Finite Group Databasebeta

← #11911162

Subgroups — #11911162

Order 1152.

2503 conjugacy classes of subgroups.

The subgroup lattice has 1375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64092C211yesmaximal, characteristic, complemented
2C3×#5494C211yesmaximal, characteristic, complemented
3C3×#5493C211yesmaximal, characteristic, complemented
4#10595526C212yesmaximal, complemented
5#10595494C212yesmaximal, complemented
6#10595081C211yesmaximal, characteristic, complemented
7#10595075C212yesmaximal, complemented
8#10594995C212yesmaximal, complemented
9#10594974C211yesmaximal, characteristic, complemented
10#10594930C211yesmaximal, characteristic, complemented
11#10594922C211yesmaximal, characteristic, complemented
12#10594304C212yesmaximal, complemented
13#10594281C212yesmaximal, complemented
14#10594263C212yesmaximal, complemented
15#10594237C212yesmaximal, complemented
16#10594233C212yesmaximal, complemented
17#10594221C212yesmaximal, complemented
18#10594163C212yesmaximal, complemented
19#10594127C212yesmaximal, complemented
20#86420—31nomaximal
21#86312—31nomaximal
22C22×#638C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×#67C2212yescomplemented
25C2×#3811C2212yescomplemented
26C2×D3×#67C2212yescomplemented
27C2×#3805C2212yescomplemented
28C2×#3802C2211yescharacteristic, complemented
29C2×#3796C2211yescharacteristic, complemented
30C2×C32×C22⋊C4C2211yescharacteristic, complemented
31C2×#3757C2211yescharacteristic, complemented
32C2×#3752C2211yescharacteristic, complemented
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C2×#3750C2211yescharacteristic, complemented
35#64092C2212yescomplemented
36#64092C2212yescomplemented
37#64092C2212yescomplemented
38#64092C2212yescomplemented
39C3×#953C2212yescomplemented
40C3×#930C2211yescharacteristic
41C3×#930C2212yescomplemented
42C3×#930C2211yescharacteristic, complemented
43C3×#930C2211yescharacteristic, complemented
44C3×C4×#67C2212yescomplemented
45C3×#924C2211yescharacteristic, complemented
46C3×#886C2212yescomplemented
47C3×#886C2212yescomplemented
48C3×#885C2212yescomplemented
49C3×#884C2212yescomplemented
50C3×#883C2212yescomplemented
51C3×#882C2212yescomplemented
52C3×#882C2212yescomplemented
53C3×#879C2212yescomplemented
54#63983C2212yes—
55#63981C2212yescomplemented
56#63980C2212yescomplemented
57#63980C2212yescomplemented
58#63979C2212yescomplemented
59#63978C2212yescomplemented
60#63977C2212yescomplemented
61#63976C2212yescomplemented
62#67⋊Dic3C2212yescomplemented
63#67⋊Dic3C2212yescomplemented
64Dic3×#67C2212yescomplemented
65#63971C2212yescomplemented
66#63970C2212yescomplemented
67#63970C2212yescomplemented
68#63969C2212yescomplemented
69D3×#217C2212yescomplemented
70#63964C2212yescomplemented
71#63962C2212yescomplemented
72#63959C2212yescomplemented
73#63958C2212yes—
74#63952C2212yescomplemented
75#63922C2212yescomplemented
76#63921C2212yescomplemented
77D3×(C2×D3)⋊C4C2212yescomplemented
78#63916C2211yescharacteristic, complemented
79#63916C2211yescharacteristic, complemented
80#63916C2211yescharacteristic, complemented
81#63912C2212yescomplemented
82#63908C2212yescomplemented
83#63906C2212yescomplemented
84#63900C2211yescharacteristic, complemented
85#63899C2212yescomplemented
86#63899C2212yescomplemented
87#63895C2212yescomplemented
88Dic3×D12C2212yescomplemented
89#63891C2212yescomplemented
90#63891C2212yescomplemented
91#63890C2212yescomplemented
92#63887C2212yescomplemented
93#63886C2212yescomplemented
94#63885C2212yescomplemented
95#63885C2212yescomplemented
96#63884C2212yescomplemented
97#63881C2212yescomplemented
98#63880C2212yescomplemented
99#63871C2211yescharacteristic, complemented
100#63869C2212yescomplemented
101#63861C2212yescomplemented
102#63861C2212yescomplemented
103#63858C2212yescomplemented
104#63853C2212yescomplemented
105#63852C2212yescomplemented
106#63849C2211yescharacteristic, complemented
107#63846C2212yescomplemented
108#63841C2212yescomplemented
109C3×#538—31no—
110C3×#534—31no—
111#5806—32no—
112D4×#67—32no—
113#5707—32no—
114#5704—32no—
115#5684—32no—
116#5676—32no—
117#5667—32no—
118#5666—32no—
119#5663—32no—
120#5660—32no—
121#5659—32no—
122#5658—32no—
123#5645—31no—
124#5627—31no—
125#5619—32no—
126#5618—32no—
127#5610—32no—
128#5606—31no—
129#5605—32no—
130D3×#121—31no—
131D3×#121—31no—
132#5602—31no—
133#5597—31no—
134#5597—31no—
135#5595—32no—
136#5593—32no—
137#5591—32no—
138#5591—32no—
139#5590—32no—
140#5589—32no—
141#5565—32no—
142#5554—32no—
143#5494D311yescharacteristic, complemented
144#5493D311yescharacteristic, complemented
145C2×#883—31no—
146C2×#883—31no—
147C2×#883—61no—
148C24×C32C2311yescharacteristic
149C23×C3⋊D3C2311yescharacteristic
150C23×C3×D3C2312yes—
151C22×D32C2312yes—
152C22×C32×C4C2311yescharacteristic
153C22×C32×C4C2311yescharacteristic
154C2×#638—42no—
155C2×#638C2312yes—
156C2×#638C2312yes—
157C22×C3⋊Dic3C2311yescharacteristic
158C22×C3⋊Dic3C2311yescharacteristic
159C22×C3⋊Dic3C2311yescharacteristic
160C2×C4×C3⋊D3—42no—
161C2×C4×C3⋊D3C2311yescharacteristic
162C2×C4×C3⋊D3C2311yescharacteristic
163C2×C4×C3⋊D3C2311yescharacteristic
164C2×C4×C3⋊D3C2311yescharacteristic
165C2×C3×#67—44no—
166C2×C3×#67C2312yes—
167C2×C3×#67C2312yes—
168C2×C3×#67C2312yes—
169C2×C3×#67C2312yes—
170C2×C3×#67C2312yes—
171C2×C3×#67C2312yes—
172C2×C3×#67C2312yes—
173C22×C3×Dic3C2312yes—
174C2×C3×D12C2311yescharacteristic
175C2×C3×D12C2311yescharacteristic
176C2×C3×D12C2312yes—
177C2×C3×D12C2311yescharacteristic
178C2×C3×C4×D3C2312yes—
179C2×C3×Dic6C2311yescharacteristic
180#3811—44no—
181D3×#67—44no—
182C2×#627C2312yes—
183C2×#626C2312yes—
184C2×#626C2312yes—
185C2×#626C2312yes—
186C2×#626C2312yes—
187C2×#625C2312yes—
188C2×#625C2312yes—
189C2×#625C2312yes—
190C2×#624C2312yes—
191#3805—44no—
192C2×D3×Dic3C2312yes—
193C2×D3×Dic3C2312yes—
194C2×D3×Dic3C2312yes—
195C2×D3×Dic3C2312yes—
196#3802—42no—
197#3796—42no—
198C32×C22⋊C4C2312yes—
199C32×C22⋊C4C2312yes—
200#3757C2312yes—
201#3757C2312yes—
202#3752C2312yes—
203#3752C2312yes—
204C4⋊(C3⋊Dic3)C2312yes—
205C4⋊(C3⋊Dic3)C2312yes—
206#3750C2312yes—
207#3750C2312yes—
208C3×#217C2312yes—
209C3×#217C2312yes—
210C3×#217C2312yes—
211C3×(C2×D3)⋊C4C2312yes—
212C3×(C2×D3)⋊C4C2312yes—
213C3×(C2×D3)⋊C4C2312yes—
214C3×(C2×D3)⋊C4C2312yes—
215C3×(C2×D3)⋊C4C2312yes—
216C3×(C2×D3)⋊C4C2312yes—
217C3×C4⋊Dic3C2311yescharacteristic
218C3×C4⋊Dic3C2311yescharacteristic
219C3×C4⋊Dic3C2311yescharacteristic
220C3×C4⋊Dic3C2312yes—
221C3×C4⋊Dic3C2311yescharacteristic
222C3×Dic3⋊C4C2312yes—
223C3×Dic3⋊C4C2312yes—
224C3×C4×Dic3C2312yes—
225#3724C2312yes—
226#3724C2312yes—
227Dic3⋊Dic3C2312yes—
228Dic3⋊Dic3C2312yes—
229Dic3⋊Dic3C2312yes—
230Dic3⋊Dic3C2312yes—
231#3722C2312yes—
232#3722C2312yes—
233(C2×D3)⋊Dic3C2312yes—
234(C2×D3)⋊Dic3C2312yes—
235(C2×D3)⋊Dic3C2312yes—
236(C2×D3)⋊Dic3C2312yes—
237(C2×D3)⋊Dic3C2312yes—
238(C2×D3)⋊Dic3C2312yes—
239(C2×D3)⋊Dic3C2312yes—
240(C2×D3)⋊Dic3C2312yes—
241Dic32C2312yes—
242Dic32C2312yes—
243#3534—91noSylow
244C22×C3×D4—32no—
245C22×#67—31no—
246C22×#67—31no—
247C22×#67—32no—
248C22×#67—61no—
249C22×#67C2×D312yescomplemented
250C2×#239—31no—
251C2×#237—32no—
252C2×#237—32no—
253C2×#237—31no—
254C2×D3×D4—32no—
255C2×D3×D4—32no—
256C2×D3×D4—32no—
257C2×D3×D4—31no—
258C2×D3×D4—31no—
259C22×C4×D3—31no—
260C22×C4×D3—31no—
261C22×C4×D3—61no—
262C3×#126—32no—
263C3×#124—32no—
264C3×#123—32no—
265C3×#123—32no—
266C3×#123—32no—
267C3×C22⋊Q8—31no—
268C3×#121—31no—
269C3×#121—31no—
270C3×#121—31no—
271C3×#121—32no—
272C3×#121—32no—
273C3×#120—32no—
274C3×#120—32no—
275C3×#120—32no—
276C3×C4×D4—32no—
277C2×C3×C22⋊C4—21no—
278C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
279C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
280#953—32no—
281#953—32no—
282#953C2×D312yescomplemented
283C2×#217—31no—
284C2×#217—31no—
285C2×#217—32no—
286C2×#217—61no—
287#946—32no—
288#946—31no—
289#940—32no—
290#940—32no—
291#939—32no—
292#939—32no—
293#939—32no—
294#939—32no—
295#939—32no—
296#939—32no—
297#939—32no—
298#939—32no—
299#939—32no—
300#939—32no—
301#939—32no—
302#938—32no—
303#938—32no—
304#938—32no—
305#938—32no—
306#938—31no—
307#938—31no—
308#938—31no—
309#937—32no—
310#937—32no—
311#937—32no—
312#937—32no—
313#937—32no—
314#936—32no—
315#935—32no—
316#935—32no—
317#935—32no—
318D4×Dic3—32no—
319D4×Dic3—32no—
320D4×Dic3—32no—
321D4×Dic3—32no—
322#930—32no—
323#930—32no—
324#930—32no—
325#930C2×D311yescharacteristic
326#930C2×D312yescomplemented
327#930C2×D311yescharacteristic, complemented
328#930C2×D311yescharacteristic, complemented
329C4×#67—32no—
330C4×#67—32no—
331C4×#67C2×D312yescomplemented
332C2×(C2×D3)⋊C4—31no—
333C2×(C2×D3)⋊C4—31no—
334C2×(C2×D3)⋊C4—32no—
335C2×(C2×D3)⋊C4—61no—
336#926—32no—
337C2×C4⋊Dic3—31no—
338C2×C4⋊Dic3—31no—
339C2×C4⋊Dic3—61no—
340#924—32no—
341#924C2×D311yescharacteristic, complemented
342C2×Dic3⋊C4—31no—
343C2×Dic3⋊C4—31no—
344C2×Dic3⋊C4—61no—
345#898—32no—
346#898—32no—
347#898—32no—
348#897—31no—
349#897—32no—
350#896—32no—
351#896—32no—
352#896—32no—
353#895—31no—
354#895—31no—
355#895—32no—
356#895—31no—
357#894—32no—
358#894—32no—
359#894—32no—
360#893—32no—
361#892—32no—
362#892—31no—
363#892—31no—
364D3×C4⋊C4—31no—
365D3×C4⋊C4—31no—
366#890—32no—
367#890—32no—
368#889—32no—
369#886—32no—
370#886—32no—
371#886—32no—
372#886—32no—
373#886C2×D312yescomplemented
374#886C2×D312yescomplemented
375#885—32no—
376#885—32no—
377#885C2×D312yescomplemented
378#884—32no—
379#884—32no—
380#884—32no—
381#884—32no—
382#884—32no—
383#884—32no—
384#884—32no—
385#884C2×D312yescomplemented
386#883—32no—
387#883—32no—
388#883—32no—
389#883—32no—
390#883—32no—
391#883—32no—
392#883—32no—
393#883—32no—
394#883—32no—
395#883—32no—
396#883—32no—
397#883—32no—
398#883—62no—
399#883—62no—
400#883—62no—
401#883—62no—
402#883C2×D312yescomplemented
403#882—32no—
404#882—32no—
405#882—32no—
406#882C2×D312yescomplemented
407#882C2×D312yescomplemented
408#67⋊C4—32no—
409#67⋊C4—32no—
410#67⋊C4—32no—
411#67⋊C4—32no—
412#67⋊C4—32no—
413D3×C22⋊C4—32no—
414D3×C22⋊C4—32no—
415D3×C22⋊C4—32no—
416D3×C22⋊C4—32no—
417#879—32no—
418#879—32no—
419#879—32no—
420#879C2×D312yescomplemented
421#878—32no—
422#878—32no—
423#878—32no—
424#878—32no—
425#875—32no—
426C4×D12—32no—
427C4×D12—32no—
428#870—32no—
429C23×C32—22no—
430C23×C32—41no—
431C23×C32—41no—
432C23×C32C2412yes—
433C23×C32C2411yescharacteristic
434C22×C3⋊D3—22no—
435C22×C3⋊D3—22no—
436C22×C3⋊D3—41no—
437C22×C3⋊D3C2411yescharacteristic
438C22×C3⋊D3C2411yescharacteristic
439C22×C3×D3—42no—
440C22×C3×D3—42no—
441C22×C3×D3—42no—
442C22×C3×D3C2412yes—
443C22×C3×D3C2412yes—
444C22×C3×D3C2412yes—
445C2×D32—24no—
446C2×D32—42no—
447C2×D32—42no—
448C2×C32×C4—41no—
449C2×C32×C4—41no—
450C2×C32×C4C2412yes—
451C2×C32×C4C2411yescharacteristic
452C2×C32×C4C2411yescharacteristic
453#638—24no—
454#638—42no—
455C2×C3⋊Dic3—22no—
456C2×C3⋊Dic3—41no—
457C2×C3⋊Dic3—41no—
458C2×C3⋊Dic3C2411yescharacteristic
459C2×C3⋊Dic3C2412yes—
460C2×C3⋊Dic3C2411yescharacteristic
461C2×C3⋊Dic3C2412yes—
462C4×C3⋊D3—22no—
463C4×C3⋊D3—22no—
464C4×C3⋊D3—41no—
465C4×C3⋊D3—41no—
466C3×#67—24no—
467C3×#67—24no—
468C3×#67—24no—
469C3×#67—42no—
470C3×#67—42no—
471C3×#67—42no—
472C3×#67—42no—
473C2×C3×Dic3—42no—
474C2×C3×Dic3C2412yes—
475C2×C3×Dic3C2412yes—
476C2×C3×Dic3C2412yes—
477C2×C3×Dic3C2412yes—
478C2×C3×Dic3C2412yes—
479C3×D12—41no—
480C3×D12—41no—
481C3×D12—41no—
482C3×D12—42no—
483C3×C4×D3—42no—
484C3×Dic6—41no—
485#627—42no—
486#626—24no—
487#626—42no—
488#626—42no—
489#626—42no—
490#625—42no—
491#625—42no—
492#625—42no—
493#624—42no—
494D3×Dic3—42no—
495D3×Dic3—42no—
496D3×Dic3—42no—
497D3×Dic3—42no—
498#562—92no—
499#560—92no—
500#553—92no—
501#551—92no—
502#546—92no—
503#546—92no—
504#546—92no—
505D42—92no—
506#540—92no—
507#539—91no—
508#539—92no—
509#538—31no—
510#538—92no—
511#537—91no—
512#534—31no—
513#534—92no—
514#525—91no—
515C2×#123—91no—
516C2×#121—91no—
517C24×C3—21no—
518C24×C3—32no—
519C24×C3C22×D311yescharacteristic
520C24×C3C22×D311yescharacteristic
521C23×D3—31no—
522C23×D3—31no—
523C23×D3—32no—
524C23×D3—32no—
525C23×D3—61no—
526C23×D3C22×D312yes—
527C2×C3×Q8—31no—
528C2×C3×D4—32no—
529C2×C3×D4—32no—
530C2×C3×D4—32no—
531C2×C3×D4—32no—
532C2×C3×D4—32no—
533C2×C3×D4—32no—
534C2×C3×D4—32no—
535C2×C3×D4—32no—
536C2×C3×D4—31no—
537C2×C3×D4—31no—
538C2×C3×D4—31no—
539C2×C3×D4—124no—
540C22×C3×C4—21no—
541C22×C3×C4—21no—
542C22×C3×C4—32no—
543C22×C3×C4—32no—
544C22×C3×C4C22×D311yescharacteristic
545C22×C3×C4C22×D311yescharacteristic
546C22×C3×C4C22×D311yescharacteristic
547C22×C3×C4C22×D311yescharacteristic
548C2×#67—32no—
549C2×#67—32no—
550C2×#67—32no—
551C2×#67—32no—
552C2×#67—32no—
553C2×#67—32no—
554C2×#67—32no—
555C2×#67—32no—
556C2×#67—32no—
557C2×#67—32no—
558C2×#67—32no—
559C2×#67—32no—
560C2×#67—32no—
561C2×#67—32no—
562C2×#67—44no—
563C2×#67—62no—
564C2×#67—62no—
565C2×#67—124no—
566C2×#67—122no—
567C2×#67—122no—
568C2×#67—124no—
569C2×#67C22×D312yes—
570C2×#67C22×D312yes—
571C2×#67C22×D312yes—
572C2×#67C22×D312yes—
573C2×#67C22×D312yes—
574C2×#67C22×D312yes—
575C2×#67C22×D312yes—
576C22×Dic3—31no—
577C22×Dic3—31no—
578C22×Dic3—31no—
579C22×Dic3—31no—
580C22×Dic3—31no—
581C22×Dic3—31no—
582C22×Dic3—32no—
583C22×Dic3—32no—
584C22×Dic3—32no—
585C22×Dic3—32no—
586C22×Dic3—61no—
587C22×Dic3—61no—
588C22×Dic3—61no—
589C22×Dic3C22×D312yes—
590#239—122no—
591#237—122no—
592#237—124no—
593#237—124no—
594D3×D4—122no—
595D3×D4—122no—
596D3×D4—124no—
597D3×D4—124no—
598D3×D4—124no—
599C2×D12—32no—
600C2×D12—32no—
601C2×D12—32no—
602C2×D12—32no—
603C2×D12C22×D312yes—
604C2×D12C22×D311yescharacteristic
605C2×D12C22×D311yescharacteristic
606C2×D12C22×D311yescharacteristic
607C2×C4×D3—31no—
608C2×C4×D3—31no—
609C2×C4×D3—31no—
610C2×C4×D3—31no—
611C2×C4×D3—32no—
612C2×C4×D3—32no—
613C2×C4×D3—32no—
614C2×C4×D3—32no—
615C2×C4×D3—31no—
616C2×C4×D3—31no—
617C2×C4×D3—31no—
618C2×C4×D3—31no—
619C2×C4×D3—32no—
620C2×C4×D3—32no—
621C2×C4×D3—61no—
622C2×C4×D3—61no—
623C2×C4×D3—61no—
624C2×C4×D3—61no—
625C2×C4×D3—122no—
626C2×C4×D3—122no—
627C2×C4×D3—124no—
628C2×C4×D3C22×D312yes—
629C2×Dic6—32no—
630C2×Dic6—32no—
631C2×Dic6C22×D311yescharacteristic
632C3×C4⋊C4—31no—
633C3×C4⋊C4—32no—
634C3×C4⋊C4—32no—
635C3×C4⋊C4—31no—
636C3×C4⋊C4—31no—
637C3×C4⋊C4—31no—
638C3×C4⋊C4—32no—
639C3×C22⋊C4—22no—
640C3×C22⋊C4—22no—
641C3×C22⋊C4—32no—
642C3×C22⋊C4—32no—
643C3×C22⋊C4—32no—
644C3×C22⋊C4—32no—
645C3×C22⋊C4—32no—
646C3×C22⋊C4—32no—
647C3×C22⋊C4—32no—
648C3×C22⋊C4—32no—
649C3×C22⋊C4—32no—
650C3×C22⋊C4C22×D312yes—
651C3×C22⋊C4C22×D312yes—
652C3×C22⋊C4C22×D312yes—
653C3×C22⋊C4C22×D312yes—
654C3×C42—32no—
655#217—32no—
656#217—32no—
657#217—32no—
658#217—32no—
659#217—32no—
660#217—32no—
661#217—32no—
662#217—32no—
663#217—32no—
664#217—32no—
665#217—32no—
666#217—32no—
667#217—62no—
668#217—62no—
669#217C22×D312yes—
670#217C22×D312yes—
671#217C22×D312yes—
672(C2×D3)⋊C4—32no—
673(C2×D3)⋊C4—32no—
674(C2×D3)⋊C4—32no—
675(C2×D3)⋊C4—32no—
676(C2×D3)⋊C4—32no—
677(C2×D3)⋊C4—32no—
678(C2×D3)⋊C4—32no—
679(C2×D3)⋊C4—32no—
680(C2×D3)⋊C4—32no—
681(C2×D3)⋊C4—32no—
682(C2×D3)⋊C4—32no—
683(C2×D3)⋊C4—32no—
684(C2×D3)⋊C4—32no—
685(C2×D3)⋊C4—32no—
686(C2×D3)⋊C4—32no—
687(C2×D3)⋊C4—32no—
688(C2×D3)⋊C4—62no—
689(C2×D3)⋊C4—62no—
690(C2×D3)⋊C4C22×D312yes—
691(C2×D3)⋊C4C22×D312yes—
692(C2×D3)⋊C4C22×D312yes—
693(C2×D3)⋊C4C22×D312yes—
694(C2×D3)⋊C4C22×D312yes—
695(C2×D3)⋊C4C22×D312yes—
696C4⋊Dic3—32no—
697C4⋊Dic3—32no—
698C4⋊Dic3—32no—
699C4⋊Dic3—32no—
700C4⋊Dic3—32no—
701C4⋊Dic3—32no—
702C4⋊Dic3—32no—
703C4⋊Dic3—32no—
704C4⋊Dic3—62no—
705C4⋊Dic3—62no—
706C4⋊Dic3C22×D312yes—
707C4⋊Dic3C22×D311yescharacteristic
708C4⋊Dic3C22×D311yescharacteristic
709C4⋊Dic3C22×D311yescharacteristic
710C4⋊Dic3C22×D311yescharacteristic
711Dic3⋊C4—32no—
712Dic3⋊C4—32no—
713Dic3⋊C4—32no—
714Dic3⋊C4—32no—
715Dic3⋊C4—32no—
716Dic3⋊C4—32no—
717Dic3⋊C4—32no—
718Dic3⋊C4—32no—
719Dic3⋊C4—32no—
720Dic3⋊C4—32no—
721Dic3⋊C4—32no—
722Dic3⋊C4—32no—
723Dic3⋊C4—62no—
724Dic3⋊C4—62no—
725Dic3⋊C4C22×D312yes—
726Dic3⋊C4C22×D312yes—
727C4×Dic3—32no—
728C4×Dic3—32no—
729C4×Dic3—32no—
730C4×Dic3—32no—
731C4×Dic3C22×D312yes—
732C22×C32—21no—
733C22×C32—21no—
734C22×C32—22no—
735C22×C32—22no—
736C22×C32—22no—
737C22×C32—82no—
738C22×C32H(5,𝔽2)12yes—
739C22×C32C2511yescharacteristic
740C2×C3⋊D3—21no—
741C2×C3⋊D3—21no—
742C2×C3⋊D3—21no—
743C2×C3⋊D3—21no—
744C2×C3⋊D3—21no—
745C2×C3⋊D3—44no—
746C2×C3⋊D3H(5,𝔽2)12yes—
747C2×C3×D3—22no—
748C2×C3×D3—22no—
749C2×C3×D3—22no—
750C2×C3×D3—22no—
751C2×C3×D3—22no—
752C2×C3×D3—22no—
753C2×C3×D3—22no—
754C2×C3×D3—22no—
755C2×C3×D3—22no—
756C2×C3×D3—84no—
757D32—84no—
758C32×C4—21no—
759C32×C4—21no—
760C32×C4—22no—
761C3⋊Dic3—22no—
762C3⋊Dic3—21no—
763C3⋊Dic3—22no—
764C3⋊Dic3—21no—
765C3×Dic3—22no—
766C3×Dic3—22no—
767C3×Dic3—22no—
768C3×Dic3—22no—
769C3×Dic3—22no—
770C2×#41—92no—
771C2×#41—91no—
772C22×D4—32no—
773C22×D4—91no—
774C22×D4—92no—
775C22×D4—92no—
776C22×D4—91no—
777C23×C4—91no—
778#127—92no—
779#126—32no—
780#126—92no—
781#126—92no—
782#126—92no—
783#125—92no—
784#125—92no—
785#124—32no—
786#124—92no—
787#124—92no—
788#123—32no—
789#123—32no—
790#123—32no—
791#123—92no—
792#123—92no—
793#123—92no—
794#123—92no—
795#123—92no—
796#123—92no—
797#123—92no—
798#123—92no—
799#123—92no—
800#123—92no—
801#123—92no—
802C22⋊Q8—31no—
803C22⋊Q8—92no—
804C22⋊Q8—92no—
805C22⋊Q8—92no—
806C22⋊Q8—92no—
807C22⋊Q8—92no—
808C22⋊Q8—91no—
809#121—31no—
810#121—31no—
811#121—31no—
812#121—32no—
813#121—32no—
814#121—92no—
815#121—92no—
816#121—92no—
817#121—92no—
818#121—92no—
819#121—92no—
820#121—91no—
821#121—91no—
822#121—91no—
823#121—92no—
824#121—92no—
825#121—92no—
826#121—92no—
827#121—92no—
828#121—92no—
829#121—92no—
830#120—32no—
831#120—32no—
832#120—32no—
833#120—92no—
834#120—92no—
835#120—92no—
836#120—92no—
837#120—92no—
838C4×D4—32no—
839C4×D4—92no—
840C4×D4—92no—
841C4×D4—92no—
842C4×D4—92no—
843C4×D4—92no—
844C4×D4—92no—
845C4×D4—92no—
846#117—91no—
847#117—92no—
848C2×C4⋊C4—91no—
849C2×C4⋊C4—91no—
850C2×C4⋊C4—91no—
851C2×C22⋊C4—92no—
852C2×C22⋊C4—92no—
853C2×C22⋊C4—92no—
854C2×C22⋊C4—91no—
855C2×C22⋊C4—91no—
856C2×C22⋊C4D3211yescharacteristic, complemented
857C23×C3—22no—
858C23×C3—22no—
859C23×C3—21no—
860C23×C3—22no—
861C23×C3—32no—
862C23×C3—32no—
863C23×C3—32no—
864C23×C3—42no—
865C23×C3—41no—
866C23×C3—41no—
867C23×C3—41no—
868C23×C3—41no—
869C23×C3—42no—
870C23×C3—42no—
871C23×C3—122no—
872C23×C3—122no—
873C23×C3—122no—
874C23×C3C23×D312yes—
875C23×C3C23×D312yes—
876C23×C3C23×D311yescharacteristic
877C23×C3C23×D311yescharacteristic
878C22×D3—31no—
879C22×D3—31no—
880C22×D3—31no—
881C22×D3—31no—
882C22×D3—42no—
883C22×D3—42no—
884C22×D3—42no—
885C22×D3—61no—
886C22×D3—61no—
887C22×D3—64no—
888C22×D3—64no—
889C22×D3—62no—
890C22×D3—62no—
891C22×D3—64no—
892C22×D3—62no—
893C22×D3—62no—
894C22×D3—122no—
895C22×D3—122no—
896C22×D3—122no—
897C22×D3—122no—
898C22×D3—122no—
899C22×D3—121no—
900C22×D3—121no—
901C22×D3—122no—
902C22×D3C23×D312yes—
903C22×D3C23×D312yes—
904C22×D3C23×D312yes—
905C3×Q8—121no—
906C3×D4—64no—
907C3×D4—64no—
908C3×D4—64no—
909C3×D4—121no—
910C3×D4—121no—
911C3×D4—121no—
912C3×D4—122no—
913C3×D4—122no—
914C3×D4—122no—
915C3×D4—122no—
916C3×D4—122no—
917C2×C3×C4—21no—
918C2×C3×C4—21no—
919C2×C3×C4—22no—
920C2×C3×C4—32no—
921C2×C3×C4—32no—
922C2×C3×C4—32no—
923C2×C3×C4—32no—
924C2×C3×C4—32no—
925C2×C3×C4—41no—
926C2×C3×C4—41no—
927C2×C3×C4—41no—
928C2×C3×C4—41no—
929C2×C3×C4—42no—
930C2×C3×C4—42no—
931C2×C3×C4—122no—
932C2×C3×C4—122no—
933C2×C3×C4C23×D312yes—
934C2×C3×C4C23×D311yescharacteristic
935C2×C3×C4C23×D311yescharacteristic
936C2×C3×C4C23×D311yescharacteristic
937C2×C3×C4C23×D311yescharacteristic
938C2×C3×C4C23×D312yes—
939#67—24no—
940#67—24no—
941#67—24no—
942#67—42no—
943#67—42no—
944#67—42no—
945#67—42no—
946#67—64no—
947#67—64no—
948#67—64no—
949#67—124no—
950#67—122no—
951#67—122no—
952#67—122no—
953#67—122no—
954#67—122no—
955#67—122no—
956#67—122no—
957#67—122no—
958#67—122no—
959#67—122no—
960#67—122no—
961#67—124no—
962C2×Dic3—31no—
963C2×Dic3—31no—
964C2×Dic3—32no—
965C2×Dic3—32no—
966C2×Dic3—31no—
967C2×Dic3—32no—
968C2×Dic3—31no—
969C2×Dic3—32no—
970C2×Dic3—42no—
971C2×Dic3—62no—
972C2×Dic3—62no—
973C2×Dic3—61no—
974C2×Dic3—61no—
975C2×Dic3—62no—
976C2×Dic3—62no—
977C2×Dic3—122no—
978C2×Dic3—122no—
979C2×Dic3—122no—
980C2×Dic3—122no—
981C2×Dic3—122no—
982C2×Dic3—121no—
983C2×Dic3—121no—
984C2×Dic3—121no—
985C2×Dic3—121no—
986C2×Dic3—122no—
987C2×Dic3—122no—
988C2×Dic3C23×D312yes—
989C2×Dic3C23×D312yes—
990C2×Dic3C23×D312yes—
991C2×Dic3C23×D312yes—
992C2×Dic3C23×D312yes—
993D12—42no—
994D12—41no—
995D12—41no—
996D12—41no—
997D12—64no—
998D12—122no—
999D12—122no—
1000D12—122no—
1001C4×D3—42no—
1002C4×D3—62no—
1003C4×D3—62no—
1004C4×D3—62no—
1005C4×D3—62no—
1006C4×D3—122no—
1007C4×D3—122no—
1008C4×D3—122no—
1009C4×D3—122no—
1010C4×D3—121no—
1011C4×D3—121no—
1012C4×D3—121no—
1013C4×D3—121no—
1014C4×D3—122no—
1015C4×D3—122no—
1016C4×D3—122no—
1017C4×D3—122no—
1018C4×D3—122no—
1019C4×D3—122no—
1020Dic6—41no—
1021Dic6—122no—
1022Dic6—122no—
1023C2×C32—22no—
1024C2×C32—42no—
1025C2×C32C2×H(5,𝔽2)11yescharacteristic
1026C2×C32C2×H(5,𝔽2)11yescharacteristic
1027C2×C32#58511yescharacteristic
1028C3⋊D3—22no—
1029C3⋊D3—41no—
1030C3×D3—42no—
1031C3×D3—42no—
1032C3×D3—42no—
1033C24—32no—
1034C24—92no—
1035C24—91no—
1036C24C2×D3211yescharacteristic
1037#41—364no—
1038#41—362no—
1039C2×Q8—31no—
1040C2×Q8—92no—
1041C2×D4—32no—
1042C2×D4—32no—
1043C2×D4—32no—
1044C2×D4—32no—
1045C2×D4—32no—
1046C2×D4—32no—
1047C2×D4—32no—
1048C2×D4—32no—
1049C2×D4—31no—
1050C2×D4—31no—
1051C2×D4—31no—
1052C2×D4—92no—
1053C2×D4—92no—
1054C2×D4—92no—
1055C2×D4—92no—
1056C2×D4—92no—
1057C2×D4—92no—
1058C2×D4—92no—
1059C2×D4—92no—
1060C2×D4—92no—
1061C2×D4—124no—
1062C2×D4—362no—
1063C2×D4—364no—
1064C2×D4—364no—
1065C2×D4—362no—
1066C22×C4—32no—
1067C22×C4—32no—
1068C22×C4—92no—
1069C22×C4—92no—
1070C22×C4—92no—
1071C22×C4—92no—
1072C22×C4—92no—
1073C22×C4—91no—
1074C22×C4—91no—
1075C22×C4—91no—
1076C22×C4—91no—
1077C22×C4—91no—
1078C22×C4—91no—
1079C22×C4—91no—
1080C22×C4—362no—
1081C22×C4C2×D3211yescharacteristic
1082C22×C4C2×D3211yescharacteristic
1083C4⋊C4—31no—
1084C4⋊C4—31no—
1085C4⋊C4—31no—
1086C4⋊C4—32no—
1087C4⋊C4—31no—
1088C4⋊C4—32no—
1089C4⋊C4—32no—
1090C4⋊C4—92no—
1091C4⋊C4—92no—
1092C4⋊C4—92no—
1093C4⋊C4—92no—
1094C4⋊C4—92no—
1095C4⋊C4—92no—
1096C4⋊C4—92no—
1097C4⋊C4—92no—
1098C4⋊C4—92no—
1099C4⋊C4—92no—
1100C22⋊C4—32no—
1101C22⋊C4—32no—
1102C22⋊C4—32no—
1103C22⋊C4—32no—
1104C22⋊C4—32no—
1105C22⋊C4—32no—
1106C22⋊C4—32no—
1107C22⋊C4—32no—
1108C22⋊C4—32no—
1109C22⋊C4—92no—
1110C22⋊C4—92no—
1111C22⋊C4—92no—
1112C22⋊C4—92no—
1113C22⋊C4—92no—
1114C22⋊C4—92no—
1115C22⋊C4—92no—
1116C22⋊C4—92no—
1117C22⋊C4—92no—
1118C22⋊C4—92no—
1119C22⋊C4—92no—
1120C22⋊C4—92no—
1121C22⋊C4—92no—
1122C22⋊C4—92no—
1123C22⋊C4C2×D3212yes—
1124C22⋊C4C2×D3212yes—
1125C42—32no—
1126C42—92no—
1127C42—92no—
1128C22×C3—22no—
1129C22×C3—22no—
1130C22×C3—21no—
1131C22×C3—21no—
1132C22×C3—21no—
1133C22×C3—21no—
1134C22×C3—22no—
1135C22×C3—22no—
1136C22×C3—22no—
1137C22×C3—22no—
1138C22×C3—22no—
1139C22×C3—22no—
1140C22×C3—22no—
1141C22×C3—21no—
1142C22×C3—42no—
1143C22×C3—42no—
1144C22×C3—42no—
1145C22×C3—62no—
1146C22×C3—62no—
1147C22×C3—62no—
1148C22×C3—62no—
1149C22×C3—62no—
1150C22×C3—62no—
1151C22×C3—62no—
1152C22×C3—62no—
1153C22×C3—62no—
1154C22×C3—82no—
1155C22×C3—82no—
1156C22×C3—84no—
1157C22×C3—244no—
1158C22×C3#100412yes—
1159C22×C3#100912yes—
1160C22×C3C24×D311yescharacteristic
1161C22×C3C24×D311yescharacteristic
1162C2×D3—22no—
1163C2×D3—22no—
1164C2×D3—22no—
1165C2×D3—22no—
1166C2×D3—22no—
1167C2×D3—22no—
1168C2×D3—22no—
1169C2×D3—22no—
1170C2×D3—22no—
1171C2×D3—32no—
1172C2×D3—32no—
1173C2×D3—62no—
1174C2×D3—61no—
1175C2×D3—61no—
1176C2×D3—61no—
1177C2×D3—61no—
1178C2×D3—62no—
1179C2×D3—61no—
1180C2×D3—61no—
1181C2×D3—61no—
1182C2×D3—61no—
1183C2×D3—61no—
1184C2×D3—61no—
1185C2×D3—84no—
1186C2×D3—121no—
1187C2×D3—121no—
1188C2×D3—121no—
1189C2×D3—121no—
1190C2×D3—124no—
1191C2×D3—124no—
1192C2×D3—128no—
1193C2×D3—244no—
1194C2×D3—244no—
1195C3×C4—21no—
1196C3×C4—21no—
1197C3×C4—21no—
1198C3×C4—21no—
1199C3×C4—22no—
1200C3×C4—22no—
1201C3×C4—41no—
1202C3×C4—41no—
1203C3×C4—42no—
1204C3×C4—62no—
1205C3×C4—62no—
1206C3×C4—62no—
1207C3×C4—62no—
1208C3×C4—62no—
1209Dic3—22no—
1210Dic3—22no—
1211Dic3—22no—
1212Dic3—22no—
1213Dic3—22no—
1214Dic3—62no—
1215Dic3—62no—
1216Dic3—61no—
1217Dic3—61no—
1218Dic3—61no—
1219Dic3—61no—
1220Dic3—62no—
1221Dic3—62no—
1222Dic3—121no—
1223Dic3—121no—
1224Dic3—122no—
1225Dic3—122no—
1226C32#353411yescharacteristic, complemented, Sylow
1227C23—22no—
1228C23—32no—
1229C23—32no—
1230C23—32no—
1231C23—41no—
1232C23—41no—
1233C23—91no—
1234C23—91no—
1235C23—122no—
1236C23—122no—
1237C23—122no—
1238C23—182no—
1239C23—184no—
1240C23—182no—
1241C23—361no—
1242C23—362no—
1243C23—362no—
1244C23C22×D3212yes—
1245C23C22×D3211yescharacteristic
1246Q8—121no—
1247Q8—362no—
1248D4—64no—
1249D4—64no—
1250D4—64no—
1251D4—121no—
1252D4—121no—
1253D4—121no—
1254D4—122no—
1255D4—122no—
1256D4—122no—
1257D4—122no—
1258D4—122no—
1259D4—184no—
1260D4—184no—
1261D4—362no—
1262D4—362no—
1263D4—362no—
1264D4—362no—
1265D4—362no—
1266D4—362no—
1267D4—362no—
1268C2×C4—32no—
1269C2×C4—32no—
1270C2×C4—32no—
1271C2×C4—32no—
1272C2×C4—32no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—91no—
1276C2×C4—92no—
1277C2×C4—92no—
1278C2×C4—91no—
1279C2×C4—122no—
1280C2×C4—122no—
1281C2×C4—182no—
1282C2×C4—182no—
1283C2×C4—182no—
1284C2×C4—361no—
1285C2×C4—361no—
1286C2×C4—362no—
1287C2×C4—362no—
1288C2×C4—362no—
1289C2×C4—362no—
1290C2×C4—362no—
1291C2×C4—361no—
1292C2×C4—361no—
1293C2×C4C22×D3212yes—
1294C2×C4C22×D3211yescharacteristic
1295C2×C4C22×D3211yescharacteristic
1296C2×C3—24no—
1297C2×C3—22no—
1298C2×C3—22no—
1299C2×C3—21no—
1300C2×C3—21no—
1301C2×C3—21no—
1302C2×C3—42no—
1303C2×C3—42no—
1304C2×C3—82no—
1305C2×C3—122no—
1306C2×C3—122no—
1307C2×C3—122no—
1308C2×C3C2×#100411yescharacteristic
1309C2×C3C2×#100911yescharacteristic
1310C2×C3D3×H(5,𝔽2)11yescharacteristic
1311C2×C3D3×H(5,𝔽2)11yescharacteristic
1312C2×C3#596611yescharacteristic
1313C2×C3#596611yescharacteristic
1314D3—42no—
1315D3—42no—
1316D3—42no—
1317D3—62no—
1318D3—62no—
1319D3—122no—
1320D3—122no—
1321D3—121no—
1322D3—121no—
1323C22—21no—
1324C22—21no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—62no—
1329C22—62no—
1330C22—62no—
1331C22—62no—
1332C22—62no—
1333C22—62no—
1334C22—62no—
1335C22—62no—
1336C22—62no—
1337C22—82no—
1338C22—92no—
1339C22—181no—
1340C22—181no—
1341C22—181no—
1342C22—181no—
1343C22—181no—
1344C22—244no—
1345C22—364no—
1346C22—724no—
1347C22#6430712yes—
1348C22C23×D3211yescharacteristic
1349C4—21no—
1350C4—21no—
1351C4—22no—
1352C4—62no—
1353C4—62no—
1354C4—62no—
1355C4—62no—
1356C4—62no—
1357C4—182no—
1358C4—181no—
1359C4—181no—
1360C4—182no—
1361C3—21no—
1362C3#8631211yescharacteristic, complemented
1363C3#8642011yescharacteristic, complemented
1364C2—22no—
1365C2—42no—
1366C2—122no—
1367C2—122no—
1368C2—122no—
1369C2—182no—
1370C2—361no—
1371C2C2×#6430711yescharacteristic
1372C2#1059667511yescharacteristic
1373C2#1059667911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64092C2semidirect
2. C3×#5494C2semidirect
3. C3×#5493C2semidirect
4. #10595526C2semidirect
5. #10595494C2semidirect
6. #10595081C2semidirect
7. #10595075C2semidirect
8. #10594995C2semidirect
9. #10594974C2semidirect
10. #10594930C2semidirect
11. #10594922C2semidirect
12. #10594304C2semidirect
13. #10594281C2semidirect
14. #10594263C2semidirect
15. #10594237C2semidirect
16. #10594233C2semidirect
17. #10594221C2semidirect
18. #10594163C2semidirect
19. #10594127C2semidirect
23. C22×C4×C3⋊D3C22semidirect
24. C22×C3×#67C22semidirect
25. C2×#3811C22semidirect
26. C2×D3×#67C22semidirect
27. C2×#3805C22semidirect
28. C2×#3802C22semidirect
29. C2×#3796C22semidirect
30. C2×C32×C22⋊C4C22semidirect
31. C2×#3757C22semidirect
32. C2×#3752C22semidirect
33. C2×C4⋊(C3⋊Dic3)C22semidirect
34. C2×#3750C22semidirect
35. #64092C22semidirect
36. #64092C22semidirect
37. #64092C22semidirect
38. #64092C22semidirect
39. C3×#953C22semidirect
41. C3×#930C22semidirect
42. C3×#930C22semidirect
43. C3×#930C22semidirect
44. C3×C4×#67C22semidirect
45. C3×#924C22semidirect
46. C3×#886C22semidirect
47. C3×#886C22semidirect
48. C3×#885C22semidirect
49. C3×#884C22semidirect
50. C3×#883C22semidirect
51. C3×#882C22semidirect
52. C3×#882C22semidirect
53. C3×#879C22semidirect
55. #63981C22semidirect
56. #63980C22semidirect
57. #63980C22semidirect
58. #63979C22semidirect
59. #63978C22semidirect
60. #63977C22semidirect
61. #63976C22semidirect
62. #67⋊Dic3C22semidirect
63. #67⋊Dic3C22semidirect
64. Dic3×#67C22semidirect
65. #63971C22semidirect
66. #63970C22semidirect
67. #63970C22semidirect
68. #63969C22semidirect
69. D3×#217C22semidirect
70. #63964C22semidirect
71. #63962C22semidirect
72. #63959C22semidirect
74. #63952C22semidirect
75. #63922C22semidirect
76. #63921C22semidirect
77. D3×(C2×D3)⋊C4C22semidirect
78. #63916C22semidirect
79. #63916C22semidirect
80. #63916C22semidirect
81. #63912C22semidirect
82. #63908C22semidirect
83. #63906C22semidirect
84. #63900C22semidirect
85. #63899C22semidirect
86. #63899C22semidirect
87. #63895C22semidirect
88. Dic3×D12C22semidirect
89. #63891C22semidirect
90. #63891C22semidirect
91. #63890C22semidirect
92. #63887C22semidirect
93. #63886C22semidirect
94. #63885C22semidirect
95. #63885C22semidirect
96. #63884C22semidirect
97. #63881C22semidirect
98. #63880C22semidirect
99. #63871C22semidirect
100. #63869C22semidirect
101. #63861C22semidirect
102. #63861C22semidirect
103. #63858C22semidirect
104. #63853C22semidirect
105. #63852C22semidirect
106. #63849C22semidirect
107. #63846C22semidirect
108. #63841C22semidirect
143. #5494D3semidirect
144. #5493D3semidirect
249. C22×#67C2×D3semidirect
278. C2×C3×C22⋊C4C2×D3semidirect
279. C2×C3×C22⋊C4C2×D3semidirect
282. #953C2×D3semidirect
326. #930C2×D3semidirect
327. #930C2×D3semidirect
328. #930C2×D3semidirect
331. C4×#67C2×D3semidirect
341. #924C2×D3semidirect
373. #886C2×D3semidirect
374. #886C2×D3semidirect
377. #885C2×D3semidirect
385. #884C2×D3semidirect
402. #883C2×D3semidirect
406. #882C2×D3semidirect
407. #882C2×D3semidirect
420. #879C2×D3semidirect
856. C2×C22⋊C4D32semidirect
1226. C32#3534semidirect
1362. C3#86312semidirect
1363. C3#86420semidirect

Maximal subgroups

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

subgroupindex
C2×#640922
C3×#54942
C3×#54932
#105955262
#105954942
#105950812
#105950752
#105949952
#105949742
#105949302
#105949222
#105943042
#105942812
#105942632
#105942372
#105942332
#105942212
#105941632
#105941272
#864203
#863123