Finite Group Databasebeta

← #11910724

Subgroups — #11910724

Order 1152.

2291 conjugacy classes of subgroups.

The subgroup lattice has 1281 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#123C211yesmaximal, characteristic, complemented
2C3×#5664C211yesmaximal, characteristic, complemented
3C3×#5659C211yesmaximal, characteristic, complemented
4#10595276C211yesmaximal, characteristic, complemented
5#10595259C211yesmaximal, characteristic, complemented
6#10595242C211yesmaximal, characteristic, complemented
7#10595168C211yesmaximal, characteristic, complemented
8#10595016C212yesmaximal, complemented
9#10594943C212yesmaximal, complemented
10#10594546C212yesmaximal, complemented
11#10594371C212yesmaximal, complemented
12#10594337C212yesmaximal, complemented
13#10594330C212yesmaximal, complemented
14#10594225C212yesmaximal, complemented
15#10594196C212yesmaximal, complemented
16#10594186C212yesmaximal, complemented
17#10594175C212yesmaximal, complemented
18#10594153C212yesmaximal, complemented
19#10594090C212yesmaximal, complemented
20#87065—31nomaximal
21#86820—31nomaximal
22C2×D4×C3⋊D3C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×#626C2211yescharacteristic
25C2×#3798C2212yes—
26C2×#3796C2211yescharacteristic, complemented
27C32×#123C2211yescharacteristic
28#64144C2211yescharacteristic
29#64138C2211yescharacteristic, complemented
30#64103C2212yescomplemented
31C4⋊C4×C3⋊D3C2212yescomplemented
32#64095C2211yescharacteristic, complemented
33#64092C2212yes—
34C22⋊C4×C3⋊D3C2212yes—
35C22⋊C4×C3⋊D3C2211yescharacteristic, complemented
36C3×#940C2211yescharacteristic
37C3×#937C2211yescharacteristic
38C3×#936C2211yescharacteristic
39C3×#935C2211yescharacteristic
40C3×C4×#67C2212yescomplemented
41C3×C4×#67C2212yescomplemented
42C3×#896C2212yescomplemented
43C3×#894C2212yescomplemented
44C3×#892C2212yescomplemented
45C3×#887C2212yescomplemented
46C3×#885C2212yescomplemented
47C3×#885C2212yescomplemented
48C3×#883C2212yescomplemented
49C3×#67⋊C4C2212yescomplemented
50C3×D3×C22⋊C4C2212yescomplemented
51C3×#879C2212yescomplemented
52#63982C2212yescomplemented
53#63981C2212yes—
54#63981C2212yes—
55#63981C2212yescomplemented
56#63980C2212yescomplemented
57#63977C2211yescharacteristic
58#63976C2212yescomplemented
59#63974C2211yescharacteristic
60#63971C2212yes—
61#63971C2212yescomplemented
62#63970C2212yescomplemented
63#63969C2212yescomplemented
64#63966C2211yescharacteristic
65#63964C2212yescomplemented
66#63958C2212yes—
67#63956C2212yescomplemented
68#63956C2212yescomplemented
69#63912C2212yes—
70#63912C2212yescomplemented
71#63911C2211yescharacteristic, complemented
72#63910C2212yes—
73#63907C2212yescomplemented
74#63906C2212yescomplemented
75#63906C2212yescomplemented
76#63906C2212yescomplemented
77C4×#626C2212yes—
78C4×#626C2212yescomplemented
79C4×#626C2212yescomplemented
80#63893C2212yescomplemented
81#63891C2212yescomplemented
82#63890C2212yescomplemented
83#63888C2212yescomplemented
84#63885C2212yescomplemented
85#63881C2212yescomplemented
86#63880C2212yescomplemented
87#63879C2212yescomplemented
88D3×Dic3⋊C4C2212yescomplemented
89#63874C2211yescharacteristic, complemented
90#63874C2212yescomplemented
91#63871C2212yescomplemented
92#63869C2212yescomplemented
93#63868C2212yescomplemented
94#63867C2212yescomplemented
95#63867C2212yescomplemented
96#63865C2212yescomplemented
97#63864C2211yescharacteristic, complemented
98#63859C2212yescomplemented
99#63859C2212yescomplemented
100#63856C2212yescomplemented
101#63854C2212yescomplemented
102#63853C2212yes—
103#63853C2212yes—
104#63853C2212yescomplemented
105#63852C2212yescomplemented
106#63850C2212yescomplemented
107#63839C2212yescomplemented
108#63836C2212yescomplemented
109C3×#559—31no—
110C3×#551—31no—
111#5720—31no—
112#5715—31no—
113#5707—32no—
114#5705—32no—
115#5684—32no—
116#5679—32no—
117#5678—32no—
118#5678—32no—
119#5674—31no—
120#5672—31no—
121#5667—32no—
122#5664D311yescharacteristic, complemented
123#5663—32no—
124#5659D311yescharacteristic, complemented
125#5657—32no—
126#5655—32no—
127#5653—31no—
128D3×#123—31no—
129D3×#123—31no—
130D3×#123—61no—
131#5651—31no—
132#5640—32no—
133#5631—32no—
134#5595—31no—
135#5589—31no—
136#5582—32no—
137#5581—32no—
138#5564—32no—
139#5558—32no—
140#5550—32no—
141#5547—32no—
142#5547—32no—
143#5540—32no—
144#5535—32no—
145#5529—32no—
146#5494—32no—
147#5490—32no—
148C23×C3⋊D3C2311yescharacteristic
149C23×C3⋊D3C2311yescharacteristic
150C23×C3×D3C2311yescharacteristic
151C2×C32×D4C2311yescharacteristic
152C22×C32×C4C2311yescharacteristic
153C2×#638C2311yescharacteristic
154C2×#638C2311yescharacteristic
155C22×C3⋊Dic3C2311yescharacteristic
156D4×C3⋊D3—42no—
157C2×C4⋊(C3⋊D3)C2311yescharacteristic
158C2×C4×C3⋊D3—42no—
159C2×C4×C3⋊D3C2311yescharacteristic
160C2×C4×C3⋊D3C2312yes—
161C2×C4×C3⋊D3C2312yes—
162C2×C4×C3⋊D3C2312yes—
163C2×C3×#67C2312yes—
164C2×C3×#67C2312yes—
165C2×C3×#67C2312yes—
166C22×C3×Dic3C2311yescharacteristic
167C2×C3×D12C2311yescharacteristic
168C2×C3×C4×D3C2312yes—
169C2×C3×C4×D3C2312yes—
170C2×C3×C4×D3C2312yes—
171C2×C3×Dic6C2312yes—
172C2×C3×Dic6C2311yescharacteristic
173C2×#627C2312yes—
174C2×#626—42no—
175C2×#626C2312yes—
176C2×#626C2312yes—
177C2×#626C2312yes—
178C2×#626C2312yes—
179C2×#626C2312yes—
180C2×#626C2312yes—
181C2×#625C2312yes—
182C2×#625C2312yes—
183C2×#624C2312yes—
184C2×D3×Dic3C2312yes—
185C2×D3×Dic3C2312yes—
186#3798—44no—
187#3796—42no—
188C32×C4⋊C4C2312yes—
189C32×C22⋊C4C2312yes—
190C32×C22⋊C4C2311yescharacteristic
191#3757C2312yes—
192#3757C2311yescharacteristic
193#3752C2312yes—
194#3752C2312yes—
195#3752C2312yes—
196C4⋊(C3⋊Dic3)C2312yes—
197#3750C2312yes—
198#3750C2312yes—
199C3×#217C2311yescharacteristic
200C3×#217C2312yes—
201C3×#217C2312yes—
202C3×#217C2311yescharacteristic
203C3×#217C2312yes—
204C3×(C2×D3)⋊C4C2312yes—
205C3×(C2×D3)⋊C4C2312yes—
206C3×(C2×D3)⋊C4C2312yes—
207C3×(C2×D3)⋊C4C2312yes—
208C3×(C2×D3)⋊C4C2312yes—
209C3×(C2×D3)⋊C4C2312yes—
210C3×C4⋊Dic3C2312yes—
211C3×Dic3⋊C4C2312yes—
212C3×Dic3⋊C4C2312yes—
213C3×Dic3⋊C4C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×C4×Dic3C2312yes—
216C3×C4×Dic3C2312yes—
217C3×C4×Dic3C2312yes—
218C3×C4×Dic3C2311yescharacteristic
219C3×C4×Dic3C2311yescharacteristic
220#3724C2312yes—
221#3724C2312yes—
222#3724C2312yes—
223#3724C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226Dic3⋊Dic3C2312yes—
227Dic3⋊Dic3C2312yes—
228Dic3⋊Dic3C2312yes—
229Dic3⋊Dic3C2312yes—
230#3722C2312yes—
231#3722C2312yes—
232#3722C2312yes—
233#3722C2312yes—
234#3722C2312yes—
235(C2×D3)⋊Dic3C2312yes—
236(C2×D3)⋊Dic3C2312yes—
237(C2×D3)⋊Dic3C2312yes—
238(C2×D3)⋊Dic3C2312yes—
239Dic32C2312yes—
240#3533—91noSylow
241C22×#67—31no—
242C2×#239—31no—
243C2×#237—31no—
244C2×D3×D4—31no—
245C2×D3×D4—31no—
246C2×D3×D4—61no—
247C2×#235—32no—
248C2×#235—32no—
249C22×D12—31no—
250C22×C4×D3—31no—
251C22×C4×D3—31no—
252C22×C4×D3—61no—
253C3×#127—31no—
254C3×#126—32no—
255C3×#124—31no—
256C3×#124—32no—
257C3×#124—32no—
258C3×#123—21no—
259C3×#123—31no—
260C3×#123—32no—
261C3×#123—32no—
262C3×#123C2×D311yescharacteristic
263C3×#123C2×D311yescharacteristic
264C3×C22⋊Q8—32no—
265C3×#120—31no—
266C3×C4×Q8—32no—
267C3×C4×D4—32no—
268C3×C4×D4—32no—
269C3×C4×D4—32no—
270C3×#117—32no—
271C2×C3×C22⋊C4—32no—
272#953—32no—
273#953—31no—
274#947—32no—
275#947—31no—
276#946—32no—
277#946—32no—
278#946—32no—
279#944—32no—
280#940—31no—
281#940C2×D311yescharacteristic
282#939—32no—
283#939—32no—
284#939—32no—
285#939—32no—
286#939—32no—
287#939—32no—
288#938—32no—
289#938—32no—
290#937—32no—
291#937—32no—
292#937—32no—
293#937—32no—
294#937C2×D311yescharacteristic
295#936C2×D311yescharacteristic
296#935—31no—
297#935—31no—
298#935—32no—
299#935—61no—
300#935C2×D311yescharacteristic
301#930—32no—
302#930—32no—
303#930—32no—
304#929—31no—
305#929—31no—
306#929—31no—
307#929—32no—
308#929—61no—
309C4×#67—32no—
310C4×#67—32no—
311C4×#67—32no—
312C4×#67—32no—
313C4×#67C2×D312yescomplemented
314C4×#67C2×D312yescomplemented
315#924—32no—
316#924—32no—
317C2×Dic3⋊C4—32no—
318#898—32no—
319#897—32no—
320#897—32no—
321#896—32no—
322#896—32no—
323#896—32no—
324#896C2×D312yescomplemented
325#895—32no—
326#894—32no—
327#894—32no—
328#894—32no—
329#894—32no—
330#894—32no—
331#894—32no—
332#894—32no—
333#894—32no—
334#894—62no—
335#894C2×D312yescomplemented
336#893—32no—
337#892—32no—
338#892C2×D312yescomplemented
339D3×C4⋊C4—32no—
340D3×C4⋊C4—32no—
341D3×C4⋊C4—32no—
342D3×C4⋊C4—62no—
343#890—32no—
344#889—32no—
345#889—32no—
346#888—32no—
347#887C2×D312yescomplemented
348#886—31no—
349#886—31no—
350#886—31no—
351#886—32no—
352#886—32no—
353#886—61no—
354#885—32no—
355#885—32no—
356#885C2×D312yescomplemented
357#885C2×D312yescomplemented
358#884—32no—
359#884—32no—
360#884—32no—
361#884—32no—
362#884—32no—
363#884—32no—
364#884—32no—
365#884—32no—
366#884—32no—
367#884—32no—
368#884—32no—
369#884—32no—
370#883—32no—
371#883—32no—
372#883—32no—
373#883—32no—
374#883—32no—
375#883—32no—
376#883—32no—
377#883—32no—
378#883—62no—
379#883C2×D312yescomplemented
380#882—31no—
381#882—32no—
382#882—32no—
383#882—32no—
384#67⋊C4—32no—
385#67⋊C4—32no—
386#67⋊C4—32no—
387#67⋊C4C2×D312yescomplemented
388D3×C22⋊C4—31no—
389D3×C22⋊C4—31no—
390D3×C22⋊C4—32no—
391D3×C22⋊C4—32no—
392D3×C22⋊C4—31no—
393D3×C22⋊C4—31no—
394D3×C22⋊C4—62no—
395D3×C22⋊C4—61no—
396D3×C22⋊C4C2×D312yescomplemented
397#879—32no—
398#879—32no—
399#879—32no—
400#879—32no—
401#879—32no—
402#879—32no—
403#879C2×D312yescomplemented
404#878—32no—
405#878—32no—
406#878—32no—
407#878—32no—
408#876—32no—
409#876—32no—
410#876—32no—
411#875—31no—
412#875—32no—
413#874—31no—
414C4×D12—32no—
415C4×D12—32no—
416C4×D12—32no—
417C4×D12—32no—
418#872—32no—
419#872—31no—
420#872—32no—
421#872—32no—
422#872—31no—
423#870—32no—
424#870—32no—
425#870—32no—
426C23×C32C2411yescharacteristic
427C23×C32C2411yescharacteristic
428C22×C3⋊D3—22no—
429C22×C3⋊D3—22no—
430C22×C3⋊D3—42no—
431C22×C3⋊D3—42no—
432C22×C3⋊D3C2411yescharacteristic
433C22×C3⋊D3C2411yescharacteristic
434C22×C3⋊D3C2411yescharacteristic
435C22×C3×D3—42no—
436C22×C3×D3—41no—
437C22×C3×D3C2412yes—
438C22×C3×D3C2412yes—
439C32×D4—41no—
440C2×C32×C4—41no—
441C2×C32×C4C2411yescharacteristic
442C2×C32×C4C2412yes—
443C2×C32×C4C2412yes—
444#638—41no—
445#638—41no—
446C2×C3⋊Dic3—41no—
447C2×C3⋊Dic3C2412yes—
448C2×C3⋊Dic3C2411yescharacteristic
449C2×C3⋊Dic3C2412yes—
450C4⋊(C3⋊D3)—41no—
451C4×C3⋊D3—22no—
452C4×C3⋊D3—24no—
453C4×C3⋊D3—42no—
454C4×C3⋊D3—42no—
455C3×#67—42no—
456C3×#67—42no—
457C3×#67—42no—
458C2×C3×Dic3—41no—
459C2×C3×Dic3C2412yes—
460C2×C3×Dic3C2412yes—
461C2×C3×Dic3C2412yes—
462C2×C3×Dic3C2412yes—
463C2×C3×Dic3C2412yes—
464C2×C3×Dic3C2412yes—
465C3×D12—41no—
466C3×C4×D3—42no—
467C3×C4×D3—42no—
468C3×C4×D3—42no—
469C3×Dic6—41no—
470C3×Dic6—42no—
471#627—42no—
472#626—24no—
473#626—24no—
474#626—42no—
475#626—42no—
476#626—42no—
477#626—42no—
478#625—42no—
479#625—42no—
480#624—42no—
481D3×Dic3—42no—
482D3×Dic3—42no—
483#563—91no—
484#562—92no—
485#560—91no—
486#559—31no—
487#553—92no—
488#552—92no—
489#551—31no—
490#551—92no—
491#547—92no—
492#546—92no—
493#542—92no—
494#540—92no—
495#539—92no—
496#538—92no—
497#538—92no—
498#535—91no—
499#534—91no—
500#525—92no—
501C2×#123—91no—
502C24×C3—31no—
503C23×D3—31no—
504C23×D3—31no—
505C23×D3—31no—
506C23×D3—31no—
507C23×D3—61no—
508C23×D3—61no—
509C23×D3C22×D311yescharacteristic
510C2×C3×Q8—31no—
511C2×C3×Q8—32no—
512C2×C3×D4—21no—
513C2×C3×D4—32no—
514C2×C3×D4—32no—
515C2×C3×D4—32no—
516C2×C3×D4—31no—
517C2×C3×D4C22×D311yescharacteristic
518C2×C3×D4C22×D311yescharacteristic
519C22×C3×C4—21no—
520C22×C3×C4—31no—
521C22×C3×C4—32no—
522C22×C3×C4—32no—
523C22×C3×C4—32no—
524C22×C3×C4C22×D311yescharacteristic
525C22×C3×C4C22×D311yescharacteristic
526C2×#67—31no—
527C2×#67—31no—
528C2×#67—31no—
529C2×#67—31no—
530C2×#67—32no—
531C2×#67—32no—
532C2×#67—32no—
533C2×#67—32no—
534C2×#67—32no—
535C2×#67—32no—
536C2×#67—32no—
537C2×#67—32no—
538C2×#67—32no—
539C2×#67—32no—
540C2×#67—61no—
541C2×#67—61no—
542C2×#67—122no—
543C2×#67C22×D312yes—
544C2×#67C22×D312yes—
545C2×#67C22×D312yes—
546C22×Dic3—31no—
547C22×Dic3—31no—
548C22×Dic3—32no—
549C22×Dic3—32no—
550C22×Dic3—61no—
551C22×Dic3C22×D311yescharacteristic
552#239—122no—
553#237—122no—
554D3×D4—122no—
555D3×D4—122no—
556D3×D4—124no—
557#235—124no—
558#235—124no—
559C2×D12—32no—
560C2×D12—32no—
561C2×D12—32no—
562C2×D12—32no—
563C2×D12—32no—
564C2×D12—32no—
565C2×D12—31no—
566C2×D12—31no—
567C2×D12—61no—
568C2×D12—122no—
569C2×D12C22×D311yescharacteristic
570C2×C4×D3—32no—
571C2×C4×D3—32no—
572C2×C4×D3—31no—
573C2×C4×D3—31no—
574C2×C4×D3—32no—
575C2×C4×D3—32no—
576C2×C4×D3—32no—
577C2×C4×D3—32no—
578C2×C4×D3—32no—
579C2×C4×D3—32no—
580C2×C4×D3—32no—
581C2×C4×D3—32no—
582C2×C4×D3—62no—
583C2×C4×D3—62no—
584C2×C4×D3—62no—
585C2×C4×D3—61no—
586C2×C4×D3—122no—
587C2×C4×D3—122no—
588C2×C4×D3—124no—
589C2×C4×D3C22×D312yes—
590C2×C4×D3C22×D312yes—
591C2×C4×D3C22×D312yes—
592C2×Dic6—32no—
593C2×Dic6—32no—
594C2×Dic6C22×D311yescharacteristic
595C2×Dic6C22×D312yes—
596C3×C4⋊C4—22no—
597C3×C4⋊C4—32no—
598C3×C4⋊C4—32no—
599C3×C4⋊C4—32no—
600C3×C4⋊C4—32no—
601C3×C4⋊C4—32no—
602C3×C4⋊C4C22×D312yes—
603C3×C4⋊C4C22×D312yes—
604C3×C22⋊C4—22no—
605C3×C22⋊C4—21no—
606C3×C22⋊C4—32no—
607C3×C22⋊C4—32no—
608C3×C22⋊C4—32no—
609C3×C22⋊C4—31no—
610C3×C22⋊C4—31no—
611C3×C22⋊C4—32no—
612C3×C22⋊C4—32no—
613C3×C22⋊C4—32no—
614C3×C22⋊C4—32no—
615C3×C22⋊C4—32no—
616C3×C22⋊C4—32no—
617C3×C22⋊C4C22×D312yes—
618C3×C22⋊C4C22×D312yes—
619C3×C22⋊C4C22×D311yescharacteristic
620C3×C22⋊C4C22×D311yescharacteristic
621C3×C42—31no—
622C3×C42—32no—
623C3×C42—32no—
624C3×C42—32no—
625C3×C42—31no—
626#217—32no—
627#217—31no—
628#217—31no—
629#217—32no—
630#217—32no—
631#217—32no—
632#217—32no—
633#217—32no—
634#217—62no—
635#217—61no—
636#217C22×D312yes—
637#217C22×D312yes—
638#217C22×D311yescharacteristic
639#217C22×D312yes—
640#217C22×D311yescharacteristic
641(C2×D3)⋊C4—32no—
642(C2×D3)⋊C4—32no—
643(C2×D3)⋊C4—32no—
644(C2×D3)⋊C4—32no—
645(C2×D3)⋊C4—32no—
646(C2×D3)⋊C4—32no—
647(C2×D3)⋊C4—32no—
648(C2×D3)⋊C4—32no—
649(C2×D3)⋊C4—32no—
650(C2×D3)⋊C4—32no—
651(C2×D3)⋊C4—32no—
652(C2×D3)⋊C4—32no—
653(C2×D3)⋊C4—32no—
654(C2×D3)⋊C4—32no—
655(C2×D3)⋊C4—32no—
656(C2×D3)⋊C4—32no—
657(C2×D3)⋊C4—32no—
658(C2×D3)⋊C4—32no—
659(C2×D3)⋊C4—32no—
660(C2×D3)⋊C4—32no—
661(C2×D3)⋊C4—62no—
662(C2×D3)⋊C4—62no—
663(C2×D3)⋊C4—62no—
664(C2×D3)⋊C4C22×D312yes—
665(C2×D3)⋊C4C22×D312yes—
666(C2×D3)⋊C4C22×D312yes—
667(C2×D3)⋊C4C22×D312yes—
668(C2×D3)⋊C4C22×D312yes—
669(C2×D3)⋊C4C22×D312yes—
670C4⋊Dic3—32no—
671C4⋊Dic3—32no—
672C4⋊Dic3—32no—
673C4⋊Dic3—32no—
674C4⋊Dic3—32no—
675C4⋊Dic3—32no—
676C4⋊Dic3—32no—
677C4⋊Dic3—32no—
678C4⋊Dic3—62no—
679C4⋊Dic3C22×D312yes—
680Dic3⋊C4—32no—
681Dic3⋊C4—32no—
682Dic3⋊C4—32no—
683Dic3⋊C4—32no—
684Dic3⋊C4—32no—
685Dic3⋊C4—32no—
686Dic3⋊C4—32no—
687Dic3⋊C4—32no—
688Dic3⋊C4—32no—
689Dic3⋊C4—32no—
690Dic3⋊C4—32no—
691Dic3⋊C4—32no—
692Dic3⋊C4—32no—
693Dic3⋊C4—32no—
694Dic3⋊C4—32no—
695Dic3⋊C4—32no—
696Dic3⋊C4—32no—
697Dic3⋊C4—32no—
698Dic3⋊C4—62no—
699Dic3⋊C4—62no—
700Dic3⋊C4C22×D312yes—
701Dic3⋊C4C22×D312yes—
702Dic3⋊C4C22×D312yes—
703Dic3⋊C4C22×D312yes—
704C4×Dic3—32no—
705C4×Dic3—32no—
706C4×Dic3C22×D311yescharacteristic
707C4×Dic3C22×D312yes—
708C4×Dic3C22×D312yes—
709C4×Dic3C22×D311yescharacteristic
710C4×Dic3C22×D312yes—
711C22×C32—21no—
712C22×C32—21no—
713C22×C32—22no—
714C22×C32—22no—
715C22×C32C2511yescharacteristic
716C2×C3⋊D3—22no—
717C2×C3⋊D3—21no—
718C2×C3⋊D3—21no—
719C2×C3⋊D3—22no—
720C2×C3⋊D3—22no—
721C2×C3⋊D3—44no—
722C2×C3⋊D3—82no—
723C2×C3⋊D3H(5,𝔽2)12yes—
724C2×C3×D3—22no—
725C2×C3×D3—22no—
726C2×C3×D3—22no—
727C2×C3×D3—22no—
728C2×C3×D3—22no—
729C2×C3×D3—22no—
730C2×C3×D3—82no—
731C32×C4—21no—
732C32×C4—22no—
733C32×C4—22no—
734C3⋊Dic3—21no—
735C3⋊Dic3—22no—
736C3⋊Dic3—22no—
737C3×Dic3—22no—
738C3×Dic3—22no—
739C3×Dic3—22no—
740C3×Dic3—22no—
741C3×Dic3—22no—
742C3×Dic3—22no—
743C2×#41—92no—
744C2×#41—91no—
745C22×D4—91no—
746C22×D4—91no—
747C23×C4—91no—
748C4⋊Q8—92no—
749#127—31no—
750#127—91no—
751#126—32no—
752#126—92no—
753#126—92no—
754#126—92no—
755#126—92no—
756#126—92no—
757#125—92no—
758#125—92no—
759#125—92no—
760#124—31no—
761#124—32no—
762#124—32no—
763#124—92no—
764#124—91no—
765#124—92no—
766#123—31no—
767#123—32no—
768#123—32no—
769#123—92no—
770#123—92no—
771#123—92no—
772#123—92no—
773#123—92no—
774#123—92no—
775#123—91no—
776#123—92no—
777#123—92no—
778#123—91no—
779#123—91no—
780#123—92no—
781#123—92no—
782#123—91no—
783#123D3211yescharacteristic
784C22⋊Q8—32no—
785C22⋊Q8—92no—
786C22⋊Q8—92no—
787C22⋊Q8—92no—
788C22⋊Q8—92no—
789C22⋊Q8—92no—
790C22⋊Q8—92no—
791C22⋊Q8—92no—
792#121—92no—
793#121—92no—
794#121—92no—
795#121—92no—
796#121—92no—
797#121—92no—
798#121—92no—
799#121—92no—
800#121—92no—
801#121—92no—
802#121—92no—
803#121—92no—
804#120—31no—
805#120—92no—
806#120—92no—
807#120—92no—
808#120—91no—
809#120—92no—
810C4×Q8—32no—
811C4×D4—32no—
812C4×D4—32no—
813C4×D4—32no—
814C4×D4—92no—
815C4×D4—92no—
816C4×D4—92no—
817C4×D4—92no—
818C4×D4—92no—
819C4×D4—92no—
820#117—32no—
821#117—92no—
822#117—91no—
823#117—92no—
824C2×C4⋊C4—92no—
825C2×C4⋊C4—92no—
826C2×C22⋊C4—32no—
827C2×C22⋊C4—91no—
828C2×C22⋊C4—91no—
829C2×C22⋊C4—92no—
830C23×C3—21no—
831C23×C3—21no—
832C23×C3—32no—
833C23×C3—32no—
834C23×C3—121no—
835C23×C3—122no—
836C23×C3C23×D311yescharacteristic
837C23×C3C23×D311yescharacteristic
838C23×C3C23×D311yescharacteristic
839C23×C3C23×D311yescharacteristic
840C22×D3—31no—
841C22×D3—31no—
842C22×D3—31no—
843C22×D3—31no—
844C22×D3—31no—
845C22×D3—31no—
846C22×D3—41no—
847C22×D3—42no—
848C22×D3—61no—
849C22×D3—61no—
850C22×D3—61no—
851C22×D3—62no—
852C22×D3—62no—
853C22×D3—62no—
854C22×D3—62no—
855C22×D3—64no—
856C22×D3—122no—
857C22×D3—122no—
858C22×D3—122no—
859C22×D3—122no—
860C22×D3—122no—
861C22×D3—124no—
862C22×D3—124no—
863C22×D3C23×D312yes—
864C22×D3C23×D312yes—
865C3×Q8—121no—
866C3×Q8—122no—
867C3×D4—41no—
868C3×D4—41no—
869C3×D4—42no—
870C3×D4—121no—
871C3×D4—122no—
872C3×D4—122no—
873C3×D4—122no—
874C2×C3×C4—21no—
875C2×C3×C4—22no—
876C2×C3×C4—22no—
877C2×C3×C4—32no—
878C2×C3×C4—32no—
879C2×C3×C4—32no—
880C2×C3×C4—32no—
881C2×C3×C4—32no—
882C2×C3×C4—32no—
883C2×C3×C4—41no—
884C2×C3×C4—41no—
885C2×C3×C4—42no—
886C2×C3×C4—122no—
887C2×C3×C4—122no—
888C2×C3×C4—122no—
889C2×C3×C4—121no—
890C2×C3×C4C23×D311yescharacteristic
891C2×C3×C4C23×D311yescharacteristic
892C2×C3×C4C23×D312yes—
893C2×C3×C4C23×D312yes—
894C2×C3×C4C23×D312yes—
895C2×C3×C4C23×D312yes—
896#67—42no—
897#67—42no—
898#67—42no—
899#67—64no—
900#67—64no—
901#67—122no—
902#67—122no—
903#67—122no—
904#67—122no—
905#67—122no—
906#67—122no—
907#67—122no—
908#67—122no—
909#67—121no—
910#67—121no—
911#67—121no—
912#67—121no—
913#67—122no—
914#67—122no—
915C2×Dic3—32no—
916C2×Dic3—32no—
917C2×Dic3—31no—
918C2×Dic3—31no—
919C2×Dic3—32no—
920C2×Dic3—32no—
921C2×Dic3—41no—
922C2×Dic3—61no—
923C2×Dic3—62no—
924C2×Dic3—62no—
925C2×Dic3—122no—
926C2×Dic3—122no—
927C2×Dic3—121no—
928C2×Dic3—121no—
929C2×Dic3—122no—
930C2×Dic3C23×D312yes—
931C2×Dic3C23×D312yes—
932C2×Dic3C23×D312yes—
933C2×Dic3C23×D312yes—
934C2×Dic3C23×D312yes—
935C2×Dic3C23×D312yes—
936D12—41no—
937D12—64no—
938D12—64no—
939D12—121no—
940D12—121no—
941D12—122no—
942D12—122no—
943D12—122no—
944D12—122no—
945D12—122no—
946C4×D3—42no—
947C4×D3—42no—
948C4×D3—42no—
949C4×D3—64no—
950C4×D3—64no—
951C4×D3—62no—
952C4×D3—62no—
953C4×D3—124no—
954C4×D3—122no—
955C4×D3—122no—
956C4×D3—122no—
957C4×D3—122no—
958C4×D3—122no—
959C4×D3—122no—
960C4×D3—122no—
961C4×D3—122no—
962C4×D3—122no—
963C4×D3—124no—
964C4×D3—124no—
965Dic6—42no—
966Dic6—41no—
967Dic6—122no—
968Dic6—122no—
969C2×C32—41no—
970C2×C32—41no—
971C2×C32C2×H(5,𝔽2)11yescharacteristic
972C2×C32#58512yes—
973C3⋊D3—22no—
974C3⋊D3—41no—
975C3⋊D3—41no—
976C3×D3—42no—
977C3×D3—42no—
978C24—31no—
979C24—91no—
980C24—91no—
981#41—364no—
982#41—362no—
983C2×Q8—32no—
984C2×Q8—31no—
985C2×Q8—92no—
986C2×D4—32no—
987C2×D4—32no—
988C2×D4—32no—
989C2×D4—31no—
990C2×D4—92no—
991C2×D4—92no—
992C2×D4—92no—
993C2×D4—92no—
994C2×D4—92no—
995C2×D4—92no—
996C2×D4—92no—
997C2×D4—92no—
998C2×D4—91no—
999C2×D4—91no—
1000C2×D4—91no—
1001C2×D4—362no—
1002C2×D4—362no—
1003C2×D4C2×D3211yescharacteristic
1004C22×C4—31no—
1005C22×C4—32no—
1006C22×C4—32no—
1007C22×C4—32no—
1008C22×C4—92no—
1009C22×C4—92no—
1010C22×C4—92no—
1011C22×C4—91no—
1012C22×C4—92no—
1013C22×C4—91no—
1014C22×C4—92no—
1015C22×C4—92no—
1016C22×C4—362no—
1017C22×C4C2×D3211yescharacteristic
1018C4⋊C4—32no—
1019C4⋊C4—32no—
1020C4⋊C4—32no—
1021C4⋊C4—32no—
1022C4⋊C4—32no—
1023C4⋊C4—92no—
1024C4⋊C4—92no—
1025C4⋊C4—92no—
1026C4⋊C4—92no—
1027C4⋊C4—92no—
1028C4⋊C4—92no—
1029C4⋊C4—92no—
1030C4⋊C4—92no—
1031C4⋊C4—92no—
1032C4⋊C4—92no—
1033C4⋊C4—92no—
1034C4⋊C4—92no—
1035C4⋊C4—92no—
1036C4⋊C4C2×D3212yes—
1037C22⋊C4—32no—
1038C22⋊C4—31no—
1039C22⋊C4—31no—
1040C22⋊C4—32no—
1041C22⋊C4—32no—
1042C22⋊C4—32no—
1043C22⋊C4—32no—
1044C22⋊C4—32no—
1045C22⋊C4—32no—
1046C22⋊C4—32no—
1047C22⋊C4—32no—
1048C22⋊C4—92no—
1049C22⋊C4—92no—
1050C22⋊C4—92no—
1051C22⋊C4—92no—
1052C22⋊C4—92no—
1053C22⋊C4—92no—
1054C22⋊C4—92no—
1055C22⋊C4—92no—
1056C22⋊C4—92no—
1057C22⋊C4—92no—
1058C22⋊C4—91no—
1059C22⋊C4—92no—
1060C22⋊C4—92no—
1061C22⋊C4—92no—
1062C22⋊C4C2×D3212yes—
1063C22⋊C4C2×D3211yescharacteristic
1064C42—31no—
1065C42—32no—
1066C42—32no—
1067C42—31no—
1068C42—32no—
1069C42—92no—
1070C22×C3—22no—
1071C22×C3—22no—
1072C22×C3—22no—
1073C22×C3—22no—
1074C22×C3—22no—
1075C22×C3—21no—
1076C22×C3—21no—
1077C22×C3—21no—
1078C22×C3—21no—
1079C22×C3—21no—
1080C22×C3—42no—
1081C22×C3—41no—
1082C22×C3—42no—
1083C22×C3—62no—
1084C22×C3—62no—
1085C22×C3—62no—
1086C22×C3—62no—
1087C22×C3—62no—
1088C22×C3—62no—
1089C22×C3—242no—
1090C22×C3C24×D311yescharacteristic
1091C22×C3C24×D311yescharacteristic
1092C2×D3—22no—
1093C2×D3—22no—
1094C2×D3—22no—
1095C2×D3—22no—
1096C2×D3—22no—
1097C2×D3—22no—
1098C2×D3—32no—
1099C2×D3—32no—
1100C2×D3—62no—
1101C2×D3—64no—
1102C2×D3—62no—
1103C2×D3—62no—
1104C2×D3—62no—
1105C2×D3—62no—
1106C2×D3—62no—
1107C2×D3—62no—
1108C2×D3—62no—
1109C2×D3—61no—
1110C2×D3—61no—
1111C2×D3—61no—
1112C2×D3—61no—
1113C2×D3—82no—
1114C2×D3—122no—
1115C2×D3—121no—
1116C2×D3—122no—
1117C2×D3—128no—
1118C2×D3—124no—
1119C2×D3—124no—
1120C2×D3—242no—
1121C2×D3—242no—
1122C2×D3—244no—
1123C3×C4—22no—
1124C3×C4—22no—
1125C3×C4—21no—
1126C3×C4—22no—
1127C3×C4—22no—
1128C3×C4—21no—
1129C3×C4—42no—
1130C3×C4—41no—
1131C3×C4—42no—
1132C3×C4—62no—
1133C3×C4—62no—
1134C3×C4—62no—
1135C3×C4—62no—
1136C3×C4—62no—
1137C3×C4—62no—
1138Dic3—22no—
1139Dic3—22no—
1140Dic3—22no—
1141Dic3—22no—
1142Dic3—22no—
1143Dic3—22no—
1144Dic3—62no—
1145Dic3—62no—
1146Dic3—62no—
1147Dic3—62no—
1148Dic3—61no—
1149Dic3—61no—
1150Dic3—122no—
1151Dic3—121no—
1152Dic3—122no—
1153C32#353311yescharacteristic, complemented, Sylow
1154C23—32no—
1155C23—32no—
1156C23—91no—
1157C23—91no—
1158C23—91no—
1159C23—121no—
1160C23—122no—
1161C23—182no—
1162C23—182no—
1163C23—362no—
1164C23—362no—
1165C23C22×D3211yescharacteristic
1166C23C22×D3211yescharacteristic
1167Q8—121no—
1168Q8—122no—
1169Q8—362no—
1170D4—41no—
1171D4—121no—
1172D4—122no—
1173D4—122no—
1174D4—122no—
1175D4—184no—
1176D4—184no—
1177D4—361no—
1178D4—362no—
1179D4—362no—
1180D4—362no—
1181D4—362no—
1182D4—361no—
1183D4—361no—
1184D4—362no—
1185D4—362no—
1186C2×C4—32no—
1187C2×C4—32no—
1188C2×C4—32no—
1189C2×C4—32no—
1190C2×C4—32no—
1191C2×C4—32no—
1192C2×C4—41no—
1193C2×C4—92no—
1194C2×C4—92no—
1195C2×C4—91no—
1196C2×C4—122no—
1197C2×C4—122no—
1198C2×C4—122no—
1199C2×C4—121no—
1200C2×C4—184no—
1201C2×C4—182no—
1202C2×C4—362no—
1203C2×C4—362no—
1204C2×C4—362no—
1205C2×C4—362no—
1206C2×C4—362no—
1207C2×C4—361no—
1208C2×C4C22×D3212yes—
1209C2×C4C22×D3211yescharacteristic
1210C2×C4C22×D3212yes—
1211C2×C3—21no—
1212C2×C3—22no—
1213C2×C3—42no—
1214C2×C3—41no—
1215C2×C3—41no—
1216C2×C3—41no—
1217C2×C3—41no—
1218C2×C3—81no—
1219C2×C3—122no—
1220C2×C3—122no—
1221C2×C3#596412yes—
1222C2×C3#596412yes—
1223C2×C3D3×H(5,𝔽2)11yescharacteristic
1224C2×C3D3×H(5,𝔽2)11yescharacteristic
1225D3—42no—
1226D3—42no—
1227D3—64no—
1228D3—62no—
1229D3—62no—
1230D3—122no—
1231D3—121no—
1232D3—121no—
1233D3—121no—
1234D3—121no—
1235D3—241no—
1236C22—21no—
1237C22—21no—
1238C22—22no—
1239C22—22no—
1240C22—62no—
1241C22—62no—
1242C22—62no—
1243C22—62no—
1244C22—62no—
1245C22—62no—
1246C22—92no—
1247C22—182no—
1248C22—181no—
1249C22—181no—
1250C22—182no—
1251C22—182no—
1252C22—242no—
1253C22—364no—
1254C22—722no—
1255C22C23×D3211yescharacteristic
1256C4—22no—
1257C4—21no—
1258C4—22no—
1259C4—62no—
1260C4—62no—
1261C4—62no—
1262C4—62no—
1263C4—62no—
1264C4—62no—
1265C4—181no—
1266C4—182no—
1267C4—182no—
1268C3—21no—
1269C3#8682011yescharacteristic, complemented
1270C3#8706511yescharacteristic, complemented
1271C2—41no—
1272C2—41no—
1273C2—122no—
1274C2—122no—
1275C2—182no—
1276C2—361no—
1277C2—361no—
1278C2#1059667511yescharacteristic
1279C2#1059669512yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#123C22
hypercenter#123D32
hypocenterC32#3533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×#123C2semidirect
2. C3×#5664C2semidirect
3. C3×#5659C2semidirect
4. #10595276C2semidirect
5. #10595259C2semidirect
6. #10595242C2semidirect
7. #10595168C2semidirect
8. #10595016C2semidirect
9. #10594943C2semidirect
10. #10594546C2semidirect
11. #10594371C2semidirect
12. #10594337C2semidirect
13. #10594330C2semidirect
14. #10594225C2semidirect
15. #10594196C2semidirect
16. #10594186C2semidirect
17. #10594175C2semidirect
18. #10594153C2semidirect
19. #10594090C2semidirect
23. C22×C4×C3⋊D3C22semidirect
26. C2×#3796C22semidirect
29. #64138C22semidirect
30. #64103C22semidirect
31. C4⋊C4×C3⋊D3C22semidirect
32. #64095C22semidirect
35. C22⋊C4×C3⋊D3C22semidirect
40. C3×C4×#67C22semidirect
41. C3×C4×#67C22semidirect
42. C3×#896C22semidirect
43. C3×#894C22semidirect
44. C3×#892C22semidirect
45. C3×#887C22semidirect
46. C3×#885C22semidirect
47. C3×#885C22semidirect
48. C3×#883C22semidirect
49. C3×#67⋊C4C22semidirect
50. C3×D3×C22⋊C4C22semidirect
51. C3×#879C22semidirect
52. #63982C22semidirect
55. #63981C22semidirect
56. #63980C22semidirect
58. #63976C22semidirect
61. #63971C22semidirect
62. #63970C22semidirect
63. #63969C22semidirect
65. #63964C22semidirect
67. #63956C22semidirect
68. #63956C22semidirect
70. #63912C22semidirect
71. #63911C22semidirect
73. #63907C22semidirect
74. #63906C22semidirect
75. #63906C22semidirect
76. #63906C22semidirect
78. C4×#626C22semidirect
79. C4×#626C22semidirect
80. #63893C22semidirect
81. #63891C22semidirect
82. #63890C22semidirect
83. #63888C22semidirect
84. #63885C22semidirect
85. #63881C22semidirect
86. #63880C22semidirect
87. #63879C22semidirect
88. D3×Dic3⋊C4C22semidirect
89. #63874C22semidirect
90. #63874C22semidirect
91. #63871C22semidirect
92. #63869C22semidirect
93. #63868C22semidirect
94. #63867C22semidirect
95. #63867C22semidirect
96. #63865C22semidirect
97. #63864C22semidirect
98. #63859C22semidirect
99. #63859C22semidirect
100. #63856C22semidirect
101. #63854C22semidirect
104. #63853C22semidirect
105. #63852C22semidirect
106. #63850C22semidirect
107. #63839C22semidirect
108. #63836C22semidirect
122. #5664D3semidirect
124. #5659D3semidirect
313. C4×#67C2×D3semidirect
314. C4×#67C2×D3semidirect
324. #896C2×D3semidirect
335. #894C2×D3semidirect
338. #892C2×D3semidirect
347. #887C2×D3semidirect
356. #885C2×D3semidirect
357. #885C2×D3semidirect
379. #883C2×D3semidirect
387. #67⋊C4C2×D3semidirect
396. D3×C22⋊C4C2×D3semidirect
403. #879C2×D3semidirect
1153. C32#3533semidirect
1269. C3#86820semidirect
1270. C3#87065semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1232
C3×#56642
C3×#56592
#105952762
#105952592
#105952422
#105951682
#105950162
#105949432
#105945462
#105943712
#105943372
#105943302
#105942252
#105941962
#105941862
#105941752
#105941532
#105940902
#870653
#868203