Finite Group Databasebeta

← #11873304

Subgroups — #11873304

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 695 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595347C211yesmaximal, characteristic
2#10594345C211yesmaximal, characteristic
3#10592495C211yesmaximal, characteristic, complemented
4C3×#4809C211yesmaximal, characteristic
5C3×#4790C211yesmaximal, characteristic, complemented
6#10591633C211yesmaximal, characteristic, complemented
7#10591594C211yesmaximal, characteristic
8#10591576C211yesmaximal, characteristic, complemented
9Dic3×Dic12C211yesmaximal, characteristic, complemented
10#10590798C211yesmaximal, characteristic, complemented
11#10590710C211yesmaximal, characteristic
12#10590696C211yesmaximal, characteristic
13#10590494C211yesmaximal, characteristic, complemented
14#10590477C211yesmaximal, characteristic, complemented
15#10590448C211yesmaximal, characteristic
16#80177—31nomaximal
17#79724—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic
20#64099C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#887C2211yescharacteristic
27#63873C2211yescharacteristic
28#63869—21no—
29#63861—21no—
30#63859—21no—
31#63856C2211yescharacteristic
32#63855—21no—
33#63855C2211yescharacteristic
34#63847—21no—
35#63843—21no—
36#63843C2211yescharacteristic
37Dic3×Dic6—21no—
38Dic3×Dic6C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40#63841—21no—
41#63841C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C32×#103C2211yescharacteristic
44#63662C2211yescharacteristic
45#63645C2211yescharacteristic
46#63641C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63573C2211yescharacteristic
54#63572C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61#5812—31no—
62#5625—31no—
63#5583—31no—
64#5572—31no—
65C3×#451—31no—
66C3×C4×Q16—31no—
67#5228—31no—
68#5186—31no—
69#5184—31no—
70#5182—31no—
71#5182—31no—
72#5182—31no—
73Dic3×Q16—31no—
74#5045—31no—
75#5030—31no—
76#5030—31no—
77#4888—31no—
78#4877—31no—
79#4814—31no—
80#4809D311yescharacteristic
81#4799—31no—
82#4796—31no—
83#4796—31no—
84#4796—61no—
85#4795—31no—
86#4790D311yescharacteristic, complemented
87#4789—31no—
88#4723—31no—
89#4720—31no—
90C4×Dic12—31no—
91#4690—31no—
92C2×C32×Q8C2311yescharacteristic
93C3×D3×Q8—22no—
94C3×D3×Q8—22no—
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C32×C4⋊C4C2311yescharacteristic
103C4⋊(C3⋊Dic3)—21no—
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#216—22no—
112C3×#216—22no—
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×C4×Dic3—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C3×Dic12—22no—
124#3724—21no—
125#3724—21no—
126#3724—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3D411yescharacteristic
135(C2×D3)⋊Dic3D411yescharacteristic
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32—21no—
140#3718—22no—
141#3127—91noSylow
142C22×C3×Q8—31no—
143C2×D3×Q8C2×D311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C2×C3×Q16—31no—
147C3×C22⋊Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×Q8—31no—
150#946—31no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—31no—
155Q8×Dic3—31no—
156Q8×Dic3—61no—
157Q8×Dic3—61no—
158Q8×Dic3—61no—
159Q8×Dic3C2×D311yescharacteristic
160#944—31no—
161#944—31no—
162C2×#216—31no—
163C2×#216—31no—
164C2×#216C2×D311yescharacteristic
165C2×#216C2×D311yescharacteristic
166#926—31no—
167#926—31no—
168#926—61no—
169#926—61no—
170#924—31no—
171C2×Dic12C2×D311yescharacteristic
172#898—61no—
173#897C2×D311yescharacteristic
174#892—31no—
175#892—61no—
176#890—31no—
177#890—31no—
178#890—61no—
179#890—61no—
180#889—61no—
181#889—61no—
182#887—31no—
183#887—61no—
184#887C2×D311yescharacteristic
185#879—61no—
186#879—61no—
187#876—61no—
188#872—31no—
189#872—61no—
190#870—61no—
191C4×Dic6—31no—
192C4×Dic6—31no—
193C4×Dic6—61no—
194C3×#107—31no—
195C3×#103—21no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#103C2×D311yescharacteristic
199C3×#103C2×D311yescharacteristic
200C3×C22⋊C8—31no—
201C3×C4×C8—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—61no—
209#830—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8C2×D311yescharacteristic
212#818—31no—
213#818—31no—
214#818—61no—
215#817—31no—
216#816—31no—
217#816—31no—
218#816—31no—
219#816C2×D311yescharacteristic
220#815—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—61no—
226C8×Dic3C2×D311yescharacteristic
227#810—31no—
228#810C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—31no—
232#808—61no—
233#807C2×D311yescharacteristic
234#803—31no—
235C22×C3×D3C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8#4112yes—
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
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×C4×D3—24no—
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×Dic6—24no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6#4112yes—
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—91no—
273#462—91no—
274#451—31no—
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×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×Q8—62no—
287C2×C3×Q8—62no—
288C2×C3×Q8C22×D311yescharacteristic
289C2×C3×Q8C22×D311yescharacteristic
290C22×C3×C4—31no—
291C22×C3×C4—61no—
292D3×Q8—22no—
293D3×Q8—22no—
294C2×C4×D3—21no—
295C2×C4×D3C22×D311yescharacteristic
296C2×Dic6—21no—
297C2×Dic6C22×D311yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C3×Q16—62no—
301C3×Q16—62no—
302C3×Q16—62no—
303C2×C3×C8—21no—
304C2×C3×C8—31no—
305C2×C3×C8—31no—
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C3×C4⋊C4—21no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4C22×D311yescharacteristic
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C22⋊C4—61no—
316C3×C42—31no—
317C3×C42—61no—
318C3×C42—61no—
319#217—31no—
320#217—31no—
321#217—61no—
322#217—61no—
323#216—22no—
324#216—22no—
325#216—62no—
326#216—62no—
327(C2×D3)⋊C4—21no—
328(C2×D3)⋊C4—31no—
329(C2×D3)⋊C4—31no—
330(C2×D3)⋊C4—61no—
331(C2×D3)⋊C4—61no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—121no—
350C4⋊Dic3—121no—
351C4⋊Dic3C22×D311yescharacteristic
352Dic3⋊C4—21no—
353Dic3⋊C4—31no—
354Dic3⋊C4—31no—
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—61no—
366Dic3⋊C4—121no—
367C4×Dic3—21no—
368C4×Dic3—21no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—61no—
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—61no—
381C4×Dic3—61no—
382C4×Dic3—121no—
383C4×Dic3C22×D311yescharacteristic
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—61no—
387C2×C3⋊C8C22×D311yescharacteristic
388C2×C3⋊C8C22×D311yescharacteristic
389Dic12—22no—
390C22×C32C22×D411yescharacteristic
391C2×C3×D3—21no—
392C2×C3×D3—21no—
393C2×C3×D3—21no—
394C32×C4—22no—
395C32×C4—41no—
396C32×C4C2×#4111yescharacteristic
397C32×C4C2×#4111yescharacteristic
398C3⋊Dic3—21no—
399C3⋊Dic3—21no—
400C3⋊Dic3—41no—
401C3⋊Dic3—41no—
402C3×Dic3—21no—
403C3×Dic3—22no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C22×Q8—31no—
410C2×Q16—31no—
411C2×Q16—31no—
412C2×Q16—31no—
413C2×Q16—91no—
414C4⋊Q8—91no—
415#126—181no—
416#126—181no—
417#125—91no—
418#125—181no—
419#125—181no—
420C22⋊Q8—31no—
421C22⋊Q8—91no—
422C4×Q8—31no—
423C4×Q8—31no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—181no—
429C4×Q8—181no—
430#117—91no—
431#117—91no—
432#117—181no—
433#117—181no—
434#107—31no—
435#107—91no—
436#106—91no—
437#106—91no—
438C4⋊C8—91no—
439C4⋊C8—91no—
440#103—31no—
441#103—31no—
442#103—91no—
443#103—91no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103D3211yescharacteristic
448C22⋊C8—31no—
449C22⋊C8—91no—
450#97—91no—
451C4×C8—31no—
452C23×C3—31no—
453C22×D3D3×D411yescharacteristic
454C3×Q8—21no—
455C3×Q8—21no—
456C3×Q8—22no—
457C3×Q8—32no—
458C3×Q8—41no—
459C3×Q8—64no—
460C3×Q8—61no—
461C3×Q8—61no—
462C3×Q8—61no—
463C3×Q8—61no—
464C3×Q8—61no—
465C3×Q8#23512yes—
466C3×Q8#23712yes—
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—64no—
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×C4C23×D311yescharacteristic
485C2×C3×C4C23×D311yescharacteristic
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—121no—
501C2×Dic3—121no—
502C2×Dic3D3×D411yescharacteristic
503C2×Dic3D3×D411yescharacteristic
504C2×Dic3D3×D411yescharacteristic
505C4×D3—24no—
506C4×D3—21no—
507C4×D3—21no—
508Dic6—24no—
509Dic6—21no—
510Dic6—21no—
511Dic6—21no—
512Dic6—21no—
513Dic6—21no—
514Dic6#23712yes—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—41no—
518C3×C8—61no—
519C3×C8—61no—
520C3⋊C8—21no—
521C3⋊C8—21no—
522C3⋊C8—61no—
523C3⋊C8—61no—
524C3⋊C8—121no—
525C2×C32#52511yescharacteristic
526C2×C32#57811yescharacteristic
527C2×C32#57811yescharacteristic
528C3×D3—41no—
529C2×Q8—31no—
530C2×Q8—31no—
531C2×Q8—31no—
532C2×Q8—61no—
533C2×Q8—62no—
534C2×Q8—62no—
535C2×Q8C2×D3211yescharacteristic
536C22×C4—31no—
537C22×C4—61no—
538Q16—62no—
539Q16—62no—
540Q16—62no—
541Q16—182no—
542C2×C8—31no—
543C2×C8—31no—
544C2×C8—91no—
545C2×C8C2×D3211yescharacteristic
546C4⋊C4—31no—
547C4⋊C4—61no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—91no—
551C4⋊C4—91no—
552C4⋊C4—91no—
553C4⋊C4—91no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4C2×D3211yescharacteristic
564C22⋊C4—61no—
565C22⋊C4—91no—
566C22⋊C4—91no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C42—31no—
570C42—61no—
571C42—61no—
572C42—91no—
573C42—181no—
574C42—181no—
575C42—181no—
576C42—181no—
577C42—181no—
578C22×C3—21no—
579C22×C3—61no—
580C22×C3—61no—
581C22×C3—61no—
582C22×C3C2×D3×D411yescharacteristic
583C22×C3C2×D3×D411yescharacteristic
584C2×D3—21no—
585C2×D3—21no—
586C2×D3—21no—
587C3×C4—22no—
588C3×C4—22no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—42no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—61no—
595C3×C4—61no—
596C3×C4—61no—
597C3×C4—62no—
598C3×C4—81no—
599C3×C4—121no—
600C3×C4—121no—
601C3×C4—121no—
602C3×C4C2×#23511yescharacteristic
603C3×C4C2×#23711yescharacteristic
604C3×C4C2×#23711yescharacteristic
605C3×C4D3×#4111yescharacteristic
606Dic3—21no—
607Dic3—21no—
608Dic3—21no—
609Dic3—22no—
610Dic3—41no—
611Dic3—41no—
612Dic3—41no—
613Dic3—61no—
614Dic3—61no—
615Dic3—61no—
616Dic3—61no—
617Dic3—121no—
618Dic3—121no—
619Dic3—121no—
620Dic3—121no—
621Dic3—121no—
622Dic3—121no—
623Dic3—241no—
624Dic3—241no—
625C32#312711yescharacteristic, complemented, Sylow
626C23—31no—
627Q8—21no—
628Q8—32no—
629Q8—64no—
630Q8—61no—
631Q8—61no—
632Q8—61no—
633Q8—61no—
634Q8—61no—
635Q8#379512yes—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—31no—
639C2×C4—31no—
640C2×C4—31no—
641C2×C4—64no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—91no—
649C2×C4—91no—
650C2×C4—181no—
651C2×C4—181no—
652C2×C4C22×D3211yescharacteristic
653C8—21no—
654C8—61no—
655C8—61no—
656C8—181no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—121no—
661C2×C3#554711yescharacteristic
662C2×C3#558611yescharacteristic
663C2×C3#576611yescharacteristic
664C2×C3#576611yescharacteristic
665C2×C3#577111yescharacteristic
666C2×C3#577911yescharacteristic
667D3—41no—
668C22—61no—
669C22—61no—
670C22—61no—
671C22D32×D411yescharacteristic
672C4—22no—
673C4—41no—
674C4—61no—
675C4—62no—
676C4—61no—
677C4—61no—
678C4—121no—
679C4—121no—
680C4—121no—
681C4—181no—
682C4—181no—
683C4—361no—
684C4—361no—
685C4C2×#379511yescharacteristic
686C4D3×#23711yescharacteristic
687C3—21no—
688C3#7972411yescharacteristic, complemented
689C3#8017711yescharacteristic, complemented
690C2—121no—
691C2#1059405411yescharacteristic
692C2#1059475611yescharacteristic
693C2#1059476511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#103D32
hypocenterC32#3127
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. #10592495C2semidirect
5. C3×#4790C2semidirect
6. #10591633C2semidirect
8. #10591576C2semidirect
9. Dic3×Dic12C2semidirect
10. #10590798C2semidirect
13. #10590494C2semidirect
14. #10590477C2semidirect
86. #4790D3semidirect
625. C32#3127semidirect
688. C3#79724semidirect
689. C3#80177semidirect

Maximal subgroups

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

subgroupindex
#105953472
#105943452
#105924952
C3×#48092
C3×#47902
#105916332
#105915942
#105915762
Dic3×Dic122
#105907982
#105907102
#105906962
#105904942
#105904772
#105904482
#801773
#797243