Finite Group Databasebeta

← #34057160

Subgroups — #34057160

Order 19072.

388 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#23750328C211yesmaximal, characteristic, complemented
2#23750278C211yesmaximal, characteristic, complemented
3#23749952C211yesmaximal, characteristic, complemented
4#23749945C211yesmaximal, characteristic, complemented
5#23749945C211yesmaximal, characteristic, complemented
6#23749940C211yesmaximal, characteristic, complemented
7#23749922C211yesmaximal, characteristic, complemented
8#23749912C211yesmaximal, characteristic, complemented
9#23749879C211yesmaximal, characteristic, complemented
10#23749862C211yesmaximal, characteristic, complemented
11#23749738C211yesmaximal, characteristic, complemented
12#23749698C211yesmaximal, characteristic, complemented
13#23749666C211yesmaximal, characteristic, complemented
14#106×D149C211yesmaximal, characteristic, complemented
15#501×C149C211yesmaximal, characteristic, complemented
16C2×#14558737—21no—
17C2×D1192C2211yescharacteristic
18C2×#14558719C2211yescharacteristic
19C2×C8×D149C2211yescharacteristic
20#18011906—21no—
21#18011896—21no—
22#18011896—21no—
23#18011896—21no—
24#18011887—21no—
25#18011886—21no—
26#18011886C2211yescharacteristic
27#18011886C2211yescharacteristic
28#18011886C2211yescharacteristic
29#18011886C2211yescharacteristic
30C4×D596C2211yescharacteristic
31C4×D596C2211yescharacteristic
32C4×D596C2211yescharacteristic
33#18011873—21no—
34#18011869C2211yescharacteristic
35C4⋊C4×D149C2211yescharacteristic
36C4⋊C4×D149C2211yescharacteristic
37C4⋊C4×D149C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011842C2211yescharacteristic
43C4⋊#11924746C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C4⋊Q8×C149C2211yescharacteristic
53#125×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#106×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59#14558737—44no—
60C2×D596—21no—
61C2×D596—21no—
62C2×D596—21no—
63C2×D596—21no—
64C2×D596D411yescharacteristic
65C2×D596C2311yescharacteristic
66C2×D596C2311yescharacteristic
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72C2×C4×D149C2311yescharacteristic
73C2×C4×D149C2311yescharacteristic
74D1192—22no—
75#14558719—22no—
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C8×D149—22no—
79C4⋊Dic149D411yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713D411yescharacteristic
93#14558713D411yescharacteristic
94C4×Dic149—21no—
95C2×Q8×C149—21no—
96C2×C8×C149C2311yescharacteristic
97C2×C8×C149C2311yescharacteristic
98C4⋊C4×C149—21no—
99C4⋊C4×C149—21no—
100C4⋊C4×C149—21no—
101C4⋊C4×C149C2311yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C42×C149C2311yescharacteristic
106C22×D149—21no—
107C22×D149—21no—
108C22×D149C2×D411yescharacteristic
109C22×D149C2×D411yescharacteristic
110D596—22no—
111D596—21no—
112D596—21no—
113D596—21no—
114D596—21no—
115D596—42no—
116D596—42no—
117D596—42no—
118D596—81no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C4×D149—21no—
124C4×D149—21no—
125C4×D149—21no—
126C4×D149—21no—
127C4×D149—42no—
128C4×D149—42no—
129C4×D149—42no—
130C4×D149—81no—
131C4×D149—81no—
132#11924746—21no—
133#11924746—21no—
134Q8×C149—42no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2411yescharacteristic
142C8×C149—21no—
143C8×C149#4112yescomplemented
144C22×C149C22×D411yescharacteristic
145C2×D149—21no—
146C2×D149—21no—
147C2×D149—21no—
148C2×D149—21no—
149C2×D149—21no—
150C2×D149—41no—
151C2×D149—41no—
152C2×D149—41no—
153C2×D149—41no—
154C2×D149—41no—
155C2×D149—41no—
156C2×D149AGL(1,ℤ/8)12yes—
157C4×C149—21no—
158C4×C149—21no—
159C4×C149—41no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149C2×#4111yescharacteristic
164C4×C1492−1+411yescharacteristic
165Dic149—21no—
166Dic149—21no—
167Dic149—41no—
168Dic149—41no—
169C2×C149#54711yescharacteristic
170C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C149#57711yescharacteristic
172D149—22no—
173D149—41no—
174D149—81no—
175D149—81no—
176C149#334511yescharacteristic, complemented, Sylow
177#3345—1491nomaximal, Sylow
178#553—1491no—
179#547—1491no—
180#501D14911yescharacteristic, complemented
181#482—1491no—
182#481—1491no—
183#481—1491no—
184#480—1491no—
185#478—1491no—
186#476—1491no—
187#469—1491no—
188#466—1491no—
189#442—1491no—
190#435—1491no—
191#428—1491no—
192C2×#106—1491no—
193C2×#41—2981no—
194C2×D8—1491no—
195C2×M16—1491no—
196C22×C8—1491no—
197C4⋊Q8C2×D14911yescharacteristic
198#126—2981no—
199#125C2×D14911yescharacteristic
200#123—2981no—
201#123—2981no—
202#123—2981no—
203C22⋊Q8—2981no—
204#121—2981no—
205#121—1491no—
206#121—1491no—
207#121—1491no—
208#121—1491no—
209C4×D4—2981no—
210C4×D4—1491no—
211C4×D4—1491no—
212C4×D4—1491no—
213#117—1491no—
214C2×C4⋊C4—1491no—
215C2×C4⋊C4—1491no—
216C2×C4⋊C4—1491no—
217#107—1491no—
218#107C2×D14911yescharacteristic
219#107C2×D14911yescharacteristic
220#106—1491no—
221#106—1491no—
222#106—1491no—
223#106—1491no—
224#106C2×D14911yescharacteristic
225#106C2×D14911yescharacteristic
226C4⋊C8—1491no—
227#102—1491no—
228#102—1491no—
229#102—1491no—
230#102—1491no—
231#102—1491no—
232#102—1491no—
233C22⋊C8—1491no—
234C22⋊C8—1491no—
235#97C2×D14911yescharacteristic
236#41—5964no—
237C2×Q8—21no—
238C2×D4—2981no—
239C2×D4—2981no—
240C2×D4—2981no—
241C2×D4—2981no—
242C2×D4—1491no—
243C2×D4—1491no—
244C2×D4—1491no—
245C22×C4—2981no—
246C22×C4—2981no—
247C22×C4—2981no—
248C22×C4—2981no—
249C22×C4—2981no—
250C22×C4—1491no—
251C22×C4—1491no—
252D8—2982no—
253M16—2982no—
254C2×C8—2982no—
255C2×C8—1491no—
256C2×C8—1491no—
257C2×C8C22×D14911yescharacteristic
258C2×C8C22×D14911yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—2981no—
263C4⋊C4—2981no—
264C4⋊C4—2981no—
265C4⋊C4—1491no—
266C4⋊C4—1491no—
267C4⋊C4—1491no—
268C4⋊C4C22×D14911yescharacteristic
269C4⋊C4C22×D14911yescharacteristic
270C4⋊C4C22×D14911yescharacteristic
271C4⋊C4C22×D14911yescharacteristic
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—1491no—
280C22⋊C4—1491no—
281C42—2981no—
282C42C22×D14911yescharacteristic
283C23—2981no—
284C23—2981no—
285C23—1491no—
286C23—1491no—
287Q8—42no—
288D4—2982no—
289D4—2981no—
290D4—2981no—
291D4—2981no—
292D4—2981no—
293D4—5962no—
294D4—5962no—
295D4—5962no—
296D4—11921no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—2981no—
306C2×C4—2981no—
307C2×C4—5962no—
308C2×C4—5962no—
309C2×C4—5962no—
310C2×C4—1491no—
311C2×C4—1491no—
312C2×C4—11921no—
313C2×C4—11921no—
314C2×C4D4×D14911yescharacteristic
315C2×C4D4×D14911yescharacteristic
316C2×C4C23×D14911yescharacteristic
317C8—21no—
318C8—2981no—
319C8—2981no—
320C8#1455873712yescomplemented
321C22—2981no—
322C22—2981no—
323C22—2981no—
324C22—2981no—
325C22—2981no—
326C22—5961no—
327C22—5961no—
328C22—5961no—
329C22—5961no—
330C22—5961no—
331C22—5961no—
332C22—1492no—
333C22C2×D4×D14911yescharacteristic
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—2981no—
341C4—2981no—
342C4—5961no—
343C4—5961no—
344C4C2×#1455873711yescharacteristic
345C4#1801195911yescharacteristic
346C2—2982no—
347C2—5961no—
348C2—11921no—
349C2—11921no—
350C2#2375027811yescharacteristic
351C2AGL(1,ℤ/8)×D14911yescharacteristic
352C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#501×C149C2
socleC22×C149C22×D4
hypercenter#501D149
hypocenterC149#3345
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #23750328C2semidirect
2. #23750278C2semidirect
3. #23749952C2semidirect
4. #23749945C2semidirect
5. #23749945C2semidirect
6. #23749940C2semidirect
7. #23749922C2semidirect
8. #23749912C2semidirect
9. #23749879C2semidirect
10. #23749862C2semidirect
11. #23749738C2semidirect
12. #23749698C2semidirect
13. #23749666C2semidirect
14. #106×D149C2semidirect
15. #501×C149C2semidirect
143. C8×C149#41semidirect
176. C149#3345semidirect
180. #501D149semidirect
320. C8#14558737semidirect

Maximal subgroups

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

subgroupindex
#237503282
#237502782
#237499522
#237499452
#237499402
#237499222
#237499122
#237498792
#237498622
#237497382
#237496982
#237496662
#106×D1492
#501×C1492
#3345149