Finite Group Databasebeta

← #34057451

Subgroups — #34057451

Order 19072.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750358C211yesmaximal, characteristic, complemented
2#23750336C211yesmaximal, characteristic, complemented
3#23749988C211yesmaximal, characteristic, complemented
4#23749987C211yesmaximal, characteristic, complemented
5#23749978C211yesmaximal, characteristic, complemented
6#23749931C211yesmaximal, characteristic, complemented
7#23749928C211yesmaximal, characteristic, complemented
8#23749841C211yesmaximal, characteristic, complemented
9#23749839C211yesmaximal, characteristic, complemented
10#23749819C211yesmaximal, characteristic
11#23749754C211yesmaximal, characteristic, complemented
12#23749735C211yesmaximal, characteristic, complemented
13#23749724C211yesmaximal, characteristic, complemented
14#23749707C211yesmaximal, characteristic, complemented
15#474×C149C211yesmaximal, characteristic, complemented
16C2×#14558725C2211yescharacteristic
17C2×D1192C2211yescharacteristic
18C2×#14558721C2211yescharacteristic
19#18011907C2211yescharacteristic
20#18011902C2211yescharacteristic
21#18011902C2211yescharacteristic
22#18011899C2211yescharacteristic
23#18011898C2211yescharacteristic
24#18011897—21no—
25#18011894—21no—
26#18011893—21no—
27#18011891—21no—
28#18011887—21no—
29#18011887—21no—
30C4×Dic298C2211yescharacteristic
31#18011876C2211yescharacteristic
32C4×D596C2211yescharacteristic
33#18011873C2211yescharacteristic
34#18011873C2211yescharacteristic
35#18011873C2211yescharacteristic
36C4×C22⋊D149—21no—
37C4⋊C4×D149—21no—
38#18011842C2211yescharacteristic
39#18011840C2211yescharacteristic
40#18011840C2211yescharacteristic
41#18011836C2211yescharacteristic
42#18011834C2211yescharacteristic
43#18011834C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011832C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011822C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C4⋊Q8×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C2×Dic298D411yescharacteristic
60C2×Dic298C2311yescharacteristic
61C2×D596C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C4×D149—21no—
66C2×C4×D149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69#14558725—22no—
70D1192—22no—
71#14558721—22no—
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149D411yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715D411yescharacteristic
82#14558715D411yescharacteristic
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91C4×Dic149—21no—
92C4×Dic149C2311yescharacteristic
93C4×Dic149C2311yescharacteristic
94C2×Q8×C149—21no—
95C2×D4×C149C2311yescharacteristic
96C22×C4×C149—21no—
97C2×C8×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C4⋊C4×C149—21no—
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C22⋊C4×C149—21no—
104C42×C149C2311yescharacteristic
105C22×D149—21no—
106C22×D149—21no—
107Dic298—21no—
108Dic298—21no—
109Dic298—41no—
110D596—21no—
111D596—21no—
112D596—21no—
113D596#4112yes—
114C22⋊D149—42no—
115C22⋊D149—81no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149C2×D411yescharacteristic
119C2×Dic149C2×D411yescharacteristic
120C2×Dic149C2×D411yescharacteristic
121C2×Dic149C2×D411yescharacteristic
122C4×D149—42no—
123C4×D149—81no—
124C4×D149—81no—
125C4×D149—81no—
126#11924746—21no—
127#11924746—21no—
128C23×C149—21no—
129Q8×C149—81no—
130D4×C149—21no—
131D4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—81no—
136C2×C4×C149C2×D411yescharacteristic
137C2×C4×C149C2×D411yescharacteristic
138C2×C4×C149C2411yescharacteristic
139C8×C149—21no—
140C8×C149—21no—
141C22×C149—41no—
142C22×C149—41no—
143C22×C149—41no—
144C22×C149C22×D411yescharacteristic
145C2×D149—22no—
146C2×D149—41no—
147C2×D149—41no—
148C2×D149—41no—
149C2×D149—41no—
150C2×D149—41no—
151C4×C149—21no—
152C4×C149—21no—
153C4×C149—41no—
154C4×C149—41no—
155C4×C149—41no—
156C4×C149C2×#4111yescharacteristic
157C4×C1492−1+411yescharacteristic
158Dic149—21no—
159Dic149—21no—
160Dic149—21no—
161Dic149—21no—
162Dic149—41no—
163Dic149—41no—
164C2×C149—81no—
165C2×C149#54811yescharacteristic
166C2×C149#57511yescharacteristic
167C2×C149#57611yescharacteristic
168D149—42no—
169D149—81no—
170C149#337011yescharacteristic, complemented, Sylow
171#3370—1491nomaximal, Sylow
172#559—1491no—
173#554—1491no—
174#490—1491no—
175#489—1491no—
176#488—1491no—
177#479—1491no—
178#478—1491no—
179#474D14911yescharacteristic, complemented
180#463—1491no—
181#463—1491no—
182#459—1491no—
183#446—1491no—
184#442—1491no—
185#440—1491no—
186C4×D8—1491no—
187C2×SD16—1491no—
188C2×D8—1491no—
189C2×D8—1491no—
190C4⋊Q8C2×D14911yescharacteristic
191#127—1491no—
192#125—1491no—
193#125—1491no—
194#124—2981no—
195#124—1491no—
196#124—1491no—
197#123—2981no—
198#123—2981no—
199C22⋊Q8—2981no—
200C22⋊Q8—2981no—
201C22⋊Q8—2981no—
202C4×Q8—1491no—
203C4×Q8—1491no—
204C4×D4—2981no—
205C4×D4—1491no—
206C4×D4—1491no—
207C4×D4—1491no—
208C4×D4—1491no—
209C4×D4C2×D14911yescharacteristic
210C2×C4⋊C4—2981no—
211#107C2×D14911yescharacteristic
212#107C2×D14911yescharacteristic
213#106—1491no—
214C4⋊C8—1491no—
215C4⋊C8—1491no—
216C4⋊C8C2×D14911yescharacteristic
217#103—1491no—
218#103—1491no—
219#103—1491no—
220#102—1491no—
221#102—1491no—
222#102—1491no—
223#102—1491no—
224#102—1491no—
225#102C2×D14911yescharacteristic
226#102C2×D14911yescharacteristic
227#97—1491no—
228#97—1491no—
229C4×C8—1491no—
230C2×Q8—21no—
231C2×Q8—1491no—
232C2×Q8—1491no—
233C2×D4—2981no—
234C2×D4—2981no—
235C2×D4—1491no—
236C2×D4—1491no—
237C2×D4C22×D14911yescharacteristic
238C22×C4—21no—
239C22×C4—2981no—
240C22×C4—2981no—
241C22×C4—2981no—
242C22×C4—2981no—
243SD16—2982no—
244D8—2982no—
245D8—2982no—
246C2×C8—1491no—
247C2×C8—1491no—
248C2×C8C22×D14911yescharacteristic
249C2×C8C22×D14911yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—2981no—
252C4⋊C4—2981no—
253C4⋊C4—2981no—
254C4⋊C4—2981no—
255C4⋊C4—2981no—
256C4⋊C4—1491no—
257C4⋊C4—1491no—
258C4⋊C4—1491no—
259C4⋊C4—1491no—
260C4⋊C4C22×D14911yescharacteristic
261C4⋊C4C22×D14911yescharacteristic
262C4⋊C4C22×D14911yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—2981no—
265C22⋊C4—2981no—
266C22⋊C4—2981no—
267C22⋊C4—2981no—
268C22⋊C4—2981no—
269C22⋊C4—2981no—
270C22⋊C4—2981no—
271C22⋊C4—2981no—
272C42—2981no—
273C42—1491no—
274C42—1491no—
275C42C22×D14911yescharacteristic
276C23—21no—
277C23—2981no—
278C23—2981no—
279Q8—81no—
280Q8—2981no—
281Q8—2981no—
282Q8—5961no—
283D4—21no—
284D4—21no—
285D4—2981no—
286D4—2981no—
287D4—2981no—
288D4—5962no—
289D4—1492no—
290D4—11921no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—2981no—
296C2×C4—2981no—
297C2×C4—5962no—
298C2×C4—1491no—
299C2×C4—1491no—
300C2×C4—1491no—
301C2×C4—1491no—
302C2×C4—11921no—
303C2×C4—11921no—
304C2×C4—11921no—
305C2×C4D4×D14911yescharacteristic
306C2×C4D4×D14911yescharacteristic
307C2×C4C23×D14911yescharacteristic
308C8—21no—
309C8—21no—
310C8—2981no—
311C8—2981no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—2982no—
316C22—5961no—
317C22—5961no—
318C22—5961no—
319C22—5961no—
320C22—5961no—
321C22C2×D4×D14911yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—2981no—
328C4—2981no—
329C4—2981no—
330C4—2981no—
331C4—5961no—
332C4—5961no—
333C4#41×D14911yescharacteristic
334C4#1801195911yescharacteristic
335C2—81no—
336C2—5962no—
337C2—11921no—
338C2#2375028511yescharacteristic
339C2#2375042411yescharacteristic
340C2#2375042611yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#474×C149C2
socleC22×C149C22×D4
prime radical#23749819C2
hypercenter#474D149
hypocenterC149#3370
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #23750358C2semidirect
2. #23750336C2semidirect
3. #23749988C2semidirect
4. #23749987C2semidirect
5. #23749978C2semidirect
6. #23749931C2semidirect
7. #23749928C2semidirect
8. #23749841C2semidirect
9. #23749839C2semidirect
11. #23749754C2semidirect
12. #23749735C2semidirect
13. #23749724C2semidirect
14. #23749707C2semidirect
15. #474×C149C2semidirect
170. C149#3370semidirect
179. #474D149semidirect

Maximal subgroups

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

subgroupindex
#237503582
#237503362
#237499882
#237499872
#237499782
#237499312
#237499282
#237498412
#237498392
#237498192
#237497542
#237497352
#237497242
#237497072
#474×C1492
#3370149