C22×C149—21no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149C2×D812yes—
153C22×C149C22×D411yescharacteristic
154C2×D149—21no—
155C2×D149—21no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—41no—
159C2×D149C2×D812yes—
160C4×C149—21no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149—41no—
164C4×C149C2×#4111yescharacteristic
165C4×C1492−1+411yescharacteristic
166Dic149—21no—
167Dic149—21no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171Dic149C2×D812yes—
172C2×C149—22no—
173C2×C149—81no—
174C2×C149#54711yescharacteristic
175C2×C149C22×D811yescharacteristic
176C2×C149#57811yescharacteristic
177D149—22no—
178D149—81no—
179C149#333411yescharacteristic, complemented, Sylow
180#3334—1491nomaximal, Sylow
181#547—1491no—
182#547—1491no—
183#500—1491no—
184#480—1491no—
185#480—1491no—
186#480—1491no—
187#480D14911yescharacteristic, complemented
188#474—1491no—
189#474—1491no—
190#466—1491no—
191#466—1491no—
192C4×D8—1491no—
193C8×D4—1491no—
194C2×#107—1491no—
195C2×#107—1491no—
196C2×#41—2981no—
197C2×#41—2981no—
198C2×D8—1491no—
199C22×C8—1491no—
200C22×C8—1491no—
201C4⋊Q8—1491no—
202C4⋊Q8—1491no—
203#123—2981no—
204#123—2981no—
205#123—2981no—
206#123—2981no—
207C22⋊Q8—2981no—
208C22⋊Q8—2981no—
209#121—1491no—
210#121—1491no—
211#121—1491no—
212#121C2×D14911yescharacteristic
213C4×D4—1491no—
214C4×D4—1491no—
215C4×D4—1491no—
216C2×C4⋊C4—1491no—
217C2×C4⋊C4—1491no—
218C2×C4⋊C4—1491no—
219C2×C4⋊C4C2×D14911yescharacteristic
220#107—1491no—
221#107—1491no—
222#107—1491no—
223#107—1491no—
224#107—1491no—
225#107—1491no—
226#107—1491no—
227#107C2×D14911yescharacteristic
228#107C2×D14911yescharacteristic
229C4⋊C8—1491no—
230#102—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#102C2×D14911yescharacteristic
235#102C2×D14911yescharacteristic
236C22⋊C8—1491no—
237C22⋊C8C2×D14911yescharacteristic
238C4×C8—1491no—
239#41—5964no—
240#41—5964no—
241C2×Q8—2981no—
242C2×Q8—2981no—
243C2×D4—21no—
244C2×D4—2981no—
245C2×D4—2981no—
246C2×D4—2981no—
247C2×D4—1491no—
248C2×D4—1491no—
249C2×D4C22×D14911yescharacteristic
250C22×C4—21no—
251C22×C4—2981no—
252C22×C4—2981no—
253C22×C4—2981no—
254C22×C4—2981no—
255C22×C4—2981no—
256C22×C4—1491no—
257C22×C4C22×D14911yescharacteristic
258D8—2982no—
259C2×C8—2982no—
260C2×C8—2982no—
261C2×C8—1491no—
262C2×C8—1491no—
263C2×C8C22×D14911yescharacteristic
264C2×C8C22×D14911yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—1491no—
272C4⋊C4—1491no—
273C4⋊C4—1491no—
274C4⋊C4—1491no—
275C4⋊C4C22×D14911yescharacteristic
276C4⋊C4C22×D14911yescharacteristic
277C4⋊C4C22×D14911yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—1491no—
285C22⋊C4—1491no—
286C42—1491no—
287C23—21no—
288C23—2981no—
289C23—1491no—
290C23D4×D14911yescharacteristic
291Q8—5962no—
292Q8—5962no—
293D4—21no—
294D4—21no—
295D4—42no—
296D4—2981no—
297D4—2981no—
298D4—5962no—
299D4—5962no—
300D4—5962no—
301D4—1494no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—2981no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—5962no—
314C2×C4—5962no—
315C2×C4—5962no—
316C2×C4—5962no—
317C2×C4—5962no—
318C2×C4—1491no—
319C2×C4—1491no—
320C2×C4—1491no—
321C2×C4D4×D14911yescharacteristic
322C2×C4C23×D14911yescharacteristic
323C8—21no—
324C8—21no—
325C8—2981no—
326C8—1492no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—2981no—
333C22—2981no—
334C22—5961no—
335C22—5961no—
336C22—5961no—
337C22—1492no—
338C22D8×D14912yes—
339C22C2×D4×D14911yescharacteristic
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—2981no—
345C4—2981no—
346C4—5961no—
347C4—5961no—
348C4—5961no—
349C4—1492no—
350C4#41×D14911yescharacteristic
351C4#1801195811yescharacteristic
352C2—22no—
353C2—81no—
354C2—2982no—
355C2—11921no—
356C2#2375027311yescharacteristic
357C2C2×D8×D14911yescharacteristic
358C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#480×C149C2
socleC22×C149C22×D4
hypercenter#480D149
hypocenterC149#3334
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #23750276C2semidirect
2. #23750275C2semidirect
3. #23750029C2semidirect
4. #23749940C2semidirect
5. #23749939C2semidirect
6. #23749937C2semidirect
7. #23749904C2semidirect
8. #23749903C2semidirect
9. #23749860C2semidirect
10. #23749859C2semidirect
11. #23749705C2semidirect
12. #23749688C2semidirect
13. C2×#18011844C2semidirect
14. #107×D149C2semidirect
15. #480×C149C2semidirect
116. C22⋊D149D8semidirect
131. #11924746#41semidirect
179. C149#3334semidirect
187. #480D149semidirect

Maximal subgroups

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

subgroupindex
#237502762
#237502752
#237500292
#237499402
#237499392
#237499372
#237499042
#237499032
#237498602
#237498592
#237497052
#237496882
C2×#180118442
#107×D1492
#480×C1492
#3334149