Finite Group Databasebeta

← #34056970

Subgroups — #34056970

Order 19072.

374 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750343C211yesmaximal, characteristic
2Q8×C22⋊D149C211yesmaximal, characteristic
3#23749974C211yesmaximal, characteristic, complemented
4#23749966C211yesmaximal, characteristic, complemented
5#23749964C211yesmaximal, characteristic, complemented
6#23749908C211yesmaximal, characteristic, complemented
7#23749883C211yesmaximal, characteristic, complemented
8#23749882C211yesmaximal, characteristic, complemented
9#23749834C211yesmaximal, characteristic, complemented
10#23749782C211yesmaximal, characteristic, complemented
11#23749781C211yesmaximal, characteristic, complemented
12#23749717C211yesmaximal, characteristic, complemented
13#23749701C211yesmaximal, characteristic
14#23749632C211yesmaximal, characteristic, complemented
15#419×C149C211yesmaximal, characteristic, complemented
16C2×Q8×D149C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558726C2211yescharacteristic
20C2×#14558719C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011909—21no—
23#18011909C2211yescharacteristic
24#18011905—21no—
25#18011904—21no—
26#18011897—21no—
27#18011891C2211yescharacteristic
28#18011890—21no—
29#18011890C2211yescharacteristic
30#18011890C2211yescharacteristic
31#18011887—21no—
32#18011887C2211yescharacteristic
33Q8×Dic149C2211yescharacteristic
34C4×Dic298—21no—
35#18011876C2211yescharacteristic
36C4×C22⋊D149—21no—
37C4×C22⋊D149C2211yescharacteristic
38#18011869C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011834C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C22×Q8×C149C2211yescharacteristic
53C2×M16×C149C2211yescharacteristic
54#117×C149C2211yescharacteristic
55#103×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#103×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×Dic298C2311yescharacteristic
62C2×Dic298C2311yescharacteristic
63Q8×D149—22no—
64Q8×D149—41no—
65C2×C22⋊D149D411yescharacteristic
66C2×C4×D149—21no—
67C2×C4×D149C2311yescharacteristic
68Dic596—41no—
69#14558726—22no—
70#14558726—41no—
71#14558719—41no—
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715D411yescharacteristic
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149D411yescharacteristic
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713D411yescharacteristic
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149—21no—
98C2×Q8×C149—22no—
99C2×Q8×C149—41no—
100C2×Q8×C149C2311yescharacteristic
101C2×Q8×C149C2311yescharacteristic
102C22×C4×C149—21no—
103C22×C4×C149C2311yescharacteristic
104M16×C149—41no—
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C4⋊C4×C149C2311yescharacteristic
109C22⋊C4×C149—21no—
110C42×C149—21no—
111C22×D149C2×D411yescharacteristic
112Dic298—21no—
113Dic298—21no—
114Dic298—21no—
115Dic298—21no—
116Dic298—42no—
117Dic298—42no—
118C22⋊D149—22no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C4×D149—21no—
127C4×D149—21no—
128C4×D149—42no—
129#11924746—21no—
130#11924746—21no—
131C23×C149C2×D411yescharacteristic
132Q8×C149—21no—
133Q8×C149—21no—
134Q8×C149—21no—
135Q8×C149—42no—
136Q8×C149#4112yes—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—42no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2411yescharacteristic
146C8×C149—21no—
147C8×C149—21no—
148C22×C149—21no—
149C22×C149—21no—
150C22×C149—21no—
151C22×C149C22×D411yescharacteristic
152C2×D149—21no—
153C2×D149—21no—
154C2×D149—21no—
155C4×C149—21no—
156C4×C149—22no—
157C4×C149—41no—
158C4×C149—41no—
159C4×C149—41no—
160C4×C149C2×#4111yescharacteristic
161C4×C149H(5,𝔽2)11yescharacteristic
162Dic149—21no—
163Dic149—21no—
164Dic149—41no—
165Dic149—41no—
166Dic149—41no—
167Dic149—41no—
168Dic149#13712yes—
169C2×C149—41no—
170C2×C149#54611yescharacteristic
171C2×C149C2×#13711yescharacteristic
172C2×C149#57811yescharacteristic
173D149—41no—
174C149#332811yescharacteristic, complemented, Sylow
175#3328—1491nomaximal, Sylow
176#556—1491no—
177D4×Q8—1491no—
178#487—1491no—
179#485—1491no—
180#485—1491no—
181#475—1491no—
182#470—1491no—
183#470—1491no—
184#462—1491no—
185#451—1491no—
186#451—1491no—
187C4×Q16—1491no—
188#436—1491no—
189#419—1491no—
190#419D14911yescharacteristic, complemented
191C22×Q8—1491no—
192C22×Q8C2×D14911yescharacteristic
193C2×Q16—1491no—
194C2×Q16—1491no—
195C2×Q16—1491no—
196C2×M16—1491no—
197C2×M16C2×D14911yescharacteristic
198C4⋊Q8—2981no—
199C4⋊Q8—1491no—
200C4⋊Q8—1491no—
201#126—2981no—
202#126—2981no—
203#124—2981no—
204C22⋊Q8—2981no—
205C22⋊Q8—2981no—
206C22⋊Q8—1491no—
207C22⋊Q8—1491no—
208C22⋊Q8—1491no—
209C22⋊Q8—1491no—
210C4×Q8—2981no—
211C4×Q8—1491no—
212C4×Q8—1491no—
213C4×D4—2981no—
214C4×D4—1491no—
215#117—1491no—
216#117C2×D14911yescharacteristic
217#107—1491no—
218#106—1491no—
219#106—1491no—
220C4⋊C8—1491no—
221#103—1491no—
222#103—1491no—
223#103—1491no—
224#103—1491no—
225#103—1491no—
226#103—1491no—
227#103C2×D14911yescharacteristic
228#103C2×D14911yescharacteristic
229#103C2×D14911yescharacteristic
230#103C2×D14911yescharacteristic
231C22⋊C8—1491no—
232C22⋊C8—1491no—
233C4×C8—1491no—
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—2981no—
238C2×Q8—2981no—
239C2×Q8—2982no—
240C2×Q8—5961no—
241C2×Q8—1491no—
242C2×Q8—1491no—
243C2×Q8C22×D14911yescharacteristic
244C2×Q8C22×D14911yescharacteristic
245C2×D4—1491no—
246C22×C4—21no—
247C22×C4—2981no—
248C22×C4—1491no—
249C22×C4C22×D14911yescharacteristic
250Q16—2982no—
251Q16—5961no—
252Q16—5961no—
253M16—41no—
254M16—5961no—
255C2×C8—1491no—
256C2×C8—1491no—
257C2×C8C22×D14911yescharacteristic
258C2×C8C22×D14911yescharacteristic
259C4⋊C4—2981no—
260C4⋊C4—2981no—
261C4⋊C4—2981no—
262C4⋊C4—2981no—
263C4⋊C4—2981no—
264C4⋊C4—2981no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—1491no—
269C4⋊C4—1491no—
270C4⋊C4—1491no—
271C4⋊C4C22×D14911yescharacteristic
272C4⋊C4C22×D14911yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—1491no—
280C22⋊C4—1491no—
281C42—21no—
282C42—2981no—
283C42—2981no—
284C42—2981no—
285C42—1491no—
286C23—1491no—
287C23D4×D14911yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—42no—
292Q8—2981no—
293Q8—2981no—
294Q8—2981no—
295Q8—2981no—
296Q8—5962no—
297Q8—5962no—
298Q8#1455873612yes—
299D4—2982no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—2981no—
308C2×C4—2981no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—5962no—
314C2×C4—1491no—
315C2×C4—1491no—
316C2×C4—1491no—
317C2×C4D4×D14911yescharacteristic
318C2×C4C23×D14911yescharacteristic
319C8—21no—
320C8—21no—
321C8—2981no—
322C8—2981no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—2981no—
327C22—2981no—
328C22—2981no—
329C22C2×D4×D14911yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—2981no—
336C4—2981no—
337C4—5961no—
338C4—5961no—
339C4—5961no—
340C4—5961no—
341C4—1492no—
342C4C2×#1455873611yescharacteristic
343C4#1801195611yescharacteristic
344C2—41no—
345C2—5961no—
346C2#2375026511yescharacteristic
347C2#137×D14911yescharacteristic
348C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#419×C149C2
socleC22×C149C22×D4
prime radicalC2×C22⋊D149D4
hypercenter#419D149
hypocenterC149#3328
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #23749974C2semidirect
4. #23749966C2semidirect
5. #23749964C2semidirect
6. #23749908C2semidirect
7. #23749883C2semidirect
8. #23749882C2semidirect
9. #23749834C2semidirect
10. #23749782C2semidirect
11. #23749781C2semidirect
12. #23749717C2semidirect
14. #23749632C2semidirect
15. #419×C149C2semidirect
174. C149#3328semidirect
190. #419D149semidirect

Maximal subgroups

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

subgroupindex
#237503432
Q8×C22⋊D1492
#237499742
#237499662
#237499642
#237499082
#237498832
#237498822
#237498342
#237497822
#237497812
#237497172
#237497012
#237496322
#419×C1492
#3328149