Finite Group Databasebeta

← #49134879

Subgroups — #49134879

Order 36224.

1094 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827190C211yesmaximal, characteristic, complemented
2#31827189C211yesmaximal, characteristic, complemented
3#31827186C212yesmaximal, complemented
4#31827149C212yesmaximal, complemented
5#31827147C214yesmaximal, complemented
6#31827130C211yesmaximal, characteristic, complemented
7#31827125C212yesmaximal, complemented
8#31827118C211yesmaximal, characteristic, complemented
9#31827117C212yesmaximal, complemented
10#31827019C212yesmaximal, complemented
11#31827002C212yesmaximal, complemented
12#31826993C214yesmaximal, complemented
13C4×#17985393C212yesmaximal, complemented
14C4×#17985392C211yesmaximal, characteristic, complemented
15C4×#17985392C211yesmaximal, characteristic, complemented
16C4×Q8×D283C212yesmaximal, complemented
17#533×C283C211yesmaximal, characteristic, complemented
18C2×#17985393C2212yes—
19C2×#17985392C2211yescharacteristic
20C2×#17985392C2211yescharacteristic
21C2×Q8×D283C2212yes—
22#22583609C2212yes—
23#22583608C2212yes—
24#22583605C2214yes—
25#22583605C2214yes—
26#22583603C2214yes—
27#22583601C2212yes—
28#22583600C2214yes—
29#22583600C2214yes—
30#22583599C2212yes—
31#22583596C2214yes—
32#22583595C2214yes—
33#22583595C2214yes—
34#22583592C2214yes—
35#22583590C2212yes—
36#22583588C2214yes—
37#22583588C2214yes—
38#22583586C2212yes—
39#22583586C2212yes—
40#22583585C2212yes—
41#22583583C2214yes—
42Q8×Dic283C2212yes—
43Q8×Dic283C2212yes—
44C4×Dic566C2214yes—
45C4×Dic566C2211yescharacteristic
46C4×Dic566C2211yescharacteristic
47C4×Dic566C2211yescharacteristic
48C4×Dic566C2211yescharacteristic
49#22583575C2212yes—
50#22583575C2214yes—
51C4×D1132C2214yes—
52C4×D1132C2211yescharacteristic
53C4×D1132C2211yescharacteristic
54C4×D1132C2211yescharacteristic
55C4×D1132C2211yescharacteristic
56#22583572C2212yes—
57#22583572C2214yes—
58C4×C22⋊D283C2212yes—
59C4×C22⋊D283C2212yes—
60C4×C22⋊D283C2212yes—
61C4×C22⋊D283C2212yes—
62#22583569C2211yescharacteristic
63#22583569C2211yescharacteristic
64#22583568C2214yes—
65#22583568C2212yes—
66#22583567C2214yes—
67#22583567C2212yes—
68#22583567C2212yes—
69C4⋊C4×D283C2214yes—
70C4⋊C4×D283C2212yes—
71C42×D283C2214yes—
72C42×D283C2212yes—
73C42×D283C2212yes—
74C4⋊Q8×C283C2211yescharacteristic
75C4⋊Q8×C283C2211yescharacteristic
76#125×C283C2212yes—
77C22⋊Q8×C283C2212yes—
78C22⋊Q8×C283C2212yes—
79C4×Q8×C283C2212yes—
80C4×Q8×C283C2212yes—
81#117×C283C2212yes—
82C2×C42×C283C2211yescharacteristic
83#17985393—28no—
84#17985392—24no—
85#17985392—24no—
86C2×Dic566C2314yes—
87C2×Dic566C2311yescharacteristic
88C2×Dic566C2311yescharacteristic
89Q8×D283—28no—
90C2×D1132C2314yes—
91C2×D1132C2311yescharacteristic
92C2×D1132C2311yescharacteristic
93C2×C22⋊D283C2312yes—
94C2×C22⋊D283C2312yes—
95C2×C4×D283C2312yes—
96C2×C4×D283C2312yes—
97C2×C4×D283C2314yes—
98C2×C4×D283C2312yes—
99C2×C4×D283C2314yes—
100C2×C4×D283C2312yes—
101C2×C4×D283C2312yes—
102C2×C4×D283C2312yes—
103C4⋊Dic283C2311yescharacteristic
104C4⋊Dic283C2314yes—
105C4⋊Dic283C2311yescharacteristic
106C4⋊Dic283C2314yes—
107C4⋊Dic283C2311yescharacteristic
108C4⋊Dic283C2311yescharacteristic
109Dic283⋊C4C2312yes—
110Dic283⋊C4C2314yes—
111Dic283⋊C4C2314yes—
112Dic283⋊C4C2312yes—
113Dic283⋊C4C2312yes—
114Dic283⋊C4C2312yes—
115Dic283⋊C4C2314yes—
116Dic283⋊C4C2314yes—
117C22⋊Dic283C2312yes—
118C22⋊Dic283C2312yes—
119(C2×D283)⋊C4C2312yes—
120(C2×D283)⋊C4C2312yes—
121(C2×D283)⋊C4C2312yes—
122(C2×D283)⋊C4C2312yes—
123(C2×D283)⋊C4C2314yes—
124(C2×D283)⋊C4C2314yes—
125(C2×D283)⋊C4C2314yes—
126(C2×D283)⋊C4C2314yes—
127C4×Dic283C2312yes—
128C4×Dic283C2312yes—
129C4×Dic283C2312yes—
130C4×Dic283C2312yes—
131C4×Dic283C2314yes—
132C4×Dic283C2312yes—
133C4×Dic283C2312yes—
134C4×Dic283C2314yes—
135C2×Q8×C283C2312yes—
136C2×Q8×C283C2312yes—
137C22×C4×C283C2311yescharacteristic
138C22×C4×C283C2311yescharacteristic
139C22×C4×C283C2311yescharacteristic
140C4⋊C4×C283C2312yes—
141C4⋊C4×C283C2314yes—
142C4⋊C4×C283C2314yes—
143C4⋊C4×C283C2312yes—
144C4⋊C4×C283C2312yes—
145C4⋊C4×C283C2312yes—
146C22⋊C4×C283C2314yes—
147C42×C283C2311yescharacteristic
148C42×C283C2311yescharacteristic
149C42×C283C2314yes—
150C42×C283C2311yescharacteristic
151C42×C283C2311yescharacteristic
152C22×D283C2412yes—
153C22×D283C2412yes—
154Dic566—22no—
155Dic566—28no—
156Dic566#4114yescomplemented
157D1132—28no—
158D1132—22no—
159D1132#4114yescomplemented
160C22⋊D283—24no—
161C22⋊D283—24no—
162C2×Dic283C2412yes—
163C2×Dic283C2412yes—
164C2×Dic283C2412yes—
165C2×Dic283C2412yes—
166C2×Dic283C2412yes—
167C2×Dic283C2412yes—
168C4×D283—24no—
169C4×D283—28no—
170C4×D283—24no—
171C4×D283—24no—
172C4×D283—24no—
173C4×D283—24no—
174C4×D283—28no—
175C4×D283—24no—
176C23×C283C2411yescharacteristic
177Q8×C283—24no—
178Q8×C283—24no—
179C2×C4×C283—22no—
180C2×C4×C283—22no—
181C2×C4×C283—22no—
182C2×C4×C283C2411yescharacteristic
183C2×C4×C283C2411yescharacteristic
184C2×C4×C283C2411yescharacteristic
185C2×C4×C283C2414yes—
186C2×C4×C283C2414yes—
187C2×C4×C283C2411yescharacteristic
188C2×C4×C283C2411yescharacteristic
189C2×C4×C283C2411yescharacteristic
190C22×C283—21no—
191C22×C283—21no—
192C22×C283—21no—
193C22×C283C2511yescharacteristic
194C2×D283—22no—
195C2×D283—22no—
196C2×D283—22no—
197C2×D283—22no—
198C2×D283—22no—
199C2×D283C2×#4114yes—
200C4×C283—21no—
201C4×C283—21no—
202C4×C283—24no—
203C4×C283—24no—
204C4×C283—21no—
205C4×C283C2×#4112yes—
206C4×C283C2×#4112yes—
207C4×C2832−1+412yes—
208Dic283—22no—
209Dic283—22no—
210Dic283—22no—
211Dic283—22no—
212Dic283—22no—
213Dic283C2×#4114yes—
214C2×C283—41no—
215C2×C283C22×#4111yescharacteristic
216C2×C283C22×#4111yescharacteristic
217C2×C283C2×2−1+411yescharacteristic
218D283—24no—
219D283—42no—
220C283#348211yescharacteristic, complemented, Sylow
221#3482—2831nomaximal, Sylow
222#557—2831no—
223#556—2831no—
224#556—2832no—
225#552—2834no—
226#552—2832no—
227D4×Q8—2831no—
228#548—2832no—
229#547—2831no—
230#547—2832no—
231#533—2832no—
232#533D28311yescharacteristic, complemented
233#529—2832no—
234#529—2834no—
235C4×#41—2832no—
236C4×#41—2831no—
237C4×#41—2831no—
238C2×C4×Q8—2832no—
239C2×#41—2832no—
240C2×#41—2831no—
241C2×#41—2831no—
242C22×Q8—2832no—
243C4⋊Q8—2832no—
244C4⋊Q8—2832no—
245C4⋊Q8C2×D28311yescharacteristic
246C4⋊Q8C2×D28311yescharacteristic
247#126—2834no—
248#126—2834no—
249#126—2834no—
250#125—2834no—
251#125—2832no—
252#125—2834no—
253#125C2×D28312yes—
254#124—2832no—
255#124—2834no—
256#123—2834no—
257#123—2834no—
258#123—2834no—
259C22⋊Q8—2832no—
260C22⋊Q8—2832no—
261C22⋊Q8—2834no—
262C22⋊Q8—2832no—
263C22⋊Q8—2834no—
264C22⋊Q8C2×D28312yes—
265C22⋊Q8C2×D28312yes—
266#121—2832no—
267#121—2834no—
268C4×Q8—2832no—
269C4×Q8—2832no—
270C4×Q8—2832no—
271C4×Q8—2834no—
272C4×Q8—2831no—
273C4×Q8—2834no—
274C4×Q8—2831no—
275C4×Q8—2831no—
276C4×Q8—2831no—
277C4×Q8C2×D28312yes—
278C4×Q8C2×D28312yes—
279C4×D4—2832no—
280C4×D4—2832no—
281C4×D4—2832no—
282C4×D4—2832no—
283C4×D4—2832no—
284C4×D4—2834no—
285C4×D4—2831no—
286C4×D4—2831no—
287C4×D4—2834no—
288C4×D4—2831no—
289C4×D4—2831no—
290#117—2831no—
291#117—2831no—
292#117—2834no—
293#117—2832no—
294#117—2832no—
295#117—2832no—
296#117—2834no—
297#117C2×D28312yes—
298C2×C4⋊C4—2834no—
299C2×C4⋊C4—2832no—
300C2×C42—2834no—
301C2×C42—2832no—
302C2×C42—2832no—
303C2×C42C2×D28311yescharacteristic
304#41—5664no—
305#41—5664no—
306#41—5668no—
307C2×Q8—2831no—
308C2×Q8—2834no—
309C2×Q8—2831no—
310C2×Q8—5668no—
311C2×Q8C22×D28312yes—
312C2×Q8C22×D28312yes—
313C2×D4—2832no—
314C2×D4—2832no—
315C2×D4—2831no—
316C2×D4—2834no—
317C2×D4—2831no—
318C22×C4—2834no—
319C22×C4—2832no—
320C22×C4—2834no—
321C22×C4—2832no—
322C22×C4—2832no—
323C22×C4—2832no—
324C22×C4—2832no—
325C22×C4—2832no—
326C22×C4C22×D28311yescharacteristic
327C22×C4C22×D28311yescharacteristic
328C22×C4C22×D28311yescharacteristic
329C4⋊C4—2832no—
330C4⋊C4—2834no—
331C4⋊C4—2834no—
332C4⋊C4—2832no—
333C4⋊C4—2832no—
334C4⋊C4—2832no—
335C4⋊C4—2834no—
336C4⋊C4—2834no—
337C4⋊C4—2831no—
338C4⋊C4—2834no—
339C4⋊C4—2831no—
340C4⋊C4—2831no—
341C4⋊C4—2831no—
342C4⋊C4—2834no—
343C4⋊C4C22×D28312yes—
344C4⋊C4C22×D28314yes—
345C4⋊C4C22×D28314yes—
346C4⋊C4C22×D28312yes—
347C4⋊C4C22×D28312yes—
348C4⋊C4C22×D28312yes—
349C22⋊C4—2832no—
350C22⋊C4—2832no—
351C22⋊C4—2832no—
352C22⋊C4—2834no—
353C22⋊C4—2832no—
354C22⋊C4—2832no—
355C22⋊C4—2832no—
356C22⋊C4—2834no—
357C22⋊C4—2834no—
358C22⋊C4—2834no—
359C22⋊C4C22×D28314yes—
360C42—2832no—
361C42—2834no—
362C42—2832no—
363C42—2832no—
364C42—2834no—
365C42—2832no—
366C42—2832no—
367C42—2832no—
368C42C22×D28311yescharacteristic
369C42C22×D28311yescharacteristic
370C42C22×D28311yescharacteristic
371C42C22×D28311yescharacteristic
372C42C22×D28314yes—
373C23—2832no—
374C23—2832no—
375C23C23×D28311yescharacteristic
376Q8—24no—
377Q8—24no—
378Q8—2834no—
379Q8—5668no—
380Q8—5662no—
381D4—2834no—
382D4—5668no—
383D4—5664no—
384D4—5664no—
385D4—5662no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—2832no—
390C2×C4—2832no—
391C2×C4—2832no—
392C2×C4—2832no—
393C2×C4—2832no—
394C2×C4—2832no—
395C2×C4—5668no—
396C2×C4—5664no—
397C2×C4—5664no—
398C2×C4—5668no—
399C2×C4—5664no—
400C2×C4—5664no—
401C2×C4—5664no—
402C2×C4—5664no—
403C2×C4C23×D28311yescharacteristic
404C2×C4C23×D28311yescharacteristic
405C2×C4C23×D28314yes—
406C2×C4C23×D28314yes—
407C2×C4C23×D28311yescharacteristic
408C2×C4C23×D28311yescharacteristic
409C2×C4C23×D28311yescharacteristic
410C2×C4C23×D28311yescharacteristic
411C22—21no—
412C22—21no—
413C22—21no—
414C22—2834no—
415C22—5662no—
416C22—5662no—
417C22—5662no—
418C22—5662no—
419C22—5662no—
420C22C24×D28311yescharacteristic
421C4—21no—
422C4—21no—
423C4—24no—
424C4—24no—
425C4—21no—
426C4—2834no—
427C4—5662no—
428C4—5662no—
429C4—5662no—
430C4—5662no—
431C4—5662no—
432C4#41×D28312yes—
433C4#41×D28312yes—
434C4#2258365812yes—
435C2—41no—
436C2—5664no—
437C2—11322no—
438C2C2×#41×D28311yescharacteristic
439C2C2×#41×D28311yescharacteristic
440C2C2×#2258365811yescharacteristic
subgroupG/H
centerC2×C4C23×D283
commutator, socle, cosocleC22×C283C25
FrattiniC22C24×D283
Fitting#533×C283C2
hypercenter#533D283
hypocenterC283#3482
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
1. #31827190C2semidirect
2. #31827189C2semidirect
3. #31827186C2semidirect
4. #31827149C2semidirect
5. #31827147C2semidirect
6. #31827130C2semidirect
7. #31827125C2semidirect
8. #31827118C2semidirect
9. #31827117C2semidirect
10. #31827019C2semidirect
11. #31827002C2semidirect
12. #31826993C2semidirect
13. C4×#17985393C2semidirect
14. C4×#17985392C2semidirect
15. C4×#17985392C2semidirect
16. C4×Q8×D283C2semidirect
17. #533×C283C2semidirect
156. Dic566#41semidirect
159. D1132#41semidirect
220. C283#3482semidirect
232. #533D283semidirect

Maximal subgroups

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

subgroupindex
#318271902
#318271892
#318271862
#318271492
#318271472
#318271302
#318271252
#318271182
#318271172
#318270192
#318270022
#318269932
C4×#179853932
C4×#179853922
C4×Q8×D2832
#533×C2832
#3482283