Finite Group Databasebeta

← #49098641

Subgroups — #49098641

Order 35968.

908 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#17985137C211yesmaximal, characteristic, complemented
2C2×#22582856C211yesmaximal, characteristic, complemented
3C2×#22582851C211yesmaximal, characteristic, complemented
4C2×D4×Dic281C211yesmaximal, characteristic, complemented
5#31823379C211yesmaximal, characteristic, complemented
6#31823377C211yesmaximal, characteristic, complemented
7#31823371C211yesmaximal, characteristic, complemented
8#31823367C211yesmaximal, characteristic, complemented
9#31823363C211yesmaximal, characteristic, complemented
10#31823343C211yesmaximal, characteristic, complemented
11#31823339C211yesmaximal, characteristic, complemented
12#31823338C211yesmaximal, characteristic, complemented
13#31823337C211yesmaximal, characteristic, complemented
14#31823321C211yesmaximal, characteristic, complemented
15#392×C281C211yesmaximal, characteristic, complemented
16C2×#17985137—24no—
17C2×#17985137—24no—
18C2×#17985137—24no—
19C22×Dic562C2211yescharacteristic
20C22×C22⋊D281C2211yescharacteristic
21C22×C22⋊D281C2211yescharacteristic
22C22×C22⋊D281C2211yescharacteristic
23C23×Dic281C2211yescharacteristic
24C23×Dic281C2211yescharacteristic
25C23×Dic281C2211yescharacteristic
26C22×C4×D281C2211yescharacteristic
27#22582856—24no—
28#22582851—24no—
29D4×Dic281—24no—
30C2×C4⋊Dic281C2211yescharacteristic
31C2×C4⋊Dic281C2211yescharacteristic
32C2×#17985117C2211yescharacteristic
33C2×#17985117C2211yescharacteristic
34C2×#17985117C2211yescharacteristic
35C2×C22⋊Dic281C2211yescharacteristic
36C2×C22⋊Dic281C2211yescharacteristic
37C2×C22⋊Dic281C2211yescharacteristic
38C2×C22⋊Dic281C2211yescharacteristic
39C2×C22⋊Dic281C2211yescharacteristic
40C2×C22⋊Dic281C2211yescharacteristic
41C2×#17985115C2211yescharacteristic
42C2×#17985115C2211yescharacteristic
43C2×#17985115C2211yescharacteristic
44C2×C4×Dic281C2211yescharacteristic
45#22582786C2211yescharacteristic
46#22582786C2211yescharacteristic
47#22582786C2211yescharacteristic
48#22582786C2211yescharacteristic
49#22582786C2211yescharacteristic
50C22×D4×C281C2211yescharacteristic
51C22×D4×C281C2211yescharacteristic
52C22×D4×C281C2211yescharacteristic
53C2×C22⋊C4×C281C2211yescharacteristic
54C2×C22⋊C4×C281C2211yescharacteristic
55C2×C22⋊C4×C281C2211yescharacteristic
56#95×C281C2211yescharacteristic
57C23×D281C2311yescharacteristic
58#17985137—232no—
59C2×Dic562—22no—
60C2×Dic562—22no—
61C2×Dic562D414yescomplemented
62C2×C22⋊D281—22no—
63C2×C22⋊D281—22no—
64C2×C22⋊D281—22no—
65C2×C22⋊D281—22no—
66C2×C22⋊D281—22no—
67C2×C22⋊D281—22no—
68C2×C22⋊D281—22no—
69C2×C22⋊D281—41no—
70C2×C22⋊D281D414yescomplemented
71C22×Dic281—22no—
72C22×Dic281—22no—
73C22×Dic281—22no—
74C22×Dic281—22no—
75C22×Dic281—22no—
76C22×Dic281—22no—
77C22×Dic281—22no—
78C22×Dic281—22no—
79C22×Dic281D414yescomplemented
80C22×Dic281C2311yescharacteristic
81C22×Dic281C2311yescharacteristic
82C22×Dic281C2311yescharacteristic
83C22×Dic281C2311yescharacteristic
84C22×Dic281C2311yescharacteristic
85C22×Dic281C2311yescharacteristic
86C22×Dic281C2311yescharacteristic
87C2×C4×D281—22no—
88C2×C4×D281—22no—
89C2×C4×D281—22no—
90C4⋊Dic281—22no—
91C4⋊Dic281—22no—
92#17985117—22no—
93#17985117—22no—
94#17985117—22no—
95C22⋊Dic281—22no—
96C22⋊Dic281—22no—
97C22⋊Dic281—22no—
98C22⋊Dic281—22no—
99C22⋊Dic281—41no—
100C22⋊Dic281—41no—
101#17985115—22no—
102#17985115—22no—
103#17985115—41no—
104C4×Dic281—22no—
105C24×C281C2311yescharacteristic
106C24×C281C2311yescharacteristic
107C24×C281C2311yescharacteristic
108C2×D4×C281—22no—
109C2×D4×C281—22no—
110C2×D4×C281—22no—
111C2×D4×C281—22no—
112C2×D4×C281—22no—
113C2×D4×C281—22no—
114C2×D4×C281—22no—
115C2×D4×C281—22no—
116C2×D4×C281—41no—
117C22×C4×C281C2311yescharacteristic
118C22×C4×C281C2311yescharacteristic
119C22×C4×C281C2311yescharacteristic
120C22×C4×C281C2311yescharacteristic
121C22⋊C4×C281—22no—
122C22⋊C4×C281—22no—
123C22⋊C4×C281—41no—
124C22×D281—21no—
125C22×D281—21no—
126C22×D281—21no—
127C22×D281—21no—
128C22×D281—21no—
129C22×D281—21no—
130C22×D281C2×D412yes—
131Dic562—28no—
132C22⋊D281—28no—
133C22⋊D281—28no—
134C22⋊D281—44no—
135C2×Dic281—28no—
136C2×Dic281—21no—
137C2×Dic281—21no—
138C2×Dic281—21no—
139C2×Dic281—21no—
140C2×Dic281—28no—
141C2×Dic281—21no—
142C2×Dic281—21no—
143C2×Dic281—21no—
144C2×Dic281—21no—
145C2×Dic281—21no—
146C2×Dic281—21no—
147C2×Dic281—21no—
148C2×Dic281—21no—
149C2×Dic281—21no—
150C2×Dic281—21no—
151C2×Dic281—21no—
152C2×Dic281—21no—
153C2×Dic281—44no—
154C2×Dic281C2×D412yes—
155C2×Dic281C2×D412yes—
156C2×Dic281C2×D412yes—
157C2×Dic281C2×D412yes—
158C2×Dic281C2×D412yes—
159C4×D281—28no—
160C23×C281—21no—
161C23×C281—21no—
162C23×C281—21no—
163C23×C281—21no—
164C23×C281—21no—
165C23×C281—21no—
166C23×C281—21no—
167C23×C281—21no—
168C23×C281—21no—
169C23×C281—21no—
170C23×C281—21no—
171C23×C281—21no—
172C23×C281—21no—
173C23×C281—21no—
174C23×C281—21no—
175C23×C281—21no—
176C23×C281—21no—
177C23×C281—21no—
178C23×C281C2×D412yes—
179C23×C281C2×D412yes—
180C23×C281#4112yescomplemented
181C23×C281C2411yescharacteristic
182D4×C281—28no—
183D4×C281—28no—
184D4×C281—44no—
185C2×C4×C281—21no—
186C2×C4×C281—21no—
187C2×C4×C281—21no—
188C2×C4×C281—21no—
189C2×C4×C281—21no—
190C2×C4×C281—21no—
191C2×C4×C281—21no—
192C2×C4×C281—21no—
193C2×C4×C281—21no—
194C2×C4×C281—21no—
195C2×C4×C281C2×D412yes—
196C2×C4×C281#4112yescomplemented
197C22×C281—22no—
198C22×C281—22no—
199C22×C281—22no—
200C22×C281—22no—
201C22×C281—22no—
202C22×C281—22no—
203C22×C281—22no—
204C22×C281—22no—
205C22×C281—22no—
206C22×C281—41no—
207C22×C281—41no—
208C22×C281—41no—
209C22×C281—41no—
210C22×C281—41no—
211C22×C281—41no—
212C22×C281—41no—
213C22×C281—41no—
214C22×C281—41no—
215C22×C281—41no—
216C22×C281—41no—
217C22×C281—41no—
218C22×C281C22×D411yescharacteristic
219C22×C281C22×D411yescharacteristic
220C22×C281C22×D411yescharacteristic
221C22×C281C2×#4111yescharacteristic
222C22×C281C2×#4111yescharacteristic
223C22×C281H(5,𝔽2)11yescharacteristic
224C22×C2812−1+411yescharacteristic
225C2×D281—22no—
226C2×D281—22no—
227C2×D281—22no—
228C2×D281—41no—
229C2×D281—41no—
230C2×D281—41no—
231C2×D281—41no—
232C4×C281—22no—
233C4×C281—22no—
234C4×C281—41no—
235C4×C281—41no—
236Dic281—22no—
237Dic281—22no—
238Dic281—41no—
239Dic281—41no—
240Dic281—41no—
241Dic281—41no—
242Dic281#12014yes—
243C2×C281—42no—
244C2×C281—42no—
245C2×C281—42no—
246C2×C281C2×#12011yescharacteristic
247C2×C281#52511yescharacteristic
248C2×C281#53711yescharacteristic
249C2×C281#54611yescharacteristic
250C2×C281#54711yescharacteristic
251C2×C281#54811yescharacteristic
252C2×C281#55011yescharacteristic
253D281—42no—
254C281#240711yescharacteristic, complemented, Sylow
255#2407—2811nomaximal, Sylow
256C22×#41—2811no—
257C2×C22⋊Q8—2811no—
258C2×#121—2811no—
259C2×C4×D4—2811no—
260#394—2811no—
261#394—2811no—
262#392—2811no—
263#392D28111yescharacteristic, complemented
264#391—2811no—
265#390—2811no—
266#386—2811no—
267#386—2811no—
268#385—2811no—
269#385—2811no—
270#380—2811no—
271C2×#41—5624no—
272C2×#41—5624no—
273C2×#41—5624no—
274C22×Q8—2811no—
275C22×D4—2811no—
276C22×D4—2811no—
277C22×D4—2811no—
278C22×D4C2×D28111yescharacteristic
279C22×D4C2×D28111yescharacteristic
280C22×D4C2×D28111yescharacteristic
281C23×C4—2811no—
282C23×C4—2811no—
283C23×C4—2811no—
284C23×C4—2811no—
285C22⋊Q8—5624no—
286#121—5624no—
287C4×D4—5624no—
288C2×C4⋊C4—2811no—
289C2×C4⋊C4—2811no—
290C2×C4⋊C4—2811no—
291C2×C4⋊C4—2811no—
292C2×C4⋊C4—2811no—
293C2×C22⋊C4—2811no—
294C2×C22⋊C4—2811no—
295C2×C22⋊C4—2811no—
296C2×C22⋊C4—2811no—
297C2×C22⋊C4—2811no—
298C2×C22⋊C4—2811no—
299C2×C22⋊C4—2811no—
300C2×C22⋊C4—2811no—
301C2×C22⋊C4—2811no—
302C2×C22⋊C4C2×D28111yescharacteristic
303C2×C22⋊C4C2×D28111yescharacteristic
304C2×C22⋊C4C2×D28111yescharacteristic
305C2×C42—2811no—
306#95—2811no—
307#95—2811no—
308#95—2811no—
309#95—2811no—
310#95—2811no—
311#95C2×D28111yescharacteristic
312C24—2811no—
313C24C22×D28111yescharacteristic
314C24C22×D28111yescharacteristic
315C24C22×D28111yescharacteristic
316#41—56232no—
317C2×Q8—2814no—
318C2×Q8—5622no—
319C2×Q8—5622no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—41no—
329C2×D4—2814no—
330C2×D4—5622no—
331C2×D4—5622no—
332C2×D4—5622no—
333C2×D4—5622no—
334C2×D4—5622no—
335C2×D4—5622no—
336C2×D4—5622no—
337C2×D4—11241no—
338C22×C4—2811no—
339C22×C4—2814no—
340C22×C4—2811no—
341C22×C4—2811no—
342C22×C4—2811no—
343C22×C4—2811no—
344C22×C4—2811no—
345C22×C4—2811no—
346C22×C4—5622no—
347C22×C4—5622no—
348C22×C4—5622no—
349C22×C4—5622no—
350C22×C4—5622no—
351C22×C4—5622no—
352C22×C4—5622no—
353C22×C4—5622no—
354C22×C4—5622no—
355C22×C4—5622no—
356C22×C4—5622no—
357C22×C4C22×D28111yescharacteristic
358C22×C4C22×D28111yescharacteristic
359C22×C4C22×D28111yescharacteristic
360C22×C4C22×D28111yescharacteristic
361C4⋊C4—5622no—
362C4⋊C4—5622no—
363C4⋊C4—5622no—
364C4⋊C4—5622no—
365C4⋊C4—5622no—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C22⋊C4—41no—
369C22⋊C4—5622no—
370C22⋊C4—5622no—
371C22⋊C4—5622no—
372C22⋊C4—5622no—
373C22⋊C4—5622no—
374C22⋊C4—5622no—
375C22⋊C4—11241no—
376C22⋊C4—11241no—
377C22⋊C4—11241no—
378C42—5622no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—2812no—
398C23—5621no—
399C23—5621no—
400C23—5621no—
401C23—5621no—
402C23—5621no—
403C23—5621no—
404C23D4×D28112yes—
405C23D4×D28112yes—
406C23#1798513712yescomplemented
407C23C23×D28111yescharacteristic
408Q8—5628no—
409D4—28no—
410D4—28no—
411D4—44no—
412D4—5628no—
413D4—5628no—
414D4—11244no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—2812no—
426C2×C4—2812no—
427C2×C4—2812no—
428C2×C4—2812no—
429C2×C4—2812no—
430C2×C4—5628no—
431C2×C4—5628no—
432C2×C4—5628no—
433C2×C4—5621no—
434C2×C4—5621no—
435C2×C4—5621no—
436C2×C4—5621no—
437C2×C4—5621no—
438C2×C4—5621no—
439C2×C4—5621no—
440C2×C4—5621no—
441C2×C4—5621no—
442C2×C4—5621no—
443C2×C4—5621no—
444C2×C4—5621no—
445C2×C4—5621no—
446C2×C4—5621no—
447C2×C4—5621no—
448C2×C4—5621no—
449C2×C4—11244no—
450C2×C4D4×D28112yes—
451C2×C4#1798513712yescomplemented
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—5622no—
474C22—5622no—
475C22—5622no—
476C22—11241no—
477C22—11241no—
478C22—11241no—
479C22—11241no—
480C22C2×D4×D28111yescharacteristic
481C22C2×D4×D28111yescharacteristic
482C22C2×D4×D28111yescharacteristic
483C22C2×#1798513711yescharacteristic
484C22C2×#1798513711yescharacteristic
485C22#2258292411yescharacteristic
486C22#2258292611yescharacteristic
487C4—22no—
488C4—22no—
489C4—41no—
490C4—41no—
491C4—2814no—
492C4—5622no—
493C4—5622no—
494C4—11241no—
495C4—11241no—
496C4—11241no—
497C4—11241no—
498C2—42no—
499C2—42no—
500C2—42no—
501C2—11242no—
502C2#120×D28111yescharacteristic
503C2#3182396911yescharacteristic
504C2#3182404011yescharacteristic
505C2#3182410011yescharacteristic
506C2#3182411311yescharacteristic
507C2#3182411911yescharacteristic
508C2#3182413311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#392×C281C2
hypercenter#392D281
hypocenterC281#2407
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#17985137C2semidirect
2. C2×#22582856C2semidirect
3. C2×#22582851C2semidirect
4. C2×D4×Dic281C2semidirect
5. #31823379C2semidirect
6. #31823377C2semidirect
7. #31823371C2semidirect
8. #31823367C2semidirect
9. #31823363C2semidirect
10. #31823343C2semidirect
11. #31823339C2semidirect
12. #31823338C2semidirect
13. #31823337C2semidirect
14. #31823321C2semidirect
15. #392×C281C2semidirect
61. C2×Dic562D4semidirect
70. C2×C22⋊D281D4semidirect
79. C22×Dic281D4semidirect
180. C23×C281#41semidirect
196. C2×C4×C281#41semidirect
254. C281#2407semidirect
263. #392D281semidirect
406. C23#17985137semidirect
451. C2×C4#17985137semidirect

Maximal subgroups

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

subgroupindex
C22×#179851372
C2×#225828562
C2×#225828512
C2×D4×Dic2812
#318233792
#318233772
#318233712
#318233672
#318233632
#318233432
#318233392
#318233382
#318233372
#318233212
#392×C2812
#2407281