Finite Group Databasebeta

← #44408612

Subgroups — #44408612

Order 29056.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20300309C211yesmaximal, characteristic
2#28409514C211yesmaximal, characteristic, complemented
3#28409511C211yesmaximal, characteristic, complemented
4#28409142C211yesmaximal, characteristic, complemented
5#28409141C211yesmaximal, characteristic, complemented
6#28409137C211yesmaximal, characteristic, complemented
7#28409136C211yesmaximal, characteristic, complemented
8C4×#16813873C211yesmaximal, characteristic, complemented
9SD16×Dic227C211yesmaximal, characteristic, complemented
10#28409119C211yesmaximal, characteristic, complemented
11#106×D227C211yesmaximal, characteristic, complemented
12#28409032C211yesmaximal, characteristic, complemented
13#28409030C211yesmaximal, characteristic, complemented
14#28408986C211yesmaximal, characteristic, complemented
15C4×SD16×C227C211yesmaximal, characteristic, complemented
16C2×#16813885C2211yescharacteristic
17C2×#16813883C2211yescharacteristic
18#20300309C418yescomplemented
19C2×#16813874C2211yescharacteristic
20C2×#16813873C2211yescharacteristic
21C2×#16813869C2211yescharacteristic
22C2×#16813867C2211yescharacteristic
23C2×C8×D227C2211yescharacteristic
24Q8×Dic227C2211yescharacteristic
25C4×Dic454C2211yescharacteristic
26#20300253C2211yescharacteristic
27C4×D908—21no—
28C4×D908C2211yescharacteristic
29D4×Dic227C2211yescharacteristic
30#20300250—21no—
31#20300250C2211yescharacteristic
32C4×C22⋊D227—21no—
33(C22⋊D227)⋊C4—21no—
34#20300245—21no—
35#20300245C2211yescharacteristic
36#20300244—21no—
37C2×Dic227⋊C4—21no—
38C4⋊C4×D227—21no—
39C4⋊C4×D227C2211yescharacteristic
40C4⋊C4×D227C2211yescharacteristic
41#20300220C2211yescharacteristic
42#20300219C2211yescharacteristic
43#20300219C2211yescharacteristic
44#20300213C2211yescharacteristic
45#20300212C2211yescharacteristic
46#20300211C2211yescharacteristic
47#20300210C2211yescharacteristic
48#20300209C2211yescharacteristic
49#20300208C2211yescharacteristic
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#16813885—22no—
61#16813885C2×C414yescomplemented
62#16813883—22no—
63#16813883C2×C414yescomplemented
64C2×Dic454C2311yescharacteristic
65C2×D908—21no—
66C2×D908C2311yescharacteristic
67C2×C22⋊D227—21no—
68C22×Dic227—21no—
69C22×Dic227—21no—
70C2×C4×D227—21no—
71C2×C4×D227—21no—
72C2×C4×D227—21no—
73C2×C4×D227—21no—
74C2×C4×D227—21no—
75C2×C4×D227C2311yescharacteristic
76#16813874C2×C414yescomplemented
77#16813873C2×C414yescomplemented
78#16813869C2×C414yescomplemented
79#16813867—22no—
80C2×C227⋊C8C2311yescharacteristic
81C2×C227⋊C8C2311yescharacteristic
82C8×D227C2×C414yescomplemented
83C4⋊Dic227—21no—
84C4⋊Dic227C2311yescharacteristic
85C4⋊Dic227C2311yescharacteristic
86Dic227⋊C4—21no—
87Dic227⋊C4—21no—
88Dic227⋊C4—21no—
89Dic227⋊C4—21no—
90Dic227⋊C4D411yescharacteristic
91Dic227⋊C4D411yescharacteristic
92C22⋊Dic227—21no—
93(C2×D227)⋊C4—21no—
94(C2×D227)⋊C4—21no—
95(C2×D227)⋊C4D411yescharacteristic
96(C2×D227)⋊C4D411yescharacteristic
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×D227—21no—
114C22×D227C2×D411yescharacteristic
115Dic454—21no—
116Dic454C22×C412yes—
117D908—24no—
118D908—21no—
119D908C22×C412yes—
120C22⋊D227—24no—
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×D227—81no—
132C4×D227—81no—
133C4×D227—81no—
134C4×D227C22×C412yes—
135C4×D227#4112yes—
136C227⋊C8—21no—
137C227⋊C8C22×C412yes—
138C23×C227—21no—
139Q8×C227—21no—
140Q8×C227C22×C412yes—
141D4×C227—21no—
142D4×C227C22×C412yes—
143C2×C4×C227—21no—
144C2×C4×C227—21no—
145C2×C4×C227—21no—
146C2×C4×C227—81no—
147C2×C4×C227C2×D411yescharacteristic
148C2×C4×C227C2×D411yescharacteristic
149C2×C4×C227C2411yescharacteristic
150C8×C227—21no—
151C8×C227C22×C412yes—
152C22×C227—22no—
153C22×C227—41no—
154C22×C227—41no—
155C22×C227C22×D411yescharacteristic
156C2×D227—21no—
157C2×D227—21no—
158C2×D227—22no—
159C2×D227—41no—
160C2×D227—41no—
161C2×D227C4×D412yes—
162C4×C227—22no—
163C4×C227—21no—
164C4×C227—21no—
165C4×C227—41no—
166C4×C227—41no—
167C4×C227C23×C411yescharacteristic
168C4×C227C2×#4111yescharacteristic
169Dic227—22no—
170Dic227—21no—
171Dic227—21no—
172Dic227—41no—
173Dic227—41no—
174Dic227C4×D412yes—
175C2×C227—42no—
176C2×C227C2×C4×D411yescharacteristic
177C2×C227#57711yescharacteristic
178C2×C227#57711yescharacteristic
179D227—22no—
180D227—42no—
181C227#295211yescharacteristic, complemented, Sylow
182#2952—2271nomaximal, Sylow
183C2×#135—2271no—
184#520—2271no—
185#520—2271no—
186#442—2271no—
187#442—2271no—
188#441—2271no—
189#441—2271no—
190C4×SD16—2271no—
191C4×SD16—2271no—
192C4×SD16—2271no—
193C4×SD16D22711yescharacteristic, complemented
194C2×#106—2271no—
195#417—2271no—
196#417—2271no—
197#405—2271no—
198C2×#41—2271no—
199C2×#41—2271no—
200#135—2278no—
201C2×Q16—2271no—
202C2×SD16—2271no—
203C2×SD16C2×D22711yescharacteristic
204C2×D8—2271no—
205C2×M16—2271no—
206C22×C8—2271no—
207C4×Q8—2271no—
208C4×Q8—2271no—
209C4×Q8—2271no—
210C4×Q8C2×D22711yescharacteristic
211C4×D4—4541no—
212C4×D4—4541no—
213C4×D4—4541no—
214C4×D4—4541no—
215C4×D4—2271no—
216C4×D4—2271no—
217C4×D4—2271no—
218C4×D4C2×D22711yescharacteristic
219#117—4541no—
220#117—4541no—
221#117—2271no—
222C2×C4⋊C4—4541no—
223C2×C4⋊C4—4541no—
224C2×C4⋊C4—2271no—
225C2×C4⋊C4—2271no—
226#106—2271no—
227#106—2271no—
228#106—2271no—
229#106C2×D22711yescharacteristic
230#103—2271no—
231#103—2271no—
232#103—2271no—
233#103C2×D22711yescharacteristic
234#102—2271no—
235#102—2271no—
236#102—2271no—
237#102C2×D22711yescharacteristic
238#97—2271no—
239#97—2271no—
240C4×C8—2271no—
241C4×C8C2×D22711yescharacteristic
242#41—4542no—
243#41—4542no—
244#41—2274no—
245#41—2274no—
246C2×Q8—2271no—
247C2×Q8C22×D22711yescharacteristic
248C2×D4—4541no—
249C2×D4—4541no—
250C2×D4—2271no—
251C2×D4C22×D22711yescharacteristic
252C22×C4—21no—
253C22×C4—4541no—
254C22×C4—4541no—
255C22×C4—4541no—
256C22×C4—4541no—
257C22×C4—4541no—
258C22×C4—4541no—
259C22×C4—4541no—
260C22×C4—2271no—
261Q16—2274no—
262SD16—2274no—
263SD16C4×D22714yescomplemented
264D8—2274no—
265M16—4542no—
266C2×C8—2271no—
267C2×C8—2271no—
268C2×C8—2274no—
269C2×C8C22×D22711yescharacteristic
270C2×C8C22×D22711yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—4541no—
273C4⋊C4—4541no—
274C4⋊C4—4541no—
275C4⋊C4—4541no—
276C4⋊C4—4541no—
277C4⋊C4—2271no—
278C4⋊C4—2271no—
279C4⋊C4—2271no—
280C4⋊C4—2271no—
281C4⋊C4C22×D22711yescharacteristic
282C4⋊C4C22×D22711yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—4541no—
285C22⋊C4—4541no—
286C22⋊C4—4541no—
287C22⋊C4—2271no—
288C22⋊C4—2271no—
289C42—21no—
290C42—4541no—
291C42—4541no—
292C42—4541no—
293C42—2271no—
294C42C22×D22711yescharacteristic
295C23—21no—
296C23—4541no—
297C23—2271no—
298Q8—21no—
299Q8—4541no—
300Q8—2272no—
301Q8C2×C4×D22712yes—
302D4—21no—
303D4—4544no—
304D4—4544no—
305D4—4541no—
306D4—2272no—
307D4C2×C4×D22712yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—18161no—
313C2×C4—18161no—
314C2×C4—18161no—
315C2×C4—18161no—
316C2×C4—18161no—
317C2×C4—4544no—
318C2×C4—4541no—
319C2×C4—4541no—
320C2×C4—4541no—
321C2×C4—4544no—
322C2×C4—2271no—
323C2×C4—2271no—
324C2×C4—2271no—
325C2×C4—2272no—
326C2×C4—2272no—
327C2×C4D4×D22711yescharacteristic
328C2×C4D4×D22711yescharacteristic
329C2×C4C23×D22711yescharacteristic
330C8—21no—
331C8—4541no—
332C8—2272no—
333C8C2×C4×D22712yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—9081no—
338C22—9081no—
339C22—4542no—
340C22—4541no—
341C22—4541no—
342C22—2272no—
343C22C2×D4×D22711yescharacteristic
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—9081no—
350C4—9081no—
351C4—4542no—
352C4—4541no—
353C4—4541no—
354C4—2272no—
355C4C22×C4×D22711yescharacteristic
356C4#41×D22711yescharacteristic
357C2—42no—
358C2—9082no—
359C2—4542no—
360C2C4×D4×D22711yescharacteristic
361C2#2840983811yescharacteristic
362C2#2840983911yescharacteristic
subgroupG/H
centerC22C2×D4×D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
FittingC4×SD16×C227C2
socleC22×C227C22×D4
prime radicalC2×#20300309C2
cosocleC2×C4×C227C24
hypercenterC4×SD16D227
hypocenterC227#2952
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
2. #28409514C2semidirect
3. #28409511C2semidirect
4. #28409142C2semidirect
5. #28409141C2semidirect
6. #28409137C2semidirect
7. #28409136C2semidirect
8. C4×#16813873C2semidirect
9. SD16×Dic227C2semidirect
10. #28409119C2semidirect
11. #106×D227C2semidirect
12. #28409032C2semidirect
13. #28409030C2semidirect
14. #28408986C2semidirect
15. C4×SD16×C227C2semidirect
18. #20300309C4semidirect
61. #16813885C2×C4semidirect
63. #16813883C2×C4semidirect
76. #16813874C2×C4semidirect
77. #16813873C2×C4semidirect
78. #16813869C2×C4semidirect
82. C8×D227C2×C4semidirect
104. SD16×C227C2×C4semidirect
181. C227#2952semidirect
193. C4×SD16D227semidirect
263. SD16C4×D227semidirect

Maximal subgroups

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

subgroupindex
C2×#203003092
#284095142
#284095112
#284091422
#284091412
#284091372
#284091362
C4×#168138732
SD16×Dic2272
#284091192
#106×D2272
#284090322
#284090302
#284089862
C4×SD16×C2272
#2952227