Finite Group Databasebeta

← #49098002

Subgroups — #49098002

Order 35968.

696 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22582854C211yesmaximal, characteristic
2C2×C4×D1124C211yesmaximal, characteristic, complemented
3C2×#22582841C211yesmaximal, 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#31823322C211yesmaximal, characteristic, complemented
14#95×D281C211yesmaximal, characteristic, complemented
15#387×C281C211yesmaximal, characteristic, complemented
16C22×D1124C2211yescharacteristic
17C22×D1124C2211yescharacteristic
18C22×D1124C2211yescharacteristic
19C22×C4×D281C2211yescharacteristic
20C22×C4×D281C2211yescharacteristic
21C22×C4×D281C2211yescharacteristic
22C22×C4×D281C2211yescharacteristic
23C22×C4×D281C2211yescharacteristic
24#22582854C418yescomplemented
25C4×D1124—24no—
26#22582841—24no—
27C2×C4⋊Dic281C2211yescharacteristic
28C2×#17985117C2211yescharacteristic
29C2×#17985117C2211yescharacteristic
30C2×#17985115C2211yescharacteristic
31C2×#17985115C2211yescharacteristic
32C2×#17985115C2211yescharacteristic
33C2×#17985115C2211yescharacteristic
34C2×#17985115C2211yescharacteristic
35C2×#17985115C2211yescharacteristic
36C2×#17985115C2211yescharacteristic
37C2×#17985115C2211yescharacteristic
38C2×#17985115C2211yescharacteristic
39C2×#17985115C2211yescharacteristic
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
56C23×D281C2311yescharacteristic
57C2×D1124—22no—
58C2×D1124—22no—
59C2×D1124—22no—
60C2×D1124—22no—
61C2×D1124—41no—
62C2×D1124—41no—
63C2×D1124C2×C414yescomplemented
64C2×D1124C2×C414yescomplemented
65C2×D1124C2×C414yescomplemented
66C22×Dic281C2311yescharacteristic
67C22×Dic281C2311yescharacteristic
68C22×Dic281C2311yescharacteristic
69C22×Dic281C2311yescharacteristic
70C22×Dic281C2311yescharacteristic
71C2×C4×D281—22no—
72C2×C4×D281—22no—
73C2×C4×D281—22no—
74C2×C4×D281—41no—
75C2×C4×D281—41no—
76C2×C4×D281—41no—
77C2×C4×D281—41no—
78C2×C4×D281—41no—
79C2×C4×D281—41no—
80C2×C4×D281—41no—
81C2×C4×D281—41no—
82C2×C4×D281—41no—
83C2×C4×D281—41no—
84C2×C4×D281C2×C414yescomplemented
85C2×C4×D281D414yescomplemented
86C4⋊Dic281—22no—
87#17985117—41no—
88#17985117—41no—
89#17985115—22no—
90#17985115—22no—
91#17985115—22no—
92#17985115—22no—
93#17985115—41no—
94#17985115—41no—
95#17985115—41no—
96#17985115—41no—
97#17985115C2×C414yescomplemented
98#17985115C2×C414yescomplemented
99C4×Dic281—22no—
100C22×C4×C281C2311yescharacteristic
101C22×C4×C281C2311yescharacteristic
102C22×C4×C281C2311yescharacteristic
103C22×C4×C281C2311yescharacteristic
104C22×C4×C281C2311yescharacteristic
105C22×C4×C281C2311yescharacteristic
106C22×C4×C281C2311yescharacteristic
107C4⋊C4×C281—22no—
108C4⋊C4×C281C2×C414yescomplemented
109C42×C281—22no—
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×D281—21no—
123C22×D281—21no—
124C22×D281—21no—
125C22×D281—21no—
126C22×D281C22×C412yes—
127C22×D281C22×C412yes—
128C22×D281C22×C412yes—
129C22×D281C2×D412yes—
130C22×D281#4112yes—
131D1124—28no—
132D1124—28no—
133D1124—44no—
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×Dic281—21no—
143C2×Dic281—21no—
144C2×Dic281—21no—
145C2×Dic281—21no—
146C2×Dic281—21no—
147C2×Dic281C22×C412yes—
148C2×Dic281C2×D412yes—
149C4×D281—44no—
150C4×D281—44no—
151C4×D281—44no—
152C4×D281—44no—
153C4×D281—44no—
154C23×C281C2411yescharacteristic
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×C281—21no—
166C2×C4×C281—21no—
167C2×C4×C281—21no—
168C2×C4×C281—21no—
169C2×C4×C281—21no—
170C2×C4×C281—21no—
171C2×C4×C281—21no—
172C2×C4×C281C22×C412yes—
173C2×C4×C281C22×C412yes—
174C2×C4×C281C22×C412yes—
175C2×C4×C281C2×D412yes—
176C22×C281C23×C411yescharacteristic
177C22×C281C22×D411yescharacteristic
178C22×C281C2×#4111yescharacteristic
179C22×C281H(5,𝔽2)11yescharacteristic
180C22×C281H(5,𝔽2)11yescharacteristic
181C22×C281H(5,𝔽2)11yescharacteristic
182C22×C2812−1+411yescharacteristic
183C2×D281—22no—
184C2×D281—22no—
185C2×D281—22no—
186C2×D281—22no—
187C2×D281—22no—
188C2×D281—22no—
189C2×D281—22no—
190C2×D281—22no—
191C2×D281—22no—
192C2×D281—22no—
193C2×D281—22no—
194C2×D281—22no—
195C2×D281—41no—
196C2×D281—41no—
197C2×D281—41no—
198C2×D281—41no—
199C2×D281—41no—
200C2×D281—41no—
201C2×D281—41no—
202C2×D281—41no—
203C2×D281C4×D414yes—
204C4×C281—22no—
205C4×C281—22no—
206C4×C281—22no—
207C4×C281—22no—
208C4×C281—41no—
209C4×C281—41no—
210C4×C281—41no—
211Dic281—22no—
212Dic281—22no—
213Dic281—41no—
214Dic281—41no—
215Dic281—41no—
216C2×C281C2×C4×D411yescharacteristic
217C2×C281#51811yescharacteristic
218C2×C281#52011yescharacteristic
219C2×C281#53411yescharacteristic
220C2×C281#53711yescharacteristic
221C2×C281#53811yescharacteristic
222C2×C281#53911yescharacteristic
223D281—24no—
224D281—42no—
225D281—42no—
226C281#232511yescharacteristic, complemented, Sylow
227#2325—2811nomaximal, Sylow
228C2×#121—2811no—
229C2×C4×D4—2811no—
230C2×C4×D4—2811no—
231#388—2811no—
232#388—2811no—
233#387—2811no—
234#387D28111yescharacteristic, complemented
235#386—2811no—
236#386—2811no—
237#386—2811no—
238#386—2811no—
239#385—2811no—
240#385—2811no—
241#380—2811no—
242C2×#95—2811no—
243C22×D4—2811no—
244C22×D4—2811no—
245C22×D4—2811no—
246C23×C4—2811no—
247C23×C4—2811no—
248C23×C4—2811no—
249C23×C4—2811no—
250C23×C4—2811no—
251#121—2818no—
252C4×D4—5624no—
253C4×D4—5624no—
254C2×C4⋊C4—2811no—
255C2×C4⋊C4—2811no—
256C2×C4⋊C4—2811no—
257C2×C4⋊C4C2×D28111yescharacteristic
258C2×C4⋊C4C2×D28111yescharacteristic
259C2×C22⋊C4—2811no—
260C2×C22⋊C4—2811no—
261C2×C22⋊C4—2811no—
262C2×C22⋊C4—2811no—
263C2×C22⋊C4—2811no—
264C2×C22⋊C4—2811no—
265C2×C22⋊C4—2811no—
266C2×C22⋊C4—2811no—
267C2×C22⋊C4—2811no—
268C2×C22⋊C4—2811no—
269C2×C42—2811no—
270C2×C42C2×D28111yescharacteristic
271#95—2811no—
272#95—2811no—
273#95—2811no—
274#95—2811no—
275#95—2811no—
276#95—2811no—
277#95C2×D28111yescharacteristic
278#95C2×D28111yescharacteristic
279#95C2×D28111yescharacteristic
280#95C2×D28111yescharacteristic
281C24—2811no—
282C24—2811no—
283C24—2811no—
284C2×D4—2814no—
285C2×D4—2814no—
286C2×D4—2814no—
287C2×D4—5622no—
288C2×D4—5622no—
289C2×D4—5622no—
290C2×D4—5622no—
291C2×D4—11241no—
292C2×D4—11241no—
293C22×C4—2811no—
294C22×C4—2811no—
295C22×C4—2814no—
296C22×C4—2814no—
297C22×C4—2811no—
298C22×C4—2811no—
299C22×C4—2811no—
300C22×C4—5622no—
301C22×C4—5622no—
302C22×C4—5622no—
303C22×C4—11241no—
304C22×C4—11241no—
305C22×C4—11241no—
306C22×C4—11241no—
307C22×C4—11241no—
308C22×C4—11241no—
309C22×C4—11241no—
310C22×C4—11241no—
311C22×C4—11241no—
312C22×C4—11241no—
313C22×C4C22×D28111yescharacteristic
314C22×C4C22×D28111yescharacteristic
315C22×C4C22×D28111yescharacteristic
316C22×C4C22×D28111yescharacteristic
317C22×C4C22×D28111yescharacteristic
318C22×C4C22×D28111yescharacteristic
319C22×C4C22×D28111yescharacteristic
320C4⋊C4—22no—
321C4⋊C4—5622no—
322C4⋊C4—11241no—
323C4⋊C4—11241no—
324C4⋊C4C4×D28114yescomplemented
325C22⋊C4—2814no—
326C22⋊C4—2814no—
327C22⋊C4—5622no—
328C22⋊C4—5622no—
329C22⋊C4—5622no—
330C22⋊C4—5622no—
331C22⋊C4—11241no—
332C22⋊C4—11241no—
333C22⋊C4—11241no—
334C22⋊C4—11241no—
335C42—22no—
336C42—5622no—
337C23—2812no—
338C23—2812no—
339C23—2812no—
340C23—2812no—
341C23—2812no—
342C23—5621no—
343C23—5621no—
344C23—5621no—
345C23—5621no—
346C23—5621no—
347C23—5621no—
348C23—5621no—
349C23—5621no—
350C23—5621no—
351C23—5621no—
352C23—5621no—
353C23—5621no—
354C23—5621no—
355C23—5621no—
356C23—5621no—
357C23—5621no—
358C23C23×D28111yescharacteristic
359D4—5628no—
360D4—5628no—
361D4—11244no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—2812no—
380C2×C4—2812no—
381C2×C4—5621no—
382C2×C4—5621no—
383C2×C4—5621no—
384C2×C4—5621no—
385C2×C4—5621no—
386C2×C4—5621no—
387C2×C4—5621no—
388C2×C4—5621no—
389C2×C4—5621no—
390C2×C4—5621no—
391C2×C4—5621no—
392C2×C4—5621no—
393C2×C4—5621no—
394C2×C4—11244no—
395C2×C4—11244no—
396C2×C4—11244no—
397C2×C4—11244no—
398C2×C4—11244no—
399C2×C4C2×C4×D28112yes—
400C2×C4C2×C4×D28112yes—
401C2×C4C2×C4×D28112yes—
402C2×C4D4×D28112yes—
403C22—2814no—
404C22—5622no—
405C22—5622no—
406C22—5622no—
407C22—5622no—
408C22—5622no—
409C22—5622no—
410C22—5622no—
411C22—5622no—
412C22—5622no—
413C22—5622no—
414C22—5622no—
415C22—5622no—
416C22—11241no—
417C22—11241no—
418C22—11241no—
419C22—11241no—
420C22—11241no—
421C22—11241no—
422C22—11241no—
423C22—11241no—
424C22C22×C4×D28111yescharacteristic
425C22C2×D4×D28111yescharacteristic
426C22#41×D28111yescharacteristic
427C22#2258292511yescharacteristic
428C22#2258292511yescharacteristic
429C22#2258292511yescharacteristic
430C22#2258292711yescharacteristic
431C4—22no—
432C4—22no—
433C4—22no—
434C4—22no—
435C4—41no—
436C4—41no—
437C4—41no—
438C4—5622no—
439C4—5622no—
440C4—11241no—
441C4—11241no—
442C4—11241no—
443C2—5624no—
444C2—11242no—
445C2—11242no—
446C2C4×D4×D28111yescharacteristic
447C2#3182393711yescharacteristic
448C2#3182394511yescharacteristic
449C2#3182402411yescharacteristic
450C2#3182404311yescharacteristic
451C2#3182405211yescharacteristic
452C2#3182406111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#387×C281C2
socle, cosocleC23×C281C24
prime radicalC2×#22582854C2
hypercenter#387D281
hypocenterC281#2325
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C2×C4×D1124C2semidirect
3. C2×#22582841C2semidirect
4. #31823354C2semidirect
5. #31823352C2semidirect
6. #31823349C2semidirect
7. #31823341C2semidirect
8. #31823341C2semidirect
9. #31823341C2semidirect
10. #31823341C2semidirect
11. #31823337C2semidirect
12. #31823334C2semidirect
13. #31823322C2semidirect
14. #95×D281C2semidirect
15. #387×C281C2semidirect
24. #22582854C4semidirect
63. C2×D1124C2×C4semidirect
64. C2×D1124C2×C4semidirect
65. C2×D1124C2×C4semidirect
84. C2×C4×D281C2×C4semidirect
85. C2×C4×D281D4semidirect
97. #17985115C2×C4semidirect
98. #17985115C2×C4semidirect
108. C4⋊C4×C281C2×C4semidirect
226. C281#2325semidirect
234. #387D281semidirect
324. 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
C2×C4×D11242
C2×#225828412
#318233542
#318233522
#318233492
#318233412
#318233372
#318233342
#318233222
#95×D2812
#387×C2812
#2325281