Finite Group Databasebeta

← #34053533

Subgroups — #34053533

Order 19072.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011943C211yesmaximal, characteristic
2#23750107C211yesmaximal, characteristic
3#23750101C211yesmaximal, characteristic, complemented
4#23749729C211yesmaximal, characteristic, complemented
5#23749728C211yesmaximal, characteristic, complemented
6#23749727C211yesmaximal, characteristic, complemented
7Q16×Dic149C211yesmaximal, characteristic, complemented
8C4×#14558726C211yesmaximal, characteristic, complemented
9C4×#14558723C211yesmaximal, characteristic, complemented
10#23749712C211yesmaximal, characteristic, complemented
11#23749664C211yesmaximal, characteristic, complemented
12#23749620C211yesmaximal, characteristic
13#103×D149C211yesmaximal, characteristic, complemented
14#23749582C211yesmaximal, characteristic, complemented
15#441×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic
18#18011943C418yescomplemented
19C2×#14558726C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21C2×#14558723C2211yescharacteristic
22C2×#14558719C2211yescharacteristic
23C2×C8×D149C2211yescharacteristic
24Q8×Dic149C2211yescharacteristic
25Q8×Dic149C2211yescharacteristic
26C4×Dic298—21no—
27C4×Dic298C2211yescharacteristic
28#18011876—21no—
29#18011876C2211yescharacteristic
30C4×D596—21no—
31C4×D596C2211yescharacteristic
32#18011873—21no—
33#18011873C2211yescharacteristic
34#18011869—21no—
35#18011869C2211yescharacteristic
36#18011868—21no—
37#18011868—21no—
38#18011868C2211yescharacteristic
39C4⋊C4×D149—21no—
40C4⋊C4×D149C2211yescharacteristic
41#18011845C2211yescharacteristic
42#18011844C2211yescharacteristic
43#18011842C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011821C2211yescharacteristic
51C4×#11924746C2211yescharacteristic
52C8×Dic149C2211yescharacteristic
53C2×Q16×C149C2211yescharacteristic
54C4×Q8×C149C2211yescharacteristic
55C4×Q8×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#103×C149C2211yescharacteristic
59#97×C149C2211yescharacteristic
60#14558737—22no—
61#14558737C2×C414yes—
62C2×Dic298—21no—
63C2×Dic298C2311yescharacteristic
64Q8×D149—22no—
65Q8×D149C2×C414yescomplemented
66C2×D596—21no—
67C2×D596C2311yescharacteristic
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73C2×C4×D149C2311yescharacteristic
74#14558726C2×C414yescomplemented
75#14558725C2×C414yescomplemented
76#14558723C2×C414yescomplemented
77#14558719C2×C414yescomplemented
78C2×#11924746C2311yescharacteristic
79C2×#11924746C2311yescharacteristic
80C8×D149—22no—
81C4⋊Dic149—21no—
82C4⋊Dic149—21no—
83C4⋊Dic149C2311yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715D411yescharacteristic
89#14558715D411yescharacteristic
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713D411yescharacteristic
94#14558713D411yescharacteristic
95C4×Dic149—21no—
96C4×Dic149—21no—
97C4×Dic149—21no—
98C4×Dic149—21no—
99C4×Dic149—21no—
100C4×Dic149C2311yescharacteristic
101C2×Q8×C149C2311yescharacteristic
102C2×Q8×C149C2311yescharacteristic
103Q16×C149C2×C414yescomplemented
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C4⋊C4×C149—21no—
107C4⋊C4×C149—21no—
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C42×C149—21no—
111C42×C149—21no—
112C42×C149C2311yescharacteristic
113C22×D149—21no—
114C22×D149C2×D411yescharacteristic
115Dic298—21no—
116Dic298—24no—
117Dic298C22×C412yes—
118D596—24no—
119D596—21no—
120D596C22×C412yes—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C4×D149—24no—
128C4×D149—24no—
129C4×D149—81no—
130C4×D149—81no—
131C4×D149—81no—
132C4×D149C22×C412yes—
133C4×D149#4112yes—
134#11924746—21no—
135#11924746C22×C412yes—
136Q8×C149—21no—
137Q8×C149—21no—
138Q8×C149C22×C412yes—
139Q8×C149C22×C412yes—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2411yescharacteristic
147C8×C149—21no—
148C8×C149C22×C412yes—
149C22×C149C22×D411yescharacteristic
150C2×D149—21no—
151C2×D149—21no—
152C2×D149—22no—
153C2×D149—41no—
154C2×D149—41no—
155C2×D149C4×D412yes—
156C4×C149—22no—
157C4×C149—22no—
158C4×C149—21no—
159C4×C149—21no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149C23×C411yescharacteristic
163C4×C149C2×#4111yescharacteristic
164Dic149—22no—
165Dic149—21no—
166Dic149—21no—
167Dic149—41no—
168Dic149—41no—
169Dic149C4×D412yes—
170C2×C149C2×C4×D411yescharacteristic
171C2×C149#57711yescharacteristic
172C2×C149#57811yescharacteristic
173D149—22no—
174D149—42no—
175C149#294711yescharacteristic, complemented, Sylow
176#2947—1491nomaximal, Sylow
177C2×#137—1491no—
178#520—1491no—
179#519—1491no—
180#441—1491no—
181#441D14911yescharacteristic, complemented
182#440—1491no—
183#440—1491no—
184C4×Q16—1491no—
185C4×Q16—1491no—
186C4×SD16—1491no—
187C4×SD16—1491no—
188#428—1491no—
189#416—1491no—
190C2×#103—1491no—
191#405—1491no—
192C2×#41—1491no—
193C22×Q8—1491no—
194#137—1498no—
195C2×Q16—1491no—
196C2×Q16C2×D14911yescharacteristic
197C2×SD16—1491no—
198C2×SD16—1491no—
199C2×M16—1491no—
200C22×C8—1491no—
201C4×Q8—2981no—
202C4×Q8—2981no—
203C4×Q8—1491no—
204C4×Q8—1491no—
205C4×Q8—1491no—
206C4×Q8—1491no—
207C4×Q8C2×D14911yescharacteristic
208C4×Q8C2×D14911yescharacteristic
209C4×D4—2981no—
210C4×D4—2981no—
211C4×D4—1491no—
212C4×D4—1491no—
213#117—2981no—
214#117—2981no—
215#117—2981no—
216#117—1491no—
217#117—1491no—
218C2×C4⋊C4—2981no—
219C2×C4⋊C4—1491no—
220#107—1491no—
221#107—1491no—
222#106—1491no—
223#106C2×D14911yescharacteristic
224#103—1491no—
225#103—1491no—
226#103—1491no—
227#103—1491no—
228#103C2×D14911yescharacteristic
229#103C2×D14911yescharacteristic
230#102—1491no—
231#102—1491no—
232#97—1491no—
233#97C2×D14911yescharacteristic
234C4×C8—1491no—
235C4×C8—1491no—
236#41—2982no—
237#41—1494no—
238C2×Q8—2981no—
239C2×Q8—2982no—
240C2×Q8—1494no—
241C2×Q8—1491no—
242C2×Q8C22×D14911yescharacteristic
243C2×Q8C22×D14911yescharacteristic
244C2×D4—2981no—
245C2×D4—1491no—
246C22×C4—2981no—
247C22×C4—2981no—
248C22×C4—2981no—
249C22×C4—2981no—
250C22×C4—2981no—
251C22×C4—1491no—
252Q16—1494no—
253Q16C4×D14914yescomplemented
254SD16—1494no—
255SD16—1494no—
256M16—1494no—
257C2×C8—2982no—
258C2×C8—1491no—
259C2×C8—1491no—
260C2×C8C22×D14911yescharacteristic
261C2×C8C22×D14911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—2981no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—1491no—
270C4⋊C4—1491no—
271C4⋊C4—1491no—
272C4⋊C4—1491no—
273C4⋊C4C22×D14911yescharacteristic
274C4⋊C4C22×D14911yescharacteristic
275C22⋊C4—2981no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—1491no—
279C22⋊C4—1491no—
280C42—21no—
281C42—21no—
282C42—2981no—
283C42—2981no—
284C42—2981no—
285C42—2981no—
286C42—2981no—
287C42—1491no—
288C42C22×D14911yescharacteristic
289C23—2981no—
290C23—1491no—
291Q8—21no—
292Q8—21no—
293Q8—2984no—
294Q8—2981no—
295Q8—1492no—
296Q8C2×C4×D14912yes—
297Q8C2×C4×D14912yes—
298D4—2984no—
299D4—2981no—
300D4—1492no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—2984no—
306C2×C4—2984no—
307C2×C4—2981no—
308C2×C4—2981no—
309C2×C4—2981no—
310C2×C4—1491no—
311C2×C4—1491no—
312C2×C4—1491no—
313C2×C4—1492no—
314C2×C4—1492no—
315C2×C4—11921no—
316C2×C4—11921no—
317C2×C4—11921no—
318C2×C4D4×D14911yescharacteristic
319C2×C4D4×D14911yescharacteristic
320C2×C4C23×D14911yescharacteristic
321C8—21no—
322C8—2981no—
323C8—1492no—
324C8C2×C4×D14912yes—
325C22—2981no—
326C22—2981no—
327C22—2982no—
328C22—5961no—
329C22—5961no—
330C22—1492no—
331C22C2×D4×D14911yescharacteristic
332C4—21no—
333C4—21no—
334C4—22no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—2981no—
339C4—2981no—
340C4—2982no—
341C4—5961no—
342C4—5961no—
343C4—1492no—
344C4C22×C4×D14911yescharacteristic
345C4#41×D14911yescharacteristic
346C2—2982no—
347C2—5962no—
348C2C4×D4×D14911yescharacteristic
349C2#2375043411yescharacteristic
350C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutatorC4×C149C23×C4
FrattiniC2×C4C23×D149
Fitting#441×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558737C22
cosocleC2×C4×C149C24
hypercenter#441D149
hypocenterC149#2947
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. #23750101C2semidirect
4. #23749729C2semidirect
5. #23749728C2semidirect
6. #23749727C2semidirect
7. Q16×Dic149C2semidirect
8. C4×#14558726C2semidirect
9. C4×#14558723C2semidirect
10. #23749712C2semidirect
11. #23749664C2semidirect
13. #103×D149C2semidirect
14. #23749582C2semidirect
15. #441×C149C2semidirect
18. #18011943C4semidirect
65. Q8×D149C2×C4semidirect
74. #14558726C2×C4semidirect
75. #14558725C2×C4semidirect
76. #14558723C2×C4semidirect
77. #14558719C2×C4semidirect
103. Q16×C149C2×C4semidirect
175. C149#2947semidirect
181. #441D149semidirect
253. Q16C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119432
#237501072
#237501012
#237497292
#237497282
#237497272
Q16×Dic1492
C4×#145587262
C4×#145587232
#237497122
#237496642
#237496202
#103×D1492
#237495822
#441×C1492
#2947149