Finite Group Databasebeta

← #41×#626 #11902819

Subgroups — #41×#626 #11902819

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×C3×D3×#41C211yesmaximal, characteristic, complemented
3C3×Dic3×#41C211yesmaximal, characteristic, complemented
4#10595414C211yesmaximal, characteristic, complemented
5#10595410C211yesmaximal, characteristic, complemented
6Q8×#626C211yesmaximal, characteristic, complemented
7#10595342C211yesmaximal, characteristic, complemented
8#10595254C213yesmaximal, complemented
9#10595248C213yesmaximal, complemented
10#10595246C213yesmaximal, complemented
11D4×#626C213yesmaximal, complemented
12#10595034C213yesmaximal, complemented
13#10595029C213yesmaximal, complemented
14#10595023C213yesmaximal, complemented
15C2×C4×#626C213yesmaximal, complemented
16#41×#67—31nomaximal
17#41×D12—31nomaximal
18C2×C32×#41C2211yescharacteristic
19#41×C3⋊D3—28no—
20C2×#3832C2211yescharacteristic, complemented
21C2×Q8×C3⋊D3C2211yescharacteristic, complemented
22C2×#3830C2213yescomplemented
23C2×D4×C3⋊D3C2213yescomplemented
24C2×#3828C2213yescomplemented
25C22×C4×C3⋊D3C2213yescomplemented
26C3×D3×#41—28no—
27C2×C3×#239C2211yescharacteristic, complemented
28C2×C3×D3×Q8C2211yescharacteristic, complemented
29C2×C3×#237C2213yescomplemented
30C2×C3×D3×D4C2213yescomplemented
31C2×C3×#235C2213yescomplemented
32C22×C3×C4×D3C2213yescomplemented
33C22×#626C2213yes—
34C3×Q8×Dic3C2211yescharacteristic, complemented
35C3×Q8×Dic3C2211yescharacteristic, complemented
36C3×D4×Dic3C2213yescomplemented
37C3×D4×Dic3C2213yescomplemented
38C3×#926C2213yescomplemented
39C2×C3×C4×Dic3C2213yescomplemented
40#63981C2216yescomplemented
41#63978C2216yescomplemented
42#63978C2216yescomplemented
43#63977C2216yescomplemented
44#63966C2216yescomplemented
45C2×Dic3⋊Dic3C2213yescomplemented
46C2×#3722C2213yescomplemented
47#63962C2216yescomplemented
48C2×(C2×D3)⋊Dic3C2213yescomplemented
49#63916C2213yescomplemented
50#63916C2213yescomplemented
51#63911C2213yescomplemented
52#63909C2213yescomplemented
53#63909C2213yescomplemented
54C4×#626C2213yes—
55C4×#626C2211yescharacteristic
56C4×#626C2213yescomplemented
57C4×#626C2213yescomplemented
58C4×#626C2213yescomplemented
59C4×#626C2213yescomplemented
60C4×#626C2213yescomplemented
61C4×#626C2213yescomplemented
62C4×#626C2216yescomplemented
63#63871C2213yescomplemented
64#63871C2213yescomplemented
65#63866C2213yescomplemented
66#63864C2213yescomplemented
67#63860C2213yescomplemented
68#63857C2213yescomplemented
69#63857C2213yescomplemented
70C22×C3×#41—31no—
71C2×D3×#41—31no—
72C2×D3×#41—31no—
73C2×D3×#41—61no—
74C2×D3×#41D311yescharacteristic, complemented
75C3×C4×#41—31no—
76#5834—31no—
77#5832—33no—
78#5831—31no—
79#5829—33no—
80#5828—33no—
81Dic3×#41D311yescharacteristic, complemented
82#5824—33no—
83#5817—31no—
84Q8×#67—31no—
85#5806—33no—
86D4×#67—33no—
87#5791—33no—
88C2×C4×#67—33no—
89#5577—31no—
90#5576—31no—
91#5576—31no—
92Q8×D12—31no—
93#5555—33no—
94#5554—33no—
95#5554—33no—
96D4×D12—33no—
97#5524—33no—
98#5524—33no—
99#5477—33no—
100C2×C4×D12—33no—
101C23×C3⋊D3C2313yes—
102C23×C3×D3C2313yes—
103C32×#41D418yescomplemented
104C2×C32×Q8C2311yescharacteristic
105C2×C32×D4C2313yes—
106C22×C32×C4C2313yes—
107C2×#638C2316yes—
108C22×C3⋊Dic3C2313yes—
109#3832—24no—
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×#67C2316yes—
122C22×C3×Dic3C2313yes—
123C22×C3×Dic3C2313yes—
124C22×C3×Dic3C2313yes—
125C3×#239—24no—
126C3×D3×Q8—24no—
127C3×#237—212no—
128C3×D3×D4—212no—
129C3×#235—212no—
130C2×C3×D12C2313yes—
131C2×C3×C4×D3—212no—
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2313yes—
134C2×C3×C4×D3C2313yes—
135C2×C3×C4×D3C2313yes—
136C2×C3×Dic6C2313yes—
137C2×#626—212no—
138C2×#626C2313yes—
139C2×#626C2313yes—
140C2×#626C2313yes—
141C2×#626C2316yes—
142C2×#626C2311yescharacteristic
143C3×#217C2316yes—
144C3×C4⋊Dic3C2313yes—
145C3×C4⋊Dic3C2313yes—
146C3×C4×Dic3C2311yescharacteristic
147C3×C4×Dic3C2313yes—
148C3×C4×Dic3C2313yes—
149C3×C4×Dic3C2313yes—
150Dic3⋊Dic3C2313yes—
151Dic3⋊Dic3C2316yes—
152Dic3⋊Dic3C2313yes—
153Dic3⋊Dic3C2313yes—
154Dic3⋊Dic3C2311yescharacteristic
155#3722C2313yes—
156#3722C2316yes—
157#3722C2313yes—
158#3722C2311yescharacteristic
159#3722C2313yes—
160(C2×D3)⋊Dic3C2313yes—
161(C2×D3)⋊Dic3C2316yes—
162(C2×D3)⋊Dic3C2313yes—
163(C2×D3)⋊Dic3C2311yescharacteristic
164(C2×D3)⋊Dic3C2313yes—
165D4×#41—91noSylow
166C2×C3×#41—21no—
167C2×C3×#41—31no—
168C2×C3×#41—33no—
169C2×C3×#41—33no—
170C2×C3×#41—68no—
171C2×C3×#41C2×D311yescharacteristic
172C2×C3×#41C2×D311yescharacteristic
173C22×C3×Q8—31no—
174C22×C3×D4—33no—
175C23×C3×C4—33no—
176C22×#67—33no—
177D3×#41—28no—
178D3×#41—616no—
179D3×#41—68no—
180D3×#41—68no—
181C2×#239—31no—
182C2×#239—31no—
183C2×#239—61no—
184C2×#239C2×D311yescharacteristic, complemented
185C2×D3×Q8—31no—
186C2×D3×Q8—31no—
187C2×D3×Q8—61no—
188C2×D3×Q8C2×D311yescharacteristic, complemented
189C2×#237—33no—
190C2×#237—33no—
191C2×#237—63no—
192C2×#237C2×D313yescomplemented
193C2×D3×D4—33no—
194C2×D3×D4—33no—
195C2×D3×D4—63no—
196C2×D3×D4C2×D313yescomplemented
197C2×#235—33no—
198C2×#235—33no—
199C2×#235—63no—
200C2×#235C2×D313yescomplemented
201C22×D12—33no—
202C22×C4×D3—33no—
203C22×C4×D3—33no—
204C22×C4×D3—63no—
205C22×C4×D3C2×D313yescomplemented
206C3×C4×Q8—31no—
207C3×C4×Q8—31no—
208C3×C4×D4—33no—
209C3×C4×D4—33no—
210C3×#117—33no—
211C2×C3×C42—33no—
212#953—36no—
213C2×#217—33no—
214#947—33no—
215#946—33no—
216#946—33no—
217Q8×Dic3C2×D311yescharacteristic, complemented
218Q8×Dic3C2×D311yescharacteristic, complemented
219#944—33no—
220#940—33no—
221#939—36no—
222#939—36no—
223#938—33no—
224#938—33no—
225#937—36no—
226#936—33no—
227#935—36no—
228D4×Dic3C2×D313yescomplemented
229D4×Dic3C2×D313yescomplemented
230#930—36no—
231#930—36no—
232#930—33no—
233#930—33no—
234#929—36no—
235C4×#67—31no—
236C4×#67—33no—
237C4×#67—33no—
238C4×#67—33no—
239C4×#67—33no—
240C4×#67—33no—
241C4×#67—33no—
242C4×#67—33no—
243C4×#67—36no—
244C2×(C2×D3)⋊C4—33no—
245C2×(C2×D3)⋊C4—33no—
246C2×(C2×D3)⋊C4—33no—
247#926C2×D313yescomplemented
248C2×C4⋊Dic3—33no—
249#924—33no—
250#924—33no—
251C2×Dic3⋊C4—33no—
252C2×C4×Dic3C2×D313yescomplemented
253#897—33no—
254#897—33no—
255#897—33no—
256#897—33no—
257#895—33no—
258#895—33no—
259#895—33no—
260#895—33no—
261#886—36no—
262#886—36no—
263#882—36no—
264#882—36no—
265#875—33no—
266#875—33no—
267#874—33no—
268C4×D12—31no—
269C4×D12—33no—
270C4×D12—33no—
271C4×D12—33no—
272C4×D12—33no—
273C4×D12—33no—
274C4×D12—33no—
275C4×D12—33no—
276C4×D12—36no—
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×D3—26no—
285C22×C3×D3—26no—
286C22×C3×D3—43no—
287C22×C3×D3C2413yes—
288C22×C3×D3C2411yescharacteristic
289C32×Q8C2×D414yescomplemented
290C32×D4C2×D4112yescomplemented
291C2×C32×C4C2×D4112yescomplemented
292C2×C32×C4C2411yescharacteristic
293C2×C32×C4C2413yes—
294#638—212no—
295C2×C3⋊Dic3—26no—
296C2×C3⋊Dic3C2413yes—
297C2×C3⋊Dic3C2411yescharacteristic
298C4⋊(C3⋊D3)—26no—
299C4×C3⋊D3—22no—
300C4×C3⋊D3—26no—
301C4×C3⋊D3—26no—
302C4×C3⋊D3—26no—
303#634—26no—
304C3×#67—212no—
305C2×C3×Dic3—26no—
306C2×C3×Dic3—26no—
307C2×C3×Dic3—43no—
308C2×C3×Dic3C2411yescharacteristic
309C2×C3×Dic3C2413yes—
310C2×C3×Dic3C2413yes—
311C2×C3×Dic3C2413yes—
312C2×C3×Dic3C2411yescharacteristic
313C2×C3×Dic3C2411yescharacteristic
314C3×D12—26no—
315C3×C4×D3—22no—
316C3×C4×D3—26no—
317C3×C4×D3—26no—
318C3×C4×D3—26no—
319C3×Dic6—26no—
320#626—26no—
321#626—26no—
322#626—26no—
323#626—46no—
324#626#4114yesdirect product factor
325C22×#41—31no—
326C22×#41—91no—
327#550—91no—
328D4×Q8—91no—
329#548—91no—
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—31no—
339C2×C4×D4—93no—
340C24×C3—33no—
341C23×D3—33no—
342C23×D3—33no—
343C23×D3—63no—
344C23×D3C22×D313yes—
345C3×#41—28no—
346C3×#41—64no—
347C3×#41—612no—
348C3×#41—612no—
349C3×#41D1218yescomplemented
350C3×#41#6718yescomplemented
351C2×C3×Q8—21no—
352C2×C3×Q8—33no—
353C2×C3×Q8—64no—
354C2×C3×Q8C22×D311yescharacteristic
355C2×C3×Q8C22×D311yescharacteristic
356C2×C3×D4—23no—
357C2×C3×D4—36no—
358C2×C3×D4—33no—
359C2×C3×D4—612no—
360C2×C3×D4C22×D313yes—
361C2×C3×D4C22×D313yes—
362C22×C3×C4—23no—
363C22×C3×C4—33no—
364C22×C3×C4—33no—
365C22×C3×C4—33no—
366C22×C3×C4—33no—
367C22×C3×C4—33no—
368C22×C3×C4—31no—
369C22×C3×C4—33no—
370C22×C3×C4—612no—
371C22×C3×C4C22×D313yes—
372C22×C3×C4C22×D313yes—
373C2×#67—36no—
374C2×#67—36no—
375C2×#67—31no—
376C2×#67—33no—
377C2×#67—33no—
378C2×#67—33no—
379C2×#67—36no—
380C2×#67—66no—
381C2×#67—612no—
382C2×#67C22×D316yes—
383C22×Dic3—33no—
384C22×Dic3—33no—
385C22×Dic3—63no—
386C22×Dic3C22×D313yes—
387C22×Dic3C22×D313yes—
388C22×Dic3C22×D313yes—
389#239—24no—
390#239—68no—
391#239—64no—
392#239—64no—
393D3×Q8—24no—
394D3×Q8—68no—
395D3×Q8—64no—
396D3×Q8—64no—
397#237—212no—
398#237—624no—
399#237—612no—
400#237—612no—
401D3×D4—212no—
402D3×D4—624no—
403D3×D4—612no—
404D3×D4—612no—
405#235—212no—
406#235—624no—
407#235—612no—
408#235—612no—
409C2×D12—31no—
410C2×D12—33no—
411C2×D12—33no—
412C2×D12—33no—
413C2×D12—33no—
414C2×D12—33no—
415C2×D12—36no—
416C2×D12—63no—
417C2×D12—612no—
418C2×D12C22×D313yes—
419C2×C4×D3—212no—
420C2×C4×D3—31no—
421C2×C4×D3—33no—
422C2×C4×D3—33no—
423C2×C4×D3—33no—
424C2×C4×D3—31no—
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—624no—
433C2×C4×D3—612no—
434C2×C4×D3—612no—
435C2×C4×D3C22×D311yescharacteristic
436C2×C4×D3C22×D313yes—
437C2×C4×D3C22×D313yes—
438C2×C4×D3C22×D313yes—
439C2×Dic6—33no—
440C2×Dic6—33no—
441C2×Dic6—63no—
442C2×Dic6C22×D313yes—
443C3×C4⋊C4—33no—
444C3×C4⋊C4—33no—
445C3×C22⋊C4—36no—
446C3×C42—33no—
447C3×C42—31no—
448C3×C42—33no—
449C3×C42—33no—
450#217—33no—
451#217—36no—
452#217—31no—
453#217—33no—
454#217—33no—
455#217C22×D316yes—
456(C2×D3)⋊C4—31no—
457(C2×D3)⋊C4—33no—
458(C2×D3)⋊C4—33no—
459(C2×D3)⋊C4—33no—
460(C2×D3)⋊C4—36no—
461(C2×D3)⋊C4—31no—
462(C2×D3)⋊C4—33no—
463(C2×D3)⋊C4—33no—
464(C2×D3)⋊C4—33no—
465(C2×D3)⋊C4—36no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—33no—
468(C2×D3)⋊C4—33no—
469(C2×D3)⋊C4—33no—
470(C2×D3)⋊C4—36no—
471C4⋊Dic3—33no—
472C4⋊Dic3—36no—
473C4⋊Dic3—31no—
474C4⋊Dic3—33no—
475C4⋊Dic3—33no—
476C4⋊Dic3C22×D313yes—
477C4⋊Dic3C22×D313yes—
478Dic3⋊C4—31no—
479Dic3⋊C4—33no—
480Dic3⋊C4—33no—
481Dic3⋊C4—33no—
482Dic3⋊C4—36no—
483C4×Dic3C22×D311yescharacteristic
484C4×Dic3C22×D313yes—
485C4×Dic3C22×D313yes—
486C4×Dic3C22×D313yes—
487C22×C32—23no—
488C22×C32—23no—
489C22×C32C22×D416yes—
490C22×C32C2511yescharacteristic
491C2×C3⋊D3—21no—
492C2×C3⋊D3—21no—
493C2×C3⋊D3—23no—
494C2×C3⋊D3—23no—
495C2×C3⋊D3—23no—
496C2×C3⋊D3—412no—
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×D3—412no—
504C2×C3×D3C2×#4112yescomplemented
505C32×C4C22×D416yes—
506C32×C4C22×D412yes—
507C3⋊Dic3—23no—
508C3⋊Dic3—21no—
509C3×Dic3—23no—
510C3×Dic3—21no—
511C3×Dic3—23no—
512C3×Dic3—23no—
513C3×Dic3—21no—
514C3×Dic3C2×#4112yescomplemented
515C2×#41—31no—
516C2×#41—33no—
517C2×#41—33no—
518C2×#41—68no—
519C2×#41—91no—
520C2×#41—93no—
521C2×#41—93no—
522C2×#41—188no—
523C2×#41D3211yescharacteristic
524C22×Q8—31no—
525C22×Q8—91no—
526C22×D4—33no—
527C22×D4—93no—
528C22×D4—93no—
529C23×C4—33no—
530C23×C4—93no—
531C4⋊Q8—93no—
532#127—93no—
533#124—93no—
534#124—93no—
535#123—96no—
536#123—96no—
537C22⋊Q8—93no—
538C22⋊Q8—93no—
539C22⋊Q8—93no—
540C22⋊Q8—93no—
541#121—93no—
542#121—93no—
543#121—93no—
544#121—93no—
545#121—96no—
546#121—96no—
547#120—96no—
548#120—96no—
549C4×Q8—31no—
550C4×Q8—31no—
551C4×D4—33no—
552C4×D4—33no—
553C4×D4—91no—
554C4×D4—93no—
555C4×D4—93no—
556C4×D4—93no—
557C4×D4—93no—
558C4×D4—93no—
559C4×D4—93no—
560C4×D4—93no—
561C4×D4—96no—
562#117—33no—
563C2×C4⋊C4—93no—
564C2×C22⋊C4—93no—
565C2×C22⋊C4—93no—
566C2×C42—33no—
567C23×C3—23no—
568C23×C3—31no—
569C23×C3—33no—
570C23×C3—66no—
571C23×C3—66no—
572C23×C3—123no—
573C23×C3C23×D313yes—
574C23×C3C23×D313yes—
575C22×D3—26no—
576C22×D3—26no—
577C22×D3—31no—
578C22×D3—31no—
579C22×D3—33no—
580C22×D3—33no—
581C22×D3—43no—
582C22×D3—61no—
583C22×D3—63no—
584C22×D3—66no—
585C22×D3—66no—
586C22×D3—612no—
587C22×D3—66no—
588C22×D3—66no—
589C22×D3—126no—
590C22×D3—123no—
591C22×D3—123no—
592C22×D3—126no—
593C22×D3C23×D313yes—
594C22×D3C23×D311yescharacteristic
595C3×Q8—24no—
596C3×Q8—66no—
597C3×Q8C2×D1214yescomplemented
598C3×Q8C2×#6714yescomplemented
599C3×D4—212no—
600C3×D4—612no—
601C3×D4—66no—
602C3×D4C2×D12112yescomplemented
603C3×D4C2×#67112yescomplemented
604C2×C3×C4—23no—
605C2×C3×C4—21no—
606C2×C3×C4—212no—
607C2×C3×C4—31no—
608C2×C3×C4—31no—
609C2×C3×C4—33no—
610C2×C3×C4—33no—
611C2×C3×C4—33no—
612C2×C3×C4—31no—
613C2×C3×C4—66no—
614C2×C3×C4—66no—
615C2×C3×C4—62no—
616C2×C3×C4—66no—
617C2×C3×C4—66no—
618C2×C3×C4—66no—
619C2×C3×C4—123no—
620C2×C3×C4C2×D12112yescomplemented
621C2×C3×C4C2×#67112yescomplemented
622C2×C3×C4C23×D313yes—
623C2×C3×C4C23×D313yes—
624C2×C3×C4C23×D311yescharacteristic
625C2×C3×C4C23×D311yescharacteristic
626#67—212no—
627#67—34no—
628#67—66no—
629#67—66no—
630#67—624no—
631#67—612no—
632#67—612no—
633#67—66no—
634#67—126no—
635C2×Dic3—26no—
636C2×Dic3—26no—
637C2×Dic3—33no—
638C2×Dic3—31no—
639C2×Dic3—33no—
640C2×Dic3—31no—
641C2×Dic3—43no—
642C2×Dic3—63no—
643C2×Dic3—61no—
644C2×Dic3—612no—
645C2×Dic3—66no—
646C2×Dic3—66no—
647C2×Dic3C23×D311yescharacteristic
648C2×Dic3C23×D313yes—
649C2×Dic3C23×D313yes—
650C2×Dic3C23×D313yes—
651C2×Dic3C23×D311yescharacteristic
652C2×Dic3C23×D311yescharacteristic
653D12—26no—
654D12—34no—
655D12—612no—
656D12—66no—
657D12—66no—
658D12—66no—
659D12—66no—
660D12—66no—
661D12—126no—
662C4×D3—22no—
663C4×D3—26no—
664C4×D3—26no—
665C4×D3—26no—
666C4×D3—64no—
667C4×D3—612no—
668C4×D3—612no—
669C4×D3—612no—
670C4×D3—62no—
671C4×D3—66no—
672C4×D3—66no—
673C4×D3—66no—
674C4×D3—62no—
675C4×D3—66no—
676C4×D3—66no—
677C4×D3—66no—
678Dic6—26no—
679Dic6—612no—
680Dic6—66no—
681Dic6—66no—
682C2×C32—26no—
683C2×C32C23×D411yescharacteristic
684C2×C32C22×#4111yescharacteristic
685C2×C32#58511yescharacteristic
686C3⋊D3—22no—
687C3⋊D3—43no—
688C3×D3—22no—
689C3×D3—43no—
690C24—33no—
691C24—93no—
692#41—64no—
693#41—612no—
694#41—612no—
695#41—184no—
696#41—1812no—
697#41—1812no—
698#41#62618yesdirect product factor
699C2×Q8—33no—
700C2×Q8—64no—
701C2×Q8—93no—
702C2×Q8—184no—
703C2×Q8C2×D3211yescharacteristic
704C2×D4—36no—
705C2×D4—33no—
706C2×D4—612no—
707C2×D4—91no—
708C2×D4—93no—
709C2×D4—93no—
710C2×D4—93no—
711C2×D4—96no—
712C2×D4—96no—
713C2×D4—93no—
714C2×D4—1812no—
715C2×D4—1812no—
716C2×D4C2×D3213yes—
717C22×C4—33no—
718C22×C4—33no—
719C22×C4—33no—
720C22×C4—33no—
721C22×C4—33no—
722C22×C4—31no—
723C22×C4—33no—
724C22×C4—612no—
725C22×C4—93no—
726C22×C4—93no—
727C22×C4—93no—
728C22×C4—91no—
729C22×C4—93no—
730C22×C4—1812no—
731C22×C4C2×D3213yes—
732C4⋊C4—33no—
733C4⋊C4—33no—
734C4⋊C4—91no—
735C4⋊C4—93no—
736C4⋊C4—93no—
737C4⋊C4—93no—
738C4⋊C4—96no—
739C22⋊C4—36no—
740C22⋊C4—91no—
741C22⋊C4—93no—
742C22⋊C4—93no—
743C22⋊C4—93no—
744C22⋊C4—96no—
745C22⋊C4—91no—
746C22⋊C4—93no—
747C22⋊C4—93no—
748C22⋊C4—93no—
749C22⋊C4—96no—
750C42—33no—
751C42—33no—
752C42—31no—
753C42—33no—
754C22×C3—23no—
755C22×C3—23no—
756C22×C3—23no—
757C22×C3—23no—
758C22×C3—26no—
759C22×C3—21no—
760C22×C3—32no—
761C22×C3—43no—
762C22×C3—43no—
763C22×C3—61no—
764C22×C3—61no—
765C22×C3—63no—
766C22×C3—63no—
767C22×C3—63no—
768C22×C3—1212no—
769C22×C3C22×D1216yes—
770C22×C3C22×#6716yes—
771C22×C3C24×D311yescharacteristic
772C22×C3C24×D311yescharacteristic
773C2×D3—21no—
774C2×D3—21no—
775C2×D3—23no—
776C2×D3—23no—
777C2×D3—23no—
778C2×D3—32no—
779C2×D3—32no—
780C2×D3—412no—
781C2×D3—62no—
782C2×D3—62no—
783C2×D3—62no—
784C2×D3—61no—
785C2×D3—61no—
786C2×D3—61no—
787C2×D3—61no—
788C2×D3—66no—
789C2×D3—63no—
790C2×D3—63no—
791C2×D3—63no—
792C2×D3—63no—
793C2×D3—63no—
794C2×D3—63no—
795C2×D3—123no—
796C2×D3—123no—
797C2×D3—1212no—
798C2×D3—1212no—
799C2×D3—1224no—
800C2×D3D3×#4112yescomplemented
801C3×C4—26no—
802C3×C4—22no—
803C3×C4—32no—
804C3×C4—61no—
805C3×C4—63no—
806C3×C4—63no—
807C3×C4—63no—
808C3×C4—61no—
809C3×C4C22×D1216yes—
810C3×C4C22×D1212yes—
811C3×C4C22×#6716yes—
812C3×C4C22×#6712yes—
813Dic3—23no—
814Dic3—21no—
815Dic3—23no—
816Dic3—23no—
817Dic3—21no—
818Dic3—66no—
819Dic3—62no—
820Dic3—63no—
821Dic3—61no—
822Dic3—63no—
823Dic3—61no—
824Dic3D3×#4112yescomplemented
825C32D4×#4111yescharacteristic, complemented, Sylow
826C23—31no—
827C23—33no—
828C23—66no—
829C23—66no—
830C23—91no—
831C23—93no—
832C23—123no—
833C23—186no—
834C23—186no—
835C23—363no—
836C23C22×D3213yes—
837Q8—66no—
838Q8—186no—
839Q8C2×#62614yescomplemented
840D4—612no—
841D4—66no—
842D4—94no—
843D4—186no—
844D4—186no—
845D4—186no—
846D4—1812no—
847D4—186no—
848D4—366no—
849D4C2×#626112yescomplemented
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—33no—
853C2×C4—33no—
854C2×C4—31no—
855C2×C4—33no—
856C2×C4—66no—
857C2×C4—66no—
858C2×C4—62no—
859C2×C4—66no—
860C2×C4—66no—
861C2×C4—66no—
862C2×C4—91no—
863C2×C4—93no—
864C2×C4—123no—
865C2×C4—186no—
866C2×C4—182no—
867C2×C4—186no—
868C2×C4—186no—
869C2×C4—186no—
870C2×C4C2×#626112yescomplemented
871C2×C4C22×D3213yes—
872C2×C4C22×D3211yescharacteristic
873C2×C3—26no—
874C2×C3—26no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—46no—
879C2×C3—62no—
880C2×C3—123no—
881C2×C3C23×D1211yescharacteristic
882C2×C3C2×D3×#4111yescharacteristic
883C2×C3C2×D3×#4111yescharacteristic
884C2×C3#596411yescharacteristic
885C2×C3#596411yescharacteristic
886C2×C3C23×#6711yescharacteristic
887D3—22no—
888D3—43no—
889D3—64no—
890D3—62no—
891D3—62no—
892D3—126no—
893D3—123no—
894D3—123no—
895C22—23no—
896C22—23no—
897C22—32no—
898C22—61no—
899C22—61no—
900C22—63no—
901C22—63no—
902C22—63no—
903C22—92no—
904C22—1212no—
905C22—181no—
906C22—181no—
907C22—183no—
908C22—183no—
909C22—183no—
910C22—3612no—
911C22C22×#62616yes—
912C22C23×D3211yescharacteristic
913C4—32no—
914C4—63no—
915C4—61no—
916C4—63no—
917C4—61no—
918C4—63no—
919C4—181no—
920C4—183no—
921C4C22×#62612yes—
922C4C22×#62616yes—
923C3—21no—
924C3#41×D1211yescharacteristic, complemented
925C3#41×#6711yescharacteristic, complemented
926C2—26no—
927C2—62no—
928C2—123no—
929C2—182no—
930C2—363no—
931C2D32×#4111yescharacteristic
932C2#1059669511yescharacteristic
933C2C23×#62611yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32D4×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×C3⋊D3C2semidirect
2. C2×C3×D3×#41C2semidirect
3. C3×Dic3×#41C2semidirect
4. #10595414C2semidirect
5. #10595410C2semidirect
6. Q8×#626C2semidirect
7. #10595342C2semidirect
8. #10595254C2semidirect
9. #10595248C2semidirect
10. #10595246C2semidirect
11. D4×#626C2semidirect
12. #10595034C2semidirect
13. #10595029C2semidirect
14. #10595023C2semidirect
15. C2×C4×#626C2semidirect
20. C2×#3832C22semidirect
21. C2×Q8×C3⋊D3C22semidirect
22. C2×#3830C22semidirect
23. C2×D4×C3⋊D3C22semidirect
24. C2×#3828C22semidirect
25. C22×C4×C3⋊D3C22semidirect
27. C2×C3×#239C22semidirect
28. C2×C3×D3×Q8C22semidirect
29. C2×C3×#237C22semidirect
30. C2×C3×D3×D4C22semidirect
31. C2×C3×#235C22semidirect
32. C22×C3×C4×D3C22semidirect
34. C3×Q8×Dic3C22semidirect
35. C3×Q8×Dic3C22semidirect
36. C3×D4×Dic3C22semidirect
37. C3×D4×Dic3C22semidirect
38. C3×#926C22semidirect
39. C2×C3×C4×Dic3C22semidirect
40. #63981C22semidirect
41. #63978C22semidirect
42. #63978C22semidirect
43. #63977C22semidirect
44. #63966C22semidirect
45. C2×Dic3⋊Dic3C22semidirect
46. C2×#3722C22semidirect
47. #63962C22semidirect
48. C2×(C2×D3)⋊Dic3C22semidirect
49. #63916C22semidirect
50. #63916C22semidirect
51. #63911C22semidirect
52. #63909C22semidirect
53. #63909C22semidirect
56. C4×#626C22semidirect
57. C4×#626C22semidirect
58. C4×#626C22semidirect
59. C4×#626C22semidirect
60. C4×#626C22semidirect
61. C4×#626C22semidirect
62. C4×#626C22semidirect
63. #63871C22semidirect
64. #63871C22semidirect
65. #63866C22semidirect
66. #63864C22semidirect
67. #63860C22semidirect
68. #63857C22semidirect
69. #63857C22semidirect
74. C2×D3×#41D3semidirect
81. Dic3×#41D3semidirect
103. C32×#41D4semidirect
184. C2×#239C2×D3semidirect
188. C2×D3×Q8C2×D3semidirect
192. C2×#237C2×D3semidirect
196. C2×D3×D4C2×D3semidirect
200. C2×#235C2×D3semidirect
205. C22×C4×D3C2×D3semidirect
217. Q8×Dic3C2×D3semidirect
218. Q8×Dic3C2×D3semidirect
228. D4×Dic3C2×D3semidirect
229. D4×Dic3C2×D3semidirect
247. #926C2×D3semidirect
252. C2×C4×Dic3C2×D3semidirect
289. C32×Q8C2×D4semidirect
290. C32×D4C2×D4semidirect
291. C2×C32×C4C2×D4semidirect
324. #626#41direct (N × H)
349. C3×#41D12semidirect
350. C3×#41#67semidirect
497. C2×C3⋊D3C2×#41semidirect
504. C2×C3×D3C2×#41semidirect
514. C3×Dic3C2×#41semidirect
597. C3×Q8C2×D12semidirect
598. C3×Q8C2×#67semidirect
602. C3×D4C2×D12semidirect
603. C3×D4C2×#67semidirect
620. C2×C3×C4C2×D12semidirect
621. C2×C3×C4C2×#67semidirect
698. #41#626direct (N × H)
800. C2×D3D3×#41semidirect
824. Dic3D3×#41semidirect
825. C32D4×#41semidirect
839. Q8C2×#626semidirect
849. D4C2×#626semidirect
870. C2×C4C2×#626semidirect
924. C3#41×D12semidirect
925. C3#41×#67semidirect

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×C3×D3×#412
C3×Dic3×#412
#105954142
#105954102
Q8×#6262
#105953422
#105952542
#105952482
#105952462
D4×#6262
#105950342
#105950292
#105950232
C2×C4×#6262
#41×#673
#41×D123