Finite Group Databasebeta

← #11896089

Subgroups — #11896089

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595389C211yesmaximal, characteristic
2#10594312C211yesmaximal, characteristic, complemented
3#10592491C211yesmaximal, characteristic, complemented
4C3×#4798C211yesmaximal, characteristic
5C3×#4791C211yesmaximal, characteristic, complemented
6#10591624C211yesmaximal, characteristic
7#10591580C211yesmaximal, characteristic, complemented
8#10591576C211yesmaximal, characteristic, complemented
9#10590859C211yesmaximal, characteristic
10#10590802C211yesmaximal, characteristic, complemented
11#10590788C211yesmaximal, characteristic, complemented
12#10590775C211yesmaximal, characteristic
13#10590531C211yesmaximal, characteristic
14#10590480C211yesmaximal, characteristic, complemented
15#10590472C211yesmaximal, characteristic
16#81004—31nomaximal
17#80582—31nomaximal
18#64153C2211yescharacteristic
19#64097C2211yescharacteristic
20C3×#947C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C2×C3×#204C2211yescharacteristic
24C3×#888C2211yescharacteristic
25C3×#887C2211yescharacteristic
26#63918C2211yescharacteristic
27C4×#627C2211yescharacteristic
28#63899—21no—
29#63898C2211yescharacteristic
30#63877—21no—
31#63866—21no—
32#63860C2211yescharacteristic
33#63859—21no—
34#63858—21no—
35#63844C2211yescharacteristic
36#63843C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38#63840—21no—
39#63839—21no—
40#63837—21no—
41C2×#3719C2211yescharacteristic
42C32×#103C2211yescharacteristic
43#63662C2211yescharacteristic
44#63643C2211yescharacteristic
45C8×C3⋊Dic3C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63573C2211yescharacteristic
54#63572C2211yescharacteristic
55#63567C2211yescharacteristic
56#63565C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60#63554C2211yescharacteristic
61#5722—31no—
62#5671—31no—
63#5568—31no—
64Q8×Dic6—31no—
65C3×#475—31no—
66C3×#464—31no—
67#5184—31no—
68#5182—31no—
69#5166—31no—
70Dic3×SD16—31no—
71#5089—31no—
72#5055—31no—
73#5030—31no—
74#5030—31no—
75#4870—31no—
76#4854—31no—
77#4853—31no—
78#4852—31no—
79#4851—31no—
80#4845—31no—
81#4828—31no—
82#4828—31no—
83#4798D311yescharacteristic
84#4795—31no—
85#4794—31no—
86#4792—31no—
87#4792—31no—
88#4792—61no—
89#4791D311yescharacteristic, complemented
90#4765—31no—
91#4761—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C2×#634C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×Dic6—21no—
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#627D411yescharacteristic
100C2×D3×Dic3—21no—
101C2×C32×C8C2311yescharacteristic
102C32×C4⋊C4C2311yescharacteristic
103C4⋊(C3⋊Dic3)C2311yescharacteristic
104#3750—21no—
105#3750—21no—
106#3750—21no—
107C4×C3⋊Dic3C2311yescharacteristic
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C3×#216—22no—
110C3×(C2×D3)⋊C4—21no—
111C3×(C2×D3)⋊C4—21no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3C2311yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×C4×Dic3—21no—
118C3×C4×Dic3—21no—
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C3×#204—22no—
124#3724—21no—
125#3724D411yescharacteristic
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3D411yescharacteristic
130Dic3⋊Dic3D411yescharacteristic
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137#3719—22no—
138#3369—91noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—31no—
141C3×C4⋊Q8—31no—
142C3×#124—31no—
143C3×C4×Q8—31no—
144C3×C4×Q8—31no—
145#947C2×D311yescharacteristic
146Q8×Dic3—31no—
147Q8×Dic3—31no—
148Q8×Dic3C2×D311yescharacteristic
149#944—31no—
150#944—31no—
151#944—61no—
152#944—61no—
153#944—61no—
154C2×#216—31no—
155C2×#216C2×D311yescharacteristic
156#936—31no—
157D4×Dic3—31no—
158C2×Dic12—31no—
159C2×#204C2×D311yescharacteristic
160#898—61no—
161#896—61no—
162#893—31no—
163#888—31no—
164#888—31no—
165#888—31no—
166#888—61no—
167#888—61no—
168#888—61no—
169#888—61no—
170#888C2×D311yescharacteristic
171#887—31no—
172#887—31no—
173#887—61no—
174#887C2×D311yescharacteristic
175#879—61no—
176#879—61no—
177#878—61no—
178#877—61no—
179#876—61no—
180#875—31no—
181#872—61no—
182#869—31no—
183#869—61no—
184C4×Dic6—31no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C3×#106—31no—
190C3×#106—31no—
191C3×C4⋊C8—31no—
192C3×C4⋊C8—31no—
193C3×#103—21no—
194C3×#103—31no—
195C3×#103C2×D311yescharacteristic
196C3×#103C2×D311yescharacteristic
197C3×#102—31no—
198#835—31no—
199#835—31no—
200#835—31no—
201#835—61no—
202#835C2×D311yescharacteristic
203#832—31no—
204#832—31no—
205#821—31no—
206#817—31no—
207#817C2×D311yescharacteristic
208#816—31no—
209#816—31no—
210#816—31no—
211#816—61no—
212#815—31no—
213#815—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8C2×D311yescharacteristic
217Dic3⋊C8C2×D311yescharacteristic
218C8×Dic3—31no—
219C8×Dic3—31no—
220C8×Dic3—61no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—61no—
226#809—31no—
227#809C2×D311yescharacteristic
228#808—31no—
229#808C2×D311yescharacteristic
230#803—31no—
231#803—31no—
232C22×C3×D3—21no—
233C32×Q8—21no—
234C32×Q8—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242#634—21no—
243#634—21no—
244#634—81no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×D12—21no—
253C3×D12—21no—
254C3×Dic6—21no—
255C3×Dic6—81no—
256C3×Dic6#4112yes—
257#627—22no—
258#627—81no—
259D3×Dic3—42no—
260C32×C8—21no—
261C3⋊(C3⋊C8)—21no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8—21no—
264Q82—91no—
265#556—91no—
266#489—91no—
267#489—91no—
268#487—91no—
269#476—91no—
270#475—31no—
271#475—91no—
272#464—31no—
273#464—91no—
274#462—91no—
275#446—91no—
276#441—91no—
277#441—91no—
278C4×SD16—91no—
279C2×C3×Q8—21no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×D4—31no—
285C22×Dic3—61no—
286C2×D12C22×D311yescharacteristic
287C2×C4×D3—61no—
288C2×Dic6—21no—
289C2×Dic6—31no—
290C2×Dic6—31no—
291C2×Dic6—31no—
292C2×Dic6—31no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—121no—
299C2×Dic6C22×D311yescharacteristic
300C3×Q16—62no—
301C3×SD16—62no—
302C2×C3×C8—21no—
303C2×C3×C8—31no—
304C2×C3×C8—31no—
305C2×C3×C8C22×D311yescharacteristic
306C2×C3×C8C22×D311yescharacteristic
307C3×C4⋊C4—21no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4C22×D311yescharacteristic
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C22⋊C4—61no—
316C3×C22⋊C4—61no—
317C3×C42—31no—
318C3×C42—31no—
319C3×C42—61no—
320C3×C42—61no—
321#217—61no—
322#217—61no—
323#217—61no—
324#216—22no—
325#216—62no—
326(C2×D3)⋊C4—21no—
327(C2×D3)⋊C4—21no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331C4⋊Dic3—21no—
332C4⋊Dic3—31no—
333C4⋊Dic3—31no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—61no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3C22×D311yescharacteristic
341C4⋊Dic3C22×D311yescharacteristic
342Dic3⋊C4—21no—
343Dic3⋊C4—21no—
344Dic3⋊C4—31no—
345Dic3⋊C4—31no—
346Dic3⋊C4—31no—
347Dic3⋊C4—31no—
348Dic3⋊C4—61no—
349Dic3⋊C4—61no—
350Dic3⋊C4—61no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—121no—
360Dic3⋊C4—121no—
361Dic3⋊C4—121no—
362C4×Dic3—21no—
363C4×Dic3—21no—
364C4×Dic3—31no—
365C4×Dic3—31no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3C22×D311yescharacteristic
374C4×Dic3C22×D311yescharacteristic
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—61no—
378C2×C3⋊C8C22×D311yescharacteristic
379C2×C3⋊C8C22×D311yescharacteristic
380Dic12—62no—
381#204—22no—
382C22×C32C22×D411yescharacteristic
383C2×C3×D3—41no—
384C2×C3×D3—41no—
385C2×C3×D3—41no—
386C32×C4—41no—
387C32×C4—41no—
388C32×C4C2×#4111yescharacteristic
389C32×C42−1+411yescharacteristic
390C3⋊Dic3—21no—
391C3⋊Dic3—41no—
392C3⋊Dic3—41no—
393C3⋊Dic3#13712yes—
394C3×Dic3—22no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—21no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C2×Q16—31no—
402C2×Q16—91no—
403C2×SD16—31no—
404C4⋊Q8—31no—
405C4⋊Q8—91no—
406C4⋊Q8—91no—
407C4⋊Q8—91no—
408C4⋊Q8—181no—
409C4⋊Q8—181no—
410C4⋊Q8—181no—
411#126—181no—
412#126—181no—
413#124—31no—
414#124—91no—
415C22⋊Q8—181no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8—91no—
419C4×Q8—91no—
420C4×Q8—91no—
421C4×Q8—91no—
422C4×Q8—181no—
423C4×D4—91no—
424#117—181no—
425#106—31no—
426#106—31no—
427#106—91no—
428C4⋊C8—31no—
429C4⋊C8—31no—
430C4⋊C8—91no—
431#103—31no—
432#103—91no—
433#103—91no—
434#103—91no—
435#103—91no—
436#103—91no—
437#103D3211yescharacteristic
438#102—31no—
439#102—91no—
440#102—91no—
441#97—91no—
442#97—91no—
443C4×C8—91no—
444C23×C3—61no—
445C22×D3—21no—
446C3×Q8—21no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—21no—
450C3×Q8—32no—
451C3×Q8—41no—
452C3×Q8—41no—
453C3×Q8—61no—
454C3×Q8—241no—
455C3×D4—61no—
456C3×D4—61no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4C23×D311yescharacteristic
472C2×C3×C4C23×D311yescharacteristic
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—31no—
477C2×Dic3—31no—
478C2×Dic3—31no—
479C2×Dic3—31no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—121no—
487C2×Dic3—121no—
488C2×Dic3—122no—
489C2×Dic3D3×D411yescharacteristic
490C2×Dic3D3×D411yescharacteristic
491C2×Dic3D3×D411yescharacteristic
492C2×Dic3D3×D411yescharacteristic
493D12—21no—
494D12—21no—
495C4×D3—122no—
496Dic6—21no—
497Dic6—62no—
498Dic6—62no—
499Dic6—61no—
500Dic6—61no—
501Dic6—61no—
502Dic6—61no—
503Dic6—81no—
504Dic6—121no—
505Dic6—121no—
506Dic6—241no—
507Dic6—241no—
508Dic6—241no—
509Dic6—241no—
510Dic6—242no—
511Dic6#23712yes—
512C3×C8—21no—
513C3×C8—21no—
514C3×C8—41no—
515C3×C8—61no—
516C3×C8—61no—
517C3⋊C8—21no—
518C3⋊C8—21no—
519C3⋊C8—61no—
520C3⋊C8—61no—
521C3⋊C8—121no—
522C2×C32#54811yescharacteristic
523C2×C32C2×#13711yescharacteristic
524C2×C32#57711yescharacteristic
525C3×D3—81no—
526C2×Q8—31no—
527C2×Q8—61no—
528C2×Q8—91no—
529C2×Q8—91no—
530C2×Q8—181no—
531C2×Q8—181no—
532C2×Q8C2×D3211yescharacteristic
533C2×D4—31no—
534C22×C4—181no—
535Q16—62no—
536Q16—182no—
537SD16—62no—
538C2×C8—31no—
539C2×C8—31no—
540C2×C8—91no—
541C2×C8C2×D3211yescharacteristic
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—91no—
548C4⋊C4—91no—
549C4⋊C4—91no—
550C4⋊C4—91no—
551C4⋊C4—181no—
552C4⋊C4—181no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4C2×D3211yescharacteristic
559C22⋊C4—61no—
560C22⋊C4—61no—
561C22⋊C4—181no—
562C22⋊C4—181no—
563C22⋊C4—181no—
564C42—31no—
565C42—31no—
566C42—61no—
567C42—61no—
568C42—91no—
569C42—181no—
570C42—181no—
571C42—181no—
572C22×C3—21no—
573C22×C3—121no—
574C22×C3—121no—
575C22×C3—121no—
576C22×C3C2×D3×D411yescharacteristic
577C22×C3C2×D3×D411yescharacteristic
578C2×D3—41no—
579C2×D3—41no—
580C2×D3—41no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—41no—
584C3×C4—41no—
585C3×C4—41no—
586C3×C4—41no—
587C3×C4—62no—
588C3×C4—61no—
589C3×C4—61no—
590C3×C4—61no—
591C3×C4—61no—
592C3×C4—81no—
593C3×C4—81no—
594C3×C4—121no—
595C3×C4—121no—
596C3×C4C2×#23711yescharacteristic
597C3×C4#100711yescharacteristic
598C3×C4D3×#4111yescharacteristic
599C3×C4#101011yescharacteristic
600Dic3—21no—
601Dic3—21no—
602Dic3—21no—
603Dic3—21no—
604Dic3—22no—
605Dic3—32no—
606Dic3—32no—
607Dic3—41no—
608Dic3—41no—
609Dic3—62no—
610Dic3—62no—
611Dic3—61no—
612Dic3—61no—
613Dic3—121no—
614Dic3—121no—
615Dic3—121no—
616Dic3—121no—
617Dic3—241no—
618Dic3—241no—
619C32#336911yescharacteristic, complemented, Sylow
620C23—61no—
621Q8—21no—
622Q8—21no—
623Q8—32no—
624Q8—61no—
625Q8—182no—
626Q8—181no—
627Q8—181no—
628Q8—241no—
629Q8—721no—
630Q8—721no—
631D4—61no—
632D4—61no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—31no—
636C2×C4—31no—
637C2×C4—31no—
638C2×C4—31no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—91no—
643C2×C4—91no—
644C2×C4—181no—
645C2×C4—181no—
646C2×C4—362no—
647C2×C4C22×D3211yescharacteristic
648C8—21no—
649C8—61no—
650C8—61no—
651C8—181no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—241no—
656C2×C3#559811yescharacteristic
657C2×C3#563311yescharacteristic
658C2×C3#576211yescharacteristic
659C2×C3#577011yescharacteristic
660C2×C3D3×#13711yescharacteristic
661C2×C3D3×#13711yescharacteristic
662D3—81no—
663C22—121no—
664C22—121no—
665C22—121no—
666C22D32×D411yescharacteristic
667C4—41no—
668C4—41no—
669C4—62no—
670C4—61no—
671C4—61no—
672C4—61no—
673C4—61no—
674C4—92no—
675C4—121no—
676C4—121no—
677C4—181no—
678C4—361no—
679C4—361no—
680C4#6429711yescharacteristic
681C4D3×#23711yescharacteristic
682C3—21no—
683C3#8058211yescharacteristic, complemented
684C3#8100411yescharacteristic, complemented
685C2—241no—
686C2#1059407411yescharacteristic
687C2#1059475311yescharacteristic
688C2#1059476011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenter#103D32
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594312C2semidirect
3. #10592491C2semidirect
5. C3×#4791C2semidirect
7. #10591580C2semidirect
8. #10591576C2semidirect
10. #10590802C2semidirect
11. #10590788C2semidirect
14. #10590480C2semidirect
89. #4791D3semidirect
619. C32#3369semidirect
683. C3#80582semidirect
684. C3#81004semidirect

Maximal subgroups

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

subgroupindex
#105953892
#105943122
#105924912
C3×#47982
C3×#47912
#105916242
#105915802
#105915762
#105908592
#105908022
#105907882
#105907752
#105905312
#105904802
#105904722
#810043
#805823