Finite Group Databasebeta

← #11896096

Subgroups — #11896096

Order 1152.

726 conjugacy classes of subgroups.

The subgroup lattice has 693 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595387C211yesmaximal, characteristic
2#10594312C211yesmaximal, characteristic, complemented
3#10592493C211yesmaximal, characteristic
4C3×#4792C211yesmaximal, characteristic, complemented
5C3×#4789C211yesmaximal, characteristic, complemented
6#10591579C211yesmaximal, characteristic
7#10591574C211yesmaximal, characteristic, complemented
8#10591544C211yesmaximal, characteristic, complemented
9#10590893C211yesmaximal, characteristic
10#10590792C211yesmaximal, characteristic
11#10590791C211yesmaximal, characteristic, complemented
12#10590784C211yesmaximal, characteristic, complemented
13#10590536C211yesmaximal, characteristic
14#10590497C211yesmaximal, characteristic, complemented
15#10590466C211yesmaximal, characteristic
16#81626—31nomaximal
17#79815—31nomaximal
18#64156C2211yescharacteristic
19#64097C2211yescharacteristic
20C3×Q8×Dic3C2211yescharacteristic
21C3×#944C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C3×#888C2211yescharacteristic
24C3×#887C2211yescharacteristic
25#63918C2211yescharacteristic
26C4×#627C2211yescharacteristic
27#63895—21no—
28#63894C2211yescharacteristic
29#63868—21no—
30#63866—21no—
31#63864C2211yescharacteristic
32#63848—21no—
33#63843C2211yescharacteristic
34#63843C2211yescharacteristic
35Dic3×Dic6C2211yescharacteristic
36#63840—21no—
37#63839—21no—
38#63837—21no—
39#63836—21no—
40C2×#3718C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C32×#103C2211yescharacteristic
43#63662C2211yescharacteristic
44#63648C2211yescharacteristic
45#63642C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#808C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57Dic3⋊(C3⋊C8)C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63566C2211yescharacteristic
60#63564C2211yescharacteristic
61#5732—31no—
62#5722—31no—
63#5568—31no—
64Q8×Dic6—31no—
65C3×#487—31no—
66C3×#441—31no—
67#5185—31no—
68#5182—31no—
69#5090—31no—
70#5084—31no—
71#5028—31no—
72#5020—31no—
73#4870—31no—
74#4854—31no—
75#4798—31no—
76#4798—31no—
77#4794—31no—
78#4794—31no—
79#4794—31no—
80#4794—61no—
81#4792D311yescharacteristic, complemented
82#4791—31no—
83#4791—31no—
84#4789—31no—
85#4789—31no—
86#4789D311yescharacteristic, complemented
87#4788—31no—
88#4714—31no—
89#4701—31no—
90C4×#204—31no—
91#4679—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×#634—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#627D411yescharacteristic
100C2×#624—21no—
101C2×C32×C8C2311yescharacteristic
102C32×C4⋊C4C2311yescharacteristic
103#3752—21no—
104#3752—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106#3750—21no—
107C4×C3⋊Dic3C2311yescharacteristic
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C3×#216—22no—
110C3×C4⋊Dic3—21no—
111C3×C4⋊Dic3C2311yescharacteristic
112C3×C4⋊Dic3C2311yescharacteristic
113C3×Dic3⋊C4—21no—
114C3×Dic3⋊C4—21no—
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
123#3724D411yescharacteristic
124Dic3⋊Dic3—21no—
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130#3722—21no—
131#3722—21no—
132#3722—21no—
133Dic32—21no—
134Dic32—21no—
135Dic32—21no—
136#3718—22no—
137#3717—22no—
138#3369—91noSylow
139C2×C3×Q16—31no—
140C3×C4⋊Q8—31no—
141C3×C4⋊Q8—31no—
142C3×C4×Q8—31no—
143C3×C4×Q8—31no—
144#947—31no—
145#947—31no—
146#947—31no—
147#947—61no—
148Q8×Dic3—31no—
149Q8×Dic3—31no—
150Q8×Dic3—31no—
151Q8×Dic3C2×D311yescharacteristic
152#944—61no—
153#944—61no—
154#944C2×D311yescharacteristic
155C2×#216—31no—
156C2×#216—31no—
157C2×#216C2×D311yescharacteristic
158C2×#215—31no—
159C2×#204—31no—
160#898—61no—
161#898—61no—
162#898—61no—
163#897—61no—
164#896—61no—
165#893—31no—
166#892—61no—
167#888—31no—
168#888—31no—
169#888—31no—
170#888—61no—
171#888—61no—
172#888—61no—
173#888—61no—
174#888C2×D311yescharacteristic
175#887—31no—
176#887—31no—
177#887—61no—
178#887C2×D311yescharacteristic
179#876—61no—
180#875—31no—
181C4×D12—31no—
182#872—61no—
183#869—31no—
184#869—61no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C3×#106—31no—
190C3×#103—21no—
191C3×#103—31no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#103C2×D311yescharacteristic
196C3×#103C2×D311yescharacteristic
197C3×#97—31no—
198C3×C4×C8—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—61no—
203#835C2×D311yescharacteristic
204#821—31no—
205#821—31no—
206#821—31no—
207#821—61no—
208#817—31no—
209#816—31no—
210#816C2×D311yescharacteristic
211#816C2×D311yescharacteristic
212#815—31no—
213#815—31no—
214#815—61no—
215#815C2×D311yescharacteristic
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220C8×Dic3C2×D311yescharacteristic
221#810C2×D311yescharacteristic
222#809—31no—
223#809—31no—
224#809—31no—
225#809—61no—
226#808—31no—
227#808—31no—
228#808—31no—
229#808C2×D311yescharacteristic
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—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⋊Dic3C2×D411yescharacteristic
240C2×C3⋊Dic3C2×D411yescharacteristic
241C4⋊(C3⋊D3)—21no—
242C4⋊(C3⋊D3)—21no—
243#634—81no—
244C2×C3×Dic3—21no—
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×Dic6—21no—
253C3×Dic6—21no—
254C3×Dic6—21no—
255C3×Dic6—81no—
256C3×Dic6#4112yes—
257#627—22no—
258#627—81no—
259#624—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—31no—
269#476—91no—
270#475—91no—
271#475—91no—
272#464—91no—
273#464—91no—
274#462—91no—
275#446—91no—
276#441—31no—
277#441—91no—
278C4×SD16—91no—
279C2×C3×Q8—21no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—61no—
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×Q8C22×D311yescharacteristic
285C2×D12—31no—
286C2×D12—31no—
287C2×D12—61no—
288C2×C4×D3—61no—
289C2×C4×D3—61no—
290C2×Dic6—21no—
291C2×Dic6—31no—
292C2×Dic6—31no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—121no—
298C2×Dic6C22×D311yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C3×Q16—62no—
301C2×C3×C8—21no—
302C2×C3×C8—31no—
303C2×C3×C8—31no—
304C2×C3×C8C22×D311yescharacteristic
305C2×C3×C8C22×D311yescharacteristic
306C3×C4⋊C4—21no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—61no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C42—31no—
317C3×C42—31no—
318C3×C42—61no—
319C3×C42—61no—
320#216—22no—
321#216—62no—
322#216—62no—
323#215—62no—
324(C2×D3)⋊C4—61no—
325(C2×D3)⋊C4—61no—
326(C2×D3)⋊C4—61no—
327(C2×D3)⋊C4—61no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—121no—
335(C2×D3)⋊C4—121no—
336C4⋊Dic3—21no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3C22×D311yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—21no—
349Dic3⋊C4—21no—
350Dic3⋊C4—21no—
351Dic3⋊C4—21no—
352Dic3⋊C4—31no—
353Dic3⋊C4—31no—
354Dic3⋊C4—31no—
355Dic3⋊C4—31no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—121no—
363C4×Dic3—21no—
364C4×Dic3—21no—
365C4×Dic3—31no—
366C4×Dic3—31no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3C22×D311yescharacteristic
375C4×Dic3C22×D311yescharacteristic
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8C22×D311yescharacteristic
380C2×C3⋊C8C22×D311yescharacteristic
381#204—62no—
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—21no—
392C3⋊Dic3—41no—
393C3×Dic3—22no—
394C3×Dic3—21no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—41no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3#13712yes—
401C2×Q16—31no—
402C2×Q16—91no—
403C2×SD16—91no—
404C4⋊Q8—31no—
405C4⋊Q8—31no—
406C4⋊Q8—91no—
407C4⋊Q8—91no—
408C4⋊Q8—181no—
409C4⋊Q8—181no—
410C4⋊Q8—181no—
411#126—181no—
412#126—181no—
413#124—91no—
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—91no—
427#106—91no—
428C4⋊C8—91no—
429C4⋊C8—91no—
430C4⋊C8—91no—
431#103—31no—
432#103—31no—
433#103—31no—
434#103—31no—
435#103—91no—
436#103—91no—
437#103D3211yescharacteristic
438#102—91no—
439#102—91no—
440#102—91no—
441#97—31no—
442#97—91no—
443C4×C8—31no—
444C22×D3—61no—
445C22×D3—61no—
446C22×D3—121no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—21no—
450C3×Q8—21no—
451C3×Q8—32no—
452C3×Q8—41no—
453C3×Q8—41no—
454C3×Q8—61no—
455C3×Q8—61no—
456C3×Q8—61no—
457C3×Q8—241no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C23×D311yescharacteristic
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—31no—
480C2×Dic3—31no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—121no—
488C2×Dic3D3×D411yescharacteristic
489C2×Dic3D3×D411yescharacteristic
490C2×Dic3D3×D411yescharacteristic
491C2×Dic3D3×D411yescharacteristic
492D12—61no—
493D12—61no—
494D12—61no—
495D12—61no—
496D12—121no—
497D12—121no—
498C4×D3—122no—
499C4×D3—122no—
500Dic6—21no—
501Dic6—21no—
502Dic6—21no—
503Dic6—62no—
504Dic6—62no—
505Dic6—81no—
506Dic6—241no—
507Dic6—241no—
508Dic6—241no—
509Dic6—241no—
510Dic6—242no—
511Dic6#23512yes—
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—31no—
528C2×Q8—61no—
529C2×Q8—91no—
530C2×Q8—181no—
531C2×Q8—181no—
532C2×Q8C2×D3211yescharacteristic
533C2×D4—91no—
534C22×C4—181no—
535Q16—62no—
536Q16—182no—
537SD16—182no—
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—61no—
548C4⋊C4—61no—
549C4⋊C4—91no—
550C4⋊C4—91no—
551C4⋊C4—91no—
552C4⋊C4—91no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4C2×D3211yescharacteristic
559C22⋊C4—181no—
560C22⋊C4—181no—
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×C3C2×D3×D411yescharacteristic
574C22×C3C2×D3×D411yescharacteristic
575C2×D3—121no—
576C2×D3—121no—
577C2×D3—121no—
578C2×D3—121no—
579C2×D3—121no—
580C2×D3—121no—
581C2×D3—241no—
582C2×D3—241no—
583C2×D3—241no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—32no—
587C3×C4—41no—
588C3×C4—41no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—62no—
592C3×C4—61no—
593C3×C4—61no—
594C3×C4—61no—
595C3×C4—81no—
596C3×C4—81no—
597C3×C4—121no—
598C3×C4—121no—
599C3×C4—121no—
600C3×C4C2×#23511yescharacteristic
601C3×C4D3×#4111yescharacteristic
602C3×C4#101011yescharacteristic
603C3×C4#101011yescharacteristic
604Dic3—21no—
605Dic3—21no—
606Dic3—21no—
607Dic3—22no—
608Dic3—41no—
609Dic3—41no—
610Dic3—41no—
611Dic3—61no—
612Dic3—61no—
613Dic3—61no—
614Dic3—61no—
615Dic3—121no—
616Dic3—121no—
617Dic3—121no—
618Dic3—121no—
619Dic3—241no—
620Dic3#91812yes—
621C32#336911yescharacteristic, complemented, Sylow
622C23—181no—
623Q8—21no—
624Q8—21no—
625Q8—32no—
626Q8—61no—
627Q8—61no—
628Q8—61no—
629Q8—182no—
630Q8—241no—
631Q8—721no—
632Q8—721no—
633D4—181no—
634D4—181no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—31no—
638C2×C4—31no—
639C2×C4—31no—
640C2×C4—31no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—91no—
646C2×C4—91no—
647C2×C4—181no—
648C2×C4—362no—
649C2×C4C22×D3211yescharacteristic
650C8—21no—
651C8—61no—
652C8—61no—
653C8—181no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3#555211yescharacteristic
658C2×C3#567711yescharacteristic
659C2×C3#576211yescharacteristic
660C2×C3C2×#91811yescharacteristic
661C2×C3D3×#13711yescharacteristic
662C2×C3#577811yescharacteristic
663D3—241no—
664D3—241no—
665D3—481no—
666C22—361no—
667C22—361no—
668C22—361no—
669C22D32×D411yescharacteristic
670C4—32no—
671C4—41no—
672C4—41no—
673C4—62no—
674C4—61no—
675C4—61no—
676C4—61no—
677C4—121no—
678C4—121no—
679C4—121no—
680C4—181no—
681C4—181no—
682C4—361no—
683C4D3×#23511yescharacteristic
684C4#6430911yescharacteristic
685C3—21no—
686C3#7981511yescharacteristic, complemented
687C3#8162611yescharacteristic, complemented
688C2—721no—
689C2#1059407311yescharacteristic
690C2#1059475111yescharacteristic
691C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
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
4. C3×#4792C2semidirect
5. C3×#4789C2semidirect
7. #10591574C2semidirect
8. #10591544C2semidirect
11. #10590791C2semidirect
12. #10590784C2semidirect
14. #10590497C2semidirect
81. #4792D3semidirect
86. #4789D3semidirect
621. C32#3369semidirect
686. C3#79815semidirect
687. C3#81626semidirect

Maximal subgroups

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

subgroupindex
#105953872
#105943122
#105924932
C3×#47922
C3×#47892
#105915792
#105915742
#105915442
#105908932
#105907922
#105907912
#105907842
#105905362
#105904972
#105904662
#816263
#798153