Finite Group Databasebeta

← #11897582

Subgroups — #11897582

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 703 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594485C211yesmaximal, characteristic, complemented
2#10594376C211yesmaximal, characteristic, complemented
3#10592554C211yesmaximal, characteristic, complemented
4C3×#4871C211yesmaximal, characteristic, complemented
5C3×#4870C211yesmaximal, characteristic, complemented
6#10590788C211yesmaximal, characteristic, complemented
7#10590772C211yesmaximal, characteristic, complemented
8#10590757C211yesmaximal, characteristic, complemented
9#10590740C211yesmaximal, characteristic
10#10590472C211yesmaximal, characteristic, complemented
11#10590471C211yesmaximal, characteristic, complemented
12#10590455C211yesmaximal, characteristic
13#10590455C211yesmaximal, characteristic
14#10590420C211yesmaximal, characteristic, complemented
15#10590419C211yesmaximal, characteristic, complemented
16#81158—31nomaximal
17#81055—31nomaximal
18C2×D3×Dic6—21no—
19#64097C2211yescharacteristic
20#64097C2211yescharacteristic
21C3×#893C2211yescharacteristic
22C3×#893C2211yescharacteristic
23C3×#890C2211yescharacteristic
24C3×#888C2211yescharacteristic
25#63918C2211yescharacteristic
26C4×#627C2211yescharacteristic
27#63899—21no—
28#63898C2211yescharacteristic
29#63898C2211yescharacteristic
30#63896—21no—
31#63896—21no—
32Dic3×D12C2211yescharacteristic
33Dic3×D12C2211yescharacteristic
34#63887—21no—
35D3×Dic3⋊C4—21no—
36#63869C2211yescharacteristic
37#63857—21no—
38#63851—21no—
39C2×#3713C2211yescharacteristic
40C32×#106C2211yescharacteristic
41#63644C2211yescharacteristic
42C8×C3⋊Dic3C2211yescharacteristic
43#63635C2211yescharacteristic
44#63635C2211yescharacteristic
45C3×#821C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×Dic3⋊C8C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63576C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63554C2211yescharacteristic
60#63554C2211yescharacteristic
61#5727—31no—
62#5690—31no—
63#5539—31no—
64D4×Dic6—31no—
65C3×#478—31no—
66C3×#476—31no—
67#5081—31no—
68#5064—31no—
69#5014—31no—
70#5014—31no—
71#4890—31no—
72#4876—31no—
73#4871D311yescharacteristic, complemented
74#4870—31no—
75#4870D311yescharacteristic, complemented
76#4856—31no—
77#4855—31no—
78#4855—31no—
79#4855—61no—
80#4847—31no—
81#4842—31no—
82#4828—31no—
83#4828—31no—
84#4785—31no—
85#4785—31no—
86#4763—31no—
87#4761—31no—
88#4761—31no—
89#4759—31no—
90#4756—31no—
91#4756—31no—
92C2×#634—21no—
93C2×#634—21no—
94C2×C3×D12C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3—21no—
98C2×C3×Dic6—21no—
99C2×#627—21no—
100C2×#627D411yescharacteristic
101C2×D3×Dic3—21no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105D3×Dic6—44no—
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111#3750—21no—
112#3750—21no—
113C4×C3⋊Dic3C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×C4×Dic3C2311yescharacteristic
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126#3724—21no—
127#3724D411yescharacteristic
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136#3713Q814yescomplemented
137#3384—91noSylow
138C2×D3×Q8—61no—
139C22×Dic6—61no—
140C3×C4⋊Q8—31no—
141C3×#125—31no—
142C3×C4×D4—31no—
143C3×C4×D4—31no—
144#946—61no—
145D4×Dic3—31no—
146D4×Dic3—31no—
147D4×Dic3—31no—
148D4×Dic3—31no—
149C2×#213—31no—
150C2×#213—31no—
151#924—61no—
152#924—61no—
153C2×Dic3⋊C4—61no—
154#897—61no—
155#896—61no—
156#896—61no—
157#896—61no—
158#896—61no—
159#893—31no—
160#893—31no—
161#893C2×D311yescharacteristic
162#893C2×D311yescharacteristic
163D3×C4⋊C4—61no—
164#890—31no—
165#890C2×D311yescharacteristic
166#888—31no—
167#888—31no—
168#888—31no—
169#888—31no—
170#888—31no—
171#888—61no—
172#888—61no—
173#888C2×D311yescharacteristic
174#878—61no—
175#878—61no—
176#878—61no—
177#878—61no—
178C4×D12—31no—
179C4×D12—31no—
180#870—31no—
181#869—31no—
182C4×Dic6—31no—
183C4×Dic6—31no—
184C3×#107—31no—
185C3×#106—21no—
186C3×#106—31no—
187C3×#106C2×D311yescharacteristic
188C3×#106C2×D311yescharacteristic
189C3×C4⋊C8—31no—
190C3×C4⋊C8—31no—
191C3×#102—31no—
192C3×#102—31no—
193C3×#102—31no—
194C3×#102—31no—
195#832—31no—
196#832—31no—
197#821—31no—
198#821—31no—
199#821C2×D311yescharacteristic
200#821C2×D311yescharacteristic
201#818—31no—
202#817—31no—
203#817—31no—
204#817—31no—
205#817—61no—
206#815—31no—
207#815—31no—
208Dic3⋊C8—31no—
209Dic3⋊C8—31no—
210Dic3⋊C8C2×D311yescharacteristic
211Dic3⋊C8C2×D311yescharacteristic
212C8×Dic3—31no—
213C8×Dic3—31no—
214C8×Dic3—61no—
215#809C2×D311yescharacteristic
216#809C2×D311yescharacteristic
217#808—31no—
218#808—31no—
219#808—31no—
220#808—31no—
221#808—31no—
222#808—61no—
223#808—61no—
224#808C2×D311yescharacteristic
225#807—31no—
226#807—31no—
227#807—31no—
228#807C2×D311yescharacteristic
229#803—31no—
230#803—31no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4C2411yescharacteristic
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3C2×D411yescharacteristic
239C2×C3⋊Dic3C2×D411yescharacteristic
240#634—42no—
241#634—81no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3C2×D411yescharacteristic
245C2×C3×Dic3C2×D411yescharacteristic
246C2×C3×Dic3C2×D411yescharacteristic
247C2×C3×Dic3C2×D411yescharacteristic
248C3×D12—21no—
249C3×D12—21no—
250C3×D12C2×Q812yes—
251C3×D12C2×Q812yescomplemented
252C3×C4×D3—42no—
253C3×C4×D3—81no—
254C3×Dic6—42no—
255#627—22no—
256#627—42no—
257D3×Dic3—42no—
258D3×Dic3—42no—
259D3×Dic3—42no—
260D3×Dic3—81no—
261C32×C8—21no—
262C3⋊(C3⋊C8)C2×Q812yescomplemented
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#554—91no—
266D4×Q8—91no—
267#501—91no—
268#501—91no—
269#498—91no—
270#478—31no—
271#478—91no—
272#476—31no—
273#476—91no—
274#476—91no—
275#474—91no—
276#446—91no—
277#442—91no—
278#442—91no—
279C4×D8—91no—
280C2×C3×Q8—61no—
281C2×C3×D4—31no—
282C2×C3×D4—31no—
283C22×C3×C4—61no—
284C22×C3×C4—61no—
285C22×Dic3—61no—
286C22×Dic3—61no—
287C22×Dic3—61no—
288C22×Dic3—61no—
289D3×Q8—124no—
290C2×D12C22×D311yescharacteristic
291C2×D12C22×D311yescharacteristic
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—61no—
295C2×C4×D3—61no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×Dic6—21no—
299C2×Dic6—31no—
300C2×Dic6—31no—
301C2×Dic6—61no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—121no—
308C2×Dic6—121no—
309C2×Dic6—124no—
310C2×C3×C8—21no—
311C2×C3×C8—31no—
312C2×C3×C8—31no—
313C2×C3×C8C22×D311yescharacteristic
314C2×C3×C8C22×D311yescharacteristic
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C42—31no—
329C3×C42—31no—
330#217—61no—
331#217—61no—
332#217—61no—
333#217—61no—
334#213—34no—
335#213—34no—
336(C2×D3)⋊C4—21no—
337(C2×D3)⋊C4—21no—
338(C2×D3)⋊C4—61no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341(C2×D3)⋊C4—61no—
342C4⋊Dic3—21no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3C22×D311yescharacteristic
354C4⋊Dic3C22×D311yescharacteristic
355Dic3⋊C4—21no—
356Dic3⋊C4—21no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—121no—
370Dic3⋊C4—121no—
371C4×Dic3—31no—
372C4×Dic3—31no—
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
381C22×C32C22×D411yescharacteristic
382C2×C3×D3—22no—
383C2×C3×D3—22no—
384C2×C3×D3—41no—
385C2×C3×D3—41no—
386C2×C3×D3—41no—
387C2×C3×D3—41no—
388C32×C4—41no—
389C32×C4—41no—
390C32×C4C22×Q811yescharacteristic
391C32×C42−1+411yescharacteristic
392C3⋊Dic3—21no—
393C3⋊Dic3—41no—
394C3⋊Dic3—41no—
395C3⋊Dic3AGL(1,ℤ/8)12yes—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C22×Q8—181no—
403C2×D8—91no—
404C4⋊Q8—31no—
405C4⋊Q8—91no—
406C4⋊Q8—91no—
407C4⋊Q8—91no—
408#125—31no—
409#125—91no—
410C22⋊Q8—181no—
411C22⋊Q8—181no—
412C22⋊Q8—181no—
413C22⋊Q8—181no—
414C22⋊Q8—181no—
415C22⋊Q8—181no—
416C4×Q8—91no—
417C4×D4—31no—
418C4×D4—31no—
419C4×D4—91no—
420C4×D4—91no—
421C4×D4—91no—
422C4×D4—91no—
423C2×C4⋊C4—181no—
424#107—31no—
425#107—91no—
426#107—91no—
427#106—31no—
428#106—91no—
429#106—91no—
430#106—91no—
431#106—91no—
432#106D3211yescharacteristic
433C4⋊C8—31no—
434C4⋊C8—31no—
435C4⋊C8—91no—
436#102—31no—
437#102—31no—
438#102—31no—
439#102—31no—
440#102—91no—
441#102—91no—
442#97—91no—
443#97—91no—
444C4×C8—91no—
445C23×C3—61no—
446C23×C3—61no—
447C22×D3—21no—
448C22×D3—21no—
449C3×Q8—122no—
450C3×D4—32no—
451C3×D4—32no—
452C3×D4—61no—
453C3×D4—61no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—31no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—122no—
468C2×C3×C4—241no—
469C2×C3×C4C23×D311yescharacteristic
470C2×C3×C4C23×D311yescharacteristic
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—31no—
474C2×Dic3—31no—
475C2×Dic3—31no—
476C2×Dic3—31no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—121no—
484C2×Dic3—121no—
485C2×Dic3—122no—
486C2×Dic3—122no—
487C2×Dic3—122no—
488C2×Dic3—241no—
489C2×Dic3D3×D411yescharacteristic
490C2×Dic3D3×D411yescharacteristic
491C2×Dic3D3×D411yescharacteristic
492C2×Dic3D3×D411yescharacteristic
493D12—21no—
494D12—21no—
495D12D3×Q812yes—
496D12D3×Q812yescomplemented
497C4×D3—42no—
498C4×D3—81no—
499C4×D3—122no—
500C4×D3—122no—
501C4×D3—122no—
502C4×D3—241no—
503Dic6—42no—
504Dic6—62no—
505Dic6—62no—
506Dic6—122no—
507Dic6—122no—
508Dic6—122no—
509Dic6—122no—
510Dic6—242no—
511Dic6—241no—
512Dic6—241no—
513Dic6—242no—
514C3×C8—22no—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—61no—
518C3×C8—61no—
519C3⋊C8—21no—
520C3⋊C8—21no—
521C3⋊C8—32no—
522C3⋊C8—32no—
523C3⋊C8—62no—
524C2×C32D4×Q811yescharacteristic
525C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
526C2×C32#57711yescharacteristic
527C3×D3—42no—
528C3×D3—42no—
529C2×Q8—61no—
530C2×Q8—91no—
531C2×Q8—181no—
532C2×Q8—181no—
533C2×Q8—181no—
534C2×Q8—364no—
535C2×D4—31no—
536C2×D4—31no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—181no—
540C22×C4—181no—
541C22×C4—181no—
542C22×C4—181no—
543D8—94no—
544C2×C8—31no—
545C2×C8—31no—
546C2×C8—91no—
547C2×C8C2×D3211yescharacteristic
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—91no—
554C4⋊C4—91no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—91no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4C2×D3211yescharacteristic
564C4⋊C4C2×D3211yescharacteristic
565C22⋊C4—61no—
566C22⋊C4—61no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C42—31no—
572C42—31no—
573C42—91no—
574C22×C3—21no—
575C22×C3—62no—
576C22×C3—62no—
577C22×C3—121no—
578C22×C3—121no—
579C22×C3—121no—
580C22×C3—121no—
581C22×C3C2×D3×D411yescharacteristic
582C22×C3C2×D3×D411yescharacteristic
583C2×D3—22no—
584C2×D3—22no—
585C2×D3—41no—
586C2×D3—41no—
587C2×D3—41no—
588C2×D3—41no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—61no—
596C3×C4—61no—
597C3×C4—61no—
598C3×C4—61no—
599C3×C4—81no—
600C3×C4—81no—
601C3×C4—121no—
602C3×C4—121no—
603C3×C4C2×D3×Q811yescharacteristic
604C3×C4C2×D3×Q811yescharacteristic
605C3×C4#101011yescharacteristic
606C3×C4#101011yescharacteristic
607Dic3—21no—
608Dic3—21no—
609Dic3—21no—
610Dic3—21no—
611Dic3—32no—
612Dic3—32no—
613Dic3—41no—
614Dic3—41no—
615Dic3—62no—
616Dic3—62no—
617Dic3—61no—
618Dic3—61no—
619Dic3—121no—
620Dic3—121no—
621Dic3—121no—
622Dic3—121no—
623Dic3—241no—
624Dic3—241no—
625C32#338411yescharacteristic, complemented, Sylow
626C23—61no—
627C23—61no—
628Q8—122no—
629Q8—182no—
630Q8—362no—
631Q8—362no—
632Q8—721no—
633D4—32no—
634D4—32no—
635D4—61no—
636D4—61no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—31no—
640C2×C4—31no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—91no—
646C2×C4—91no—
647C2×C4—122no—
648C2×C4—181no—
649C2×C4—181no—
650C2×C4—241no—
651C2×C4—362no—
652C2×C4—362no—
653C2×C4—362no—
654C2×C4—721no—
655C2×C4C22×D3211yescharacteristic
656C8—21no—
657C8—61no—
658C8—61no—
659C8—92no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—122no—
664C2×C3—122no—
665C2×C3#563211yescharacteristic
666C2×C3#563211yescharacteristic
667C2×C3#576211yescharacteristic
668C2×C3#577011yescharacteristic
669C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
670C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
671D3—42no—
672D3—42no—
673C22—62no—
674C22—62no—
675C22—121no—
676C22—121no—
677C22—121no—
678C22—121no—
679C22D32×D411yescharacteristic
680C4—41no—
681C4—41no—
682C4—61no—
683C4—61no—
684C4—61no—
685C4—61no—
686C4—92no—
687C4—121no—
688C4—121no—
689C4—181no—
690C4—361no—
691C4—361no—
692C4#6429811yescharacteristic
693C4D32×Q811yescharacteristic
694C3—21no—
695C3#8105511yescharacteristic, complemented
696C3#8115811yescharacteristic, complemented
697C2—122no—
698C2—122no—
699C2#1059437711yescharacteristic
700C2#1059474011yescharacteristic
701C2#1059475311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenter#106D32
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. #10594485C2semidirect
2. #10594376C2semidirect
3. #10592554C2semidirect
4. C3×#4871C2semidirect
5. C3×#4870C2semidirect
6. #10590788C2semidirect
7. #10590772C2semidirect
8. #10590757C2semidirect
10. #10590472C2semidirect
11. #10590471C2semidirect
14. #10590420C2semidirect
15. #10590419C2semidirect
73. #4871D3semidirect
75. #4870D3semidirect
136. #3713Q8semidirect
251. C3×D12C2×Q8semidirect
262. C3⋊(C3⋊C8)C2×Q8semidirect
496. D12D3×Q8semidirect
625. C32#3384semidirect
695. C3#81055semidirect
696. C3#81158semidirect

Maximal subgroups

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

subgroupindex
#105944852
#105943762
#105925542
C3×#48712
C3×#48702
#105907882
#105907722
#105907572
#105907402
#105904722
#105904712
#105904552
#105904202
#105904192
#811583
#810553