Finite Group Databasebeta

← #34053527

Subgroups — #34053527

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×#18011940C211yesmaximal, characteristic
2#23750104C211yesmaximal, characteristic
3#23750101C211yesmaximal, characteristic, complemented
4#23749731C211yesmaximal, characteristic, complemented
5#23749730C211yesmaximal, characteristic, complemented
6#23749726C211yesmaximal, characteristic, complemented
7#23749725C211yesmaximal, characteristic, complemented
8C4×Dic596C211yesmaximal, characteristic, complemented
9#23749717C211yesmaximal, characteristic, complemented
10#23749716C211yesmaximal, characteristic, complemented
11#23749664C211yesmaximal, characteristic, complemented
12#23749618C211yesmaximal, characteristic
13#103×D149C211yesmaximal, characteristic, complemented
14#23749579C211yesmaximal, characteristic, complemented
15C4×SD16×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic
18#18011940C418yescomplemented
19C2×Dic596C2211yescharacteristic
20C2×#14558726C2211yescharacteristic
21C2×#14558724C2211yescharacteristic
22C2×#14558719C2211yescharacteristic
23C2×C8×D149C2211yescharacteristic
24Q8×Dic149C2211yescharacteristic
25C4×Dic298—21no—
26C4×Dic298C2211yescharacteristic
27C4×Dic298C2211yescharacteristic
28#18011876—21no—
29#18011876C2211yescharacteristic
30#18011876C2211yescharacteristic
31D4×Dic149C2211yescharacteristic
32C4×C22⋊D149—21no—
33#18011871—21no—
34#18011869—21no—
35#18011869C2211yescharacteristic
36#18011868—21no—
37#18011868C2211yescharacteristic
38#18011867—21no—
39C2×#14558715—21no—
40C4⋊C4×D149C2211yescharacteristic
41#18011845C2211yescharacteristic
42#18011844C2211yescharacteristic
43#18011842C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011834C2211yescharacteristic
49#18011832C2211yescharacteristic
50#18011822C2211yescharacteristic
51#18011821C2211yescharacteristic
52C8×Dic149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54C4×Q8×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C4×C8×C149C2211yescharacteristic
60#14558735—22no—
61#14558735C2×C414yes—
62C2×Dic298—21no—
63C2×Dic298C2311yescharacteristic
64C2×Dic298C2311yescharacteristic
65Q8×D149—22no—
66Q8×D149C2×C414yescomplemented
67C2×C22⋊D149—21no—
68C22×Dic149—21no—
69C22×Dic149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72C2×C4×D149C2311yescharacteristic
73Dic596C2×C414yescomplemented
74#14558726C2×C414yescomplemented
75#14558724C2×C414yescomplemented
76#14558719C2×C414yescomplemented
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C8×D149—22no—
80C4⋊Dic149—21no—
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715D411yescharacteristic
89#14558715D411yescharacteristic
90C22⋊Dic149—21no—
91#14558713—21no—
92#14558713D411yescharacteristic
93#14558713D411yescharacteristic
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149—21no—
97C4×Dic149—21no—
98C4×Dic149—21no—
99C4×Dic149—21no—
100C4×Dic149C2311yescharacteristic
101C2×Q8×C149C2311yescharacteristic
102C2×D4×C149C2311yescharacteristic
103C22×C4×C149—21no—
104SD16×C149C2×C414yescomplemented
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149—21no—
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C22⋊C4×C149—21no—
111C42×C149—21no—
112C42×C149C2311yescharacteristic
113C22×D149C2×D411yescharacteristic
114Dic298—21no—
115Dic298—21no—
116Dic298—24no—
117Dic298C22×C412yes—
118Dic298C22×C412yes—
119C22⋊D149—24no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—24no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—81no—
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C4×D149—24no—
130C4×D149—81no—
131C4×D149C22×C412yes—
132C4×D149#4112yes—
133#11924746—21no—
134#11924746C22×C412yes—
135C23×C149—21no—
136Q8×C149—21no—
137Q8×C149C22×C412yes—
138D4×C149—21no—
139D4×C149C22×C412yes—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—81no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2411yescharacteristic
147C8×C149—21no—
148C8×C149C22×C412yes—
149C22×C149—22no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149C22×D411yescharacteristic
153C2×D149—21no—
154C2×D149—21no—
155C2×D149C4×D412yes—
156C4×C149—22no—
157C4×C149—21no—
158C4×C149—21no—
159C4×C149—41no—
160C4×C149—41no—
161C4×C149C23×C411yescharacteristic
162C4×C149C2×#4111yescharacteristic
163Dic149—22no—
164Dic149—22no—
165Dic149—21no—
166Dic149—21no—
167Dic149—41no—
168Dic149—41no—
169Dic149C4×D412yes—
170C2×C149—42no—
171C2×C149C2×C4×D411yescharacteristic
172C2×C149#57711yescharacteristic
173C2×C149#57811yescharacteristic
174D149—22no—
175C149#294711yescharacteristic, complemented, Sylow
176#2947—1491nomaximal, Sylow
177C2×#137—1491no—
178#520—1491no—
179#519—1491no—
180#441—1491no—
181#441—1491no—
182#440—1491no—
183#440—1491no—
184C4×Q16—1491no—
185C4×Q16—1491no—
186C4×SD16—1491no—
187C4×SD16D14911yescharacteristic, complemented
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×Q16—1491no—
197C2×SD16—1491no—
198C2×SD16C2×D14911yescharacteristic
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×Q8—1491no—
208C4×Q8C2×D14911yescharacteristic
209C4×D4—2981no—
210C4×D4—2981no—
211C4×D4—1491no—
212C4×D4C2×D14911yescharacteristic
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#103—1491no—
229#103C2×D14911yescharacteristic
230#102—1491no—
231#102C2×D14911yescharacteristic
232#97—1491no—
233#97—1491no—
234C4×C8—1491no—
235C4×C8C2×D14911yescharacteristic
236#41—2982no—
237#41—1494no—
238C2×Q8—2981no—
239C2×Q8—2982no—
240C2×Q8—1494no—
241C2×Q8—1491no—
242C2×Q8—1491no—
243C2×Q8C22×D14911yescharacteristic
244C2×D4—2981no—
245C2×D4C22×D14911yescharacteristic
246C22×C4—21no—
247C22×C4—2981no—
248C22×C4—2981no—
249C22×C4—2981no—
250C22×C4—2981no—
251C22×C4—1491no—
252Q16—1494no—
253Q16—1494no—
254SD16—1494no—
255SD16C4×D14914yescomplemented
256M16—1494no—
257C2×C8—2982no—
258C2×C8—1491no—
259C2×C8—1491no—
260C2×C8C22×D14911yescharacteristic
261C2×C8C22×D14911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—2981no—
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—21no—
276C22⋊C4—2981no—
277C22⋊C4—2981no—
278C22⋊C4—1491no—
279C22⋊C4—1491no—
280C42—21no—
281C42—2981no—
282C42—2981no—
283C42—2981no—
284C42—2981no—
285C42—2981no—
286C42—2981no—
287C42—1491no—
288C42C22×D14911yescharacteristic
289C23—21no—
290C23—1491no—
291Q8—21no—
292Q8—2984no—
293Q8—2981no—
294Q8—2981no—
295Q8—1492no—
296Q8—1492no—
297Q8C2×C4×D14912yes—
298D4—21no—
299D4—2984no—
300D4C2×C4×D14912yes—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—2984no—
306C2×C4—2981no—
307C2×C4—2981no—
308C2×C4—2984no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—1491no—
312C2×C4—1491no—
313C2×C4—1491no—
314C2×C4—1492no—
315C2×C4—1492no—
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—22no—
326C22—41no—
327C22—41no—
328C22—2981no—
329C22—2981no—
330C22—1492no—
331C22C2×D4×D14911yescharacteristic
332C4—21no—
333C4—21no—
334C4—22no—
335C4—41no—
336C4—41no—
337C4—2981no—
338C4—2981no—
339C4—2982no—
340C4—2982no—
341C4—5961no—
342C4—5961no—
343C4—1492no—
344C4C22×C4×D14911yescharacteristic
345C4#41×D14911yescharacteristic
346C2—42no—
347C2—2982no—
348C2C4×D4×D14911yescharacteristic
349C2#2375043111yescharacteristic
350C2#2375043911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutatorC4×C149C23×C4
FrattiniC2×C4C23×D149
FittingC4×SD16×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558735C22
cosocleC2×C4×C149C24
hypercenterC4×SD16D149
hypocenterC149#2947
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
3. #23750101C2semidirect
4. #23749731C2semidirect
5. #23749730C2semidirect
6. #23749726C2semidirect
7. #23749725C2semidirect
8. C4×Dic596C2semidirect
9. #23749717C2semidirect
10. #23749716C2semidirect
11. #23749664C2semidirect
13. #103×D149C2semidirect
14. #23749579C2semidirect
15. C4×SD16×C149C2semidirect
18. #18011940C4semidirect
66. Q8×D149C2×C4semidirect
73. Dic596C2×C4semidirect
74. #14558726C2×C4semidirect
75. #14558724C2×C4semidirect
76. #14558719C2×C4semidirect
104. SD16×C149C2×C4semidirect
175. C149#2947semidirect
187. C4×SD16D149semidirect
255. SD16C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119402
#237501042
#237501012
#237497312
#237497302
#237497262
#237497252
C4×Dic5962
#237497172
#237497162
#237496642
#237496182
#103×D1492
#237495792
C4×SD16×C1492
#2947149