Finite Group Databasebeta

← #11872837

Subgroups — #11872837

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5545C211yesmaximal, characteristic
2#10593880C211yesmaximal, characteristic, complemented
3C4×#3754C211yesmaximal, characteristic, complemented
4C3×#5018C211yesmaximal, characteristic, complemented
5#10591489C211yesmaximal, characteristic, complemented
6#10591459C211yesmaximal, characteristic
7#10591458C211yesmaximal, characteristic
8#10591411C211yesmaximal, characteristic, complemented
9#10590559C211yesmaximal, characteristic, complemented
10#10590542C211yesmaximal, characteristic, complemented
11#10590519C211yesmaximal, characteristic, complemented
12#10590429C211yesmaximal, characteristic, complemented
13#10590360C211yesmaximal, characteristic, complemented
14C4×#3715C211yesmaximal, characteristic, complemented
15#10590265C211yesmaximal, characteristic, complemented
16#82545—31nomaximal
17#79787—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21C4×#634C2211yescharacteristic, complemented
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×(C2×D3)⋊C4—21no—
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28C3×#67⋊C4—21no—
29C3×D3×C22⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#872C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic, complemented
33#63870—21no—
34#63869C2211yescharacteristic, complemented
35#63867—21no—
36#63866C2211yescharacteristic, complemented
37#63862—21no—
38#63859—21no—
39#63857C2211yescharacteristic
40#63856C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43#63659C2211yescharacteristic
44#63637C2211yescharacteristic, complemented
45#63635C2211yescharacteristic, complemented
46C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic, complemented
49C3×#807C2211yescharacteristic, complemented
50C3×#803C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63574C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#518—31no—
62#5583—31no—
63#5545D311yescharacteristic
64#5518—31no—
65C3×#440—31no—
66#5218—31no—
67#5218—31no—
68#5169—31no—
69#5162—31no—
70C4×#215—31no—
71#5019—31no—
72#5019—31no—
73#5018—31no—
74#5018D311yescharacteristic, complemented
75C4×#214—31no—
76C4×#214—31no—
77C4×#214—31no—
78C4×#214—61no—
79#5009—31no—
80#5009—31no—
81#5000—31no—
82#4996—31no—
83#4996—31no—
84#4891—31no—
85#4888—31no—
86#4818—31no—
87#4814—31no—
88#4776—31no—
89#4766—31no—
90#4710—31no—
91#4709—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×D3×D4—22no—
99C3×D3×D4—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C22⋊C4—21no—
107C32×C42C2311yescharacteristic
108#3754—22no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111C4×C3⋊Dic3—21no—
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×#214—22no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4D411yescharacteristic
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3716—22no—
140#3715—22no—
141#3123—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C3×C4×Q8—31no—
146C3×C4×D4—21no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C3×C4×D4—61no—
151C3×C4×D4—61no—
152C3×C4×D4C2×D311yescharacteristic
153C3×C4×D4C2×D311yescharacteristic
154C3×#117—31no—
155C3×#117—31no—
156C2×C3×C22⋊C4—61no—
157C2×C3×C22⋊C4—61no—
158#946—31no—
159#944—31no—
160C2×#215—31no—
161D4×Dic3C2×D311yescharacteristic
162C2×#214—31no—
163C2×#214—31no—
164C2×#214—31no—
165C2×#214—31no—
166C2×#214—61no—
167C2×#214C2×D311yescharacteristic
168C4×#67—21no—
169C2×(C2×D3)⋊C4—21no—
170#924—31no—
171#924—31no—
172C2×#204—31no—
173#898—61no—
174#897—31no—
175#893C2×D311yescharacteristic
176#892C2×D311yescharacteristic
177#890—31no—
178#889—61no—
179#889—61no—
180#889—61no—
181#67⋊C4—21no—
182D3×C22⋊C4—21no—
183#879—61no—
184#879—61no—
185#876—61no—
186C4×D12C2×D311yescharacteristic
187#872C2×D311yescharacteristic
188#870—31no—
189#870—61no—
190#869—31no—
191C4×Dic6—31no—
192C4×Dic6—31no—
193C4×Dic6—61no—
194C4×Dic6C2×D311yescharacteristic, complemented
195C3×#107—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×#97—31no—
199#835—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—61no—
205#832C2×D311yescharacteristic
206#830—31no—
207#830—31no—
208#821—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211#818—31no—
212#816—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—61no—
220#810C2×D311yescharacteristic, complemented
221#809—31no—
222#808—31no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808—61no—
227#807—31no—
228#807C2×D311yescharacteristic, complemented
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231#803C2×D311yescharacteristic, complemented
232C4×C3⋊C8—31no—
233C4×C3⋊C8—31no—
234C4×C3⋊C8—61no—
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3—24no—
238C22×C3×D3—81no—
239C22×C3×D3—81no—
240C22×C3×D3C2×D411yescharacteristic
241C32×D4—21no—
242C32×D4#4112yes—
243C2×C32×C4—21no—
244C2×C32×C4—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250#634—21no—
251#634—21no—
252C3×#67—24no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—81no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12#4112yes—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—81no—
265C3×C4×D3—81no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—91no—
273#518—31no—
274#485—91no—
275#485—91no—
276#478—91no—
277#478—91no—
278#461—91no—
279#461—91no—
280#450—91no—
281#450—91no—
282#440—31no—
283#440—91no—
284C4×SD16—91no—
285C4×SD16—91no—
286#433—91no—
287C24×C3—61no—
288C23×D3—21no—
289C2×C3×Q8—31no—
290C2×C3×D4—21no—
291C2×C3×D4—31no—
292C2×C3×D4—61no—
293C2×C3×D4—62no—
294C2×C3×D4—62no—
295C2×C3×D4C22×D311yescharacteristic
296C2×C3×D4C22×D311yescharacteristic
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—41no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—21no—
305C22×Dic3—21no—
306D3×D4—22no—
307D3×D4—22no—
308C2×D12C22×D311yescharacteristic
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3C22×D311yescharacteristic
312C2×Dic6—31no—
313C2×Dic6—31no—
314C2×Dic6—61no—
315C2×Dic6C22×D311yescharacteristic
316C3×SD16—62no—
317C2×C3×C8—31no—
318C2×C3×C8—31no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C22⋊C4—21no—
328C3×C22⋊C4—21no—
329C3×C22⋊C4—31no—
330C3×C22⋊C4—31no—
331C3×C22⋊C4—41no—
332C3×C22⋊C4—61no—
333C3×C22⋊C4—61no—
334C3×C22⋊C4—61no—
335C3×C22⋊C4—61no—
336C3×C42—21no—
337C3×C42—31no—
338C3×C42—61no—
339C3×C42—61no—
340C3×C42C22×D311yescharacteristic
341C3×C42C22×D311yescharacteristic
342#217—21no—
343#217—61no—
344#217—61no—
345#215—62no—
346#214—22no—
347#214—62no—
348#214—62no—
349#214—64no—
350#214—62no—
351#214—62no—
352(C2×D3)⋊C4—21no—
353(C2×D3)⋊C4—21no—
354(C2×D3)⋊C4—21no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4#6711yescharacteristic
358(C2×D3)⋊C4#6711yescharacteristic
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3C22×D311yescharacteristic
367C4⋊Dic3C22×D311yescharacteristic
368Dic3⋊C4—21no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—121no—
380Dic3⋊C4#6711yescharacteristic
381Dic3⋊C4#6711yescharacteristic
382C4×Dic3—21no—
383C4×Dic3—21no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—121no—
387C4×Dic3C22×D311yescharacteristic
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⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396#204—62no—
397C22×C32—22no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32C22×D411yescharacteristic
401C2×C3×D3—21no—
402C2×C3×D3—22no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—84no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—41no—
411C32×C4C2×#4111yescharacteristic
412C32×C4C2×#4111yescharacteristic
413C3⋊Dic3—41no—
414C3⋊Dic3—41no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C22×D4—31no—
422C2×SD16—31no—
423C2×SD16—91no—
424C2×SD16—91no—
425C2×SD16—91no—
426C4⋊Q8—91no—
427#126—181no—
428#126—181no—
429#125—91no—
430#125—181no—
431#125—181no—
432C22⋊Q8—91no—
433C22⋊Q8—91no—
434C4×Q8—31no—
435C4×Q8—91no—
436C4×D4—31no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—61no—
440C4×D4—61no—
441C4×D4D3211yescharacteristic
442#117—31no—
443#117—31no—
444C2×C22⋊C4—61no—
445C2×C22⋊C4—61no—
446#107—31no—
447#107—91no—
448#106—91no—
449#106—91no—
450C4⋊C8—91no—
451C4⋊C8—91no—
452#103—31no—
453#103—91no—
454#103—91no—
455#103—91no—
456#102—31no—
457#102—91no—
458#102—91no—
459#102—91no—
460C22⋊C8—91no—
461C22⋊C8—91no—
462#97—31no—
463C4×C8—91no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—31no—
467C23×C3—41no—
468C23×C3—64no—
469C23×C3—61no—
470C23×C3—241no—
471C23×C3—241no—
472C22×D3—21no—
473C22×D3—24no—
474C22×D3—81no—
475C22×D3—81no—
476C22×D3C2×#6711yescharacteristic
477C3×Q8—61no—
478C3×Q8—61no—
479C3×D4—21no—
480C3×D4—21no—
481C3×D4—22no—
482C3×D4—32no—
483C3×D4—41no—
484C3×D4—64no—
485C3×D4—61no—
486C3×D4#23512yes—
487C3×D4#23512yes—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—41no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—81no—
503C2×C3×C4—81no—
504C2×C3×C4—82no—
505C2×C3×C4—241no—
506C2×C3×C4—241no—
507C2×C3×C4—241no—
508C2×C3×C4D3×D411yescharacteristic
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4C2×#6711yescharacteristic
511C2×C3×C4C2×#6711yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514#67—24no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—81no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3C2×#6711yescharacteristic
526C2×Dic3C2×#6711yescharacteristic
527C2×Dic3C2×#6711yescharacteristic
528D12—21no—
529D12#23512yes—
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—81no—
533C4×D3—81no—
534Dic6—21no—
535Dic6—21no—
536Dic6—62no—
537Dic6—61no—
538Dic6—61no—
539Dic6—61no—
540Dic6—61no—
541Dic6—121no—
542C3×C8—61no—
543C3×C8—61no—
544C3⋊C8—21no—
545C3⋊C8—21no—
546C3⋊C8—62no—
547C3⋊C8—61no—
548C3⋊C8—61no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—121no—
552C2×C32—42no—
553C2×C32#52511yescharacteristic
554C2×C32#57711yescharacteristic
555C2×C32#57711yescharacteristic
556C3×D3—41no—
557C3×D3—42no—
558C24—61no—
559C2×Q8—31no—
560C2×Q8—91no—
561C2×D4—31no—
562C2×D4—61no—
563C2×D4—62no—
564C2×D4—62no—
565C2×D4C2×D3211yescharacteristic
566C22×C4—21no—
567C22×C4—31no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571SD16—62no—
572SD16—182no—
573SD16—182no—
574SD16—182no—
575C2×C8—31no—
576C2×C8—31no—
577C2×C8—91no—
578C2×C8—91no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—61no—
584C4⋊C4—91no—
585C4⋊C4—181no—
586C4⋊C4—181no—
587C4⋊C4—181no—
588C4⋊C4—181no—
589C4⋊C4—181no—
590C4⋊C4—181no—
591C4⋊C4—181no—
592C4⋊C4C2×D3211yescharacteristic
593C22⋊C4—21no—
594C22⋊C4—31no—
595C22⋊C4—31no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—61no—
599C22⋊C4—61no—
600C22⋊C4—181no—
601C22⋊C4—181no—
602C42—31no—
603C42—61no—
604C42—61no—
605C42—181no—
606C42C2×D3211yescharacteristic
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—21no—
610C22×C3—42no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—62no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3—244no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C22×#6711yescharacteristic
626C2×D3—21no—
627C2×D3—22no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—84no—
633C3×C4—22no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—81no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4C2×#23511yescharacteristic
651C3×C4C2×#23511yescharacteristic
652C3×C4C2×#23511yescharacteristic
653C3×C4D3×#4111yescharacteristic
654Dic3—21no—
655Dic3—21no—
656Dic3—21no—
657Dic3—41no—
658Dic3—41no—
659Dic3—41no—
660Dic3—122no—
661Dic3—121no—
662Dic3—121no—
663Dic3—121no—
664Dic3—121no—
665Dic3—241no—
666C32#312311yescharacteristic, complemented, Sylow
667C23—21no—
668C23—31no—
669C23—64no—
670C23—61no—
671C23—241no—
672C23—241no—
673Q8—61no—
674Q8—61no—
675Q8—181no—
676Q8—181no—
677D4—21no—
678D4—32no—
679D4—64no—
680D4—61no—
681D4#379812yes—
682C2×C4—21no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—81no—
692C2×C4—181no—
693C2×C4—181no—
694C2×C4—241no—
695C2×C4—241no—
696C2×C4—241no—
697C2×C4D3×#6711yescharacteristic
698C2×C4D3×#6711yescharacteristic
699C2×C4C22×D3211yescharacteristic
700C8—61no—
701C8—61no—
702C8—181no—
703C8—181no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—42no—
708C2×C3—42no—
709C2×C3—82no—
710C2×C3—121no—
711C2×C3—122no—
712C2×C3#554711yescharacteristic
713C2×C3#577511yescharacteristic
714C2×C3#577811yescharacteristic
715C2×C3#579111yescharacteristic
716C2×C3#583611yescharacteristic
717C2×C3#583611yescharacteristic
718D3—41no—
719D3—42no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—61no—
724C22—61no—
725C22—61no—
726C22—62no—
727C22—121no—
728C22—121no—
729C22—244no—
730C22C2×D3×#6711yescharacteristic
731C4—21no—
732C4—21no—
733C4—41no—
734C4—61no—
735C4—61no—
736C4—61no—
737C4—121no—
738C4—121no—
739C4—121no—
740C4—361no—
741C4—361no—
742C4C2×#379811yescharacteristic
743C4D3×#23511yescharacteristic
744C3—21no—
745C3#7978711yescharacteristic, complemented
746C3#8254511yescharacteristic, complemented
747C2—42no—
748C2—121no—
749C2—122no—
750C2#1059500211yescharacteristic
751C2#1059510611yescharacteristic
752C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC4×D4D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593880C2semidirect
3. C4×#3754C2semidirect
4. C3×#5018C2semidirect
5. #10591489C2semidirect
8. #10591411C2semidirect
9. #10590559C2semidirect
10. #10590542C2semidirect
11. #10590519C2semidirect
12. #10590429C2semidirect
13. #10590360C2semidirect
14. C4×#3715C2semidirect
15. #10590265C2semidirect
21. C4×#634C22semidirect
32. C3×C4×Dic6C22semidirect
34. #63869C22semidirect
36. #63866C22semidirect
44. #63637C22semidirect
45. #63635C22semidirect
46. C4×C3⋊(C3⋊C8)C22semidirect
48. C3×#810C22semidirect
49. C3×#807C22semidirect
50. C3×#803C22semidirect
51. #63575C22semidirect
52. #63574C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63565C22semidirect
74. #5018D3semidirect
194. C4×Dic6C2×D3semidirect
220. #810C2×D3semidirect
228. #807C2×D3semidirect
231. #803C2×D3semidirect
666. C32#3123semidirect
745. C3#79787semidirect
746. C3#82545semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
#105938802
C4×#37542
C3×#50182
#105914892
#105914592
#105914582
#105914112
#105905592
#105905422
#105905192
#105904292
#105903602
C4×#37152
#105902652
#825453
#797873