Finite Group Databasebeta

← #49098035

Subgroups — #49098035

Order 35968.

528 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22582855C211yesmaximal, characteristic
2#31823370C211yesmaximal, characteristic, complemented
3#31823360C211yesmaximal, characteristic, complemented
4#31823358C211yesmaximal, characteristic, complemented
5#31823348C211yesmaximal, characteristic, complemented
6#31823347C211yesmaximal, characteristic, complemented
7#31823346C211yesmaximal, characteristic, complemented
8#31823345C211yesmaximal, characteristic, complemented
9#31823337C211yesmaximal, characteristic
10#31823334C211yesmaximal, characteristic
11#31823322C211yesmaximal, characteristic
12C4×#17985115C211yesmaximal, characteristic
13#31823310C211yesmaximal, characteristic
14#95×D281C211yesmaximal, characteristic
15#391×C281C211yesmaximal, characteristic, complemented
16C22×C4×D281C2211yescharacteristic
17C22×C4×D281C2211yescharacteristic
18C22×C4×D281C2211yescharacteristic
19#22582855C418yescomplemented
20C2×C4⋊Dic281C2211yescharacteristic
21C2×C4⋊Dic281C2211yescharacteristic
22C2×#17985117C2211yescharacteristic
23C2×#17985117C2211yescharacteristic
24C2×#17985117C2211yescharacteristic
25C2×#17985117C2211yescharacteristic
26C2×#17985117C2211yescharacteristic
27C2×#17985117C2211yescharacteristic
28C2×#17985115C2211yescharacteristic
29C2×#17985115C2211yescharacteristic
30C2×#17985115C2211yescharacteristic
31C2×#17985115C2211yescharacteristic
32C2×C4×Dic281C2211yescharacteristic
33C2×C4×Dic281C2211yescharacteristic
34C2×C4×Dic281C2211yescharacteristic
35#22582786C2211yescharacteristic
36#22582786C2211yescharacteristic
37#22582786C2211yescharacteristic
38#22582786C2211yescharacteristic
39#22582786C2211yescharacteristic
40#22582786C2211yescharacteristic
41#22582786C2211yescharacteristic
42#22582786C2211yescharacteristic
43#22582786C2211yescharacteristic
44#22582786C2211yescharacteristic
45C22×Q8×C281C2211yescharacteristic
46C2×C4⋊C4×C281C2211yescharacteristic
47C2×C42×C281C2211yescharacteristic
48#95×C281C2211yescharacteristic
49#95×C281C2211yescharacteristic
50#95×C281C2211yescharacteristic
51#95×C281C2211yescharacteristic
52C23×D281C2311yescharacteristic
53C22×Dic281C2311yescharacteristic
54C22×Dic281C2311yescharacteristic
55C22×Dic281C2311yescharacteristic
56C22×Dic281C2311yescharacteristic
57C22×Dic281C2311yescharacteristic
58C22×Dic281C2311yescharacteristic
59C22×Dic281C2311yescharacteristic
60C2×C4×D281—22no—
61C2×C4×D281—41no—
62C2×C4×D281—41no—
63C2×C4×D281—41no—
64C2×C4×D281—41no—
65C2×C4×D281—41no—
66C2×C4×D281—41no—
67C2×C4×D281C2×C414yes—
68C2×C4×D281Q814yescomplemented
69C4⋊Dic281—41no—
70C4⋊Dic281C2×C414yescomplemented
71#17985117—41no—
72#17985117—41no—
73#17985117—41no—
74#17985117—41no—
75#17985117C2×C414yescomplemented
76#17985117C2×C414yescomplemented
77#17985115—22no—
78#17985115—22no—
79#17985115C2×C414yes—
80#17985115C2×C414yes—
81C4×Dic281—41no—
82C4×Dic281—41no—
83C4×Dic281—41no—
84C2×Q8×C281—41no—
85C2×Q8×C281—41no—
86C2×Q8×C281C2×C414yescomplemented
87C22×C4×C281C2311yescharacteristic
88C22×C4×C281C2311yescharacteristic
89C22×C4×C281C2311yescharacteristic
90C22×C4×C281C2311yescharacteristic
91C22×C4×C281C2311yescharacteristic
92C22×C4×C281C2311yescharacteristic
93C22×C4×C281C2311yescharacteristic
94C4⋊C4×C281—41no—
95C42×C281—41no—
96C22×D281—21no—
97C22×D281—21no—
98C22×D281—21no—
99C22×D281—21no—
100C22×D281C22×C412yes—
101C22×D281C2×Q812yes—
102C22×D281#4112yes—
103C2×Dic281—21no—
104C2×Dic281—21no—
105C2×Dic281—21no—
106C2×Dic281—21no—
107C2×Dic281—21no—
108C2×Dic281—21no—
109C2×Dic281—21no—
110C2×Dic281—21no—
111C2×Dic281—21no—
112C2×Dic281—21no—
113C2×Dic281—21no—
114C2×Dic281—21no—
115C2×Dic281—21no—
116C2×Dic281—21no—
117C2×Dic281—21no—
118C2×Dic281—21no—
119C2×Dic281—21no—
120C2×Dic281C22×C412yes—
121C2×Dic281C22×C412yes—
122C2×Dic281C22×C412yes—
123C2×Dic281C2×Q812yes—
124C4×D281—44no—
125C4×D281—44no—
126C4×D281—44no—
127C23×C281C2411yescharacteristic
128Q8×C281—44no—
129C2×C4×C281—21no—
130C2×C4×C281—21no—
131C2×C4×C281—21no—
132C2×C4×C281—21no—
133C2×C4×C281—21no—
134C2×C4×C281—21no—
135C2×C4×C281—21no—
136C2×C4×C281—21no—
137C2×C4×C281—21no—
138C2×C4×C281—21no—
139C2×C4×C281—21no—
140C2×C4×C281—21no—
141C2×C4×C281—21no—
142C2×C4×C281—21no—
143C2×C4×C281—21no—
144C2×C4×C281—21no—
145C2×C4×C281—21no—
146C2×C4×C281C22×C412yes—
147C2×C4×C281C22×C412yes—
148C2×C4×C281C22×C412yes—
149C2×C4×C281C2×Q812yes—
150C22×C281C23×C411yescharacteristic
151C22×C281C22×Q811yescharacteristic
152C22×C281C2×#4111yescharacteristic
153C22×C281H(5,𝔽2)11yescharacteristic
154C22×C281H(5,𝔽2)11yescharacteristic
155C22×C281H(5,𝔽2)11yescharacteristic
156C22×C2812−1+411yescharacteristic
157C2×D281—22no—
158C2×D281—22no—
159C2×D281—22no—
160C2×D281—22no—
161C2×D281—22no—
162C2×D281—22no—
163C2×D281C4×Q814yes—
164C4×C281—22no—
165C4×C281—22no—
166C4×C281—22no—
167C4×C281—22no—
168C4×C281—41no—
169C4×C281—41no—
170C4×C281—41no—
171Dic281—22no—
172Dic281—22no—
173Dic281—22no—
174Dic281—22no—
175Dic281—41no—
176Dic281—41no—
177Dic281—41no—
178C2×C281C2×C4×Q811yescharacteristic
179C2×C281#51811yescharacteristic
180C2×C281#52011yescharacteristic
181C2×C281#53811yescharacteristic
182C2×C281#53911yescharacteristic
183C2×C281#54311yescharacteristic
184C2×C281#54411yescharacteristic
185D281—24no—
186C281#232911yescharacteristic, complemented, Sylow
187#2329—2811nomaximal, Sylow
188C2×C22⋊Q8—2811no—
189#391—2811no—
190#391D28111yescharacteristic, complemented
191#389—2811no—
192#389—2811no—
193#387—2811no—
194#387—2811no—
195#387—2811no—
196#387—2811no—
197#385—2811no—
198#385—2811no—
199#380—2811no—
200C4×C22⋊C4—2811no—
201C4×C22⋊C4—2811no—
202C2×#95—2811no—
203C22×Q8C2×D28111yescharacteristic
204C23×C4—2811no—
205C23×C4—2811no—
206C23×C4—2811no—
207C22⋊Q8—2818no—
208C2×C4⋊C4—2811no—
209C2×C4⋊C4—2811no—
210C2×C4⋊C4—2811no—
211C2×C4⋊C4—2811no—
212C2×C4⋊C4—2811no—
213C2×C4⋊C4—2811no—
214C2×C4⋊C4—2811no—
215C2×C4⋊C4—2811no—
216C2×C4⋊C4C2×D28111yescharacteristic
217C2×C22⋊C4—2811no—
218C2×C22⋊C4—2811no—
219C2×C22⋊C4—2811no—
220C2×C22⋊C4—2811no—
221C2×C42—2811no—
222C2×C42—2811no—
223C2×C42—2811no—
224C2×C42C2×D28111yescharacteristic
225#95—2811no—
226#95—2811no—
227#95—2811no—
228#95—2811no—
229#95—2811no—
230#95—2811no—
231#95—2811no—
232#95—2811no—
233#95—2811no—
234#95—2811no—
235#95C2×D28111yescharacteristic
236#95C2×D28111yescharacteristic
237#95C2×D28111yescharacteristic
238#95C2×D28111yescharacteristic
239C24—2811no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8C4×D28114yescomplemented
243C22×C4—2811no—
244C22×C4—2811no—
245C22×C4—2811no—
246C22×C4—2811no—
247C22×C4—2814no—
248C22×C4—2814no—
249C22×C4—2811no—
250C22×C4—2811no—
251C22×C4—2811no—
252C22×C4—5622no—
253C22×C4—11241no—
254C22×C4—11241no—
255C22×C4—11241no—
256C22×C4—11241no—
257C22×C4—11241no—
258C22×C4—11241no—
259C22×C4C22×D28111yescharacteristic
260C22×C4C22×D28111yescharacteristic
261C22×C4C22×D28111yescharacteristic
262C22×C4C22×D28111yescharacteristic
263C22×C4C22×D28111yescharacteristic
264C22×C4C22×D28111yescharacteristic
265C22×C4C22×D28111yescharacteristic
266C4⋊C4—41no—
267C4⋊C4—2814no—
268C4⋊C4—2814no—
269C4⋊C4—2814no—
270C4⋊C4—11241no—
271C4⋊C4—11241no—
272C4⋊C4—11241no—
273C4⋊C4—11241no—
274C4⋊C4—11241no—
275C22⋊C4—2814no—
276C22⋊C4—2814no—
277C22⋊C4—5622no—
278C22⋊C4—5622no—
279C42—41no—
280C42—11241no—
281C42—11241no—
282C42—11241no—
283C23—2812no—
284C23—2812no—
285C23—2812no—
286C23—5621no—
287C23—5621no—
288C23—5621no—
289C23—5621no—
290C23C23×D28111yescharacteristic
291Q8—44no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2812no—
310C2×C4—2812no—
311C2×C4—2812no—
312C2×C4—2812no—
313C2×C4—5621no—
314C2×C4—5621no—
315C2×C4—5621no—
316C2×C4—5621no—
317C2×C4—5621no—
318C2×C4—5621no—
319C2×C4—5621no—
320C2×C4—5621no—
321C2×C4—5621no—
322C2×C4—5621no—
323C2×C4—5621no—
324C2×C4—5621no—
325C2×C4—5621no—
326C2×C4—5621no—
327C2×C4—5621no—
328C2×C4—5621no—
329C2×C4—5621no—
330C2×C4—11244no—
331C2×C4—11244no—
332C2×C4—11244no—
333C2×C4C2×C4×D28112yes—
334C2×C4C2×C4×D28112yes—
335C2×C4C2×C4×D28112yes—
336C2×C4Q8×D28112yes—
337C22—2814no—
338C22—5622no—
339C22—5622no—
340C22—5622no—
341C22—5622no—
342C22—5622no—
343C22—5622no—
344C22C22×C4×D28111yescharacteristic
345C22C2×Q8×D28111yescharacteristic
346C22#41×D28111yescharacteristic
347C22#2258292411yescharacteristic
348C22#2258292411yescharacteristic
349C22#2258292511yescharacteristic
350C22#2258292711yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—5622no—
359C4—5622no—
360C4—5622no—
361C4—5622no—
362C4—11241no—
363C4—11241no—
364C4—11241no—
365C2—5624no—
366C2C4×Q8×D28111yescharacteristic
367C2#3182393611yescharacteristic
368C2#3182394511yescharacteristic
369C2#3182404711yescharacteristic
370C2#3182405911yescharacteristic
371C2#3182408811yescharacteristic
372C2#3182409011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#391×C281C2
socle, cosocleC23×C281C24
prime radicalC23×D281C23
hypercenter#391D281
hypocenterC281#2329
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. #31823370C2semidirect
3. #31823360C2semidirect
4. #31823358C2semidirect
5. #31823348C2semidirect
6. #31823347C2semidirect
7. #31823346C2semidirect
8. #31823345C2semidirect
15. #391×C281C2semidirect
19. #22582855C4semidirect
68. C2×C4×D281Q8semidirect
70. C4⋊Dic281C2×C4semidirect
75. #17985117C2×C4semidirect
76. #17985117C2×C4semidirect
86. C2×Q8×C281C2×C4semidirect
186. C281#2329semidirect
190. #391D281semidirect
242. C2×Q8C4×D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828552
#318233702
#318233602
#318233582
#318233482
#318233472
#318233462
#318233452
#318233372
#318233342
#318233222
C4×#179851152
#318233102
#95×D2812
#391×C2812
#2329281