Finite Group Databasebeta

← #11904815

Subgroups — #11904815

Order 1152.

3441 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64364C211yesmaximal, characteristic, complemented
2C2×D3×#239C211yesmaximal, characteristic, complemented
3C3×#5817C211yesmaximal, characteristic, complemented
4C3×Q8×#67C211yesmaximal, characteristic, complemented
5#10595431C213yesmaximal, complemented
6#10595429C213yesmaximal, complemented
7#10595414C211yesmaximal, characteristic, complemented
8Q8×#626C211yesmaximal, characteristic, complemented
9#10595364C213yesmaximal, complemented
10#10595353C211yesmaximal, characteristic, complemented
11#10595341C213yesmaximal, complemented
12#10595078C213yesmaximal, complemented
13#10595076C213yesmaximal, complemented
14#10594923C213yesmaximal, complemented
15#10594834C213yesmaximal, complemented
16#86745—31nomaximal
17#86714—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19#64364—28no—
20C2×#3832C2211yescharacteristic
21C2×#3832C2213yescomplemented
22C2×Q8×C3⋊D3C2213yescomplemented
23C2×Q8×C3⋊D3C2211yescharacteristic, complemented
24C2×#3828C2213yescomplemented
25C2×#3828C2213yescomplemented
26C2×C3×#239C2211yescharacteristic
27C2×C3×D3×Q8C2211yescharacteristic
28D3×#239—28no—
29C2×D3×D12C2213yes—
30C2×C4×D32C2213yes—
31C2×#3799C2213yes—
32C2×#3796C2213yes—
33C3×#947C2213yescomplemented
34C3×#946C2213yes—
35C3×#946C2213yescomplemented
36C3×Q8×Dic3C2211yescharacteristic, complemented
37C3×Q8×Dic3C2211yescharacteristic, complemented
38C3×#944C2213yescomplemented
39C3×#930C2213yescomplemented
40C3×C4×#67C2213yes—
41C3×C4×#67C2213yescomplemented
42C3×#924C2213yescomplemented
43#63983C2213yes—
44#63975C2213yescomplemented
45#63971C2211yescharacteristic
46#63971C2213yescomplemented
47#63958C2216yescomplemented
48#63923C2213yes—
49#63921C2216yes—
50#63916C2213yescomplemented
51#63910C2216yescomplemented
52C4×#626C2213yes—
53C4×#626C2213yescomplemented
54#63900C2213yescomplemented
55#63897C2213yescomplemented
56#63896C2213yes—
57#63896C2213yescomplemented
58#63896C2216yescomplemented
59#63894C2213yescomplemented
60#63894C2213yescomplemented
61#63883C2216yescomplemented
62#63874C2213yescomplemented
63#63871C2213yescomplemented
64#63866C2213yescomplemented
65#63860C2213yescomplemented
66#63857C2213yes—
67#63857C2213yescomplemented
68#63853C2216yescomplemented
69#63853C2216yescomplemented
70C2×D3×#41—31no—
71C2×#1007—31no—
72C2×#1007—31no—
73C2×#1007—61no—
74C22×#239—31no—
75C3×D4×Q8—31no—
76C3×#548—31no—
77#5831—31no—
78#5817D311yescharacteristic, complemented
79Q8×#67—31no—
80Q8×#67D311yescharacteristic, complemented
81#5726—33no—
82#5724—33no—
83#5676—33no—
84#5675—33no—
85#5631—33no—
86#5631—33no—
87#5630—33no—
88#5629—33no—
89D3×C22⋊Q8—33no—
90D3×C22⋊Q8—33no—
91#5612—33no—
92#5608—33no—
93#5576—31no—
94Q8×D12—31no—
95#5574—31no—
96#5574—31no—
97#5551—33no—
98#5550—33no—
99#5547—33no—
100#5547—33no—
101C22×D32C2313yes—
102C2×C32×Q8—24no—
103C2×C32×Q8C2313yes—
104C2×C32×Q8C2311yescharacteristic
105C22×C32×C4C2313yes—
106C2×#638C2313yes—
107C2×#638C2311yescharacteristic
108#3832—212no—
109#3832D418yescomplemented
110Q8×C3⋊D3—24no—
111Q8×C3⋊D3—212no—
112#3828—212no—
113#3828—212no—
114C2×C4⋊(C3⋊D3)C2313yes—
115C2×C4⋊(C3⋊D3)C2313yes—
116C2×C4×C3⋊D3C2316yes—
117C2×C4×C3⋊D3C2313yes—
118C2×C4×C3⋊D3C2313yes—
119C2×#634C2313yes—
120C2×#634C2313yes—
121C2×C3×#67C2311yescharacteristic
122C2×C3×#67C2313yes—
123C3×#239—24no—
124C3×D3×Q8—24no—
125C2×C3×D12C2313yes—
126C2×C3×C4×D3C2313yes—
127C2×C3×C4×D3C2313yes—
128C2×C3×Dic6C2313yes—
129C2×#626C2316yes—
130C2×#626C2311yescharacteristic
131C2×#626C2313yes—
132C2×#624C2313yes—
133C2×#624C2316yes—
134C2×D3×Dic3C2313yes—
135C2×D3×Dic3C2311yescharacteristic
136D3×D12—212no—
137C4×D32—212no—
138#3799—212no—
139#3796—212no—
140C3×#217C2313yes—
141C3×#217C2311yescharacteristic
142C3×(C2×D3)⋊C4C2313yes—
143C3×(C2×D3)⋊C4C2313yes—
144C3×(C2×D3)⋊C4C2316yes—
145C3×C4⋊Dic3C2313yes—
146C3×C4⋊Dic3C2313yes—
147C3×Dic3⋊C4C2316yes—
148C3×Dic3⋊C4C2313yes—
149C3×Dic3⋊C4C2313yes—
150C3×C4×Dic3C2313yes—
151C3×C4×Dic3C2313yes—
152#3724C2311yescharacteristic
153#3724C2313yes—
154Dic3⋊Dic3C2313yes—
155Dic3⋊Dic3C2316yes—
156Dic3⋊Dic3C2313yes—
157#3722C2313yes—
158#3722C2313yes—
159#3722C2313yes—
160#3722C2311yescharacteristic
161(C2×D3)⋊Dic3C2313yes—
162(C2×D3)⋊Dic3C2316yes—
163(C2×D3)⋊Dic3C2313yes—
164#3489—91noSylow
165C2×C3×#41—31no—
166C22×C3×Q8—21no—
167C22×C3×Q8—31no—
168C22×C3×Q8C2×D311yescharacteristic, complemented
169C22×C3×Q8C2×D311yescharacteristic, complemented
170D3×#41—68no—
171#1007—68no—
172#1007—68no—
173#1007—616no—
174C2×#239—31no—
175C2×#239—31no—
176C2×#239—33no—
177C2×#239—33no—
178C2×#239—33no—
179C2×#239—33no—
180C2×#239—61no—
181C2×#239—63no—
182C2×#239—68no—
183C2×#239C2×D311yescharacteristic
184C2×D3×Q8—33no—
185C2×D3×Q8—33no—
186C2×D3×Q8—31no—
187C2×D3×Q8—31no—
188C2×D3×Q8—63no—
189C2×D3×Q8—61no—
190C2×D3×Q8C2×D311yescharacteristic
191C2×#237—33no—
192C2×D3×D4—33no—
193C2×#235—33no—
194C2×#235—33no—
195C2×#235—33no—
196C2×#235—33no—
197C2×#235—33no—
198C2×#235—63no—
199C2×#235—63no—
200C22×D12—33no—
201C22×C4×D3—33no—
202C22×C4×D3—33no—
203C3×C4⋊Q8—33no—
204C3×#124—33no—
205C3×C22⋊Q8—33no—
206C3×C22⋊Q8—33no—
207C3×C22⋊Q8—33no—
208C3×#121—33no—
209C3×C4×Q8—31no—
210C3×C4×Q8—31no—
211C3×C4×D4—33no—
212C3×C4×D4—33no—
213#947C2×D313yescomplemented
214#946—33no—
215#946C2×D313yes—
216#946C2×D313yescomplemented
217Q8×Dic3C2×D311yescharacteristic, complemented
218Q8×Dic3C2×D311yescharacteristic, complemented
219#944—33no—
220#944C2×D313yescomplemented
221#939—31no—
222#939—33no—
223#938—36no—
224#938—33no—
225#937—33no—
226#937—33no—
227#936—33no—
228#930C2×D313yescomplemented
229C4×#67—33no—
230C4×#67—33no—
231C4×#67C2×D313yes—
232C4×#67C2×D313yescomplemented
233#924—33no—
234#924—33no—
235#924C2×D313yescomplemented
236#897—33no—
237#897—33no—
238#897—33no—
239#896—33no—
240#896—36no—
241#896—33no—
242#895—33no—
243#895—36no—
244#894—36no—
245#894—36no—
246#894—33no—
247#894—33no—
248#893—33no—
249#893—33no—
250D3×C4⋊C4—33no—
251D3×C4⋊C4—33no—
252D3×C4⋊C4—36no—
253D3×C4⋊C4—36no—
254#884—31no—
255#884—33no—
256#884—36no—
257#884—36no—
258#883—33no—
259#883—33no—
260#883—36no—
261#883—36no—
262#882—33no—
263#882—33no—
264D3×C22⋊C4—36no—
265D3×C22⋊C4—36no—
266#878—33no—
267#878—36no—
268#878—33no—
269#875—33no—
270C4×D12—33no—
271C4×D12—33no—
272C4×D12—33no—
273C4×D12—33no—
274#872—33no—
275#872—33no—
276#869—33no—
277C23×C32C2411yescharacteristic
278C22×C3⋊D3C2411yescharacteristic
279C22×C3⋊D3C2413yes—
280C22×C3×D3C2413yes—
281C22×C3×D3C2411yescharacteristic
282C2×D32—26no—
283C2×D32—26no—
284C2×D32—43no—
285C32×Q8—26no—
286C32×Q8C2×D414yes—
287C2×C32×C4—26no—
288C2×C32×C4C2413yes—
289C2×C32×C4C2413yes—
290#638—26no—
291#638—22no—
292C2×C3⋊Dic3C2413yes—
293C2×C3⋊Dic3C2411yescharacteristic
294C4⋊(C3⋊D3)—26no—
295C4⋊(C3⋊D3)C2×D4112yes—
296C4×C3⋊D3—212no—
297C4×C3⋊D3—26no—
298C4×C3⋊D3C2×D4112yes—
299#634—26no—
300#634—26no—
301C3×#67—22no—
302C3×#67—43no—
303C2×C3×Dic3C2411yescharacteristic
304C2×C3×Dic3C2413yes—
305C2×C3×Dic3C2413yes—
306C2×C3×Dic3C2411yescharacteristic
307C2×C3×Dic3C2411yescharacteristic
308C2×C3×Dic3C2413yes—
309C3×D12—26no—
310C3×C4×D3—26no—
311C3×C4×D3—26no—
312C3×Dic6—26no—
313#626—212no—
314#626—22no—
315#626—43no—
316#624—26no—
317#624—46no—
318D3×Dic3—26no—
319D3×Dic3—22no—
320C2×2−1+4—91no—
321C22×#41—91no—
322D4×Q8—31no—
323D4×Q8—91no—
324#548—31no—
325#548—91no—
326#547—93no—
327#547—93no—
328#546—93no—
329#546—93no—
330#537—93no—
331#536—93no—
332#525—93no—
333C2×C22⋊Q8—93no—
334#520—91no—
335C23×D3—33no—
336C23×D3—33no—
337C3×#41—64no—
338C2×C3×Q8—28no—
339C2×C3×Q8—24no—
340C2×C3×Q8—24no—
341C2×C3×Q8—23no—
342C2×C3×Q8—21no—
343C2×C3×Q8—33no—
344C2×C3×Q8—64no—
345C2×C3×Q8C22×D313yes—
346C2×C3×Q8C22×D313yes—
347C2×C3×Q8C22×D311yescharacteristic
348C2×C3×Q8C22×D311yescharacteristic
349C2×C3×D4—31no—
350C2×C3×D4—33no—
351C2×C3×D4—33no—
352C22×C3×C4—23no—
353C22×C3×C4—33no—
354C22×C3×C4—33no—
355C22×C3×C4C22×D313yes—
356C22×C3×C4C22×D313yes—
357C2×#67—33no—
358C2×#67—33no—
359C2×#67—31no—
360C2×#67—31no—
361C2×#67—31no—
362C2×#67—36no—
363C2×#67—33no—
364C2×#67—63no—
365C2×#67—61no—
366C2×#67C22×D311yescharacteristic
367C2×#67C22×D313yes—
368C22×Dic3—31no—
369C22×Dic3—33no—
370#239—24no—
371#239—38no—
372#239—38no—
373#239—68no—
374#239—612no—
375#239—612no—
376#239—612no—
377#239—612no—
378#239—624no—
379D3×Q8—24no—
380D3×Q8—612no—
381D3×Q8—612no—
382D3×Q8—624no—
383D3×Q8—68no—
384D3×Q8—64no—
385D3×Q8—64no—
386#237—612no—
387D3×D4—612no—
388#235—612no—
389#235—612no—
390#235—612no—
391#235—612no—
392#235—612no—
393#235—624no—
394#235—624no—
395C2×D12—33no—
396C2×D12—33no—
397C2×D12—31no—
398C2×D12—36no—
399C2×D12—33no—
400C2×D12—33no—
401C2×D12—33no—
402C2×D12—63no—
403C2×D12—63no—
404C2×D12—612no—
405C2×D12C22×D313yes—
406C2×C4×D3—33no—
407C2×C4×D3—33no—
408C2×C4×D3—31no—
409C2×C4×D3—33no—
410C2×C4×D3—33no—
411C2×C4×D3—33no—
412C2×C4×D3—36no—
413C2×C4×D3—36no—
414C2×C4×D3—33no—
415C2×C4×D3—33no—
416C2×C4×D3—36no—
417C2×C4×D3—36no—
418C2×C4×D3—63no—
419C2×C4×D3—66no—
420C2×C4×D3—63no—
421C2×C4×D3—612no—
422C2×C4×D3—612no—
423C2×C4×D3C22×D313yes—
424C2×C4×D3C22×D313yes—
425C2×Dic6—33no—
426C2×Dic6—33no—
427C2×Dic6—33no—
428C2×Dic6—33no—
429C2×Dic6—63no—
430C2×Dic6—63no—
431C2×Dic6C22×D313yes—
432C3×C4⋊C4—33no—
433C3×C4⋊C4—33no—
434C3×C4⋊C4—33no—
435C3×C4⋊C4—36no—
436C3×C4⋊C4—33no—
437C3×C22⋊C4—31no—
438C3×C22⋊C4—33no—
439C3×C22⋊C4—33no—
440C3×C22⋊C4—36no—
441C3×C22⋊C4—33no—
442C3×C42—33no—
443C3×C42—33no—
444#217—33no—
445#217—36no—
446#217—33no—
447#217C22×D311yescharacteristic
448#217C22×D313yes—
449(C2×D3)⋊C4—33no—
450(C2×D3)⋊C4—33no—
451(C2×D3)⋊C4—36no—
452(C2×D3)⋊C4—33no—
453(C2×D3)⋊C4—33no—
454(C2×D3)⋊C4—33no—
455(C2×D3)⋊C4—33no—
456(C2×D3)⋊C4—31no—
457(C2×D3)⋊C4—33no—
458(C2×D3)⋊C4—31no—
459(C2×D3)⋊C4—33no—
460(C2×D3)⋊C4C22×D313yes—
461(C2×D3)⋊C4C22×D316yes—
462(C2×D3)⋊C4C22×D313yes—
463C4⋊Dic3—33no—
464C4⋊Dic3—36no—
465C4⋊Dic3—33no—
466C4⋊Dic3C22×D313yes—
467C4⋊Dic3C22×D313yes—
468Dic3⋊C4—31no—
469Dic3⋊C4—31no—
470Dic3⋊C4—33no—
471Dic3⋊C4—33no—
472Dic3⋊C4—33no—
473Dic3⋊C4—33no—
474Dic3⋊C4—36no—
475Dic3⋊C4C22×D313yes—
476Dic3⋊C4C22×D316yes—
477Dic3⋊C4C22×D313yes—
478C4×Dic3C22×D313yes—
479C4×Dic3C22×D313yes—
480C22×C32—21no—
481C22×C32—21no—
482C22×C32—21no—
483C22×C32C2511yescharacteristic
484C2×C3⋊D3—21no—
485C2×C3⋊D3—23no—
486C2×C3⋊D3—23no—
487C2×C3⋊D3—21no—
488C2×C3⋊D3—21no—
489C2×C3⋊D3C22×D416yes—
490C2×C3×D3—21no—
491C2×C3×D3—21no—
492C2×C3×D3—23no—
493C2×C3×D3—23no—
494C2×C3×D3—23no—
495C2×C3×D32−1+412yescomplemented
496D32—412no—
497C32×C4—23no—
498C32×C4C22×D416yes—
499C3⋊Dic3—23no—
500C3⋊Dic3C22×D412yes—
501C3×Dic3—21no—
502C3×Dic3—23no—
503C3×Dic3—21no—
504C3×Dic3—21no—
505C3×Dic3—23no—
506C3×Dic3—23no—
5072−1+4—188no—
508C2×#41—31no—
509C2×#41—93no—
510C2×#41—93no—
511C2×#41—91no—
512C2×#41—93no—
513C2×#41—93no—
514C2×#41—93no—
515C2×#41—188no—
516C22×Q8—31no—
517C22×Q8—93no—
518C22×Q8—91no—
519C22×Q8D3211yescharacteristic, complemented
520C22×D4—93no—
521C23×C4—93no—
522C4⋊Q8—33no—
523C4⋊Q8—93no—
524#124—33no—
525#124—93no—
526#123—93no—
527#123—96no—
528#123—96no—
529#123—93no—
530C22⋊Q8—33no—
531C22⋊Q8—33no—
532C22⋊Q8—33no—
533C22⋊Q8—93no—
534C22⋊Q8—96no—
535C22⋊Q8—93no—
536C22⋊Q8—93no—
537C22⋊Q8—93no—
538C22⋊Q8—93no—
539#121—33no—
540#121—96no—
541#121—91no—
542#121—93no—
543#121—96no—
544#121—93no—
545#120—93no—
546#120—93no—
547C4×Q8—31no—
548C4×Q8—31no—
549C4×D4—33no—
550C4×D4—33no—
551C4×D4—93no—
552C4×D4—93no—
553C4×D4—93no—
554C4×D4—93no—
555#117—93no—
556C2×C4⋊C4—93no—
557C2×C4⋊C4—96no—
558C2×C22⋊C4—96no—
559C23×C3—21no—
560C23×C3—31no—
561C23×C3—33no—
562C23×C3C23×D311yescharacteristic
563C23×C3C23×D311yescharacteristic
564C22×D3—33no—
565C22×D3—33no—
566C22×D3—31no—
567C22×D3—31no—
568C22×D3—63no—
569C22×D3—61no—
570C22×D3—66no—
571C22×D3—66no—
572C22×D3—66no—
573C22×D3—66no—
574C22×D3—123no—
575C22×D3—123no—
576C22×D3C23×D313yes—
577C22×D3C23×D311yescharacteristic
578C3×Q8—212no—
579C3×Q8—26no—
580C3×Q8—26no—
581C3×Q8—24no—
582C3×Q8—66no—
583C3×Q8D3×D414yes—
584C3×Q8D3×D414yes—
585C3×D4—62no—
586C3×D4—66no—
587C3×D4—123no—
588C2×C3×C4—212no—
589C2×C3×C4—26no—
590C2×C3×C4—26no—
591C2×C3×C4—23no—
592C2×C3×C4—23no—
593C2×C3×C4—31no—
594C2×C3×C4—33no—
595C2×C3×C4—31no—
596C2×C3×C4—33no—
597C2×C3×C4—33no—
598C2×C3×C4—31no—
599C2×C3×C4—66no—
600C2×C3×C4—66no—
601C2×C3×C4C23×D313yes—
602C2×C3×C4C23×D313yes—
603C2×C3×C4C23×D313yes—
604C2×C3×C4C23×D313yes—
605#67—22no—
606#67—43no—
607#67—612no—
608#67—62no—
609#67—62no—
610#67—62no—
611#67—66no—
612#67—66no—
613#67—64no—
614#67—612no—
615#67—123no—
616C2×Dic3—31no—
617C2×Dic3—31no—
618C2×Dic3—33no—
619C2×Dic3—33no—
620C2×Dic3—61no—
621C2×Dic3—63no—
622C2×Dic3—62no—
623C2×Dic3—66no—
624C2×Dic3C23×D311yescharacteristic
625C2×Dic3C23×D311yescharacteristic
626C2×Dic3C23×D313yes—
627C2×Dic3C23×D313yes—
628C2×Dic3C23×D313yes—
629C2×Dic3C23×D311yescharacteristic
630D12—26no—
631D12—312no—
632D12—312no—
633D12—612no—
634D12—66no—
635D12—66no—
636D12—612no—
637D12—612no—
638D12—62no—
639D12—123no—
640C4×D3—26no—
641C4×D3—26no—
642C4×D3—312no—
643C4×D3—312no—
644C4×D3—612no—
645C4×D3—66no—
646C4×D3—66no—
647C4×D3—62no—
648C4×D3—66no—
649C4×D3—612no—
650C4×D3—612no—
651C4×D3—624no—
652C4×D3—612no—
653C4×D3—66no—
654C4×D3—66no—
655C4×D3—126no—
656C4×D3—126no—
657Dic6—26no—
658Dic6—66no—
659Dic6—66no—
660Dic6—612no—
661Dic6—612no—
662Dic6—66no—
663Dic6—66no—
664C2×C32—41no—
665C2×C32C23×D411yescharacteristic
666C2×C32C2×2−1+411yescharacteristic
667C2×C32#58511yescharacteristic
668C3⋊D3—26no—
669C3⋊D3—41no—
670C3×D3—22no—
671C3×D3—43no—
672C24—93no—
673#41—64no—
674#41—98no—
675#41—1812no—
676#41—1812no—
677#41—1812no—
678#41—1812no—
679#41—1812no—
680C2×Q8—24no—
681C2×Q8—33no—
682C2×Q8—64no—
683C2×Q8—93no—
684C2×Q8—93no—
685C2×Q8—1812no—
686C2×Q8—184no—
687C2×Q8C2×D3213yes—
688C2×Q8C2×D3211yescharacteristic
689C2×D4—31no—
690C2×D4—33no—
691C2×D4—33no—
692C2×D4—91no—
693C2×D4—96no—
694C2×D4—93no—
695C2×D4—93no—
696C2×D4—91no—
697C2×D4—93no—
698C2×D4—93no—
699C2×D4—1812no—
700C22×C4—33no—
701C22×C4—33no—
702C22×C4—93no—
703C22×C4—96no—
704C22×C4—91no—
705C22×C4—93no—
706C22×C4—93no—
707C22×C4—96no—
708C22×C4—93no—
709C22×C4—1812no—
710C22×C4C2×D3213yes—
711C4⋊C4—33no—
712C4⋊C4—33no—
713C4⋊C4—33no—
714C4⋊C4—36no—
715C4⋊C4—33no—
716C4⋊C4—93no—
717C4⋊C4—93no—
718C4⋊C4—96no—
719C4⋊C4—91no—
720C4⋊C4—93no—
721C22⋊C4—31no—
722C22⋊C4—33no—
723C22⋊C4—33no—
724C22⋊C4—36no—
725C22⋊C4—33no—
726C22⋊C4—93no—
727C22⋊C4—93no—
728C22⋊C4—91no—
729C22⋊C4—93no—
730C22⋊C4—93no—
731C22⋊C4—96no—
732C22⋊C4—93no—
733C42—33no—
734C42—33no—
735C22×C3—22no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—32no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—63no—
749C22×C3—63no—
750C22×C3—63no—
751C22×C3C24×D311yescharacteristic
752C22×C3C24×D311yescharacteristic
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—23no—
756C2×D3—23no—
757C2×D3—23no—
758C2×D3—36no—
759C2×D3—36no—
760C2×D3—66no—
761C2×D3—63no—
762C2×D3—63no—
763C2×D3—63no—
764C2×D3—63no—
765C2×D3—62no—
766C2×D3—61no—
767C2×D3—61no—
768C2×D3—61no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—123no—
773C2×D3—123no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—1212no—
777C2×D3—1212no—
778C2×D3#100712yescomplemented
779C3×C4—26no—
780C3×C4—23no—
781C3×C4—23no—
782C3×C4—26no—
783C3×C4—61no—
784C3×C4—63no—
785C3×C4—61no—
786C3×C4—63no—
787C3×C4—61no—
788C3×C4—63no—
789C3×C4C2×D3×D416yes—
790C3×C4C2×D3×D416yes—
791Dic3—23no—
792Dic3—21no—
793Dic3—21no—
794Dic3—23no—
795Dic3—21no—
796Dic3—23no—
797Dic3—32no—
798Dic3—32no—
799Dic3—62no—
800Dic3—66no—
801Dic3—63no—
802Dic3—63no—
803C32#348911yescharacteristic, complemented, Sylow
804C23—31no—
805C23—33no—
806C23—93no—
807C23—91no—
808C23—186no—
809C23—186no—
810C23—363no—
811C23C22×D3211yescharacteristic
812Q8—26no—
813Q8—66no—
814Q8—186no—
815Q8—186no—
816Q8#381114yes—
817D4—62no—
818D4—66no—
819D4—912no—
820D4—123no—
821D4—186no—
822D4—182no—
823D4—1812no—
824D4—182no—
825D4—186no—
826D4—363no—
827C2×C4—26no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—33no—
831C2×C4—33no—
832C2×C4—31no—
833C2×C4—33no—
834C2×C4—66no—
835C2×C4—66no—
836C2×C4—91no—
837C2×C4—912no—
838C2×C4—93no—
839C2×C4—1812no—
840C2×C4—186no—
841C2×C4—182no—
842C2×C4—186no—
843C2×C4—186no—
844C2×C4—366no—
845C2×C4C22×D3213yes—
846C2×C4C22×D3213yes—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—42no—
851C2×C3—41no—
852C2×C3—41no—
853C2×C3—62no—
854C2×C3—123no—
855C2×C3C22×D3×D411yescharacteristic
856C2×C3C22×D3×D411yescharacteristic
857C2×C3C2×#100711yescharacteristic
858C2×C3#596411yescharacteristic
859C2×C3D3×2−1+411yescharacteristic
860C2×C3#596811yescharacteristic
861D3—22no—
862D3—43no—
863D3—66no—
864D3—66no—
865D3—126no—
866D3—122no—
867D3—121no—
868D3—121no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—32no—
873C22—61no—
874C22—61no—
875C22—63no—
876C22—63no—
877C22—63no—
878C22—96no—
879C22—183no—
880C22—183no—
881C22—181no—
882C22—181no—
883C22—181no—
884C22—3612no—
885C22C23×D3211yescharacteristic
886C4—23no—
887C4—61no—
888C4—61no—
889C4—63no—
890C4—63no—
891C4—61no—
892C4—63no—
893C4—92no—
894C4—183no—
895C4C2×#381116yes—
896C3—21no—
897C3#8671411yescharacteristic, complemented
898C3#8674511yescharacteristic, complemented
899C2—41no—
900C2—62no—
901C2—123no—
902C2—186no—
903C2—361no—
904C2D3×#100711yescharacteristic
905C2#1059668811yescharacteristic
906C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64364C2semidirect
2. C2×D3×#239C2semidirect
3. C3×#5817C2semidirect
4. C3×Q8×#67C2semidirect
5. #10595431C2semidirect
6. #10595429C2semidirect
7. #10595414C2semidirect
8. Q8×#626C2semidirect
9. #10595364C2semidirect
10. #10595353C2semidirect
11. #10595341C2semidirect
12. #10595078C2semidirect
13. #10595076C2semidirect
14. #10594923C2semidirect
15. #10594834C2semidirect
18. C22×C32×Q8C22semidirect
21. C2×#3832C22semidirect
22. C2×Q8×C3⋊D3C22semidirect
23. C2×Q8×C3⋊D3C22semidirect
24. C2×#3828C22semidirect
25. C2×#3828C22semidirect
33. C3×#947C22semidirect
35. C3×#946C22semidirect
36. C3×Q8×Dic3C22semidirect
37. C3×Q8×Dic3C22semidirect
38. C3×#944C22semidirect
39. C3×#930C22semidirect
41. C3×C4×#67C22semidirect
42. C3×#924C22semidirect
44. #63975C22semidirect
46. #63971C22semidirect
47. #63958C22semidirect
50. #63916C22semidirect
51. #63910C22semidirect
53. C4×#626C22semidirect
54. #63900C22semidirect
55. #63897C22semidirect
57. #63896C22semidirect
58. #63896C22semidirect
59. #63894C22semidirect
60. #63894C22semidirect
61. #63883C22semidirect
62. #63874C22semidirect
63. #63871C22semidirect
64. #63866C22semidirect
65. #63860C22semidirect
67. #63857C22semidirect
68. #63853C22semidirect
69. #63853C22semidirect
78. #5817D3semidirect
80. Q8×#67D3semidirect
109. #3832D4semidirect
168. C22×C3×Q8C2×D3semidirect
169. C22×C3×Q8C2×D3semidirect
213. #947C2×D3semidirect
216. #946C2×D3semidirect
217. Q8×Dic3C2×D3semidirect
218. Q8×Dic3C2×D3semidirect
220. #944C2×D3semidirect
228. #930C2×D3semidirect
232. C4×#67C2×D3semidirect
235. #924C2×D3semidirect
495. C2×C3×D32−1+4semidirect
519. C22×Q8D32semidirect
778. C2×D3#1007semidirect
803. C32#3489semidirect
897. C3#86714semidirect
898. C3#86745semidirect

Maximal subgroups

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

subgroupindex
C2×#643642
C2×D3×#2392
C3×#58172
C3×Q8×#672
#105954312
#105954292
#105954142
Q8×#6262
#105953642
#105953532
#105953412
#105950782
#105950762
#105949232
#105948342
#867453
#867143