Finite Group Databasebeta

← #34057762

Subgroups — #34057762

Order 19072.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750358C211yesmaximal, characteristic, complemented
2#23750345C211yesmaximal, characteristic, complemented
3#23750019C211yesmaximal, characteristic, complemented
4#23750013C211yesmaximal, characteristic
5#23750008C211yesmaximal, characteristic, complemented
6#23749846C211yesmaximal, characteristic, complemented
7#23749846C211yesmaximal, characteristic, complemented
8#23749840C211yesmaximal, characteristic, complemented
9#23749839C211yesmaximal, characteristic, complemented
10#23749830C211yesmaximal, characteristic, complemented
11#23749824C211yesmaximal, characteristic, complemented
12#23749753C211yesmaximal, characteristic, complemented
13#23749731C211yesmaximal, characteristic, complemented
14#23749712C211yesmaximal, characteristic, complemented
15#442×C149C211yesmaximal, characteristic, complemented
16C2×Dic596C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558724C2211yescharacteristic
21C2×#14558724C2211yescharacteristic
22C2×#14558724C2211yescharacteristic
23C2×#14558721C2211yescharacteristic
24#18011911C2211yescharacteristic
25#18011907C2211yescharacteristic
26#18011904—21no—
27#18011904—21no—
28#18011899C2211yescharacteristic
29#18011898C2211yescharacteristic
30#18011898C2211yescharacteristic
31#18011898C2211yescharacteristic
32#18011897—21no—
33#18011894—21no—
34#18011893—21no—
35#18011890—21no—
36C4×Dic298C2211yescharacteristic
37#18011876C2211yescharacteristic
38#18011876C2211yescharacteristic
39#18011876C2211yescharacteristic
40#18011873C2211yescharacteristic
41C4×C22⋊D149—21no—
42#18011870—21no—
43C4⋊#11924746C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011834C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×D8×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59C2×Dic298D411yescharacteristic
60C2×Dic298C2311yescharacteristic
61C2×Dic298C2311yescharacteristic
62C2×Dic298C2311yescharacteristic
63C2×D596C2311yescharacteristic
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C4×D149—21no—
67Dic596—22no—
68Dic596—41no—
69#14558725—22no—
70#14558725—41no—
71#14558724—41no—
72#14558724—41no—
73#14558724—41no—
74#14558721—41no—
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C4⋊Dic149—21no—
78C4⋊Dic149—21no—
79C4⋊Dic149D411yescharacteristic
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715D411yescharacteristic
84#14558715D411yescharacteristic
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149—21no—
97C4×Dic149C2311yescharacteristic
98C4×Dic149C2311yescharacteristic
99C2×D4×C149C2311yescharacteristic
100C2×D4×C149C2311yescharacteristic
101C22×C4×C149—21no—
102C22×C4×C149—21no—
103D8×C149—22no—
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C4⋊C4×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C22⋊C4×C149—21no—
109C22⋊C4×C149—21no—
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112Dic298—21no—
113Dic298—21no—
114Dic298—21no—
115Dic298—21no—
116Dic298—21no—
117Dic298—21no—
118Dic298—41no—
119D596—21no—
120D596—21no—
121C22⋊D149—42no—
122C22⋊D149—81no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C4×D149—81no—
131#11924746—21no—
132#11924746—21no—
133C23×C149—21no—
134C23×C149—21no—
135D4×C149—21no—
136D4×C149—21no—
137D4×C149—21no—
138D4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—42no—
142C2×C4×C149—81no—
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2411yescharacteristic
146C8×C149—21no—
147C8×C149#4112yes—
148C22×C149—41no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149C22×D411yescharacteristic
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C4×C149—21no—
159C4×C149—21no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149C2×#4111yescharacteristic
163C4×C149H(5,𝔽2)11yescharacteristic
164Dic149—21no—
165Dic149—21no—
166Dic149—21no—
167Dic149—21no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171C2×C149—81no—
172C2×C149—81no—
173C2×C149#55011yescharacteristic
174C2×C149#57511yescharacteristic
175C2×C149#57711yescharacteristic
176D149—81no—
177C149#340111yescharacteristic, complemented, Sylow
178#3401—1491nomaximal, Sylow
179#559—1491no—
180#556—1491no—
181#497—1491no—
182#496—1491no—
183#495—1491no—
184#464—1491no—
185#464—1491no—
186#463—1491no—
187#463—1491no—
188#461—1491no—
189#460—1491no—
190#446—1491no—
191#442D14911yescharacteristic, complemented
192#441—1491no—
193C4×SD16—1491no—
194C2×Q16—1491no—
195C2×Q16—1491no—
196C2×SD16—1491no—
197C2×SD16—1491no—
198C2×SD16—1491no—
199C2×SD16—1491no—
200C2×SD16—1491no—
201C2×D8—1491no—
202C2×D8C2×D14911yescharacteristic
203C4⋊Q8—1491no—
204#127—1491no—
205#126—2981no—
206#126—2981no—
207#124—2981no—
208#124—1491no—
209#124—1491no—
210#124—1491no—
211#124—1491no—
212#123—2981no—
213#123—2981no—
214C22⋊Q8—2981no—
215C4×Q8—1491no—
216C4×Q8—1491no—
217C4×Q8—1491no—
218C4×Q8—1491no—
219C4×D4—2981no—
220C4×D4—1491no—
221C4×D4C2×D14911yescharacteristic
222C4×D4C2×D14911yescharacteristic
223#117—2981no—
224#106C2×D14911yescharacteristic
225C4⋊C8—1491no—
226C4⋊C8—1491no—
227C4⋊C8—1491no—
228#103—1491no—
229#103—1491no—
230#103—1491no—
231#102—1491no—
232#102C2×D14911yescharacteristic
233#102C2×D14911yescharacteristic
234#97—1491no—
235#97C2×D14911yescharacteristic
236C4×C8—1491no—
237C2×Q8—1491no—
238C2×Q8—1491no—
239C2×Q8—1491no—
240C2×Q8—1491no—
241C2×D4—2981no—
242C2×D4—2981no—
243C2×D4—1491no—
244C2×D4C22×D14911yescharacteristic
245C2×D4C22×D14911yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—2981no—
249Q16—2982no—
250Q16—5961no—
251SD16—2982no—
252SD16—5961no—
253SD16—5961no—
254SD16—5961no—
255SD16—5961no—
256D8—22no—
257D8—5961no—
258C2×C8—1491no—
259C2×C8—1491no—
260C2×C8C22×D14911yescharacteristic
261C2×C8C22×D14911yescharacteristic
262C4⋊C4—2981no—
263C4⋊C4—2981no—
264C4⋊C4—2981no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—1491no—
268C4⋊C4—1491no—
269C4⋊C4—1491no—
270C4⋊C4C22×D14911yescharacteristic
271C4⋊C4C22×D14911yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C42—2981no—
284C42—2981no—
285C42—2981no—
286C42—1491no—
287C42—1491no—
288C42C22×D14911yescharacteristic
289C23—21no—
290C23—21no—
291C23—2981no—
292Q8—2981no—
293Q8—2981no—
294Q8—2981no—
295Q8—2981no—
296Q8—2981no—
297Q8—2981no—
298Q8—5961no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—2981no—
304D4—2981no—
305D4—5962no—
306D4—11921no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—81no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—1491no—
315C2×C4—1491no—
316C2×C4—1491no—
317C2×C4—1491no—
318C2×C4—11921no—
319C2×C4D4×D14911yescharacteristic
320C2×C4D4×D14911yescharacteristic
321C2×C4C23×D14911yescharacteristic
322C8—21no—
323C8—2981no—
324C8—2981no—
325C8#1455873612yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—5961no—
333C22—5961no—
334C22—5961no—
335C22C2×D4×D14911yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—2981no—
341C4—2981no—
342C4—2981no—
343C4—2981no—
344C4—5961no—
345C4—5961no—
346C4—5961no—
347C4C2×#1455873611yescharacteristic
348C4#1801195711yescharacteristic
349C2—81no—
350C2—81no—
351C2—11921no—
352C2#2375029611yescharacteristic
353C2#2375042111yescharacteristic
354C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#442×C149C2
socleC22×C149C22×D4
prime radical#23750013C2
hypercenter#442D149
hypocenterC149#3401
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #23750358C2semidirect
2. #23750345C2semidirect
3. #23750019C2semidirect
5. #23750008C2semidirect
6. #23749846C2semidirect
7. #23749846C2semidirect
8. #23749840C2semidirect
9. #23749839C2semidirect
10. #23749830C2semidirect
11. #23749824C2semidirect
12. #23749753C2semidirect
13. #23749731C2semidirect
14. #23749712C2semidirect
15. #442×C149C2semidirect
177. C149#3401semidirect
191. #442D149semidirect

Maximal subgroups

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

subgroupindex
#237503582
#237503452
#237500192
#237500132
#237500082
#237498462
#237498402
#237498392
#237498302
#237498242
#237497532
#237497312
#237497122
#442×C1492
#3401149