Finite Group Databasebeta

← #49097976

Subgroups — #49097976

Order 35968.

632 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22582864C211yesmaximal, characteristic
2C2×C4×D1124C211yesmaximal, characteristic
3C2×C4⋊C4×D281C211yesmaximal, characteristic, complemented
4#31823362C211yesmaximal, characteristic, complemented
5#31823360C211yesmaximal, characteristic, complemented
6#31823355C211yesmaximal, characteristic, complemented
7#31823352C211yesmaximal, characteristic, complemented
8#31823347C211yesmaximal, characteristic, complemented
9#31823341C211yesmaximal, characteristic
10#31823337C211yesmaximal, characteristic, complemented
11#31823337C211yesmaximal, characteristic, complemented
12#31823334C211yesmaximal, characteristic, complemented
13#31823325C211yesmaximal, characteristic, complemented
14#31823310C211yesmaximal, characteristic, complemented
15#387×C281C211yesmaximal, characteristic, complemented
16C22×D1124C2211yescharacteristic
17C22×C4×D281C2211yescharacteristic
18C22×C4×D281C2211yescharacteristic
19C22×C4×D281C2211yescharacteristic
20C22×C4×D281C2211yescharacteristic
21#22582864C418yescomplemented
22C4×D1124—24no—
23C2×C4⋊Dic281C2211yescharacteristic
24C2×C4⋊Dic281C2211yescharacteristic
25C2×C4⋊Dic281C2211yescharacteristic
26C2×#17985117C2211yescharacteristic
27C2×#17985117C2211yescharacteristic
28C2×#17985117C2211yescharacteristic
29C2×#17985117C2211yescharacteristic
30C4⋊C4×D281—24no—
31C2×#17985115C2211yescharacteristic
32C2×#17985115C2211yescharacteristic
33C2×#17985115C2211yescharacteristic
34C2×#17985115C2211yescharacteristic
35C2×#17985115C2211yescharacteristic
36C2×#17985115C2211yescharacteristic
37C2×#17985115C2211yescharacteristic
38C2×#17985115C2211yescharacteristic
39C2×C4×Dic281C2211yescharacteristic
40C2×C4×Dic281C2211yescharacteristic
41#22582786C2211yescharacteristic
42#22582786C2211yescharacteristic
43#22582786C2211yescharacteristic
44#22582786C2211yescharacteristic
45#22582786C2211yescharacteristic
46#22582786C2211yescharacteristic
47C2×C4⋊C4×C281C2211yescharacteristic
48C2×C4⋊C4×C281C2211yescharacteristic
49C2×C42×C281C2211yescharacteristic
50#95×C281C2211yescharacteristic
51#95×C281C2211yescharacteristic
52#95×C281C2211yescharacteristic
53#95×C281C2211yescharacteristic
54C23×D281C2311yescharacteristic
55C23×D281C2311yescharacteristic
56C2×D1124—22no—
57C2×D1124—22no—
58C2×D1124C2×C414yes—
59C22×Dic281C2311yescharacteristic
60C22×Dic281C2311yescharacteristic
61C22×Dic281C2311yescharacteristic
62C22×Dic281C2311yescharacteristic
63C22×Dic281C2311yescharacteristic
64C22×Dic281C2311yescharacteristic
65C2×C4×D281—22no—
66C2×C4×D281—22no—
67C2×C4×D281—22no—
68C2×C4×D281—22no—
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×D281C2×C414yescomplemented
76C2×C4×D281D414yes—
77C4⋊Dic281—22no—
78C4⋊Dic281—22no—
79C4⋊Dic281—41no—
80#17985117—22no—
81#17985117—22no—
82#17985117—41no—
83#17985117C2×C414yescomplemented
84#17985115—22no—
85#17985115—22no—
86#17985115—22no—
87#17985115—41no—
88#17985115—41no—
89#17985115C2×C414yescomplemented
90#17985115C2×C414yescomplemented
91#17985115C2×C414yescomplemented
92C4×Dic281—41no—
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—22no—
102C4⋊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×D281—21no—
111C22×D281—21no—
112C22×D281—21no—
113C22×D281—21no—
114C22×D281C22×C412yes—
115C22×D281C22×C412yes—
116C22×D281C2×D412yes—
117C22×D281#4112yes—
118D1124—28no—
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—21no—
128C2×Dic281—21no—
129C2×Dic281—21no—
130C2×Dic281—21no—
131C2×Dic281—21no—
132C2×Dic281—21no—
133C2×Dic281—21no—
134C2×Dic281C22×C412yes—
135C2×Dic281C22×C412yes—
136C2×Dic281C2×D412yes—
137C4×D281—28no—
138C4×D281—44no—
139C4×D281—44no—
140C4×D281—44no—
141C23×C281C2411yescharacteristic
142C2×C4×C281—21no—
143C2×C4×C281—21no—
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×C281—21no—
159C2×C4×C281C22×C412yes—
160C2×C4×C281C22×C412yes—
161C2×C4×C281C22×C412yes—
162C2×C4×C281C2×D412yes—
163C22×C281C23×C411yescharacteristic
164C22×C281C22×D411yescharacteristic
165C22×C281C2×#4111yescharacteristic
166C22×C281H(5,𝔽2)11yescharacteristic
167C22×C281H(5,𝔽2)11yescharacteristic
168C22×C2812−1+411yescharacteristic
169C22×C2812−1+411yescharacteristic
170C2×D281—22no—
171C2×D281—22no—
172C2×D281—22no—
173C2×D281—22no—
174C2×D281—22no—
175C2×D281—22no—
176C2×D281—22no—
177C2×D281—22no—
178C2×D281—22no—
179C2×D281—41no—
180C2×D281—41no—
181C2×D281—41no—
182C2×D281—41no—
183C2×D281C4×D414yes—
184C4×C281—22no—
185C4×C281—22no—
186C4×C281—22no—
187C4×C281—22no—
188C4×C281—41no—
189C4×C281—41no—
190C4×C281—41no—
191Dic281—22no—
192Dic281—22no—
193Dic281—22no—
194Dic281—41no—
195Dic281—41no—
196Dic281—41no—
197C2×C281C2×C4×D411yescharacteristic
198C2×C281#52011yescharacteristic
199C2×C281#52011yescharacteristic
200C2×C281#53411yescharacteristic
201C2×C281#53611yescharacteristic
202C2×C281#53911yescharacteristic
203C2×C281#53911yescharacteristic
204D281—24no—
205D281—42no—
206C281#232211yescharacteristic, complemented, Sylow
207#2322—2811nomaximal, Sylow
208C2×#123—2811no—
209C2×C4×D4—2811no—
210C22×C4⋊C4—2811no—
211#389—2811no—
212#389—2811no—
213#388—2811no—
214#388—2811no—
215#387—2811no—
216#387D28111yescharacteristic, complemented
217#386—2811no—
218#385—2811no—
219#385—2811no—
220#385—2811no—
221#381—2811no—
222C4×C22⋊C4—2811no—
223C22×D4—2811no—
224C23×C4—2811no—
225C23×C4—2811no—
226C23×C4—2811no—
227C23×C4—2811no—
228#123—2818no—
229C4×D4—5624no—
230C2×C4⋊C4—2811no—
231C2×C4⋊C4—2811no—
232C2×C4⋊C4—2811no—
233C2×C4⋊C4—2811no—
234C2×C4⋊C4—2811no—
235C2×C4⋊C4—2811no—
236C2×C4⋊C4—2811no—
237C2×C4⋊C4—5624no—
238C2×C4⋊C4C2×D28111yescharacteristic
239C2×C4⋊C4C2×D28111yescharacteristic
240C2×C22⋊C4—2811no—
241C2×C22⋊C4—2811no—
242C2×C22⋊C4—2811no—
243C2×C22⋊C4—2811no—
244C2×C22⋊C4—2811no—
245C2×C22⋊C4—2811no—
246C2×C22⋊C4—2811no—
247C2×C22⋊C4—2811no—
248C2×C42—2811no—
249C2×C42—2811no—
250C2×C42C2×D28111yescharacteristic
251#95—2811no—
252#95—2811no—
253#95—2811no—
254#95—2811no—
255#95—2811no—
256#95—2811no—
257#95C2×D28111yescharacteristic
258#95C2×D28111yescharacteristic
259#95C2×D28111yescharacteristic
260#95C2×D28111yescharacteristic
261C24—2811no—
262C24—2811no—
263C2×D4—2814no—
264C2×D4—5622no—
265C2×D4—5622no—
266C22×C4—2811no—
267C22×C4—2811no—
268C22×C4—2811no—
269C22×C4—2814no—
270C22×C4—2814no—
271C22×C4—2811no—
272C22×C4—2811no—
273C22×C4—2811no—
274C22×C4—5622no—
275C22×C4—5622no—
276C22×C4—5622no—
277C22×C4—5622no—
278C22×C4—11241no—
279C22×C4—11241no—
280C22×C4—11241no—
281C22×C4—11241no—
282C22×C4—11241no—
283C22×C4—11241no—
284C22×C4C22×D28111yescharacteristic
285C22×C4C22×D28111yescharacteristic
286C22×C4C22×D28111yescharacteristic
287C22×C4C22×D28111yescharacteristic
288C22×C4C22×D28111yescharacteristic
289C22×C4C22×D28111yescharacteristic
290C22×C4C22×D28111yescharacteristic
291C4⋊C4—22no—
292C4⋊C4—2814no—
293C4⋊C4—5622no—
294C4⋊C4—5622no—
295C4⋊C4—5622no—
296C4⋊C4—5622no—
297C4⋊C4—11241no—
298C4⋊C4—11241no—
299C4⋊C4C4×D28114yescomplemented
300C22⋊C4—2814no—
301C22⋊C4—2814no—
302C22⋊C4—2814no—
303C22⋊C4—5622no—
304C22⋊C4—5622no—
305C22⋊C4—5622no—
306C22⋊C4—11241no—
307C22⋊C4—11241no—
308C42—22no—
309C42—11241no—
310C42—11241no—
311C23—2812no—
312C23—2812no—
313C23—2812no—
314C23—2812no—
315C23—5621no—
316C23—5621no—
317C23—5621no—
318C23—5621no—
319C23—5621no—
320C23—5621no—
321C23—5621no—
322C23—5621no—
323C23—5621no—
324C23—5621no—
325C23C23×D28111yescharacteristic
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—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—2812no—
345C2×C4—2812no—
346C2×C4—2812no—
347C2×C4—5628no—
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—5621no—
363C2×C4—11244no—
364C2×C4—11244no—
365C2×C4—11244no—
366C2×C4C2×C4×D28112yes—
367C2×C4C2×C4×D28112yes—
368C2×C4C2×C4×D28112yes—
369C2×C4D4×D28112yes—
370C22—2814no—
371C22—5622no—
372C22—5622no—
373C22—5622no—
374C22—5622no—
375C22—5622no—
376C22—5622no—
377C22—5622no—
378C22—5622no—
379C22—5622no—
380C22—11241no—
381C22—11241no—
382C22—11241no—
383C22—11241no—
384C22C22×C4×D28111yescharacteristic
385C22C2×D4×D28111yescharacteristic
386C22#41×D28111yescharacteristic
387C22#2258292511yescharacteristic
388C22#2258292511yescharacteristic
389C22#2258292611yescharacteristic
390C22#2258292711yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—5622no—
399C4—5622no—
400C4—5622no—
401C4—11241no—
402C4—11241no—
403C4—11241no—
404C2—5624no—
405C2—11242no—
406C2C4×D4×D28111yescharacteristic
407C2#3182394311yescharacteristic
408C2#3182394511yescharacteristic
409C2#3182402411yescharacteristic
410C2#3182403611yescharacteristic
411C2#3182405411yescharacteristic
412C2#3182406111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#387×C281C2
socle, cosocleC23×C281C24
prime radicalC22×D1124C22
hypercenter#387D281
hypocenterC281#2322
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×D281C2semidirect
4. #31823362C2semidirect
5. #31823360C2semidirect
6. #31823355C2semidirect
7. #31823352C2semidirect
8. #31823347C2semidirect
10. #31823337C2semidirect
11. #31823337C2semidirect
12. #31823334C2semidirect
13. #31823325C2semidirect
14. #31823310C2semidirect
15. #387×C281C2semidirect
21. #22582864C4semidirect
75. C2×C4×D281C2×C4semidirect
83. #17985117C2×C4semidirect
89. #17985115C2×C4semidirect
90. #17985115C2×C4semidirect
91. #17985115C2×C4semidirect
102. C4⋊C4×C281C2×C4semidirect
206. C281#2322semidirect
216. #387D281semidirect
299. C4⋊C4C4×D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828642
C2×C4×D11242
C2×C4⋊C4×D2812
#318233622
#318233602
#318233552
#318233522
#318233472
#318233412
#318233372
#318233342
#318233252
#318233102
#387×C2812
#2322281