Finite Group Databasebeta

← #34055260

Subgroups — #34055260

Order 19072.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750160C211yesmaximal, characteristic, complemented
2#23750154C211yesmaximal, characteristic, complemented
3#23750024C211yesmaximal, characteristic, complemented
4#23750007C211yesmaximal, characteristic, complemented
5#23749980C211yesmaximal, characteristic, complemented
6#23749865C211yesmaximal, characteristic, complemented
7#23749860C211yesmaximal, characteristic
8#23749857C211yesmaximal, characteristic, complemented
9#23749853C211yesmaximal, characteristic, complemented
10#23749717C211yesmaximal, characteristic, complemented
11#23749716C211yesmaximal, characteristic, complemented
12#23749710C211yesmaximal, characteristic, complemented
13#23749705C211yesmaximal, characteristic, complemented
14C4×C8×D149C211yesmaximal, characteristic, complemented
15#488×C149C211yesmaximal, characteristic, complemented
16C2×#14558726C2211yescharacteristic
17C2×#14558724C2211yescharacteristic
18C2×#14558723C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20C2×C8×D149C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic
22#18011906—21no—
23#18011904—21no—
24#18011903C2211yescharacteristic
25#18011899C2211yescharacteristic
26#18011896—21no—
27#18011893—21no—
28#18011891C2211yescharacteristic
29#18011887C2211yescharacteristic
30#18011886C2211yescharacteristic
31#18011882C2211yescharacteristic
32Q8×Dic149C2211yescharacteristic
33#18011876C2211yescharacteristic
34D4×Dic149C2211yescharacteristic
35#18011873—21no—
36#18011873C2211yescharacteristic
37#18011871—21no—
38#18011869—21no—
39#18011867—21no—
40C42×D149C2211yescharacteristic
41#18011844C2211yescharacteristic
42#18011844C2211yescharacteristic
43#18011842C2211yescharacteristic
44#18011842C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011833C2211yescharacteristic
49C4×#11924746C2211yescharacteristic
50C8×Dic149C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52#125×C149C2211yescharacteristic
53#124×C149C2211yescharacteristic
54#103×C149C2211yescharacteristic
55#103×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59C2×Dic298C2311yescharacteristic
60C2×D596—21no—
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C22×Dic149—21no—
64C2×C4×D149—21no—
65C2×C4×D149D411yescharacteristic
66C2×C4×D149D411yescharacteristic
67C2×C4×D149C2311yescharacteristic
68#14558726—22no—
69#14558724—22no—
70#14558723—22no—
71#14558721—22no—
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C8×D149—22no—
75C8×D149—22no—
76C4⋊Dic149—21no—
77C4⋊Dic149—21no—
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92C4×Dic149—21no—
93C4×Dic149—21no—
94C4×Dic149D411yescharacteristic
95C4×Dic149D411yescharacteristic
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149C2311yescharacteristic
98C2×D4×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C4⋊C4×C149—21no—
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C22⋊C4×C149—21no—
106C22⋊C4×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149C2×D411yescharacteristic
110Dic298—21no—
111Dic298—21no—
112D596—21no—
113D596—21no—
114D596—42no—
115C22⋊D149—42no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—42no—
120C2×Dic149C2×D411yescharacteristic
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C4×D149—22no—
124C4×D149—21no—
125C4×D149—21no—
126C4×D149—22no—
127C4×D149—42no—
128#11924746#4112yes—
129#11924746#4112yes—
130C23×C149—21no—
131Q8×C149—21no—
132Q8×C149—21no—
133D4×C149—21no—
134D4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2411yescharacteristic
141C8×C149—21no—
142C8×C149—21no—
143C22×C149—41no—
144C22×C149—41no—
145C22×C149—41no—
146C22×C149C22×D411yescharacteristic
147C2×D149—21no—
148C2×D149—21no—
149C2×D149—41no—
150C2×D149—41no—
151C2×D149—41no—
152C2×D149#13512yes—
153C4×C149—21no—
154C4×C149—21no—
155C4×C149—41no—
156C4×C149—41no—
157C4×C149—41no—
158C4×C149C2×#4111yescharacteristic
159C4×C149C2×#4111yescharacteristic
160Dic149—21no—
161Dic149—21no—
162Dic149—41no—
163Dic149—41no—
164Dic149—41no—
165Dic149#13512yes—
166C2×C149—81no—
167C2×C149#53211yescharacteristic
168C2×C149C2×#13511yescharacteristic
169C2×C149C2×#13511yescharacteristic
170D149—22no—
171D149—81no—
172C149#316811yescharacteristic, complemented, Sylow
173#3168—1491nomaximal, Sylow
174#529—1491no—
175#529—1491no—
176#499—1491no—
177#495—1491no—
178#488—1491no—
179#488D14911yescharacteristic, complemented
180#467—1491no—
181#466—1491no—
182#465—1491no—
183#465—1491no—
184C4×Q16—1491no—
185C4×SD16—1491no—
186C4×SD16—1491no—
187C4×D8—1491no—
188C2×C4×C8—1491no—
189C2×Q16—1491no—
190C2×SD16—1491no—
191C2×SD16—1491no—
192C2×D8—1491no—
193C22×C8—1491no—
194C22×C8—1491no—
195#126—2981no—
196#126—2981no—
197#125—1491no—
198#125C2×D14911yescharacteristic
199#124—1491no—
200#124C2×D14911yescharacteristic
201#123—2981no—
202#123—2981no—
203C22⋊Q8—1491no—
204C22⋊Q8—1491no—
205#121—1491no—
206#121—1491no—
207C4×Q8—1491no—
208C4×Q8—1491no—
209C4×D4—2981no—
210C4×D4—2981no—
211C4×D4—1491no—
212C4×D4—1491no—
213#117—2981no—
214#117—2981no—
215C2×C42—1491no—
216#107—1491no—
217#107—1491no—
218#106—1491no—
219#106—1491no—
220#103—1491no—
221#103—1491no—
222#103C2×D14911yescharacteristic
223#103C2×D14911yescharacteristic
224#102—1491no—
225#102—1491no—
226#102C2×D14911yescharacteristic
227#102C2×D14911yescharacteristic
228C4×C8—1491no—
229C4×C8—1491no—
230C4×C8—1491no—
231C4×C8C2×D14911yescharacteristic
232C2×Q8—1491no—
233C2×Q8C22×D14911yescharacteristic
234C2×D4—2981no—
235C2×D4—2981no—
236C2×D4—1491no—
237C2×D4C22×D14911yescharacteristic
238C22×C4—2981no—
239C22×C4—2981no—
240C22×C4—1491no—
241C22×C4—1491no—
242C22×C4—1491no—
243Q16—2982no—
244SD16—2982no—
245SD16—2982no—
246D8—2982no—
247C2×C8—2982no—
248C2×C8—2982no—
249C2×C8—1491no—
250C2×C8—1491no—
251C2×C8C22×D14911yescharacteristic
252C2×C8C22×D14911yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—2981no—
256C4⋊C4—2981no—
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—2981no—
260C4⋊C4—2981no—
261C4⋊C4—1491no—
262C4⋊C4—1491no—
263C4⋊C4C22×D14911yescharacteristic
264C4⋊C4C22×D14911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—2981no—
268C22⋊C4—2981no—
269C22⋊C4—2981no—
270C22⋊C4—2981no—
271C22⋊C4—2981no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C42—2981no—
276C42—2981no—
277C42—1491no—
278C42—1491no—
279C42—1491no—
280C42C22×D14911yescharacteristic
281C23—21no—
282C23—2981no—
283C23—1491no—
284Q8—21no—
285Q8—21no—
286Q8—2981no—
287Q8—2981no—
288D4—21no—
289D4—21no—
290D4—2981no—
291D4—2981no—
292D4—5962no—
293D4—5962no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—2982no—
298C2×C4—2982no—
299C2×C4—2981no—
300C2×C4—2981no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—5962no—
305C2×C4—5962no—
306C2×C4—1491no—
307C2×C4—1491no—
308C2×C4—1491no—
309C2×C4D4×D14911yescharacteristic
310C2×C4D4×D14911yescharacteristic
311C2×C4C23×D14911yescharacteristic
312C8—21no—
313C8—21no—
314C8—1492no—
315C8—1492no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—2981no—
320C22—2981no—
321C22—5961no—
322C22—5961no—
323C22—5961no—
324C22—1492no—
325C22C2×D4×D14911yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—2981no—
332C4—2981no—
333C4—5961no—
334C4—5961no—
335C4—5961no—
336C4—1492no—
337C4#41×D14911yescharacteristic
338C4#41×D14911yescharacteristic
339C2—81no—
340C2—2982no—
341C2—11921no—
342C2#2375017411yescharacteristic
343C2#135×D14911yescharacteristic
344C2#135×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#488×C149C2
socleC22×C149C22×D4
prime radical#23749860C2
hypercenter#488D149
hypocenterC149#3168
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #23750160C2semidirect
2. #23750154C2semidirect
3. #23750024C2semidirect
4. #23750007C2semidirect
5. #23749980C2semidirect
6. #23749865C2semidirect
8. #23749857C2semidirect
9. #23749853C2semidirect
10. #23749717C2semidirect
11. #23749716C2semidirect
12. #23749710C2semidirect
13. #23749705C2semidirect
14. C4×C8×D149C2semidirect
15. #488×C149C2semidirect
172. C149#3168semidirect
179. #488D149semidirect

Maximal subgroups

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

subgroupindex
#237501602
#237501542
#237500242
#237500072
#237499802
#237498652
#237498602
#237498572
#237498532
#237497172
#237497162
#237497102
#237497052
C4×C8×D1492
#488×C1492
#3168149