Finite Group Databasebeta

← #34057714

Subgroups — #34057714

Order 19072.

406 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750344C211yesmaximal, characteristic, complemented
2#23750296C211yesmaximal, characteristic, complemented
3#23750015C211yesmaximal, characteristic, complemented
4#23750013C211yesmaximal, characteristic, complemented
5#23749996C211yesmaximal, characteristic, complemented
6#23749839C211yesmaximal, characteristic, complemented
7#23749829C211yesmaximal, characteristic, complemented
8#23749826C211yesmaximal, characteristic, complemented
9#23749823C211yesmaximal, characteristic, complemented
10#23749818C211yesmaximal, characteristic, complemented
11#23749754C211yesmaximal, characteristic, complemented
12#23749728C211yesmaximal, characteristic, complemented
13#23749725C211yesmaximal, characteristic, complemented
14#23749705C211yesmaximal, characteristic, complemented
15#463×C149C211yesmaximal, characteristic, complemented
16C2×#14558736—21no—
17C2×#14558725C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21C2×#14558723C2211yescharacteristic
22C2×#14558721C2211yescharacteristic
23C2×#14558721C2211yescharacteristic
24#18011909C2211yescharacteristic
25#18011908C2211yescharacteristic
26#18011907C2211yescharacteristic
27#18011907C2211yescharacteristic
28#18011904—21no—
29#18011904—21no—
30#18011898C2211yescharacteristic
31#18011888—21no—
32#18011885—21no—
33#18011884—21no—
34#18011884—21no—
35Q8×Dic149C2211yescharacteristic
36C4×Dic298C2211yescharacteristic
37C4×Dic298C2211yescharacteristic
38D4×Dic149C2211yescharacteristic
39#18011873C2211yescharacteristic
40#18011873C2211yescharacteristic
41#18011867—21no—
42#18011844C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011822C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C2×D8×C149C2211yescharacteristic
54#124×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558736—44no—
60C2×Dic298D411yescharacteristic
61C2×Dic298C2311yescharacteristic
62C2×D596—21no—
63C2×D596—21no—
64C2×D596C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C22×Dic149—21no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73#14558725—41no—
74#14558725—41no—
75#14558724—22no—
76#14558723—22no—
77#14558723—41no—
78#14558721—22no—
79#14558721—41no—
80C2×#11924746C2311yescharacteristic
81C2×#11924746C2311yescharacteristic
82C4⋊Dic149—21no—
83C4⋊Dic149D411yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715D411yescharacteristic
89#14558715D411yescharacteristic
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92C22⋊Dic149—21no—
93#14558713—21no—
94#14558713—21no—
95C4×Dic149—21no—
96C4×Dic149—21no—
97C4×Dic149C2311yescharacteristic
98C4×Dic149C2311yescharacteristic
99C2×Q8×C149C2311yescharacteristic
100C2×D4×C149C2311yescharacteristic
101C2×D4×C149C2311yescharacteristic
102C22×C4×C149—21no—
103SD16×C149—41no—
104D8×C149—41no—
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C22⋊C4×C149—21no—
109C22⋊C4×C149—21no—
110C22⋊C4×C149—21no—
111C42×C149C2311yescharacteristic
112C22×D149—21no—
113C22×D149—21no—
114Dic298—22no—
115Dic298—21no—
116Dic298—21no—
117D596—21no—
118D596—21no—
119D596—21no—
120D596—21no—
121D596—42no—
122D596—81no—
123C22⋊D149—42no—
124C22⋊D149—42no—
125C22⋊D149—81no—
126C22⋊D149—81no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—42no—
130C2×Dic149C2×D411yescharacteristic
131C2×Dic149C2×D411yescharacteristic
132C2×Dic149C2×D411yescharacteristic
133C2×Dic149C2×D411yescharacteristic
134C4×D149—42no—
135C4×D149—42no—
136#11924746—21no—
137#11924746#4112yescomplemented
138C23×C149—21no—
139C23×C149—21no—
140Q8×C149—21no—
141Q8×C149—21no—
142D4×C149—21no—
143D4×C149—21no—
144D4×C149—21no—
145D4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—42no—
149C2×C4×C149C2×D411yescharacteristic
150C2×C4×C149C2×D411yescharacteristic
151C2×C4×C149C2411yescharacteristic
152C8×C149—21no—
153C8×C149—21no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149C22×D411yescharacteristic
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C2×D149—41no—
165C2×D149—41no—
166C2×D149—41no—
167C4×C149—21no—
168C4×C149—21no—
169C4×C149—41no—
170C4×C149—41no—
171C4×C149C2×#4111yescharacteristic
172C4×C149H(5,𝔽2)11yescharacteristic
173Dic149—21no—
174Dic149—21no—
175Dic149—21no—
176Dic149—41no—
177Dic149—41no—
178Dic149AGL(1,ℤ/8)12yes—
179C2×C149—81no—
180C2×C149—81no—
181C2×C149#55011yescharacteristic
182C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
183C2×C149#57711yescharacteristic
184D149—81no—
185D149—81no—
186C149#339711yescharacteristic, complemented, Sylow
187#3397—1491nomaximal, Sylow
188#556—1491no—
189#550—1491no—
190#496—1491no—
191#496—1491no—
192#492—1491no—
193#463—1491no—
194#463D14911yescharacteristic, complemented
195#461—1491no—
196#460—1491no—
197#460—1491no—
198#459—1491no—
199#446—1491no—
200#440—1491no—
201#440—1491no—
202C4×D8—1491no—
203C2×#41—2981no—
204C2×SD16—1491no—
205C2×SD16—1491no—
206C2×SD16—1491no—
207C2×SD16—1491no—
208C2×SD16—1491no—
209C2×SD16C2×D14911yescharacteristic
210C2×D8—1491no—
211C2×D8—1491no—
212C2×D8C2×D14911yescharacteristic
213C4⋊Q8—1491no—
214#127—1491no—
215#127—1491no—
216#127—1491no—
217#126—2981no—
218#126—2981no—
219#124—1491no—
220#124C2×D14911yescharacteristic
221C22⋊Q8—2981no—
222#121—2981no—
223#121—2981no—
224#121—2981no—
225C4×Q8—1491no—
226C4×Q8—1491no—
227C4×Q8—1491no—
228C4×D4—1491no—
229C4×D4—1491no—
230C4×D4—1491no—
231C4×D4C2×D14911yescharacteristic
232#117—2981no—
233#107—1491no—
234C4⋊C8—1491no—
235C4⋊C8—1491no—
236C4⋊C8C2×D14911yescharacteristic
237#103—1491no—
238#103C2×D14911yescharacteristic
239#102—1491no—
240#102—1491no—
241#102—1491no—
242#102C2×D14911yescharacteristic
243#97—1491no—
244#97—1491no—
245C4×C8—1491no—
246#41—5964no—
247C2×Q8—1491no—
248C2×Q8—1491no—
249C2×Q8C22×D14911yescharacteristic
250C2×D4—2981no—
251C2×D4—2981no—
252C2×D4—2981no—
253C2×D4—2981no—
254C2×D4—2981no—
255C2×D4—2981no—
256C2×D4—1491no—
257C2×D4—1491no—
258C2×D4C22×D14911yescharacteristic
259C2×D4C22×D14911yescharacteristic
260C22×C4—21no—
261C22×C4—2981no—
262C22×C4—2981no—
263C22×C4—2981no—
264SD16—41no—
265SD16—2982no—
266SD16—2982no—
267SD16—5961no—
268SD16—5961no—
269SD16—5961no—
270D8—41no—
271D8—2982no—
272D8—5961no—
273C2×C8—1491no—
274C2×C8—1491no—
275C2×C8C22×D14911yescharacteristic
276C2×C8C22×D14911yescharacteristic
277C4⋊C4—2981no—
278C4⋊C4—2981no—
279C4⋊C4—2981no—
280C4⋊C4—2981no—
281C4⋊C4—1491no—
282C4⋊C4—1491no—
283C4⋊C4—1491no—
284C4⋊C4—1491no—
285C4⋊C4C22×D14911yescharacteristic
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C42—2981no—
295C42—2981no—
296C42—1491no—
297C42—1491no—
298C42C22×D14911yescharacteristic
299C23—21no—
300C23—21no—
301C23—2981no—
302C23—2981no—
303Q8—21no—
304Q8—21no—
305Q8—2982no—
306Q8—2981no—
307Q8—2981no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—2981no—
313D4—2981no—
314D4—2981no—
315D4—2981no—
316D4—5962no—
317D4—5962no—
318D4—5962no—
319D4—11921no—
320D4—11921no—
321D4—11921no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—2981no—
326C2×C4—2981no—
327C2×C4—5962no—
328C2×C4—5962no—
329C2×C4—5962no—
330C2×C4—1491no—
331C2×C4—1491no—
332C2×C4—1491no—
333C2×C4—1491no—
334C2×C4D4×D14911yescharacteristic
335C2×C4D4×D14911yescharacteristic
336C2×C4C23×D14911yescharacteristic
337C8—21no—
338C8—21no—
339C8—2981no—
340C8—1492no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—5961no—
348C22—5961no—
349C22—5961no—
350C22—5961no—
351C22—5961no—
352C22—5961no—
353C22C2×D4×D14911yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—2981no—
359C4—2981no—
360C4—2981no—
361C4—5961no—
362C4—5961no—
363C4—1492no—
364C4#41×D14911yescharacteristic
365C4#1801195611yescharacteristic
366C2—81no—
367C2—81no—
368C2—11921no—
369C2—11921no—
370C2#2375029311yescharacteristic
371C2AGL(1,ℤ/8)×D14911yescharacteristic
372C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#463×C149C2
socleC22×C149C22×D4
hypercenter#463D149
hypocenterC149#3397
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #23750344C2semidirect
2. #23750296C2semidirect
3. #23750015C2semidirect
4. #23750013C2semidirect
5. #23749996C2semidirect
6. #23749839C2semidirect
7. #23749829C2semidirect
8. #23749826C2semidirect
9. #23749823C2semidirect
10. #23749818C2semidirect
11. #23749754C2semidirect
12. #23749728C2semidirect
13. #23749725C2semidirect
14. #23749705C2semidirect
15. #463×C149C2semidirect
137. #11924746#41semidirect
186. C149#3397semidirect
194. #463D149semidirect

Maximal subgroups

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

subgroupindex
#237503442
#237502962
#237500152
#237500132
#237499962
#237498392
#237498292
#237498262
#237498232
#237498182
#237497542
#237497282
#237497252
#237497052
#463×C1492
#3397149