Finite Group Databasebeta

← #49097956

Subgroups — #49097956

Order 35968.

808 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22582849C211yesmaximal, characteristic
2C2×#22582841C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D281C211yesmaximal, characteristic, complemented
4#31823365C211yesmaximal, characteristic, complemented
5#31823363C211yesmaximal, characteristic, complemented
6#31823356C211yesmaximal, characteristic, complemented
7#31823353C211yesmaximal, characteristic, complemented
8#31823352C211yesmaximal, characteristic, complemented
9#31823341C211yesmaximal, characteristic, complemented
10#31823341C211yesmaximal, characteristic, complemented
11#31823339C211yesmaximal, characteristic, complemented
12#31823337C211yesmaximal, characteristic, complemented
13#31823318C211yesmaximal, characteristic, complemented
14C4×#17985115C211yesmaximal, characteristic, complemented
15#388×C281C211yesmaximal, characteristic, complemented
16C24×D281C2211yescharacteristic
17C22×D1124C2211yescharacteristic
18C22×D1124C2211yescharacteristic
19C22×C22⋊D281C2211yescharacteristic
20C22×C4×D281C2211yescharacteristic
21C22×C4×D281C2211yescharacteristic
22C22×C4×D281C2211yescharacteristic, complemented
23#22582849C418yescomplemented
24#22582841—24no—
25C2×C4⋊Dic281C2211yescharacteristic, complemented
26C2×#17985117C2211yescharacteristic, complemented
27C2×C22⋊Dic281C2211yescharacteristic
28C2×C22⋊Dic281C2211yescharacteristic
29C2×#17985115C2211yescharacteristic
30C2×#17985115C2211yescharacteristic
31C2×#17985115C2211yescharacteristic
32C2×#17985115C2211yescharacteristic
33C2×#17985115C2211yescharacteristic
34C2×#17985115C2211yescharacteristic
35C2×#17985115C2211yescharacteristic
36C2×#17985115C2211yescharacteristic
37C2×#17985115C2211yescharacteristic, complemented
38C2×#17985115C2211yescharacteristic, complemented
39C2×#17985115C2211yescharacteristic, complemented
40C22⋊C4×D281—24no—
41C2×C4×Dic281C2211yescharacteristic, complemented
42C2×C4×Dic281C2211yescharacteristic, complemented
43#22582786C2211yescharacteristic, complemented
44#22582786C2211yescharacteristic, complemented
45#22582786C2211yescharacteristic, complemented
46#22582786C2211yescharacteristic, complemented
47C2×C4⋊C4×C281C2211yescharacteristic, complemented
48C2×C22⋊C4×C281C2211yescharacteristic
49C2×C22⋊C4×C281C2211yescharacteristic
50C2×C22⋊C4×C281C2211yescharacteristic
51C2×C42×C281C2211yescharacteristic, complemented
52#95×C281C2211yescharacteristic, complemented
53#95×C281C2211yescharacteristic, complemented
54C23×D281—22no—
55C23×D281—22no—
56C23×D281—41no—
57C23×D281—41no—
58C23×D281—41no—
59C23×D281—41no—
60C23×D281C2×C414yescomplemented
61C23×D281C2311yescharacteristic
62C23×D281C2311yescharacteristic
63C23×D281C2311yescharacteristic
64C2×D1124—22no—
65C2×D1124—22no—
66C2×D1124—41no—
67C2×D1124—41no—
68C2×D1124C2×C414yes—
69C2×D1124C2×C414yescomplemented
70C2×C22⋊D281—41no—
71C2×C22⋊D281—41no—
72C2×C22⋊D281C2×C414yescomplemented
73C22×Dic281C2311yescharacteristic
74C22×Dic281C2311yescharacteristic
75C22×Dic281C2311yescharacteristic
76C22×Dic281C2311yescharacteristic
77C22×Dic281C2311yescharacteristic
78C2×C4×D281—22no—
79C2×C4×D281—22no—
80C2×C4×D281—41no—
81C2×C4×D281—41no—
82C2×C4×D281—41no—
83C2×C4×D281—41no—
84C2×C4×D281—41no—
85C2×C4×D281—41no—
86C2×C4×D281D414yescomplemented
87C4⋊Dic281—41no—
88#17985117—41no—
89C22⋊Dic281—22no—
90C22⋊Dic281—41no—
91#17985115—22no—
92#17985115—22no—
93#17985115—22no—
94#17985115—22no—
95#17985115—22no—
96#17985115—41no—
97#17985115—41no—
98#17985115—41no—
99#17985115—41no—
100#17985115C2×C414yescomplemented
101#17985115C2×C414yescomplemented
102C4×Dic281—22no—
103C4×Dic281—41no—
104C24×C281C2311yescharacteristic
105C22×C4×C281C2311yescharacteristic
106C22×C4×C281C2311yescharacteristic
107C22×C4×C281C2311yescharacteristic
108C22×C4×C281C2311yescharacteristic
109C22×C4×C281C2311yescharacteristic
110C22×C4×C281C2311yescharacteristic
111C4⋊C4×C281—22no—
112C22⋊C4×C281—22no—
113C22⋊C4×C281—41no—
114C22⋊C4×C281C2×C414yescomplemented
115C42×C281—41no—
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×D281—21no—
127C22×D281—21no—
128C22×D281—21no—
129C22×D281—21no—
130C22×D281—21no—
131C22×D281—21no—
132C22×D281—28no—
133C22×D281—44no—
134C22×D281—44no—
135C22×D281—44no—
136C22×D281—44no—
137C22×D281—44no—
138C22×D281—44no—
139C22×D281C22×C412yes—
140C22×D281C22×C412yes—
141C22×D281C22×C412yes—
142C22×D281C2×D412yes—
143C22×D281#4112yes—
144D1124—28no—
145D1124—44no—
146C22⋊D281—44no—
147C2×Dic281—21no—
148C2×Dic281—21no—
149C2×Dic281—21no—
150C2×Dic281—21no—
151C2×Dic281—21no—
152C2×Dic281—21no—
153C2×Dic281—21no—
154C2×Dic281—21no—
155C2×Dic281—21no—
156C2×Dic281—21no—
157C2×Dic281—21no—
158C2×Dic281—21no—
159C2×Dic281—21no—
160C2×Dic281C22×C412yes—
161C2×Dic281C2×D412yes—
162C4×D281—44no—
163C4×D281—44no—
164C4×D281—44no—
165C23×C281—21no—
166C23×C281—21no—
167C23×C281—21no—
168C23×C281—21no—
169C23×C281—21no—
170C23×C281—21no—
171C23×C281C22×C412yes—
172C23×C281C2411yescharacteristic
173C2×C4×C281—21no—
174C2×C4×C281—21no—
175C2×C4×C281—21no—
176C2×C4×C281—21no—
177C2×C4×C281—21no—
178C2×C4×C281—21no—
179C2×C4×C281—21no—
180C2×C4×C281—21no—
181C2×C4×C281—21no—
182C2×C4×C281—21no—
183C2×C4×C281—21no—
184C2×C4×C281—21no—
185C2×C4×C281—21no—
186C2×C4×C281—21no—
187C2×C4×C281—21no—
188C2×C4×C281C22×C412yes—
189C2×C4×C281C22×C412yes—
190C2×C4×C281C2×D412yes—
191C22×C281—22no—
192C22×C281—22no—
193C22×C281—22no—
194C22×C281—41no—
195C22×C281—41no—
196C22×C281—41no—
197C22×C281—41no—
198C22×C281C23×C411yescharacteristic
199C22×C281C22×D411yescharacteristic
200C22×C281C2×#4111yescharacteristic
201C22×C281H(5,𝔽2)11yescharacteristic
202C22×C281H(5,𝔽2)11yescharacteristic
203C22×C281H(5,𝔽2)11yescharacteristic
204C22×C281H(5,𝔽2)11yescharacteristic
205C2×D281—22no—
206C2×D281—22no—
207C2×D281—22no—
208C2×D281—22no—
209C2×D281—22no—
210C2×D281—22no—
211C2×D281—22no—
212C2×D281—22no—
213C2×D281—22no—
214C2×D281—22no—
215C2×D281—22no—
216C2×D281—22no—
217C2×D281—416no—
218C2×D281—41no—
219C2×D281—41no—
220C2×D281—41no—
221C2×D281—41no—
222C2×D281—41no—
223C2×D281—41no—
224C2×D281—41no—
225C2×D281—41no—
226C2×D281C4×D414yes—
227C4×C281—22no—
228C4×C281—22no—
229C4×C281—22no—
230C4×C281—41no—
231C4×C281—41no—
232C4×C281—41no—
233Dic281—22no—
234Dic281—22no—
235Dic281—41no—
236Dic281—41no—
237Dic281—41no—
238C2×C281—42no—
239C2×C281C2×C4×D411yescharacteristic
240C2×C281#51811yescharacteristic
241C2×C281#51811yescharacteristic
242C2×C281#53411yescharacteristic
243C2×C281#53511yescharacteristic
244C2×C281#53811yescharacteristic
245C2×C281#53811yescharacteristic
246D281—24no—
247D281—42no—
248D281—42no—
249C281#232111yescharacteristic, complemented, Sylow
250#2321—2811nomaximal, Sylow
251C2×#120—2811no—
252C2×C4×D4—2811no—
253C22×C22⋊C4—2811no—
254#390—2811no—
255#390—2811no—
256#388—2811no—
257#388—2811no—
258#388—2811no—
259#388D28111yescharacteristic, complemented
260#386—2811no—
261#386—2811no—
262#386—2811no—
263#385—2811no—
264#379—2811no—
265C4×C22⋊C4—2811no—
266C25—2811no—
267C22×D4—2811no—
268C22×D4—2811no—
269C22×D4—2811no—
270C23×C4—2811no—
271C23×C4—2811no—
272C23×C4—2811no—
273#120—2818no—
274C4×D4—5624no—
275C2×C4⋊C4—2811no—
276C2×C4⋊C4—2811no—
277C2×C4⋊C4C2×D28111yescharacteristic, complemented
278C2×C22⋊C4—2811no—
279C2×C22⋊C4—2811no—
280C2×C22⋊C4—2811no—
281C2×C22⋊C4—2811no—
282C2×C22⋊C4—2811no—
283C2×C22⋊C4—2811no—
284C2×C22⋊C4—2811no—
285C2×C22⋊C4—2811no—
286C2×C22⋊C4—2811no—
287C2×C22⋊C4—2811no—
288C2×C22⋊C4—2811no—
289C2×C22⋊C4—2811no—
290C2×C22⋊C4—2811no—
291C2×C22⋊C4—5624no—
292C2×C22⋊C4C2×D28111yescharacteristic
293C2×C22⋊C4C2×D28111yescharacteristic
294C2×C22⋊C4C2×D28111yescharacteristic
295C2×C42—2811no—
296C2×C42—2811no—
297C2×C42C2×D28111yescharacteristic, complemented
298#95—2811no—
299#95—2811no—
300#95—2811no—
301#95—2811no—
302#95C2×D28111yescharacteristic, complemented
303#95C2×D28111yescharacteristic, complemented
304C24—2811no—
305C24—2811no—
306C24—2811no—
307C24—2814no—
308C24—5622no—
309C24—5622no—
310C24—11241no—
311C24—11241no—
312C24—11241no—
313C24—11241no—
314C24C22×D28111yescharacteristic
315C2×D4—2814no—
316C2×D4—2814no—
317C2×D4—2814no—
318C2×D4—5622no—
319C2×D4—5622no—
320C2×D4—11241no—
321C2×D4—11241no—
322C2×D4—11241no—
323C2×D4—11241no—
324C22×C4—2811no—
325C22×C4—2811no—
326C22×C4—2814no—
327C22×C4—2811no—
328C22×C4—2811no—
329C22×C4—2811no—
330C22×C4—5622no—
331C22×C4—5622no—
332C22×C4—11241no—
333C22×C4—11241no—
334C22×C4—11241no—
335C22×C4—11241no—
336C22×C4—11241no—
337C22×C4—11241no—
338C22×C4C22×D28111yescharacteristic
339C22×C4C22×D28111yescharacteristic
340C22×C4C22×D28111yescharacteristic
341C22×C4C22×D28111yescharacteristic
342C22×C4C22×D28111yescharacteristic
343C22×C4C22×D28111yescharacteristic
344C4⋊C4—22no—
345C4⋊C4—11241no—
346C4⋊C4—11241no—
347C22⋊C4—22no—
348C22⋊C4—41no—
349C22⋊C4—2814no—
350C22⋊C4—2814no—
351C22⋊C4—5622no—
352C22⋊C4—5622no—
353C22⋊C4—5622no—
354C22⋊C4—5622no—
355C22⋊C4—5622no—
356C22⋊C4—5622no—
357C22⋊C4—11241no—
358C22⋊C4—11241no—
359C22⋊C4—11241no—
360C22⋊C4—11241no—
361C22⋊C4—11241no—
362C22⋊C4C4×D28114yescomplemented
363C42—41no—
364C42—5622no—
365C42—11241no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—2812no—
373C23—2812no—
374C23—2812no—
375C23—2812no—
376C23—2812no—
377C23—5628no—
378C23—5621no—
379C23—5621no—
380C23—5621no—
381C23—5621no—
382C23—5621no—
383C23—5621no—
384C23—5621no—
385C23—5621no—
386C23—5621no—
387C23—5621no—
388C23—5621no—
389C23—5621no—
390C23—5621no—
391C23—5621no—
392C23—5621no—
393C23—5621no—
394C23—11244no—
395C23—11244no—
396C23—11244no—
397C23—11244no—
398C23—11244no—
399C23—11244no—
400C23C2×C4×D28112yes—
401C23C23×D28111yescharacteristic
402D4—5628no—
403D4—11244no—
404D4—11244no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—2812no—
421C2×C4—2812no—
422C2×C4—5621no—
423C2×C4—5621no—
424C2×C4—5621no—
425C2×C4—5621no—
426C2×C4—5621no—
427C2×C4—5621no—
428C2×C4—5621no—
429C2×C4—5621no—
430C2×C4—5621no—
431C2×C4—5621no—
432C2×C4—5621no—
433C2×C4—5621no—
434C2×C4—5621no—
435C2×C4—11244no—
436C2×C4—11244no—
437C2×C4—11244no—
438C2×C4C2×C4×D28112yes—
439C2×C4C2×C4×D28112yes—
440C2×C4D4×D28112yes—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—2814no—
449C22—5622no—
450C22—5622no—
451C22—5622no—
452C22—5622no—
453C22—5622no—
454C22—5622no—
455C22—5622no—
456C22—5622no—
457C22—5622no—
458C22—5622no—
459C22—5622no—
460C22—5622no—
461C22—112416no—
462C22—11241no—
463C22—11241no—
464C22—11241no—
465C22—11241no—
466C22—11241no—
467C22—11241no—
468C22—11241no—
469C22—11241no—
470C22C22×C4×D28111yescharacteristic
471C22C2×D4×D28111yescharacteristic
472C22#41×D28111yescharacteristic
473C22#2258292411yescharacteristic
474C22#2258292511yescharacteristic
475C22#2258292511yescharacteristic
476C22#2258292511yescharacteristic
477C4—22no—
478C4—22no—
479C4—22no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—5622no—
484C4—5622no—
485C4—11241no—
486C4—11241no—
487C4—11241no—
488C2—42no—
489C2—5624no—
490C2—11242no—
491C2—11242no—
492C2C4×D4×D28111yescharacteristic
493C2#3182393511yescharacteristic
494C2#3182393711yescharacteristic
495C2#3182402111yescharacteristic
496C2#3182403111yescharacteristic
497C2#3182404911yescharacteristic
498C2#3182405211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#388×C281C2
socle, cosocleC23×C281C24
prime radicalC2×#22582849C2
hypercenter#388D281
hypocenterC281#2321
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#22582841C2semidirect
3. C2×C22⋊C4×D281C2semidirect
4. #31823365C2semidirect
5. #31823363C2semidirect
6. #31823356C2semidirect
7. #31823353C2semidirect
8. #31823352C2semidirect
9. #31823341C2semidirect
10. #31823341C2semidirect
11. #31823339C2semidirect
12. #31823337C2semidirect
13. #31823318C2semidirect
14. C4×#17985115C2semidirect
15. #388×C281C2semidirect
22. C22×C4×D281C22semidirect
23. #22582849C4semidirect
25. C2×C4⋊Dic281C22semidirect
26. C2×#17985117C22semidirect
37. C2×#17985115C22semidirect
38. C2×#17985115C22semidirect
39. C2×#17985115C22semidirect
41. C2×C4×Dic281C22semidirect
42. C2×C4×Dic281C22semidirect
43. #22582786C22semidirect
44. #22582786C22semidirect
45. #22582786C22semidirect
46. #22582786C22semidirect
47. C2×C4⋊C4×C281C22semidirect
51. C2×C42×C281C22semidirect
52. #95×C281C22semidirect
53. #95×C281C22semidirect
60. C23×D281C2×C4semidirect
69. C2×D1124C2×C4semidirect
72. C2×C22⋊D281C2×C4semidirect
86. C2×C4×D281D4semidirect
100. #17985115C2×C4semidirect
101. #17985115C2×C4semidirect
114. C22⋊C4×C281C2×C4semidirect
249. C281#2321semidirect
259. #388D281semidirect
277. C2×C4⋊C4C2×D281semidirect
297. C2×C42C2×D281semidirect
302. #95C2×D281semidirect
303. #95C2×D281semidirect
362. C22⋊C4C4×D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828492
C2×#225828412
C2×C22⋊C4×D2812
#318233652
#318233632
#318233562
#318233532
#318233522
#318233412
#318233392
#318233372
#318233182
C4×#179851152
#388×C2812
#2321281