Finite Group Databasebeta

← #49124417

Subgroups — #49124417

Order 36224.

576 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583583C211yesmaximal, characteristic
2#31826366C211yesmaximal, characteristic, complemented
3#31826365C211yesmaximal, characteristic, complemented
4#31826358C211yesmaximal, characteristic, complemented
5#31826355C211yesmaximal, characteristic, complemented
6#31826347C211yesmaximal, characteristic, complemented
7#31826346C211yesmaximal, characteristic, complemented
8#31826344C211yesmaximal, characteristic, complemented
9#31826344C211yesmaximal, characteristic, complemented
10#31826343C211yesmaximal, characteristic, complemented
11#31826341C211yesmaximal, characteristic, complemented
12#31826339C211yesmaximal, characteristic, complemented
13#31826327C211yesmaximal, characteristic, complemented
14#31826322C211yesmaximal, characteristic, complemented
15#385×C283C211yesmaximal, characteristic, complemented
16C22×D1132C2211yescharacteristic
17C22×C22⋊D283C2211yescharacteristic
18C22×C22⋊D283C2211yescharacteristic
19C22×C4×D283C2211yescharacteristic
20C22×C4×D283C2211yescharacteristic
21#22583583C418yescomplemented
22C2×C4⋊Dic283C2211yescharacteristic
23C2×Dic283⋊C4C2211yescharacteristic
24C2×Dic283⋊C4C2211yescharacteristic
25C2×C22⋊Dic283C2211yescharacteristic
26C2×C22⋊Dic283C2211yescharacteristic
27C2×(C2×D283)⋊C4C2211yescharacteristic
28C2×(C2×D283)⋊C4C2211yescharacteristic
29C2×(C2×D283)⋊C4C2211yescharacteristic
30C2×(C2×D283)⋊C4C2211yescharacteristic
31C2×(C2×D283)⋊C4C2211yescharacteristic
32C2×(C2×D283)⋊C4C2211yescharacteristic
33C2×(C2×D283)⋊C4C2211yescharacteristic
34C2×(C2×D283)⋊C4C2211yescharacteristic
35C2×C4×Dic283C2211yescharacteristic
36C2×C4×Dic283C2211yescharacteristic
37C283⋊#95C2211yescharacteristic
38C283⋊#95C2211yescharacteristic
39C283⋊#95C2211yescharacteristic
40C283⋊#95C2211yescharacteristic
41C283⋊#95C2211yescharacteristic
42C283⋊#95C2211yescharacteristic
43C283⋊#95C2211yescharacteristic
44C283⋊#95C2211yescharacteristic
45C23×C4×C283C2211yescharacteristic
46C2×C4⋊C4×C283C2211yescharacteristic
47C2×C4⋊C4×C283C2211yescharacteristic
48C2×C22⋊C4×C283C2211yescharacteristic
49C2×C22⋊C4×C283C2211yescharacteristic
50#95×C283C2211yescharacteristic
51#95×C283C2211yescharacteristic
52C23×D283C2311yescharacteristic
53C23×D283C2311yescharacteristic
54C2×D1132—41no—
55C2×D1132—41no—
56C2×D1132C2×C414yescomplemented
57C2×C22⋊D283—41no—
58C2×C22⋊D283—41no—
59C2×C22⋊D283—41no—
60C2×C22⋊D283—41no—
61C2×C22⋊D283C2×C414yes—
62C2×C22⋊D283C2×C414yescomplemented
63C22×Dic283C2311yescharacteristic
64C22×Dic283C2311yescharacteristic
65C22×Dic283C2311yescharacteristic
66C22×Dic283C2311yescharacteristic
67C22×Dic283C2311yescharacteristic
68C22×Dic283C2311yescharacteristic
69C2×C4×D283—41no—
70C2×C4×D283—41no—
71C2×C4×D283—41no—
72C2×C4×D283—41no—
73C2×C4×D283—41no—
74C2×C4×D283C2×C414yescomplemented
75C4⋊Dic283—41no—
76Dic283⋊C4—41no—
77Dic283⋊C4C2×C414yescomplemented
78C22⋊Dic283—41no—
79C22⋊Dic283—41no—
80(C2×D283)⋊C4—41no—
81(C2×D283)⋊C4—41no—
82(C2×D283)⋊C4—41no—
83(C2×D283)⋊C4—41no—
84(C2×D283)⋊C4—41no—
85(C2×D283)⋊C4—41no—
86(C2×D283)⋊C4—41no—
87(C2×D283)⋊C4C2×C414yescomplemented
88C4×Dic283—41no—
89C4×Dic283—41no—
90C24×C283C2311yescharacteristic
91C22×C4×C283—41no—
92C22×C4×C283—41no—
93C22×C4×C283—41no—
94C22×C4×C283C2311yescharacteristic
95C22×C4×C283C2311yescharacteristic
96C22×C4×C283C2311yescharacteristic
97C22×C4×C283C2311yescharacteristic
98C22×C4×C283C2311yescharacteristic
99C22×C4×C283C2311yescharacteristic
100C4⋊C4×C283—41no—
101C4⋊C4×C283—41no—
102C22⋊C4×C283—41no—
103C22⋊C4×C283C2×C414yescomplemented
104C22×D283—21no—
105C22×D283—21no—
106C22×D283—21no—
107C22×D283—21no—
108C22×D283—21no—
109C22×D283—21no—
110C22×D283—21no—
111C22×D283—21no—
112C22×D283—21no—
113C22×D283—21no—
114C22×D283—21no—
115C22×D283—21no—
116C22×D283C22×C412yes—
117C22×D283C22×C412yes—
118D1132—44no—
119C22⋊D283—44no—
120C22⋊D283—44no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—21no—
130C2×Dic283—21no—
131C2×Dic283—21no—
132C2×Dic283—21no—
133C2×Dic283—21no—
134C2×Dic283—21no—
135C2×Dic283—21no—
136C2×Dic283—21no—
137C2×Dic283C22×C412yes—
138C2×Dic283C22×C412yes—
139C4×D283—44no—
140C4×D283—44no—
141C23×C283—21no—
142C23×C283—21no—
143C23×C283—21no—
144C23×C283—21no—
145C23×C283—21no—
146C23×C283—21no—
147C23×C283C22×C412yes—
148C23×C283C2411yescharacteristic
149C2×C4×C283—21no—
150C2×C4×C283—21no—
151C2×C4×C283—21no—
152C2×C4×C283—21no—
153C2×C4×C283—21no—
154C2×C4×C283—21no—
155C2×C4×C283—21no—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283—21no—
159C2×C4×C283—21no—
160C2×C4×C283—21no—
161C2×C4×C283—21no—
162C2×C4×C283—21no—
163C2×C4×C283—21no—
164C2×C4×C283—21no—
165C2×C4×C283—44no—
166C2×C4×C283C22×C412yes—
167C2×C4×C283C22×C412yes—
168C22×C283—22no—
169C22×C283—22no—
170C22×C283—22no—
171C22×C283—41no—
172C22×C283—41no—
173C22×C283—41no—
174C22×C283—41no—
175C22×C283C23×C411yescharacteristic
176C22×C283H(5,𝔽2)11yescharacteristic
177C22×C283H(5,𝔽2)11yescharacteristic
178C22×C283H(5,𝔽2)11yescharacteristic
179C22×C283H(5,𝔽2)11yescharacteristic
180C22×C283H(5,𝔽2)11yescharacteristic
181C22×C2832−1+411yescharacteristic
182C2×D283—22no—
183C2×D283—22no—
184C2×D283—22no—
185C2×D283—22no—
186C2×D283—22no—
187C2×D283—22no—
188C2×D283—41no—
189C2×D283—41no—
190C2×D283—41no—
191C2×D283—41no—
192C2×D283—41no—
193C2×D283—41no—
194C2×D283—41no—
195C2×D283—41no—
196C4×C283—22no—
197C4×C283—22no—
198C4×C283—41no—
199C4×C283—41no—
200C4×C283—41no—
201C4×C283—41no—
202Dic283—22no—
203Dic283—22no—
204Dic283—41no—
205Dic283—41no—
206Dic283—41no—
207Dic283—41no—
208C2×C283—42no—
209C2×C283#51811yescharacteristic
210C2×C283#51811yescharacteristic
211C2×C283#52011yescharacteristic
212C2×C283#56011yescharacteristic
213C2×C283#56011yescharacteristic
214C2×C283#56211yescharacteristic
215C2×C283#56211yescharacteristic
216D283—42no—
217D283—42no—
218C283#237711yescharacteristic, complemented, Sylow
219#2377—2831nomaximal, Sylow
220C2×#121—2831no—
221#390—2831no—
222#390—2831no—
223#388—2831no—
224#388—2831no—
225#387—2831no—
226#387—2831no—
227#386—2831no—
228#386—2831no—
229#386—2831no—
230#386—2831no—
231#385—2831no—
232#385D28311yescharacteristic, complemented
233#381—2831no—
234#380—2831no—
235C22×D4—2831no—
236C22×D4—2831no—
237C22×D4—2831no—
238C23×C4—2831no—
239C23×C4—2831no—
240C23×C4C2×D28311yescharacteristic
241#121—2838no—
242C2×C4⋊C4—2831no—
243C2×C4⋊C4—2831no—
244C2×C4⋊C4—2831no—
245C2×C4⋊C4C2×D28311yescharacteristic
246C2×C4⋊C4C2×D28311yescharacteristic
247C2×C22⋊C4—2831no—
248C2×C22⋊C4—2831no—
249C2×C22⋊C4—2831no—
250C2×C22⋊C4—2831no—
251C2×C22⋊C4—2831no—
252C2×C22⋊C4—2831no—
253C2×C22⋊C4—2831no—
254C2×C22⋊C4—2831no—
255C2×C22⋊C4—2831no—
256C2×C22⋊C4—2831no—
257C2×C22⋊C4C2×D28311yescharacteristic
258C2×C22⋊C4C2×D28311yescharacteristic
259C2×C42—2831no—
260C2×C42—2831no—
261#95—2831no—
262#95—2831no—
263#95—2831no—
264#95—2831no—
265#95—2831no—
266#95—2831no—
267#95—2831no—
268#95—2831no—
269#95C2×D28311yescharacteristic
270#95C2×D28311yescharacteristic
271C24—2831no—
272C24—2831no—
273C24C22×D28311yescharacteristic
274C2×D4—2834no—
275C2×D4—2834no—
276C2×D4—2834no—
277C2×D4—11321no—
278C2×D4—11321no—
279C2×D4—11321no—
280C2×D4—11321no—
281C2×D4—11321no—
282C2×D4—11321no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—2831no—
287C22×C4—2831no—
288C22×C4—2834no—
289C22×C4—2831no—
290C22×C4—2831no—
291C22×C4—2831no—
292C22×C4—2831no—
293C22×C4—11321no—
294C22×C4—11321no—
295C22×C4—11321no—
296C22×C4—11321no—
297C22×C4—11321no—
298C22×C4C22×D28311yescharacteristic
299C22×C4C22×D28311yescharacteristic
300C22×C4C22×D28311yescharacteristic
301C22×C4C22×D28311yescharacteristic
302C22×C4C22×D28311yescharacteristic
303C22×C4C22×D28311yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—2834no—
307C4⋊C4—11321no—
308C4⋊C4—11321no—
309C22⋊C4—41no—
310C22⋊C4—2834no—
311C22⋊C4—11321no—
312C22⋊C4—11321no—
313C22⋊C4—11321no—
314C22⋊C4—11321no—
315C22⋊C4—11321no—
316C22⋊C4—11321no—
317C22⋊C4—11321no—
318C22⋊C4—11321no—
319C22⋊C4—11321no—
320C22⋊C4C4×D28314yescomplemented
321C42—11321no—
322C42—11321no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—2832no—
330C23—2832no—
331C23—5661no—
332C23—5661no—
333C23—5661no—
334C23—5661no—
335C23—5661no—
336C23—5661no—
337C23—5661no—
338C23—5661no—
339C23—5661no—
340C23—5661no—
341C23—5661no—
342C23—5661no—
343C23C2×C4×D28312yes—
344C23C23×D28311yescharacteristic
345D4—11324no—
346D4—11324no—
347D4—11324no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—44no—
365C2×C4—2832no—
366C2×C4—2832no—
367C2×C4—5661no—
368C2×C4—5661no—
369C2×C4—5661no—
370C2×C4—5661no—
371C2×C4—5661no—
372C2×C4—5661no—
373C2×C4—5661no—
374C2×C4—5661no—
375C2×C4—5661no—
376C2×C4—5661no—
377C2×C4—5661no—
378C2×C4—5661no—
379C2×C4—5661no—
380C2×C4—5661no—
381C2×C4—5661no—
382C2×C4—5661no—
383C2×C4—11324no—
384C2×C4—11324no—
385C2×C4C2×C4×D28312yes—
386C2×C4C2×C4×D28312yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—5662no—
395C22—5662no—
396C22—5662no—
397C22—5662no—
398C22—5662no—
399C22—5662no—
400C22—11321no—
401C22—11321no—
402C22—11321no—
403C22—11321no—
404C22—11321no—
405C22—11321no—
406C22—11321no—
407C22—11321no—
408C22C22×C4×D28311yescharacteristic
409C22#2258365511yescharacteristic
410C22#2258365511yescharacteristic
411C22#2258365511yescharacteristic
412C22#2258365611yescharacteristic
413C22#2258365611yescharacteristic
414C22#2258365811yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—5662no—
422C4—5662no—
423C4—11321no—
424C4—11321no—
425C4—11321no—
426C4—11321no—
427C2—42no—
428C2—11322no—
429C2—11322no—
430C2#3182693711yescharacteristic
431C2#3182693711yescharacteristic
432C2#3182694611yescharacteristic
433C2#3182720411yescharacteristic
434C2#3182720511yescharacteristic
435C2#3182721111yescharacteristic
436C2#3182721111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#385×C283C2
socle, cosocleC23×C283C24
prime radicalC2×#22583583C2
hypercenter#385D283
hypocenterC283#2377
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. #31826366C2semidirect
3. #31826365C2semidirect
4. #31826358C2semidirect
5. #31826355C2semidirect
6. #31826347C2semidirect
7. #31826346C2semidirect
8. #31826344C2semidirect
9. #31826344C2semidirect
10. #31826343C2semidirect
11. #31826341C2semidirect
12. #31826339C2semidirect
13. #31826327C2semidirect
14. #31826322C2semidirect
15. #385×C283C2semidirect
21. #22583583C4semidirect
56. C2×D1132C2×C4semidirect
62. C2×C22⋊D283C2×C4semidirect
74. C2×C4×D283C2×C4semidirect
77. Dic283⋊C4C2×C4semidirect
87. (C2×D283)⋊C4C2×C4semidirect
103. C22⋊C4×C283C2×C4semidirect
218. C283#2377semidirect
232. #385D283semidirect
320. C22⋊C4C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835832
#318263662
#318263652
#318263582
#318263552
#318263472
#318263462
#318263442
#318263432
#318263412
#318263392
#318263272
#318263222
#385×C2832
#2377283