Finite Group Databasebeta

← #11902849

Subgroups — #11902849

Order 1152.

3741 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×D3×#239C211yesmaximal, characteristic, complemented
3C3×#5834C211yesmaximal, characteristic, complemented
4C3×#5831C211yesmaximal, characteristic, complemented
5#10595414C211yesmaximal, characteristic, complemented
6Q8×#626C211yesmaximal, characteristic, complemented
7#10595386C211yesmaximal, characteristic, complemented
8#10595306C213yesmaximal, complemented
9#10595297C213yesmaximal, complemented
10#10595243C213yesmaximal, complemented
11#10595167C213yesmaximal, complemented
12#10595078C213yesmaximal, complemented
13C4×#3811C213yesmaximal, complemented
14#10594922C213yesmaximal, complemented
15#10594834C213yesmaximal, complemented
16#86766—31nomaximal
17#86710—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19#41×C3⋊D3—28no—
20C2×#3832C2211yescharacteristic
21C2×Q8×C3⋊D3C2211yescharacteristic, complemented
22C2×#3830C2213yescomplemented
23C2×D4×C3⋊D3C2213yescomplemented
24C2×#3828C2213yescomplemented
25C22×C4×C3⋊D3C2213yescomplemented
26C2×C3×#239C2211yescharacteristic, complemented
27C2×C3×D3×Q8C2211yescharacteristic, complemented
28C2×#3811C2213yes—
29D3×#239—28no—
30C2×D3×D12C2213yescomplemented
31C2×C4×D32C2213yescomplemented
32C2×#3799C2213yescomplemented
33C2×#3796C2213yescomplemented
34C3×Q8×Dic3C2211yescharacteristic, complemented
35C3×Q8×Dic3C2211yescharacteristic, complemented
36C3×#940C2213yescomplemented
37C3×#938C2213yescomplemented
38C3×#938C2213yescomplemented
39C3×#936C2213yescomplemented
40C3×#930C2213yescomplemented
41C3×C4×#67C2213yescomplemented
42C3×C4×#67C2213yescomplemented
43C3×#924C2213yescomplemented
44#63983C2216yescomplemented
45#63981C2216yescomplemented
46#63975C2216yescomplemented
47#63974C2213yescomplemented
48#67⋊Dic3C2213yescomplemented
49#67⋊Dic3C2216yescomplemented
50#67⋊Dic3C2213yescomplemented
51#63958C2216yescomplemented
52#63958C2216yescomplemented
53#63921C2213yescomplemented
54#63916C2213yescomplemented
55C4×#626C2213yes—
56C4×#626C2213yescomplemented
57#63894C2213yescomplemented
58#63894C2213yescomplemented
59#63883C2213yescomplemented
60C4×#624C2213yescomplemented
61#63881C2211yescharacteristic
62#63881C2213yescomplemented
63#63871C2213yescomplemented
64#63866C2213yescomplemented
65#63860C2213yescomplemented
66#63857C2213yescomplemented
67#63857C2213yescomplemented
68#63853C2216yescomplemented
69#63849C2213yescomplemented
70C2×D3×#41—31no—
71C2×D3×#41—31no—
72C2×D3×#41—31no—
73C2×D3×#41—61no—
74C22×#239—31no—
75C3×#550—31no—
76C3×#548—31no—
77#5834D311yescharacteristic, complemented
78#5831—31no—
79#5831D311yescharacteristic, complemented
80Q8×#67—31no—
81#5717—33no—
82#5716—33no—
83#5676—33no—
84#5668—33no—
85#5631—33no—
86#5627—33no—
87#5612—33no—
88#5612—33no—
89#5609—33no—
90#5606—33no—
91#5606—33no—
92#5606—33no—
93#5576—31no—
94Q8×D12—31no—
95C4×#239—31no—
96C4×#239—31no—
97#5551—33no—
98#5550—33no—
99C4×D3×D4—33no—
100C4×D3×D4—33no—
101C23×C3⋊D3C2313yes—
102C22×D32C2313yes—
103C32×#41—24no—
104C2×C32×Q8C2311yescharacteristic
105C2×C32×D4C2313yes—
106C22×C32×C4C2313yes—
107C2×#638C2316yes—
108C22×C3⋊Dic3C2313yes—
109#3832D418yescomplemented
110Q8×C3⋊D3—24no—
111#3830—212no—
112D4×C3⋊D3—212no—
113#3828—212no—
114C2×C4⋊(C3⋊D3)C2313yes—
115C2×C4×C3⋊D3—212no—
116C2×C4×C3⋊D3C2311yescharacteristic
117C2×C4×C3⋊D3C2313yes—
118C2×C4×C3⋊D3C2313yes—
119C2×C4×C3⋊D3C2313yes—
120C2×#634C2313yes—
121C2×C3×#67C2313yes—
122C2×C3×#67C2313yes—
123C2×C3×#67C2316yes—
124C3×#239—24no—
125C3×D3×Q8—24no—
126C2×C3×D12C2313yes—
127C2×C3×C4×D3C2313yes—
128C2×C3×C4×D3C2313yes—
129C2×C3×Dic6C2313yes—
130#3811—212no—
131C2×#626C2316yes—
132C2×#626C2313yes—
133C2×#626C2311yescharacteristic
134C2×#624C2313yes—
135C2×#624C2313yes—
136C2×#624C2313yes—
137C2×D3×Dic3C2313yes—
138C2×D3×Dic3C2311yescharacteristic
139D3×D12—212no—
140C4×D32—212no—
141#3799—212no—
142#3796—212no—
143C3×#217C2316yes—
144C3×#217C2313yes—
145C3×#217C2313yes—
146C3×(C2×D3)⋊C4C2311yescharacteristic
147C3×(C2×D3)⋊C4C2313yes—
148C3×C4⋊Dic3C2313yes—
149C3×C4⋊Dic3C2313yes—
150C3×Dic3⋊C4C2313yes—
151C3×Dic3⋊C4C2311yescharacteristic
152C3×C4×Dic3C2313yes—
153C3×C4×Dic3C2313yes—
154Dic3⋊Dic3C2316yes—
155Dic3⋊Dic3C2313yes—
156Dic3⋊Dic3C2313yes—
157#3722C2316yes—
158#3722C2313yes—
159#3722C2311yescharacteristic
160(C2×D3)⋊Dic3C2316yes—
161(C2×D3)⋊Dic3C2313yes—
162(C2×D3)⋊Dic3C2313yes—
163Dic32C2313yes—
164Dic32C2311yescharacteristic
165D4×#41—91noSylow
166C2×C3×#41—21no—
167C2×C3×#41—31no—
168C2×C3×#41C2×D311yescharacteristic, complemented
169C2×C3×#41C2×D311yescharacteristic, complemented
170C22×C3×Q8—31no—
171D3×#41—68no—
172D3×#41—68no—
173D3×#41—68no—
174D3×#41—616no—
175C2×#239—31no—
176C2×#239—31no—
177C2×#239—33no—
178C2×#239—33no—
179C2×#239—61no—
180C2×#239—68no—
181C2×#239C2×D311yescharacteristic, complemented
182C2×D3×Q8—31no—
183C2×D3×Q8—31no—
184C2×D3×Q8—61no—
185C2×D3×Q8C2×D311yescharacteristic, complemented
186C2×#237—33no—
187C2×#237—33no—
188C2×#237—33no—
189C2×#237—63no—
190C2×D3×D4—33no—
191C2×D3×D4—33no—
192C2×D3×D4—33no—
193C2×D3×D4—33no—
194C2×D3×D4—33no—
195C2×D3×D4—63no—
196C2×#235—33no—
197C2×#235—33no—
198C2×#235—33no—
199C2×#235—63no—
200C22×D12—33no—
201C22×C4×D3—33no—
202C22×C4×D3—33no—
203C22×C4×D3—33no—
204C22×C4×D3—33no—
205C22×C4×D3—63no—
206C3×#127—33no—
207C3×#124—33no—
208C3×C22⋊Q8—33no—
209C3×#121—33no—
210C3×#121—33no—
211C3×#121—33no—
212C3×C4×Q8—31no—
213C3×C4×Q8—31no—
214C3×C4×D4—33no—
215C3×C4×D4—33no—
216#946—33no—
217Q8×Dic3C2×D311yescharacteristic, complemented
218Q8×Dic3C2×D311yescharacteristic, complemented
219#944—33no—
220#940C2×D313yescomplemented
221#938—36no—
222#938—36no—
223#938—33no—
224#938C2×D313yescomplemented
225#938C2×D313yescomplemented
226#937—36no—
227#937—36no—
228#937—36no—
229#936—33no—
230#936C2×D313yescomplemented
231D4×Dic3—33no—
232D4×Dic3—36no—
233D4×Dic3—33no—
234#930C2×D313yescomplemented
235C4×#67—33no—
236C4×#67—33no—
237C4×#67C2×D313yescomplemented
238C4×#67C2×D313yescomplemented
239#924—33no—
240#924—33no—
241#924C2×D313yescomplemented
242#897—33no—
243#897—33no—
244#897—33no—
245#895—33no—
246#894—36no—
247#893—31no—
248#893—33no—
249#893—33no—
250#893—33no—
251#892—33no—
252#892—33no—
253D3×C4⋊C4—33no—
254D3×C4⋊C4—33no—
255#884—36no—
256#884—36no—
257#883—36no—
258#883—36no—
259#883—36no—
260#882—36no—
261#67⋊C4—33no—
262#67⋊C4—36no—
263#67⋊C4—33no—
264#67⋊C4—31no—
265#67⋊C4—33no—
266D3×C22⋊C4—33no—
267D3×C22⋊C4—33no—
268D3×C22⋊C4—33no—
269D3×C22⋊C4—33no—
270#875—33no—
271C4×D12—33no—
272C4×D12—33no—
273C4×D12—33no—
274C4×D12—33no—
275C42×D3—33no—
276C42×D3—33no—
277#869—33no—
278C23×C32C2413yes—
279C22×C3⋊D3—26no—
280C22×C3⋊D3—26no—
281C22×C3⋊D3—43no—
282C22×C3⋊D3C2413yes—
283C22×C3⋊D3C2411yescharacteristic
284C22×C3×D3C2413yes—
285C22×C3×D3C2411yescharacteristic
286C2×D32—26no—
287C2×D32—26no—
288C2×D32—43no—
289C32×Q8C2×D414yescomplemented
290C32×D4—26no—
291C2×C32×C4—26no—
292C2×C32×C4C2411yescharacteristic
293C2×C32×C4C2413yes—
294#638—212no—
295C2×C3⋊Dic3—26no—
296C2×C3⋊Dic3C2413yes—
297C2×C3⋊Dic3C2411yescharacteristic
298C4⋊(C3⋊D3)C2×D4112yescomplemented
299C4×C3⋊D3—26no—
300C4×C3⋊D3—26no—
301C4×C3⋊D3—22no—
302C4×C3⋊D3C2×D4112yescomplemented
303#634—26no—
304C3×#67—26no—
305C3×#67—26no—
306C3×#67—46no—
307C2×C3×Dic3C2411yescharacteristic
308C2×C3×Dic3C2413yes—
309C2×C3×Dic3C2413yes—
310C2×C3×Dic3C2411yescharacteristic
311C2×C3×Dic3C2413yes—
312C2×C3×Dic3C2411yescharacteristic
313C3×D12—26no—
314C3×C4×D3—26no—
315C3×C4×D3—26no—
316C3×Dic6—26no—
317#626—212no—
318#626—26no—
319#626#4114yescomplemented
320#624—26no—
321#624—26no—
322#624—43no—
323D3×Dic3—26no—
324D3×Dic3—22no—
325C22×#41—91no—
326C22×#41—91no—
327#550—31no—
328D4×Q8—91no—
329#548—31no—
330#548—91no—
331#547—93no—
332#546—93no—
333#546—93no—
334D42—93no—
335#532—93no—
336#525—93no—
337#525—93no—
338C4×#41—91no—
339C2×C4×D4—93no—
340C23×D3—33no—
341C23×D3—33no—
342C23×D3—33no—
343C23×D3—33no—
344C23×D3—63no—
345C3×#41—28no—
346C3×#41—24no—
347C3×#41—24no—
348C3×#41—64no—
349C2×C3×Q8—21no—
350C2×C3×Q8—33no—
351C2×C3×Q8—64no—
352C2×C3×Q8C22×D311yescharacteristic
353C2×C3×Q8C22×D311yescharacteristic
354C2×C3×D4—23no—
355C2×C3×D4—33no—
356C2×C3×D4—33no—
357C2×C3×D4—36no—
358C2×C3×D4—33no—
359C2×C3×D4C22×D313yes—
360C2×C3×D4C22×D313yes—
361C22×C3×C4—23no—
362C22×C3×C4—33no—
363C22×C3×C4—33no—
364C22×C3×C4C22×D313yes—
365C22×C3×C4C22×D313yes—
366C2×#67—36no—
367C2×#67—36no—
368C2×#67—31no—
369C2×#67—33no—
370C2×#67—36no—
371C2×#67—66no—
372C2×#67C22×D313yes—
373C2×#67C22×D313yes—
374C2×#67C22×D316yes—
375C22×Dic3—33no—
376C22×Dic3—33no—
377C22×Dic3—31no—
378C22×Dic3—33no—
379C22×Dic3—63no—
380#239—24no—
381#239—38no—
382#239—38no—
383#239—68no—
384#239—612no—
385#239—612no—
386D3×Q8—24no—
387D3×Q8—68no—
388D3×Q8—64no—
389D3×Q8—64no—
390#237—612no—
391#237—612no—
392#237—612no—
393#237—624no—
394D3×D4—612no—
395D3×D4—612no—
396D3×D4—612no—
397D3×D4—612no—
398D3×D4—612no—
399D3×D4—624no—
400#235—612no—
401#235—612no—
402#235—612no—
403#235—624no—
404C2×D12—31no—
405C2×D12—33no—
406C2×D12—33no—
407C2×D12—33no—
408C2×D12—36no—
409C2×D12—63no—
410C2×D12—612no—
411C2×D12C22×D313yes—
412C2×C4×D3—33no—
413C2×C4×D3—33no—
414C2×C4×D3—31no—
415C2×C4×D3—33no—
416C2×C4×D3—33no—
417C2×C4×D3—33no—
418C2×C4×D3—33no—
419C2×C4×D3—33no—
420C2×C4×D3—31no—
421C2×C4×D3—31no—
422C2×C4×D3—33no—
423C2×C4×D3—33no—
424C2×C4×D3—33no—
425C2×C4×D3—33no—
426C2×C4×D3—33no—
427C2×C4×D3—33no—
428C2×C4×D3—61no—
429C2×C4×D3—63no—
430C2×C4×D3—63no—
431C2×C4×D3—63no—
432C2×C4×D3—612no—
433C2×C4×D3—612no—
434C2×C4×D3—612no—
435C2×C4×D3—612no—
436C2×C4×D3—624no—
437C2×C4×D3C22×D313yes—
438C2×C4×D3C22×D313yes—
439C2×Dic6—33no—
440C2×Dic6—33no—
441C2×Dic6—63no—
442C2×Dic6C22×D313yes—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—33no—
445C3×C4⋊C4—33no—
446C3×C4⋊C4—33no—
447C3×C22⋊C4—33no—
448C3×C22⋊C4—33no—
449C3×C22⋊C4—36no—
450C3×C22⋊C4—31no—
451C3×C22⋊C4—33no—
452C3×C42—33no—
453C3×C42—33no—
454#217—33no—
455#217—33no—
456#217—36no—
457#217C22×D313yes—
458#217C22×D313yes—
459#217C22×D316yes—
460(C2×D3)⋊C4—33no—
461(C2×D3)⋊C4—33no—
462(C2×D3)⋊C4—36no—
463(C2×D3)⋊C4—31no—
464(C2×D3)⋊C4—33no—
465(C2×D3)⋊C4—36no—
466(C2×D3)⋊C4—36no—
467(C2×D3)⋊C4—31no—
468(C2×D3)⋊C4—33no—
469(C2×D3)⋊C4C22×D311yescharacteristic
470(C2×D3)⋊C4C22×D313yes—
471C4⋊Dic3—33no—
472C4⋊Dic3—36no—
473C4⋊Dic3—33no—
474C4⋊Dic3C22×D313yes—
475C4⋊Dic3C22×D313yes—
476Dic3⋊C4—33no—
477Dic3⋊C4—36no—
478Dic3⋊C4—33no—
479Dic3⋊C4C22×D313yes—
480Dic3⋊C4C22×D311yescharacteristic
481C4×Dic3—31no—
482C4×Dic3—31no—
483C4×Dic3—33no—
484C4×Dic3—33no—
485C4×Dic3C22×D313yes—
486C4×Dic3C22×D313yes—
487C22×C32—23no—
488C22×C32—23no—
489C22×C32—23no—
490C22×C32C2511yescharacteristic
491C2×C3⋊D3—21no—
492C2×C3⋊D3—21no—
493C2×C3⋊D3—23no—
494C2×C3⋊D3—23no—
495C2×C3⋊D3—412no—
496C2×C3⋊D3C22×D416yes—
497C2×C3⋊D3C2×#4112yescomplemented
498C2×C3×D3—21no—
499C2×C3×D3—21no—
500C2×C3×D3—23no—
501C2×C3×D3—23no—
502C2×C3×D3—23no—
503C2×C3×D3C2×#4112yescomplemented
504D32—412no—
505C32×C4—21no—
506C32×C4C22×D416yes—
507C3⋊Dic3—23no—
508C3⋊Dic3C22×D412yes—
509C3×Dic3—21no—
510C3×Dic3—23no—
511C3×Dic3—23no—
512C3×Dic3—21no—
513C3×Dic3—23no—
514C3×Dic3C2×#4112yescomplemented
515C2×#41—31no—
516C2×#41—93no—
517C2×#41—93no—
518C2×#41—91no—
519C2×#41—93no—
520C2×#41—93no—
521C2×#41—188no—
522C2×#41—188no—
523C2×#41D3211yescharacteristic, complemented
524C22×Q8—31no—
525C22×Q8—91no—
526C22×D4—93no—
527C22×D4—93no—
528C22×D4—93no—
529C23×C4—93no—
530C23×C4—93no—
531C4⋊Q8—93no—
532#127—33no—
533#124—33no—
534#124—93no—
535#123—96no—
536#123—96no—
537C22⋊Q8—33no—
538C22⋊Q8—93no—
539C22⋊Q8—93no—
540C22⋊Q8—93no—
541#121—33no—
542#121—33no—
543#121—33no—
544#121—96no—
545#121—96no—
546#121—93no—
547#120—96no—
548#120—96no—
549C4×Q8—31no—
550C4×Q8—31no—
551C4×D4—33no—
552C4×D4—33no—
553C4×D4—93no—
554C4×D4—93no—
555C4×D4—93no—
556C4×D4—93no—
557C4×D4—91no—
558C4×D4—93no—
559C4×D4—93no—
560C4×D4—93no—
561C4×D4—96no—
562#117—93no—
563C2×C4⋊C4—93no—
564C2×C22⋊C4—93no—
565C2×C22⋊C4—93no—
566C2×C42—93no—
567C23×C3—23no—
568C23×C3—31no—
569C23×C3—33no—
570C23×C3C23×D313yes—
571C23×C3C23×D313yes—
572C22×D3—31no—
573C22×D3—31no—
574C22×D3—33no—
575C22×D3—33no—
576C22×D3—61no—
577C22×D3—63no—
578C22×D3—66no—
579C22×D3—66no—
580C22×D3—66no—
581C22×D3—66no—
582C22×D3—66no—
583C22×D3—66no—
584C22×D3—66no—
585C22×D3—612no—
586C22×D3—66no—
587C22×D3—126no—
588C22×D3—123no—
589C22×D3—123no—
590C22×D3—123no—
591C22×D3—123no—
592C22×D3—126no—
593C22×D3C23×D313yes—
594C22×D3C23×D311yescharacteristic
595C3×Q8—24no—
596C3×Q8—66no—
597C3×Q8D3×D414yescomplemented
598C3×Q8D3×D414yescomplemented
599C3×D4—212no—
600C3×D4—26no—
601C3×D4—26no—
602C3×D4—66no—
603C3×D4—66no—
604C3×D4—66no—
605C3×D4—126no—
606C2×C3×C4—212no—
607C2×C3×C4—26no—
608C2×C3×C4—26no—
609C2×C3×C4—23no—
610C2×C3×C4—21no—
611C2×C3×C4—31no—
612C2×C3×C4—33no—
613C2×C3×C4—33no—
614C2×C3×C4—31no—
615C2×C3×C4—31no—
616C2×C3×C4—33no—
617C2×C3×C4—66no—
618C2×C3×C4—66no—
619C2×C3×C4C23×D311yescharacteristic
620C2×C3×C4C23×D311yescharacteristic
621C2×C3×C4C23×D313yes—
622C2×C3×C4C23×D313yes—
623#67—26no—
624#67—26no—
625#67—34no—
626#67—46no—
627#67—612no—
628#67—66no—
629#67—612no—
630#67—612no—
631#67—624no—
632C2×Dic3—31no—
633C2×Dic3—31no—
634C2×Dic3—33no—
635C2×Dic3—33no—
636C2×Dic3—63no—
637C2×Dic3—61no—
638C2×Dic3—62no—
639C2×Dic3—66no—
640C2×Dic3—66no—
641C2×Dic3—66no—
642C2×Dic3—612no—
643C2×Dic3C23×D311yescharacteristic
644C2×Dic3C23×D313yes—
645C2×Dic3C23×D313yes—
646C2×Dic3C23×D313yes—
647C2×Dic3C23×D311yescharacteristic
648C2×Dic3C23×D311yescharacteristic
649D12—26no—
650D12—34no—
651D12—312no—
652D12—312no—
653D12—612no—
654D12—612no—
655D12—66no—
656C4×D3—26no—
657C4×D3—26no—
658C4×D3—312no—
659C4×D3—312no—
660C4×D3—612no—
661C4×D3—66no—
662C4×D3—66no—
663C4×D3—66no—
664C4×D3—62no—
665C4×D3—62no—
666C4×D3—62no—
667C4×D3—66no—
668C4×D3—66no—
669C4×D3—66no—
670C4×D3—64no—
671C4×D3—612no—
672C4×D3—612no—
673C4×D3—66no—
674C4×D3—66no—
675C4×D3—66no—
676C4×D3—123no—
677C4×D3—123no—
678Dic6—26no—
679Dic6—612no—
680Dic6—66no—
681Dic6—66no—
682C2×C32—43no—
683C2×C32C23×D411yescharacteristic
684C2×C32C22×#4111yescharacteristic
685C2×C32#58511yescharacteristic
686C3⋊D3—22no—
687C3⋊D3—26no—
688C3×D3—22no—
689C3×D3—43no—
690C24—93no—
691C24—93no—
692#41—24no—
693#41—64no—
694#41—98no—
695#41—1812no—
696#41—1812no—
697#41—1812no—
698#41—1812no—
699C2×Q8—33no—
700C2×Q8—64no—
701C2×Q8—93no—
702C2×Q8—184no—
703C2×Q8C2×D3211yescharacteristic
704C2×D4—33no—
705C2×D4—33no—
706C2×D4—36no—
707C2×D4—33no—
708C2×D4—91no—
709C2×D4—93no—
710C2×D4—96no—
711C2×D4—96no—
712C2×D4—93no—
713C2×D4—1812no—
714C2×D4—1812no—
715C2×D4—1812no—
716C2×D4C2×D3213yes—
717C22×C4—33no—
718C22×C4—33no—
719C22×C4—93no—
720C22×C4—93no—
721C22×C4—93no—
722C22×C4—91no—
723C22×C4—93no—
724C22×C4—93no—
725C22×C4—93no—
726C22×C4—93no—
727C22×C4—91no—
728C22×C4—93no—
729C22×C4—1812no—
730C22×C4—1812no—
731C22×C4C2×D3213yes—
732C4⋊C4—31no—
733C4⋊C4—33no—
734C4⋊C4—33no—
735C4⋊C4—33no—
736C4⋊C4—93no—
737C4⋊C4—93no—
738C4⋊C4—96no—
739C22⋊C4—33no—
740C22⋊C4—33no—
741C22⋊C4—36no—
742C22⋊C4—31no—
743C22⋊C4—33no—
744C22⋊C4—91no—
745C22⋊C4—93no—
746C22⋊C4—96no—
747C22⋊C4—93no—
748C22⋊C4—93no—
749C22⋊C4—96no—
750C42—33no—
751C42—33no—
752C42—91no—
753C42—93no—
754C22×C3—26no—
755C22×C3—23no—
756C22×C3—23no—
757C22×C3—23no—
758C22×C3—23no—
759C22×C3—23no—
760C22×C3—23no—
761C22×C3—21no—
762C22×C3—32no—
763C22×C3—43no—
764C22×C3—43no—
765C22×C3—61no—
766C22×C3—61no—
767C22×C3—63no—
768C22×C3—63no—
769C22×C3—63no—
770C22×C3C24×D311yescharacteristic
771C22×C3C24×D311yescharacteristic
772C2×D3—21no—
773C2×D3—21no—
774C2×D3—23no—
775C2×D3—23no—
776C2×D3—23no—
777C2×D3—36no—
778C2×D3—36no—
779C2×D3—32no—
780C2×D3—32no—
781C2×D3—62no—
782C2×D3—66no—
783C2×D3—62no—
784C2×D3—62no—
785C2×D3—61no—
786C2×D3—61no—
787C2×D3—63no—
788C2×D3—63no—
789C2×D3—63no—
790C2×D3—61no—
791C2×D3—63no—
792C2×D3—61no—
793C2×D3—123no—
794C2×D3—123no—
795C2×D3—1212no—
796C2×D3—1212no—
797C2×D3—1212no—
798C2×D3—1212no—
799C2×D3—1224no—
800C2×D3D3×#4112yescomplemented
801C3×C4—22no—
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—26no—
805C3×C4—32no—
806C3×C4—61no—
807C3×C4—63no—
808C3×C4—63no—
809C3×C4—61no—
810C3×C4—63no—
811C3×C4C2×D3×D416yes—
812C3×C4C2×D3×D416yes—
813Dic3—23no—
814Dic3—21no—
815Dic3—23no—
816Dic3—23no—
817Dic3—21no—
818Dic3—32no—
819Dic3—32no—
820Dic3—62no—
821Dic3—66no—
822Dic3—63no—
823Dic3—63no—
824Dic3D3×#4112yescomplemented
825C32D4×#4111yescharacteristic, complemented, Sylow
826C23—31no—
827C23—33no—
828C23—91no—
829C23—93no—
830C23—186no—
831C23—186no—
832C23—186no—
833C23—186no—
834C23—363no—
835C23—363no—
836C23C22×D3213yes—
837Q8—66no—
838Q8—186no—
839Q8#381114yescomplemented
840D4—26no—
841D4—66no—
842D4—66no—
843D4—66no—
844D4—94no—
845D4—912no—
846D4—126no—
847D4—1812no—
848D4—186no—
849D4—1812no—
850C2×C4—26no—
851C2×C4—31no—
852C2×C4—31no—
853C2×C4—33no—
854C2×C4—33no—
855C2×C4—31no—
856C2×C4—33no—
857C2×C4—66no—
858C2×C4—66no—
859C2×C4—91no—
860C2×C4—912no—
861C2×C4—93no—
862C2×C4—182no—
863C2×C4—186no—
864C2×C4—186no—
865C2×C4—186no—
866C2×C4—182no—
867C2×C4—186no—
868C2×C4—186no—
869C2×C4—186no—
870C2×C4—363no—
871C2×C4C22×D3211yescharacteristic
872C2×C4C22×D3213yes—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—46no—
877C2×C3—43no—
878C2×C3—43no—
879C2×C3—62no—
880C2×C3—123no—
881C2×C3C22×D3×D411yescharacteristic
882C2×C3C22×D3×D411yescharacteristic
883C2×C3C2×D3×#4111yescharacteristic
884C2×C3C2×D3×#4111yescharacteristic
885C2×C3#596611yescharacteristic
886C2×C3#596811yescharacteristic
887D3—22no—
888D3—43no—
889D3—64no—
890D3—62no—
891D3—66no—
892D3—62no—
893D3—66no—
894D3—126no—
895C22—23no—
896C22—23no—
897C22—23no—
898C22—32no—
899C22—61no—
900C22—61no—
901C22—63no—
902C22—63no—
903C22—63no—
904C22—92no—
905C22—96no—
906C22—183no—
907C22—183no—
908C22—181no—
909C22—181no—
910C22—3612no—
911C22—3612no—
912C22C23×D3211yescharacteristic
913C4—21no—
914C4—32no—
915C4—63no—
916C4—61no—
917C4—63no—
918C4—61no—
919C4—63no—
920C4—92no—
921C4—183no—
922C4C2×#381116yes—
923C3—21no—
924C3#8671011yescharacteristic, complemented
925C3#8676611yescharacteristic, complemented
926C2—43no—
927C2—62no—
928C2—123no—
929C2—182no—
930C2—186no—
931C2D32×#4111yescharacteristic
932C2#1059669811yescharacteristic
933C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32D4×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×C3⋊D3C2semidirect
2. C2×D3×#239C2semidirect
3. C3×#5834C2semidirect
4. C3×#5831C2semidirect
5. #10595414C2semidirect
6. Q8×#626C2semidirect
7. #10595386C2semidirect
8. #10595306C2semidirect
9. #10595297C2semidirect
10. #10595243C2semidirect
11. #10595167C2semidirect
12. #10595078C2semidirect
13. C4×#3811C2semidirect
14. #10594922C2semidirect
15. #10594834C2semidirect
18. C2×C32×#41C22semidirect
21. C2×Q8×C3⋊D3C22semidirect
22. C2×#3830C22semidirect
23. C2×D4×C3⋊D3C22semidirect
24. C2×#3828C22semidirect
25. C22×C4×C3⋊D3C22semidirect
26. C2×C3×#239C22semidirect
27. C2×C3×D3×Q8C22semidirect
30. C2×D3×D12C22semidirect
31. C2×C4×D32C22semidirect
32. C2×#3799C22semidirect
33. C2×#3796C22semidirect
34. C3×Q8×Dic3C22semidirect
35. C3×Q8×Dic3C22semidirect
36. C3×#940C22semidirect
37. C3×#938C22semidirect
38. C3×#938C22semidirect
39. C3×#936C22semidirect
40. C3×#930C22semidirect
41. C3×C4×#67C22semidirect
42. C3×C4×#67C22semidirect
43. C3×#924C22semidirect
44. #63983C22semidirect
45. #63981C22semidirect
46. #63975C22semidirect
47. #63974C22semidirect
48. #67⋊Dic3C22semidirect
49. #67⋊Dic3C22semidirect
50. #67⋊Dic3C22semidirect
51. #63958C22semidirect
52. #63958C22semidirect
53. #63921C22semidirect
54. #63916C22semidirect
56. C4×#626C22semidirect
57. #63894C22semidirect
58. #63894C22semidirect
59. #63883C22semidirect
60. C4×#624C22semidirect
62. #63881C22semidirect
63. #63871C22semidirect
64. #63866C22semidirect
65. #63860C22semidirect
66. #63857C22semidirect
67. #63857C22semidirect
68. #63853C22semidirect
69. #63849C22semidirect
77. #5834D3semidirect
79. #5831D3semidirect
109. #3832D4semidirect
168. C2×C3×#41C2×D3semidirect
169. C2×C3×#41C2×D3semidirect
181. C2×#239C2×D3semidirect
185. C2×D3×Q8C2×D3semidirect
217. Q8×Dic3C2×D3semidirect
218. Q8×Dic3C2×D3semidirect
220. #940C2×D3semidirect
224. #938C2×D3semidirect
225. #938C2×D3semidirect
230. #936C2×D3semidirect
234. #930C2×D3semidirect
237. C4×#67C2×D3semidirect
238. C4×#67C2×D3semidirect
241. #924C2×D3semidirect
289. C32×Q8C2×D4semidirect
298. C4⋊(C3⋊D3)C2×D4semidirect
302. C4×C3⋊D3C2×D4semidirect
319. #626#41semidirect
497. C2×C3⋊D3C2×#41semidirect
503. C2×C3×D3C2×#41semidirect
514. C3×Dic3C2×#41semidirect
523. C2×#41D32semidirect
597. C3×Q8D3×D4semidirect
598. C3×Q8D3×D4semidirect
800. C2×D3D3×#41semidirect
824. Dic3D3×#41semidirect
825. C32D4×#41semidirect
839. Q8#3811semidirect
924. C3#86710semidirect
925. C3#86766semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C2×D3×#2392
C3×#58342
C3×#58312
#105954142
Q8×#6262
#105953862
#105953062
#105952972
#105952432
#105951672
#105950782
C4×#38112
#105949222
#105948342
#867663
#867103