Finite Group Databasebeta

← #11878734

Subgroups — #11878734

Order 1152.

916 conjugacy classes of subgroups.

The subgroup lattice has 639 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593968C211yesmaximal, characteristic
2D3×#869C211yesmaximal, characteristic, complemented
3#10592540C211yesmaximal, characteristic, complemented
4C3×#4841C211yesmaximal, characteristic, complemented
5C3×#4833C211yesmaximal, characteristic, complemented
6#10590951C212yesmaximal, complemented
7#10590890C212yesmaximal, complemented
8#10590877C212yesmaximal, complemented
9#10590822C212yesmaximal, complemented
10#10590379C211yesmaximal, characteristic, complemented
11#10590365C211yesmaximal, characteristic, complemented
12#80432—31nomaximal
13#79312—31nomaximal
14C2×#3798—21no—
15C2×D3×Dic6C2212yes—
16C2×#3744C2212yes—
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18#64078C2211yescharacteristic
19C2×C3×#204C2212yes—
20C3×C4×D12C2211yescharacteristic
21C3×C42×D3C2211yescharacteristic
22C3×#869C2211yescharacteristic
23#63918—21no—
24#63918—21no—
25#63918C2211yescharacteristic
26#63911C2211yescharacteristic
27#63909C2211yescharacteristic
28#63908C2211yescharacteristic
29#63906—21no—
30C4×#626—21no—
31D3×C4⋊Dic3—21no—
32D3×C4⋊Dic3—21no—
33#63866C2212yes—
34#63852—21no—
35C2×#3717C2212yes—
36C2×#3716C2212yes—
37C32×C4⋊C8C2211yescharacteristic
38#63643C2212yes—
39C3×(C2×D3)⋊C8C2212yes—
40C3×#816C2212yes—
41C3×C8×Dic3C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43#63567C2212yes—
44#63566C2212yes—
45D3×C4⋊Q8—31no—
46#5548—31no—
47#5477—31no—
48C2×#869—31no—
49C3×#461—31no—
50C3×#431—31no—
51#5175—32no—
52#5170—32no—
53#5083—31no—
54#5019—31no—
55#4841—31no—
56#4841—31no—
57#4841—31no—
58#4841—31no—
59#4841—61no—
60#4841D311yescharacteristic, complemented
61#4833D311yescharacteristic, complemented
62#4806—32no—
63#4792—32no—
64#4738—32no—
65#4738—32no—
66#4693—32no—
67#4681—32no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×#634C2312yes—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×Dic6C2312yes—
77C2×#627—22no—
78C2×#627—21no—
79C2×#626—21no—
80C2×#626—21no—
81C2×#626—21no—
82C2×#625—21no—
83C2×D3×Dic3—22no—
84#3798—44no—
85D3×Dic6—42no—
86D3×Dic6—42no—
87C2×C32×C8C2312yes—
88C32×C42C2311yescharacteristic
89#3752—21no—
90C4⋊(C3⋊Dic3)—21no—
91C4⋊(C3⋊Dic3)—21no—
92C4⋊(C3⋊Dic3)C2311yescharacteristic
93#3744—42no—
94C3×(C2×D3)⋊C4—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102C3×#204—42no—
103Dic3⋊Dic3—22no—
104Dic3⋊Dic3—22no—
105Dic3⋊Dic3—21no—
106#3722—21no—
107(C2×D3)⋊Dic3—21no—
108#3717—42no—
109#3716—42no—
110#3206—91noSylow
111C2×D3×Q8—32no—
112C2×#235—61no—
113C2×#235—61no—
114C22×Dic6—32no—
115C2×C3×SD16—32no—
116C3×C4⋊Q8—31no—
117C3×C4×D4—31no—
118C2×C3×C42—31no—
119#944—32no—
120C2×#215—32no—
121#940—31no—
122#938—31no—
123C2×#214—32no—
124#930—31no—
125#930—31no—
126#930—61no—
127C4×#67—61no—
128C2×C4⋊Dic3—61no—
129C2×C4⋊Dic3—61no—
130C2×#204—32no—
131C2×#204—32no—
132C2×#204—32no—
133C2×#204—32no—
134C2×#204—62no—
135C2×#204C2×D312yes—
136#895—31no—
137D3×C4⋊C4—61no—
138D3×C4⋊C4—61no—
139#888—31no—
140#888—61no—
141#888—61no—
142#885—61no—
143#884—61no—
144#875—61no—
145#874—31no—
146C4×D12—31no—
147C4×D12—31no—
148C4×D12—61no—
149C4×D12—61no—
150C4×D12C2×D311yescharacteristic
151C42×D3C2×D311yescharacteristic
152#869—31no—
153#869—32no—
154#869—31no—
155#869—31no—
156#869—61no—
157#869—61no—
158#869—61no—
159#869C2×D311yescharacteristic
160C3×C4⋊C8—21no—
161C3×C4⋊C8—31no—
162C3×C4⋊C8C2×D311yescharacteristic
163C3×C4⋊C8C2×D311yescharacteristic
164C3×#103—32no—
165C3×C22⋊C8—32no—
166C3×C4×C8—32no—
167#835—32no—
168(C2×D3)⋊C8C2×D312yes—
169#816—32no—
170#816—32no—
171#816—32no—
172#816—32no—
173#816—62no—
174#816C2×D312yes—
175C8×Dic3C2×D312yes—
176#810—32no—
177C4⋊(C3⋊C8)C2×D311yescharacteristic
178C22×C3⋊D3—21no—
179C22×C3×D3—21no—
180C22×C3×D3C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—22no—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)—21no—
188C4×C3⋊D3—42no—
189#634—22no—
190#634—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×D12—21no—
197C3×D12—21no—
198C3×C4×D3—21no—
199C3×C4×D3—21no—
200C3×C4×D3—22no—
201C3×C4×D3—42no—
202C3×C4×D3SD1614yescomplemented
203C3×Dic6—22no—
204C3×Dic6—22no—
205#627—44no—
206#627—42no—
207#626—42no—
208#626—42no—
209#626—42no—
210#625—42no—
211D3×Dic3—44no—
212C32×C8—22no—
213C3×C3⋊C8—22no—
214#532—91no—
215C2×C4⋊Q8—91no—
216#492—92no—
217#487—92no—
218#461—31no—
219#461—91no—
220#461—91no—
221#461—91no—
222#448—92no—
223#448—92no—
224#431—31no—
225C2×C3×Q8—32no—
226C2×C3×D4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—61no—
231C2×#67—61no—
232C2×#67—61no—
233C2×#67—61no—
234C2×#67—61no—
235C2×#67—61no—
236C22×Dic3—62no—
237D3×Q8—122no—
238D3×Q8—122no—
239#235—124no—
240#235—124no—
241C2×D12—31no—
242C2×D12—31no—
243C2×D12—61no—
244C2×D12—61no—
245C2×D12—61no—
246C2×D12—61no—
247C2×D12C22×D311yescharacteristic
248C2×C4×D3—21no—
249C2×C4×D3—62no—
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×C4×D3—121no—
253C2×C4×D3D1211yescharacteristic
254C2×C4×D3D1211yescharacteristic
255C2×C4×D3C22×D311yescharacteristic
256C2×Dic6—32no—
257C2×Dic6—32no—
258C2×Dic6—62no—
259C2×Dic6—61no—
260C2×Dic6—62no—
261C2×Dic6—61no—
262C2×Dic6—62no—
263C2×Dic6—122no—
264C2×Dic6—122no—
265C2×Dic6C22×D312yes—
266C3×SD16—122no—
267C2×C3×C8—22no—
268C2×C3×C8—32no—
269C2×C3×C8C22×D312yes—
270C2×C3×C8C22×D312yes—
271C3×C4⋊C4—31no—
272C3×C4⋊C4—61no—
273C3×C4⋊C4—61no—
274C3×C22⋊C4—61no—
275C3×C42—21no—
276C3×C42—31no—
277C3×C42—31no—
278C3×C42—31no—
279C3×C42C22×D311yescharacteristic
280C3×C42C22×D311yescharacteristic
281#217—61no—
282#215—122no—
283#214—122no—
284(C2×D3)⋊C4—21no—
285(C2×D3)⋊C4—61no—
286(C2×D3)⋊C4—61no—
287(C2×D3)⋊C4—61no—
288(C2×D3)⋊C4—61no—
289(C2×D3)⋊C4—61no—
290(C2×D3)⋊C4—121no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3—31no—
294C4⋊Dic3—31no—
295C4⋊Dic3—61no—
296C4⋊Dic3—62no—
297C4⋊Dic3—62no—
298C4⋊Dic3—61no—
299C4⋊Dic3—61no—
300C4⋊Dic3—61no—
301C4⋊Dic3—61no—
302C4⋊Dic3—61no—
303C4⋊Dic3—121no—
304C4⋊Dic3—121no—
305C4⋊Dic3C22×D311yescharacteristic
306Dic3⋊C4—61no—
307Dic3⋊C4—62no—
308Dic3⋊C4—62no—
309C4×Dic3D1211yescharacteristic
310C4×Dic3D1211yescharacteristic
311C4×Dic3C22×D311yescharacteristic
312C2×C3⋊C8C22×D312yes—
313#204—42no—
314#204—122no—
315#204—122no—
316#204—124no—
317#204—122no—
318#204—122no—
319C22×C32C22×D411yescharacteristic
320C2×C3⋊D3—41no—
321C2×C3⋊D3—41no—
322C2×C3⋊D3—41no—
323C2×C3×D3—21no—
324C2×C3×D3—21no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C2×C3×D3C2×SD1612yes—
329C32×C4—21no—
330C32×C4C2×SD1612yes—
331C32×C4H(5,𝔽2)11yescharacteristic
332C32×C4H(5,𝔽2)11yescharacteristic
333C3⋊Dic3—42no—
334C3⋊Dic3—41no—
335C3×Dic3—21no—
336C3×Dic3—42no—
337C3×Dic3—41no—
338C3×Dic3C2×SD1612yes—
339C3×Dic3#13712yes—
340C2×#41—181no—
341C22×Q8—92no—
342C2×SD16—32no—
343C2×SD16—92no—
344C2×SD16—92no—
345C2×SD16—92no—
346C4⋊Q8—31no—
347C4⋊Q8—91no—
348C4⋊Q8—92no—
349C4⋊Q8—91no—
350C4⋊Q8—181no—
351C4⋊Q8—181no—
352#127—91no—
353#124—181no—
354#121—91no—
355#121—91no—
356#121—181no—
357C4×D4—31no—
358C4×D4—91no—
359C4×D4—181no—
360C2×C4⋊C4—181no—
361C2×C4⋊C4—181no—
362C2×C42—31no—
363C4⋊C8—31no—
364C4⋊C8D3211yescharacteristic
365#103—32no—
366#103—92no—
367#103—92no—
368#103—92no—
369C22⋊C8—32no—
370C4×C8—32no—
371C23×C3—31no—
372C23×C3—61no—
373C22×D3—21no—
374C22×D3—61no—
375C22×D3—61no—
376C22×D3—121no—
377C22×D3C2×D1211yescharacteristic
378C3×Q8—62no—
379C3×Q8—62no—
380C3×D4—61no—
381C3×D4—61no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—31no—
386C2×C3×C4—31no—
387C2×C3×C4—34no—
388C2×C3×C4—31no—
389C2×C3×C4—62no—
390C2×C3×C4—61no—
391C2×C3×C4—61no—
392C2×C3×C4—62no—
393C2×C3×C4—61no—
394C2×C3×C4—122no—
395C2×C3×C4C2×D1211yescharacteristic
396C2×C3×C4C2×D1211yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401#67—122no—
402#67—122no—
403#67—122no—
404#67—122no—
405#67—122no—
406C2×Dic3—22no—
407C2×Dic3—21no—
408C2×Dic3—62no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—62no—
412C2×Dic3—121no—
413C2×Dic3—122no—
414C2×Dic3—124no—
415C2×Dic3C2×D1211yescharacteristic
416C2×Dic3C2×D1211yescharacteristic
417C2×Dic3C2×D1211yescharacteristic
418D12—21no—
419D12—21no—
420D12—62no—
421D12—61no—
422D12—61no—
423D12—61no—
424D12—61no—
425D12—121no—
426D12—122no—
427D12—122no—
428D12—122no—
429C4×D3—21no—
430C4×D3—21no—
431C4×D3—22no—
432C4×D3—42no—
433C4×D3—124no—
434C4×D3—122no—
435C4×D3—122no—
436C4×D3—242no—
437C4×D3#20414yescomplemented
438Dic6—22no—
439Dic6—22no—
440Dic6—62no—
441Dic6—62no—
442Dic6—62no—
443Dic6—62no—
444Dic6—122no—
445Dic6—122no—
446Dic6—124no—
447Dic6—122no—
448Dic6—124no—
449Dic6—122no—
450C3×C8—22no—
451C3×C8—22no—
452C3×C8—42no—
453C3×C8—62no—
454C3⋊C8—22no—
455C2×C32#53511yescharacteristic
456C2×C32C22×SD1611yescharacteristic
457C2×C32C2×#13711yescharacteristic
458C3⋊D3—81no—
459C3×D3—22no—
460C3×D3—81no—
461#41—364no—
462C2×Q8—32no—
463C2×Q8—92no—
464C2×Q8—181no—
465C2×Q8—182no—
466C2×Q8—362no—
467C2×Q8—362no—
468C2×D4—31no—
469C2×D4—91no—
470C2×D4—181no—
471C2×D4—181no—
472C2×D4—181no—
473C2×D4—181no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—61no—
478C22×C4—182no—
479C22×C4—181no—
480SD16—122no—
481SD16—362no—
482SD16—362no—
483SD16—362no—
484C2×C8—32no—
485C2×C8C2×D3212yes—
486C4⋊C4—31no—
487C4⋊C4—61no—
488C4⋊C4—61no—
489C4⋊C4—91no—
490C4⋊C4—182no—
491C4⋊C4—182no—
492C4⋊C4—181no—
493C4⋊C4—181no—
494C4⋊C4—181no—
495C22⋊C4—61no—
496C22⋊C4—181no—
497C22⋊C4—181no—
498C22⋊C4—181no—
499C42—31no—
500C42—31no—
501C42—31no—
502C42C2×D3211yescharacteristic
503C22×C3—21no—
504C22×C3—32no—
505C22×C3—61no—
506C22×C3—61no—
507C22×C3—121no—
508C22×C3—121no—
509C22×C3—121no—
510C22×C3C22×D1211yescharacteristic
511C22×C3C2×D3×D411yescharacteristic
512C2×D3—21no—
513C2×D3—21no—
514C2×D3—41no—
515C2×D3—41no—
516C2×D3—41no—
517C2×D3—122no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—121no—
522C2×D3—121no—
523C2×D3—121no—
524C2×D3—241no—
525C2×D3—241no—
526C2×D3C2×#20412yes—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—22no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—32no—
533C3×C4—32no—
534C3×C4—41no—
535C3×C4—61no—
536C3×C4—121no—
537C3×C4—122no—
538C3×C4C2×#20412yes—
539C3×C4D3×SD1612yes—
540C3×C4#100411yescharacteristic
541C3×C4#100911yescharacteristic
542C3×C4#100911yescharacteristic
543C3×C4#100911yescharacteristic
544Dic3—21no—
545Dic3—41no—
546Dic3—42no—
547Dic3—121no—
548Dic3—121no—
549Dic3—122no—
550Dic3—122no—
551Dic3—242no—
552Dic3—241no—
553Dic3C2×#20412yes—
554Dic3#90912yes—
555C32#320611yescharacteristic, complemented, Sylow
556C23—31no—
557C23—61no—
558C23—181no—
559Q8—62no—
560Q8—62no—
561Q8—182no—
562Q8—182no—
563Q8—362no—
564Q8—364no—
565D4—61no—
566D4—61no—
567D4—181no—
568D4—181no—
569D4—362no—
570D4—362no—
571D4—362no—
572D4—362no—
573C2×C4—31no—
574C2×C4—31no—
575C2×C4—34no—
576C2×C4—31no—
577C2×C4—62no—
578C2×C4—61no—
579C2×C4—61no—
580C2×C4—61no—
581C2×C4—62no—
582C2×C4—122no—
583C2×C4—181no—
584C2×C4—182no—
585C2×C4—364no—
586C2×C4—362no—
587C2×C4D3×D1211yescharacteristic
588C2×C4D3×D1211yescharacteristic
589C2×C4C22×D3211yescharacteristic
590C8—22no—
591C8—62no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—62no—
596C2×C3—241no—
597C2×C3#552511yescharacteristic
598C2×C3#560711yescharacteristic
599C2×C3C22×#20411yescharacteristic
600C2×C3C2×#90911yescharacteristic
601C2×C3C2×D3×SD1611yescharacteristic
602C2×C3D3×#13711yescharacteristic
603D3—22no—
604D3—81no—
605D3—242no—
606D3—241no—
607D3—241no—
608C22—32no—
609C22—61no—
610C22—61no—
611C22—121no—
612C22—121no—
613C22—121no—
614C22—361no—
615C22—361no—
616C22—361no—
617C22C2×D3×D1211yescharacteristic
618C4—21no—
619C4—32no—
620C4—32no—
621C4—61no—
622C4—122no—
623C4—121no—
624C4—362no—
625C4—361no—
626C4D3×#20412yes—
627C4#6431411yescharacteristic
628C4#6432011yescharacteristic
629C3—21no—
630C3#7931211yescharacteristic, complemented
631C3#8043211yescharacteristic, complemented
632C2—62no—
633C2—241no—
634C2—721no—
635C2#1059462811yescharacteristic
636C2C2×D3×#20411yescharacteristic
637C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593968C2
hypercenterC4⋊C8D32
hypocenterC32#3206
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. D3×#869C2semidirect
3. #10592540C2semidirect
4. C3×#4841C2semidirect
5. C3×#4833C2semidirect
6. #10590951C2semidirect
7. #10590890C2semidirect
8. #10590877C2semidirect
9. #10590822C2semidirect
10. #10590379C2semidirect
11. #10590365C2semidirect
60. #4841D3semidirect
61. #4833D3semidirect
202. C3×C4×D3SD16semidirect
437. C4×D3#204semidirect
555. C32#3206semidirect
630. C3#79312semidirect
631. C3#80432semidirect

Maximal subgroups

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

subgroupindex
#105939682
D3×#8692
#105925402
C3×#48412
C3×#48332
#105909512
#105908902
#105908772
#105908222
#105903792
#105903652
#804323
#793123