Finite Group Databasebeta

← #11870823

Subgroups — #11870823

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 717 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595367C211yesmaximal, characteristic
2D3×#887C211yesmaximal, characteristic
3#10592494C211yesmaximal, characteristic, complemented
4C3×#4811C211yesmaximal, characteristic
5C3×#4790C211yesmaximal, characteristic, complemented
6#10591653C211yesmaximal, characteristic
7#10591580C211yesmaximal, characteristic, complemented
8#10591537C211yesmaximal, characteristic, complemented
9#10590952C211yesmaximal, characteristic
10#10590817C211yesmaximal, characteristic, complemented
11#10590807C211yesmaximal, characteristic, complemented
12#10590655C211yesmaximal, characteristic
13#10590481C211yesmaximal, characteristic, complemented
14#10590432C211yesmaximal, characteristic, complemented
15#10590427C211yesmaximal, characteristic
16#81452—31nomaximal
17#79722—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19#64153C2211yescharacteristic
20C2×#3756C2211yescharacteristic
21C2×#3746C2211yescharacteristic
22#64096C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63919C2211yescharacteristic
29#63899—21no—
30#63877—21no—
31D3×Dic3⋊C4—21no—
32C4×D3×Dic3—21no—
33C4×D3×Dic3C2211yescharacteristic
34#63857C2211yescharacteristic
35#63847—21no—
36#63844C2211yescharacteristic
37#63844C2211yescharacteristic
38#63843C2211yescharacteristic
39#63838—21no—
40#63837—21no—
41#63837—21no—
42C2×#3719C2211yescharacteristic
43C32×#103C2211yescharacteristic
44#63641C2211yescharacteristic
45#63637C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63576C2211yescharacteristic
54#63572C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5622—31no—
62#5578—31no—
63C4×D3×Q8—31no—
64C2×#887—31no—
65C3×#484—31no—
66C3×C4×Q16—31no—
67#5186—31no—
68#5182—31no—
69#5050—31no—
70C4×#216—31no—
71C4×#216—31no—
72#4970—31no—
73#4884—31no—
74#4875—31no—
75#4875—31no—
76#4875—31no—
77#4873—31no—
78#4873—31no—
79#4811D311yescharacteristic
80#4809—31no—
81#4795—31no—
82#4795—31no—
83#4795—31no—
84#4795—61no—
85#4793—31no—
86#4790—31no—
87#4790D311yescharacteristic, complemented
88#4739—31no—
89#4718—31no—
90C4×Dic12—31no—
91#4685—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#627—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3D411yescharacteristic
102C2×D3×Dic3D411yescharacteristic
103D3×Dic6—22no—
104D3×Dic6—22no—
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107#3756—22no—
108#3750—21no—
109#3750—21no—
110#3750—21no—
111C4×C3⋊Dic3—21no—
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114#3746—22no—
115C3×#216—22no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129#3724—21no—
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32D411yescharacteristic
139Dic32D411yescharacteristic
140#3719—22no—
141#3104—91noSylow
142C2×D3×Q8—31no—
143C22×Dic6—31no—
144C2×C3×Q16—31no—
145C3×C22⋊Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C2×C3×C4⋊C4—31no—
149#946C2×D311yescharacteristic
150Q8×Dic3—31no—
151Q8×Dic3C2×D311yescharacteristic
152#944—31no—
153#944—31no—
154#944—61no—
155C2×#216—31no—
156C2×#216—31no—
157C2×#216—31no—
158C2×#216—61no—
159C2×#216C2×D311yescharacteristic
160#924—31no—
161C2×Dic3⋊C4—61no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—61no—
164C2×Dic12—31no—
165C2×Dic12—31no—
166C2×Dic12—31no—
167C2×Dic12—61no—
168#897—31no—
169#896—61no—
170D3×C4⋊C4—61no—
171D3×C4⋊C4C2×D311yescharacteristic
172#889—61no—
173#889—61no—
174#888—31no—
175#888—31no—
176#887—31no—
177#887—31no—
178#887—31no—
179#887—31no—
180#887—31no—
181#887—61no—
182#887—61no—
183#887—61no—
184#887—61no—
185#887—61no—
186#887C2×D311yescharacteristic
187#878—61no—
188#877—61no—
189#872—61no—
190C42×D3—31no—
191C42×D3—61no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C4×Dic6—61no—
195C4×Dic6—61no—
196C3×#107—31no—
197C3×#107—31no—
198C3×#107—31no—
199C3×#103—21no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103C2×D311yescharacteristic
203C3×#103C2×D311yescharacteristic
204C3×C22⋊C8—31no—
205C3×C4×C8—31no—
206#835—31no—
207#835C2×D311yescharacteristic
208#830—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8C2×D311yescharacteristic
211#818C2×D311yescharacteristic
212#816—31no—
213#816—31no—
214#816—31no—
215#816C2×D311yescharacteristic
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—61no—
221C8×Dic3—31no—
222C8×Dic3C2×D311yescharacteristic
223#810—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#810—61no—
230#807—31no—
231#807—31no—
232#807C2×D311yescharacteristic
233#807C2×D311yescharacteristic
234C4×C3⋊C8—31no—
235C22×C3×D3C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C2411yescharacteristic
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3C2×D411yescharacteristic
244C2×C3⋊Dic3C2×D411yescharacteristic
245#634—21no—
246#634—21no—
247#634—21no—
248#634#4112yes—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×C4×D3—21no—
257C3×C4×D3—21no—
258C3×C4×D3—42no—
259C3×Dic6—21no—
260C3×Dic6#4112yes—
261#627—24no—
262#627—42no—
263D3×Dic3—24no—
264D3×Dic3—41no—
265D3×Dic3Q1614yescomplemented
266C32×C8—21no—
267C3⋊(C3⋊C8)—21no—
268C3×C3⋊C8—21no—
269C3×C3⋊C8—21no—
270#533—91no—
271C2×C4×Q8—91no—
272#484—31no—
273#484—91no—
274#477—91no—
275#477—91no—
276#462—91no—
277#462—91no—
278#451—91no—
279#451—91no—
280C4×Q16—31no—
281C4×Q16—91no—
282C4×Q16—91no—
283C4×Q16—91no—
284#431—91no—
285C2×C3×Q8—21no—
286C2×C3×Q8—31no—
287C2×C3×Q8C22×D311yescharacteristic
288C2×C3×Q8C22×D311yescharacteristic
289C22×C3×C4—31no—
290C22×C3×C4—61no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—61no—
294D3×Q8—62no—
295D3×Q8—62no—
296C2×C4×D3—21no—
297C2×C4×D3—31no—
298C2×C4×D3—31no—
299C2×C4×D3—61no—
300C2×C4×D3C22×D311yescharacteristic
301C2×Dic6—31no—
302C2×Dic6—31no—
303C2×Dic6—31no—
304C2×Dic6—31no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—62no—
308C2×Dic6—61no—
309C2×Dic6—61no—
310C2×Dic6—62no—
311C2×Dic6—61no—
312C2×Dic6—61no—
313C2×Dic6C22×D311yescharacteristic
314C3×Q16—62no—
315C2×C3×C8—21no—
316C2×C3×C8—31no—
317C2×C3×C8—31no—
318C2×C3×C8C22×D311yescharacteristic
319C2×C3×C8C22×D311yescharacteristic
320C3×C4⋊C4—21no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—61no—
326C3×C4⋊C4—61no—
327C3×C4⋊C4—61no—
328C3×C4⋊C4C22×D311yescharacteristic
329C3×C4⋊C4C22×D311yescharacteristic
330C3×C22⋊C4—61no—
331C3×C42—31no—
332C3×C42—61no—
333C3×C42—61no—
334#217—61no—
335#216—22no—
336#216—62no—
337#216—62no—
338#216—62no—
339#216—122no—
340(C2×D3)⋊C4—21no—
341(C2×D3)⋊C4—61no—
342C4⋊Dic3—21no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3C22×D311yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—21no—
349Dic3⋊C4—21no—
350Dic3⋊C4—21no—
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—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—121no—
366Dic3⋊C4—121no—
367Dic3⋊C4—121no—
368C4×Dic3—21no—
369C4×Dic3—21no—
370C4×Dic3—31no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—121no—
386C4×Dic3C22×D311yescharacteristic
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—61no—
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392Dic12—62no—
393Dic12—62no—
394Dic12—62no—
395Dic12—122no—
396C22×C32C22×D411yescharacteristic
397C2×C3×D3—21no—
398C2×C3×D3—21no—
399C2×C3×D3C2×Q1612yes—
400C32×C4—41no—
401C32×C4—41no—
402C32×C4C2×#4111yescharacteristic
403C32×C4C2×#4111yescharacteristic
404C3⋊Dic3—22no—
405C3⋊Dic3—21no—
406C3⋊Dic3—41no—
407C3⋊Dic3C2×Q1612yes—
408C3×Dic3—22no—
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—41no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C3×Dic3C2×Q1612yes—
415C22×Q8—91no—
416C2×Q16—31no—
417C2×Q16—91no—
418C2×Q16—91no—
419C2×Q16—91no—
420C4⋊Q8—91no—
421C4⋊Q8—91no—
422#125—181no—
423C22⋊Q8—31no—
424C22⋊Q8—91no—
425C22⋊Q8—181no—
426C4×Q8—31no—
427C4×Q8—31no—
428C4×Q8—91no—
429C4×Q8—91no—
430C4×Q8—91no—
431C4×Q8—91no—
432C4×Q8—181no—
433C4×Q8—181no—
434C4×Q8—181no—
435#117—181no—
436C2×C4⋊C4—31no—
437C2×C4⋊C4—181no—
438C2×C42—91no—
439C2×C42—181no—
440#107—31no—
441#107—31no—
442#107—31no—
443#107—91no—
444C4⋊C8—91no—
445C4⋊C8—91no—
446#103—31no—
447#103—31no—
448#103—91no—
449#103—91no—
450#103—91no—
451#103—91no—
452#103—91no—
453#103D3211yescharacteristic
454C22⋊C8—31no—
455C22⋊C8—91no—
456C4×C8—31no—
457C4×C8—91no—
458C23×C3—31no—
459C22×D3D3×D411yescharacteristic
460C3×Q8—21no—
461C3×Q8—21no—
462C3×Q8—21no—
463C3×Q8—21no—
464C3×Q8—32no—
465C3×Q8—41no—
466C3×Q8—41no—
467C3×Q8—61no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—122no—
485C2×C3×C4C23×D311yescharacteristic
486C2×C3×C4C23×D311yescharacteristic
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—34no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—64no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—121no—
504C2×Dic3—121no—
505C2×Dic3—121no—
506C2×Dic3D3×D411yescharacteristic
507C2×Dic3D3×D411yescharacteristic
508C2×Dic3D3×D411yescharacteristic
509C4×D3—21no—
510C4×D3—21no—
511C4×D3—34no—
512C4×D3—42no—
513C4×D3—64no—
514C4×D3—121no—
515Dic6—21no—
516Dic6—32no—
517Dic6—32no—
518Dic6—62no—
519Dic6—64no—
520Dic6—64no—
521Dic6—61no—
522Dic6—61no—
523Dic6—61no—
524Dic6—61no—
525Dic6—61no—
526Dic6—61no—
527Dic6—121no—
528Dic6—121no—
529Dic6—121no—
530Dic6—122no—
531Dic6—122no—
532Dic6#23512yes—
533C3×C8—21no—
534C3×C8—21no—
535C3×C8—41no—
536C3×C8—61no—
537C3×C8—61no—
538C3⋊C8—21no—
539C3⋊C8—21no—
540C3⋊C8—61no—
541C3⋊C8—61no—
542C3⋊C8—121no—
543C2×C32#52511yescharacteristic
544C2×C32C22×Q1611yescharacteristic
545C2×C32#57511yescharacteristic
546C3×D3—22no—
547C2×Q8—31no—
548C2×Q8—91no—
549C2×Q8—91no—
550C2×Q8—181no—
551C2×Q8—181no—
552C2×Q8—182no—
553C2×Q8—182no—
554C2×Q8C2×D3211yescharacteristic
555C22×C4—31no—
556C22×C4—61no—
557C22×C4—91no—
558C22×C4—91no—
559C22×C4—181no—
560Q16—62no—
561Q16—182no—
562Q16—182no—
563Q16—182no—
564C2×C8—31no—
565C2×C8—31no—
566C2×C8—91no—
567C2×C8C2×D3211yescharacteristic
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—181no—
576C4⋊C4—181no—
577C4⋊C4—181no—
578C4⋊C4—181no—
579C4⋊C4—181no—
580C4⋊C4—181no—
581C4⋊C4—181no—
582C4⋊C4—181no—
583C4⋊C4C2×D3211yescharacteristic
584C22⋊C4—61no—
585C22⋊C4—181no—
586C42—31no—
587C42—61no—
588C42—61no—
589C42—91no—
590C42—91no—
591C42—91no—
592C42—181no—
593C42—181no—
594C42—181no—
595C42—181no—
596C22×C3—21no—
597C22×C3—32no—
598C22×C3—61no—
599C22×C3—61no—
600C22×C3C2×D3×D411yescharacteristic
601C22×C3C2×D3×D411yescharacteristic
602C2×D3—21no—
603C2×D3—21no—
604C2×D3D3×Q1612yes—
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—32no—
608C3×C4—41no—
609C3×C4—41no—
610C3×C4—41no—
611C3×C4—41no—
612C3×C4—62no—
613C3×C4—61no—
614C3×C4—61no—
615C3×C4—81no—
616C3×C4—81no—
617C3×C4—121no—
618C3×C4—121no—
619C3×C4—121no—
620C3×C4C2×#23511yescharacteristic
621C3×C4D3×#4111yescharacteristic
622C3×C4D3×#4111yescharacteristic
623C3×C4D3×#4111yescharacteristic
624Dic3—21no—
625Dic3—21no—
626Dic3—22no—
627Dic3—32no—
628Dic3—32no—
629Dic3—41no—
630Dic3—41no—
631Dic3—41no—
632Dic3—62no—
633Dic3—62no—
634Dic3—61no—
635Dic3—61no—
636Dic3—62no—
637Dic3—122no—
638Dic3—121no—
639Dic3—121no—
640Dic3—121no—
641Dic3—241no—
642Dic3D3×Q1612yes—
643C32#310411yescharacteristic, complemented, Sylow
644C23—31no—
645Q8—21no—
646Q8—21no—
647Q8—32no—
648Q8—61no—
649Q8—92no—
650Q8—184no—
651Q8—181no—
652Q8—181no—
653Q8—181no—
654Q8—362no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—94no—
667C2×C4—91no—
668C2×C4—91no—
669C2×C4—122no—
670C2×C4—184no—
671C2×C4—181no—
672C2×C4—181no—
673C2×C4—361no—
674C2×C4C22×D3211yescharacteristic
675C8—21no—
676C8—61no—
677C8—61no—
678C8—181no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—62no—
683C2×C3#554711yescharacteristic
684C2×C3#565611yescharacteristic
685C2×C3C2×D3×Q1611yescharacteristic
686C2×C3C2×D3×Q1611yescharacteristic
687C2×C3#576811yescharacteristic
688C2×C3#577311yescharacteristic
689D3—22no—
690C22—32no—
691C22—61no—
692C22—61no—
693C22D32×D411yescharacteristic
694C4—32no—
695C4—41no—
696C4—41no—
697C4—61no—
698C4—61no—
699C4—62no—
700C4—92no—
701C4—121no—
702C4—121no—
703C4—121no—
704C4—181no—
705C4—182no—
706C4—361no—
707C4D3×#23511yescharacteristic
708C4#6431211yescharacteristic
709C3—21no—
710C3#7972211yescharacteristic, complemented
711C3#8145211yescharacteristic, complemented
712C2—62no—
713C2#1059426611yescharacteristic
714C2#1059474511yescharacteristic
715C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#103D32
hypocenterC32#3104
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
3. #10592494C2semidirect
5. C3×#4790C2semidirect
7. #10591580C2semidirect
8. #10591537C2semidirect
10. #10590817C2semidirect
11. #10590807C2semidirect
13. #10590481C2semidirect
14. #10590432C2semidirect
87. #4790D3semidirect
265. D3×Dic3Q16semidirect
643. C32#3104semidirect
710. C3#79722semidirect
711. C3#81452semidirect

Maximal subgroups

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

subgroupindex
#105953672
D3×#8872
#105924942
C3×#48112
C3×#47902
#105916532
#105915802
#105915372
#105909522
#105908172
#105908072
#105906552
#105904812
#105904322
#105904272
#814523
#797223