Finite Group Databasebeta

← #34056994

Subgroups — #34056994

Order 19072.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750277C211yesmaximal, characteristic, complemented
2#23750276C211yesmaximal, characteristic, complemented
3#23749974C211yesmaximal, characteristic, complemented
4#23749962C211yesmaximal, characteristic, complemented
5#23749904C211yesmaximal, characteristic, complemented
6#23749873C211yesmaximal, characteristic, complemented
7#23749872C211yesmaximal, characteristic, complemented
8#23749829C211yesmaximal, characteristic, complemented
9#23749773C211yesmaximal, characteristic, complemented
10#23749772C211yesmaximal, characteristic, complemented
11#23749707C211yesmaximal, characteristic, complemented
12#23749700C211yesmaximal, characteristic, complemented
13#23749625C211yesmaximal, characteristic, complemented
14#23749624C211yesmaximal, characteristic, complemented
15#484×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558736—21no—
18C2×#14558736C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21C2×D1192C2211yescharacteristic
22C2×#14558720C2211yescharacteristic
23C2×#14558719C2211yescharacteristic
24#18011910C2211yescharacteristic
25#18011909C2211yescharacteristic
26#18011896—21no—
27#18011896—21no—
28#18011894—21no—
29#18011893—21no—
30#18011891C2211yescharacteristic
31#18011889—21no—
32#18011886C2211yescharacteristic
33#18011885C2211yescharacteristic
34#18011884—21no—
35#18011873C2211yescharacteristic
36#18011873C2211yescharacteristic
37C4×C22⋊D149C2211yescharacteristic
38C4⋊C4×D149—21no—
39C4⋊C4×D149C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C22⋊Q8×C149C2211yescharacteristic
53C2×C4⋊C4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558737—22no—
60#14558737—41no—
61#14558736—22no—
62#14558736—41no—
63#14558736—44no—
64C2×Dic298—21no—
65C2×Dic298C2311yescharacteristic
66C2×D596—21no—
67C2×D596—21no—
68C2×D596C2311yescharacteristic
69C2×D596C2311yescharacteristic
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149D411yescharacteristic
73C2×C4×D149—21no—
74C2×C4×D149—21no—
75C2×C4×D149—21no—
76C2×C4×D149—21no—
77C2×C4×D149—21no—
78C2×C4×D149C2311yescharacteristic
79#14558725—41no—
80#14558723—41no—
81D1192—22no—
82#14558720—41no—
83#14558719—41no—
84C2×#11924746C2311yescharacteristic
85C2×#11924746C2311yescharacteristic
86C4⋊Dic149—21no—
87C4⋊Dic149C2311yescharacteristic
88#14558715—21no—
89#14558715—21no—
90#14558715—21no—
91#14558715—21no—
92#14558715D411yescharacteristic
93C22⋊Dic149D411yescharacteristic
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713D411yescharacteristic
100C4×Dic149C2311yescharacteristic
101C2×Q8×C149C2311yescharacteristic
102C22×C4×C149—21no—
103C22×C4×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C4⋊C4×C149—21no—
107C4⋊C4×C149—21no—
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C22⋊C4×C149—21no—
112C22×D149—21no—
113C22×D149—21no—
114C22×D149C2×D411yescharacteristic
115Dic298—21no—
116Dic298—21no—
117Dic298—42no—
118D596—21no—
119D596—21no—
120D596—21no—
121D596—42no—
122D596—42no—
123D596#4112yescomplemented
124C22⋊D149—22no—
125C22⋊D149—42no—
126C22⋊D149—42no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149C2×D411yescharacteristic
130C2×Dic149C2×D411yescharacteristic
131C2×Dic149C2×D411yescharacteristic
132C4×D149—21no—
133C4×D149—21no—
134C4×D149—42no—
135C4×D149—42no—
136C4×D149—42no—
137C4×D149—42no—
138C4×D149—42no—
139#11924746—21no—
140#11924746—21no—
141C23×C149C2×D411yescharacteristic
142Q8×C149—21no—
143Q8×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—42no—
151C2×C4×C149C2×D411yescharacteristic
152C2×C4×C149C2411yescharacteristic
153C8×C149—21no—
154C8×C149—21no—
155C22×C149—21no—
156C22×C149—21no—
157C22×C149—21no—
158C22×C149C22×D411yescharacteristic
159C2×D149—21no—
160C2×D149—22no—
161C2×D149—21no—
162C2×D149—21no—
163C2×D149—41no—
164C2×D149—41no—
165C2×D149—41no—
166C2×D149—41no—
167C2×D149—41no—
168C4×C149—21no—
169C4×C149—41no—
170C4×C149—41no—
171C4×C149—41no—
172C4×C149—41no—
173C4×C149C2×#4111yescharacteristic
174C4×C149H(5,𝔽2)11yescharacteristic
175Dic149—21no—
176Dic149—21no—
177Dic149—41no—
178Dic149—41no—
179Dic149AGL(1,ℤ/8)12yes—
180C2×C149—41no—
181C2×C149#54611yescharacteristic
182C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
183C2×C149#57811yescharacteristic
184D149—41no—
185D149—42no—
186D149—81no—
187C149#333011yescharacteristic, complemented, Sylow
188#3330—1491nomaximal, Sylow
189#547—1491no—
190#547—1491no—
191#487—1491no—
192#484—1491no—
193#484D14911yescharacteristic, complemented
194#474—1491no—
195#468—1491no—
196#468—1491no—
197#461—1491no—
198#449—1491no—
199#449—1491no—
200C4×D8—1491no—
201#436—1491no—
202#417—1491no—
203#417—1491no—
204C2×#41—2981no—
205C2×#41—1491no—
206C2×#41—1491no—
207C2×SD16—1491no—
208C2×SD16—1491no—
209C2×D8—1491no—
210C2×M16—1491no—
211C2×M16—1491no—
212C4⋊Q8—1491no—
213C4⋊Q8—1491no—
214#123—2981no—
215#123—2981no—
216#123—2981no—
217#123—2981no—
218C22⋊Q8—2981no—
219C22⋊Q8—1491no—
220C22⋊Q8C2×D14911yescharacteristic
221#121—2981no—
222#121—1491no—
223#121—1491no—
224C4×D4—1491no—
225C4×D4—1491no—
226C4×D4—1491no—
227C2×C4⋊C4—2981no—
228C2×C4⋊C4—1491no—
229C2×C4⋊C4C2×D14911yescharacteristic
230#107—1491no—
231#107C2×D14911yescharacteristic
232#107C2×D14911yescharacteristic
233C4⋊C8—1491no—
234#103—1491no—
235#103—1491no—
236#103—1491no—
237#103—1491no—
238#103C2×D14911yescharacteristic
239#103C2×D14911yescharacteristic
240#102—1491no—
241#102—1491no—
242#102—1491no—
243#102—1491no—
244C22⋊C8—1491no—
245C22⋊C8C2×D14911yescharacteristic
246C4×C8—1491no—
247#41—2982no—
248#41—2982no—
249#41—5961no—
250#41—5964no—
251#41—5961no—
252C2×Q8—2981no—
253C2×Q8—1491no—
254C2×Q8C22×D14911yescharacteristic
255C2×D4—2981no—
256C2×D4—2981no—
257C2×D4—2981no—
258C2×D4—2981no—
259C2×D4—1491no—
260C2×D4—1491no—
261C2×D4—1491no—
262C22×C4—21no—
263C22×C4—2981no—
264C22×C4—2981no—
265C22×C4—2981no—
266C22×C4—2981no—
267C22×C4—2981no—
268C22×C4—1491no—
269C22×C4C22×D14911yescharacteristic
270SD16—5961no—
271SD16—5961no—
272D8—2982no—
273M16—5961no—
274M16—5961no—
275C2×C8—1491no—
276C2×C8—1491no—
277C2×C8C22×D14911yescharacteristic
278C2×C8C22×D14911yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—2981no—
282C4⋊C4—2981no—
283C4⋊C4—2981no—
284C4⋊C4—2981no—
285C4⋊C4—2981no—
286C4⋊C4—1491no—
287C4⋊C4—1491no—
288C4⋊C4C22×D14911yescharacteristic
289C4⋊C4C22×D14911yescharacteristic
290C4⋊C4C22×D14911yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—1491no—
298C22⋊C4—1491no—
299C42—1491no—
300C23—2981no—
301C23—2981no—
302C23—1491no—
303C23D4×D14911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2981no—
307Q8—2981no—
308Q8—5962no—
309D4—2982no—
310D4—2981no—
311D4—2981no—
312D4—2981no—
313D4—5962no—
314D4—5962no—
315D4—5962no—
316D4—5962no—
317D4—1492no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—2981no—
326C2×C4—2981no—
327C2×C4—2981no—
328C2×C4—2981no—
329C2×C4—5962no—
330C2×C4—5962no—
331C2×C4—5962no—
332C2×C4—5962no—
333C2×C4—5962no—
334C2×C4—1491no—
335C2×C4—1491no—
336C2×C4—1491no—
337C2×C4D4×D14911yescharacteristic
338C2×C4C23×D14911yescharacteristic
339C8—21no—
340C8—21no—
341C8—2981no—
342C8—2981no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—2981no—
347C22—2981no—
348C22—2981no—
349C22—2982no—
350C22—5961no—
351C22—5961no—
352C22—5961no—
353C22—5961no—
354C22—5961no—
355C22C2×D4×D14911yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—2981no—
362C4—2981no—
363C4—5961no—
364C4—5961no—
365C4—1492no—
366C4#41×D14911yescharacteristic
367C4#1801195711yescharacteristic
368C2—41no—
369C2—5961no—
370C2—5962no—
371C2—11921no—
372C2#2375026711yescharacteristic
373C2AGL(1,ℤ/8)×D14911yescharacteristic
374C2#2375043811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#484×C149C2
socleC22×C149C22×D4
hypercenter#484D149
hypocenterC149#3330
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #23750277C2semidirect
2. #23750276C2semidirect
3. #23749974C2semidirect
4. #23749962C2semidirect
5. #23749904C2semidirect
6. #23749873C2semidirect
7. #23749872C2semidirect
8. #23749829C2semidirect
9. #23749773C2semidirect
10. #23749772C2semidirect
11. #23749707C2semidirect
12. #23749700C2semidirect
13. #23749625C2semidirect
14. #23749624C2semidirect
15. #484×C149C2semidirect
123. D596#41semidirect
187. C149#3330semidirect
193. #484D149semidirect

Maximal subgroups

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

subgroupindex
#237502772
#237502762
#237499742
#237499622
#237499042
#237498732
#237498722
#237498292
#237497732
#237497722
#237497072
#237497002
#237496252
#237496242
#484×C1492
#3330149