Finite Group Databasebeta

← #11873313

Subgroups — #11873313

Order 1152.

770 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5583C211yesmaximal, characteristic
2#10593885C211yesmaximal, characteristic
3#10592729C211yesmaximal, characteristic, complemented
4C3×C4×#216C211yesmaximal, characteristic, complemented
5#10591653C211yesmaximal, characteristic
6#10591575C211yesmaximal, characteristic, complemented
7#10591574C211yesmaximal, characteristic, complemented
8#10591558C211yesmaximal, characteristic
9#10590604C211yesmaximal, characteristic
10#10590492C211yesmaximal, characteristic, complemented
11#10590491C211yesmaximal, characteristic, complemented
12#10590448C211yesmaximal, characteristic
13C4×#3719C211yesmaximal, characteristic, complemented
14#10590381C211yesmaximal, characteristic, complemented
15#10590264C211yesmaximal, characteristic
16#83451—31nomaximal
17#79724—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C2×#3756C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#944C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#898—21no—
26C3×#897C2211yescharacteristic
27C3×#890C2211yescharacteristic
28C3×#889—21no—
29C3×#876—21no—
30C3×#872C2211yescharacteristic
31C3×#870—21no—
32C3×C4×Dic6C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63878—21no—
35#63877—21no—
36#63844C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38#63841C2211yescharacteristic
39#63838—21no—
40#63837—21no—
41C2×#3719C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43#63662C2211yescharacteristic
44#63637C2211yescharacteristic
45#63635C2211yescharacteristic
46#63630C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×C4×C3⋊C8C2211yescharacteristic
51#63575C2211yescharacteristic
52#63574C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#541—31no—
62#5583D311yescharacteristic
63#5572—31no—
64#5516—31no—
65C3×C4×Q16—31no—
66#5186—31no—
67#5182—31no—
68#5090—31no—
69#5090—31no—
70#5063—31no—
71#5063—31no—
72#5050—31no—
73#5050—31no—
74#5045—31no—
75#5045—31no—
76#5030—31no—
77#5030—31no—
78#5030—31no—
79#5030—31no—
80#5030—61no—
81C4×#216—31no—
82C4×#216D311yescharacteristic, complemented
83#5000—31no—
84#4888—31no—
85#4877—31no—
86#4814—31no—
87#4809—31no—
88#4796—31no—
89#4795—31no—
90C4×Dic12—31no—
91#4690—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×C4×D3C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×D3×Dic3—21no—
99D3×Dic6—22no—
100D3×Dic6—22no—
101C32×C4⋊C4—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C42—21no—
104C32×C42C2311yescharacteristic
105#3756—22no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#216—22no—
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4D411yescharacteristic
115C3×(C2×D3)⋊C4D411yescharacteristic
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3719—22no—
140#3718—22no—
141#3127—91noSylow
142C2×D3×Q8—31no—
143C22×Dic6—31no—
144C2×C3×Q16—31no—
145C3×C4⋊Q8—31no—
146C3×#126—61no—
147C3×#126—61no—
148C3×#125—31no—
149C3×#125—61no—
150C3×#125—61no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—31no—
153C3×C4×Q8—21no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8C2×D311yescharacteristic
157C3×C4×Q8C2×D311yescharacteristic
158C3×#117—31no—
159#946C2×D311yescharacteristic
160Q8×Dic3—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—31no—
170C2×Dic12—31no—
171#898—21no—
172#897C2×D311yescharacteristic
173#892—31no—
174#892—61no—
175#890C2×D311yescharacteristic
176#889—21no—
177#887—31no—
178#887—61no—
179#887—61no—
180#887—61no—
181#877—61no—
182#877—61no—
183#876—21no—
184#872—61no—
185#872C2×D311yescharacteristic
186#870—21no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C4×Dic6—61no—
192C4×Dic6—61no—
193C4×Dic6C2×D311yescharacteristic
194C4×Dic6C2×D311yescharacteristic
195C3×#107—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×C4×C8—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#835—61no—
205#835C2×D311yescharacteristic
206#830—31no—
207#830—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8—31no—
210#818—31no—
211#816—31no—
212#816—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—61no—
221#810C2×D311yescharacteristic
222#808—31no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808—61no—
227#807—31no—
228#807C2×D311yescharacteristic
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231#803—31no—
232#803—31no—
233#803—61no—
234C4×C3⋊C8C2×D311yescharacteristic
235C22×C3×D3C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2411yescharacteristic
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245#634—21no—
246#634#4112yes—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6#4112yes—
260#627—24no—
261D3×Dic3—24no—
262C3⋊(C3⋊C8)—21no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—31no—
267#519—91no—
268#485—91no—
269#485—91no—
270#479—91no—
271#479—91no—
272#462—91no—
273#462—91no—
274#451—91no—
275#451—91no—
276#441—91no—
277#441—91no—
278C4×Q16—31no—
279C4×Q16—91no—
280#433—91no—
281C2×C3×Q8—21no—
282C2×C3×Q8—31no—
283C2×C3×Q8—31no—
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×Q8C22×D311yescharacteristic
286C22×C3×C4—31no—
287C22×Dic3—61no—
288D3×Q8—62no—
289D3×Q8—62no—
290C2×C4×D3—61no—
291C2×C4×D3C22×D311yescharacteristic
292C2×Dic6—31no—
293C2×Dic6—31no—
294C2×Dic6—61no—
295C2×Dic6—62no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—62no—
299C2×Dic6C22×D311yescharacteristic
300C2×Dic6C22×D311yescharacteristic
301C3×Q16—62no—
302C2×C3×C8—31no—
303C2×C3×C8—31no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—41no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
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⋊C4C22×D311yescharacteristic
321C3×C4⋊C4C22×D311yescharacteristic
322C3×C22⋊C4—31no—
323C3×C22⋊C4—31no—
324C3×C22⋊C4—61no—
325C3×C22⋊C4—61no—
326C3×C42—21no—
327C3×C42—21no—
328C3×C42—21no—
329C3×C42—31no—
330C3×C42—41no—
331C3×C42—61no—
332C3×C42—61no—
333C3×C42C22×D311yescharacteristic
334C3×C42C22×D311yescharacteristic
335#217—61no—
336#216—22no—
337#216—62no—
338#216—62no—
339#216—62no—
340#216—62no—
341#216—64no—
342#216—62no—
343(C2×D3)⋊C4—21no—
344(C2×D3)⋊C4—21no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4#6711yescharacteristic
347(C2×D3)⋊C4#6711yescharacteristic
348C4⋊Dic3—21no—
349C4⋊Dic3—21no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
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—121no—
368Dic3⋊C4#6711yescharacteristic
369Dic3⋊C4#6711yescharacteristic
370C4×Dic3—21no—
371C4×Dic3—21no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—121no—
381C4×Dic3C22×D311yescharacteristic
382C2×C3⋊C8—31no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—61no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390Dic12—62no—
391C22×C32C22×D411yescharacteristic
392C2×C3×D3—21no—
393C2×C3×D3—21no—
394C2×C3×D3—21no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4—41no—
398C32×C4—41no—
399C32×C4C2×#4111yescharacteristic
400C32×C4C2×#4111yescharacteristic
401C3⋊Dic3—22no—
402C3⋊Dic3—41no—
403C3×Dic3—22no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C22×Q8—91no—
411C2×Q16—31no—
412C2×Q16—91no—
413C2×Q16—91no—
414C2×Q16—91no—
415C4⋊Q8—31no—
416#126—61no—
417#126—61no—
418#125—31no—
419#125—61no—
420#125—61no—
421C22⋊Q8—31no—
422C22⋊Q8—31no—
423C4×Q8—31no—
424C4×Q8—31no—
425C4×Q8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—181no—
429C4×Q8—181no—
430C4×Q8D3211yescharacteristic
431#117—31no—
432#117—91no—
433#117—181no—
434#117—181no—
435#107—31no—
436#107—91no—
437#106—91no—
438#106—91no—
439C4⋊C8—91no—
440C4⋊C8—91no—
441#103—31no—
442#103—31no—
443#103—91no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103—91no—
448#103—91no—
449C22⋊C8—91no—
450C22⋊C8—91no—
451#97—91no—
452C4×C8—31no—
453C23×C3—31no—
454C22×D3C2×#6711yescharacteristic
455C3×Q8—22no—
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—32no—
461C3×Q8—41no—
462C3×Q8—61no—
463C3×Q8—61no—
464C3×Q8—61no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4D3×D411yescharacteristic
484C2×C3×C4D3×D411yescharacteristic
485C2×C3×C4C2×#6711yescharacteristic
486C2×C3×C4C2×#6711yescharacteristic
487C2×C3×C4C23×D311yescharacteristic
488C2×C3×C4C23×D311yescharacteristic
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—64no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—121no—
499C2×Dic3—121no—
500C2×Dic3C2×#6711yescharacteristic
501C2×Dic3C2×#6711yescharacteristic
502C2×Dic3C2×#6711yescharacteristic
503C4×D3—21no—
504C4×D3—21no—
505C4×D3—64no—
506Dic6—21no—
507Dic6—21no—
508Dic6—21no—
509Dic6—32no—
510Dic6—32no—
511Dic6—62no—
512Dic6—64no—
513Dic6—64no—
514Dic6—61no—
515Dic6—61no—
516Dic6—121no—
517Dic6#23512yes—
518C3×C8—61no—
519C3×C8—61no—
520C3⋊C8—21no—
521C3⋊C8—21no—
522C3⋊C8—62no—
523C3⋊C8—61no—
524C3⋊C8—61no—
525C3⋊C8—61no—
526C3⋊C8—61no—
527C3⋊C8—121no—
528C2×C32#52511yescharacteristic
529C2×C32#57811yescharacteristic
530C2×C32#57811yescharacteristic
531C3×D3—41no—
532C2×Q8—31no—
533C2×Q8—31no—
534C2×Q8—91no—
535C2×Q8—181no—
536C2×Q8—182no—
537C2×Q8—182no—
538C2×Q8C2×D3211yescharacteristic
539C22×C4—31no—
540C22×C4—181no—
541Q16—62no—
542Q16—182no—
543Q16—182no—
544Q16—182no—
545C2×C8—31no—
546C2×C8—31no—
547C2×C8—91no—
548C2×C8—91no—
549C4⋊C4—21no—
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—91no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4C2×D3211yescharacteristic
567C22⋊C4—31no—
568C22⋊C4—31no—
569C22⋊C4—61no—
570C22⋊C4—61no—
571C22⋊C4—181no—
572C42—21no—
573C42—31no—
574C42—61no—
575C42—61no—
576C42—181no—
577C42—181no—
578C42—181no—
579C42—181no—
580C42C2×D3211yescharacteristic
581C22×C3—21no—
582C22×C3—61no—
583C22×C3—61no—
584C22×C3—61no—
585C22×C3C2×D3×D411yescharacteristic
586C22×C3C22×#6711yescharacteristic
587C2×D3—21no—
588C2×D3—21no—
589C2×D3—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—42no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—61no—
604C3×C4—61no—
605C3×C4—61no—
606C3×C4—62no—
607C3×C4—81no—
608C3×C4—121no—
609C3×C4—121no—
610C3×C4—121no—
611C3×C4C2×#23511yescharacteristic
612C3×C4D3×#4111yescharacteristic
613C3×C4D3×#4111yescharacteristic
614C3×C4D3×#4111yescharacteristic
615Dic3—22no—
616Dic3—21no—
617Dic3—21no—
618Dic3—21no—
619Dic3—41no—
620Dic3—41no—
621Dic3—41no—
622Dic3—62no—
623Dic3—62no—
624Dic3—122no—
625Dic3—121no—
626Dic3—121no—
627Dic3—241no—
628C32#312711yescharacteristic, complemented, Sylow
629C23—31no—
630Q8—21no—
631Q8—21no—
632Q8—32no—
633Q8—61no—
634Q8—61no—
635Q8—61no—
636Q8—92no—
637Q8—184no—
638Q8—181no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—184no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4D3×#6711yescharacteristic
654C2×C4D3×#6711yescharacteristic
655C2×C4C22×D3211yescharacteristic
656C8—61no—
657C8—61no—
658C8—181no—
659C8—181no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—121no—
664C2×C3#554711yescharacteristic
665C2×C3#576611yescharacteristic
666C2×C3#577111yescharacteristic
667C2×C3#582811yescharacteristic
668C2×C3#583811yescharacteristic
669C2×C3#583811yescharacteristic
670D3—41no—
671C22—61no—
672C22—61no—
673C22—61no—
674C22C2×D3×#6711yescharacteristic
675C4—21no—
676C4—21no—
677C4—41no—
678C4—41no—
679C4—61no—
680C4—61no—
681C4—62no—
682C4—61no—
683C4—121no—
684C4—121no—
685C4—121no—
686C4—182no—
687C4—361no—
688C4D3×#23511yescharacteristic
689C4#6430611yescharacteristic
690C3—21no—
691C3#7972411yescharacteristic, complemented
692C3#8345111yescharacteristic, complemented
693C2—121no—
694C2#1059506011yescharacteristic
695C2#1059532711yescharacteristic
696C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4×Q8D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #10592729C2semidirect
4. C3×C4×#216C2semidirect
6. #10591575C2semidirect
7. #10591574C2semidirect
10. #10590492C2semidirect
11. #10590491C2semidirect
13. C4×#3719C2semidirect
14. #10590381C2semidirect
82. C4×#216D3semidirect
628. C32#3127semidirect
691. C3#79724semidirect
692. C3#83451semidirect

Maximal subgroups

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

subgroupindex
C3×#55832
#105938852
#105927292
C3×C4×#2162
#105916532
#105915752
#105915742
#105915582
#105906042
#105904922
#105904912
#105904482
C4×#37192
#105903812
#105902642
#834513
#797243