Finite Group Databasebeta

← #34056981

Subgroups — #34056981

Order 19072.

386 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#23750338C211yesmaximal, characteristic
2Q8×C22⋊D149C211yesmaximal, characteristic, complemented
3#23749974C211yesmaximal, characteristic, complemented
4#23749966C211yesmaximal, characteristic, complemented
5#23749965C211yesmaximal, characteristic, complemented
6#23749918C211yesmaximal, characteristic, complemented
7#23749874C211yesmaximal, characteristic, complemented
8#23749871C211yesmaximal, characteristic, complemented
9#23749829C211yesmaximal, characteristic, complemented
10#23749765C211yesmaximal, characteristic, complemented
11#23749764C211yesmaximal, characteristic, complemented
12#23749710C211yesmaximal, characteristic, complemented
13#23749701C211yesmaximal, characteristic, complemented
14#23749632C211yesmaximal, characteristic, complemented
15#419×C149C211yesmaximal, characteristic, complemented
16C2×Q8×D149C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558723C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×#14558719C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011909—21no—
23#18011909C2211yescharacteristic
24#18011899—21no—
25#18011897—21no—
26#18011890—21no—
27#18011890C2211yescharacteristic
28#18011887—21no—
29#18011887C2211yescharacteristic
30#18011886C2211yescharacteristic
31#18011885C2211yescharacteristic
32#18011884—21no—
33Q8×Dic149C2211yescharacteristic
34#18011873C2211yescharacteristic
35C4×C22⋊D149—21no—
36C4×C22⋊D149C2211yescharacteristic
37#18011869C2211yescharacteristic
38#18011868—21no—
39#18011845C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011833C2211yescharacteristic
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
62Q8×D149—22no—
63Q8×D149—41no—
64C2×D596—21no—
65C2×D596C2311yescharacteristic
66C2×C22⋊D149—21no—
67C2×C22⋊D149D411yescharacteristic
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149C2311yescharacteristic
71#14558725—41no—
72#14558723—22no—
73#14558723—41no—
74#14558719—41no—
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C4⋊Dic149—21no—
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715D411yescharacteristic
86C22⋊Dic149—21no—
87C22⋊Dic149D411yescharacteristic
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713D411yescharacteristic
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×D149—21no—
112C22×D149C2×D411yescharacteristic
113Dic298—21no—
114Dic298—21no—
115Dic298—42no—
116Dic298—81no—
117D596—21no—
118D596—21no—
119D596—81no—
120C22⋊D149—22no—
121C22⋊D149—81no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C4×D149—21no—
129C4×D149—21no—
130C4×D149—42no—
131C4×D149—42no—
132#11924746—21no—
133#11924746—21no—
134C23×C149C2×D411yescharacteristic
135Q8×C149—21no—
136Q8×C149—21no—
137Q8×C149—21no—
138Q8×C149—42no—
139Q8×C149#4112yes—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—42no—
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2411yescharacteristic
149C8×C149—21no—
150C8×C149—21no—
151C22×C149—21no—
152C22×C149—21no—
153C22×C149—21no—
154C22×C149C22×D411yescharacteristic
155C2×D149—21no—
156C2×D149—21no—
157C2×D149—21no—
158C2×D149—41no—
159C2×D149—41no—
160C2×D149—41no—
161C4×C149—21no—
162C4×C149—22no—
163C4×C149—41no—
164C4×C149—41no—
165C4×C149—41no—
166C4×C149C2×#4111yescharacteristic
167C4×C149H(5,𝔽2)11yescharacteristic
168Dic149—21no—
169Dic149—21no—
170Dic149—41no—
171Dic149—41no—
172Dic149—41no—
173Dic149#13712yes—
174C2×C149—41no—
175C2×C149#54611yescharacteristic
176C2×C149C2×#13711yescharacteristic
177C2×C149#57711yescharacteristic
178D149—41no—
179D149—81no—
180C149#332911yescharacteristic, complemented, Sylow
181#3329—1491nomaximal, Sylow
182#555—1491no—
183D4×Q8—1491no—
184#487—1491no—
185#485—1491no—
186#485—1491no—
187#477—1491no—
188#468—1491no—
189#468—1491no—
190#461—1491no—
191#448—1491no—
192#448—1491no—
193C4×SD16—1491no—
194#436—1491no—
195#419—1491no—
196#419D14911yescharacteristic, complemented
197C22×Q8—1491no—
198C22×Q8C2×D14911yescharacteristic
199C2×SD16—1491no—
200C2×SD16—1491no—
201C2×SD16—1491no—
202C2×M16—1491no—
203C2×M16C2×D14911yescharacteristic
204C4⋊Q8—2981no—
205C4⋊Q8—1491no—
206C4⋊Q8—1491no—
207#124—2981no—
208#124—2981no—
209C22⋊Q8—2981no—
210C22⋊Q8—2981no—
211C22⋊Q8—1491no—
212C22⋊Q8—1491no—
213#121—2981no—
214#121—1491no—
215#121—1491no—
216C4×Q8—1491no—
217C4×D4—2981no—
218C4×D4—1491no—
219C4×D4—1491no—
220#117—2981no—
221#117—1491no—
222#117C2×D14911yescharacteristic
223#107—1491no—
224#107—1491no—
225#106—1491no—
226C4⋊C8—1491no—
227#103—1491no—
228#103—1491no—
229#103—1491no—
230#103—1491no—
231#103—1491no—
232#103C2×D14911yescharacteristic
233#103C2×D14911yescharacteristic
234#103C2×D14911yescharacteristic
235#103C2×D14911yescharacteristic
236#102—1491no—
237C22⋊C8—1491no—
238C22⋊C8—1491no—
239C4×C8—1491no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—2981no—
244C2×Q8—2981no—
245C2×Q8—2982no—
246C2×Q8—5961no—
247C2×Q8—1491no—
248C2×Q8C22×D14911yescharacteristic
249C2×Q8C22×D14911yescharacteristic
250C2×D4—2981no—
251C2×D4—2981no—
252C2×D4—1491no—
253C2×D4—1491no—
254C22×C4—21no—
255C22×C4—2981no—
256C22×C4—2981no—
257C22×C4—1491no—
258C22×C4C22×D14911yescharacteristic
259SD16—2982no—
260SD16—5961no—
261SD16—5961no—
262M16—41no—
263M16—5961no—
264C2×C8—1491no—
265C2×C8—1491no—
266C2×C8C22×D14911yescharacteristic
267C2×C8C22×D14911yescharacteristic
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—2981no—
272C4⋊C4—2981no—
273C4⋊C4—2981no—
274C4⋊C4—1491no—
275C4⋊C4—1491no—
276C4⋊C4—1491no—
277C4⋊C4C22×D14911yescharacteristic
278C4⋊C4C22×D14911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—1491no—
287C22⋊C4—1491no—
288C42—21no—
289C42—2981no—
290C42—2981no—
291C42—1491no—
292C23—2981no—
293C23—1491no—
294C23D4×D14911yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—2981no—
300Q8—2981no—
301Q8—5962no—
302Q8—11921no—
303Q8#1455873612yes—
304D4—2982no—
305D4—2981no—
306D4—2981no—
307D4—11921no—
308D4—11921no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—2981no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—2981no—
321C2×C4—5962no—
322C2×C4—5962no—
323C2×C4—1491no—
324C2×C4—1491no—
325C2×C4—1491no—
326C2×C4D4×D14911yescharacteristic
327C2×C4C23×D14911yescharacteristic
328C8—21no—
329C8—21no—
330C8—2981no—
331C8—2981no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—2981no—
336C22—2981no—
337C22—2981no—
338C22—5961no—
339C22—5961no—
340C22—5961no—
341C22C2×D4×D14911yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—2981no—
348C4—2981no—
349C4—5961no—
350C4—5961no—
351C4—5961no—
352C4—1492no—
353C4C2×#1455873611yescharacteristic
354C4#1801195611yescharacteristic
355C2—41no—
356C2—5961no—
357C2—11921no—
358C2#2375026511yescharacteristic
359C2#137×D14911yescharacteristic
360C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#419×C149C2
socleC22×C149C22×D4
prime radical#23750338C2
hypercenter#419D149
hypocenterC149#3329
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
2. Q8×C22⋊D149C2semidirect
3. #23749974C2semidirect
4. #23749966C2semidirect
5. #23749965C2semidirect
6. #23749918C2semidirect
7. #23749874C2semidirect
8. #23749871C2semidirect
9. #23749829C2semidirect
10. #23749765C2semidirect
11. #23749764C2semidirect
12. #23749710C2semidirect
13. #23749701C2semidirect
14. #23749632C2semidirect
15. #419×C149C2semidirect
180. C149#3329semidirect
196. #419D149semidirect

Maximal subgroups

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

subgroupindex
#237503382
Q8×C22⋊D1492
#237499742
#237499662
#237499652
#237499182
#237498742
#237498712
#237498292
#237497652
#237497642
#237497102
#237497012
#237496322
#419×C1492
#3329149