Finite Group Databasebeta

← #11906145

Subgroups — #11906145

Order 1152.

3225 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic, complemented
2C2×#64315C211yesmaximal, characteristic, complemented
3#10596047C211yesmaximal, characteristic, complemented
4C3×#5576C211yesmaximal, characteristic, complemented
5C3×C4×#239C211yesmaximal, characteristic, complemented
6#10595414C211yesmaximal, characteristic, complemented
7#10595342C211yesmaximal, characteristic, complemented
8#10594630C213yesmaximal, complemented
9#10594629C213yesmaximal, complemented
10#10594628C213yesmaximal, complemented
11#10594380C213yesmaximal, complemented
12#10594005C213yesmaximal, complemented
13#10594003C213yesmaximal, complemented
14D3×#875C213yesmaximal, complemented
15#10593968C213yesmaximal, complemented
16#86715—31nomaximal
17#85847—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic, complemented
20C2×C3×#239C2211yescharacteristic
21C2×C3×#239C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23#64320—28no—
24#64315—28no—
25C2×#3802C2213yes—
26C2×D3×D12C2213yes—
27C2×D3×D12C2213yes—
28C2×#3798C2213yes—
29C2×#3798C2213yescomplemented
30C2×#3796C2213yescomplemented
31C2×#3795C2213yescomplemented
32C2×D3×Dic6C2213yescomplemented
33C32×C4×Q8C2211yescharacteristic, complemented
34#64106C2213yescomplemented
35#64104C2213yescomplemented
36#64084C2213yescomplemented
37C4×C4⋊(C3⋊D3)C2213yescomplemented
38C3×Q8×Dic3C2211yescharacteristic, complemented
39C3×#897C2213yescomplemented
40C3×#895C2213yescomplemented
41C3×#893C2213yescomplemented
42C3×#892C2213yescomplemented
43C3×#875C2213yescomplemented
44C3×C4×D12C2213yescomplemented
45C3×C4×D12C2213yescomplemented
46C3×C42×D3C2213yescomplemented
47#63923C2216yescomplemented
48#63922C2216yescomplemented
49D3×(C2×D3)⋊C4C2216yescomplemented
50D3×(C2×D3)⋊C4C2216yescomplemented
51#63918C2213yescomplemented
52#63916C2213yescomplemented
53#63911C2213yescomplemented
54#63909C2213yescomplemented
55#63909C2213yescomplemented
56#63908C2213yescomplemented
57#63906C2213yescomplemented
58#63906C2213yescomplemented
59C4×#626C2213yescomplemented
60C4×#626C2213yescomplemented
61#63891C2216yescomplemented
62#63890C2216yescomplemented
63#63871C2213yescomplemented
64#63864C2213yescomplemented
65#63860C2213yescomplemented
66#63857C2213yescomplemented
67#63852C2216yescomplemented
68#63852C2211yescharacteristic, complemented
69#63852C2213yescomplemented
70C2×#1010—31no—
71C2×#1009—31no—
72C2×#1009—31no—
73C2×#1007—31no—
74C3×#548—31no—
75C3×C4×#41—31no—
76#5831—31no—
77#5817—31no—
78#5676—33no—
79D3×#124—33no—
80#5630—33no—
81#5628—33no—
82#5612—33no—
83#5607—33no—
84#5576—31no—
85#5576—31no—
86#5576—31no—
87#5576—31no—
88#5576—61no—
89#5576D311yescharacteristic, complemented
90C4×#239D311yescharacteristic, complemented
91#5554—33no—
92#5554—33no—
93#5554—33no—
94#5554—33no—
95#5550—33no—
96#5548—33no—
97#5526—33no—
98#5525—33no—
99#5477—33no—
100C2×#875—33no—
101C22×D32C2316yes—
102C2×C32×Q8C2311yescharacteristic
103#3832—24no—
104Q8×C3⋊D3—24no—
105C2×C4⋊(C3⋊D3)C2313yes—
106C2×C4⋊(C3⋊D3)C2313yes—
107C2×C4×C3⋊D3C2313yes—
108C2×C4×C3⋊D3C2313yes—
109C2×#634C2313yes—
110C3×#239—24no—
111C3×#239D418yescomplemented
112C3×D3×Q8—24no—
113C2×C3×D12C2313yes—
114C2×C3×D12C2313yes—
115C2×C3×D12C2313yes—
116C2×C3×C4×D3C2313yes—
117C2×C3×C4×D3C2313yes—
118C2×C3×C4×D3C2313yes—
119C2×C3×C4×D3C2313yes—
120C2×C3×C4×D3C2313yes—
121C2×C3×Dic6C2313yes—
122C2×#627C2313yes—
123C2×#627C2311yescharacteristic
124C2×#626C2313yes—
125C2×#626C2313yes—
126C2×#626C2313yes—
127C2×#626C2311yescharacteristic
128C2×#626C2313yes—
129C2×#626C2313yes—
130C2×#625C2313yes—
131C2×#625C2313yes—
132C2×D3×Dic3C2316yes—
133#3802—212no—
134D3×D12—212no—
135D3×D12—212no—
136#3798—212no—
137#3798—212no—
138#3796—212no—
139#3795—212no—
140D3×Dic6—212no—
141C32×C4⋊C4C2313yes—
142C32×C42C2313yes—
143#3752C2311yescharacteristic
144#3752C2313yes—
145#3752C2316yes—
146C4⋊(C3⋊Dic3)C2313yes—
147C3×(C2×D3)⋊C4C2316yes—
148C3×(C2×D3)⋊C4C2316yes—
149C3×(C2×D3)⋊C4C2311yescharacteristic
150C3×(C2×D3)⋊C4C2313yes—
151C3×C4⋊Dic3C2313yes—
152C3×C4⋊Dic3C2313yes—
153C3×C4×Dic3C2313yes—
154C3×C4×Dic3C2313yes—
155C3×C4×Dic3C2311yescharacteristic
156Dic3⋊Dic3C2313yes—
157Dic3⋊Dic3C2313yes—
158#3722C2313yes—
159#3722C2316yes—
160#3722C2311yescharacteristic
161(C2×D3)⋊Dic3C2316yes—
162(C2×D3)⋊Dic3C2313yes—
163(C2×D3)⋊Dic3C2311yescharacteristic
164#3500—91noSylow
165C2×C3×#41—31no—
166C2×C3×#41—31no—
167C22×C3×Q8—31no—
168#1010—68no—
169#1009—68no—
170#1009—68no—
171#1007—68no—
172C2×#239—31no—
173C2×#239—31no—
174C2×#239—33no—
175C2×#239—61no—
176C2×#239C2×D311yescharacteristic
177C2×#239C2×D311yescharacteristic
178C2×D3×Q8—31no—
179C2×D3×Q8—31no—
180C2×D3×Q8—33no—
181C2×D3×Q8—61no—
182C2×D3×Q8C2×D311yescharacteristic, complemented
183C2×#237—33no—
184C2×#237—33no—
185C2×D3×D4—33no—
186C2×D3×D4—33no—
187C2×D3×D4—33no—
188C2×D3×D4—33no—
189C2×#235—33no—
190C2×#235—33no—
191C2×#235—33no—
192C2×#235—33no—
193C2×#235—33no—
194C22×D12—33no—
195C22×D12—33no—
196C22×Dic6—33no—
197C3×#124—33no—
198C3×C22⋊Q8—33no—
199C3×#121—33no—
200C3×C4×Q8—21no—
201C3×C4×Q8—31no—
202C3×C4×Q8C2×D311yescharacteristic, complemented
203C3×C4×Q8C2×D311yescharacteristic, complemented
204C3×C4×D4—33no—
205C3×C4×D4—33no—
206C3×C4×D4—33no—
207C3×#117—33no—
208C2×C3×C42—33no—
209#947—33no—
210#946—33no—
211Q8×Dic3C2×D311yescharacteristic, complemented
212#940—33no—
213#938—33no—
214#938—33no—
215#937—36no—
216#936—33no—
217#930—33no—
218#930—33no—
219#930—33no—
220#930—33no—
221#930—33no—
222C4×#67—33no—
223C4×#67—33no—
224C2×(C2×D3)⋊C4—36no—
225C2×(C2×D3)⋊C4—36no—
226#924—33no—
227#897—33no—
228#897—33no—
229#897—33no—
230#897—33no—
231#897—63no—
232#897C2×D313yescomplemented
233#895—33no—
234#895—33no—
235#895—33no—
236#895—33no—
237#895—33no—
238#895—63no—
239#895C2×D313yescomplemented
240#894—36no—
241#893C2×D313yescomplemented
242#892C2×D313yescomplemented
243#888—33no—
244#886—36no—
245#886—36no—
246#885—33no—
247#885—36no—
248#885—31no—
249#884—33no—
250#884—33no—
251#883—36no—
252#882—36no—
253#882—36no—
254#882—36no—
255D3×C22⋊C4—36no—
256D3×C22⋊C4—36no—
257#875—33no—
258#875—33no—
259#875—33no—
260#875—33no—
261#875—33no—
262#875—36no—
263#875—31no—
264#875—63no—
265#875C2×D313yescomplemented
266#874—33no—
267C4×D12—33no—
268C4×D12—33no—
269C4×D12—33no—
270C4×D12—33no—
271C4×D12—63no—
272C4×D12C2×D313yescomplemented
273C4×D12C2×D313yescomplemented
274C42×D3C2×D313yescomplemented
275#869—33no—
276C22×C3⋊D3C2413yes—
277C22×C3⋊D3C2411yescharacteristic
278C22×C3×D3C2413yes—
279C22×C3×D3C2411yescharacteristic
280C22×C3×D3C2413yes—
281C2×D32—212no—
282C2×D32—46no—
283C2×D32—46no—
284C32×Q8C2×D414yes—
285C2×C32×C4C2413yes—
286C2×C32×C4C2411yescharacteristic
287C2×C32×C4C2413yes—
288C2×C3⋊Dic3C2413yes—
289C2×C3⋊Dic3C2411yescharacteristic
290C4⋊(C3⋊D3)—26no—
291C4⋊(C3⋊D3)—43no—
292C4×C3⋊D3—26no—
293C4×C3⋊D3—26no—
294#634—26no—
295C2×C3×Dic3C2411yescharacteristic
296C2×C3×Dic3C2413yes—
297C2×C3×Dic3C2413yes—
298C2×C3×Dic3C2411yescharacteristic
299C2×C3×Dic3C2411yescharacteristic
300C3×D12—26no—
301C3×D12—43no—
302C3×D12C2×D4112yes—
303C3×C4×D3—26no—
304C3×C4×D3—26no—
305C3×C4×D3—43no—
306C3×C4×D3—43no—
307C3×C4×D3C2×D4112yes—
308C3×Dic6—26no—
309#627—26no—
310#627—22no—
311#626—26no—
312#626—26no—
313#626—22no—
314#626—26no—
315#626—43no—
316#626—43no—
317#625—26no—
318#625—26no—
319D3×Dic3—212no—
320C2×2−1+4—91no—
321C2×H(5,𝔽2)—91no—
322#548—31no—
323#548—91no—
324#548—91no—
325#548—91no—
326#546—93no—
327#546—93no—
328#546—93no—
329#546—93no—
330#536—93no—
331#535—93no—
332#532—93no—
333C2×#124—93no—
334C4×#41—31no—
335C23×D3—36no—
336C23×D3—36no—
337C3×#41—38no—
338C3×#41—64no—
339C2×C3×Q8—21no—
340C2×C3×Q8—33no—
341C2×C3×Q8—64no—
342C2×C3×Q8C22×D311yescharacteristic
343C2×C3×Q8C22×D311yescharacteristic
344C2×C3×D4—33no—
345C2×C3×D4—33no—
346C2×C3×D4—33no—
347C22×C3×C4—33no—
348C22×C3×C4—33no—
349C22×C3×C4—33no—
350C22×C3×C4—33no—
351C22×C3×C4—33no—
352C2×#67—33no—
353C2×#67—33no—
354C2×#67—33no—
355C2×#67—33no—
356C2×#67—33no—
357C2×#67—33no—
358C2×#67—31no—
359C2×#67—33no—
360C2×#67—33no—
361C2×#67—33no—
362C22×Dic3—36no—
363#239—24no—
364#239—64no—
365#239—64no—
366#239—612no—
367#239—124no—
368#239D1218yescomplemented
369D3×Q8—24no—
370D3×Q8—64no—
371D3×Q8—64no—
372D3×Q8—612no—
373D3×Q8—124no—
374#237—612no—
375#237—612no—
376D3×D4—612no—
377D3×D4—612no—
378D3×D4—612no—
379D3×D4—612no—
380#235—612no—
381#235—612no—
382#235—612no—
383#235—612no—
384#235—612no—
385C2×D12—31no—
386C2×D12—33no—
387C2×D12—33no—
388C2×D12—33no—
389C2×D12—33no—
390C2×D12—33no—
391C2×D12—33no—
392C2×D12—33no—
393C2×D12—33no—
394C2×D12—33no—
395C2×D12—63no—
396C2×D12—63no—
397C2×D12—612no—
398C2×D12—612no—
399C2×D12C22×D313yes—
400C2×D12C22×D313yes—
401C2×D12C22×D313yes—
402C2×C4×D3—36no—
403C2×C4×D3—33no—
404C2×C4×D3—33no—
405C2×C4×D3—33no—
406C2×C4×D3—33no—
407C2×C4×D3—63no—
408C2×C4×D3—63no—
409C2×C4×D3C22×D313yes—
410C2×C4×D3C22×D313yes—
411C2×C4×D3C22×D313yes—
412C2×C4×D3C22×D313yes—
413C2×C4×D3C22×D313yes—
414C2×Dic6—33no—
415C2×Dic6—33no—
416C2×Dic6—31no—
417C2×Dic6—33no—
418C2×Dic6—33no—
419C2×Dic6—31no—
420C2×Dic6—63no—
421C2×Dic6—612no—
422C2×Dic6C22×D313yes—
423C3×C4⋊C4—23no—
424C3×C4⋊C4—33no—
425C3×C4⋊C4—33no—
426C3×C4⋊C4C22×D313yes—
427C3×C4⋊C4C22×D313yes—
428C3×C22⋊C4—33no—
429C3×C22⋊C4—36no—
430C3×C22⋊C4—36no—
431C3×C22⋊C4—31no—
432C3×C42—23no—
433C3×C42—33no—
434C3×C42—33no—
435C3×C42—31no—
436C3×C42C22×D313yes—
437C3×C42C22×D313yes—
438#217—33no—
439#217—36no—
440#217—31no—
441(C2×D3)⋊C4—31no—
442(C2×D3)⋊C4—33no—
443(C2×D3)⋊C4—36no—
444(C2×D3)⋊C4—31no—
445(C2×D3)⋊C4—31no—
446(C2×D3)⋊C4—33no—
447(C2×D3)⋊C4—33no—
448(C2×D3)⋊C4—36no—
449(C2×D3)⋊C4—36no—
450(C2×D3)⋊C4—31no—
451(C2×D3)⋊C4—33no—
452(C2×D3)⋊C4—36no—
453(C2×D3)⋊C4—33no—
454(C2×D3)⋊C4—36no—
455(C2×D3)⋊C4—31no—
456(C2×D3)⋊C4—61no—
457(C2×D3)⋊C4—63no—
458(C2×D3)⋊C4—66no—
459(C2×D3)⋊C4C22×D311yescharacteristic
460(C2×D3)⋊C4C22×D313yes—
461(C2×D3)⋊C4C22×D316yes—
462(C2×D3)⋊C4C22×D316yes—
463C4⋊Dic3—33no—
464C4⋊Dic3—33no—
465C4⋊Dic3—33no—
466C4⋊Dic3—33no—
467C4⋊Dic3—63no—
468C4⋊Dic3C22×D313yes—
469C4⋊Dic3C22×D313yes—
470Dic3⋊C4—33no—
471Dic3⋊C4—33no—
472C4×Dic3C22×D311yescharacteristic
473C4×Dic3C22×D313yes—
474C4×Dic3C22×D313yes—
475C22×C32C2511yescharacteristic
476C2×C3⋊D3—21no—
477C2×C3⋊D3—21no—
478C2×C3⋊D3—23no—
479C2×C3⋊D3—21no—
480C2×C3⋊D3—23no—
481C2×C3⋊D3—23no—
482C2×C3×D3—23no—
483C2×C3×D3—23no—
484C2×C3×D3—21no—
485C2×C3×D3—23no—
486C2×C3×D3—21no—
487C2×C3×D3—23no—
488C2×C3×D3—21no—
489C2×C3×D3—23no—
490C2×C3×D3C22×D416yes—
491D32—812no—
492C32×C4—21no—
493C32×C4—23no—
494C32×C4C22×D416yes—
495C3⋊Dic3—23no—
496C3⋊Dic3—21no—
497C3×Dic3—23no—
498C3×Dic3—21no—
499C3×Dic3—23no—
500C3×Dic3—21no—
501C3×Dic3C22×D412yes—
5022−1+4—188no—
503H(5,𝔽2)—188no—
504C2×#41—31no—
505C2×#41—31no—
506C2×#41—93no—
507C2×#41—93no—
508C2×#41—93no—
509C2×#41—93no—
510C2×#41—91no—
511C22×Q8—31no—
512C22×Q8—93no—
513C22×Q8—91no—
514C22×D4—93no—
515C22×D4—93no—
516C22×D4—93no—
517C4⋊Q8—93no—
518#127—93no—
519#124—33no—
520#124—93no—
521#124—96no—
522#124—91no—
523#124—93no—
524#124—93no—
525#124—93no—
526#123—96no—
527#123—96no—
528C22⋊Q8—33no—
529C22⋊Q8—93no—
530C22⋊Q8—93no—
531C22⋊Q8—93no—
532#121—33no—
533#121—93no—
534#121—93no—
535#121—93no—
536#121—93no—
537#121—93no—
538#121—93no—
539#121—93no—
540#120—96no—
541#120—96no—
542C4×Q8—31no—
543C4×Q8D3211yescharacteristic, complemented
544C4×D4—33no—
545C4×D4—33no—
546C4×D4—33no—
547C4×D4—93no—
548C4×D4—93no—
549C4×D4—93no—
550#117—33no—
551C2×C22⋊C4—96no—
552C2×C22⋊C4—96no—
553C2×C42—33no—
554C23×C3—33no—
555C23×C3—33no—
556C23×C3—31no—
557C22×D3—33no—
558C22×D3—33no—
559C22×D3—31no—
560C22×D3—31no—
561C22×D3—61no—
562C22×D3—63no—
563C22×D3—612no—
564C22×D3—612no—
565C22×D3—126no—
566C22×D3—126no—
567C22×D3—126no—
568C22×D3—126no—
569C22×D3C23×D313yes—
570C22×D3C23×D311yescharacteristic
571C22×D3C23×D313yes—
572C3×Q8—24no—
573C3×Q8—66no—
574C3×Q8C2×D1214yes—
575C3×Q8D3×D414yes—
576C3×D4—312no—
577C3×D4—66no—
578C3×D4—123no—
579C2×C3×C4—23no—
580C2×C3×C4—23no—
581C2×C3×C4—21no—
582C2×C3×C4—31no—
583C2×C3×C4—312no—
584C2×C3×C4—31no—
585C2×C3×C4—33no—
586C2×C3×C4—33no—
587C2×C3×C4—31no—
588C2×C3×C4—66no—
589C2×C3×C4—66no—
590C2×C3×C4—123no—
591C2×C3×C4—123no—
592C2×C3×C4C23×D313yes—
593C2×C3×C4C23×D311yescharacteristic
594C2×C3×C4C23×D313yes—
595C2×C3×C4C23×D311yescharacteristic
596C2×C3×C4C23×D313yes—
597C2×C3×C4C23×D313yes—
598#67—66no—
599#67—66no—
600#67—66no—
601#67—66no—
602#67—66no—
603#67—66no—
604#67—62no—
605#67—66no—
606#67—123no—
607#67—123no—
608C2×Dic3—31no—
609C2×Dic3—33no—
610C2×Dic3—31no—
611C2×Dic3—33no—
612C2×Dic3—61no—
613C2×Dic3—63no—
614C2×Dic3—612no—
615C2×Dic3C23×D311yescharacteristic
616C2×Dic3C23×D313yes—
617C2×Dic3C23×D311yescharacteristic
618C2×Dic3C23×D313yes—
619C2×Dic3C23×D311yescharacteristic
620D12—26no—
621D12—43no—
622D12—66no—
623D12—62no—
624D12—66no—
625D12—66no—
626D12—66no—
627D12—66no—
628D12—126no—
629D12—123no—
630D12—123no—
631D12—126no—
632D12—123no—
633D12—123no—
634D12C2×D12112yes—
635C4×D3—26no—
636C4×D3—26no—
637C4×D3—43no—
638C4×D3—43no—
639C4×D3—612no—
640C4×D3—66no—
641C4×D3—66no—
642C4×D3—66no—
643C4×D3—66no—
644C4×D3—126no—
645C4×D3—126no—
646C4×D3C2×D12112yes—
647Dic6—26no—
648Dic6—66no—
649Dic6—62no—
650Dic6—66no—
651Dic6—66no—
652Dic6—62no—
653Dic6—66no—
654Dic6—126no—
655C2×C32C23×D411yescharacteristic
656C2×C32#58511yescharacteristic
657C2×C32#58511yescharacteristic
658C3⋊D3—41no—
659C3⋊D3—43no—
660C3×D3—26no—
661C3×D3—43no—
662C3×D3—41no—
663C24—96no—
664#41—38no—
665#41—64no—
666#41—1812no—
667#41—1812no—
668#41—1812no—
669#41—1812no—
670#41—184no—
671C2×Q8—33no—
672C2×Q8—64no—
673C2×Q8—93no—
674C2×Q8—91no—
675C2×Q8—93no—
676C2×Q8—1812no—
677C2×Q8—184no—
678C2×Q8C2×D3211yescharacteristic
679C2×D4—33no—
680C2×D4—33no—
681C2×D4—33no—
682C2×D4—93no—
683C2×D4—93no—
684C2×D4—93no—
685C2×D4—91no—
686C2×D4—93no—
687C2×D4—93no—
688C2×D4—93no—
689C2×D4—93no—
690C2×D4—93no—
691C2×D4—93no—
692C2×D4—1812no—
693C2×D4—1812no—
694C2×D4—1812no—
695C22×C4—33no—
696C22×C4—33no—
697C22×C4—33no—
698C22×C4—33no—
699C22×C4—33no—
700C22×C4—96no—
701C22×C4—93no—
702C22×C4—93no—
703C4⋊C4—33no—
704C4⋊C4—33no—
705C4⋊C4—93no—
706C4⋊C4—93no—
707C4⋊C4—93no—
708C4⋊C4C2×D3213yes—
709C22⋊C4—33no—
710C22⋊C4—36no—
711C22⋊C4—36no—
712C22⋊C4—31no—
713C22⋊C4—93no—
714C22⋊C4—96no—
715C22⋊C4—91no—
716C22⋊C4—93no—
717C22⋊C4—96no—
718C22⋊C4—91no—
719C22⋊C4—93no—
720C22⋊C4—96no—
721C22⋊C4—91no—
722C42—31no—
723C42—33no—
724C42—33no—
725C42C2×D3213yes—
726C22×C3—21no—
727C22×C3—36no—
728C22×C3—63no—
729C22×C3—63no—
730C22×C3—61no—
731C22×C3—63no—
732C22×C3—61no—
733C22×C3—63no—
734C22×C3—61no—
735C22×C3—63no—
736C22×C3C24×D311yescharacteristic
737C22×C3C24×D311yescharacteristic
738C2×D3—23no—
739C2×D3—23no—
740C2×D3—21no—
741C2×D3—23no—
742C2×D3—21no—
743C2×D3—23no—
744C2×D3—21no—
745C2×D3—23no—
746C2×D3—62no—
747C2×D3—61no—
748C2×D3—63no—
749C2×D3—61no—
750C2×D3—63no—
751C2×D3—61no—
752C2×D3—61no—
753C2×D3—63no—
754C2×D3—63no—
755C2×D3—61no—
756C2×D3—63no—
757C2×D3—61no—
758C2×D3—63no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—123no—
762C2×D3—123no—
763C2×D3—123no—
764C2×D3—2412no—
765C2×D3—2412no—
766C2×D3C22×D1216yes—
767C3×C4—21no—
768C3×C4—23no—
769C3×C4—23no—
770C3×C4—21no—
771C3×C4—26no—
772C3×C4—32no—
773C3×C4—43no—
774C3×C4—41no—
775C3×C4—63no—
776C3×C4—61no—
777C3×C4—61no—
778C3×C4—63no—
779C3×C4C22×D1216yes—
780C3×C4C2×D3×D416yes—
781Dic3—23no—
782Dic3—21no—
783Dic3—21no—
784Dic3—23no—
785Dic3—63no—
786Dic3—61no—
787Dic3—63no—
788Dic3—61no—
789Dic3—123no—
790Dic3—121no—
791Dic3C22×D1212yes—
792C32#350011yescharacteristic, complemented, Sylow
793C23—33no—
794C23—33no—
795C23—31no—
796C23—93no—
797C23—91no—
798C23—1812no—
799C23—366no—
800C23—366no—
801Q8—66no—
802Q8—186no—
803Q8—182no—
804Q8—186no—
805Q8D3×D1214yes—
806D4—312no—
807D4—66no—
808D4—123no—
809D4—186no—
810D4—182no—
811D4—186no—
812D4—186no—
813D4—186no—
814D4—186no—
815D4—186no—
816D4—363no—
817D4—363no—
818D4—363no—
819C2×C4—31no—
820C2×C4—312no—
821C2×C4—31no—
822C2×C4—33no—
823C2×C4—33no—
824C2×C4—31no—
825C2×C4—66no—
826C2×C4—66no—
827C2×C4—93no—
828C2×C4—91no—
829C2×C4—123no—
830C2×C4—123no—
831C2×C4—1812no—
832C2×C4—186no—
833C2×C4—186no—
834C2×C4C22×D3211yescharacteristic
835C2×C4C22×D3213yes—
836C2×C4C22×D3213yes—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—66no—
841C2×C3—123no—
842C2×C3—121no—
843C2×C3C23×D1211yescharacteristic
844C2×C3C22×D3×D411yescharacteristic
845C2×C3#596411yescharacteristic
846C2×C3#596411yescharacteristic
847C2×C3#596411yescharacteristic
848C2×C3#596811yescharacteristic
849D3—26no—
850D3—43no—
851D3—41no—
852D3—122no—
853D3—123no—
854D3—121no—
855D3—123no—
856D3—121no—
857D3—243no—
858C22—36no—
859C22—63no—
860C22—63no—
861C22—61no—
862C22—63no—
863C22—61no—
864C22—63no—
865C22—61no—
866C22—63no—
867C22—181no—
868C22—183no—
869C22—181no—
870C22—183no—
871C22—181no—
872C22—183no—
873C22—7212no—
874C22C23×D3211yescharacteristic
875C4—21no—
876C4—23no—
877C4—32no—
878C4—61no—
879C4—63no—
880C4—63no—
881C4—61no—
882C4—181no—
883C4—183no—
884C4C2×D3×D1216yes—
885C3—21no—
886C3#8584711yescharacteristic, complemented
887C3#8671511yescharacteristic, complemented
888C2—66no—
889C2—123no—
890C2—121no—
891C2—363no—
892C2—361no—
893C2C22×D3×D1211yescharacteristic
894C2#1059668811yescharacteristic
895C2#1059669511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3500
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64320C2semidirect
2. C2×#64315C2semidirect
3. #10596047C2semidirect
4. C3×#5576C2semidirect
5. C3×C4×#239C2semidirect
6. #10595414C2semidirect
7. #10595342C2semidirect
8. #10594630C2semidirect
9. #10594629C2semidirect
10. #10594628C2semidirect
11. #10594380C2semidirect
12. #10594005C2semidirect
13. #10594003C2semidirect
14. D3×#875C2semidirect
15. #10593968C2semidirect
19. C2×Q8×C3⋊D3C22semidirect
22. C2×C3×D3×Q8C22semidirect
29. C2×#3798C22semidirect
30. C2×#3796C22semidirect
31. C2×#3795C22semidirect
32. C2×D3×Dic6C22semidirect
33. C32×C4×Q8C22semidirect
34. #64106C22semidirect
35. #64104C22semidirect
36. #64084C22semidirect
37. C4×C4⋊(C3⋊D3)C22semidirect
38. C3×Q8×Dic3C22semidirect
39. C3×#897C22semidirect
40. C3×#895C22semidirect
41. C3×#893C22semidirect
42. C3×#892C22semidirect
43. C3×#875C22semidirect
44. C3×C4×D12C22semidirect
45. C3×C4×D12C22semidirect
46. C3×C42×D3C22semidirect
47. #63923C22semidirect
48. #63922C22semidirect
49. D3×(C2×D3)⋊C4C22semidirect
50. D3×(C2×D3)⋊C4C22semidirect
51. #63918C22semidirect
52. #63916C22semidirect
53. #63911C22semidirect
54. #63909C22semidirect
55. #63909C22semidirect
56. #63908C22semidirect
57. #63906C22semidirect
58. #63906C22semidirect
59. C4×#626C22semidirect
60. C4×#626C22semidirect
61. #63891C22semidirect
62. #63890C22semidirect
63. #63871C22semidirect
64. #63864C22semidirect
65. #63860C22semidirect
66. #63857C22semidirect
67. #63852C22semidirect
68. #63852C22semidirect
69. #63852C22semidirect
89. #5576D3semidirect
90. C4×#239D3semidirect
111. C3×#239D4semidirect
182. C2×D3×Q8C2×D3semidirect
202. C3×C4×Q8C2×D3semidirect
203. C3×C4×Q8C2×D3semidirect
211. Q8×Dic3C2×D3semidirect
232. #897C2×D3semidirect
239. #895C2×D3semidirect
241. #893C2×D3semidirect
242. #892C2×D3semidirect
265. #875C2×D3semidirect
272. C4×D12C2×D3semidirect
273. C4×D12C2×D3semidirect
274. C42×D3C2×D3semidirect
368. #239D12semidirect
543. C4×Q8D32semidirect
792. C32#3500semidirect
886. C3#85847semidirect
887. C3#86715semidirect

Maximal subgroups

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

subgroupindex
C2×#643202
C2×#643152
#105960472
C3×#55762
C3×C4×#2392
#105954142
#105953422
#105946302
#105946292
#105946282
#105943802
#105940052
#105940032
D3×#8752
#105939682
#867153
#858473