Finite Group Databasebeta

← #11869681

Subgroups — #11869681

Order 1152.

888 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#117C211yesmaximal, characteristic, complemented
2#10594892C211yesmaximal, characteristic
3#10592695C211yesmaximal, characteristic, complemented
4C3×#5003C211yesmaximal, characteristic, complemented
5D3×#830C211yesmaximal, characteristic, complemented
6#10591134C211yesmaximal, characteristic, complemented
7#10591090C211yesmaximal, characteristic, complemented
8#10590608C211yesmaximal, characteristic, complemented
9#10590608C211yesmaximal, characteristic, complemented
10#10590572C211yesmaximal, characteristic, complemented
11#10590571C211yesmaximal, characteristic, complemented
12#10590500C211yesmaximal, characteristic, complemented
13#10590498C211yesmaximal, characteristic, complemented
14#10590427C211yesmaximal, characteristic, complemented
15#10590426C211yesmaximal, characteristic, complemented
16#82215—31nomaximal
17#81371—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×#117C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×#930C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×D3×C22⋊C4—21no—
29C3×#877—21no—
30C3×#872—21no—
31C3×C42×D3—21no—
32#63976—21no—
33Dic3×#67—21no—
34#63908C2211yescharacteristic
35#63905—21no—
36#63879—21no—
37#63857C2211yescharacteristic
38#63841C2211yescharacteristic
39C2×D3×C3⋊C8C2211yescharacteristic
40C2×D3×C3⋊C8C2211yescharacteristic
41#63657C2211yescharacteristic
42#63637C2211yescharacteristic, complemented
43#63637C2211yescharacteristic, complemented
44#63635C2211yescharacteristic, complemented
45#63634C2211yescharacteristic, complemented
46C3×#830C2211yescharacteristic
47C3×#809C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C2×C3×#117—31no—
62#5791—31no—
63#5606—31no—
64D3×#117D311yescharacteristic, complemented
65C3×#482—31no—
66C2×#830—31no—
67#5035—31no—
68#5003—31no—
69#5003D311yescharacteristic, complemented
70#5002—31no—
71#5002—31no—
72#4998—31no—
73#4998—31no—
74#4996—31no—
75#4996—31no—
76#4996—31no—
77#4996—61no—
78#4971—31no—
79#4970—31no—
80#4968—31no—
81#4967—31no—
82#4884—31no—
83#4880—31no—
84#4862—31no—
85#4860—31no—
86#4777—31no—
87#4774—31no—
88#4772—31no—
89#4772—31no—
90D3×C22⋊C8—31no—
91#4723—31no—
92C23×C3×D3D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C22×C3×Dic3D411yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—22no—
99C2×C3×C4×D3—22no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3D411yescharacteristic
103C2×C3×C4×D3D411yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×#625—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109#3795—22no—
110#3795—22no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42—21no—
115#3757—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139D3×C3⋊C8—22no—
140D3×C3⋊C8—22no—
141#3091—91noSylow
142C23×C3×C4—31no—
143C2×#237—31no—
144C2×#235—31no—
145C22×C4×D3C2×D311yescharacteristic
146C3×#121—31no—
147C3×#117—21no—
148C3×#117—31no—
149C3×#117—31no—
150C3×#117—31no—
151C3×#117—61no—
152C3×#117—61no—
153C3×#117C2×D311yescharacteristic
154C3×#117C2×D311yescharacteristic
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C22⋊C4—61no—
158C2×C3×C42—61no—
159#953—61no—
160#938—31no—
161#937—61no—
162D4×Dic3—61no—
163#930—31no—
164#930C2×D311yescharacteristic
165#929—61no—
166C4×#67—61no—
167C4×#67—61no—
168#926—31no—
169#926C2×D311yescharacteristic
170#924—31no—
171#924—31no—
172#924—31no—
173#924—61no—
174C22×C3⋊C8—31no—
175C22×C3⋊C8—31no—
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178#897—31no—
179#892—31no—
180#892C2×D311yescharacteristic
181#892C2×D311yescharacteristic
182D3×C4⋊C4C2×D311yescharacteristic
183D3×C4⋊C4C2×D311yescharacteristic
184#883—61no—
185#67⋊C4—61no—
186D3×C22⋊C4—21no—
187#877—21no—
188#872—21no—
189C42×D3—21no—
190C3×#107—31no—
191C3×#106—31no—
192C3×#102—31no—
193C3×#102—31no—
194C3×C22⋊C8—31no—
195#832—31no—
196#832—31no—
197#830—31no—
198#830—31no—
199#830—31no—
200#830—31no—
201#830—61no—
202#830C2×D311yescharacteristic
203(C2×D3)⋊C8—31no—
204(C2×D3)⋊C8—31no—
205#818—31no—
206#817—31no—
207#816—31no—
208#816—31no—
209#810—31no—
210#810—31no—
211#810—31no—
212#810—31no—
213#810—31no—
214#810—31no—
215#810—61no—
216#810—61no—
217#809—31no—
218#809—31no—
219#809C2×D311yescharacteristic, complemented
220#809C2×D311yescharacteristic, complemented
221#808—31no—
222#808—31no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808—61no—
227#808C2×D311yescharacteristic, complemented
228#807—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—61no—
234#807C2×D311yescharacteristic, complemented
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—22no—
237C22×C3×D3—22no—
238C22×C3×D3—21no—
239C22×C3×D3—41no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250#634—21no—
251#634—21no—
252C3×#67—42no—
253C2×C3×Dic3—22no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×C4×D3—22no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—22no—
265C3×C4×D3—42no—
266C3×C4×D3—42no—
267C3×C4×D3#4112yes—
268C3×C4×D3#4112yes—
269#625—42no—
270#625—42no—
271D3×Dic3—42no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#525—91no—
277C2×#117—31no—
278#485—91no—
279#485—91no—
280#484—91no—
281#483—91no—
282#482—31no—
283#482—91no—
284#481—91no—
285#480—91no—
286#427—91no—
287#427—91no—
288#416—91no—
289#416—91no—
290C2×C22⋊C8—91no—
291C24×C3—31no—
292C23×D3#6711yescharacteristic
293C2×C3×D4—31no—
294C2×C3×D4—61no—
295C22×C3×C4—21no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—62no—
302C22×C3×C4—62no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—21no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C22×Dic3—61no—
313C22×Dic3#6711yescharacteristic
314#237—62no—
315#237—62no—
316#235—62no—
317#235—62no—
318C2×D12C22×D311yescharacteristic
319C2×C4×D3—22no—
320C2×C4×D3—22no—
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—61no—
324C2×C4×D3#6711yescharacteristic
325C2×C4×D3#6711yescharacteristic
326C2×C4×D3C22×D311yescharacteristic
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—61no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—41no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C42—21no—
352C3×C42—21no—
353C3×C42—41no—
354C3×C42—61no—
355C3×C42—61no—
356C3×C42—61no—
357#217—21no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—121no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—121no—
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8—62no—
395C2×C3⋊C8—62no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398D3×C8—62no—
399D3×C8—62no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32C22×D411yescharacteristic
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—44no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3#12312yes—
413C2×C3×D3#13512yes—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3#12312yes—
426C2×#41—91no—
427C23×C4—31no—
428C22×C8—91no—
429C22×C8—91no—
430#123—181no—
431C22⋊Q8—91no—
432C22⋊Q8—91no—
433#121—31no—
434#121—91no—
435#120—181no—
436C4×D4—181no—
437C4×D4—181no—
438#117—31no—
439#117—31no—
440#117—31no—
441#117—61no—
442#117—61no—
443#117—91no—
444#117D3211yescharacteristic
445C2×C4⋊C4—31no—
446C2×C4⋊C4—31no—
447C2×C22⋊C4—61no—
448C2×C42—61no—
449#107—31no—
450#107—91no—
451#107—91no—
452#107—91no—
453#106—31no—
454#106—91no—
455#106—91no—
456#106—91no—
457#103—91no—
458#103—91no—
459#103—91no—
460#103—91no—
461#102—31no—
462#102—31no—
463#102—91no—
464#102—91no—
465C22⋊C8—31no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468C22⋊C8—91no—
469C23×C3—21no—
470C23×C3—31no—
471C23×C3—31no—
472C23×C3—62no—
473C23×C3—62no—
474C23×C3—61no—
475C23×C3—121no—
476C23×C3D3×D411yescharacteristic
477C23×C3C2×#6711yescharacteristic
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—21no—
481C22×D3—41no—
482C22×D3C2×#6711yescharacteristic
483C22×D3C2×#6711yescharacteristic
484C3×D4—61no—
485C3×D4—61no—
486C3×D4—122no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—31no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—62no—
506C2×C3×C4—62no—
507C2×C3×C4—62no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—122no—
514C2×C3×C4—122no—
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4C2×#6711yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519#67—42no—
520#67—122no—
521#67—122no—
522#67—122no—
523#67—122no—
524C2×Dic3—22no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—122no—
535C2×Dic3C2×#6711yescharacteristic
536C2×Dic3C2×#6711yescharacteristic
537D12—21no—
538D12—21no—
539C4×D3—22no—
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—22no—
543C4×D3—42no—
544C4×D3—42no—
545C4×D3—122no—
546C4×D3#23512yes—
547C4×D3#23512yes—
548Dic6—61no—
549Dic6—61no—
550Dic6—61no—
551Dic6—61no—
552Dic6—121no—
553Dic6—121no—
554C3×C8—61no—
555C3×C8—61no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C3⋊C8—121no—
564C2×C32—41no—
565C2×C32C2×#12311yescharacteristic
566C2×C32C2×#13511yescharacteristic
567C2×C32#57511yescharacteristic
568C3×D3—22no—
569C3×D3—22no—
570C3×D3—81no—
571C24—31no—
572#41—182no—
573#41—182no—
574C2×Q8—91no—
575C2×D4—31no—
576C2×D4—61no—
577C2×D4—181no—
578C2×D4—181no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—181no—
589C22×C4C2×D3211yescharacteristic
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—91no—
593C2×C8—91no—
594C2×C8—182no—
595C2×C8—182no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4C2×D3211yescharacteristic
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—21no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—21no—
616C42—61no—
617C42—61no—
618C42—61no—
619C42—181no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—32no—
628C22×C3—32no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—124no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C22×#6711yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—44no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3#92912yes—
651C2×D3#95012yes—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—32no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—61no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4C2×#23511yescharacteristic
669C3×C4C2×#23511yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4D3×#4111yescharacteristic
672Dic3—21no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3—241no—
682Dic3#92912yes—
683C32#309111yescharacteristic, complemented, Sylow
684C23—31no—
685C23—31no—
686C23—62no—
687C23—62no—
688C23—61no—
689C23—121no—
690C23D3×#6711yescharacteristic
691Q8—181no—
692Q8—181no—
693D4—61no—
694D4—61no—
695D4—122no—
696D4—362no—
697D4—362no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—31no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—362no—
719C2×C4D3×#6711yescharacteristic
720C2×C4C22×D3211yescharacteristic
721C8—61no—
722C8—61no—
723C8—181no—
724C8—181no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—41no—
729C2×C3—41no—
730C2×C3—62no—
731C2×C3—62no—
732C2×C3—81no—
733C2×C3—241no—
734C2×C3D3×#12311yescharacteristic
735C2×C3D3×#13511yescharacteristic
736C2×C3#577311yescharacteristic
737C2×C3C2×#92911yescharacteristic
738C2×C3C2×#95011yescharacteristic
739C2×C3#582211yescharacteristic
740D3—22no—
741D3—22no—
742D3—81no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—32no—
747C22—32no—
748C22—61no—
749C22—61no—
750C22—61no—
751C22—61no—
752C22—124no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22C2×D3×#6711yescharacteristic
757C4—21no—
758C4—32no—
759C4—41no—
760C4—41no—
761C4—61no—
762C4—121no—
763C4—121no—
764C4—121no—
765C4—361no—
766C4—361no—
767C4D3×#23511yescharacteristic
768C4D3×#23511yescharacteristic
769C3—21no—
770C3#8137111yescharacteristic, complemented
771C3#8221511yescharacteristic, complemented
772C2—41no—
773C2—62no—
774C2—62no—
775C2—241no—
776C2D3×#92911yescharacteristic
777C2D3×#95011yescharacteristic
778C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10594892C2
hypercenter#117D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×D3×#117C2semidirect
3. #10592695C2semidirect
4. C3×#5003C2semidirect
5. D3×#830C2semidirect
6. #10591134C2semidirect
7. #10591090C2semidirect
8. #10590608C2semidirect
9. #10590608C2semidirect
10. #10590572C2semidirect
11. #10590571C2semidirect
12. #10590500C2semidirect
13. #10590498C2semidirect
14. #10590427C2semidirect
15. #10590426C2semidirect
42. #63637C22semidirect
43. #63637C22semidirect
44. #63635C22semidirect
45. #63634C22semidirect
47. C3×#809C22semidirect
48. C3×#809C22semidirect
49. C3×#808C22semidirect
50. C3×#807C22semidirect
51. #63576C22semidirect
52. #63575C22semidirect
53. #63574C22semidirect
54. #63573C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
64. D3×#117D3semidirect
69. #5003D3semidirect
219. #809C2×D3semidirect
220. #809C2×D3semidirect
227. #808C2×D3semidirect
234. #807C2×D3semidirect
683. C32#3091semidirect
770. C3#81371semidirect
771. C3#82215semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1172
#105948922
#105926952
C3×#50032
D3×#8302
#105911342
#105910902
#105906082
#105905722
#105905712
#105905002
#105904982
#105904272
#105904262
#822153
#813713