Finite Group Databasebeta

← #34054892

Subgroups — #34054892

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#23750230C211yesmaximal, characteristic, complemented
2#23750105C211yesmaximal, characteristic, complemented
3#23749944C211yesmaximal, characteristic, complemented
4#23749939C211yesmaximal, characteristic, complemented
5#23749933C211yesmaximal, characteristic, complemented
6#23749926C211yesmaximal, characteristic, complemented
7#23749826C211yesmaximal, characteristic, complemented
8#23749821C211yesmaximal, characteristic, complemented
9#23749772C211yesmaximal, characteristic, complemented
10#23749772C211yesmaximal, characteristic, complemented
11#23749738C211yesmaximal, characteristic, complemented
12#23749727C211yesmaximal, characteristic, complemented
13C4×#14558725C211yesmaximal, characteristic, complemented
14C4×D1192C211yesmaximal, characteristic, complemented
15#433×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×D1192C2211yescharacteristic
20C2×D1192C2211yescharacteristic
21#18011908C2211yescharacteristic
22#18011903C2211yescharacteristic
23#18011896—21no—
24#18011896—21no—
25#18011885C2211yescharacteristic
26#18011885C2211yescharacteristic
27#18011884—21no—
28#18011884—21no—
29C4×Dic298C2211yescharacteristic
30C4×Dic298C2211yescharacteristic
31C4×D596C2211yescharacteristic
32C4×D596C2211yescharacteristic
33C4×D596C2211yescharacteristic
34C4×D596C2211yescharacteristic
35#18011871—21no—
36#18011871—21no—
37#18011869—21no—
38C2×C4⋊Dic149C2211yescharacteristic
39C4⋊C4×D149—21no—
40#18011845C2211yescharacteristic
41#18011845C2211yescharacteristic
42#18011843C2211yescharacteristic
43#18011843C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011833C2211yescharacteristic
51#18011833C2211yescharacteristic
52#117×C149C2211yescharacteristic
53C4⋊C8×C149C2211yescharacteristic
54C4⋊C8×C149C2211yescharacteristic
55C22⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57#97×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59#14558736—22no—
60#14558736—22no—
61C2×Dic298C2311yescharacteristic
62C2×D596—21no—
63C2×D596—21no—
64C2×D596C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×D596C2311yescharacteristic
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C22×Dic149—21no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73C2×C4×D149—21no—
74C2×C4×D149—21no—
75C2×C4×D149—21no—
76#14558725—22no—
77#14558725—22no—
78D1192—22no—
79D1192—22no—
80C4⋊Dic149—21no—
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83C4⋊Dic149C2311yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95C4×Dic149—21no—
96C4×Dic149—21no—
97C22×C4×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C4⋊C4×C149D411yescharacteristic
103C4⋊C4×C149D411yescharacteristic
104C22⋊C4×C149D411yescharacteristic
105C22⋊C4×C149D411yescharacteristic
106C42×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149—21no—
110C22×D149—21no—
111Dic298—21no—
112Dic298#4112yes—
113D596—21no—
114D596—21no—
115D596—21no—
116D596—21no—
117D596—21no—
118D596—81no—
119D596—81no—
120D596#4112yes—
121C22⋊D149—24no—
122C22⋊D149—81no—
123C22⋊D149—81no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—81no—
130C4×D149—24no—
131C4×D149—81no—
132C4×D149—81no—
133C4×D149—81no—
134C4×D149—81no—
135C23×C149C2×D411yescharacteristic
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2×D411yescharacteristic
143C2×C4×C149C2411yescharacteristic
144C8×C149—21no—
145C8×C149—21no—
146C8×C149—21no—
147C8×C149—21no—
148C22×C149—21no—
149C22×C149—21no—
150C22×C149—21no—
151C22×C149C22×D411yescharacteristic
152C2×D149—22no—
153C2×D149—41no—
154C2×D149—41no—
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—41no—
159C2×D149—41no—
160C2×D149—41no—
161C4×C149—21no—
162C4×C149—21no—
163C4×C149—21no—
164C4×C149—21no—
165C4×C149—21no—
166C4×C149C2×#4111yescharacteristic
167C4×C149C2×#4111yescharacteristic
168Dic149—22no—
169Dic149—41no—
170Dic149—41no—
171Dic149—41no—
172Dic149—41no—
173C2×C149—41no—
174C2×C149#52511yescharacteristic
175C2×C149#57611yescharacteristic
176C2×C149#57711yescharacteristic
177D149—42no—
178D149—81no—
179D149—81no—
180C149#311911yescharacteristic, complemented, Sylow
181#3119—1491nomaximal, Sylow
182#540—1491no—
183#520—1491no—
184#481—1491no—
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#433D14911yescharacteristic, complemented
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#121—1491no—
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#117C2×D14911yescharacteristic
220C2×C4⋊C4—2981no—
221C2×C4⋊C4—1491no—
222#107—1491no—
223#107—1491no—
224#106—1491no—
225#106—1491no—
226C4⋊C8C2×D14911yescharacteristic
227C4⋊C8C2×D14911yescharacteristic
228#103—1491no—
229#103—1491no—
230#102—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#102—1491no—
235#102—1491no—
236C22⋊C8C2×D14911yescharacteristic
237C22⋊C8C2×D14911yescharacteristic
238#97C2×D14911yescharacteristic
239C4×C8C2×D14911yescharacteristic
240#41—2982no—
241#41—2982no—
242C2×Q8—1491no—
243C2×D4—2981no—
244C2×D4—2981no—
245C2×D4—2981no—
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—1491no—
249C2×D4—1491no—
250C2×D4—1491no—
251C22×C4—2981no—
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×C8C22×D14911yescharacteristic
263C2×C8C22×D14911yescharacteristic
264C2×C8C22×D14911yescharacteristic
265C2×C8C22×D14911yescharacteristic
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⋊C4D59611yescharacteristic
276C4⋊C4D59611yescharacteristic
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4D59611yescharacteristic
284C22⋊C4D59611yescharacteristic
285C42—2981no—
286C42—2981no—
287C42C22×D14911yescharacteristic
288C42C22×D14911yescharacteristic
289C23—2981no—
290C23—2981no—
291C23—2981no—
292C23C2×D59611yescharacteristic
293Q8—2981no—
294Q8—1492no—
295D4—2984no—
296D4—2981no—
297D4—2981no—
298D4—2981no—
299D4—2981no—
300D4—2981no—
301D4—1492no—
302D4—11921no—
303D4—11921no—
304D4—11921no—
305D4—11921no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—2984no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—11921no—
315C2×C4—11921no—
316C2×C4—11921no—
317C2×C4—11921no—
318C2×C4—11921no—
319C2×C4C2×D59611yescharacteristic
320C2×C4C2×D59611yescharacteristic
321C2×C4C2×D59611yescharacteristic
322C2×C4C2×D59611yescharacteristic
323C2×C4C2×D59611yescharacteristic
324C2×C4C23×D14911yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—2982no—
333C22—5961no—
334C22—5961no—
335C22—5961no—
336C22—5961no—
337C22—5961no—
338C22—5961no—
339C22—5961no—
340C22—5961no—
341C22C22×D59611yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—2982no—
348C4—5961no—
349C4—5961no—
350C4—5961no—
351C4—5961no—
352C4#41×D14911yescharacteristic
353C4#41×D14911yescharacteristic
354C2—41no—
355C2—5962no—
356C2—11921no—
357C2—11921no—
358C2#2375013711yescharacteristic
359C2#2375043011yescharacteristic
360C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#433×C149C2
socleC22×C149C22×D4
hypercenter#433D149
hypocenterC149#3119
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23750230C2semidirect
2. #23750105C2semidirect
3. #23749944C2semidirect
4. #23749939C2semidirect
5. #23749933C2semidirect
6. #23749926C2semidirect
7. #23749826C2semidirect
8. #23749821C2semidirect
9. #23749772C2semidirect
10. #23749772C2semidirect
11. #23749738C2semidirect
12. #23749727C2semidirect
13. C4×#14558725C2semidirect
14. C4×D1192C2semidirect
15. #433×C149C2semidirect
180. C149#3119semidirect
196. #433D149semidirect

Maximal subgroups

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

subgroupindex
#237502302
#237501052
#237499442
#237499392
#237499332
#237499262
#237498262
#237498212
#237497722
#237497382
#237497272
C4×#145587252
C4×D11922
#433×C1492
#3119149