Finite Group Databasebeta

← #11902846

Subgroups — #11902846

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
1C22×#3832C211yesmaximal, characteristic, complemented
2C2×D3×#239C211yesmaximal, characteristic, complemented
3C3×#5817C211yesmaximal, characteristic, complemented
4C3×Q8×#67C211yesmaximal, characteristic, complemented
5#10595431C213yesmaximal, complemented
6#10595430C213yesmaximal, complemented
7#10595410C211yesmaximal, characteristic, complemented
8#10595386C211yesmaximal, characteristic, complemented
9#10595363C213yesmaximal, complemented
10#10595342C211yesmaximal, characteristic, complemented
11#10595341C213yesmaximal, complemented
12#10595074C213yesmaximal, complemented
13C4×#3811C213yesmaximal, complemented
14#10595018C213yesmaximal, complemented
15#10594922C213yesmaximal, complemented
16D4×#239—31nomaximal
17#86710—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C2×#3832—28no—
20C2×#3832C2211yescharacteristic
21C2×#3832C2213yescomplemented
22C2×#3832C2211yescharacteristic, complemented
23C2×#3832C2213yescomplemented
24C22×C4⋊(C3⋊D3)C2213yescomplemented
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×#947C2213yescomplemented
35C3×#946C2213yescomplemented
36C3×#946C2213yescomplemented
37C3×Q8×Dic3C2211yescharacteristic, complemented
38C3×Q8×Dic3C2211yescharacteristic, complemented
39C3×#944C2213yescomplemented
40C3×#930C2213yescomplemented
41C3×C4×#67C2213yes—
42C3×C4×#67C2213yescomplemented
43C3×#924C2213yescomplemented
44#63981C2216yescomplemented
45#63974C2213yescomplemented
46#67⋊Dic3C2211yescharacteristic
47#67⋊Dic3C2213yescomplemented
48#63923C2216yescomplemented
49#63921C2213yescomplemented
50#63916C2213yescomplemented
51#63911C2213yescomplemented
52#63910C2216yescomplemented
53#63910C2216yescomplemented
54#63909C2213yescomplemented
55#63909C2213yescomplemented
56C4×#626C2213yescomplemented
57C4×#626C2213yescomplemented
58#63897C2216yescomplemented
59#63894C2213yescomplemented
60#63894C2213yescomplemented
61#63883C2213yescomplemented
62C4×#624C2213yescomplemented
63#63881C2213yescomplemented
64#63881C2216yescomplemented
65#63881C2213yescomplemented
66#63871C2213yescomplemented
67#63864C2213yescomplemented
68#63853C2216yescomplemented
69#63849C2213yescomplemented
70C2×D3×#41—31no—
71C22×#239—31no—
72C22×#239—31no—
73C22×#239—31no—
74C22×#239—61no—
75C3×D4×Q8—31no—
76C3×#548—31no—
77#5834—31no—
78#5817—31no—
79#5817D311yescharacteristic, complemented
80Q8×#67D311yescharacteristic, complemented
81#5726—33no—
82#5725—33no—
83#5676—33no—
84#5668—33no—
85#5631—33no—
86#5630—33no—
87#5630—33no—
88#5627—33no—
89#5627—33no—
90#5627—33no—
91#5609—33no—
92#5606—33no—
93#5577—31no—
94#5576—31no—
95C4×#239—31no—
96C4×#239—31no—
97#5550—33no—
98D4×D12—33no—
99C4×D3×D4—33no—
100C4×D3×D4—33no—
101C23×C3⋊D3C2313yes—
102C22×D32C2313yes—
103C2×C32×Q8—24no—
104C2×C32×Q8C2313yes—
105C2×C32×Q8C2311yescharacteristic
106C22×C32×C4C2313yes—
107C22×C3⋊Dic3C2311yescharacteristic
108#3832—24no—
109#3832—212no—
110#3832—212no—
111#3832D418yescomplemented
112C2×C4⋊(C3⋊D3)—212no—
113C2×C4⋊(C3⋊D3)C2313yes—
114C2×C4⋊(C3⋊D3)C2316yes—
115C2×C4⋊(C3⋊D3)C2313yes—
116C2×C4×C3⋊D3—212no—
117C2×C4×C3⋊D3C2313yes—
118C2×C4×C3⋊D3C2313yes—
119C2×C4×C3⋊D3C2313yes—
120C2×C4×C3⋊D3C2313yes—
121C2×C3×#67C2313yes—
122C2×C3×#67C2311yescharacteristic
123C3×#239—24no—
124C3×D3×Q8—24no—
125C2×C3×D12C2313yes—
126C2×C3×C4×D3C2313yes—
127C2×C3×C4×D3C2313yes—
128C2×C3×Dic6C2313yes—
129#3811—212no—
130C2×#626C2316yes—
131C2×#626C2313yes—
132C2×#626C2313yes—
133C2×#626C2316yes—
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×#217C2313yes—
144C3×#217C2311yescharacteristic
145C3×(C2×D3)⋊C4C2313yes—
146C3×(C2×D3)⋊C4C2313yes—
147C3×(C2×D3)⋊C4C2316yes—
148C3×C4⋊Dic3C2313yes—
149C3×C4⋊Dic3C2313yes—
150C3×Dic3⋊C4C2316yes—
151C3×Dic3⋊C4C2313yes—
152C3×Dic3⋊C4C2313yes—
153C3×C4×Dic3C2313yes—
154C3×C4×Dic3C2313yes—
155Dic3⋊Dic3C2313yes—
156Dic3⋊Dic3C2311yescharacteristic
157#3722C2316yes—
158#3722C2313yes—
159#3722C2316yes—
160#3722C2313yes—
161(C2×D3)⋊Dic3C2313yes—
162(C2×D3)⋊Dic3C2311yescharacteristic
163Dic32C2313yes—
164Dic32C2311yescharacteristic
165D4×#41—91noSylow
166C2×C3×#41—31no—
167C22×C3×Q8—21no—
168C22×C3×Q8—31no—
169C22×C3×Q8C2×D311yescharacteristic, complemented
170C22×C3×Q8C2×D311yescharacteristic, complemented
171D3×#41—68no—
172C2×#239—31no—
173C2×#239—31no—
174C2×#239—33no—
175C2×#239—33no—
176C2×#239—33no—
177C2×#239—33no—
178C2×#239—31no—
179C2×#239—31no—
180C2×#239—33no—
181C2×#239—33no—
182C2×#239—61no—
183C2×#239—63no—
184C2×#239—63no—
185C2×#239—61no—
186C2×#239—68no—
187C2×#239—68no—
188C2×#239—68no—
189C2×#239—616no—
190C2×#239C2×D311yescharacteristic, complemented
191C2×D3×Q8C2×D311yescharacteristic, complemented
192C2×#237—33no—
193C2×D3×D4—33no—
194C2×D3×D4—33no—
195C2×D3×D4—33no—
196C2×#235—33no—
197C22×D12—33no—
198C22×D12—33no—
199C22×D12—33no—
200C22×D12—63no—
201C22×C4×D3—33no—
202C22×C4×D3—33no—
203C22×C4×D3—33no—
204C22×C4×D3—33no—
205C22×C4×D3—63no—
206C3×C4⋊Q8—33no—
207C3×#124—33no—
208C3×C22⋊Q8—33no—
209C3×C22⋊Q8—33no—
210C3×C22⋊Q8—33no—
211C3×#121—33no—
212C3×C4×Q8—31no—
213C3×C4×Q8—31no—
214C3×C4×D4—33no—
215C3×C4×D4—33no—
216#947—33no—
217#947C2×D313yescomplemented
218#946—33no—
219#946C2×D313yescomplemented
220#946C2×D313yescomplemented
221Q8×Dic3C2×D311yescharacteristic, complemented
222Q8×Dic3C2×D311yescharacteristic, complemented
223#944C2×D313yescomplemented
224#940—33no—
225#938—33no—
226#937—36no—
227D4×Dic3—31no—
228D4×Dic3—33no—
229#930—33no—
230#930—33no—
231#930C2×D313yescomplemented
232C4×#67—33no—
233C4×#67—33no—
234C4×#67C2×D313yes—
235C4×#67C2×D313yescomplemented
236#924C2×D313yescomplemented
237#897—33no—
238#895—33no—
239#895—33no—
240#895—33no—
241#895—36no—
242#895—36no—
243#894—36no—
244#894—36no—
245#894—36no—
246#893—33no—
247#893—36no—
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#882—36no—
259#882—36no—
260#882—36no—
261#67⋊C4—31no—
262#67⋊C4—33no—
263#67⋊C4—33no—
264#67⋊C4—36no—
265#67⋊C4—33no—
266D3×C22⋊C4—33no—
267D3×C22⋊C4—33no—
268D3×C22⋊C4—33no—
269D3×C22⋊C4—33no—
270#875—33no—
271#874—33no—
272C4×D12—33no—
273C4×D12—33no—
274C4×D12—33no—
275C4×D12—33no—
276C42×D3—33no—
277C42×D3—33no—
278C23×C32C2411yescharacteristic
279C22×C3⋊D3—26no—
280C22×C3⋊D3—26no—
281C22×C3⋊D3—43no—
282C22×C3⋊D3C2413yes—
283C22×C3⋊D3C2413yes—
284C22×C3×D3C2413yes—
285C22×C3×D3C2411yescharacteristic
286C2×D32—26no—
287C2×D32—26no—
288C2×D32—43no—
289C32×Q8—26no—
290C32×Q8C2×D414yescomplemented
291C2×C32×C4—26no—
292C2×C32×C4C2413yes—
293C2×C32×C4C2413yes—
294C2×C3⋊Dic3—22no—
295C2×C3⋊Dic3C2411yescharacteristic
296C2×C3⋊Dic3C2411yescharacteristic
297C4⋊(C3⋊D3)—212no—
298C4⋊(C3⋊D3)—26no—
299C4⋊(C3⋊D3)C2×D4112yescomplemented
300C4×C3⋊D3—26no—
301C4×C3⋊D3—26no—
302C4×C3⋊D3—26no—
303C4×C3⋊D3C2×D4112yescomplemented
304C3×#67—26no—
305C3×#67#4114yescomplemented
306C2×C3×Dic3C2411yescharacteristic
307C2×C3×Dic3C2413yes—
308C2×C3×Dic3C2413yes—
309C2×C3×Dic3C2411yescharacteristic
310C2×C3×Dic3C2413yes—
311C2×C3×Dic3C2411yescharacteristic
312C3×D12—26no—
313C3×C4×D3—26no—
314C3×C4×D3—26no—
315C3×Dic6—26no—
316#626—212no—
317#626—26no—
318#626—26no—
319#626—46no—
320#624—26no—
321#624—26no—
322#624—43no—
323D3×Dic3—26no—
324D3×Dic3—22no—
325C22×#41—91no—
326C22×#41—91no—
327#550—91no—
328D4×Q8—31no—
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—64no—
346C2×C3×Q8—28no—
347C2×C3×Q8—24no—
348C2×C3×Q8—24no—
349C2×C3×Q8—23no—
350C2×C3×Q8—21no—
351C2×C3×Q8—33no—
352C2×C3×Q8—64no—
353C2×C3×Q8C22×D313yes—
354C2×C3×Q8C22×D313yes—
355C2×C3×Q8C22×D311yescharacteristic
356C2×C3×Q8C22×D311yescharacteristic
357C2×C3×D4—31no—
358C2×C3×D4—33no—
359C2×C3×D4—33no—
360C22×C3×C4—23no—
361C22×C3×C4—33no—
362C22×C3×C4—33no—
363C22×C3×C4C22×D313yes—
364C22×C3×C4C22×D313yes—
365C2×#67—33no—
366C2×#67—33no—
367C2×#67—36no—
368C2×#67—36no—
369C2×#67C22×D313yes—
370C2×#67C22×D311yescharacteristic
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—33no—
375C22×Dic3—61no—
376#239—24no—
377#239—38no—
378#239—38no—
379#239—68no—
380#239—612no—
381#239—612no—
382#239—612no—
383#239—612no—
384#239—612no—
385#239—612no—
386#239—624no—
387#239—624no—
388#239—68no—
389#239—64no—
390#239—64no—
391D3×Q8—24no—
392#237—612no—
393D3×D4—612no—
394D3×D4—612no—
395D3×D4—612no—
396#235—612no—
397C2×D12—33no—
398C2×D12—33no—
399C2×D12—33no—
400C2×D12—33no—
401C2×D12—36no—
402C2×D12—33no—
403C2×D12—33no—
404C2×D12—36no—
405C2×D12—36no—
406C2×D12—36no—
407C2×D12—63no—
408C2×D12—66no—
409C2×D12—63no—
410C2×D12—612no—
411C2×D12—612no—
412C2×D12—612no—
413C2×D12—624no—
414C2×D12C22×D313yes—
415C2×C4×D3—33no—
416C2×C4×D3—33no—
417C2×C4×D3—31no—
418C2×C4×D3—33no—
419C2×C4×D3—33no—
420C2×C4×D3—33no—
421C2×C4×D3—33no—
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—33no—
429C2×C4×D3—33no—
430C2×C4×D3—33no—
431C2×C4×D3—63no—
432C2×C4×D3—63no—
433C2×C4×D3—63no—
434C2×C4×D3—63no—
435C2×C4×D3—612no—
436C2×C4×D3—612no—
437C2×C4×D3—612no—
438C2×C4×D3—612no—
439C2×C4×D3—624no—
440C2×C4×D3C22×D313yes—
441C2×C4×D3C22×D313yes—
442C2×Dic6C22×D313yes—
443C3×C4⋊C4—33no—
444C3×C4⋊C4—33no—
445C3×C4⋊C4—33no—
446C3×C4⋊C4—33no—
447C3×C4⋊C4—36no—
448C3×C22⋊C4—31no—
449C3×C22⋊C4—33no—
450C3×C22⋊C4—33no—
451C3×C22⋊C4—33no—
452C3×C22⋊C4—36no—
453C3×C42—33no—
454C3×C42—33no—
455#217—31no—
456#217—33no—
457#217C22×D311yescharacteristic
458#217C22×D313yes—
459(C2×D3)⋊C4—31no—
460(C2×D3)⋊C4—33no—
461(C2×D3)⋊C4—33no—
462(C2×D3)⋊C4—33no—
463(C2×D3)⋊C4—36no—
464(C2×D3)⋊C4—36no—
465(C2×D3)⋊C4—36no—
466(C2×D3)⋊C4—33no—
467(C2×D3)⋊C4—33no—
468(C2×D3)⋊C4—36no—
469(C2×D3)⋊C4C22×D313yes—
470(C2×D3)⋊C4C22×D313yes—
471(C2×D3)⋊C4C22×D316yes—
472C4⋊Dic3—31no—
473C4⋊Dic3—33no—
474C4⋊Dic3C22×D313yes—
475C4⋊Dic3C22×D313yes—
476Dic3⋊C4—31no—
477Dic3⋊C4—33no—
478Dic3⋊C4C22×D316yes—
479Dic3⋊C4C22×D313yes—
480Dic3⋊C4C22×D313yes—
481C4×Dic3—31no—
482C4×Dic3—31no—
483C4×Dic3—33no—
484C4×Dic3—33no—
485C4×Dic3C22×D313yes—
486C4×Dic3C22×D313yes—
487C22×C32—21no—
488C22×C32—21no—
489C22×C32C2×#4112yescomplemented
490C22×C32C2511yescharacteristic
491C2×C3⋊D3—23no—
492C2×C3⋊D3—23no—
493C2×C3⋊D3—23no—
494C2×C3⋊D3—23no—
495C2×C3⋊D3—23no—
496C2×C3⋊D3—412no—
497C2×C3⋊D3C22×D416yes—
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—23no—
506C32×C4C22×D416yes—
507C3⋊Dic3—21no—
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—91no—
522C2×#41—188no—
523C2×#41—188no—
524C22×Q8—31no—
525C22×Q8D3211yescharacteristic, complemented
526C22×D4—93no—
527C22×D4—93no—
528C22×D4—93no—
529C23×C4—93no—
530C23×C4—93no—
531C4⋊Q8—33no—
532#127—93no—
533#124—33no—
534#124—93no—
535#123—96no—
536#123—96no—
537C22⋊Q8—33no—
538C22⋊Q8—33no—
539C22⋊Q8—33no—
540C22⋊Q8—93no—
541#121—33no—
542#121—96no—
543#121—96no—
544#121—93no—
545#121—93no—
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—93no—
558C4×D4—93no—
559C4×D4—96no—
560C4×D4—91no—
561C4×D4—93no—
562#117—93no—
563C2×C4⋊C4—93no—
564C2×C22⋊C4—93no—
565C2×C22⋊C4—93no—
566C2×C42—93no—
567C23×C3—21no—
568C23×C3—31no—
569C23×C3—33no—
570C23×C3C23×D311yescharacteristic
571C23×C3C23×D311yescharacteristic
572C22×D3—33no—
573C22×D3—33no—
574C22×D3—33no—
575C22×D3—33no—
576C22×D3—63no—
577C22×D3—63no—
578C22×D3—66no—
579C22×D3—66no—
580C22×D3—66no—
581C22×D3—66no—
582C22×D3—66no—
583C22×D3—612no—
584C22×D3—66no—
585C22×D3—66no—
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—212no—
596C3×Q8—26no—
597C3×Q8—26no—
598C3×Q8—24no—
599C3×Q8—66no—
600C3×Q8D3×D414yescomplemented
601C3×Q8D3×D414yescomplemented
602C3×D4—34no—
603C3×D4—66no—
604C3×D4—66no—
605C2×C3×C4—212no—
606C2×C3×C4—26no—
607C2×C3×C4—26no—
608C2×C3×C4—23no—
609C2×C3×C4—23no—
610C2×C3×C4—31no—
611C2×C3×C4—33no—
612C2×C3×C4—31no—
613C2×C3×C4—33no—
614C2×C3×C4—31no—
615C2×C3×C4—33no—
616C2×C3×C4—66no—
617C2×C3×C4—66no—
618C2×C3×C4C23×D313yes—
619C2×C3×C4C23×D313yes—
620C2×C3×C4C23×D313yes—
621C2×C3×C4C23×D313yes—
622#67—26no—
623#67—612no—
624#67—66no—
625#67—66no—
626#67—126no—
627#67#23914yescomplemented
628C2×Dic3—31no—
629C2×Dic3—31no—
630C2×Dic3—31no—
631C2×Dic3—31no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—62no—
635C2×Dic3—66no—
636C2×Dic3—62no—
637C2×Dic3—62no—
638C2×Dic3—64no—
639C2×Dic3C23×D311yescharacteristic
640C2×Dic3C23×D313yes—
641C2×Dic3C23×D313yes—
642C2×Dic3C23×D313yes—
643C2×Dic3C23×D311yescharacteristic
644C2×Dic3C23×D311yescharacteristic
645D12—26no—
646D12—312no—
647D12—312no—
648D12—612no—
649D12—612no—
650D12—612no—
651D12—624no—
652D12—612no—
653D12—66no—
654D12—612no—
655D12—66no—
656D12—66no—
657D12—66no—
658D12—126no—
659C4×D3—26no—
660C4×D3—26no—
661C4×D3—312no—
662C4×D3—312no—
663C4×D3—612no—
664C4×D3—66no—
665C4×D3—66no—
666C4×D3—66no—
667C4×D3—66no—
668C4×D3—66no—
669C4×D3—62no—
670C4×D3—66no—
671C4×D3—66no—
672C4×D3—66no—
673C4×D3—612no—
674C4×D3—612no—
675C4×D3—612no—
676C4×D3—66no—
677C4×D3—66no—
678C4×D3—66no—
679C4×D3—123no—
680C4×D3—123no—
681Dic6—26no—
682C2×C32—22no—
683C2×C32C23×D411yescharacteristic
684C2×C32C22×#4111yescharacteristic
685C2×C32#58511yescharacteristic
686C3⋊D3—26no—
687C3⋊D3—43no—
688C3×D3—22no—
689C3×D3—43no—
690C24—93no—
691C24—93no—
692#41—64no—
693#41—98no—
694#41—1812no—
695#41—1812no—
696#41—1812no—
697#41—1812no—
698#41—184no—
699C2×Q8—24no—
700C2×Q8—33no—
701C2×Q8—64no—
702C2×Q8C2×D3213yes—
703C2×Q8C2×D3211yescharacteristic
704C2×D4—31no—
705C2×D4—33no—
706C2×D4—33no—
707C2×D4—93no—
708C2×D4—93no—
709C2×D4—96no—
710C2×D4—96no—
711C2×D4—93no—
712C2×D4—96no—
713C2×D4—93no—
714C2×D4—1812no—
715C2×D4—1812no—
716C2×D4—1812no—
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—91no—
726C22×C4—93no—
727C22×C4—93no—
728C22×C4—93no—
729C22×C4—1812no—
730C22×C4—1812no—
731C22×C4C2×D3213yes—
732C4⋊C4—33no—
733C4⋊C4—33no—
734C4⋊C4—33no—
735C4⋊C4—33no—
736C4⋊C4—36no—
737C4⋊C4—91no—
738C4⋊C4—93no—
739C22⋊C4—31no—
740C22⋊C4—33no—
741C22⋊C4—33no—
742C22⋊C4—33no—
743C22⋊C4—36no—
744C22⋊C4—93no—
745C22⋊C4—93no—
746C22⋊C4—96no—
747C22⋊C4—96no—
748C22⋊C4—91no—
749C22⋊C4—93no—
750C42—33no—
751C42—33no—
752C42—91no—
753C42—93no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—22no—
761C22×C3—21no—
762C22×C3—32no—
763C22×C3—61no—
764C22×C3—61no—
765C22×C3—63no—
766C22×C3—63no—
767C22×C3—63no—
768C22×C3C2×#23912yescomplemented
769C22×C3D3×#4112yescomplemented
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—66no—
780C2×D3—63no—
781C2×D3—63no—
782C2×D3—63no—
783C2×D3—63no—
784C2×D3—66no—
785C2×D3—63no—
786C2×D3—63no—
787C2×D3—63no—
788C2×D3—63no—
789C2×D3—63no—
790C2×D3—63no—
791C2×D3—123no—
792C2×D3—123no—
793C2×D3—123no—
794C2×D3—123no—
795C2×D3—1212no—
796C2×D3—1212no—
797C2×D3—1212no—
798C2×D3—1212no—
799C2×D3—1224no—
800C2×D3C2×#23912yescomplemented
801C3×C4—26no—
802C3×C4—23no—
803C3×C4—23no—
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—21no—
817Dic3—23no—
818Dic3—32no—
819Dic3—32no—
820Dic3—62no—
821Dic3—62no—
822Dic3—61no—
823Dic3—61no—
824Dic3C2×#23912yescomplemented
825C32D4×#4111yescharacteristic, complemented, Sylow
826C23—31no—
827C23—33no—
828C23—93no—
829C23—93no—
830C23—186no—
831C23—186no—
832C23—186no—
833C23—186no—
834C23—363no—
835C23—363no—
836C23C22×D3211yescharacteristic
837Q8—26no—
838Q8—66no—
839Q8#381114yescomplemented
840D4—34no—
841D4—66no—
842D4—66no—
843D4—912no—
844D4—1812no—
845D4—186no—
846D4—186no—
847D4—1812no—
848D4—186no—
849D4—366no—
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—91no—
862C2×C4—186no—
863C2×C4—186no—
864C2×C4—186no—
865C2×C4—186no—
866C2×C4—182no—
867C2×C4—186no—
868C2×C4—182no—
869C2×C4—186no—
870C2×C4—363no—
871C2×C4C22×D3213yes—
872C2×C4C22×D3213yes—
873C2×C3—24no—
874C2×C3—22no—
875C2×C3—22no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—62no—
880C2×C3—123no—
881C2×C3C22×D3×D411yescharacteristic
882C2×C3C22×D3×D411yescharacteristic
883C2×C3C22×#23911yescharacteristic
884C2×C3C2×D3×#4111yescharacteristic
885C2×C3#596811yescharacteristic
886C2×C3#596811yescharacteristic
887D3—22no—
888D3—43no—
889D3—66no—
890D3—66no—
891D3—126no—
892D3—126no—
893D3—123no—
894D3—123no—
895C22—21no—
896C22—21no—
897C22—32no—
898C22—61no—
899C22—61no—
900C22—63no—
901C22—63no—
902C22—63no—
903C22—96no—
904C22—183no—
905C22—183no—
906C22—183no—
907C22—183no—
908C22—183no—
909C22—3612no—
910C22—3612no—
911C22D3×#23912yescomplemented
912C22C23×D3211yescharacteristic
913C4—23no—
914C4—32no—
915C4—63no—
916C4—61no—
917C4—63no—
918C4—61no—
919C4—63no—
920C4—92no—
921C4—181no—
922C4C2×#381116yes—
923C3—21no—
924C3#8671011yescharacteristic, complemented
925C3D4×#23911yescharacteristic, complemented
926C2—22no—
927C2—62no—
928C2—123no—
929C2—186no—
930C2—363no—
931C2C2×D3×#23911yescharacteristic
932C2#1059668911yescharacteristic
933C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32D4×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3832C2semidirect
2. C2×D3×#239C2semidirect
3. C3×#5817C2semidirect
4. C3×Q8×#67C2semidirect
5. #10595431C2semidirect
6. #10595430C2semidirect
7. #10595410C2semidirect
8. #10595386C2semidirect
9. #10595363C2semidirect
10. #10595342C2semidirect
11. #10595341C2semidirect
12. #10595074C2semidirect
13. C4×#3811C2semidirect
14. #10595018C2semidirect
15. #10594922C2semidirect
18. C22×C32×Q8C22semidirect
21. C2×#3832C22semidirect
22. C2×#3832C22semidirect
23. C2×#3832C22semidirect
24. C22×C4⋊(C3⋊D3)C22semidirect
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×#947C22semidirect
35. C3×#946C22semidirect
36. C3×#946C22semidirect
37. C3×Q8×Dic3C22semidirect
38. C3×Q8×Dic3C22semidirect
39. C3×#944C22semidirect
40. C3×#930C22semidirect
42. C3×C4×#67C22semidirect
43. C3×#924C22semidirect
44. #63981C22semidirect
45. #63974C22semidirect
47. #67⋊Dic3C22semidirect
48. #63923C22semidirect
49. #63921C22semidirect
50. #63916C22semidirect
51. #63911C22semidirect
52. #63910C22semidirect
53. #63910C22semidirect
54. #63909C22semidirect
55. #63909C22semidirect
56. C4×#626C22semidirect
57. C4×#626C22semidirect
58. #63897C22semidirect
59. #63894C22semidirect
60. #63894C22semidirect
61. #63883C22semidirect
62. C4×#624C22semidirect
63. #63881C22semidirect
64. #63881C22semidirect
65. #63881C22semidirect
66. #63871C22semidirect
67. #63864C22semidirect
68. #63853C22semidirect
69. #63849C22semidirect
79. #5817D3semidirect
80. Q8×#67D3semidirect
111. #3832D4semidirect
169. C22×C3×Q8C2×D3semidirect
170. C22×C3×Q8C2×D3semidirect
190. C2×#239C2×D3semidirect
191. C2×D3×Q8C2×D3semidirect
217. #947C2×D3semidirect
219. #946C2×D3semidirect
220. #946C2×D3semidirect
221. Q8×Dic3C2×D3semidirect
222. Q8×Dic3C2×D3semidirect
223. #944C2×D3semidirect
231. #930C2×D3semidirect
235. C4×#67C2×D3semidirect
236. #924C2×D3semidirect
290. C32×Q8C2×D4semidirect
299. C4⋊(C3⋊D3)C2×D4semidirect
303. C4×C3⋊D3C2×D4semidirect
305. C3×#67#41semidirect
489. C22×C32C2×#41semidirect
503. C2×C3×D3C2×#41semidirect
514. C3×Dic3C2×#41semidirect
525. C22×Q8D32semidirect
600. C3×Q8D3×D4semidirect
601. C3×Q8D3×D4semidirect
627. #67#239semidirect
768. C22×C3C2×#239semidirect
769. C22×C3D3×#41semidirect
800. C2×D3C2×#239semidirect
824. Dic3C2×#239semidirect
825. C32D4×#41semidirect
839. Q8#3811semidirect
911. C22D3×#239semidirect
924. C3#86710semidirect
925. C3D4×#239semidirect

Maximal subgroups

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

subgroupindex
C22×#38322
C2×D3×#2392
C3×#58172
C3×Q8×#672
#105954312
#105954302
#105954102
#105953862
#105953632
#105953422
#105953412
#105950742
C4×#38112
#105950182
#105949222
D4×#2393
#867103