Finite Group Databasebeta

← #11911159

Subgroups — #11911159

Order 1152.

2545 conjugacy classes of subgroups.

The subgroup lattice has 1382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#121C211yesmaximal, characteristic, complemented
2C3×#5605C211yesmaximal, characteristic, complemented
3C3×#5602C211yesmaximal, characteristic, complemented
4#10595242C212yesmaximal, complemented
5D4×#626C212yesmaximal, complemented
6#10595193C212yesmaximal, complemented
7#10595185C212yesmaximal, complemented
8#10595163C212yesmaximal, complemented
9#10595148C212yesmaximal, complemented
10#10595038C211yesmaximal, characteristic, complemented
11#10594922C211yesmaximal, characteristic, complemented
12#10594911C211yesmaximal, characteristic, complemented
13C2×#63853C211yesmaximal, characteristic, complemented
14#10594572C212yesmaximal, complemented
15#10594467C212yesmaximal, complemented
16#10594236C212yesmaximal, complemented
17#10594228C212yesmaximal, complemented
18#10594063C212yesmaximal, complemented
19#10594043C212yesmaximal, complemented
20#86459—31nomaximal
21#86312—31nomaximal
22C2×D4×C3⋊D3C2212yescomplemented
23C2×D4×C3⋊D3C2211yescharacteristic, complemented
24C22×C4×C3⋊D3C2211yescharacteristic, complemented
25C2×C3×D3×D4C2212yescomplemented
26C22×#626C2211yescharacteristic
27C22×#626C2212yescomplemented
28C2×#3804C2212yescomplemented
29C2×#3796C2211yescharacteristic, complemented
30C32×#121C2211yescharacteristic
31#64148C2212yescomplemented
32#64147C2211yescharacteristic, complemented
33#64139C2211yescharacteristic, complemented
34#64104C2211yescharacteristic, complemented
35C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
36#64093C2212yescomplemented
37C22⋊C4×C3⋊D3C2212yescomplemented
38C3×#939C2212yescomplemented
39C3×#937C2212yescomplemented
40C3×#935C2212yescomplemented
41C3×#935C2212yescomplemented
42C3×D4×Dic3C2212yescomplemented
43C3×#930C2211yescharacteristic, complemented
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C3×#924C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C3×#894C2212yescomplemented
48C3×#889C2212yescomplemented
49C3×#883C2212yescomplemented
50C3×#882C2212yescomplemented
51C3×#879C2212yescomplemented
52C3×#878C2212yescomplemented
53#63981C2212yes—
54#63981C2212yescomplemented
55#63981C2212yescomplemented
56#63978C2212yescomplemented
57#63978C2212yescomplemented
58#63977C2212yescomplemented
59#63977C2212yescomplemented
60#63977C2212yescomplemented
61#63974C2212yescomplemented
62#67⋊Dic3C2212yescomplemented
63Dic3×#67C2212yescomplemented
64#63971C2212yescomplemented
65D3×#217C2212yescomplemented
66#63966C2212yescomplemented
67C2×Dic3⋊Dic3C2211yescharacteristic, complemented
68C2×#3722C2211yescharacteristic, complemented
69C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
70#63959C2212yescomplemented
71#63958C2212yescomplemented
72#63958C2212yescomplemented
73#63956C2212yescomplemented
74#63953C2212yescomplemented
75#63952C2212yescomplemented
76#63916C2212yes—
77#63916C2211yescharacteristic, complemented
78#63911C2212yescomplemented
79#63910C2212yescomplemented
80#63910C2212yescomplemented
81#63910C2212yescomplemented
82#63909C2212yescomplemented
83#63907C2212yescomplemented
84#63904C2212yescomplemented
85C4×#626C2212yescomplemented
86#63897C2212yescomplemented
87#63895C2212yescomplemented
88#63893C2212yescomplemented
89#63890C2212yescomplemented
90#63886C2212yescomplemented
91#63886C2212yescomplemented
92#63884C2212yescomplemented
93#63881C2212yescomplemented
94#63881C2212yescomplemented
95#63871C2211yescharacteristic, complemented
96#63865C2212yescomplemented
97#63861C2212yescomplemented
98#63859C2212yescomplemented
99#63854C2212yescomplemented
100#63853C2212yescomplemented
101#63853C2212yescomplemented
102#63853C2212yescomplemented
103#63853C2212yescomplemented
104#63853C2212yescomplemented
105#63851C2212yescomplemented
106#63849C2211yescharacteristic, complemented
107#63846C2212yescomplemented
108#63836C2212yescomplemented
109C3×#539—31no—
110C3×#534—31no—
111#5806—32no—
112D4×#67—32no—
113#5711—32no—
114#5705—32no—
115#5697—32no—
116#5692—32no—
117#5667—32no—
118#5663—32no—
119#5660—32no—
120#5659—32no—
121#5657—32no—
122#5654—32no—
123#5654—32no—
124#5653—32no—
125#5647—32no—
126#5644—31no—
127#5630—32no—
128#5627—31no—
129#5618—32no—
130#5610—32no—
131#5606—31no—
132#5605D311yescharacteristic, complemented
133D3×#121—31no—
134D3×#121—31no—
135D3×#121—61no—
136#5602D311yescharacteristic, complemented
137#5597—31no—
138#5595—32no—
139#5593—32no—
140#5591—32no—
141#5589—32no—
142D4×D12—32no—
143#5540—32no—
144#5510—31no—
145C2×#894—31no—
146#5494—31no—
147C2×#883—31no—
148C23×C3⋊D3C2311yescharacteristic
149C23×C3⋊D3C2312yes—
150C23×C3×D3C2311yescharacteristic
151C23×C3×D3C2312yes—
152C2×C32×D4C2312yes—
153C2×C32×D4C2311yescharacteristic
154C22×C32×C4C2311yescharacteristic
155C2×#638C2312yes—
156C2×#638C2312yes—
157C2×#638C2312yes—
158C22×C3⋊Dic3C2311yescharacteristic
159D4×C3⋊D3—42no—
160D4×C3⋊D3—44no—
161C2×C4⋊(C3⋊D3)C2312yes—
162C2×C4⋊(C3⋊D3)C2311yescharacteristic
163C2×C4×C3⋊D3—42no—
164C2×C4×C3⋊D3C2311yescharacteristic
165C2×C4×C3⋊D3C2311yescharacteristic
166C2×C4×C3⋊D3C2312yes—
167C2×C4×C3⋊D3C2311yescharacteristic
168C2×C4×C3⋊D3C2311yescharacteristic
169C2×C3×#67C2312yes—
170C2×C3×#67C2312yes—
171C2×C3×#67C2312yes—
172C22×C3×Dic3C2311yescharacteristic
173C22×C3×Dic3C2312yes—
174C22×C3×Dic3C2311yescharacteristic
175C22×C3×Dic3C2311yescharacteristic
176C3×D3×D4—44no—
177C2×C3×D12C2311yescharacteristic
178C2×C3×D12C2312yes—
179C2×C3×C4×D3C2312yes—
180C2×C3×Dic6C2311yescharacteristic
181C2×#627C2312yes—
182C2×#626—42no—
183C2×#626—44no—
184C2×#626C2312yes—
185C2×#626C2312yes—
186C2×#626C2312yes—
187C2×#626C2312yes—
188C2×#626C2312yes—
189C2×#626C2312yes—
190C2×#626C2312yes—
191C2×#626C2312yes—
192C2×#624C2312yes—
193C2×#624C2312yes—
194#3804—44no—
195C2×D3×Dic3C2312yes—
196C2×D3×Dic3C2312yes—
197#3796—42no—
198C32×C4⋊C4C2311yescharacteristic
199C32×C22⋊C4C2312yes—
200#3757C2312yes—
201#3752C2312yes—
202#3752C2312yes—
203C4⋊(C3⋊Dic3)C2311yescharacteristic
204#3750C2312yes—
205C3×#217C2312yes—
206C3×#217C2312yes—
207C3×#217C2312yes—
208C3×#217C2312yes—
209C3×#217C2312yes—
210C3×(C2×D3)⋊C4C2312yes—
211C3×(C2×D3)⋊C4C2312yes—
212C3×(C2×D3)⋊C4C2312yes—
213C3×(C2×D3)⋊C4C2312yes—
214C3×C4⋊Dic3C2312yes—
215C3×C4⋊Dic3C2311yescharacteristic
216C3×C4⋊Dic3C2311yescharacteristic
217C3×Dic3⋊C4C2312yes—
218C3×Dic3⋊C4C2312yes—
219C3×Dic3⋊C4C2312yes—
220C3×Dic3⋊C4C2312yes—
221C3×Dic3⋊C4C2312yes—
222C3×Dic3⋊C4C2312yes—
223C3×C4×Dic3C2312yes—
224#3724C2312yes—
225Dic3⋊Dic3C2312yes—
226Dic3⋊Dic3C2312yes—
227Dic3⋊Dic3C2312yes—
228Dic3⋊Dic3C2312yes—
229#3722C2312yes—
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—
239(C2×D3)⋊Dic3C2312yes—
240(C2×D3)⋊Dic3C2312yes—
241Dic32C2312yes—
242Dic32C2312yes—
243#3534—91noSylow
244C22×C3×D4—32no—
245C22×#67—31no—
246C22×#67—32no—
247C2×#239—31no—
248C2×#237—32no—
249C2×#237—31no—
250C2×D3×D4—31no—
251C2×D3×D4—32no—
252C2×D3×D4—32no—
253C2×D3×D4—31no—
254C2×D3×D4—61no—
255C2×D3×D4—62no—
256C2×D3×D4C2×D312yescomplemented
257C2×#235—32no—
258C22×D12—32no—
259C22×D12—31no—
260C22×C4×D3—31no—
261C22×C4×D3—31no—
262C22×C4×D3—61no—
263C3×#126—32no—
264C3×#125—32no—
265C3×#123—32no—
266C3×#123—32no—
267C3×#123—32no—
268C3×#123—32no—
269C3×C22⋊Q8—31no—
270C3×C22⋊Q8—32no—
271C3×#121—21no—
272C3×#121—32no—
273C3×#121—31no—
274C3×#121C2×D311yescharacteristic
275C3×#121C2×D311yescharacteristic
276C3×#120—32no—
277C3×#120—32no—
278C3×C4×D4—32no—
279C2×C3×C4⋊C4—31no—
280C2×C3×C22⋊C4—31no—
281#953—32no—
282#953—32no—
283#953—32no—
284C2×#217—31no—
285C2×#217—32no—
286#947—32no—
287#946—31no—
288#940—32no—
289#939—32no—
290#939—32no—
291#939—32no—
292#939—32no—
293#939—32no—
294#939—32no—
295#939—32no—
296#939—62no—
297#939C2×D312yescomplemented
298#938—31no—
299#938—31no—
300#938—32no—
301#938—32no—
302#938—32no—
303#938—31no—
304#938—61no—
305#937—32no—
306#937—32no—
307#937—32no—
308#937C2×D312yescomplemented
309#936—32no—
310#935—32no—
311#935C2×D312yescomplemented
312#935C2×D312yescomplemented
313D4×Dic3—32no—
314D4×Dic3—32no—
315D4×Dic3C2×D312yescomplemented
316#930—31no—
317#930—31no—
318#930—32no—
319#930—32no—
320#930—32no—
321#930—61no—
322#930C2×D311yescharacteristic, complemented
323#929—32no—
324C4×#67—32no—
325C4×#67—32no—
326C4×#67—32no—
327C4×#67—32no—
328C2×(C2×D3)⋊C4—31no—
329C2×(C2×D3)⋊C4—31no—
330C2×(C2×D3)⋊C4—31no—
331C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
332C2×C4⋊Dic3—31no—
333#924—32no—
334#924C2×D311yescharacteristic, complemented
335C2×Dic3⋊C4—31no—
336C2×Dic3⋊C4C2×D311yescharacteristic, complemented
337#898—32no—
338#897—31no—
339#897—32no—
340#897—32no—
341#896—32no—
342#896—32no—
343#896—32no—
344#896—32no—
345#895—32no—
346#895—32no—
347#895—31no—
348#895—32no—
349#895—32no—
350#895—31no—
351#895—31no—
352#895—32no—
353#895—32no—
354#895—32no—
355#895—61no—
356#894—32no—
357#894—32no—
358#894—32no—
359#894—32no—
360#894—32no—
361#894—32no—
362#894—32no—
363#894—32no—
364#894—32no—
365#894—32no—
366#894C2×D312yescomplemented
367#893—32no—
368#893—32no—
369#893—32no—
370#892—31no—
371#892—31no—
372#892—32no—
373D3×C4⋊C4—31no—
374D3×C4⋊C4—31no—
375D3×C4⋊C4—61no—
376#890—32no—
377#889—32no—
378#889C2×D312yescomplemented
379#886—32no—
380#886—32no—
381#885—32no—
382#885—32no—
383#885—32no—
384#885—32no—
385#884—32no—
386#884—32no—
387#884—32no—
388#884—32no—
389#884—32no—
390#884—32no—
391#884—32no—
392#884—32no—
393#884—62no—
394#883—32no—
395#883—32no—
396#883—32no—
397#883—32no—
398#883—32no—
399#883—32no—
400#883C2×D312yescomplemented
401#882—32no—
402#882—32no—
403#882—32no—
404#882—32no—
405#882—32no—
406#882—32no—
407#882C2×D312yescomplemented
408#67⋊C4—32no—
409#67⋊C4—32no—
410#67⋊C4—32no—
411#67⋊C4—32no—
412D3×C22⋊C4—32no—
413D3×C22⋊C4—32no—
414D3×C22⋊C4—32no—
415D3×C22⋊C4—32no—
416D3×C22⋊C4—32no—
417D3×C22⋊C4—62no—
418#879—32no—
419#879—32no—
420#879—32no—
421#879—32no—
422#879C2×D312yescomplemented
423#878—32no—
424#878C2×D312yescomplemented
425#876—32no—
426#874—32no—
427C4×D12—32no—
428#872—32no—
429C23×C32C2412yes—
430C23×C32C2411yescharacteristic
431C22×C3⋊D3—22no—
432C22×C3⋊D3—22no—
433C22×C3⋊D3—24no—
434C22×C3⋊D3—41no—
435C22×C3⋊D3—42no—
436C22×C3⋊D3—42no—
437C22×C3⋊D3C2411yescharacteristic
438C22×C3⋊D3C2412yes—
439C22×C3⋊D3C2411yescharacteristic
440C22×C3×D3—22no—
441C22×C3×D3—42no—
442C22×C3×D3—41no—
443C22×C3×D3—42no—
444C22×C3×D3—41no—
445C22×C3×D3—42no—
446C22×C3×D3C2412yes—
447C22×C3×D3C2412yes—
448C32×D4—24no—
449C32×D4—41no—
450C2×C32×C4—41no—
451C2×C32×C4C2412yes—
452C2×C32×C4C2411yescharacteristic
453C2×C32×C4C2411yescharacteristic
454#638—24no—
455#638—42no—
456#638—42no—
457C2×C3⋊Dic3—41no—
458C2×C3⋊Dic3C2411yescharacteristic
459C2×C3⋊Dic3C2412yes—
460C2×C3⋊Dic3C2411yescharacteristic
461C4⋊(C3⋊D3)—41no—
462C4⋊(C3⋊D3)—42no—
463C4×C3⋊D3—22no—
464C4×C3⋊D3—22no—
465C4×C3⋊D3—41no—
466C4×C3⋊D3—41no—
467C4×C3⋊D3—42no—
468C3×#67—24no—
469C3×#67—42no—
470C3×#67—42no—
471C2×C3×Dic3—22no—
472C2×C3×Dic3—42no—
473C2×C3×Dic3—41no—
474C2×C3×Dic3—41no—
475C2×C3×Dic3C2412yes—
476C2×C3×Dic3C2412yes—
477C2×C3×Dic3C2412yes—
478C2×C3×Dic3C2412yes—
479C2×C3×Dic3C2412yes—
480C2×C3×Dic3C2412yes—
481C3×D12—41no—
482C3×D12—42no—
483C3×C4×D3—42no—
484C3×Dic6—41no—
485#627—42no—
486#626—24no—
487#626—24no—
488#626—42no—
489#626—42no—
490#626—42no—
491#626—42no—
492#626—42no—
493#626—42no—
494#624—42no—
495#624—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—31no—
508#539—92no—
509#538—91no—
510#538—92no—
511#537—91no—
512#534—31no—
513#534—92no—
514#525—91no—
515C2×#123—91no—
516C2×#121—91no—
517C24×C3—31no—
518C24×C3—32no—
519C23×D3—31no—
520C23×D3—31no—
521C23×D3—32no—
522C23×D3—32no—
523C23×D3—61no—
524C23×D3—62no—
525C23×D3C22×D311yescharacteristic
526C23×D3C22×D312yes—
527C2×C3×Q8—31no—
528C2×C3×D4—21no—
529C2×C3×D4—22no—
530C2×C3×D4—32no—
531C2×C3×D4—32no—
532C2×C3×D4—32no—
533C2×C3×D4—32no—
534C2×C3×D4—31no—
535C2×C3×D4—124no—
536C2×C3×D4C22×D312yes—
537C2×C3×D4C22×D312yes—
538C2×C3×D4C22×D311yescharacteristic
539C2×C3×D4C22×D311yescharacteristic
540C22×C3×C4—21no—
541C22×C3×C4—31no—
542C22×C3×C4—31no—
543C22×C3×C4—31no—
544C22×C3×C4—32no—
545C22×C3×C4—32no—
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—62no—
563C2×#67—62no—
564C2×#67—62no—
565C2×#67—124no—
566C2×#67—122no—
567C2×#67C22×D312yes—
568C2×#67C22×D312yes—
569C2×#67C22×D312yes—
570C22×Dic3—31no—
571C22×Dic3—31no—
572C22×Dic3—32no—
573C22×Dic3—32no—
574C22×Dic3—61no—
575C22×Dic3C22×D311yescharacteristic
576C22×Dic3C22×D312yes—
577C22×Dic3C22×D311yescharacteristic
578C22×Dic3C22×D311yescharacteristic
579#239—122no—
580#237—122no—
581#237—124no—
582D3×D4—44no—
583D3×D4—122no—
584D3×D4—122no—
585D3×D4—124no—
586D3×D4—124no—
587D3×D4—124no—
588D3×D4—128no—
589#235—124no—
590C2×D12—32no—
591C2×D12—32no—
592C2×D12—32no—
593C2×D12—32no—
594C2×D12—32no—
595C2×D12—32no—
596C2×D12—32no—
597C2×D12—32no—
598C2×D12—32no—
599C2×D12—31no—
600C2×D12—32no—
601C2×D12—31no—
602C2×D12—62no—
603C2×D12—61no—
604C2×D12—122no—
605C2×D12—124no—
606C2×D12C22×D312yes—
607C2×D12C22×D311yescharacteristic
608C2×C4×D3—31no—
609C2×C4×D3—31no—
610C2×C4×D3—31no—
611C2×C4×D3—31no—
612C2×C4×D3—32no—
613C2×C4×D3—32no—
614C2×C4×D3—32no—
615C2×C4×D3—32no—
616C2×C4×D3—31no—
617C2×C4×D3—31no—
618C2×C4×D3—31no—
619C2×C4×D3—31no—
620C2×C4×D3—32no—
621C2×C4×D3—32no—
622C2×C4×D3—32no—
623C2×C4×D3—32no—
624C2×C4×D3—61no—
625C2×C4×D3—61no—
626C2×C4×D3—62no—
627C2×C4×D3—61no—
628C2×C4×D3—61no—
629C2×C4×D3—122no—
630C2×C4×D3—122no—
631C2×C4×D3—124no—
632C2×C4×D3C22×D312yes—
633C2×Dic6—32no—
634C2×Dic6—32no—
635C2×Dic6C22×D311yescharacteristic
636C3×C4⋊C4—21no—
637C3×C4⋊C4—32no—
638C3×C4⋊C4—32no—
639C3×C4⋊C4—31no—
640C3×C4⋊C4—31no—
641C3×C4⋊C4—32no—
642C3×C4⋊C4—32no—
643C3×C4⋊C4—32no—
644C3×C4⋊C4—32no—
645C3×C4⋊C4—32no—
646C3×C4⋊C4C22×D311yescharacteristic
647C3×C4⋊C4C22×D311yescharacteristic
648C3×C22⋊C4—22no—
649C3×C22⋊C4—32no—
650C3×C22⋊C4—32no—
651C3×C22⋊C4—32no—
652C3×C22⋊C4—32no—
653C3×C22⋊C4—32no—
654C3×C22⋊C4—32no—
655C3×C22⋊C4—32no—
656C3×C22⋊C4—32no—
657C3×C22⋊C4—32no—
658C3×C22⋊C4C22×D312yes—
659C3×C22⋊C4C22×D312yes—
660C3×C42—32no—
661#217—32no—
662#217—32no—
663#217—32no—
664#217—32no—
665#217—32no—
666#217—32no—
667#217—32no—
668#217—32no—
669#217—62no—
670#217C22×D312yes—
671#217C22×D312yes—
672#217C22×D312yes—
673#217C22×D312yes—
674#217C22×D312yes—
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—32no—
689(C2×D3)⋊C4—32no—
690(C2×D3)⋊C4—32no—
691(C2×D3)⋊C4—32no—
692(C2×D3)⋊C4—32no—
693(C2×D3)⋊C4—32no—
694(C2×D3)⋊C4—32no—
695(C2×D3)⋊C4—32no—
696(C2×D3)⋊C4—32no—
697(C2×D3)⋊C4—62no—
698(C2×D3)⋊C4—62no—
699(C2×D3)⋊C4C22×D312yes—
700(C2×D3)⋊C4C22×D312yes—
701(C2×D3)⋊C4C22×D312yes—
702(C2×D3)⋊C4C22×D312yes—
703C4⋊Dic3—31no—
704C4⋊Dic3—31no—
705C4⋊Dic3—32no—
706C4⋊Dic3—32no—
707C4⋊Dic3—32no—
708C4⋊Dic3—32no—
709C4⋊Dic3—61no—
710C4⋊Dic3C22×D312yes—
711C4⋊Dic3C22×D311yescharacteristic
712C4⋊Dic3C22×D311yescharacteristic
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—62no—
722Dic3⋊C4C22×D312yes—
723Dic3⋊C4C22×D312yes—
724Dic3⋊C4C22×D312yes—
725Dic3⋊C4C22×D312yes—
726Dic3⋊C4C22×D312yes—
727Dic3⋊C4C22×D312yes—
728C4×Dic3—32no—
729C4×Dic3—32no—
730C4×Dic3—32no—
731C4×Dic3—32no—
732C4×Dic3C22×D312yes—
733C22×C32—21no—
734C22×C32—21no—
735C22×C32—22no—
736C22×C32—22no—
737C22×C32—22no—
738C22×C32H(5,𝔽2)12yes—
739C22×C32C2511yescharacteristic
740C2×C3⋊D3—21no—
741C2×C3⋊D3—21no—
742C2×C3⋊D3—21no—
743C2×C3⋊D3—22no—
744C2×C3⋊D3—21no—
745C2×C3⋊D3—22no—
746C2×C3⋊D3—22no—
747C2×C3⋊D3—21no—
748C2×C3⋊D3—44no—
749C2×C3⋊D3—84no—
750C2×C3⋊D3H(5,𝔽2)12yes—
751C2×C3×D3—22no—
752C2×C3×D3—22no—
753C2×C3×D3—22no—
754C2×C3×D3—22no—
755C2×C3×D3—22no—
756C2×C3×D3—22no—
757C2×C3×D3—82no—
758C2×C3×D3—84no—
759C32×C4—21no—
760C32×C4—21no—
761C32×C4—22no—
762C3⋊Dic3—21no—
763C3⋊Dic3—21no—
764C3⋊Dic3—22no—
765C3×Dic3—22no—
766C3×Dic3—22no—
767C3×Dic3—22no—
768C3×Dic3—22no—
769C3×Dic3—22no—
770C3×Dic3—22no—
771C2×#41—92no—
772C2×#41—91no—
773C22×D4—32no—
774C22×D4—91no—
775C22×D4—92no—
776C22×D4—91no—
777C22×D4—92no—
778C23×C4—91no—
779#127—92no—
780#126—32no—
781#126—92no—
782#126—92no—
783#126—92no—
784#125—32no—
785#125—92no—
786#124—92no—
787#124—92no—
788#124—92no—
789#123—32no—
790#123—32no—
791#123—32no—
792#123—32no—
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—
802#123—92no—
803C22⋊Q8—31no—
804C22⋊Q8—32no—
805C22⋊Q8—92no—
806C22⋊Q8—92no—
807C22⋊Q8—92no—
808C22⋊Q8—92no—
809C22⋊Q8—91no—
810#121—32no—
811#121—31no—
812#121—92no—
813#121—92no—
814#121—92no—
815#121—92no—
816#121—92no—
817#121—92no—
818#121—92no—
819#121—91no—
820#121—92no—
821#121—92no—
822#121—92no—
823#121—92no—
824#121—92no—
825#121—91no—
826#121—92no—
827#121—91no—
828#121—91no—
829#121—92no—
830#121D3211yescharacteristic
831#120—32no—
832#120—32no—
833#120—92no—
834#120—92no—
835#120—92no—
836#120—92no—
837#120—92no—
838#120—92no—
839C4×D4—32no—
840C4×D4—92no—
841C4×D4—92no—
842C4×D4—92no—
843C4×D4—92no—
844C4×D4—92no—
845C4×D4—92no—
846C4×D4—92no—
847#117—92no—
848#117—91no—
849C2×C4⋊C4—31no—
850C2×C4⋊C4—91no—
851C2×C4⋊C4—91no—
852C2×C22⋊C4—31no—
853C2×C22⋊C4—92no—
854C2×C22⋊C4—92no—
855C2×C22⋊C4—91no—
856C2×C22⋊C4—91no—
857C2×C22⋊C4—92no—
858C23×C3—21no—
859C23×C3—22no—
860C23×C3—32no—
861C23×C3—32no—
862C23×C3—62no—
863C23×C3—121no—
864C23×C3—122no—
865C23×C3—122no—
866C23×C3—121no—
867C23×C3—122no—
868C23×C3C23×D312yes—
869C23×C3C23×D312yes—
870C23×C3C23×D311yescharacteristic
871C23×C3C23×D311yescharacteristic
872C22×D3—22no—
873C22×D3—31no—
874C22×D3—31no—
875C22×D3—32no—
876C22×D3—31no—
877C22×D3—32no—
878C22×D3—31no—
879C22×D3—42no—
880C22×D3—41no—
881C22×D3—42no—
882C22×D3—42no—
883C22×D3—41no—
884C22×D3—61no—
885C22×D3—61no—
886C22×D3—62no—
887C22×D3—62no—
888C22×D3—62no—
889C22×D3—64no—
890C22×D3—64no—
891C22×D3—64no—
892C22×D3—62no—
893C22×D3—62no—
894C22×D3—122no—
895C22×D3—124no—
896C22×D3—121no—
897C22×D3—121no—
898C22×D3—122no—
899C22×D3—122no—
900C22×D3—122no—
901C22×D3—122no—
902C22×D3—122no—
903C22×D3—124no—
904C22×D3—124no—
905C22×D3C23×D312yes—
906C22×D3C23×D312yes—
907C3×Q8—121no—
908C3×D4—24no—
909C3×D4—24no—
910C3×D4—44no—
911C3×D4—41no—
912C3×D4—41no—
913C3×D4—42no—
914C3×D4—64no—
915C3×D4—121no—
916C3×D4—122no—
917C3×D4—122no—
918C3×D4—122no—
919C2×C3×C4—21no—
920C2×C3×C4—22no—
921C2×C3×C4—21no—
922C2×C3×C4—32no—
923C2×C3×C4—32no—
924C2×C3×C4—32no—
925C2×C3×C4—32no—
926C2×C3×C4—32no—
927C2×C3×C4—32no—
928C2×C3×C4—41no—
929C2×C3×C4—41no—
930C2×C3×C4—42no—
931C2×C3×C4—62no—
932C2×C3×C4—122no—
933C2×C3×C4—122no—
934C2×C3×C4—121no—
935C2×C3×C4—121no—
936C2×C3×C4C23×D312yes—
937C2×C3×C4C23×D312yes—
938C2×C3×C4C23×D311yescharacteristic
939C2×C3×C4C23×D311yescharacteristic
940C2×C3×C4C23×D311yescharacteristic
941C2×C3×C4C23×D311yescharacteristic
942#67—24no—
943#67—42no—
944#67—42no—
945#67—64no—
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—124no—
961#67—124no—
962C2×Dic3—22no—
963C2×Dic3—31no—
964C2×Dic3—31no—
965C2×Dic3—32no—
966C2×Dic3—32no—
967C2×Dic3—31no—
968C2×Dic3—31no—
969C2×Dic3—41no—
970C2×Dic3—42no—
971C2×Dic3—41no—
972C2×Dic3—61no—
973C2×Dic3—62no—
974C2×Dic3—61no—
975C2×Dic3—122no—
976C2×Dic3—122no—
977C2×Dic3—121no—
978C2×Dic3—121no—
979C2×Dic3—122no—
980C2×Dic3C23×D312yes—
981C2×Dic3C23×D312yes—
982C2×Dic3C23×D312yes—
983C2×Dic3C23×D312yes—
984C2×Dic3C23×D312yes—
985C2×Dic3C23×D312yes—
986D12—42no—
987D12—41no—
988D12—64no—
989D12—64no—
990D12—122no—
991D12—122no—
992D12—121no—
993D12—121no—
994D12—122no—
995D12—124no—
996D12—122no—
997D12—122no—
998D12—122no—
999D12—122no—
1000D12—122no—
1001D12—122no—
1002C4×D3—42no—
1003C4×D3—62no—
1004C4×D3—62no—
1005C4×D3—62no—
1006C4×D3—62no—
1007C4×D3—64no—
1008C4×D3—122no—
1009C4×D3—122no—
1010C4×D3—122no—
1011C4×D3—122no—
1012C4×D3—122no—
1013C4×D3—121no—
1014C4×D3—121no—
1015C4×D3—121no—
1016C4×D3—121no—
1017C4×D3—122no—
1018C4×D3—122no—
1019C4×D3—122no—
1020C4×D3—122no—
1021C4×D3—122no—
1022C4×D3—122no—
1023C4×D3—124no—
1024Dic6—41no—
1025Dic6—122no—
1026Dic6—122no—
1027C2×C32—22no—
1028C2×C32—42no—
1029C2×C32C2×H(5,𝔽2)11yescharacteristic
1030C2×C32C2×H(5,𝔽2)11yescharacteristic
1031C2×C32#58511yescharacteristic
1032C3⋊D3—22no—
1033C3⋊D3—41no—
1034C3⋊D3—42no—
1035C3×D3—42no—
1036C3×D3—42no—
1037C24—31no—
1038C24—32no—
1039C24—91no—
1040C24—92no—
1041#41—364no—
1042#41—362no—
1043C2×Q8—31no—
1044C2×Q8—92no—
1045C2×D4—32no—
1046C2×D4—32no—
1047C2×D4—32no—
1048C2×D4—31no—
1049C2×D4—32no—
1050C2×D4—92no—
1051C2×D4—92no—
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—91no—
1062C2×D4—92no—
1063C2×D4—124no—
1064C2×D4—362no—
1065C2×D4—364no—
1066C2×D4—362no—
1067C2×D4—364no—
1068C2×D4C2×D3212yes—
1069C2×D4C2×D3211yescharacteristic
1070C22×C4—31no—
1071C22×C4—31no—
1072C22×C4—31no—
1073C22×C4—32no—
1074C22×C4—32no—
1075C22×C4—92no—
1076C22×C4—92no—
1077C22×C4—92no—
1078C22×C4—92no—
1079C22×C4—91no—
1080C22×C4—91no—
1081C22×C4—91no—
1082C22×C4—92no—
1083C22×C4—91no—
1084C22×C4—91no—
1085C22×C4—362no—
1086C22×C4C2×D3211yescharacteristic
1087C4⋊C4—32no—
1088C4⋊C4—32no—
1089C4⋊C4—31no—
1090C4⋊C4—32no—
1091C4⋊C4—31no—
1092C4⋊C4—32no—
1093C4⋊C4—32no—
1094C4⋊C4—32no—
1095C4⋊C4—32no—
1096C4⋊C4—92no—
1097C4⋊C4—92no—
1098C4⋊C4—92no—
1099C4⋊C4—92no—
1100C4⋊C4—92no—
1101C4⋊C4—91no—
1102C4⋊C4—92no—
1103C4⋊C4C2×D3211yescharacteristic
1104C22⋊C4—32no—
1105C22⋊C4—32no—
1106C22⋊C4—32no—
1107C22⋊C4—32no—
1108C22⋊C4—32no—
1109C22⋊C4—32no—
1110C22⋊C4—32no—
1111C22⋊C4—32no—
1112C22⋊C4—32no—
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⋊C4—92no—
1124C22⋊C4—92no—
1125C22⋊C4—92no—
1126C22⋊C4—92no—
1127C22⋊C4—92no—
1128C22⋊C4C2×D3212yes—
1129C42—32no—
1130C42—92no—
1131C42—92no—
1132C22×C3—21no—
1133C22×C3—21no—
1134C22×C3—21no—
1135C22×C3—21no—
1136C22×C3—22no—
1137C22×C3—22no—
1138C22×C3—22no—
1139C22×C3—22no—
1140C22×C3—22no—
1141C22×C3—22no—
1142C22×C3—22no—
1143C22×C3—21no—
1144C22×C3—41no—
1145C22×C3—41no—
1146C22×C3—42no—
1147C22×C3—42no—
1148C22×C3—42no—
1149C22×C3—62no—
1150C22×C3—62no—
1151C22×C3—62no—
1152C22×C3—62no—
1153C22×C3—62no—
1154C22×C3—62no—
1155C22×C3—242no—
1156C22×C3—244no—
1157C22×C3#100412yes—
1158C22×C3#100912yes—
1159C22×C3C24×D311yescharacteristic
1160C22×C3C24×D311yescharacteristic
1161C2×D3—22no—
1162C2×D3—22no—
1163C2×D3—22no—
1164C2×D3—22no—
1165C2×D3—22no—
1166C2×D3—22no—
1167C2×D3—32no—
1168C2×D3—32no—
1169C2×D3—62no—
1170C2×D3—62no—
1171C2×D3—62no—
1172C2×D3—61no—
1173C2×D3—61no—
1174C2×D3—61no—
1175C2×D3—61no—
1176C2×D3—62no—
1177C2×D3—62no—
1178C2×D3—61no—
1179C2×D3—62no—
1180C2×D3—61no—
1181C2×D3—61no—
1182C2×D3—61no—
1183C2×D3—62no—
1184C2×D3—62no—
1185C2×D3—62no—
1186C2×D3—61no—
1187C2×D3—62no—
1188C2×D3—61no—
1189C2×D3—82no—
1190C2×D3—84no—
1191C2×D3—121no—
1192C2×D3—121no—
1193C2×D3—122no—
1194C2×D3—122no—
1195C2×D3—122no—
1196C2×D3—124no—
1197C2×D3—124no—
1198C2×D3—128no—
1199C2×D3—244no—
1200C2×D3—244no—
1201C2×D3—248no—
1202C3×C4—22no—
1203C3×C4—22no—
1204C3×C4—22no—
1205C3×C4—21no—
1206C3×C4—21no—
1207C3×C4—21no—
1208C3×C4—21no—
1209C3×C4—41no—
1210C3×C4—42no—
1211C3×C4—62no—
1212C3×C4—62no—
1213C3×C4—62no—
1214C3×C4—62no—
1215C3×C4—62no—
1216C3×C4—62no—
1217Dic3—22no—
1218Dic3—22no—
1219Dic3—22no—
1220Dic3—22no—
1221Dic3—22no—
1222Dic3—22no—
1223Dic3—62no—
1224Dic3—62no—
1225Dic3—62no—
1226Dic3—61no—
1227Dic3—61no—
1228Dic3—61no—
1229Dic3—61no—
1230Dic3—121no—
1231Dic3—122no—
1232C32#353411yescharacteristic, complemented, Sylow
1233C23—32no—
1234C23—32no—
1235C23—62no—
1236C23—91no—
1237C23—91no—
1238C23—92no—
1239C23—122no—
1240C23—121no—
1241C23—122no—
1242C23—121no—
1243C23—122no—
1244C23—182no—
1245C23—184no—
1246C23—182no—
1247C23—361no—
1248C23—362no—
1249C23—362no—
1250C23C22×D3212yes—
1251C23C22×D3211yescharacteristic
1252Q8—121no—
1253Q8—362no—
1254D4—24no—
1255D4—41no—
1256D4—64no—
1257D4—122no—
1258D4—121no—
1259D4—122no—
1260D4—122no—
1261D4—184no—
1262D4—184no—
1263D4—184no—
1264D4—361no—
1265D4—362no—
1266D4—362no—
1267D4—362no—
1268D4—362no—
1269D4—362no—
1270D4—362no—
1271D4—362no—
1272D4—362no—
1273D4—362no—
1274C2×C4—32no—
1275C2×C4—32no—
1276C2×C4—32no—
1277C2×C4—32no—
1278C2×C4—32no—
1279C2×C4—32no—
1280C2×C4—41no—
1281C2×C4—62no—
1282C2×C4—91no—
1283C2×C4—92no—
1284C2×C4—91no—
1285C2×C4—122no—
1286C2×C4—121no—
1287C2×C4—122no—
1288C2×C4—121no—
1289C2×C4—182no—
1290C2×C4—182no—
1291C2×C4—361no—
1292C2×C4—361no—
1293C2×C4—362no—
1294C2×C4—362no—
1295C2×C4—362no—
1296C2×C4—362no—
1297C2×C4—362no—
1298C2×C4—361no—
1299C2×C4C22×D3212yes—
1300C2×C4C22×D3211yescharacteristic
1301C2×C4C22×D3211yescharacteristic
1302C2×C3—22no—
1303C2×C3—22no—
1304C2×C3—21no—
1305C2×C3—21no—
1306C2×C3—21no—
1307C2×C3—42no—
1308C2×C3—42no—
1309C2×C3—42no—
1310C2×C3—82no—
1311C2×C3—122no—
1312C2×C3—122no—
1313C2×C3C2×#100411yescharacteristic
1314C2×C3C2×#100911yescharacteristic
1315C2×C3D3×H(5,𝔽2)11yescharacteristic
1316C2×C3D3×H(5,𝔽2)11yescharacteristic
1317C2×C3#596611yescharacteristic
1318C2×C3#596811yescharacteristic
1319D3—42no—
1320D3—42no—
1321D3—64no—
1322D3—62no—
1323D3—62no—
1324D3—122no—
1325D3—121no—
1326D3—122no—
1327D3—121no—
1328D3—122no—
1329D3—242no—
1330C22—21no—
1331C22—21no—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—62no—
1336C22—62no—
1337C22—62no—
1338C22—62no—
1339C22—62no—
1340C22—62no—
1341C22—92no—
1342C22—181no—
1343C22—181no—
1344C22—181no—
1345C22—182no—
1346C22—182no—
1347C22—181no—
1348C22—182no—
1349C22—181no—
1350C22—242no—
1351C22—244no—
1352C22—364no—
1353C22—724no—
1354C22#6431412yes—
1355C22C23×D3211yescharacteristic
1356C4—21no—
1357C4—21no—
1358C4—22no—
1359C4—62no—
1360C4—62no—
1361C4—62no—
1362C4—62no—
1363C4—62no—
1364C4—62no—
1365C4—181no—
1366C4—181no—
1367C4—182no—
1368C3—21no—
1369C3#8631211yescharacteristic, complemented
1370C3#8645911yescharacteristic, complemented
1371C2—22no—
1372C2—42no—
1373C2—122no—
1374C2—122no—
1375C2—182no—
1376C2—361no—
1377C2—362no—
1378C2#1059667511yescharacteristic
1379C2C2×#6431411yescharacteristic
1380C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#121C22
hypercenter#121D32
hypocenterC32#3534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×#121C2semidirect
2. C3×#5605C2semidirect
3. C3×#5602C2semidirect
4. #10595242C2semidirect
5. D4×#626C2semidirect
6. #10595193C2semidirect
7. #10595185C2semidirect
8. #10595163C2semidirect
9. #10595148C2semidirect
10. #10595038C2semidirect
11. #10594922C2semidirect
12. #10594911C2semidirect
13. C2×#63853C2semidirect
14. #10594572C2semidirect
15. #10594467C2semidirect
16. #10594236C2semidirect
17. #10594228C2semidirect
18. #10594063C2semidirect
19. #10594043C2semidirect
22. C2×D4×C3⋊D3C22semidirect
23. C2×D4×C3⋊D3C22semidirect
24. C22×C4×C3⋊D3C22semidirect
25. C2×C3×D3×D4C22semidirect
27. C22×#626C22semidirect
28. C2×#3804C22semidirect
29. C2×#3796C22semidirect
31. #64148C22semidirect
32. #64147C22semidirect
33. #64139C22semidirect
34. #64104C22semidirect
35. C4⋊C4×C3⋊D3C22semidirect
36. #64093C22semidirect
37. C22⋊C4×C3⋊D3C22semidirect
38. C3×#939C22semidirect
39. C3×#937C22semidirect
40. C3×#935C22semidirect
41. C3×#935C22semidirect
42. C3×D4×Dic3C22semidirect
43. C3×#930C22semidirect
44. C2×C3×(C2×D3)⋊C4C22semidirect
45. C3×#924C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C3×#894C22semidirect
48. C3×#889C22semidirect
49. C3×#883C22semidirect
50. C3×#882C22semidirect
51. C3×#879C22semidirect
52. C3×#878C22semidirect
54. #63981C22semidirect
55. #63981C22semidirect
56. #63978C22semidirect
57. #63978C22semidirect
58. #63977C22semidirect
59. #63977C22semidirect
60. #63977C22semidirect
61. #63974C22semidirect
62. #67⋊Dic3C22semidirect
63. Dic3×#67C22semidirect
64. #63971C22semidirect
65. D3×#217C22semidirect
66. #63966C22semidirect
67. C2×Dic3⋊Dic3C22semidirect
68. C2×#3722C22semidirect
69. C2×(C2×D3)⋊Dic3C22semidirect
70. #63959C22semidirect
71. #63958C22semidirect
72. #63958C22semidirect
73. #63956C22semidirect
74. #63953C22semidirect
75. #63952C22semidirect
77. #63916C22semidirect
78. #63911C22semidirect
79. #63910C22semidirect
80. #63910C22semidirect
81. #63910C22semidirect
82. #63909C22semidirect
83. #63907C22semidirect
84. #63904C22semidirect
85. C4×#626C22semidirect
86. #63897C22semidirect
87. #63895C22semidirect
88. #63893C22semidirect
89. #63890C22semidirect
90. #63886C22semidirect
91. #63886C22semidirect
92. #63884C22semidirect
93. #63881C22semidirect
94. #63881C22semidirect
95. #63871C22semidirect
96. #63865C22semidirect
97. #63861C22semidirect
98. #63859C22semidirect
99. #63854C22semidirect
100. #63853C22semidirect
101. #63853C22semidirect
102. #63853C22semidirect
103. #63853C22semidirect
104. #63853C22semidirect
105. #63851C22semidirect
106. #63849C22semidirect
107. #63846C22semidirect
108. #63836C22semidirect
132. #5605D3semidirect
136. #5602D3semidirect
256. C2×D3×D4C2×D3semidirect
297. #939C2×D3semidirect
308. #937C2×D3semidirect
311. #935C2×D3semidirect
312. #935C2×D3semidirect
315. D4×Dic3C2×D3semidirect
322. #930C2×D3semidirect
331. C2×(C2×D3)⋊C4C2×D3semidirect
334. #924C2×D3semidirect
336. C2×Dic3⋊C4C2×D3semidirect
366. #894C2×D3semidirect
378. #889C2×D3semidirect
400. #883C2×D3semidirect
407. #882C2×D3semidirect
422. #879C2×D3semidirect
424. #878C2×D3semidirect
1232. C32#3534semidirect
1369. C3#86312semidirect
1370. C3#86459semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1212
C3×#56052
C3×#56022
#105952422
D4×#6262
#105951932
#105951852
#105951632
#105951482
#105950382
#105949222
#105949112
C2×#638532
#105945722
#105944672
#105942362
#105942282
#105940632
#105940432
#864593
#863123