Finite Group Databasebeta

← #11873308

Subgroups — #11873308

Order 1152.

790 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595354C211yesmaximal, characteristic
2#10595339C211yesmaximal, characteristic
3#10592885C211yesmaximal, characteristic
4C3×#5184C211yesmaximal, characteristic, complemented
5C3×#5182C211yesmaximal, characteristic, complemented
6#10591603C211yesmaximal, characteristic
7#10591575C211yesmaximal, characteristic, complemented
8Dic3×#216C211yesmaximal, characteristic, complemented
9#10591561C211yesmaximal, characteristic
10#10591545C211yesmaximal, characteristic, complemented
11#10591537C211yesmaximal, characteristic, complemented
12#10590809C211yesmaximal, characteristic, complemented
13#10590794C211yesmaximal, characteristic, complemented
14#10590713C211yesmaximal, characteristic
15#10590647C211yesmaximal, characteristic
16#80461—31nomaximal
17#79836—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20#64155C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×#944C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27#63874—21no—
28#63874C2211yescharacteristic
29#63871C2211yescharacteristic
30#63869C2211yescharacteristic
31#63868—21no—
32#63867—21no—
33#63849—21no—
34#63849C2211yescharacteristic
35#63848—21no—
36#63847—21no—
37#63844—21no—
38#63844—21no—
39#63844C2211yescharacteristic
40#63844C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43#63662C2211yescharacteristic
44#63647C2211yescharacteristic
45#63643C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#815C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53#63576C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63567C2211yescharacteristic
58#63565C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5731—31no—
62#5583—31no—
63#5572—31no—
64#5572—31no—
65C3×#462—31no—
66C3×#441—31no—
67#5186—31no—
68#5186—31no—
69#5186—31no—
70#5186—61no—
71#5184D311yescharacteristic, complemented
72#5182D311yescharacteristic, complemented
73Dic3×Q16—31no—
74#5090—31no—
75C4×#216—31no—
76C4×#216—31no—
77#5022—31no—
78#4868—31no—
79#4857—31no—
80#4840—31no—
81#4829—31no—
82#4815—31no—
83#4815—31no—
84#4814—31no—
85#4809—31no—
86#4799—31no—
87#4795—31no—
88#4790—31no—
89#4789—31no—
90#4716—31no—
91#4709—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94Q8×C3⋊D3—22no—
95Q8×C3⋊D3—22no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634—21no—
99C2×#634C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C32×Q16—22no—
102C2×C32×C8C2311yescharacteristic
103#3756—22no—
104#3752—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106#3750—21no—
107C2×C3⋊(C3⋊C8)C2311yescharacteristic
108C3×#216—22no—
109C3×C4⋊Dic3—21no—
110C3×C4⋊Dic3—21no—
111C3×C4⋊Dic3—21no—
112C3×C4⋊Dic3C2311yescharacteristic
113C3×C4⋊Dic3C2311yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×C4×Dic3—21no—
118C3×C4×Dic3—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124#3724—21no—
125#3724—21no—
126#3724—21no—
127#3724D411yescharacteristic
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132#3722—21no—
133#3722—21no—
134#3722D411yescharacteristic
135#3722D411yescharacteristic
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32—21no—
140#3719—22no—
141#3127—91noSylow
142C2×D3×Q8—31no—
143C2×D3×Q8—31no—
144C2×D3×Q8—61no—
145C2×C3×Q16—21no—
146C2×C3×Q16—31no—
147C2×C3×Q16C2×D311yescharacteristic
148C2×C3×Q16C2×D311yescharacteristic
149C3×C4⋊Q8—31no—
150C3×C4×Q8—31no—
151C3×C4×Q8—31no—
152C3×C4×Q8—31no—
153#946—31no—
154#946—31no—
155#946—31no—
156#946—61no—
157Q8×Dic3—31no—
158Q8×Dic3C2×D311yescharacteristic
159Q8×Dic3C2×D311yescharacteristic
160Q8×Dic3C2×D311yescharacteristic
161#944C2×D311yescharacteristic
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—31no—
165C2×#216—61no—
166C2×#216C2×D311yescharacteristic
167C2×Dic12—31no—
168#898—61no—
169#898—61no—
170#898—61no—
171#897—31no—
172#892—31no—
173#892—31no—
174#892—61no—
175#892—61no—
176#890—31no—
177#889—61no—
178#889—61no—
179#889—61no—
180#887—31no—
181#887—31no—
182#887—61no—
183#887—61no—
184#876—61no—
185#872—31no—
186#872—31no—
187#872—61no—
188#872—61no—
189#870—31no—
190#870—61no—
191C4×Dic6—31no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C4×Dic6—61no—
195C4×Dic6—61no—
196C3×#106—31no—
197C3×C4⋊C8—31no—
198C3×#103—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#97—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—61no—
207#835C2×D311yescharacteristic
208#835C2×D311yescharacteristic
209#835C2×D311yescharacteristic
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—61no—
215#818—31no—
216#817—31no—
217#817C2×D311yescharacteristic
218#816—31no—
219#816—31no—
220#816—31no—
221#816—61no—
222#816C2×D311yescharacteristic
223#815C2×D311yescharacteristic
224Dic3⋊C8—31no—
225Dic3⋊C8C2×D311yescharacteristic
226C8×Dic3—31no—
227#810—31no—
228#810—31no—
229#808—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233C4⋊(C3⋊C8)—31no—
234C4×C3⋊C8—31no—
235C22×C3⋊D3C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8—21no—
238C32×Q8—21no—
239C32×Q8#4112yes—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2411yescharacteristic
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C2×D411yescharacteristic
246C4×C3⋊D3—24no—
247C4×C3⋊D3—21no—
248C4×C3⋊D3—21no—
249#634—24no—
250#634—21no—
251#634#4112yes—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×Dic6—21no—
261C3×Dic6—21no—
262C32×C8—21no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—91no—
267#519—91no—
268#485—91no—
269#485—91no—
270#479—91no—
271#479—91no—
272#462—31no—
273#462—91no—
274#451—91no—
275#451—91no—
276#441—31no—
277#441—91no—
278C4×Q16—91no—
279C4×Q16—91no—
280#433—91no—
281C2×C3×Q8—21no—
282C2×C3×Q8—21no—
283C2×C3×Q8—31no—
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×Q8C22×D311yescharacteristic
286C2×C3×Q8C22×D311yescharacteristic
287C2×C3×Q8C22×D311yescharacteristic
288D3×Q8—62no—
289D3×Q8—62no—
290D3×Q8—62no—
291D3×Q8—62no—
292D3×Q8—122no—
293D3×Q8—122no—
294C2×C4×D3—31no—
295C2×C4×D3—31no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×C4×D3—61no—
299C2×C4×D3—121no—
300C2×Dic6—31no—
301C2×Dic6—31no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6—61no—
305C2×Dic6—121no—
306C2×Dic6C22×D311yescharacteristic
307C3×Q16—22no—
308C3×Q16—22no—
309C3×Q16—42no—
310C3×Q16—62no—
311C2×C3×C8—21no—
312C2×C3×C8—31no—
313C2×C3×C8—31no—
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C3×C4⋊C4—31no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C42—31no—
325C3×C42—31no—
326C3×C42—61no—
327C3×C42—61no—
328C3×C42—61no—
329#216—22no—
330#216—62no—
331#216—62no—
332#216—62no—
333#216—122no—
334(C2×D3)⋊C4—31no—
335(C2×D3)⋊C4—31no—
336(C2×D3)⋊C4—31no—
337(C2×D3)⋊C4—31no—
338(C2×D3)⋊C4—61no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341(C2×D3)⋊C4—61no—
342(C2×D3)⋊C4—61no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—121no—
345C4⋊Dic3—21no—
346C4⋊Dic3—21no—
347C4⋊Dic3—21no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3C22×D311yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356C4⋊Dic3C22×D311yescharacteristic
357Dic3⋊C4—21no—
358Dic3⋊C4—21no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—121no—
375C4×Dic3—21no—
376C4×Dic3—21no—
377C4×Dic3—21no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3C22×D311yescharacteristic
387C4×Dic3C22×D311yescharacteristic
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—61no—
391C2×C3⋊C8C22×D311yescharacteristic
392C2×C3⋊C8C22×D311yescharacteristic
393Dic12—62no—
394C22×C32C22×D411yescharacteristic
395C2×C3⋊D3—21no—
396C2×C3⋊D3—21no—
397C2×C3⋊D3—21no—
398C32×C4—22no—
399C32×C4—41no—
400C32×C4C2×#4111yescharacteristic
401C32×C4C2×#4111yescharacteristic
402C3⋊Dic3—21no—
403C3⋊Dic3—22no—
404C3⋊Dic3—41no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—21no—
408C3×Dic3—21no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C3×Dic3—41no—
412C3×Dic3—41no—
413C22×Q8—91no—
414C2×Q16—31no—
415C2×Q16—91no—
416C2×Q16—91no—
417C2×Q16D3211yescharacteristic
418C4⋊Q8—31no—
419#126—181no—
420#126—181no—
421#125—91no—
422#125—181no—
423#125—181no—
424C22⋊Q8—91no—
425C22⋊Q8—91no—
426C4×Q8—31no—
427C4×Q8—31no—
428C4×Q8—31no—
429C4×Q8—91no—
430C4×Q8—91no—
431C4×Q8—91no—
432C4×Q8—181no—
433C4×Q8—181no—
434#117—91no—
435#117—91no—
436#117—181no—
437#117—181no—
438#107—91no—
439#107—91no—
440#106—31no—
441#106—91no—
442C4⋊C8—31no—
443C4⋊C8—91no—
444#103—31no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—91no—
449#103—91no—
450#103—91no—
451#103—91no—
452C22⋊C8—91no—
453C22⋊C8—91no—
454#97—31no—
455C4×C8—91no—
456C22×D3—31no—
457C22×D3—31no—
458C22×D3—61no—
459C3×Q8—21no—
460C3×Q8—21no—
461C3×Q8—21no—
462C3×Q8—21no—
463C3×Q8—21no—
464C3×Q8—21no—
465C3×Q8—22no—
466C3×Q8—41no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×Q8—61no—
470C3×Q8—61no—
471C3×Q8#23512yes—
472C3×Q8#23712yes—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4C23×D311yescharacteristic
489C2×C3×C4C23×D311yescharacteristic
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—121no—
502C2×Dic3—121no—
503C2×Dic3D3×D411yescharacteristic
504C2×Dic3D3×D411yescharacteristic
505C2×Dic3D3×D411yescharacteristic
506C2×Dic3D3×D411yescharacteristic
507C4×D3—64no—
508C4×D3—64no—
509C4×D3—61no—
510C4×D3—61no—
511C4×D3—61no—
512C4×D3—61no—
513C4×D3—121no—
514C4×D3—121no—
515C4×D3—124no—
516Dic6—21no—
517Dic6—21no—
518Dic6—32no—
519Dic6—32no—
520Dic6—62no—
521Dic6—64no—
522Dic6—64no—
523Dic6—61no—
524Dic6—61no—
525Dic6—121no—
526Dic6—124no—
527C3×C8—21no—
528C3×C8—21no—
529C3×C8—41no—
530C3×C8—61no—
531C3×C8—61no—
532C3⋊C8—21no—
533C3⋊C8—21no—
534C3⋊C8—61no—
535C3⋊C8—61no—
536C3⋊C8—121no—
537C2×C32#52511yescharacteristic
538C2×C32#57811yescharacteristic
539C2×C32#57811yescharacteristic
540C3⋊D3—41no—
541C2×Q8—31no—
542C2×Q8—91no—
543C2×Q8—181no—
544C2×Q8—182no—
545C2×Q8—182no—
546C2×Q8C2×D3211yescharacteristic
547C2×Q8C2×D3211yescharacteristic
548C22×C4—91no—
549C22×C4—181no—
550Q16—22no—
551Q16—62no—
552Q16—182no—
553Q16—182no—
554C2×C8—31no—
555C2×C8—31no—
556C2×C8—91no—
557C2×C8C2×D3211yescharacteristic
558C4⋊C4—31no—
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—91no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C4⋊C4—181no—
576C22⋊C4—91no—
577C22⋊C4—91no—
578C22⋊C4—181no—
579C22⋊C4—181no—
580C22⋊C4—181no—
581C42—31no—
582C42—31no—
583C42—61no—
584C42—61no—
585C42—61no—
586C42—181no—
587C42—181no—
588C42—181no—
589C42—181no—
590C22×C3—21no—
591C22×C3C2×D3×D411yescharacteristic
592C22×C3C2×D3×D411yescharacteristic
593C2×D3—62no—
594C2×D3—61no—
595C2×D3—61no—
596C2×D3—61no—
597C2×D3—61no—
598C2×D3—61no—
599C2×D3—61no—
600C2×D3—121no—
601C2×D3—121no—
602C3×C4—22no—
603C3×C4—22no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—42no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—61no—
610C3×C4—61no—
611C3×C4—61no—
612C3×C4—61no—
613C3×C4—81no—
614C3×C4—121no—
615C3×C4—121no—
616C3×C4—121no—
617C3×C4—121no—
618C3×C4C2×#23511yescharacteristic
619C3×C4C2×#23711yescharacteristic
620C3×C4D3×#4111yescharacteristic
621C3×C4D3×#4111yescharacteristic
622Dic3—21no—
623Dic3—21no—
624Dic3—21no—
625Dic3—21no—
626Dic3—41no—
627Dic3—41no—
628Dic3—41no—
629Dic3—41no—
630Dic3—62no—
631Dic3—61no—
632Dic3—62no—
633Dic3—61no—
634Dic3—122no—
635Dic3—121no—
636Dic3—121no—
637Dic3—121no—
638Dic3—241no—
639C32#312711yescharacteristic, complemented, Sylow
640C23—91no—
641Q8—21no—
642Q8—21no—
643Q8—21no—
644Q8—61no—
645Q8—61no—
646Q8—92no—
647Q8—184no—
648Q8—181no—
649Q8#380412yes—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—31no—
655C2×C4—31no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—91no—
661C2×C4—184no—
662C2×C4—181no—
663C2×C4—181no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4C22×D3211yescharacteristic
667C8—21no—
668C8—61no—
669C8—61no—
670C8—181no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3#554711yescharacteristic
675C2×C3#560611yescharacteristic
676C2×C3#576611yescharacteristic
677C2×C3#577911yescharacteristic
678C2×C3#577911yescharacteristic
679C2×C3#577911yescharacteristic
680D3—122no—
681D3—121no—
682D3—121no—
683C22—181no—
684C22—181no—
685C22—181no—
686C22D32×D411yescharacteristic
687C4—22no—
688C4—41no—
689C4—61no—
690C4—61no—
691C4—61no—
692C4—61no—
693C4—121no—
694C4—121no—
695C4—121no—
696C4—121no—
697C4—181no—
698C4—182no—
699C4—361no—
700C4#6431211yescharacteristic
701C4C2×#380411yescharacteristic
702C3—21no—
703C3#7983611yescharacteristic, complemented
704C3#8046111yescharacteristic, complemented
705C2—361no—
706C2#1059476611yescharacteristic
707C2#1059476911yescharacteristic
708C2#1059513811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC2×Q16D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
4. C3×#5184C2semidirect
5. C3×#5182C2semidirect
7. #10591575C2semidirect
8. Dic3×#216C2semidirect
10. #10591545C2semidirect
11. #10591537C2semidirect
12. #10590809C2semidirect
13. #10590794C2semidirect
71. #5184D3semidirect
72. #5182D3semidirect
639. C32#3127semidirect
703. C3#79836semidirect
704. C3#80461semidirect

Maximal subgroups

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

subgroupindex
#105953542
#105953392
#105928852
C3×#51842
C3×#51822
#105916032
#105915752
Dic3×#2162
#105915612
#105915452
#105915372
#105908092
#105907942
#105907132
#105906472
#804613
#798363