Finite Group Databasebeta

← #34054837

Subgroups — #34054837

Order 19072.

430 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750170C211yesmaximal, characteristic, complemented
2#23750093C211yesmaximal, characteristic, complemented
3#23749949C211yesmaximal, characteristic, complemented
4#23749909C211yesmaximal, characteristic, complemented
5#23749904C211yesmaximal, characteristic, complemented
6#23749824C211yesmaximal, characteristic, complemented
7#23749819C211yesmaximal, characteristic, complemented
8#23749772C211yesmaximal, characteristic, complemented
9#23749768C211yesmaximal, characteristic, complemented
10#23749736C211yesmaximal, characteristic, complemented
11#23749734C211yesmaximal, characteristic, complemented
12#23749724C211yesmaximal, characteristic, complemented
13#23749722C211yesmaximal, characteristic, complemented
14#23749679C211yesmaximal, characteristic, complemented
15#482×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558735—21no—
18C2×#14558725C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×D1192C2211yescharacteristic
21C2×#14558721C2211yescharacteristic
22#18011910C2211yescharacteristic
23#18011907C2211yescharacteristic
24#18011897—21no—
25#18011885C2211yescharacteristic
26#18011883—21no—
27#18011876C2211yescharacteristic
28#18011876C2211yescharacteristic
29D4×Dic149C2211yescharacteristic
30#18011873C2211yescharacteristic
31#18011873C2211yescharacteristic
32#18011873C2211yescharacteristic
33#18011871—21no—
34#18011871—21no—
35#18011871—21no—
36#18011868—21no—
37C2×C4×Dic149C2211yescharacteristic
38C42×D149—21no—
39#18011844C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic
51#18011821C2211yescharacteristic
52#121×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558736—22no—
60#14558736—22no—
61#14558735—44no—
62C2×Dic298—21no—
63C2×Dic298C2311yescharacteristic
64C2×D596C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C22×Dic149—21no—
71C22×Dic149D411yescharacteristic
72C22×Dic149D411yescharacteristic
73C2×C4×D149—21no—
74C2×C4×D149—21no—
75C2×C4×D149—21no—
76C2×C4×D149—21no—
77#14558725—22no—
78#14558724—22no—
79D1192—22no—
80#14558721—22no—
81C2×#11924746C2311yescharacteristic
82C2×#11924746C2311yescharacteristic
83C4⋊Dic149C2311yescharacteristic
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87C22⋊Dic149—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92C4×Dic149—21no—
93C4×Dic149—21no—
94C4×Dic149D411yescharacteristic
95C4×Dic149D411yescharacteristic
96C4×Dic149C2311yescharacteristic
97C4×Dic149C2311yescharacteristic
98C2×D4×C149—21no—
99C2×D4×C149C2311yescharacteristic
100C22×C4×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C22⋊C4×C149—21no—
108C42×C149—21no—
109C22×D149—21no—
110C22×D149—21no—
111Dic298—21no—
112Dic298—42no—
113Dic298#4112yescomplemented
114D596—21no—
115D596—21no—
116D596—21no—
117D596#4112yescomplemented
118C22⋊D149—24no—
119C22⋊D149—42no—
120C22⋊D149—42no—
121C22⋊D149—42no—
122C2×Dic149—21no—
123C2×Dic149—22no—
124C2×Dic149—21no—
125C2×Dic149—41no—
126C2×Dic149—42no—
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C2×Dic149C2×D411yescharacteristic
131C4×D149—24no—
132C4×D149—42no—
133C4×D149—42no—
134C4×D149—42no—
135#11924746—21no—
136#11924746—21no—
137C23×C149—21no—
138C23×C149C2×D411yescharacteristic
139D4×C149—21no—
140D4×C149—21no—
141D4×C149—42no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2411yescharacteristic
149C8×C149—21no—
150C8×C149—21no—
151C22×C149—21no—
152C22×C149—21no—
153C22×C149—21no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149C22×D411yescharacteristic
158C2×D149—22no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C4×C149—21no—
165C4×C149—41no—
166C4×C149—41no—
167C4×C149—41no—
168C4×C149C2×#4111yescharacteristic
169C4×C149C2×#4111yescharacteristic
170Dic149—22no—
171Dic149—21no—
172Dic149—21no—
173Dic149—21no—
174Dic149—41no—
175Dic149AGL(1,ℤ/8)12yes—
176C2×C149—41no—
177C2×C149—81no—
178C2×C149#52511yescharacteristic
179C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C149#57511yescharacteristic
181D149—42no—
182D149—81no—
183C149#311511yescharacteristic, complemented, Sylow
184#3115—1491nomaximal, Sylow
185#532—1491no—
186C4×#41—1491no—
187#482—1491no—
188#482D14911yescharacteristic, complemented
189#475—1491no—
190#474—1491no—
191#460—1491no—
192#459—1491no—
193#449—1491no—
194#449—1491no—
195#442—1491no—
196#442—1491no—
197#440—1491no—
198#440—1491no—
199#432—1491no—
200C2×#41—2981no—
201C2×#41—1491no—
202C2×SD16—1491no—
203C2×SD16—1491no—
204C2×D8—1491no—
205C2×D8—1491no—
206C4⋊Q8—1491no—
207#127—1491no—
208#124—2981no—
209#121—2981no—
210#121—1491no—
211#121C2×D14911yescharacteristic
212C4×Q8—1491no—
213C4×Q8—1491no—
214C4×D4—2981no—
215C4×D4—2981no—
216C4×D4—2981no—
217C4×D4—1491no—
218C4×D4—1491no—
219C4×D4—1491no—
220C4×D4—1491no—
221#117—2981no—
222#117C2×D14911yescharacteristic
223C2×C42—2981no—
224C2×C42—1491no—
225#107—1491no—
226#107C2×D14911yescharacteristic
227#106—1491no—
228#106C2×D14911yescharacteristic
229C4⋊C8—1491no—
230C4⋊C8—1491no—
231#103—1491no—
232#103—1491no—
233#102—1491no—
234#102—1491no—
235#102—1491no—
236#102—1491no—
237#102C2×D14911yescharacteristic
238#102C2×D14911yescharacteristic
239C22⋊C8—1491no—
240C22⋊C8C2×D14911yescharacteristic
241#97—1491no—
242#97—1491no—
243#41—2982no—
244#41—2982no—
245#41—5964no—
246C2×Q8—2981no—
247C2×Q8—1491no—
248C2×D4—21no—
249C2×D4—2981no—
250C2×D4—2981no—
251C2×D4—2981no—
252C2×D4—2981no—
253C2×D4—1491no—
254C2×D4—1491no—
255C2×D4C22×D14911yescharacteristic
256C22×C4—2981no—
257C22×C4—2981no—
258C22×C4—2981no—
259C22×C4—2981no—
260C22×C4—2981no—
261C22×C4—1491no—
262C22×C4—1491no—
263C22×C4C22×D14911yescharacteristic
264SD16—2982no—
265SD16—2982no—
266D8—2982no—
267D8—2982no—
268C2×C8—1491no—
269C2×C8—1491no—
270C2×C8C22×D14911yescharacteristic
271C2×C8C22×D14911yescharacteristic
272C4⋊C4—2981no—
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—1491no—
276C4⋊C4C22×D14911yescharacteristic
277C4⋊C4C22×D14911yescharacteristic
278C4⋊C4C22×D14911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C42—21no—
287C42—2981no—
288C42—2981no—
289C42—1491no—
290C42—1491no—
291C42—1491no—
292C42—1491no—
293C23—21no—
294C23—2981no—
295C23—2981no—
296C23D4×D14911yescharacteristic
297Q8—2981no—
298Q8—5962no—
299Q8—1492no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—2984no—
304D4—2981no—
305D4—2981no—
306D4—2981no—
307D4—5962no—
308D4—5962no—
309D4—5962no—
310D4—1492no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—2984no—
317C2×C4—2981no—
318C2×C4—2982no—
319C2×C4—2981no—
320C2×C4—5962no—
321C2×C4—5962no—
322C2×C4—5962no—
323C2×C4—5961no—
324C2×C4—5962no—
325C2×C4—1491no—
326C2×C4—1491no—
327C2×C4—1491no—
328C2×C4—1491no—
329C2×C4D4×D14911yescharacteristic
330C2×C4C23×D14911yescharacteristic
331C8—21no—
332C8—21no—
333C8—2981no—
334C8—2981no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—2982no—
342C22—5961no—
343C22—5961no—
344C22—5961no—
345C22—5961no—
346C22—5961no—
347C22C2×D4×D14911yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—2981no—
353C4—2981no—
354C4—2981no—
355C4—2982no—
356C4—5961no—
357C4—1492no—
358C4#41×D14911yescharacteristic
359C4#41×D14911yescharacteristic
360C2—41no—
361C2—81no—
362C2—5962no—
363C2—11921no—
364C2#2375013311yescharacteristic
365C2AGL(1,ℤ/8)×D14911yescharacteristic
366C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#482×C149C2
socleC22×C149C22×D4
hypercenter#482D149
hypocenterC149#3115
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. #23750170C2semidirect
2. #23750093C2semidirect
3. #23749949C2semidirect
4. #23749909C2semidirect
5. #23749904C2semidirect
6. #23749824C2semidirect
7. #23749819C2semidirect
8. #23749772C2semidirect
9. #23749768C2semidirect
10. #23749736C2semidirect
11. #23749734C2semidirect
12. #23749724C2semidirect
13. #23749722C2semidirect
14. #23749679C2semidirect
15. #482×C149C2semidirect
113. Dic298#41semidirect
117. D596#41semidirect
183. C149#3115semidirect
188. #482D149semidirect

Maximal subgroups

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

subgroupindex
#237501702
#237500932
#237499492
#237499092
#237499042
#237498242
#237498192
#237497722
#237497682
#237497362
#237497342
#237497242
#237497222
#237496792
#482×C1492
#3115149