Finite Group Databasebeta

← #49098644

Subgroups — #49098644

Order 35968.

908 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#17985137C211yesmaximal, characteristic, complemented
2C2×#22582858C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D281C211yesmaximal, characteristic, complemented
4#31823378C212yesmaximal, complemented
5#31823371C212yesmaximal, complemented
6#31823368C211yesmaximal, characteristic, complemented
7#31823366C211yesmaximal, characteristic, complemented
8#31823343C212yesmaximal, complemented
9#31823335C212yesmaximal, complemented
10#31823320C211yesmaximal, characteristic, complemented
11C2×#121×C281C211yesmaximal, characteristic, complemented
12C2×#17985137—24no—
13C2×#17985137—24no—
14C2×#17985137—24no—
15C22×Dic562C2211yescharacteristic
16C22×C22⋊D281C2211yescharacteristic
17C22×C22⋊D281C2212yes—
18C23×Dic281C2212yes—
19C22×C4×D281C2211yescharacteristic
20#22582858—24no—
21C4×C22⋊D281—24no—
22C2×C4⋊Dic281C2211yescharacteristic
23C2×#17985117C2212yes—
24C2×#17985117C2211yescharacteristic
25C2×C22⋊Dic281C2212yes—
26C2×C22⋊Dic281C2212yes—
27C2×C22⋊Dic281C2211yescharacteristic
28C2×C22⋊Dic281C2212yes—
29C2×#17985115C2211yescharacteristic
30C2×#17985115C2212yes—
31C2×C4×Dic281C2211yescharacteristic
32#22582786C2212yes—
33#22582786C2212yes—
34#22582786C2212yes—
35C22×D4×C281C2212yes—
36C22×D4×C281C2211yescharacteristic
37C23×C4×C281C2211yescharacteristic
38#121×C281—24no—
39C2×C4⋊C4×C281C2211yescharacteristic
40C2×C22⋊C4×C281C2212yes—
41C23×D281C2311yescharacteristic
42#17985137—232no—
43C2×Dic562—22no—
44C2×Dic562—22no—
45C2×Dic562D414yescomplemented
46C2×C22⋊D281—22no—
47C2×C22⋊D281—24no—
48C2×C22⋊D281—24no—
49C2×C22⋊D281—22no—
50C2×C22⋊D281—24no—
51C2×C22⋊D281—22no—
52C22×Dic281—24no—
53C22×Dic281—24no—
54C22×Dic281—24no—
55C22×Dic281C2311yescharacteristic
56C22×Dic281C2312yes—
57C22×Dic281C2311yescharacteristic
58C22×Dic281C2312yes—
59C22×Dic281C2311yescharacteristic
60C2×C4×D281—22no—
61C2×C4×D281—22no—
62C2×C4×D281D414yescomplemented
63C4⋊Dic281—22no—
64#17985117—22no—
65#17985117—24no—
66C22⋊Dic281—22no—
67C22⋊Dic281—24no—
68C22⋊Dic281—24no—
69C22⋊Dic281—42no—
70#17985115—22no—
71#17985115—42no—
72C4×Dic281—22no—
73C24×C281C2312yes—
74C24×C281C2311yescharacteristic
75C2×D4×C281—24no—
76C2×D4×C281—24no—
77C2×D4×C281—22no—
78C2×D4×C281—22no—
79C2×D4×C281—42no—
80C2×D4×C281D414yescomplemented
81C22×C4×C281—22no—
82C22×C4×C281—22no—
83C22×C4×C281—22no—
84C22×C4×C281C2312yes—
85C22×C4×C281C2311yescharacteristic
86C22×C4×C281C2311yescharacteristic
87C4⋊C4×C281—22no—
88C22⋊C4×C281—24no—
89C22×D281—21no—
90C22×D281—21no—
91C22×D281—21no—
92C22×D281—21no—
93C22×D281—21no—
94C22×D281—21no—
95C22×D281C2×D412yes—
96Dic562—28no—
97C22⋊D281—28no—
98C22⋊D281—216no—
99C2×Dic281—216no—
100C2×Dic281—21no—
101C2×Dic281—21no—
102C2×Dic281—21no—
103C2×Dic281—22no—
104C2×Dic281—22no—
105C2×Dic281—21no—
106C2×Dic281—21no—
107C2×Dic281—22no—
108C2×Dic281—22no—
109C2×Dic281—22no—
110C2×Dic281—21no—
111C2×Dic281—21no—
112C2×Dic281C2×D412yes—
113C2×Dic281C2×D414yes—
114C2×Dic281#4112yescomplemented
115C4×D281—28no—
116C23×C281—21no—
117C23×C281—21no—
118C23×C281—21no—
119C23×C281—22no—
120C23×C281—22no—
121C23×C281—22no—
122C23×C281—22no—
123C23×C281—21no—
124C23×C281—21no—
125C23×C281—22no—
126C23×C281—22no—
127C23×C281—21no—
128C23×C281C2×D414yes—
129C23×C281#4112yescomplemented
130C23×C281C2411yescharacteristic
131D4×C281—28no—
132D4×C281—48no—
133C2×C4×C281—21no—
134C2×C4×C281—22no—
135C2×C4×C281—21no—
136C2×C4×C281—21no—
137C2×C4×C281—22no—
138C2×C4×C281—22no—
139C2×C4×C281—44no—
140C2×C4×C281C2×D412yes—
141C2×C4×C281C2×D412yes—
142C2×C4×C281C2×D412yes—
143C22×C281—24no—
144C22×C281—22no—
145C22×C281—22no—
146C22×C281—24no—
147C22×C281—24no—
148C22×C281—22no—
149C22×C281—41no—
150C22×C281—42no—
151C22×C281—41no—
152C22×C281—42no—
153C22×C281—41no—
154C22×C281—42no—
155C22×C281—41no—
156C22×C281—42no—
157C22×C281C22×D411yescharacteristic
158C22×C281C22×D411yescharacteristic
159C22×C281C22×D411yescharacteristic
160C22×C281C2×#4111yescharacteristic
161C22×C281C2×#4111yescharacteristic
162C22×C281H(5,𝔽2)11yescharacteristic
163C22×C2812−1+411yescharacteristic
164C2×D281—22no—
165C2×D281—22no—
166C2×D281—22no—
167C2×D281—41no—
168C2×D281—41no—
169C2×D281—41no—
170C2×D281—41no—
171C4×C281—41no—
172C4×C281—42no—
173C4×C281#12014yes—
174Dic281—22no—
175Dic281—24no—
176Dic281—22no—
177Dic281—41no—
178Dic281—42no—
179C2×C281—44no—
180C2×C281—42no—
181C2×C281C2×#12011yescharacteristic
182C2×C281#52511yescharacteristic
183C2×C281#53711yescharacteristic
184C2×C281#54611yescharacteristic
185C2×C281#54711yescharacteristic
186C2×C281#54811yescharacteristic
187C2×C281#55011yescharacteristic
188D281—42no—
189C281#240711yescharacteristic, complemented, Sylow
190#2407—2811nomaximal, Sylow
191C22×#41—2811no—
192C2×C22⋊Q8—2811no—
193C2×#121D28111yescharacteristic, complemented
194C2×C4×D4—2811no—
195#394—2812no—
196#392—2812no—
197#391—2811no—
198#390—2811no—
199#386—2812no—
200#385—2812no—
201#380—2811no—
202C2×#41—5624no—
203C2×#41—5624no—
204C2×#41—5624no—
205C22×Q8—2811no—
206C22×D4—2811no—
207C22×D4—2812no—
208C22×D4C2×D28112yes—
209C22×D4C2×D28111yescharacteristic
210C23×C4—2811no—
211C23×C4—2812no—
212C23×C4C2×D28111yescharacteristic
213C22⋊Q8—5624no—
214#121—24no—
215C4×D4—5624no—
216C2×C4⋊C4—2811no—
217C2×C4⋊C4—2812no—
218C2×C4⋊C4—2811no—
219C2×C4⋊C4C2×D28111yescharacteristic
220C2×C22⋊C4—2811no—
221C2×C22⋊C4—2812no—
222C2×C22⋊C4—2812no—
223C2×C22⋊C4—2811no—
224C2×C22⋊C4—2812no—
225C2×C22⋊C4—2812no—
226C2×C22⋊C4C2×D28112yes—
227C2×C42—2811no—
228#95—2812no—
229#95—2812no—
230#95—2812no—
231C24—2811no—
232C24C22×D28112yes—
233C24C22×D28111yescharacteristic
234#41—56232no—
235C2×Q8—2814no—
236C2×Q8—5622no—
237C2×Q8—5622no—
238C2×D4—24no—
239C2×D4—24no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—42no—
243C2×D4—5622no—
244C2×D4—5624no—
245C2×D4—5622no—
246C2×D4—5624no—
247C2×D4—5624no—
248C2×D4—5622no—
249C2×D4C22⋊D28114yescomplemented
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—2811no—
254C22×C4—2811no—
255C22×C4—2812no—
256C22×C4—2814no—
257C22×C4—2811no—
258C22×C4—2812no—
259C22×C4—5624no—
260C22×C4—5624no—
261C22×C4—5624no—
262C22×C4—5622no—
263C22×C4—5622no—
264C22×C4C22×D28112yes—
265C22×C4C22×D28111yescharacteristic
266C22×C4C22×D28111yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—5622no—
269C4⋊C4—5624no—
270C4⋊C4—5622no—
271C22⋊C4—24no—
272C22⋊C4—5622no—
273C22⋊C4—5624no—
274C22⋊C4—5622no—
275C22⋊C4—5624no—
276C22⋊C4—11242no—
277C22⋊C4—11242no—
278C42—5622no—
279C23—21no—
280C23—21no—
281C23—22no—
282C23—22no—
283C23—21no—
284C23—22no—
285C23—21no—
286C23—22no—
287C23—22no—
288C23—21no—
289C23—22no—
290C23—21no—
291C23—2812no—
292C23—5621no—
293C23—5621no—
294C23—5621no—
295C23—5621no—
296C23—5621no—
297C23—5621no—
298C23C2×C22⋊D28114yes—
299C23#1798513712yescomplemented
300C23C23×D28111yescharacteristic
301Q8—5628no—
302D4—28no—
303D4—48no—
304D4—56216no—
305D4—5628no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—44no—
313C2×C4—2812no—
314C2×C4—2814no—
315C2×C4—2812no—
316C2×C4—56216no—
317C2×C4—5621no—
318C2×C4—5621no—
319C2×C4—5622no—
320C2×C4—5621no—
321C2×C4—5622no—
322C2×C4—5621no—
323C2×C4—5628no—
324C2×C4—5621no—
325C2×C4—5622no—
326C2×C4—5622no—
327C2×C4—5622no—
328C2×C4—5621no—
329C2×C4—5621no—
330C2×C4D4×D28112yes—
331C2×C4D4×D28112yes—
332C2×C4C2×C22⋊D28112yes—
333C22—24no—
334C22—22no—
335C22—22no—
336C22—24no—
337C22—24no—
338C22—22no—
339C22—41no—
340C22—42no—
341C22—41no—
342C22—42no—
343C22—41no—
344C22—42no—
345C22—41no—
346C22—42no—
347C22—5622no—
348C22—5622no—
349C22—5622no—
350C22—11241no—
351C22—11241no—
352C22—11241no—
353C22—11241no—
354C22C2×D4×D28111yescharacteristic
355C22C2×D4×D28111yescharacteristic
356C22C22×C22⋊D28111yescharacteristic
357C22#41×D28111yescharacteristic
358C22C2×#1798513711yescharacteristic
359C22#2258292411yescharacteristic
360C22#2258292611yescharacteristic
361C4—41no—
362C4—42no—
363C4—5622no—
364C4—5624no—
365C4—5622no—
366C4—11242no—
367C4—11241no—
368C4#2258284714yes—
369C2—44no—
370C2—42no—
371C2—11242no—
372C2C2×#2258284711yescharacteristic
373C2#3182397311yescharacteristic
374C2#3182404211yescharacteristic
375C2#3182410711yescharacteristic
376C2#3182411211yescharacteristic
377C2#3182411911yescharacteristic
378C2#3182413111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
FittingC2×#121×C281C2
hypercenterC2×#121D281
hypocenterC281#2407
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#17985137C2semidirect
2. C2×#22582858C2semidirect
3. C2×C4×C22⋊D281C2semidirect
4. #31823378C2semidirect
5. #31823371C2semidirect
6. #31823368C2semidirect
7. #31823366C2semidirect
8. #31823343C2semidirect
9. #31823335C2semidirect
10. #31823320C2semidirect
11. C2×#121×C281C2semidirect
45. C2×Dic562D4semidirect
62. C2×C4×D281D4semidirect
80. C2×D4×C281D4semidirect
114. C2×Dic281#41semidirect
129. C23×C281#41semidirect
189. C281#2407semidirect
193. C2×#121D281semidirect
249. C2×D4C22⋊D281semidirect
299. C23#17985137semidirect

Maximal subgroups

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

subgroupindex
C22×#179851372
C2×#225828582
C2×C4×C22⋊D2812
#318233782
#318233712
#318233682
#318233662
#318233432
#318233352
#318233202
C2×#121×C2812
#2407281