Finite Group Databasebeta

← #49098377

Subgroups — #49098377

Order 35968.

632 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22582865C211yesmaximal, characteristic
2C2×C4×Dic562C211yesmaximal, characteristic, complemented
3C2×#22582839C211yesmaximal, characteristic
4#31823367C211yesmaximal, characteristic, complemented
5#31823363C211yesmaximal, characteristic
6#31823357C211yesmaximal, characteristic, complemented
7#31823355C211yesmaximal, characteristic, complemented
8#31823353C211yesmaximal, characteristic, complemented
9#31823338C211yesmaximal, characteristic, complemented
10#31823337C211yesmaximal, characteristic, complemented
11C4⋊C4×Dic281C211yesmaximal, characteristic, complemented
12#31823314C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic281C211yesmaximal, characteristic, complemented
14C4×#17985115C211yesmaximal, characteristic, complemented
15#388×C281C211yesmaximal, characteristic, complemented
16C22×Dic562C2211yescharacteristic
17C22×C22⋊D281C2211yescharacteristic
18C23×Dic281C2211yescharacteristic
19C22×C4×D281C2211yescharacteristic
20#22582865C418yescomplemented
21C4×Dic562—24no—
22#22582839—24no—
23C2×C4⋊Dic281C2211yescharacteristic
24C2×C4⋊Dic281C2211yescharacteristic
25C2×#17985117C2211yescharacteristic
26C2×#17985117C2211yescharacteristic
27C2×#17985117C2211yescharacteristic
28C2×C22⋊Dic281C2211yescharacteristic
29C2×C22⋊Dic281C2211yescharacteristic
30C2×#17985115C2211yescharacteristic
31C2×#17985115C2211yescharacteristic
32C2×#17985115C2211yescharacteristic
33C2×#17985115C2211yescharacteristic
34C2×#17985115C2211yescharacteristic
35C2×C4×Dic281C2211yescharacteristic
36C2×C4×Dic281C2211yescharacteristic
37C2×C4×Dic281C2211yescharacteristic
38C2×C4×Dic281C2211yescharacteristic
39C2×C4×Dic281C2211yescharacteristic
40C2×C4×Dic281C2211yescharacteristic
41#22582786C2211yescharacteristic
42#22582786C2211yescharacteristic
43#22582786C2211yescharacteristic
44#22582786C2211yescharacteristic
45#22582786C2211yescharacteristic
46#22582786C2211yescharacteristic
47C2×C4⋊C4×C281C2211yescharacteristic
48C2×C22⋊C4×C281C2211yescharacteristic
49C2×C22⋊C4×C281C2211yescharacteristic
50C2×C22⋊C4×C281C2211yescharacteristic
51C2×C42×C281C2211yescharacteristic
52#95×C281C2211yescharacteristic
53#95×C281C2211yescharacteristic
54C23×D281C2311yescharacteristic
55C2×Dic562—22no—
56C2×Dic562—22no—
57C2×Dic562C2×C414yescomplemented
58C2×C22⋊D281—22no—
59C2×C22⋊D281—22no—
60C2×C22⋊D281C2×C414yes—
61C22×Dic281—22no—
62C22×Dic281—22no—
63C22×Dic281—41no—
64C22×Dic281C2311yescharacteristic
65C22×Dic281C2311yescharacteristic
66C22×Dic281C2311yescharacteristic
67C22×Dic281C2311yescharacteristic
68C22×Dic281C2311yescharacteristic
69C22×Dic281C2311yescharacteristic
70C22×Dic281C2311yescharacteristic
71C2×C4×D281—22no—
72C2×C4×D281—22no—
73C2×C4×D281—41no—
74C4⋊Dic281—22no—
75C4⋊Dic281—22no—
76#17985117—22no—
77#17985117—22no—
78#17985117D414yes—
79C22⋊Dic281—41no—
80C22⋊Dic281C2×C414yescomplemented
81#17985115—22no—
82#17985115—22no—
83#17985115—41no—
84#17985115C2×C414yescomplemented
85#17985115C2×C414yescomplemented
86C4×Dic281—22no—
87C4×Dic281—22no—
88C4×Dic281—22no—
89C4×Dic281—41no—
90C4×Dic281—41no—
91C4×Dic281C2×C414yescomplemented
92C24×C281C2311yescharacteristic
93C22×C4×C281C2311yescharacteristic
94C22×C4×C281C2311yescharacteristic
95C22×C4×C281C2311yescharacteristic
96C22×C4×C281C2311yescharacteristic
97C22×C4×C281C2311yescharacteristic
98C22×C4×C281C2311yescharacteristic
99C4⋊C4×C281—22no—
100C22⋊C4×C281—22no—
101C22⋊C4×C281—22no—
102C22⋊C4×C281C2×C414yescomplemented
103C42×C281—22no—
104C22×D281—21no—
105C22×D281—21no—
106C22×D281—21no—
107C22×D281—21no—
108C22×D281—21no—
109C22×D281—21no—
110C22×D281C22×C412yes—
111Dic562—28no—
112C22⋊D281—28no—
113C2×Dic281—21no—
114C2×Dic281—21no—
115C2×Dic281—21no—
116C2×Dic281—21no—
117C2×Dic281—21no—
118C2×Dic281—21no—
119C2×Dic281—21no—
120C2×Dic281—21no—
121C2×Dic281—21no—
122C2×Dic281—21no—
123C2×Dic281—21no—
124C2×Dic281—21no—
125C2×Dic281—21no—
126C2×Dic281—21no—
127C2×Dic281—44no—
128C2×Dic281C22×C412yes—
129C2×Dic281C22×C412yes—
130C2×Dic281C22×C412yes—
131C2×Dic281C2×D412yes—
132C2×Dic281C2×D412yes—
133C2×Dic281#4112yes—
134C2×Dic281#4112yes—
135C4×D281—44no—
136C23×C281—21no—
137C23×C281—21no—
138C23×C281—21no—
139C23×C281—21no—
140C23×C281—21no—
141C23×C281—21no—
142C23×C281C22×C412yes—
143C23×C281C2411yescharacteristic
144C2×C4×C281—21no—
145C2×C4×C281—21no—
146C2×C4×C281—21no—
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×C281C22×C412yes—
159C2×C4×C281C22×C412yes—
160C2×C4×C281C2×D412yes—
161C2×C4×C281#4112yes—
162C22×C281—22no—
163C22×C281—22no—
164C22×C281—22no—
165C22×C281—41no—
166C22×C281—41no—
167C22×C281—41no—
168C22×C281—41no—
169C22×C281C23×C411yescharacteristic
170C22×C281C22×D411yescharacteristic
171C22×C281C2×#4111yescharacteristic
172C22×C281C2×#4111yescharacteristic
173C22×C281C2×#4111yescharacteristic
174C22×C281H(5,𝔽2)11yescharacteristic
175C22×C2812−1+411yescharacteristic
176C2×D281—22no—
177C2×D281—22no—
178C2×D281—22no—
179C2×D281—41no—
180C2×D281—41no—
181C2×D281—41no—
182C2×D281—41no—
183C4×C281—22no—
184C4×C281—22no—
185C4×C281—22no—
186C4×C281—22no—
187C4×C281—41no—
188C4×C281—41no—
189Dic281—22no—
190Dic281—22no—
191Dic281—22no—
192Dic281—22no—
193Dic281—41no—
194Dic281—41no—
195Dic281C4×D414yes—
196C2×C281—42no—
197C2×C281C2×C4×D411yescharacteristic
198C2×C281C4×#4111yescharacteristic
199C2×C281#52011yescharacteristic
200C2×C281#54611yescharacteristic
201C2×C281#54811yescharacteristic
202C2×C281#55611yescharacteristic
203C2×C281#55911yescharacteristic
204D281—42no—
205C281#236711yescharacteristic, complemented, Sylow
206#2367—2811nomaximal, Sylow
207C2×#124—2811no—
208C2×C4×Q8—2811no—
209C2×C4×D4—2811no—
210#391—2811no—
211#390—2811no—
212#388—2811no—
213#388—2811no—
214#388—2811no—
215#388D28111yescharacteristic, complemented
216#385—2811no—
217#385—2811no—
218C4×C4⋊C4—2811no—
219C4×C4⋊C4—2811no—
220C4×C22⋊C4—2811no—
221C4×C22⋊C4—2811no—
222C22×Q8—2811no—
223C22×D4—2811no—
224C23×C4—2811no—
225C23×C4—2811no—
226#124—2818no—
227C4×Q8—5624no—
228C4×D4—5624no—
229C2×C4⋊C4—2811no—
230C2×C4⋊C4—2811no—
231C2×C4⋊C4—2811no—
232C2×C4⋊C4—2811no—
233C2×C4⋊C4—2811no—
234C2×C4⋊C4C2×D28111yescharacteristic
235C2×C22⋊C4—2811no—
236C2×C22⋊C4—2811no—
237C2×C22⋊C4—2811no—
238C2×C22⋊C4—2811no—
239C2×C22⋊C4—2811no—
240C2×C22⋊C4—2811no—
241C2×C22⋊C4—2811no—
242C2×C22⋊C4C2×D28111yescharacteristic
243C2×C22⋊C4C2×D28111yescharacteristic
244C2×C22⋊C4C2×D28111yescharacteristic
245C2×C42—2811no—
246C2×C42—2811no—
247C2×C42—2811no—
248C2×C42—2811no—
249C2×C42—2811no—
250C2×C42—2811no—
251C2×C42C2×D28111yescharacteristic
252#95—2811no—
253#95—2811no—
254#95—2811no—
255#95—2811no—
256#95—2811no—
257#95—2811no—
258#95C2×D28111yescharacteristic
259#95C2×D28111yescharacteristic
260C24—2811no—
261C24C22×D28111yescharacteristic
262C2×Q8—2814no—
263C2×Q8—5622no—
264C2×Q8—5622no—
265C2×D4—2814no—
266C2×D4—5622no—
267C2×D4—5622no—
268C22×C4—2811no—
269C22×C4—2811no—
270C22×C4—2811no—
271C22×C4—2811no—
272C22×C4—2811no—
273C22×C4—2811no—
274C22×C4—2811no—
275C22×C4—5622no—
276C22×C4—5622no—
277C22×C4—5622no—
278C22×C4—5622no—
279C22×C4—11241no—
280C22×C4—11241no—
281C22×C4C22×D28111yescharacteristic
282C22×C4C22×D28111yescharacteristic
283C22×C4C22×D28111yescharacteristic
284C22×C4C22×D28111yescharacteristic
285C22×C4C22×D28111yescharacteristic
286C22×C4C22×D28111yescharacteristic
287C4⋊C4—22no—
288C4⋊C4—2814no—
289C4⋊C4—5622no—
290C4⋊C4—5622no—
291C4⋊C4—5622no—
292C4⋊C4—5622no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—2814no—
296C22⋊C4—2814no—
297C22⋊C4—2814no—
298C22⋊C4—5622no—
299C22⋊C4—5622no—
300C22⋊C4—11241no—
301C22⋊C4—11241no—
302C22⋊C4C4×D28114yescomplemented
303C42—22no—
304C42—2814no—
305C42—5622no—
306C42—5622no—
307C42—5622no—
308C42—11241no—
309C42—11241no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—2812no—
317C23—5621no—
318C23—5621no—
319C23—5621no—
320C23—5621no—
321C23—5621no—
322C23—5621no—
323C23C2×C4×D28112yes—
324C23C23×D28111yescharacteristic
325Q8—5628no—
326D4—5628no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—2812no—
342C2×C4—2812no—
343C2×C4—2812no—
344C2×C4—2812no—
345C2×C4—2812no—
346C2×C4—2812no—
347C2×C4—2812no—
348C2×C4—5621no—
349C2×C4—5621no—
350C2×C4—5621no—
351C2×C4—5621no—
352C2×C4—5621no—
353C2×C4—5621no—
354C2×C4—5621no—
355C2×C4—5621no—
356C2×C4—5621no—
357C2×C4—5621no—
358C2×C4—5621no—
359C2×C4—5621no—
360C2×C4—5621no—
361C2×C4—5621no—
362C2×C4—11244no—
363C2×C4—11244no—
364C2×C4C2×C4×D28112yes—
365C2×C4C2×C4×D28112yes—
366C2×C4D4×D28112yes—
367C2×C4#1798513712yes—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—5622no—
376C22—5622no—
377C22—5622no—
378C22—11241no—
379C22—11241no—
380C22—11241no—
381C22—11241no—
382C22C22×C4×D28111yescharacteristic
383C22C2×D4×D28111yescharacteristic
384C22#41×D28111yescharacteristic
385C22#41×D28111yescharacteristic
386C22C2×#1798513711yescharacteristic
387C22#2258292511yescharacteristic
388C22#2258292611yescharacteristic
389C4—22no—
390C4—22no—
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—2814no—
396C4—5622no—
397C4—5622no—
398C4—5622no—
399C4—5622no—
400C4—11241no—
401C4—11241no—
402C2—42no—
403C2—11242no—
404C2C4×D4×D28111yescharacteristic
405C2C4×#1798513711yescharacteristic
406C2#3182394311yescharacteristic
407C2#3182410511yescharacteristic
408C2#3182411911yescharacteristic
409C2#3182418011yescharacteristic
410C2#3182419511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#388×C281C2
socle, cosocleC23×C281C24
prime radicalC22×C22⋊D281C22
hypercenter#388D281
hypocenterC281#2367
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic562C2semidirect
4. #31823367C2semidirect
6. #31823357C2semidirect
7. #31823355C2semidirect
8. #31823353C2semidirect
9. #31823338C2semidirect
10. #31823337C2semidirect
11. C4⋊C4×Dic281C2semidirect
12. #31823314C2semidirect
13. C22⋊C4×Dic281C2semidirect
14. C4×#17985115C2semidirect
15. #388×C281C2semidirect
20. #22582865C4semidirect
57. C2×Dic562C2×C4semidirect
80. C22⋊Dic281C2×C4semidirect
84. #17985115C2×C4semidirect
85. #17985115C2×C4semidirect
91. C4×Dic281C2×C4semidirect
102. C22⋊C4×C281C2×C4semidirect
205. C281#2367semidirect
215. #388D281semidirect
302. C22⋊C4C4×D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828652
C2×C4×Dic5622
C2×#225828392
#318233672
#318233632
#318233572
#318233552
#318233532
#318233382
#318233372
C4⋊C4×Dic2812
#318233142
C22⋊C4×Dic2812
C4×#179851152
#388×C2812
#2367281