Finite Group Databasebeta

← #11860238

Subgroups — #11860238

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#239C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic
3#10594362C211yesmaximal, characteristic, complemented
4#10592516C211yesmaximal, characteristic, complemented
5C3×#4804C211yesmaximal, characteristic, complemented
6C3×#4789C211yesmaximal, characteristic, complemented
7#10591582C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9#10590746C211yesmaximal, characteristic, complemented
10#10590743C211yesmaximal, characteristic, complemented
11#10590690C211yesmaximal, characteristic, complemented
12D3×#815C211yesmaximal, characteristic, complemented
13#10590572C211yesmaximal, characteristic, complemented
14#10590462C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#79828—31nomaximal
17#78819—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22#64102C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×#892C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63949C418yescomplemented
29#63898—21no—
30#63898C2211yescharacteristic
31#63894C2211yescharacteristic
32Dic3×D12—21no—
33Dic3×D12C2211yescharacteristic
34C4×#624—21no—
35#63881—21no—
36#63880—21no—
37C4×D3×Dic3—21no—
38C4×D3×Dic3C2211yescharacteristic
39#63843C2211yescharacteristic
40#63841—21no—
41#63841C2211yescharacteristic
42#63836—21no—
43C2×#3715C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46C32×#103C2211yescharacteristic
47#63648C2211yescharacteristic
48#63642C2211yescharacteristic
49#63634C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#815C2211yescharacteristic
54C3×#809C2211yescharacteristic
55C3×#808C2211yescharacteristic
56#63576C2211yescharacteristic
57#63573C2211yescharacteristic
58#63566C2211yescharacteristic
59#63564C2211yescharacteristic
60#63555C2211yescharacteristic
61#63554C2211yescharacteristic
62Dic3×#41—31no—
63C2×#950—31no—
64C2×#919—31no—
65C4×#239—31no—
66C4×#239—31no—
67#5522—31no—
68C3×#441—31no—
69C3×#416—31no—
70#5184—31no—
71#5113—31no—
72C2×#815—31no—
73#5026—31no—
74#5026—31no—
75#4998—31no—
76#4869—31no—
77#4860—31no—
78#4817—31no—
79#4817—31no—
80#4817—31no—
81#4817—31no—
82#4817—61no—
83#4804—31no—
84#4804D311yescharacteristic, complemented
85#4789—31no—
86#4789D311yescharacteristic, complemented
87#4785—31no—
88#4785—31no—
89#4757—31no—
90#4757—31no—
91#4711—31no—
92D3×#97—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C3×#239—22no—
97C3×#239C2×C414yescomplemented
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×#624—21no—
105C2×#624—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3D411yescharacteristic
109C2×D3×Dic3D411yescharacteristic
110#3799—22no—
111#3799C2×C414yescomplemented
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3755C2×C414yescomplemented
115#3752—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#216C2×C414yescomplemented
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×D3×C8—22no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32D411yescharacteristic
142Dic32D411yescharacteristic
143#3715C2×C414yescomplemented
144#3714C2×C414yescomplemented
145D3×C3⋊C8C2×C414yescomplemented
146#2943—91noSylow
147C2×C3×#41—31no—
148C2×#239—31no—
149C2×#239C2×D311yescharacteristic
150C2×#235—31no—
151C2×C3×Q16—31no—
152C22×C3×C8—31no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×#117—31no—
156#950—38no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159Q8×Dic3—31no—
160Q8×Dic3—61no—
161Q8×Dic3C2×D311yescharacteristic
162C2×#216C2×D311yescharacteristic
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—61no—
167D4×Dic3—31no—
168D4×Dic3—31no—
169D4×Dic3—61no—
170D4×Dic3—61no—
171C2×#214—31no—
172C2×#213—31no—
173#926—31no—
174#926—61no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—61no—
177C22×C3⋊C8—31no—
178#919—38no—
179C2×D24—31no—
180C2×D3×C8—31no—
181C2×D3×C8C2×D311yescharacteristic
182#893—31no—
183#893—31no—
184#893—31no—
185#893—31no—
186#893—61no—
187#893—61no—
188#893—61no—
189#892—31no—
190#892—61no—
191#892—61no—
192#892C2×D311yescharacteristic
193#887—31no—
194#887C2×D311yescharacteristic
195#67⋊C4—61no—
196#67⋊C4—61no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—61no—
200C4×D12—61no—
201#872—61no—
202C42×D3—31no—
203C42×D3—61no—
204C42×D3—61no—
205C42×D3—61no—
206C3×#106—31no—
207C3×#103—21no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212C3×#102—31no—
213C3×#102—31no—
214C3×#97—31no—
215#835—31no—
216#835C2×D311yescharacteristic
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221#821C2×D311yescharacteristic
222#817—31no—
223#816—31no—
224#816C2×D311yescharacteristic
225#815—31no—
226#815—31no—
227#815—31no—
228#815—31no—
229#815—31no—
230#815—61no—
231#815C2×D311yescharacteristic
232#809—31no—
233#809C2×D311yescharacteristic
234#808—31no—
235#808C2×D311yescharacteristic
236#807—31no—
237#807—31no—
238#807—31no—
239#807—31no—
240#807—61no—
241#803—31no—
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8C22×C412yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)C22×C412yes—
255C4×C3⋊D3—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—24no—
263C3×D12—21no—
264C3×D12C22×C412yes—
265C3×C4×D3—24no—
266C3×C4×D3C22×C412yes—
267C3×C4×D3#4112yes—
268C3×Dic6—21no—
269C3×Dic6C22×C412yes—
270#626—24no—
271#624—24no—
272#624—42no—
273D3×Dic3—41no—
274D3×Dic3—41no—
275D3×Dic3—42no—
276D3×Dic3—42no—
277C32×C8—21no—
278C3⋊(C3⋊C8)C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C2×#135—91no—
282C4×#41—91no—
283C4×#41—91no—
284#442—91no—
285#442—91no—
286#441—31no—
287#441—91no—
288#440—91no—
289#440—91no—
290#440—91no—
291#440—91no—
292#427—91no—
293#416—31no—
294#416—91no—
295C2×#97—91no—
296C3×#41—34no—
297C3×#41—62no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C2×#67—61no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311#239—22no—
312#239—34no—
313#239—62no—
314#239C4×D314yescomplemented
315#235—34no—
316#235—62no—
317C2×D12—21no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—121no—
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C3×Q16—34no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—62no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—61no—
352C3×C42—31no—
353C3×C42—61no—
354C3×C42—61no—
355C3×C42—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#216C4×D314yescomplemented
360#215—34no—
361#215—34no—
362#215—34no—
363#215—64no—
364#214—34no—
365#213—34no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—121no—
375C4⋊Dic3—21no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—121no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—61no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—121no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—34no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D24—34no—
412D3×C8—22no—
413D3×C8—34no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—22no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3C4×D412yes—
424C32×C4—22no—
425C32×C4—41no—
426C32×C4C23×C411yescharacteristic
427C32×C4C2×#4111yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3C4×D412yes—
437C2×#41—31no—
438C2×#41—91no—
439#135—98no—
440C2×Q16—31no—
441C2×SD16—91no—
442C2×SD16—91no—
443C2×D8—91no—
444C22×C8—31no—
445C22×C8—91no—
446C4×Q8—31no—
447C4×Q8—31no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×D4—91no—
451C4×D4—91no—
452C4×D4—91no—
453C4×D4—91no—
454C4×D4—181no—
455C4×D4—181no—
456C4×D4—181no—
457C4×D4—181no—
458#117—31no—
459#117—91no—
460#117—181no—
461#117—181no—
462C2×C42—91no—
463C2×C42—181no—
464C2×C42—181no—
465#107—91no—
466#107—91no—
467#106—31no—
468#106—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103D3211yescharacteristic
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#97—31no—
478#97—91no—
479#97—91no—
480#97—91no—
481C23×C3—31no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—121no—
487C22×D3D3×D411yescharacteristic
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—22no—
491C3×Q8—32no—
492C3×Q8—41no—
493C3×Q8—61no—
494C3×Q8C2×C4×D312yes—
495C3×Q8C2×C4×D312yes—
496C3×D4—32no—
497C3×D4—64no—
498C3×D4—61no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—64no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—64no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—122no—
533C2×Dic3—122no—
534C2×Dic3D3×D411yescharacteristic
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537D12—24no—
538D12—21no—
539D12—32no—
540D12—32no—
541D12—62no—
542D12—64no—
543D12—61no—
544D12—61no—
545D12—121no—
546D12C2×C4×D312yes—
547C4×D3—24no—
548C4×D3—64no—
549C4×D3—64no—
550C4×D3—122no—
551C4×D3—122no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—121no—
555C4×D3—121no—
556C4×D3—122no—
557C4×D3—122no—
558C4×D3—242no—
559C4×D3C2×C4×D312yes—
560C4×D3#23712yes—
561Dic6—21no—
562Dic6C2×C4×D312yes—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—32no—
566C3×C8—41no—
567C3×C8—61no—
568C3⋊C8—21no—
569C3⋊C8—32no—
570C3⋊C8—32no—
571C3⋊C8—62no—
572C3⋊C8C2×C4×D312yes—
573C2×C32C2×C4×D411yescharacteristic
574C2×C32#57511yescharacteristic
575C2×C32#57511yescharacteristic
576C3⋊D3—42no—
577C3×D3—22no—
578C3×D3—42no—
579#41—34no—
580#41—62no—
581#41—94no—
582#41—182no—
583C2×Q8—31no—
584C2×Q8C2×D3211yescharacteristic
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—91no—
588C2×D4—181no—
589C22×C4—31no—
590C22×C4—61no—
591C22×C4—91no—
592C22×C4—91no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598Q16—34no—
599SD16—94no—
600SD16—94no—
601D8—94no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—62no—
605C2×C8—94no—
606C2×C8—91no—
607C2×C8C2×D3211yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4C2×D3211yescharacteristic
616C22⋊C4—61no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C42—31no—
623C42—61no—
624C42—61no—
625C42—61no—
626C42—91no—
627C42—91no—
628C42—91no—
629C42—181no—
630C42—181no—
631C42—181no—
632C22×C3—21no—
633C22×C3—32no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—62no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—22no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—62no—
647C2×D3—62no—
648C2×D3—122no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—241no—
654C2×D3—241no—
655C2×D3#67⋊C412yes—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—32no—
661C3×C4—42no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—62no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—81no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4C22×C4×D311yescharacteristic
671C3×C4C22×C4×D311yescharacteristic
672C3×C4C2×#23711yescharacteristic
673C3×C4D3×#4111yescharacteristic
674Dic3—21no—
675Dic3—21no—
676Dic3—22no—
677Dic3—41no—
678Dic3—41no—
679Dic3—61no—
680Dic3—61no—
681Dic3—61no—
682Dic3—61no—
683Dic3—121no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—241no—
688Dic3#67⋊C412yes—
689C32#294311yescharacteristic, complemented, Sylow
690C23—31no—
691C23—61no—
692C23—181no—
693Q8—21no—
694Q8—32no—
695Q8—61no—
696Q8C4×D3212yes—
697D4—32no—
698D4—64no—
699D4—61no—
700D4—92no—
701D4—184no—
702D4—181no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—31no—
706C2×C4—32no—
707C2×C4—32no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—64no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—91no—
715C2×C4—91no—
716C2×C4—184no—
717C2×C4—181no—
718C2×C4—362no—
719C2×C4—362no—
720C2×C4—361no—
721C2×C4—361no—
722C2×C4—362no—
723C2×C4—362no—
724C2×C4C22×D3211yescharacteristic
725C8—21no—
726C8—32no—
727C8—61no—
728C8—92no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—62no—
733C2×C3—122no—
734C2×C3C2×#67⋊C411yescharacteristic
735C2×C3C4×D3×D411yescharacteristic
736C2×C3#576811yescharacteristic
737C2×C3#576811yescharacteristic
738C2×C3#577711yescharacteristic
739C2×C3#577711yescharacteristic
740D3—22no—
741D3—42no—
742D3—122no—
743D3—122no—
744D3—242no—
745C22—32no—
746C22—61no—
747C22—61no—
748C22—62no—
749C22—121no—
750C22—121no—
751C22—182no—
752C22—361no—
753C22—361no—
754C22D32×D411yescharacteristic
755C4—22no—
756C4—32no—
757C4—41no—
758C4—61no—
759C4—61no—
760C4—62no—
761C4—121no—
762C4—121no—
763C4—181no—
764C4—181no—
765C4—361no—
766C4C2×C4×D3211yescharacteristic
767C4D3×#23711yescharacteristic
768C3—21no—
769C3#7881911yescharacteristic, complemented
770C3#7982811yescharacteristic, complemented
771C2—62no—
772C2—122no—
773C2—362no—
774C2D3×#67⋊C411yescharacteristic
775C2#1059474611yescharacteristic
776C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#63949C2
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32#2943
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. Dic3×#239C2semidirect
3. #10594362C2semidirect
4. #10592516C2semidirect
5. C3×#4804C2semidirect
6. C3×#4789C2semidirect
7. #10591582C2semidirect
8. #10591540C2semidirect
9. #10590746C2semidirect
10. #10590743C2semidirect
11. #10590690C2semidirect
12. D3×#815C2semidirect
13. #10590572C2semidirect
14. #10590462C2semidirect
15. #10590454C2semidirect
28. #63949C4semidirect
84. #4804D3semidirect
86. #4789D3semidirect
97. C3×#239C2×C4semidirect
111. #3799C2×C4semidirect
114. #3755C2×C4semidirect
121. C3×#216C2×C4semidirect
143. #3715C2×C4semidirect
144. #3714C2×C4semidirect
145. D3×C3⋊C8C2×C4semidirect
314. #239C4×D3semidirect
359. #216C4×D3semidirect
689. C32#2943semidirect
769. C3#78819semidirect
770. C3#79828semidirect

Maximal subgroups

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

subgroupindex
Dic3×#2392
C2×#639492
#105943622
#105925162
C3×#48042
C3×#47892
#105915822
#105915402
#105907462
#105907432
#105906902
D3×#8152
#105905722
#105904622
#105904542
#798283
#788193