Finite Group Databasebeta

← #34054885

Subgroups — #34054885

Order 19072.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750228C211yesmaximal, characteristic, complemented
2#23750106C211yesmaximal, characteristic, complemented
3#23749938C211yesmaximal, characteristic, complemented
4#23749935C211yesmaximal, characteristic, complemented
5#23749924C211yesmaximal, characteristic, complemented
6#23749824C211yesmaximal, characteristic, complemented
7#23749819C211yesmaximal, characteristic, complemented
8#23749772C211yesmaximal, characteristic, complemented
9#23749768C211yesmaximal, characteristic, complemented
10#23749736C211yesmaximal, characteristic, complemented
11#23749722C211yesmaximal, characteristic, complemented
12#23749712C211yesmaximal, characteristic, complemented
13#23749705C211yesmaximal, characteristic, complemented
14#23749683C211yesmaximal, characteristic, complemented
15#481×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×D1192C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21#18011907C2211yescharacteristic
22#18011902C2211yescharacteristic
23#18011895—21no—
24#18011893—21no—
25#18011885C2211yescharacteristic
26#18011883—21no—
27#18011882—21no—
28#18011876C2211yescharacteristic
29#18011876C2211yescharacteristic
30D4×Dic149C2211yescharacteristic
31#18011873C2211yescharacteristic
32#18011873C2211yescharacteristic
33#18011873C2211yescharacteristic
34C4×C22⋊D149—21no—
35C4×C22⋊D149—21no—
36#18011870C2211yescharacteristic
37#18011869—21no—
38C4⋊C4×D149—21no—
39#18011844C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52#121×C149C2211yescharacteristic
53C2×C4⋊C4×C149C2211yescharacteristic
54#106×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558736—22no—
60#14558736—22no—
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×D596C2311yescharacteristic
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C22×Dic149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73#14558725—22no—
74#14558724—22no—
75D1192—22no—
76#14558721—22no—
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C4⋊Dic149—21no—
80C4⋊Dic149D411yescharacteristic
81C4⋊Dic149D411yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149D411yescharacteristic
88C22⋊Dic149D411yescharacteristic
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149C2311yescharacteristic
96C4×Dic149C2311yescharacteristic
97C2×D4×C149—21no—
98C2×D4×C149C2311yescharacteristic
99C22×C4×C149—21no—
100C22×C4×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C4⋊C4×C149—21no—
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C4⋊C4×C149C2311yescharacteristic
107C22⋊C4×C149—21no—
108C22×D149—21no—
109C22×D149—21no—
110Dic298—21no—
111Dic298#4112yes—
112D596—21no—
113D596—21no—
114D596—21no—
115D596#4112yes—
116C22⋊D149—24no—
117C22⋊D149—81no—
118C22⋊D149—81no—
119C22⋊D149—81no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—81no—
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C4×D149—24no—
128C4×D149—81no—
129C4×D149—81no—
130C4×D149—81no—
131#11924746—21no—
132#11924746—21no—
133C23×C149—21no—
134C23×C149C2×D411yescharacteristic
135D4×C149—21no—
136D4×C149—21no—
137D4×C149—81no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—81no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2411yescharacteristic
146C8×C149—21no—
147C8×C149—21no—
148C22×C149—21no—
149C22×C149—21no—
150C22×C149—21no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149C22×D411yescharacteristic
155C2×D149—22no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—41no—
159C2×D149—41no—
160C2×D149—41no—
161C4×C149—21no—
162C4×C149—41no—
163C4×C149—41no—
164C4×C149—41no—
165C4×C149C2×#4111yescharacteristic
166C4×C149C2×#4111yescharacteristic
167Dic149—22no—
168Dic149—21no—
169Dic149—21no—
170Dic149—21no—
171Dic149—21no—
172Dic149—41no—
173C2×C149—41no—
174C2×C149—81no—
175C2×C149#52511yescharacteristic
176C2×C149#57611yescharacteristic
177C2×C149#57711yescharacteristic
178D149—42no—
179D149—81no—
180C149#311911yescharacteristic, complemented, Sylow
181#3119—1491nomaximal, Sylow
182#540—1491no—
183#520—1491no—
184#481D14911yescharacteristic, complemented
185#480—1491no—
186#479—1491no—
187#478—1491no—
188#460—1491no—
189#459—1491no—
190#449—1491no—
191#449—1491no—
192#442—1491no—
193#440—1491no—
194C4×SD16—1491no—
195C4×D8—1491no—
196#433—1491no—
197C2×#41—1491no—
198C2×SD16—1491no—
199C2×SD16—1491no—
200C2×D8—1491no—
201C2×D8—1491no—
202#127—1491no—
203#125—1491no—
204#123—2981no—
205#123—2981no—
206#121—2981no—
207#121—2981no—
208#121—1491no—
209#121C2×D14911yescharacteristic
210C4×Q8—1491no—
211C4×Q8—1491no—
212C4×D4—2981no—
213C4×D4—2981no—
214C4×D4—1491no—
215C4×D4—1491no—
216C4×D4—1491no—
217C4×D4—1491no—
218#117—2981no—
219#117—1491no—
220C2×C4⋊C4—2981no—
221C2×C4⋊C4C2×D14911yescharacteristic
222#107—1491no—
223#107—1491no—
224#106C2×D14911yescharacteristic
225#106C2×D14911yescharacteristic
226C4⋊C8—1491no—
227C4⋊C8—1491no—
228#103—1491no—
229#103—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
238#97—1491no—
239C4×C8—1491no—
240#41—2982no—
241#41—2982no—
242C2×Q8—1491no—
243C2×D4—21no—
244C2×D4—2981no—
245C2×D4—2981no—
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—1491no—
249C2×D4—1491no—
250C2×D4C22×D14911yescharacteristic
251C22×C4—21no—
252C22×C4—2981no—
253C22×C4—2981no—
254C22×C4—2981no—
255C22×C4—2981no—
256C22×C4—2981no—
257C22×C4C22×D14911yescharacteristic
258SD16—2982no—
259SD16—2982no—
260D8—2982no—
261D8—2982no—
262C2×C8—1491no—
263C2×C8—1491no—
264C2×C8C22×D14911yescharacteristic
265C2×C8C22×D14911yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—1491no—
272C4⋊C4—1491no—
273C4⋊C4—1491no—
274C4⋊C4C22×D14911yescharacteristic
275C4⋊C4C22×D14911yescharacteristic
276C4⋊C4C22×D14911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—1491no—
284C22⋊C4—1491no—
285C42—2981no—
286C42—2981no—
287C42—1491no—
288C42—1491no—
289C23—21no—
290C23—2981no—
291C23—2981no—
292C23D4×D14911yescharacteristic
293Q8—2981no—
294Q8—1492no—
295D4—21no—
296D4—21no—
297D4—81no—
298D4—2984no—
299D4—2981no—
300D4—2981no—
301D4—2981no—
302D4—1492no—
303D4—11921no—
304D4—11921no—
305D4—11921no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—2984no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—1491no—
316C2×C4—1491no—
317C2×C4—1491no—
318C2×C4—1491no—
319C2×C4—11921no—
320C2×C4—11921no—
321C2×C4—11921no—
322C2×C4—11921no—
323C2×C4D4×D14911yescharacteristic
324C2×C4C23×D14911yescharacteristic
325C8—21no—
326C8—21no—
327C8—2981no—
328C8—2981no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—2982no—
336C22—5961no—
337C22—5961no—
338C22—5961no—
339C22—5961no—
340C22—5961no—
341C22C2×D4×D14911yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—2981no—
347C4—2981no—
348C4—2981no—
349C4—2981no—
350C4—2982no—
351C4—5961no—
352C4#41×D14911yescharacteristic
353C4#41×D14911yescharacteristic
354C2—41no—
355C2—81no—
356C2—5962no—
357C2—11921no—
358C2#2375013311yescharacteristic
359C2#2375042911yescharacteristic
360C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#481×C149C2
socleC22×C149C22×D4
hypercenter#481D149
hypocenterC149#3119
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #23750228C2semidirect
2. #23750106C2semidirect
3. #23749938C2semidirect
4. #23749935C2semidirect
5. #23749924C2semidirect
6. #23749824C2semidirect
7. #23749819C2semidirect
8. #23749772C2semidirect
9. #23749768C2semidirect
10. #23749736C2semidirect
11. #23749722C2semidirect
12. #23749712C2semidirect
13. #23749705C2semidirect
14. #23749683C2semidirect
15. #481×C149C2semidirect
180. C149#3119semidirect
184. #481D149semidirect

Maximal subgroups

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

subgroupindex
#237502282
#237501062
#237499382
#237499352
#237499242
#237498242
#237498192
#237497722
#237497682
#237497362
#237497222
#237497122
#237497052
#237496832
#481×C1492
#3119149