Finite Group Databasebeta

← #11882278

Subgroups — #11882278

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593907C211yesmaximal, characteristic
2#10593882C211yesmaximal, characteristic, complemented
3C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
4C3×#4851C211yesmaximal, characteristic, complemented
5C3×#4848C211yesmaximal, characteristic, complemented
6#10590843C212yesmaximal, complemented
7#10590841C212yesmaximal, complemented
8#10590776C212yesmaximal, complemented
9#10590748C212yesmaximal, complemented
10#10590364C211yesmaximal, characteristic, complemented
11#10590285C211yesmaximal, characteristic, complemented
12#81002—31nomaximal
13#80366—31nomaximal
14C2×#3796—21no—
15C2×C8×C3⋊D3C2212yes—
16C42×C3⋊D3C2211yescharacteristic
17C2×C3×#204C2212yes—
18C3×#874C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22#63919C2211yescharacteristic
23C4×#627—21no—
24#63916—21no—
25#63916C2212yes—
26#63898—21no—
27#63898C2212yes—
28#63874—21no—
29#63873C2211yescharacteristic
30#63871C2211yescharacteristic
31#63871C2211yescharacteristic
32#63870—21no—
33#63865—21no—
34#63863—21no—
35C2×#3715C2212yes—
36C32×C4⋊C8C2211yescharacteristic
37#63641C2212yes—
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C3×#821C2212yes—
40C3×#817C2212yes—
41C3×#816C2212yes—
42#63574C2212yes—
43#63565C2212yes—
44#63562C2212yes—
45#5725—31no—
46#5716—31no—
47#5578—31no—
48#5578—31no—
49C3×#475—31no—
50C3×#460—31no—
51#5171—32no—
52#5162—32no—
53#5094—31no—
54#5075—31no—
55#5027—31no—
56#5020—31no—
57#4870—32no—
58#4864—32no—
59#4851D311yescharacteristic, complemented
60#4848D311yescharacteristic, complemented
61D3×C4⋊C8—31no—
62D3×C4⋊C8—31no—
63D3×C4⋊C8—61no—
64#4818—32no—
65#4807—32no—
66#4778—32no—
67#4761—32no—
68C2×C4×C3⋊D3D411yescharacteristic
69C2×C4×C3⋊D3D411yescharacteristic
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12C2312yes—
74C2×C3×Dic6—21no—
75C2×C3×Dic6C2311yescharacteristic
76C2×C3×Dic6C2311yescharacteristic
77C2×#627—21no—
78C2×#626—22no—
79C2×D3×Dic3—22no—
80#3796—44no—
81C2×C32×C8C2312yes—
82C32×C42C2311yescharacteristic
83C4×C3⋊Dic3D411yescharacteristic
84C4×C3⋊Dic3D411yescharacteristic
85C4×C3⋊Dic3C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2312yes—
87C8×C3⋊D3—42no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—21no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3—21no—
96C3×#204—42no—
97#3724—21no—
98#3724—21no—
99#3724—21no—
100Dic3⋊Dic3—21no—
101Dic3⋊Dic3—21no—
102#3722—21no—
103#3722—21no—
104(C2×D3)⋊Dic3—22no—
105(C2×D3)⋊Dic3—22no—
106#3715—42no—
107#3246—91noSylow
108C2×#239—61no—
109C2×#237—61no—
110C2×C3×SD16—32no—
111C3×C4⋊Q8—31no—
112C3×#127—31no—
113C3×C4×Q8—31no—
114C3×C4×Q8—31no—
115#947—61no—
116#946—31no—
117#946—31no—
118#944—31no—
119#944—31no—
120C2×#215—32no—
121#938—32no—
122#938—61no—
123#936—61no—
124D4×Dic3—32no—
125D4×Dic3—61no—
126C2×#214—32no—
127C2×#204C2×D312yes—
128C2×D3×C8—32no—
129C2×D3×C8—32no—
130C2×D3×C8—62no—
131#897—31no—
132#897—31no—
133#896—61no—
134#896—61no—
135#895—32no—
136#895—61no—
137#893—32no—
138#893—61no—
139#889—61no—
140#889—61no—
141#888—31no—
142#888—31no—
143#874C2×D311yescharacteristic
144#872—61no—
145#872—61no—
146C42×D3—31no—
147C42×D3—31no—
148C42×D3—61no—
149#869C2×D311yescharacteristic
150C4×Dic6—61no—
151C4×Dic6—61no—
152C4×Dic6C2×D311yescharacteristic
153C4×Dic6C2×D311yescharacteristic
154C3×#106—32no—
155C3×C4⋊C8—21no—
156C3×C4⋊C8C2×D311yescharacteristic
157C3×C4⋊C8C2×D311yescharacteristic
158C3×#103—32no—
159C3×#102—32no—
160#835—32no—
161#832—32no—
162#821C2×D312yes—
163#817C2×D312yes—
164#816C2×D312yes—
165Dic3⋊C8—32no—
166Dic3⋊C8—32no—
167Dic3⋊C8—62no—
168#810—32no—
169#809—32no—
170#808—32no—
171#808—32no—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—61no—
175C22×C3⋊D3C2×D411yescharacteristic
176C22×C3×D3—22no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3C2×D411yescharacteristic
181C2×C3⋊Dic3C2×D411yescharacteristic
182C2×C3⋊Dic3C2×D411yescharacteristic
183C4×C3⋊D3—21no—
184C4×C3⋊D3—21no—
185C4×C3⋊D3—41no—
186C4×C3⋊D3SD1614yescomplemented
187C2×C3×Dic3—22no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C3×D12—22no—
193C3×D12—22no—
194C3×D12—42no—
195C3×D12—42no—
196C3×Dic6—21no—
197C3×Dic6—21no—
198C3×Dic6—21no—
199C3×Dic6—21no—
200C3×Dic6—42no—
201#627—42no—
202#626—44no—
203D3×Dic3—44no—
204C32×C8—22no—
205C3⋊(C3⋊C8)—22no—
206#533—91no—
207#532—91no—
208#476—92no—
209#475—31no—
210#475—91no—
211#465—92no—
212#465—92no—
213#461—92no—
214#460—31no—
215#460—91no—
216C2×C4⋊C8—91no—
217C2×C3×Q8—31no—
218C2×C3×Q8—31no—
219C2×C3×Q8—61no—
220C2×C3×D4—32no—
221C2×C3×D4—61no—
222C2×C3×D4—61no—
223C2×#67—62no—
224C22×Dic3—62no—
225#239—124no—
226#237—124no—
227C2×D12—21no—
228C2×D12—21no—
229C2×D12—62no—
230C2×D12C22×D312yes—
231C2×C4×D3—31no—
232C2×C4×D3—31no—
233C2×C4×D3—31no—
234C2×C4×D3—31no—
235C2×C4×D3—31no—
236C2×C4×D3—31no—
237C2×C4×D3—61no—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C2×C4×D3—62no—
241C2×Dic6—21no—
242C2×Dic6—61no—
243C2×Dic6—61no—
244C2×Dic6C22×D311yescharacteristic
245C2×Dic6C22×D311yescharacteristic
246C3×SD16—122no—
247C2×C3×C8—22no—
248C2×C3×C8C22×D312yes—
249C2×C3×C8C22×D312yes—
250C3×C4⋊C4—31no—
251C3×C4⋊C4—32no—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—61no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4—61no—
256C3×C42—21no—
257C3×C42—61no—
258C3×C42—61no—
259C3×C42C22×D311yescharacteristic
260C3×C42C22×D311yescharacteristic
261#217—62no—
262#217—62no—
263#215—122no—
264#214—122no—
265(C2×D3)⋊C4—61no—
266(C2×D3)⋊C4—61no—
267(C2×D3)⋊C4—61no—
268(C2×D3)⋊C4—61no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—62no—
271C4⋊Dic3—21no—
272C4⋊Dic3—61no—
273C4⋊Dic3—61no—
274C4⋊Dic3C22×D311yescharacteristic
275C4⋊Dic3C22×D312yes—
276C4⋊Dic3C22×D311yescharacteristic
277Dic3⋊C4—21no—
278Dic3⋊C4—21no—
279Dic3⋊C4—61no—
280Dic3⋊C4—61no—
281Dic3⋊C4—61no—
282Dic3⋊C4—61no—
283Dic3⋊C4—61no—
284Dic3⋊C4—61no—
285Dic3⋊C4—61no—
286Dic3⋊C4—61no—
287C4×Dic3—21no—
288C4×Dic3—21no—
289C4×Dic3—31no—
290C4×Dic3—31no—
291C4×Dic3—31no—
292C4×Dic3—31no—
293C4×Dic3—31no—
294C4×Dic3—31no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—62no—
301#204—42no—
302D3×C8—122no—
303D3×C8—122no—
304D3×C8—124no—
305C22×C32C22×D411yescharacteristic
306C2×C3⋊D3—21no—
307C2×C3⋊D3—21no—
308C2×C3⋊D3C2×SD1612yes—
309C2×C3×D3—42no—
310C2×C3×D3—42no—
311C2×C3×D3—42no—
312C32×C4—21no—
313C32×C4C2×SD1612yes—
314C32×C4H(5,𝔽2)11yescharacteristic
315C32×C42−1+411yescharacteristic
316C3⋊Dic3—21no—
317C3⋊Dic3—21no—
318C3⋊Dic3C2×SD1612yes—
319C3×Dic3—41no—
320C3×Dic3—41no—
321C3×Dic3—42no—
322C3×Dic3—41no—
323C3×Dic3—41no—
324C2×#41—181no—
325C2×SD16—32no—
326C2×SD16—92no—
327C22×C8—92no—
328C4⋊Q8—31no—
329C4⋊Q8—91no—
330C4⋊Q8—91no—
331#127—31no—
332#125—181no—
333#124—181no—
334C22⋊Q8—91no—
335C22⋊Q8—91no—
336C22⋊Q8—181no—
337#121—92no—
338#121—181no—
339C4×Q8—31no—
340C4×Q8—31no—
341C4×Q8—181no—
342C4×D4—92no—
343C4×D4—181no—
344#117—181no—
345C2×C42—91no—
346#106—32no—
347#106—92no—
348C4⋊C8—92no—
349C4⋊C8—91no—
350C4⋊C8D3211yescharacteristic
351#103—32no—
352#103—92no—
353#102—32no—
354#102—92no—
355C23×C3—62no—
356C22×D3—22no—
357C22×D3—31no—
358C22×D3—31no—
359C22×D3—61no—
360C3×Q8—61no—
361C3×Q8—61no—
362C3×Q8—61no—
363C3×Q8—61no—
364C3×Q8—122no—
365C3×D4—62no—
366C3×D4—62no—
367C3×D4—122no—
368C3×D4—122no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—61no—
375C2×C3×C4—61no—
376C2×C3×C4—62no—
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4D3×D411yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4C23×D311yescharacteristic
382C2×C3×C4C23×D311yescharacteristic
383#67—124no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—22no—
389C2×Dic3—31no—
390C2×Dic3—31no—
391C2×Dic3—31no—
392C2×Dic3—31no—
393C2×Dic3—31no—
394C2×Dic3—31no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—124no—
399D12—22no—
400D12—22no—
401D12—42no—
402D12—42no—
403D12—124no—
404C4×D3—34no—
405C4×D3—34no—
406C4×D3—64no—
407C4×D3—62no—
408C4×D3—62no—
409C4×D3—61no—
410C4×D3—61no—
411C4×D3—61no—
412C4×D3—61no—
413C4×D3—124no—
414C4×D3—121no—
415C4×D3—121no—
416C4×D3—122no—
417Dic6—21no—
418Dic6—21no—
419Dic6—21no—
420Dic6—21no—
421Dic6—42no—
422Dic6—122no—
423Dic6—122no—
424C3×C8—22no—
425C3×C8—22no—
426C3×C8—42no—
427C3⋊C8—62no—
428C3⋊C8—62no—
429C3⋊C8—122no—
430C2×C32#53711yescharacteristic
431C2×C32C22×SD1611yescharacteristic
432C2×C32#57511yescharacteristic
433C3⋊D3—22no—
434C3×D3—82no—
435#41—364no—
436C2×Q8—31no—
437C2×Q8—31no—
438C2×Q8—61no—
439C2×Q8—181no—
440C2×D4—32no—
441C2×D4—61no—
442C2×D4—61no—
443C2×D4—182no—
444C22×C4—91no—
445C22×C4—91no—
446C22×C4—91no—
447C22×C4—182no—
448SD16—122no—
449SD16—362no—
450C2×C8—92no—
451C2×C8—362no—
452C2×C8C2×D3212yes—
453C4⋊C4—31no—
454C4⋊C4—31no—
455C4⋊C4—32no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—61no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C4⋊C4—181no—
462C4⋊C4—181no—
463C4⋊C4—181no—
464C22⋊C4—181no—
465C22⋊C4—181no—
466C22⋊C4—182no—
467C22⋊C4—182no—
468C42—61no—
469C42—61no—
470C42—91no—
471C42—91no—
472C42—91no—
473C42C2×D3211yescharacteristic
474C22×C3—21no—
475C22×C3—122no—
476C22×C3—122no—
477C22×C3—122no—
478C22×C3C2×D3×D411yescharacteristic
479C22×C3C2×D3×D411yescharacteristic
480C2×D3—32no—
481C2×D3—32no—
482C2×D3—42no—
483C2×D3—42no—
484C2×D3—42no—
485C2×D3—62no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—61no—
489C2×D3—61no—
490C2×D3—61no—
491C2×D3—61no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—22no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—41no—
498C3×C4—122no—
499C3×C4—121no—
500C3×C4—121no—
501C3×C4—121no—
502C3×C4—121no—
503C3×C4D3×SD1612yes—
504C3×C4D3×SD1612yes—
505C3×C4#100411yescharacteristic
506C3×C4#100711yescharacteristic
507C3×C4#100911yescharacteristic
508C3×C4#101011yescharacteristic
509Dic3—32no—
510Dic3—32no—
511Dic3—42no—
512Dic3—41no—
513Dic3—41no—
514Dic3—41no—
515Dic3—41no—
516Dic3—62no—
517Dic3—62no—
518Dic3—61no—
519Dic3—61no—
520Dic3—61no—
521Dic3—61no—
522Dic3—121no—
523C32#324611yescharacteristic, complemented, Sylow
524C23—62no—
525C23—91no—
526Q8—61no—
527Q8—61no—
528Q8—61no—
529Q8—61no—
530Q8—122no—
531Q8—362no—
532D4—62no—
533D4—62no—
534D4—122no—
535D4—122no—
536D4—364no—
537C2×C4—61no—
538C2×C4—61no—
539C2×C4—61no—
540C2×C4—61no—
541C2×C4—62no—
542C2×C4—91no—
543C2×C4—94no—
544C2×C4—91no—
545C2×C4—91no—
546C2×C4—181no—
547C2×C4—181no—
548C2×C4—361no—
549C2×C4—364no—
550C2×C4#380211yescharacteristic
551C2×C4#380211yescharacteristic
552C2×C4C22×D3211yescharacteristic
553C8—22no—
554C8—182no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—242no—
559C2×C3#560811yescharacteristic
560C2×C3#562911yescharacteristic
561C2×C3C2×D3×SD1611yescharacteristic
562C2×C3C2×D3×SD1611yescharacteristic
563C2×C3#577311yescharacteristic
564C2×C3#577711yescharacteristic
565D3—64no—
566D3—62no—
567D3—62no—
568D3—82no—
569C22—92no—
570C22—122no—
571C22—122no—
572C22—122no—
573C22—181no—
574C22—181no—
575C22C2×#380211yescharacteristic
576C4—21no—
577C4—92no—
578C4—122no—
579C4—121no—
580C4—121no—
581C4—121no—
582C4—121no—
583C4—181no—
584C4—181no—
585C4#6379612yes—
586C4#6431411yescharacteristic
587C4#6431511yescharacteristic
588C3—21no—
589C3#8036611yescharacteristic, complemented
590C3#8100211yescharacteristic, complemented
591C2—182no—
592C2—242no—
593C2#1059452811yescharacteristic
594C2C2×#6379611yescharacteristic
595C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593907C2
hypercenterC4⋊C8D32
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593882C2semidirect
3. C3⋊D3×C4⋊C8C2semidirect
4. C3×#4851C2semidirect
5. C3×#4848C2semidirect
6. #10590843C2semidirect
7. #10590841C2semidirect
8. #10590776C2semidirect
9. #10590748C2semidirect
10. #10590364C2semidirect
11. #10590285C2semidirect
59. #4851D3semidirect
60. #4848D3semidirect
186. C4×C3⋊D3SD16semidirect
523. C32#3246semidirect
589. C3#80366semidirect
590. C3#81002semidirect

Maximal subgroups

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

subgroupindex
#105939072
#105938822
C3⋊D3×C4⋊C82
C3×#48512
C3×#48482
#105908432
#105908412
#105907762
#105907482
#105903642
#105902852
#810023
#803663