Finite Group Databasebeta

← #11873341

Subgroups — #11873341

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#10594357C211yesmaximal, characteristic
2#10594345C211yesmaximal, characteristic
3#10592576C211yesmaximal, characteristic, complemented
4C3×#4888C211yesmaximal, characteristic
5C3×#4873C211yesmaximal, characteristic, complemented
6#10590949C211yesmaximal, characteristic
7#10590798C211yesmaximal, characteristic, complemented
8#10590793C211yesmaximal, characteristic, complemented
9#10590696C211yesmaximal, characteristic
10#10590604C211yesmaximal, characteristic
11#10590566C211yesmaximal, characteristic, complemented
12#10590519C211yesmaximal, characteristic
13#10590495C211yesmaximal, characteristic, complemented
14#10590480C211yesmaximal, characteristic, complemented
15#10590477C211yesmaximal, characteristic, complemented
16#81499—31nomaximal
17#79724—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19#64099C2211yescharacteristic
20#64096C2211yescharacteristic
21C2×C3×Dic12C2211yescharacteristic
22C3×#897C2211yescharacteristic
23C3×#892C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C3×#887C2211yescharacteristic
26C4×#627—21no—
27#63878—21no—
28#63877—21no—
29#63873C2211yescharacteristic
30#63869—21no—
31#63861—21no—
32#63859—21no—
33#63856C2211yescharacteristic
34#63855C2211yescharacteristic
35#63847—21no—
36#63844C2211yescharacteristic
37#63843C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63837—21no—
40C2×#3719C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C32×#107C2211yescharacteristic
44#63643C2211yescharacteristic
45#63641C2211yescharacteristic
46#63637C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#808C2211yescharacteristic
55#63575C2211yescharacteristic
56#63572C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61#5625—31no—
62#5583—31no—
63#5572—31no—
64#5516—31no—
65C3×#485—31no—
66C3×C4×Q16—31no—
67#5186—31no—
68#5182—31no—
69#5050—31no—
70#5030—31no—
71#5030—31no—
72#4996—31no—
73#4888D311yescharacteristic
74#4877—31no—
75#4877—31no—
76#4877—61no—
77#4873D311yescharacteristic, complemented
78#4857—31no—
79#4853—31no—
80#4814—31no—
81#4809—31no—
82#4796—31no—
83#4795—31no—
84#4795—31no—
85#4795—31no—
86#4790—31no—
87#4789—31no—
88#4739—31no—
89#4720—31no—
90C4×Dic12—31no—
91#4690—31no—
92C2×#634C2311yescharacteristic
93C2×C3×C4×D3C2311yescharacteristic
94C2×C3×Dic6C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×D3×Dic3—21no—
99D3×Dic6—22no—
100D3×Dic6—22no—
101C2×C32×C8C2311yescharacteristic
102C32×C4⋊C4C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106#3750—21no—
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×(C2×D3)⋊C4—21no—
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3—21no—
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
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C3×Dic12—22no—
124#3724—21no—
125#3724—21no—
126#3724—21no—
127#3724—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3D411yescharacteristic
134(C2×D3)⋊Dic3D411yescharacteristic
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138#3719—22no—
139#3719—22no—
140#3718—22no—
141#3127—91noSylow
142C2×D3×Q8—31no—
143C22×Dic6—31no—
144C2×C3×Q16—31no—
145C3×C22⋊Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C3×#117—31no—
149#946—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152#944—31no—
153#944—31no—
154C2×#216—31no—
155C2×#216—31no—
156C2×#216—31no—
157C2×#216—31no—
158#926—31no—
159#924—31no—
160C2×Dic12—31no—
161C2×Dic12—31no—
162C2×Dic12C2×D311yescharacteristic
163#898—61no—
164#897C2×D311yescharacteristic
165#892—61no—
166#892C2×D311yescharacteristic
167#890—31no—
168#890—31no—
169#890—61no—
170#890—61no—
171#889—61no—
172#889—61no—
173#887—31no—
174#887—31no—
175#887—31no—
176#887—31no—
177#887—61no—
178#887—61no—
179#887C2×D311yescharacteristic
180#887C2×D311yescharacteristic
181#879—61no—
182#879—61no—
183#877—61no—
184#877—61no—
185#876—61no—
186#872—31no—
187#872—61no—
188#870—61no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C4×Dic6—61no—
192C4×Dic6—61no—
193C4×Dic6—61no—
194C3×#107—21no—
195C3×#107C2×D311yescharacteristic
196C3×#107C2×D311yescharacteristic
197C3×#106—31no—
198C3×#103—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×C22⋊C8—31no—
203C3×C4×C8—31no—
204#835—31no—
205#835—31no—
206#830—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8C2×D311yescharacteristic
209#818—31no—
210#816—31no—
211#816—31no—
212#816—31no—
213#816—61no—
214#816C2×D311yescharacteristic
215#815—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—61no—
221C8×Dic3C2×D311yescharacteristic
222#810—31no—
223#810—31no—
224#810—31no—
225#810—61no—
226#810C2×D311yescharacteristic
227#810C2×D311yescharacteristic
228#810C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—61no—
232#808C2×D311yescharacteristic
233#807—31no—
234#803—31no—
235C22×C3×D3C2×D411yescharacteristic
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3C2×D411yescharacteristic
242C2×C3⋊Dic3C2×D411yescharacteristic
243#634—21no—
244#634#4112yes—
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—21no—
253C3×C4×D3—21no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6#4112yes—
260#627—24no—
261D3×Dic3—24no—
262C32×C8—21no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—91no—
267#519—91no—
268#485—31no—
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—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8—31no—
284C22×C3×C4—31no—
285C22×Dic3—61no—
286D3×Q8—62no—
287D3×Q8—62no—
288C2×C4×D3—61no—
289C2×C4×D3C22×D311yescharacteristic
290C2×Dic6—31no—
291C2×Dic6—31no—
292C2×Dic6—61no—
293C2×Dic6—62no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—62no—
297C2×Dic6C22×D311yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C3×Q16—62no—
301C2×C3×C8—21no—
302C2×C3×C8—31no—
303C2×C3×C8—31no—
304C2×C3×C8C22×D311yescharacteristic
305C2×C3×C8C22×D311yescharacteristic
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—61no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4C22×D311yescharacteristic
313C3×C4⋊C4C22×D311yescharacteristic
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C22⋊C4—61no—
317C3×C22⋊C4—61no—
318C3×C42—31no—
319C3×C42—61no—
320C3×C42—61no—
321C3×C42—61no—
322#217—31no—
323#217—31no—
324#217—61no—
325#216—62no—
326#216—62no—
327#216—62no—
328#216—62no—
329(C2×D3)⋊C4—21no—
330(C2×D3)⋊C4—21no—
331(C2×D3)⋊C4—31no—
332(C2×D3)⋊C4—31no—
333(C2×D3)⋊C4—61no—
334C4⋊Dic3—21no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—121no—
345C4⋊Dic3C22×D311yescharacteristic
346Dic3⋊C4—21no—
347Dic3⋊C4—21no—
348Dic3⋊C4—31no—
349Dic3⋊C4—31no—
350Dic3⋊C4—61no—
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—121no—
365Dic3⋊C4—121no—
366C4×Dic3—21no—
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—121no—
381C4×Dic3C22×D311yescharacteristic
382C2×C3⋊C8—31no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—61no—
385C2×C3⋊C8C22×D311yescharacteristic
386C2×C3⋊C8C22×D311yescharacteristic
387Dic12—22no—
388Dic12—62no—
389Dic12—62no—
390C22×C32C22×D411yescharacteristic
391C2×C3×D3—21no—
392C2×C3×D3—21no—
393C2×C3×D3—21no—
394C32×C4—41no—
395C32×C4—41no—
396C32×C4C2×#4111yescharacteristic
397C32×C4C2×#4111yescharacteristic
398C3⋊Dic3—22no—
399C3⋊Dic3—21no—
400C3⋊Dic3—21no—
401C3⋊Dic3—41no—
402C3×Dic3—22no—
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C22×Q8—91no—
410C2×Q16—31no—
411C2×Q16—91no—
412C2×Q16—91no—
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—31no—
431#117—91no—
432#117—181no—
433#117—181no—
434#107—91no—
435#107D3211yescharacteristic
436#106—31no—
437#106—91no—
438C4⋊C8—91no—
439C4⋊C8—91no—
440#103—31no—
441#103—31no—
442#103—31no—
443#103—31no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103—91no—
448C22⋊C8—31no—
449C22⋊C8—91no—
450#97—91no—
451C4×C8—31no—
452C23×C3—31no—
453C22×D3D3×D411yescharacteristic
454C3×Q8—32no—
455C3×Q8—61no—
456C3×Q8—61no—
457C3×Q8—61no—
458C3×Q8—61no—
459C3×Q8—61no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—31no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4C23×D311yescharacteristic
477C2×C3×C4C23×D311yescharacteristic
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—64no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—121no—
494C2×Dic3—121no—
495C2×Dic3D3×D411yescharacteristic
496C2×Dic3D3×D411yescharacteristic
497C2×Dic3D3×D411yescharacteristic
498C4×D3—21no—
499C4×D3—21no—
500C4×D3—64no—
501Dic6—21no—
502Dic6—21no—
503Dic6—21no—
504Dic6—21no—
505Dic6—21no—
506Dic6—32no—
507Dic6—32no—
508Dic6—62no—
509Dic6—64no—
510Dic6—64no—
511Dic6—61no—
512Dic6—61no—
513Dic6—121no—
514Dic6#23512yes—
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—91no—
533C2×Q8—181no—
534C2×Q8—182no—
535C2×Q8—182no—
536C22×C4—31no—
537C22×C4—181no—
538Q16—62no—
539Q16—182no—
540Q16—182no—
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—181no—
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⋊C4C2×D3211yescharacteristic
563C4⋊C4C2×D3211yescharacteristic
564C22⋊C4—61no—
565C22⋊C4—61no—
566C22⋊C4—91no—
567C22⋊C4—91no—
568C22⋊C4—181no—
569C42—31no—
570C42—61no—
571C42—61no—
572C42—61no—
573C42—91no—
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—21no—
588C3×C4—21no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—62no—
594C3×C4—61no—
595C3×C4—61no—
596C3×C4—61no—
597C3×C4—81no—
598C3×C4—81no—
599C3×C4—121no—
600C3×C4—121no—
601C3×C4—121no—
602C3×C4C2×#23511yescharacteristic
603C3×C4D3×#4111yescharacteristic
604C3×C4D3×#4111yescharacteristic
605C3×C4D3×#4111yescharacteristic
606Dic3—21no—
607Dic3—21no—
608Dic3—21no—
609Dic3—22no—
610Dic3—41no—
611Dic3—41no—
612Dic3—41no—
613Dic3—62no—
614Dic3—61no—
615Dic3—61no—
616Dic3—61no—
617Dic3—61no—
618Dic3—62no—
619Dic3—122no—
620Dic3—121no—
621Dic3—121no—
622Dic3—121no—
623Dic3—121no—
624Dic3—241no—
625C32#312711yescharacteristic, complemented, Sylow
626C23—31no—
627Q8—32no—
628Q8—61no—
629Q8—61no—
630Q8—61no—
631Q8—61no—
632Q8—61no—
633Q8—92no—
634Q8—184no—
635Q8—181no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—31no—
639C2×C4—31no—
640C2×C4—31no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—91no—
648C2×C4—91no—
649C2×C4—184no—
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#565611yescharacteristic
663C2×C3#576611yescharacteristic
664C2×C3#577111yescharacteristic
665C2×C3#577111yescharacteristic
666C2×C3#577911yescharacteristic
667D3—41no—
668C22—61no—
669C22—61no—
670C22—61no—
671C22D32×D411yescharacteristic
672C4—41no—
673C4—41no—
674C4—61no—
675C4—62no—
676C4—61no—
677C4—61no—
678C4—121no—
679C4—121no—
680C4—121no—
681C4—182no—
682C4—181no—
683C4—181no—
684C4—361no—
685C4D3×#23511yescharacteristic
686C4#6431911yescharacteristic
687C3—21no—
688C3#7972411yescharacteristic, complemented
689C3#8149911yescharacteristic, complemented
690C2—121no—
691C2#1059461411yescharacteristic
692C2#1059473711yescharacteristic
693C2#1059476611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#107D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
3. #10592576C2semidirect
5. C3×#4873C2semidirect
7. #10590798C2semidirect
8. #10590793C2semidirect
11. #10590566C2semidirect
13. #10590495C2semidirect
14. #10590480C2semidirect
15. #10590477C2semidirect
77. #4873D3semidirect
625. C32#3127semidirect
688. C3#79724semidirect
689. C3#81499semidirect

Maximal subgroups

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

subgroupindex
#105943572
#105943452
#105925762
C3×#48882
C3×#48732
#105909492
#105907982
#105907932
#105906962
#105906042
#105905662
#105905192
#105904952
#105904802
#105904772
#814993
#797243