Finite Group Databasebeta

← #44408570

Subgroups — #44408570

Order 29056.

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×#20300317C211yesmaximal, characteristic
2#28409511C211yesmaximal, characteristic
3#28409508C211yesmaximal, characteristic, complemented
4#28409138C211yesmaximal, characteristic, complemented
5#28409137C211yesmaximal, characteristic, complemented
6#28409133C211yesmaximal, characteristic, complemented
7#28409132C211yesmaximal, characteristic, complemented
8C4×Dic908C211yesmaximal, characteristic, complemented
9#28409124C211yesmaximal, characteristic, complemented
10#28409123C211yesmaximal, characteristic, complemented
11#28409071C211yesmaximal, characteristic, complemented
12#28409025C211yesmaximal, characteristic
13#103×D227C211yesmaximal, characteristic, complemented
14#28408986C211yesmaximal, characteristic, complemented
15C4×SD16×C227C211yesmaximal, characteristic, complemented
16C2×#16813883C2211yescharacteristic
17C2×Q8×D227C2211yescharacteristic
18#20300317C418yescomplemented
19C2×Dic908C2211yescharacteristic
20C2×#16813874C2211yescharacteristic
21C2×#16813872C2211yescharacteristic
22C2×#16813867C2211yescharacteristic
23C2×C8×D227C2211yescharacteristic
24Q8×Dic227C2211yescharacteristic
25C4×Dic454—21no—
26C4×Dic454C2211yescharacteristic
27C4×Dic454C2211yescharacteristic
28#20300253—21no—
29#20300253C2211yescharacteristic
30#20300253C2211yescharacteristic
31D4×Dic227C2211yescharacteristic
32C4×C22⋊D227—21no—
33(C22⋊D227)⋊C4—21no—
34#20300246—21no—
35#20300246C2211yescharacteristic
36#20300245—21no—
37#20300245C2211yescharacteristic
38#20300244—21no—
39C2×Dic227⋊C4—21no—
40C4⋊C4×D227C2211yescharacteristic
41#20300222C2211yescharacteristic
42#20300221C2211yescharacteristic
43#20300219C2211yescharacteristic
44#20300213C2211yescharacteristic
45#20300213C2211yescharacteristic
46#20300212C2211yescharacteristic
47#20300211C2211yescharacteristic
48#20300211C2211yescharacteristic
49#20300209C2211yescharacteristic
50#20300199C2211yescharacteristic
51#20300198C2211yescharacteristic
52C8×Dic227C2211yescharacteristic
53C2×SD16×C227C2211yescharacteristic
54C4×Q8×C227C2211yescharacteristic
55C4×D4×C227C2211yescharacteristic
56#106×C227C2211yescharacteristic
57#103×C227C2211yescharacteristic
58#102×C227C2211yescharacteristic
59C4×C8×C227C2211yescharacteristic
60#16813883—22no—
61#16813883C2×C414yes—
62C2×Dic454—21no—
63C2×Dic454C2311yescharacteristic
64C2×Dic454C2311yescharacteristic
65Q8×D227—22no—
66Q8×D227C2×C414yescomplemented
67C2×C22⋊D227—21no—
68C22×Dic227—21no—
69C22×Dic227—21no—
70C2×C4×D227—21no—
71C2×C4×D227—21no—
72C2×C4×D227C2311yescharacteristic
73Dic908C2×C414yescomplemented
74#16813874C2×C414yescomplemented
75#16813872C2×C414yescomplemented
76#16813867C2×C414yescomplemented
77C2×C227⋊C8C2311yescharacteristic
78C2×C227⋊C8C2311yescharacteristic
79C8×D227—22no—
80C4⋊Dic227—21no—
81C4⋊Dic227C2311yescharacteristic
82C4⋊Dic227C2311yescharacteristic
83Dic227⋊C4—21no—
84Dic227⋊C4—21no—
85Dic227⋊C4—21no—
86Dic227⋊C4—21no—
87Dic227⋊C4—21no—
88Dic227⋊C4D411yescharacteristic
89Dic227⋊C4D411yescharacteristic
90C22⋊Dic227—21no—
91(C2×D227)⋊C4—21no—
92(C2×D227)⋊C4D411yescharacteristic
93(C2×D227)⋊C4D411yescharacteristic
94C4×Dic227—21no—
95C4×Dic227—21no—
96C4×Dic227—21no—
97C4×Dic227—21no—
98C4×Dic227—21no—
99C4×Dic227—21no—
100C4×Dic227C2311yescharacteristic
101C2×Q8×C227C2311yescharacteristic
102C2×D4×C227C2311yescharacteristic
103C22×C4×C227—21no—
104SD16×C227C2×C414yescomplemented
105C2×C8×C227C2311yescharacteristic
106C2×C8×C227C2311yescharacteristic
107C4⋊C4×C227—21no—
108C4⋊C4×C227C2311yescharacteristic
109C4⋊C4×C227C2311yescharacteristic
110C22⋊C4×C227—21no—
111C42×C227—21no—
112C42×C227C2311yescharacteristic
113C22×D227C2×D411yescharacteristic
114Dic454—21no—
115Dic454—21no—
116Dic454—24no—
117Dic454C22×C412yes—
118Dic454C22×C412yes—
119C22⋊D227—24no—
120C2×Dic227—21no—
121C2×Dic227—21no—
122C2×Dic227—24no—
123C2×Dic227—21no—
124C2×Dic227—21no—
125C2×Dic227—81no—
126C2×Dic227C2×D411yescharacteristic
127C2×Dic227C2×D411yescharacteristic
128C2×Dic227C2×D411yescharacteristic
129C4×D227—24no—
130C4×D227—81no—
131C4×D227C22×C412yes—
132C4×D227#4112yes—
133C227⋊C8—21no—
134C227⋊C8C22×C412yes—
135C23×C227—21no—
136Q8×C227—21no—
137Q8×C227C22×C412yes—
138D4×C227—21no—
139D4×C227C22×C412yes—
140C2×C4×C227—21no—
141C2×C4×C227—21no—
142C2×C4×C227—21no—
143C2×C4×C227—81no—
144C2×C4×C227C2×D411yescharacteristic
145C2×C4×C227C2×D411yescharacteristic
146C2×C4×C227C2411yescharacteristic
147C8×C227—21no—
148C8×C227C22×C412yes—
149C22×C227—22no—
150C22×C227—41no—
151C22×C227—41no—
152C22×C227C22×D411yescharacteristic
153C2×D227—21no—
154C2×D227—21no—
155C2×D227C4×D412yes—
156C4×C227—22no—
157C4×C227—21no—
158C4×C227—21no—
159C4×C227—41no—
160C4×C227—41no—
161C4×C227C23×C411yescharacteristic
162C4×C227C2×#4111yescharacteristic
163Dic227—22no—
164Dic227—22no—
165Dic227—21no—
166Dic227—21no—
167Dic227—41no—
168Dic227—41no—
169Dic227C4×D412yes—
170C2×C227—42no—
171C2×C227C2×C4×D411yescharacteristic
172C2×C227#57711yescharacteristic
173C2×C227#57811yescharacteristic
174D227—22no—
175C227#294711yescharacteristic, complemented, Sylow
176#2947—2271nomaximal, Sylow
177C2×#137—2271no—
178#520—2271no—
179#519—2271no—
180#441—2271no—
181#441—2271no—
182#440—2271no—
183#440—2271no—
184C4×Q16—2271no—
185C4×Q16—2271no—
186C4×SD16—2271no—
187C4×SD16D22711yescharacteristic, complemented
188#428—2271no—
189#416—2271no—
190C2×#103—2271no—
191#405—2271no—
192C2×#41—2271no—
193C22×Q8—2271no—
194#137—2278no—
195C2×Q16—2271no—
196C2×Q16—2271no—
197C2×SD16—2271no—
198C2×SD16C2×D22711yescharacteristic
199C2×M16—2271no—
200C22×C8—2271no—
201C4×Q8—4541no—
202C4×Q8—4541no—
203C4×Q8—2271no—
204C4×Q8—2271no—
205C4×Q8—2271no—
206C4×Q8—2271no—
207C4×Q8—2271no—
208C4×Q8C2×D22711yescharacteristic
209C4×D4—4541no—
210C4×D4—4541no—
211C4×D4—2271no—
212C4×D4C2×D22711yescharacteristic
213#117—4541no—
214#117—4541no—
215#117—4541no—
216#117—2271no—
217#117—2271no—
218C2×C4⋊C4—4541no—
219C2×C4⋊C4—2271no—
220#107—2271no—
221#107—2271no—
222#106—2271no—
223#106C2×D22711yescharacteristic
224#103—2271no—
225#103—2271no—
226#103—2271no—
227#103—2271no—
228#103—2271no—
229#103C2×D22711yescharacteristic
230#102—2271no—
231#102C2×D22711yescharacteristic
232#97—2271no—
233#97—2271no—
234C4×C8—2271no—
235C4×C8C2×D22711yescharacteristic
236#41—4542no—
237#41—2274no—
238C2×Q8—4541no—
239C2×Q8—4542no—
240C2×Q8—2274no—
241C2×Q8—2271no—
242C2×Q8—2271no—
243C2×Q8C22×D22711yescharacteristic
244C2×D4—4541no—
245C2×D4C22×D22711yescharacteristic
246C22×C4—21no—
247C22×C4—4541no—
248C22×C4—4541no—
249C22×C4—4541no—
250C22×C4—4541no—
251C22×C4—2271no—
252Q16—2274no—
253Q16—2274no—
254SD16—2274no—
255SD16C4×D22714yescomplemented
256M16—2274no—
257C2×C8—4542no—
258C2×C8—2271no—
259C2×C8—2271no—
260C2×C8C22×D22711yescharacteristic
261C2×C8C22×D22711yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—4541no—
264C4⋊C4—4541no—
265C4⋊C4—4541no—
266C4⋊C4—4541no—
267C4⋊C4—4541no—
268C4⋊C4—4541no—
269C4⋊C4—2271no—
270C4⋊C4—2271no—
271C4⋊C4—2271no—
272C4⋊C4—2271no—
273C4⋊C4C22×D22711yescharacteristic
274C4⋊C4C22×D22711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—4541no—
277C22⋊C4—4541no—
278C22⋊C4—2271no—
279C22⋊C4—2271no—
280C42—21no—
281C42—4541no—
282C42—4541no—
283C42—4541no—
284C42—4541no—
285C42—4541no—
286C42—4541no—
287C42—2271no—
288C42C22×D22711yescharacteristic
289C23—21no—
290C23—2271no—
291Q8—21no—
292Q8—4544no—
293Q8—4541no—
294Q8—4541no—
295Q8—2272no—
296Q8—2272no—
297Q8C2×C4×D22712yes—
298D4—21no—
299D4—4544no—
300D4C2×C4×D22712yes—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—18161no—
306C2×C4—18161no—
307C2×C4—4544no—
308C2×C4—4541no—
309C2×C4—4541no—
310C2×C4—4541no—
311C2×C4—4541no—
312C2×C4—4544no—
313C2×C4—2271no—
314C2×C4—2271no—
315C2×C4—2271no—
316C2×C4—2272no—
317C2×C4—2272no—
318C2×C4D4×D22711yescharacteristic
319C2×C4D4×D22711yescharacteristic
320C2×C4C23×D22711yescharacteristic
321C8—21no—
322C8—4541no—
323C8—2272no—
324C8C2×C4×D22712yes—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—4541no—
329C22—4541no—
330C22—2272no—
331C22C2×D4×D22711yescharacteristic
332C4—22no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—9081no—
338C4—9081no—
339C4—4542no—
340C4—4542no—
341C4—4541no—
342C4—4541no—
343C4—2272no—
344C4C22×C4×D22711yescharacteristic
345C4#41×D22711yescharacteristic
346C2—42no—
347C2—4542no—
348C2C4×D4×D22711yescharacteristic
349C2#2840983811yescharacteristic
350C2#2840984611yescharacteristic
subgroupG/H
centerC22C2×D4×D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
FittingC4×SD16×C227C2
socleC22×C227C22×D4
prime radicalC2×#16813883C22
cosocleC2×C4×C227C24
hypercenterC4×SD16D227
hypocenterC227#2947
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
3. #28409508C2semidirect
4. #28409138C2semidirect
5. #28409137C2semidirect
6. #28409133C2semidirect
7. #28409132C2semidirect
8. C4×Dic908C2semidirect
9. #28409124C2semidirect
10. #28409123C2semidirect
11. #28409071C2semidirect
13. #103×D227C2semidirect
14. #28408986C2semidirect
15. C4×SD16×C227C2semidirect
18. #20300317C4semidirect
66. Q8×D227C2×C4semidirect
73. Dic908C2×C4semidirect
74. #16813874C2×C4semidirect
75. #16813872C2×C4semidirect
76. #16813867C2×C4semidirect
104. SD16×C227C2×C4semidirect
175. C227#2947semidirect
187. C4×SD16D227semidirect
255. SD16C4×D227semidirect

Maximal subgroups

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

subgroupindex
C2×#203003172
#284095112
#284095082
#284091382
#284091372
#284091332
#284091322
C4×Dic9082
#284091242
#284091232
#284090712
#284090252
#103×D2272
#284089862
C4×SD16×C2272
#2947227