Finite Group Databasebeta

← #11877033

Subgroups — #11877033

Order 1152.

771 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5622C211yesmaximal, characteristic
2#10594808C211yesmaximal, characteristic
3#10592751C211yesmaximal, characteristic
4C3×#5052C211yesmaximal, characteristic
5#10591626C211yesmaximal, characteristic, complemented
6#10591623C211yesmaximal, characteristic, complemented
7#10591576C211yesmaximal, characteristic, complemented
8#10591541C211yesmaximal, characteristic, complemented
9#10591189C211yesmaximal, characteristic
10#10591121C211yesmaximal, characteristic
11Dic3×#208C211yesmaximal, characteristic
12#10590560C211yesmaximal, characteristic, complemented
13#10590480C211yesmaximal, characteristic, complemented
14#10590477C211yesmaximal, characteristic, complemented
15#10590412C211yesmaximal, characteristic, complemented
16#83348—31nomaximal
17#80893—31nomaximal
18C32×C22⋊Q8C2211yescharacteristic
19C2×#3756C2211yescharacteristic
20#64133C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×#944C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29C3×#889—21no—
30C3×#888C2211yescharacteristic
31C3×#887—21no—
32C3×#887C2211yescharacteristic
33C3×#878—21no—
34C3×#877—21no—
35#63964—21no—
36#63955—21no—
37#63918C2211yescharacteristic
38#63867—21no—
39#63866C2211yescharacteristic
40#63844C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic
42#63837—21no—
43C2×#3719C2211yescharacteristic
44C2×#3718C2211yescharacteristic
45#63662C2211yescharacteristic
46#63637C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#808C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53#63567C2211yescharacteristic
54#63566C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63554C2211yescharacteristic
58#63554C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#533—31no—
62#5622—31no—
63#5622D311yescharacteristic
64#5470—31no—
65C3×#470—31no—
66#5184—31no—
67#5183—31no—
68#5137—31no—
69Dic3×M16—31no—
70#5093—31no—
71#5092—31no—
72#5080—31no—
73#5079—31no—
74#5052—31no—
75#5052—31no—
76#5052—31no—
77#5052—31no—
78#5052—31no—
79#5052—61no—
80#5052D311yescharacteristic
81#5030—31no—
82#5030—31no—
83#5030—31no—
84#5030—31no—
85C4×#208—31no—
86#4855—31no—
87#4853—31no—
88#4792—31no—
89#4792—31no—
90#4789—31no—
91#4789—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C22×C3×Dic3D411yescharacteristic
96C22×C3×Dic3D411yescharacteristic
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#627—21no—
101C32×C4⋊C4—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C22⋊C4—21no—
104#3757—21no—
105#3756—22no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108#3748—22no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#217—21no—
112C3×#217—21no—
113C3×#216—22no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3D411yescharacteristic
126C3×C4×Dic3D411yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C3×#208—22no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139#3719—22no—
140#3718—22no—
141#3185—91noSylow
142C2×C3×Q16—31no—
143C2×C3×M16—31no—
144C3×C4⋊Q8—31no—
145C3×C4⋊Q8—31no—
146C3×#125—61no—
147C3×C22⋊Q8—21no—
148C3×C22⋊Q8—31no—
149C3×C22⋊Q8—31no—
150C3×C22⋊Q8—61no—
151C3×C22⋊Q8C2×D311yescharacteristic
152C3×C22⋊Q8C2×D311yescharacteristic
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—61no—
156C3×#117—61no—
157C2×C3×C42—31no—
158Q8×Dic3—31no—
159Q8×Dic3C2×D311yescharacteristic
160#944—31no—
161#944C2×D311yescharacteristic
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#216—61no—
168C2×#216C2×D311yescharacteristic
169#926—61no—
170#924—31no—
171#924—31no—
172#924—61no—
173#924—61no—
174#924C2×D311yescharacteristic
175#924C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177C2×#208—31no—
178C2×#208—31no—
179C2×#208—61no—
180C2×#208C2×D311yescharacteristic
181C2×Dic12—31no—
182#889—21no—
183#889—61no—
184#888—31no—
185#888C2×D311yescharacteristic
186#887—21no—
187#887—31no—
188#887—61no—
189#887C2×D311yescharacteristic
190#878—21no—
191#878—61no—
192#877—21no—
193#877—61no—
194#870—61no—
195#869—31no—
196#869—31no—
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—61no—
200C3×#106—31no—
201C3×#103—31no—
202C3×#103—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—61no—
209#835C2×D311yescharacteristic
210#817—31no—
211#816—31no—
212#816—31no—
213#815—31no—
214#815—31no—
215C8×Dic3—31no—
216C8×Dic3—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—61no—
223#810C2×D311yescharacteristic
224#808—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#808—31no—
229#808—61no—
230#808C2×D311yescharacteristic
231#803—31no—
232#803—31no—
233C4×C3⋊C8—31no—
234C4×C3⋊C8—31no—
235C23×C32C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246#634—21no—
247#634—21no—
248C2×C3×Dic3—22no—
249C2×C3×Dic3—22no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6—21no—
262C3×Dic6—42no—
263#627—42no—
264C3⋊(C3⋊C8)—21no—
265C3⋊(C3⋊C8)#4112yes—
266C3×C3⋊C8—21no—
267C3×C3⋊C8#4112yes—
268#533—31no—
269#533—91no—
270#498—91no—
271#494—91no—
272#487—91no—
273#487—91no—
274#470—31no—
275#470—91no—
276#470—91no—
277#470—91no—
278#441—91no—
279#441—91no—
280#441—91no—
281#441—91no—
282C4×M16—91no—
283C2×C3×Q8—21no—
284C2×C3×Q8—31no—
285C2×C3×Q8—31no—
286C2×C3×Q8—61no—
287C2×C3×Q8C22×D311yescharacteristic
288C2×C3×Q8C22×D311yescharacteristic
289C22×C3×C4—21no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×Dic3#6711yescharacteristic
295C22×Dic3#6711yescharacteristic
296C2×Dic6—21no—
297C2×Dic6—31no—
298C2×Dic6—31no—
299C2×Dic6—61no—
300C2×Dic6—61no—
301C2×Dic6—61no—
302C2×Dic6C22×D311yescharacteristic
303C2×Dic6C22×D311yescharacteristic
304C3×Q16—62no—
305C3×M16—62no—
306C2×C3×C8—31no—
307C2×C3×C8—31no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—41no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4C22×D311yescharacteristic
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C22⋊C4—21no—
324C3×C22⋊C4—21no—
325C3×C22⋊C4—41no—
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C42—31no—
329C3×C42—31no—
330C3×C42—31no—
331C3×C42—31no—
332C3×C42—61no—
333C3×C42—61no—
334#217—21no—
335#217—21no—
336#217—61no—
337#217—61no—
338#217—121no—
339#216—22no—
340#216—62no—
341#216—62no—
342#216—62no—
343#216—62no—
344#216—62no—
345#216—122no—
346C4⋊Dic3—21no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3C22×D311yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356Dic3⋊C4—21no—
357Dic3⋊C4—21no—
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360Dic3⋊C4—21no—
361Dic3⋊C4—21no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—121no—
371C4×Dic3—21no—
372C4×Dic3—21no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3#6711yescharacteristic
378C4×Dic3#6711yescharacteristic
379C4×Dic3C22×D311yescharacteristic
380C4×Dic3C22×D311yescharacteristic
381#208—22no—
382#208—62no—
383#208—62no—
384#208—122no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—61no—
390C2×C3⋊C8—61no—
391C2×C3⋊C8C22×D311yescharacteristic
392C2×C3⋊C8C22×D311yescharacteristic
393Dic12—62no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32C22×D411yescharacteristic
398C32×C4—21no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4C2×#4111yescharacteristic
402C32×C4C2×#4111yescharacteristic
403C3⋊Dic3—41no—
404C3⋊Dic3—41no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C3×Dic3#13712yes—
412C3×Dic3#13712yes—
413C2×Q16—31no—
414C2×Q16—91no—
415C2×Q16—91no—
416C2×Q16—91no—
417C2×M16—31no—
418C2×M16—91no—
419C4⋊Q8—31no—
420C4⋊Q8—31no—
421C4⋊Q8—91no—
422C4⋊Q8—91no—
423#125—61no—
424#125—181no—
425C22⋊Q8—31no—
426C22⋊Q8—31no—
427C22⋊Q8—61no—
428C22⋊Q8—91no—
429C22⋊Q8—181no—
430C22⋊Q8D3211yescharacteristic
431C4×Q8—31no—
432C4×Q8—31no—
433C4×Q8—61no—
434C4×Q8—91no—
435C4×Q8—91no—
436C4×Q8—181no—
437#117—61no—
438#117—181no—
439C2×C42—31no—
440#106—31no—
441#106—91no—
442#106—91no—
443#106—91no—
444#103—31no—
445#103—31no—
446#103—91no—
447#103—91no—
448#103—91no—
449#103—91no—
450#103—91no—
451#103—91no—
452#97—91no—
453#97—91no—
454C4×C8—91no—
455C4×C8—91no—
456C23×C3—21no—
457C23×C3D3×D411yescharacteristic
458C23×C3C2×#6711yescharacteristic
459C3×Q8—21no—
460C3×Q8—21no—
461C3×Q8—21no—
462C3×Q8—21no—
463C3×Q8—41no—
464C3×Q8—41no—
465C3×Q8—61no—
466C3×Q8—61no—
467C3×Q8—61no—
468C3×Q8—61no—
469C3×Q8—122no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—62no—
489C2×C3×C4—62no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4D3×D411yescharacteristic
495C2×C3×C4C2×#6711yescharacteristic
496C2×C3×C4C23×D311yescharacteristic
497C2×C3×C4C23×D311yescharacteristic
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—121no—
509C2×Dic3—121no—
510C2×Dic3C2×#6711yescharacteristic
511C2×Dic3C2×#6711yescharacteristic
512C2×Dic3C2×#6711yescharacteristic
513C2×Dic3C2×#6711yescharacteristic
514Dic6—21no—
515Dic6—21no—
516Dic6—21no—
517Dic6—21no—
518Dic6—42no—
519Dic6—61no—
520Dic6—61no—
521Dic6—61no—
522Dic6—61no—
523Dic6—121no—
524Dic6—121no—
525Dic6—122no—
526Dic6—122no—
527C3×C8—32no—
528C3×C8—61no—
529C3⋊C8—21no—
530C3⋊C8—32no—
531C3⋊C8—32no—
532C3⋊C8—62no—
533C3⋊C8—61no—
534C3⋊C8—61no—
535C3⋊C8—121no—
536C3⋊C8#23712yes—
537C2×C32—41no—
538C2×C32#53211yescharacteristic
539C2×C32C2×#13711yescharacteristic
540C2×C32C2×#13711yescharacteristic
541C2×Q8—31no—
542C2×Q8—31no—
543C2×Q8—61no—
544C2×Q8—91no—
545C2×Q8—181no—
546C2×Q8C2×D3211yescharacteristic
547C22×C4—31no—
548C22×C4—31no—
549C22×C4C2×D3211yescharacteristic
550Q16—62no—
551Q16—182no—
552Q16—182no—
553Q16—182no—
554M16—62no—
555M16—182no—
556C2×C8—31no—
557C2×C8—31no—
558C2×C8—91no—
559C2×C8—91no—
560C4⋊C4—21no—
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—91no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C4⋊C4—181no—
576C4⋊C4—181no—
577C4⋊C4C2×D3211yescharacteristic
578C22⋊C4—21no—
579C22⋊C4—61no—
580C22⋊C4—61no—
581C22⋊C4—181no—
582C42—31no—
583C42—31no—
584C42—31no—
585C42—31no—
586C42—61no—
587C42—61no—
588C42—181no—
589C42—181no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3C2×D3×D411yescharacteristic
601C22×C3C22×#6711yescharacteristic
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—32no—
607C3×C4—32no—
608C3×C4—41no—
609C3×C4—41no—
610C3×C4—41no—
611C3×C4—41no—
612C3×C4—41no—
613C3×C4—61no—
614C3×C4—61no—
615C3×C4—81no—
616C3×C4—81no—
617C3×C4—121no—
618C3×C4—121no—
619C3×C4—121no—
620C3×C4—121no—
621C3×C4C2×#23711yescharacteristic
622C3×C4D3×#4111yescharacteristic
623C3×C4D3×#4111yescharacteristic
624C3×C4D3×#4111yescharacteristic
625Dic3—21no—
626Dic3—21no—
627Dic3—41no—
628Dic3—41no—
629Dic3—41no—
630Dic3—41no—
631Dic3—121no—
632Dic3—121no—
633Dic3—121no—
634Dic3—121no—
635Dic3—241no—
636Dic3—241no—
637Dic3#94212yes—
638Dic3#95112yes—
639C32#318511yescharacteristic, complemented, Sylow
640C23D3×#6711yescharacteristic
641Q8—21no—
642Q8—21no—
643Q8—61no—
644Q8—61no—
645Q8—61no—
646Q8—61no—
647Q8—122no—
648Q8—181no—
649Q8—181no—
650Q8—362no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—31no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4D3×#6711yescharacteristic
668C2×C4C22×D3211yescharacteristic
669C8—32no—
670C8—61no—
671C8—92no—
672C8—181no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—41no—
677C2×C3—41no—
678C2×C3—81no—
679C2×C3#559611yescharacteristic
680C2×C3D3×#13711yescharacteristic
681C2×C3D3×#13711yescharacteristic
682C2×C3C2×#94211yescharacteristic
683C2×C3C2×#95111yescharacteristic
684C2×C3#583211yescharacteristic
685C22—21no—
686C22—21no—
687C22—21no—
688C22C2×D3×#6711yescharacteristic
689C4—21no—
690C4—32no—
691C4—32no—
692C4—41no—
693C4—41no—
694C4—61no—
695C4—61no—
696C4—121no—
697C4—121no—
698C4—121no—
699C4—121no—
700C4—361no—
701C4—361no—
702C4D3×#23711yescharacteristic
703C4#6431211yescharacteristic
704C3—21no—
705C3#8089311yescharacteristic, complemented
706C3#8334811yescharacteristic, complemented
707C2—41no—
708C2#1059515511yescharacteristic
709C2D3×#94211yescharacteristic
710C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22⋊Q8D32
hypocenterC32#3185
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
5. #10591626C2semidirect
6. #10591623C2semidirect
7. #10591576C2semidirect
8. #10591541C2semidirect
12. #10590560C2semidirect
13. #10590480C2semidirect
14. #10590477C2semidirect
15. #10590412C2semidirect
639. C32#3185semidirect
705. C3#80893semidirect
706. C3#83348semidirect

Maximal subgroups

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

subgroupindex
C3×#56222
#105948082
#105927512
C3×#50522
#105916262
#105916232
#105915762
#105915412
#105911892
#105911212
Dic3×#2082
#105905602
#105904802
#105904772
#105904122
#833483
#808933