Finite Group Databasebeta

← #11897583

Subgroups — #11897583

Order 1152.

799 conjugacy classes of subgroups.

The subgroup lattice has 707 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594460C211yesmaximal, characteristic, complemented
2#10594379C211yesmaximal, characteristic, complemented
3#10592570C211yesmaximal, characteristic, complemented
4C3×#4870C211yesmaximal, characteristic, complemented
5C3×#4855C211yesmaximal, characteristic, complemented
6#10590785C211yesmaximal, characteristic, complemented
7#10590776C211yesmaximal, characteristic, complemented
8#10590769C211yesmaximal, characteristic, complemented
9#10590745C211yesmaximal, characteristic
10#10590589C211yesmaximal, characteristic
11#10590564C211yesmaximal, characteristic, complemented
12#10590466C211yesmaximal, characteristic, complemented
13#10590463C211yesmaximal, characteristic, complemented
14#10590462C211yesmaximal, characteristic
15#10590421C211yesmaximal, characteristic, complemented
16#81905—31nomaximal
17#81055—31nomaximal
18C2×#3797—21no—
19#64102C2211yescharacteristic
20#64099C2211yescharacteristic
21C3×#893C2211yescharacteristic
22C3×#888C2211yescharacteristic
23C3×#888C2211yescharacteristic
24C3×#888C2211yescharacteristic
25#63919C2211yescharacteristic
26C4×#627C2211yescharacteristic
27#63898C2211yescharacteristic
28#63894C2211yescharacteristic
29#63894C2211yescharacteristic
30#63893—21no—
31Dic3×D12C2211yescharacteristic
32#63888—21no—
33#63888—21no—
34#63887—21no—
35D3×Dic3⋊C4—21no—
36#63869C2211yescharacteristic
37#63865—21no—
38#63856—21no—
39C2×#3714C2211yescharacteristic
40C32×#106C2211yescharacteristic
41#63648C2211yescharacteristic
42#63641C2211yescharacteristic
43#63636C2211yescharacteristic
44#63634C2211yescharacteristic
45C3×#821C2211yescharacteristic
46C3×#817C2211yescharacteristic
47C3×Dic3⋊C8C2211yescharacteristic
48C3×C8×Dic3C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63575C2211yescharacteristic
54#63575C2211yescharacteristic
55#63574C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59#63555C2211yescharacteristic
60#63554C2211yescharacteristic
61#5730—31no—
62#5727—31no—
63#5727—31no—
64#5539—31no—
65C3×#498—31no—
66C3×#476—31no—
67#5087—31no—
68#5084—31no—
69#5081—31no—
70#5014—31no—
71#4871—31no—
72#4871—31no—
73#4871—31no—
74#4871—61no—
75#4870—31no—
76#4870—31no—
77#4870D311yescharacteristic, complemented
78#4869—31no—
79#4869—31no—
80#4856—31no—
81#4856—31no—
82#4856—31no—
83#4855D311yescharacteristic, complemented
84#4847—31no—
85#4828—31no—
86#4785—31no—
87#4761—31no—
88#4759—31no—
89#4756—31no—
90C4×D24—31no—
91#4679—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6—21no—
99C2×#627—21no—
100C2×#627D411yescharacteristic
101C2×#624—21no—
102C2×#624—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105#3797—44no—
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109#3752—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113C4×C3⋊Dic3C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C3×(C2×D3)⋊C4—21no—
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
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#3724—21no—
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132#3722—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136#3714Q814yescomplemented
137#3384—91noSylow
138C2×D3×Q8—61no—
139C2×D3×Q8—61no—
140C3×C4⋊Q8—31no—
141C3×C4⋊Q8—31no—
142C3×C4⋊Q8—31no—
143C3×C4×D4—31no—
144#946—61no—
145#946—61no—
146#946—61no—
147#946—61no—
148D4×Dic3—31no—
149D4×Dic3—31no—
150C2×#213—31no—
151#924—61no—
152C2×Dic3⋊C4—61no—
153C2×D24—31no—
154#897—61no—
155#896—61no—
156#896—61no—
157#896—61no—
158#896—61no—
159#893—31no—
160#893—31no—
161#893—31no—
162#893—31no—
163#893—31no—
164#893—61no—
165#893C2×D311yescharacteristic
166D3×C4⋊C4—61no—
167#890—31no—
168#890—31no—
169#890—31no—
170#890—61no—
171#888—31no—
172#888—31no—
173#888C2×D311yescharacteristic
174#888C2×D311yescharacteristic
175#888C2×D311yescharacteristic
176#878—61no—
177#878—61no—
178C4×D12—31no—
179C4×D12—31no—
180C4×D12—31no—
181#870—31no—
182C4×Dic6—31no—
183C4×Dic6—31no—
184C3×#106—21no—
185C3×#106—31no—
186C3×#106—31no—
187C3×#106—31no—
188C3×#106—31no—
189C3×#106C2×D311yescharacteristic
190C3×#106C2×D311yescharacteristic
191C3×C4⋊C8—31no—
192C3×#102—31no—
193C3×#102—31no—
194C3×C4×C8—31no—
195#832—31no—
196#821—31no—
197#821—31no—
198#821—31no—
199#821—61no—
200#821C2×D311yescharacteristic
201#818—31no—
202#818—31no—
203#817C2×D311yescharacteristic
204#815—31no—
205#815—31no—
206#815—31no—
207Dic3⋊C8—31no—
208Dic3⋊C8—31no—
209Dic3⋊C8—31no—
210Dic3⋊C8—61no—
211Dic3⋊C8C2×D311yescharacteristic
212C8×Dic3C2×D311yescharacteristic
213#809—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—61no—
218#809C2×D311yescharacteristic
219#808—31no—
220#808—31no—
221#808C2×D311yescharacteristic
222#808C2×D311yescharacteristic
223#808C2×D311yescharacteristic
224#807—31no—
225#807—31no—
226#807—31no—
227#807—31no—
228#807—61no—
229C4⋊(C3⋊C8)—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⋊Dic3C2×D411yescharacteristic
238C2×C3⋊Dic3C2×D411yescharacteristic
239C4⋊(C3⋊D3)—21no—
240C4⋊(C3⋊D3)C2×Q812yes—
241C4×C3⋊D3—42no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3C2×D411yescharacteristic
246C2×C3×Dic3C2×D411yescharacteristic
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C3×D12—21no—
250C3×D12C2×Q812yescomplemented
251C3×C4×D3—81no—
252C3×Dic6—42no—
253C3×Dic6—42no—
254C3×Dic6—81no—
255#627—22no—
256#627—42no—
257#624—42no—
258#624—42no—
259D3×Dic3—42no—
260D3×Dic3—81no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8C2×Q812yescomplemented
265#554—91no—
266D4×Q8—91no—
267#501—91no—
268#501—91no—
269#498—31no—
270#478—91no—
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×Q8—61no—
282C2×C3×Q8—61no—
283C2×C3×D4—31no—
284C22×C3×C4—61no—
285C22×Dic3—61no—
286C22×Dic3—61no—
287D3×Q8—124no—
288D3×Q8—124no—
289C2×D12—31no—
290C2×D12—31no—
291C2×D12—61no—
292C2×D12C22×D311yescharacteristic
293C2×C4×D3—21no—
294C2×C4×D3—61no—
295C2×C4×D3—61no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×C4×D3—61no—
299C2×C4×D3—61no—
300C2×C4×D3—61no—
301C2×C4×D3—61no—
302C2×C4×D3—121no—
303C2×Dic6—21no—
304C2×Dic6—21no—
305C2×Dic6—21no—
306C2×Dic6—31no—
307C2×Dic6—31no—
308C2×Dic6—61no—
309C2×Dic6—61no—
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—31no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C22⋊C4—61no—
328C3×C42—31no—
329C3×C42—31no—
330#217—61no—
331#217—61no—
332#213—34no—
333(C2×D3)⋊C4—21no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—61no—
338(C2×D3)⋊C4—61no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341(C2×D3)⋊C4—61no—
342(C2×D3)⋊C4—121no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—121no—
352C4⋊Dic3C22×D311yescharacteristic
353C4⋊Dic3C22×D311yescharacteristic
354C4⋊Dic3C22×D311yescharacteristic
355Dic3⋊C4—21no—
356Dic3⋊C4—21no—
357Dic3⋊C4—21no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—121no—
370C4×Dic3—31no—
371C4×Dic3—31no—
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
380D24—34no—
381C22×C32C22×D411yescharacteristic
382C2×C3⋊D3—22no—
383C2×C3⋊D3—41no—
384C2×C3⋊D3—41no—
385C2×C3×D3—22no—
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—21no—
394C3⋊Dic3—41no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3AGL(1,ℤ/8)12yes—
402C22×Q8—181no—
403C2×D8—91no—
404C4⋊Q8—31no—
405C4⋊Q8—31no—
406C4⋊Q8—31no—
407C4⋊Q8—91no—
408#125—91no—
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—91no—
419C4×D4—91no—
420C4×D4—91no—
421C4×D4—91no—
422C4×D4—91no—
423C2×C4⋊C4—181no—
424#107—91no—
425#107—91no—
426#107—91no—
427#106—31no—
428#106—31no—
429#106—31no—
430#106—31no—
431#106—91no—
432#106D3211yescharacteristic
433C4⋊C8—31no—
434C4⋊C8—91no—
435C4⋊C8—91no—
436#102—31no—
437#102—31no—
438#102—91no—
439#102—91no—
440#102—91no—
441#102—91no—
442#97—91no—
443#97—91no—
444C4×C8—31no—
445C23×C3—61no—
446C22×D3—21no—
447C22×D3—61no—
448C22×D3—61no—
449C22×D3—121no—
450C3×Q8—122no—
451C3×Q8—122no—
452C3×Q8—241no—
453C3×D4—32no—
454C3×D4—61no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—241no—
470C2×C3×C4C23×D311yescharacteristic
471C2×C3×C4C23×D311yescharacteristic
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—31no—
476C2×Dic3—31no—
477C2×Dic3—31no—
478C2×Dic3—31no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—121no—
484C2×Dic3—122no—
485C2×Dic3—241no—
486C2×Dic3D3×D411yescharacteristic
487C2×Dic3D3×D411yescharacteristic
488C2×Dic3D3×D411yescharacteristic
489C2×Dic3D3×D411yescharacteristic
490D12—21no—
491D12—32no—
492D12—32no—
493D12—62no—
494D12—61no—
495D12—61no—
496D12—121no—
497D12D3×Q812yescomplemented
498C4×D3—81no—
499C4×D3—122no—
500C4×D3—122no—
501C4×D3—122no—
502C4×D3—122no—
503C4×D3—122no—
504C4×D3—122no—
505C4×D3—122no—
506C4×D3—242no—
507C4×D3—241no—
508Dic6—42no—
509Dic6—42no—
510Dic6—62no—
511Dic6—62no—
512Dic6—81no—
513Dic6—122no—
514Dic6—122no—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—32no—
518C3×C8—41no—
519C3×C8—61no—
520C3⋊C8—21no—
521C3⋊C8—61no—
522C3⋊C8—61no—
523C3⋊C8—121no—
524C3⋊C8D3×Q812yescomplemented
525C2×C32D4×Q811yescharacteristic
526C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
527C2×C32#57711yescharacteristic
528C3⋊D3—42no—
529C3×D3—42no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—91no—
534C2×Q8—181no—
535C2×Q8—364no—
536C2×D4—31no—
537C2×D4—91no—
538C22×C4—61no—
539C22×C4—181no—
540C22×C4—181no—
541C22×C4—181no—
542C22×C4—181no—
543C22×C4—181no—
544D8—94no—
545C2×C8—31no—
546C2×C8—31no—
547C2×C8—91no—
548C2×C8C2×D3211yescharacteristic
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4C2×D3211yescharacteristic
565C4⋊C4C2×D3211yescharacteristic
566C22⋊C4—61no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C42—31no—
573C42—31no—
574C42—91no—
575C22×C3—21no—
576C22×C3—62no—
577C22×C3—121no—
578C22×C3—121no—
579C22×C3C2×D3×D411yescharacteristic
580C22×C3C2×D3×D411yescharacteristic
581C2×D3—22no—
582C2×D3—41no—
583C2×D3—41no—
584C2×D3—62no—
585C2×D3—62no—
586C2×D3—122no—
587C2×D3—121no—
588C2×D3—121no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—241no—
592C2×D3—241no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—32no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—61no—
601C3×C4—61no—
602C3×C4—61no—
603C3×C4—81no—
604C3×C4—81no—
605C3×C4—121no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4C2×D3×Q811yescharacteristic
609C3×C4C2×D3×Q811yescharacteristic
610C3×C4#100711yescharacteristic
611C3×C4#101011yescharacteristic
612Dic3—21no—
613Dic3—21no—
614Dic3—21no—
615Dic3—41no—
616Dic3—41no—
617Dic3—41no—
618Dic3—61no—
619Dic3—61no—
620Dic3—61no—
621Dic3—61no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—241no—
627Dic3#91412yes—
628C32#338411yescharacteristic, complemented, Sylow
629C23—61no—
630C23—181no—
631Q8—122no—
632Q8—122no—
633Q8—182no—
634Q8—241no—
635Q8—362no—
636D4—32no—
637D4—61no—
638D4—92no—
639D4—181no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—91no—
650C2×C4—91no—
651C2×C4—181no—
652C2×C4—241no—
653C2×C4—362no—
654C2×C4—362no—
655C2×C4—362no—
656C2×C4—362no—
657C2×C4—721no—
658C2×C4C22×D3211yescharacteristic
659C8—21no—
660C8—32no—
661C8—61no—
662C8—181no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—122no—
667C2×C3#563211yescharacteristic
668C2×C3#572711yescharacteristic
669C2×C3C2×#91411yescharacteristic
670C2×C3#576211yescharacteristic
671C2×C3#576211yescharacteristic
672C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
673D3—42no—
674D3—122no—
675D3—122no—
676D3—242no—
677C22—62no—
678C22—121no—
679C22—121no—
680C22—182no—
681C22—361no—
682C22—361no—
683C22D32×D411yescharacteristic
684C4—32no—
685C4—41no—
686C4—41no—
687C4—61no—
688C4—61no—
689C4—61no—
690C4—121no—
691C4—121no—
692C4—121no—
693C4—181no—
694C4—181no—
695C4—361no—
696C4#6429711yescharacteristic
697C4D32×Q811yescharacteristic
698C3—21no—
699C3#8105511yescharacteristic, complemented
700C3#8190511yescharacteristic, complemented
701C2—122no—
702C2—362no—
703C2#1059437811yescharacteristic
704C2D3×#91411yescharacteristic
705C2#1059474811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
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. #10594460C2semidirect
2. #10594379C2semidirect
3. #10592570C2semidirect
4. C3×#4870C2semidirect
5. C3×#4855C2semidirect
6. #10590785C2semidirect
7. #10590776C2semidirect
8. #10590769C2semidirect
11. #10590564C2semidirect
12. #10590466C2semidirect
13. #10590463C2semidirect
15. #10590421C2semidirect
77. #4870D3semidirect
83. #4855D3semidirect
136. #3714Q8semidirect
250. C3×D12C2×Q8semidirect
264. C3×C3⋊C8C2×Q8semidirect
497. D12D3×Q8semidirect
524. C3⋊C8D3×Q8semidirect
628. C32#3384semidirect
699. C3#81055semidirect
700. C3#81905semidirect

Maximal subgroups

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

subgroupindex
#105944602
#105943792
#105925702
C3×#48702
C3×#48552
#105907852
#105907762
#105907692
#105907452
#105905892
#105905642
#105904662
#105904632
#105904622
#105904212
#819053
#810553