Finite Group Databasebeta

← #49098458

Subgroups — #49098458

Order 35968.

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×#22582854C211yesmaximal, characteristic
2#31823365C211yesmaximal, characteristic, complemented
3#31823364C211yesmaximal, characteristic, complemented
4#31823354C211yesmaximal, characteristic, complemented
5#31823352C211yesmaximal, characteristic, complemented
6#31823349C211yesmaximal, characteristic, complemented
7#31823341C211yesmaximal, characteristic, complemented
8#31823341C211yesmaximal, characteristic, complemented
9#31823341C211yesmaximal, characteristic, complemented
10#31823341C211yesmaximal, characteristic, complemented
11#31823337C211yesmaximal, characteristic, complemented
12#31823334C211yesmaximal, characteristic, complemented
13#31823325C211yesmaximal, characteristic, complemented
14#31823322C211yesmaximal, characteristic, complemented
15#387×C281C211yesmaximal, characteristic, complemented
16C22×D1124C2211yescharacteristic
17C22×D1124C2211yescharacteristic
18C22×D1124C2211yescharacteristic
19C22×C4×D281C2211yescharacteristic
20C22×C4×D281C2211yescharacteristic
21C22×C4×D281C2211yescharacteristic
22#22582854C418yescomplemented
23C2×C4⋊Dic281C2211yescharacteristic
24C2×#17985117C2211yescharacteristic
25C2×#17985117C2211yescharacteristic
26C2×#17985115C2211yescharacteristic
27C2×#17985115C2211yescharacteristic
28C2×#17985115C2211yescharacteristic
29C2×#17985115C2211yescharacteristic
30C2×#17985115C2211yescharacteristic
31C2×#17985115C2211yescharacteristic
32C2×#17985115C2211yescharacteristic
33C2×#17985115C2211yescharacteristic
34C2×#17985115C2211yescharacteristic
35C2×#17985115C2211yescharacteristic
36C2×#17985115C2211yescharacteristic
37C2×#17985115C2211yescharacteristic
38C2×C4×Dic281C2211yescharacteristic
39#22582786C2211yescharacteristic
40#22582786C2211yescharacteristic
41#22582786C2211yescharacteristic
42#22582786C2211yescharacteristic
43#22582786C2211yescharacteristic
44#22582786C2211yescharacteristic
45C2×C4⋊C4×C281C2211yescharacteristic
46C2×C4⋊C4×C281C2211yescharacteristic
47C2×C42×C281C2211yescharacteristic
48#95×C281C2211yescharacteristic
49#95×C281C2211yescharacteristic
50#95×C281C2211yescharacteristic
51#95×C281C2211yescharacteristic
52C23×D281C2311yescharacteristic
53C23×D281C2311yescharacteristic
54C23×D281C2311yescharacteristic
55C2×D1124—41no—
56C2×D1124—41no—
57C2×D1124—41no—
58C2×D1124—41no—
59C2×D1124—41no—
60C2×D1124—41no—
61C2×D1124C2×C414yes—
62C2×D1124C2×C414yescomplemented
63C2×D1124C2×C414yescomplemented
64C22×Dic281C2311yescharacteristic
65C22×Dic281C2311yescharacteristic
66C22×Dic281C2311yescharacteristic
67C22×Dic281C2311yescharacteristic
68C22×Dic281C2311yescharacteristic
69C2×C4×D281—41no—
70C2×C4×D281—41no—
71C2×C4×D281—41no—
72C2×C4×D281—41no—
73C2×C4×D281—41no—
74C2×C4×D281—41no—
75C2×C4×D281—41no—
76C2×C4×D281—41no—
77C2×C4×D281C2×C414yescomplemented
78C4⋊Dic281—41no—
79#17985117—41no—
80#17985117—41no—
81#17985115—41no—
82#17985115—41no—
83#17985115—41no—
84#17985115—41no—
85#17985115—41no—
86#17985115—41no—
87#17985115—41no—
88#17985115—41no—
89#17985115—41no—
90#17985115—41no—
91#17985115C2×C414yescomplemented
92#17985115C2×C414yescomplemented
93C4×Dic281—41no—
94C22×C4×C281C2311yescharacteristic
95C22×C4×C281C2311yescharacteristic
96C22×C4×C281C2311yescharacteristic
97C22×C4×C281C2311yescharacteristic
98C22×C4×C281C2311yescharacteristic
99C22×C4×C281C2311yescharacteristic
100C22×C4×C281C2311yescharacteristic
101C4⋊C4×C281—41no—
102C4⋊C4×C281C2×C414yescomplemented
103C42×C281—41no—
104C22×D281—21no—
105C22×D281—21no—
106C22×D281—21no—
107C22×D281—21no—
108C22×D281—21no—
109C22×D281—21no—
110C22×D281—21no—
111C22×D281—21no—
112C22×D281—21no—
113C22×D281—21no—
114C22×D281—21no—
115C22×D281—21no—
116C22×D281—21no—
117C22×D281—21no—
118C22×D281—21no—
119C22×D281—21no—
120C22×D281—21no—
121C22×D281—21no—
122C22×D281C22×C412yes—
123C22×D281C22×C412yes—
124C22×D281C22×C412yes—
125D1124—44no—
126D1124—44no—
127D1124—44no—
128C2×Dic281—21no—
129C2×Dic281—21no—
130C2×Dic281—21no—
131C2×Dic281—21no—
132C2×Dic281—21no—
133C2×Dic281—21no—
134C2×Dic281—21no—
135C2×Dic281—21no—
136C2×Dic281—21no—
137C2×Dic281—21no—
138C2×Dic281—21no—
139C2×Dic281—21no—
140C2×Dic281—21no—
141C2×Dic281—21no—
142C2×Dic281C22×C412yes—
143C4×D281—44no—
144C4×D281—44no—
145C4×D281—44no—
146C23×C281C2411yescharacteristic
147C2×C4×C281—21no—
148C2×C4×C281—21no—
149C2×C4×C281—21no—
150C2×C4×C281—21no—
151C2×C4×C281—21no—
152C2×C4×C281—21no—
153C2×C4×C281—21no—
154C2×C4×C281—21no—
155C2×C4×C281—21no—
156C2×C4×C281—21no—
157C2×C4×C281—21no—
158C2×C4×C281—21no—
159C2×C4×C281—21no—
160C2×C4×C281—21no—
161C2×C4×C281—21no—
162C2×C4×C281—21no—
163C2×C4×C281—21no—
164C2×C4×C281—21no—
165C2×C4×C281C22×C412yes—
166C2×C4×C281C22×C412yes—
167C2×C4×C281C22×C412yes—
168C22×C281C23×C411yescharacteristic
169C22×C281H(5,𝔽2)11yescharacteristic
170C22×C281H(5,𝔽2)11yescharacteristic
171C22×C281H(5,𝔽2)11yescharacteristic
172C22×C281H(5,𝔽2)11yescharacteristic
173C22×C281H(5,𝔽2)11yescharacteristic
174C22×C2812−1+411yescharacteristic
175C2×D281—22no—
176C2×D281—22no—
177C2×D281—22no—
178C2×D281—22no—
179C2×D281—22no—
180C2×D281—22no—
181C2×D281—22no—
182C2×D281—22no—
183C2×D281—22no—
184C2×D281—41no—
185C2×D281—41no—
186C2×D281—41no—
187C2×D281—41no—
188C2×D281—41no—
189C2×D281—41no—
190C2×D281—41no—
191C2×D281—41no—
192C2×D281—41no—
193C2×D281—41no—
194C2×D281—41no—
195C2×D281—41no—
196C4×C281—22no—
197C4×C281—22no—
198C4×C281—22no—
199C4×C281—41no—
200C4×C281—41no—
201C4×C281—41no—
202C4×C281—41no—
203Dic281—22no—
204Dic281—41no—
205Dic281—41no—
206Dic281—41no—
207Dic281—41no—
208C2×C281#51811yescharacteristic
209C2×C281#51811yescharacteristic
210C2×C281#52011yescharacteristic
211C2×C281#56011yescharacteristic
212C2×C281#56011yescharacteristic
213C2×C281#56211yescharacteristic
214C2×C281#56211yescharacteristic
215D281—42no—
216D281—42no—
217D281—42no—
218C281#237711yescharacteristic, complemented, Sylow
219#2377—2811nomaximal, Sylow
220C2×#121—2811no—
221#390—2811no—
222#390—2811no—
223#388—2811no—
224#388—2811no—
225#387—2811no—
226#387D28111yescharacteristic, complemented
227#386—2811no—
228#386—2811no—
229#386—2811no—
230#386—2811no—
231#385—2811no—
232#385—2811no—
233#381—2811no—
234#380—2811no—
235C22×D4—2811no—
236C22×D4—2811no—
237C22×D4—2811no—
238C23×C4—2811no—
239C23×C4—2811no—
240C23×C4—2811no—
241#121—2818no—
242C2×C4⋊C4—2811no—
243C2×C4⋊C4—2811no—
244C2×C4⋊C4—2811no—
245C2×C4⋊C4C2×D28111yescharacteristic
246C2×C4⋊C4C2×D28111yescharacteristic
247C2×C22⋊C4—2811no—
248C2×C22⋊C4—2811no—
249C2×C22⋊C4—2811no—
250C2×C22⋊C4—2811no—
251C2×C22⋊C4—2811no—
252C2×C22⋊C4—2811no—
253C2×C22⋊C4—2811no—
254C2×C22⋊C4—2811no—
255C2×C22⋊C4—2811no—
256C2×C22⋊C4—2811no—
257C2×C22⋊C4—2811no—
258C2×C22⋊C4—2811no—
259C2×C42—2811no—
260C2×C42C2×D28111yescharacteristic
261#95—2811no—
262#95—2811no—
263#95—2811no—
264#95—2811no—
265#95—2811no—
266#95—2811no—
267#95C2×D28111yescharacteristic
268#95C2×D28111yescharacteristic
269#95C2×D28111yescharacteristic
270#95C2×D28111yescharacteristic
271C24—2811no—
272C24—2811no—
273C24—2811no—
274C2×D4—2814no—
275C2×D4—2814no—
276C2×D4—2814no—
277C2×D4—11241no—
278C2×D4—11241no—
279C2×D4—11241no—
280C2×D4—11241no—
281C2×D4—11241no—
282C2×D4—11241no—
283C22×C4—2811no—
284C22×C4—2814no—
285C22×C4—2811no—
286C22×C4—2811no—
287C22×C4—2811no—
288C22×C4—2811no—
289C22×C4—11241no—
290C22×C4—11241no—
291C22×C4—11241no—
292C22×C4—11241no—
293C22×C4—11241no—
294C22×C4—11241no—
295C22×C4—11241no—
296C22×C4—11241no—
297C22×C4C22×D28111yescharacteristic
298C22×C4C22×D28111yescharacteristic
299C22×C4C22×D28111yescharacteristic
300C22×C4C22×D28111yescharacteristic
301C22×C4C22×D28111yescharacteristic
302C22×C4C22×D28111yescharacteristic
303C22×C4C22×D28111yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—11241no—
306C4⋊C4—11241no—
307C4⋊C4—11241no—
308C4⋊C4C4×D28114yescomplemented
309C22⋊C4—2814no—
310C22⋊C4—2814no—
311C22⋊C4—11241no—
312C22⋊C4—11241no—
313C22⋊C4—11241no—
314C22⋊C4—11241no—
315C22⋊C4—11241no—
316C22⋊C4—11241no—
317C22⋊C4—11241no—
318C22⋊C4—11241no—
319C22⋊C4—11241no—
320C22⋊C4—11241no—
321C42—41no—
322C42—11241no—
323C23—2812no—
324C23—2812no—
325C23—2812no—
326C23—5621no—
327C23—5621no—
328C23—5621no—
329C23—5621no—
330C23—5621no—
331C23—5621no—
332C23—5621no—
333C23—5621no—
334C23—5621no—
335C23—5621no—
336C23—5621no—
337C23—5621no—
338C23—5621no—
339C23—5621no—
340C23—5621no—
341C23—5621no—
342C23—5621no—
343C23—5621no—
344C23C23×D28111yescharacteristic
345D4—11244no—
346D4—11244no—
347D4—11244no—
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—21no—
365C2×C4—21no—
366C2×C4—2812no—
367C2×C4—5621no—
368C2×C4—5621no—
369C2×C4—5621no—
370C2×C4—5621no—
371C2×C4—5621no—
372C2×C4—5621no—
373C2×C4—5621no—
374C2×C4—5621no—
375C2×C4—5621no—
376C2×C4—5621no—
377C2×C4—5621no—
378C2×C4—5621no—
379C2×C4—5621no—
380C2×C4—5621no—
381C2×C4—11244no—
382C2×C4—11244no—
383C2×C4—11244no—
384C2×C4C2×C4×D28112yes—
385C2×C4C2×C4×D28112yes—
386C2×C4C2×C4×D28112yes—
387C22—5622no—
388C22—5622no—
389C22—5622no—
390C22—5622no—
391C22—5622no—
392C22—5622no—
393C22—5622no—
394C22—5622no—
395C22—5622no—
396C22—11241no—
397C22—11241no—
398C22—11241no—
399C22—11241no—
400C22—11241no—
401C22—11241no—
402C22—11241no—
403C22—11241no—
404C22—11241no—
405C22—11241no—
406C22—11241no—
407C22—11241no—
408C22C22×C4×D28111yescharacteristic
409C22#2258292411yescharacteristic
410C22#2258292511yescharacteristic
411C22#2258292511yescharacteristic
412C22#2258292511yescharacteristic
413C22#2258292511yescharacteristic
414C22#2258292711yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—5622no—
423C4—11241no—
424C4—11241no—
425C4—11241no—
426C4—11241no—
427C2—11242no—
428C2—11242no—
429C2—11242no—
430C2#3182393511yescharacteristic
431C2#3182393711yescharacteristic
432C2#3182394511yescharacteristic
433C2#3182420311yescharacteristic
434C2#3182420411yescharacteristic
435C2#3182420911yescharacteristic
436C2#3182421111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#387×C281C2
socle, cosocleC23×C281C24
prime radicalC2×#22582854C2
hypercenter#387D281
hypocenterC281#2377
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #31823365C2semidirect
3. #31823364C2semidirect
4. #31823354C2semidirect
5. #31823352C2semidirect
6. #31823349C2semidirect
7. #31823341C2semidirect
8. #31823341C2semidirect
9. #31823341C2semidirect
10. #31823341C2semidirect
11. #31823337C2semidirect
12. #31823334C2semidirect
13. #31823325C2semidirect
14. #31823322C2semidirect
15. #387×C281C2semidirect
22. #22582854C4semidirect
62. C2×D1124C2×C4semidirect
63. C2×D1124C2×C4semidirect
77. C2×C4×D281C2×C4semidirect
91. #17985115C2×C4semidirect
92. #17985115C2×C4semidirect
102. C4⋊C4×C281C2×C4semidirect
218. C281#2377semidirect
226. #387D281semidirect
308. C4⋊C4C4×D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828542
#318233652
#318233642
#318233542
#318233522
#318233492
#318233412
#318233372
#318233342
#318233252
#318233222
#387×C2812
#2377281