Finite Group Databasebeta

← #11911150

Subgroups — #11911150

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×#5617C211yesmaximal, characteristic, complemented
3C3×#5597C211yesmaximal, characteristic, complemented
4#10595308C212yesmaximal, complemented
5#10595304C212yesmaximal, complemented
6#10595292C212yesmaximal, complemented
7#10595254C212yesmaximal, complemented
8#10595197C212yesmaximal, complemented
9#10595196C212yesmaximal, complemented
10#10595072C211yesmaximal, characteristic, complemented
11#10594980C211yesmaximal, characteristic, complemented
12#10594922C211yesmaximal, characteristic, complemented
13C2×#63853C211yesmaximal, characteristic, complemented
14#10594652C212yesmaximal, complemented
15#10594573C212yesmaximal, complemented
16#10594308C212yesmaximal, complemented
17#10594285C212yesmaximal, complemented
18#10594178C212yesmaximal, complemented
19#10594164C212yesmaximal, complemented
20#86420—31nomaximal
21#86383—31nomaximal
22C2×D4×C3⋊D3C2212yescomplemented
23C2×D4×C3⋊D3C2211yescharacteristic, complemented
24C22×C4×C3⋊D3C2211yescharacteristic, complemented
25C2×C3×#237C2212yescomplemented
26C2×#3811C2212yescomplemented
27C2×D3×#67C2212yescomplemented
28C22×#626C2211yescharacteristic
29C2×#3796C2211yescharacteristic, complemented
30C32×#121C2211yescharacteristic, complemented
31#64148C2212yescomplemented
32#64147C2211yescharacteristic, complemented
33#64139C2211yescharacteristic
34#64104C2211yescharacteristic, complemented
35C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
36#64093C2212yescomplemented
37C22⋊C4×C3⋊D3C2212yescomplemented
38C3×#939C2212yescomplemented
39C3×#939C2212yescomplemented
40C3×#939C2212yescomplemented
41C3×#937C2212yescomplemented
42C3×D4×Dic3C2212yescomplemented
43C3×#930C2211yescharacteristic, complemented
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C3×#924C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C3×#898C2212yescomplemented
48C3×#896C2212yescomplemented
49C3×#886C2212yescomplemented
50C3×#885C2212yescomplemented
51C3×#884C2212yescomplemented
52C3×#878C2212yescomplemented
53#63983C2212yescomplemented
54#63981C2212yes—
55#63981C2212yescomplemented
56#63981C2212yescomplemented
57#63979C2212yescomplemented
58#63978C2212yescomplemented
59#63978C2212yescomplemented
60#63978C2212yescomplemented
61#63978C2212yescomplemented
62#63975C2212yescomplemented
63#67⋊Dic3C2212yescomplemented
64Dic3×#67C2212yescomplemented
65#63971C2212yescomplemented
66#63970C2212yescomplemented
67#63969C2212yescomplemented
68#63966C2212yescomplemented
69#63966C2212yescomplemented
70C2×Dic3⋊Dic3C2211yescharacteristic, complemented
71C2×#3722C2211yescharacteristic, complemented
72C2×#3722C2212yescomplemented
73C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
74#63955C2212yescomplemented
75#63952C2212yescomplemented
76#63923C2212yescomplemented
77#63923C2212yescomplemented
78#63922C2212yescomplemented
79D3×(C2×D3)⋊C4C2212yescomplemented
80#63916C2211yescharacteristic, complemented
81#63912C2212yes—
82#63910C2212yescomplemented
83#63909C2212yescomplemented
84#63907C2212yescomplemented
85#63905C2212yescomplemented
86C4×#626C2212yescomplemented
87#63897C2212yescomplemented
88#63891C2212yescomplemented
89#63890C2212yescomplemented
90#63888C2212yescomplemented
91#63887C2212yescomplemented
92#63881C2212yescomplemented
93#63881C2212yescomplemented
94#63880C2212yescomplemented
95#63871C2212yescomplemented
96#63871C2211yescharacteristic, complemented
97#63867C2212yescomplemented
98#63864C2212yescomplemented
99#63858C2212yescomplemented
100#63853C2212yescomplemented
101#63853C2212yescomplemented
102#63853C2212yescomplemented
103#63853C2212yescomplemented
104#63853C2212yescomplemented
105#63849C2211yescharacteristic, complemented
106#63848C2212yescomplemented
107#63848C2212yescomplemented
108#63845C2212yescomplemented
109C3×#538—31no—
110C3×#537—31no—
111#5829—32no—
112#5829—32no—
113#5707—32no—
114#5704—32no—
115#5684—32no—
116#5676—32no—
117#5666—32no—
118#5658—32no—
119#5647—32no—
120#5645—31no—
121#5644—32no—
122#5638—32no—
123#5637—32no—
124#5627—31no—
125#5620—32no—
126#5619—32no—
127#5617D311yescharacteristic, complemented
128#5615—32no—
129#5610—32no—
130#5609—32no—
131#5606—31no—
132#5605—32no—
133#5605—32no—
134#5605—31no—
135D3×#121—31no—
136D3×#121—31no—
137D3×#121—61no—
138#5601—32no—
139#5597D311yescharacteristic, complemented
140#5591—32no—
141#5590—32no—
142#5565—32no—
143#5554—32no—
144#5515—31no—
145C2×#894—31no—
146#5493—31no—
147C2×#883—31no—
148C23×C3⋊D3C2311yescharacteristic
149C23×C3⋊D3C2312yes—
150C23×C3×D3C2311yescharacteristic
151C22×D32C2312yes—
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—
172C2×C3×#67C2312yes—
173C2×C3×#67C2312yes—
174C22×C3×Dic3C2311yescharacteristic
175C22×C3×Dic3C2312yes—
176C22×C3×Dic3C2312yes—
177C22×C3×Dic3C2311yescharacteristic
178C22×C3×Dic3C2311yescharacteristic
179C3×#237—44no—
180C2×C3×D12C2311yescharacteristic
181C2×C3×C4×D3C2312yes—
182C2×C3×Dic6C2312yes—
183C2×C3×Dic6C2311yescharacteristic
184#3811—44no—
185D3×#67—44no—
186C2×#626—42no—
187C2×#626C2312yes—
188C2×#626C2312yes—
189C2×#626C2312yes—
190C2×#626C2312yes—
191C2×#626C2312yes—
192C2×#626C2312yes—
193C2×#625C2312yes—
194C2×#624C2312yes—
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×(C2×D3)⋊C4C2312yes—
209C3×(C2×D3)⋊C4C2312yes—
210C3×(C2×D3)⋊C4C2312yes—
211C3×(C2×D3)⋊C4C2312yes—
212C3×(C2×D3)⋊C4C2312yes—
213C3×(C2×D3)⋊C4C2312yes—
214C3×C4⋊Dic3C2311yescharacteristic
215C3×C4⋊Dic3C2311yescharacteristic
216C3×C4⋊Dic3C2312yes—
217C3×Dic3⋊C4C2312yes—
218C3×Dic3⋊C4C2312yes—
219C3×Dic3⋊C4C2312yes—
220C3×Dic3⋊C4C2312yes—
221C3×C4×Dic3C2312yes—
222#3724C2312yes—
223Dic3⋊Dic3C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226Dic3⋊Dic3C2312yes—
227Dic3⋊Dic3C2312yes—
228Dic3⋊Dic3C2312yes—
229#3722C2312yes—
230#3722C2312yes—
231#3722C2312yes—
232#3722C2312yes—
233#3722C2312yes—
234#3722C2312yes—
235#3722C2312yes—
236#3722C2312yes—
237(C2×D3)⋊Dic3C2312yes—
238(C2×D3)⋊Dic3C2312yes—
239(C2×D3)⋊Dic3C2312yes—
240(C2×D3)⋊Dic3C2312yes—
241Dic32C2312yes—
242Dic32C2312yes—
243#3534—91noSylow
244C2×C3×#41—32no—
245C22×#67—32no—
246C22×#67—31no—
247C2×#239—31no—
248C2×#237—31no—
249C2×#237C2×D312yescomplemented
250C2×D3×D4—32no—
251C2×D3×D4—32no—
252C2×D3×D4—32no—
253C2×D3×D4—31no—
254C2×D3×D4—31no—
255C2×D3×D4—32no—
256C2×D3×D4—32no—
257C2×D3×D4—61no—
258C2×D3×D4—62no—
259C22×D12—31no—
260C22×C4×D3—31no—
261C22×C4×D3—31no—
262C22×C4×D3—61no—
263C3×#126—32no—
264C3×#124—32no—
265C3×#123—32no—
266C3×C22⋊Q8—31no—
267C3×C22⋊Q8—32no—
268C3×C22⋊Q8—32no—
269C3×#121—21no—
270C3×#121—32no—
271C3×#121—32no—
272C3×#121—32no—
273C3×#121—31no—
274C3×#121—32no—
275C3×#121C2×D311yescharacteristic, complemented
276C3×#121C2×D311yescharacteristic, complemented
277C3×#120—32no—
278C3×C4×D4—32no—
279C2×C3×C4⋊C4—31no—
280C2×C3×C22⋊C4—31no—
281C2×#217—31no—
282#947—32no—
283#947—32no—
284#946—32no—
285#946—32no—
286#946—31no—
287#946—32no—
288#940—32no—
289#940—32no—
290#939—32no—
291#939—32no—
292#939—32no—
293#939—32no—
294#939—32no—
295#939—32no—
296#939—32no—
297#939—32no—
298#939—62no—
299#939C2×D312yescomplemented
300#939C2×D312yescomplemented
301#939C2×D312yescomplemented
302#938—31no—
303#938—31no—
304#938—32no—
305#938—31no—
306#938—61no—
307#937—32no—
308#937—32no—
309#937—32no—
310#937—32no—
311#937—32no—
312#937—32no—
313#937C2×D312yescomplemented
314#935—32no—
315D4×Dic3—32no—
316D4×Dic3—32no—
317D4×Dic3C2×D312yescomplemented
318#930—31no—
319#930—31no—
320#930—32no—
321#930—32no—
322#930—32no—
323#930—32no—
324#930—32no—
325#930—61no—
326#930C2×D311yescharacteristic, complemented
327#929—32no—
328#929—32no—
329#929—32no—
330C4×#67—32no—
331C4×#67—32no—
332C4×#67—32no—
333C2×(C2×D3)⋊C4—31no—
334C2×(C2×D3)⋊C4—32no—
335C2×(C2×D3)⋊C4—32no—
336C2×(C2×D3)⋊C4—31no—
337C2×(C2×D3)⋊C4—31no—
338C2×(C2×D3)⋊C4—32no—
339C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
340#926—32no—
341C2×C4⋊Dic3—31no—
342#924C2×D311yescharacteristic, complemented
343C2×Dic3⋊C4—31no—
344C2×Dic3⋊C4C2×D311yescharacteristic, complemented
345#898—32no—
346#898—32no—
347#898—32no—
348#898—32no—
349#898—32no—
350#898C2×D312yescomplemented
351#897—31no—
352#897—32no—
353#896—32no—
354#896C2×D312yescomplemented
355#895—31no—
356#895—32no—
357#895—31no—
358#895—31no—
359#895—32no—
360#895—61no—
361#894—32no—
362#894—32no—
363#894—32no—
364#894—32no—
365#894—32no—
366#894—32no—
367#894—32no—
368#894—32no—
369#893—32no—
370#893—32no—
371#892—31no—
372#892—31no—
373D3×C4⋊C4—31no—
374D3×C4⋊C4—31no—
375D3×C4⋊C4—61no—
376#890—32no—
377#889—32no—
378#889—32no—
379#886—32no—
380#886—32no—
381#886—32no—
382#886—32no—
383#886C2×D312yescomplemented
384#885—32no—
385#885C2×D312yescomplemented
386#884—32no—
387#884—32no—
388#884—32no—
389#884—32no—
390#884—32no—
391#884—32no—
392#884—62no—
393#884C2×D312yescomplemented
394#883—32no—
395#883—32no—
396#883—32no—
397#883—32no—
398#883—32no—
399#883—32no—
400#883—32no—
401#883—32no—
402#883—32no—
403#883—32no—
404#882—32no—
405#882—32no—
406#882—32no—
407#882—32no—
408#882—32no—
409#882—32no—
410#882—32no—
411#882—32no—
412#67⋊C4—32no—
413#67⋊C4—32no—
414#67⋊C4—32no—
415#67⋊C4—32no—
416#67⋊C4—32no—
417D3×C22⋊C4—32no—
418D3×C22⋊C4—32no—
419D3×C22⋊C4—32no—
420D3×C22⋊C4—62no—
421#879—32no—
422#878—32no—
423#878C2×D312yescomplemented
424#877—32no—
425#875—32no—
426C4×D12—32no—
427C4×D12—32no—
428#870—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⋊D3C2412yes—
438C22×C3⋊D3C2411yescharacteristic
439C22×C3⋊D3C2411yescharacteristic
440C22×C3×D3—22no—
441C22×C3×D3—41no—
442C22×C3×D3—41no—
443C22×C3×D3C2412yes—
444C22×C3×D3C2412yes—
445C2×D32—42no—
446C2×D32—42no—
447C2×D32—42no—
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—
471C3×#67—42no—
472C3×#67—42no—
473C2×C3×Dic3—22no—
474C2×C3×Dic3—41no—
475C2×C3×Dic3—42no—
476C2×C3×Dic3—41no—
477C2×C3×Dic3—42no—
478C2×C3×Dic3C2412yes—
479C2×C3×Dic3C2412yes—
480C2×C3×Dic3C2412yes—
481C2×C3×Dic3C2412yes—
482C2×C3×Dic3C2412yes—
483C2×C3×Dic3C2412yes—
484C3×D12—41no—
485C3×C4×D3—42no—
486C3×Dic6—41no—
487C3×Dic6—42no—
488#626—24no—
489#626—24no—
490#626—42no—
491#626—42no—
492#626—42no—
493#626—42no—
494#625—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—91no—
508#539—92no—
509#538—31no—
510#538—92no—
511#537—31no—
512#534—91no—
513#534—92no—
514#525—91no—
515C2×#123—91no—
516C2×#121—91no—
517C24×C3—31no—
518C23×D3—31no—
519C23×D3—31no—
520C23×D3—32no—
521C23×D3—32no—
522C23×D3—32no—
523C23×D3—32no—
524C23×D3—61no—
525C23×D3—62no—
526C23×D3C22×D311yescharacteristic
527C3×#41—124no—
528C2×C3×Q8—31no—
529C2×C3×Q8—32no—
530C2×C3×D4—21no—
531C2×C3×D4—22no—
532C2×C3×D4—32no—
533C2×C3×D4—32no—
534C2×C3×D4—32no—
535C2×C3×D4—32no—
536C2×C3×D4—32no—
537C2×C3×D4—31no—
538C2×C3×D4C22×D312yes—
539C2×C3×D4C22×D312yes—
540C2×C3×D4C22×D311yescharacteristic
541C2×C3×D4C22×D311yescharacteristic
542C22×C3×C4—21no—
543C22×C3×C4—31no—
544C22×C3×C4—31no—
545C22×C3×C4—31no—
546C22×C3×C4—32no—
547C22×C3×C4—32no—
548C22×C3×C4—32no—
549C22×C3×C4C22×D311yescharacteristic
550C22×C3×C4C22×D311yescharacteristic
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—32no—
563C2×#67—32no—
564C2×#67—32no—
565C2×#67—62no—
566C2×#67—62no—
567C2×#67—62no—
568C2×#67—122no—
569C2×#67—124no—
570C2×#67C22×D312yes—
571C2×#67C22×D312yes—
572C2×#67C22×D312yes—
573C2×#67C22×D312yes—
574C2×#67C22×D312yes—
575C22×Dic3—31no—
576C22×Dic3—31no—
577C22×Dic3—32no—
578C22×Dic3—32no—
579C22×Dic3—61no—
580C22×Dic3C22×D311yescharacteristic
581C22×Dic3C22×D312yes—
582C22×Dic3C22×D312yes—
583C22×Dic3C22×D311yescharacteristic
584C22×Dic3C22×D311yescharacteristic
585#239—122no—
586#237—44no—
587#237—122no—
588D3×D4—122no—
589D3×D4—122no—
590D3×D4—124no—
591D3×D4—124no—
592D3×D4—124no—
593D3×D4—124no—
594D3×D4—124no—
595D3×D4—124no—
596D3×D4—128no—
597C2×D12—32no—
598C2×D12—32no—
599C2×D12—32no—
600C2×D12—32no—
601C2×D12—32no—
602C2×D12—32no—
603C2×D12—32no—
604C2×D12—31no—
605C2×D12—31no—
606C2×D12—32no—
607C2×D12—62no—
608C2×D12—61no—
609C2×D12—122no—
610C2×D12C22×D311yescharacteristic
611C2×C4×D3—31no—
612C2×C4×D3—31no—
613C2×C4×D3—31no—
614C2×C4×D3—31no—
615C2×C4×D3—32no—
616C2×C4×D3—32no—
617C2×C4×D3—32no—
618C2×C4×D3—32no—
619C2×C4×D3—31no—
620C2×C4×D3—31no—
621C2×C4×D3—31no—
622C2×C4×D3—31no—
623C2×C4×D3—32no—
624C2×C4×D3—32no—
625C2×C4×D3—61no—
626C2×C4×D3—61no—
627C2×C4×D3—62no—
628C2×C4×D3—61no—
629C2×C4×D3—61no—
630C2×C4×D3—122no—
631C2×C4×D3—122no—
632C2×C4×D3—124no—
633C2×C4×D3C22×D312yes—
634C2×Dic6C22×D312yes—
635C2×Dic6C22×D311yescharacteristic
636C3×C4⋊C4—21no—
637C3×C4⋊C4—32no—
638C3×C4⋊C4—32no—
639C3×C4⋊C4—32no—
640C3×C4⋊C4—31no—
641C3×C4⋊C4—31no—
642C3×C4⋊C4—32no—
643C3×C4⋊C4—32no—
644C3×C4⋊C4C22×D311yescharacteristic
645C3×C4⋊C4C22×D311yescharacteristic
646C3×C22⋊C4—22no—
647C3×C22⋊C4—32no—
648C3×C22⋊C4—32no—
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⋊C4C22×D312yes—
657C3×C22⋊C4C22×D312yes—
658C3×C42—32no—
659#217—32no—
660#217—32no—
661#217—32no—
662#217—32no—
663#217—32no—
664#217—32no—
665#217—62no—
666#217C22×D312yes—
667#217C22×D312yes—
668#217C22×D312yes—
669(C2×D3)⋊C4—32no—
670(C2×D3)⋊C4—32no—
671(C2×D3)⋊C4—32no—
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—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—62no—
694(C2×D3)⋊C4—62no—
695(C2×D3)⋊C4C22×D312yes—
696(C2×D3)⋊C4C22×D312yes—
697(C2×D3)⋊C4C22×D312yes—
698(C2×D3)⋊C4C22×D312yes—
699(C2×D3)⋊C4C22×D312yes—
700(C2×D3)⋊C4C22×D312yes—
701C4⋊Dic3—31no—
702C4⋊Dic3—31no—
703C4⋊Dic3—32no—
704C4⋊Dic3—32no—
705C4⋊Dic3—32no—
706C4⋊Dic3—32no—
707C4⋊Dic3—32no—
708C4⋊Dic3—32no—
709C4⋊Dic3—61no—
710C4⋊Dic3C22×D311yescharacteristic
711C4⋊Dic3C22×D312yes—
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—32no—
722Dic3⋊C4—32no—
723Dic3⋊C4—62no—
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—21no—
747C2×C3⋊D3—22no—
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—
758D32—84no—
759C32×C4—21no—
760C32×C4—22no—
761C32×C4—21no—
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—32no—
772C2×#41—91no—
773C22×D4—91no—
774C22×D4—92no—
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—92no—
785#125—92no—
786#124—32no—
787#124—92no—
788#124—92no—
789#123—32no—
790#123—92no—
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—
802#123—92no—
803C22⋊Q8—31no—
804C22⋊Q8—32no—
805C22⋊Q8—32no—
806C22⋊Q8—92no—
807C22⋊Q8—91no—
808C22⋊Q8—92no—
809C22⋊Q8—92no—
810#121—32no—
811#121—32no—
812#121—32no—
813#121—31no—
814#121—32no—
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, complemented
831#120—32no—
832#120—92no—
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—91no—
855C2×C22⋊C4—92no—
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—121no—
865C23×C3C23×D312yes—
866C23×C3C23×D312yes—
867C23×C3C23×D311yescharacteristic
868C23×C3C23×D311yescharacteristic
869C22×D3—22no—
870C22×D3—31no—
871C22×D3—31no—
872C22×D3—32no—
873C22×D3—32no—
874C22×D3—31no—
875C22×D3—31no—
876C22×D3—41no—
877C22×D3—41no—
878C22×D3—61no—
879C22×D3—61no—
880C22×D3—62no—
881C22×D3—62no—
882C22×D3—62no—
883C22×D3—64no—
884C22×D3—64no—
885C22×D3—64no—
886C22×D3—62no—
887C22×D3—62no—
888C22×D3—122no—
889C22×D3—124no—
890C22×D3—122no—
891C22×D3—122no—
892C22×D3—122no—
893C22×D3—122no—
894C22×D3—122no—
895C22×D3—122no—
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×Q8—122no—
909C3×D4—24no—
910C3×D4—24no—
911C3×D4—44no—
912C3×D4—41no—
913C3×D4—41no—
914C3×D4—42no—
915C3×D4—64no—
916C3×D4—121no—
917C3×D4—122no—
918C3×D4—122no—
919C3×D4—122no—
920C3×D4—122no—
921C2×C3×C4—21no—
922C2×C3×C4—22no—
923C2×C3×C4—21no—
924C2×C3×C4—32no—
925C2×C3×C4—32no—
926C2×C3×C4—32no—
927C2×C3×C4—32no—
928C2×C3×C4—32no—
929C2×C3×C4—32no—
930C2×C3×C4—41no—
931C2×C3×C4—41no—
932C2×C3×C4—42no—
933C2×C3×C4—62no—
934C2×C3×C4—122no—
935C2×C3×C4—121no—
936C2×C3×C4—121no—
937C2×C3×C4—122no—
938C2×C3×C4—122no—
939C2×C3×C4C23×D312yes—
940C2×C3×C4C23×D312yes—
941C2×C3×C4C23×D311yescharacteristic
942C2×C3×C4C23×D311yescharacteristic
943C2×C3×C4C23×D311yescharacteristic
944C2×C3×C4C23×D311yescharacteristic
945#67—24no—
946#67—42no—
947#67—42no—
948#67—42no—
949#67—42no—
950#67—64no—
951#67—64no—
952#67—64no—
953#67—64no—
954#67—124no—
955#67—122no—
956#67—122no—
957#67—122no—
958#67—122no—
959#67—122no—
960#67—122no—
961#67—122no—
962#67—122no—
963#67—122no—
964#67—122no—
965#67—124no—
966#67—124no—
967C2×Dic3—22no—
968C2×Dic3—31no—
969C2×Dic3—31no—
970C2×Dic3—32no—
971C2×Dic3—32no—
972C2×Dic3—31no—
973C2×Dic3—31no—
974C2×Dic3—42no—
975C2×Dic3—41no—
976C2×Dic3—42no—
977C2×Dic3—41no—
978C2×Dic3—61no—
979C2×Dic3—62no—
980C2×Dic3—61no—
981C2×Dic3—122no—
982C2×Dic3—122no—
983C2×Dic3—121no—
984C2×Dic3—121no—
985C2×Dic3—122no—
986C2×Dic3C23×D312yes—
987C2×Dic3C23×D312yes—
988C2×Dic3C23×D312yes—
989C2×Dic3C23×D312yes—
990C2×Dic3C23×D312yes—
991C2×Dic3C23×D312yes—
992D12—41no—
993D12—64no—
994D12—64no—
995D12—122no—
996D12—122no—
997D12—121no—
998D12—121no—
999D12—122no—
1000D12—124no—
1001D12—122no—
1002D12—122no—
1003D12—122no—
1004D12—122no—
1005C4×D3—42no—
1006C4×D3—62no—
1007C4×D3—62no—
1008C4×D3—62no—
1009C4×D3—62no—
1010C4×D3—64no—
1011C4×D3—122no—
1012C4×D3—122no—
1013C4×D3—122no—
1014C4×D3—121no—
1015C4×D3—121no—
1016C4×D3—121no—
1017C4×D3—121no—
1018C4×D3—122no—
1019C4×D3—122no—
1020C4×D3—122no—
1021C4×D3—122no—
1022C4×D3—122no—
1023C4×D3—122no—
1024C4×D3—124no—
1025Dic6—42no—
1026Dic6—41no—
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—92no—
1039C24—91no—
1040C24—92no—
1041#41—124no—
1042#41—362no—
1043C2×Q8—32no—
1044C2×Q8—31no—
1045C2×D4—32no—
1046C2×D4—32no—
1047C2×D4—32no—
1048C2×D4—32no—
1049C2×D4—32no—
1050C2×D4—31no—
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—362no—
1064C2×D4—362no—
1065C2×D4—364no—
1066C2×D4—364no—
1067C2×D4—364no—
1068C2×D4C2×D3212yes—
1069C2×D4C2×D3211yescharacteristic
1070C22×C4—31no—
1071C22×C4—31no—
1072C22×C4—32no—
1073C22×C4—32no—
1074C22×C4—31no—
1075C22×C4—32no—
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—31no—
1091C4⋊C4—32no—
1092C4⋊C4—32no—
1093C4⋊C4—32no—
1094C4⋊C4—92no—
1095C4⋊C4—92no—
1096C4⋊C4—92no—
1097C4⋊C4—92no—
1098C4⋊C4—92no—
1099C4⋊C4—92no—
1100C4⋊C4—92no—
1101C4⋊C4—92no—
1102C4⋊C4—91no—
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#100412yes—
1157C22×C3#100912yes—
1158C22×C3C24×D311yescharacteristic
1159C22×C3C24×D311yescharacteristic
1160C2×D3—22no—
1161C2×D3—22no—
1162C2×D3—22no—
1163C2×D3—22no—
1164C2×D3—22no—
1165C2×D3—22no—
1166C2×D3—32no—
1167C2×D3—32no—
1168C2×D3—62no—
1169C2×D3—62no—
1170C2×D3—62no—
1171C2×D3—61no—
1172C2×D3—61no—
1173C2×D3—61no—
1174C2×D3—61no—
1175C2×D3—62no—
1176C2×D3—61no—
1177C2×D3—62no—
1178C2×D3—62no—
1179C2×D3—61no—
1180C2×D3—61no—
1181C2×D3—61no—
1182C2×D3—62no—
1183C2×D3—62no—
1184C2×D3—61no—
1185C2×D3—62no—
1186C2×D3—61no—
1187C2×D3—62no—
1188C2×D3—82no—
1189C2×D3—121no—
1190C2×D3—121no—
1191C2×D3—122no—
1192C2×D3—122no—
1193C2×D3—122no—
1194C2×D3—124no—
1195C2×D3—124no—
1196C2×D3—128no—
1197C2×D3—244no—
1198C2×D3—244no—
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—92no—
1238C23—91no—
1239C23—121no—
1240C23—121no—
1241C23—182no—
1242C23—184no—
1243C23—182no—
1244C23—361no—
1245C23—362no—
1246C23—362no—
1247C23—362no—
1248C23—362no—
1249C23—362no—
1250C23C22×D3212yes—
1251C23C22×D3211yescharacteristic
1252Q8—122no—
1253Q8—121no—
1254D4—24no—
1255D4—41no—
1256D4—64no—
1257D4—121no—
1258D4—122no—
1259D4—122no—
1260D4—122no—
1261D4—122no—
1262D4—184no—
1263D4—184no—
1264D4—184no—
1265D4—361no—
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—122no—
1290C2×C4—182no—
1291C2×C4—182no—
1292C2×C4—361no—
1293C2×C4—361no—
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—181no—
1349C22—182no—
1350C22—242no—
1351C22—364no—
1352C22—724no—
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#8638311yescharacteristic, complemented
1370C3#8642011yescharacteristic, 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×#5617C2semidirect
3. C3×#5597C2semidirect
4. #10595308C2semidirect
5. #10595304C2semidirect
6. #10595292C2semidirect
7. #10595254C2semidirect
8. #10595197C2semidirect
9. #10595196C2semidirect
10. #10595072C2semidirect
11. #10594980C2semidirect
12. #10594922C2semidirect
13. C2×#63853C2semidirect
14. #10594652C2semidirect
15. #10594573C2semidirect
16. #10594308C2semidirect
17. #10594285C2semidirect
18. #10594178C2semidirect
19. #10594164C2semidirect
22. C2×D4×C3⋊D3C22semidirect
23. C2×D4×C3⋊D3C22semidirect
24. C22×C4×C3⋊D3C22semidirect
25. C2×C3×#237C22semidirect
26. C2×#3811C22semidirect
27. C2×D3×#67C22semidirect
29. C2×#3796C22semidirect
30. C32×#121C22semidirect
31. #64148C22semidirect
32. #64147C22semidirect
34. #64104C22semidirect
35. C4⋊C4×C3⋊D3C22semidirect
36. #64093C22semidirect
37. C22⋊C4×C3⋊D3C22semidirect
38. C3×#939C22semidirect
39. C3×#939C22semidirect
40. C3×#939C22semidirect
41. C3×#937C22semidirect
42. C3×D4×Dic3C22semidirect
43. C3×#930C22semidirect
44. C2×C3×(C2×D3)⋊C4C22semidirect
45. C3×#924C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C3×#898C22semidirect
48. C3×#896C22semidirect
49. C3×#886C22semidirect
50. C3×#885C22semidirect
51. C3×#884C22semidirect
52. C3×#878C22semidirect
53. #63983C22semidirect
55. #63981C22semidirect
56. #63981C22semidirect
57. #63979C22semidirect
58. #63978C22semidirect
59. #63978C22semidirect
60. #63978C22semidirect
61. #63978C22semidirect
62. #63975C22semidirect
63. #67⋊Dic3C22semidirect
64. Dic3×#67C22semidirect
65. #63971C22semidirect
66. #63970C22semidirect
67. #63969C22semidirect
68. #63966C22semidirect
69. #63966C22semidirect
70. C2×Dic3⋊Dic3C22semidirect
71. C2×#3722C22semidirect
72. C2×#3722C22semidirect
73. C2×(C2×D3)⋊Dic3C22semidirect
74. #63955C22semidirect
75. #63952C22semidirect
76. #63923C22semidirect
77. #63923C22semidirect
78. #63922C22semidirect
79. D3×(C2×D3)⋊C4C22semidirect
80. #63916C22semidirect
82. #63910C22semidirect
83. #63909C22semidirect
84. #63907C22semidirect
85. #63905C22semidirect
86. C4×#626C22semidirect
87. #63897C22semidirect
88. #63891C22semidirect
89. #63890C22semidirect
90. #63888C22semidirect
91. #63887C22semidirect
92. #63881C22semidirect
93. #63881C22semidirect
94. #63880C22semidirect
95. #63871C22semidirect
96. #63871C22semidirect
97. #63867C22semidirect
98. #63864C22semidirect
99. #63858C22semidirect
100. #63853C22semidirect
101. #63853C22semidirect
102. #63853C22semidirect
103. #63853C22semidirect
104. #63853C22semidirect
105. #63849C22semidirect
106. #63848C22semidirect
107. #63848C22semidirect
108. #63845C22semidirect
127. #5617D3semidirect
139. #5597D3semidirect
249. C2×#237C2×D3semidirect
275. C3×#121C2×D3semidirect
276. C3×#121C2×D3semidirect
299. #939C2×D3semidirect
300. #939C2×D3semidirect
301. #939C2×D3semidirect
313. #937C2×D3semidirect
317. D4×Dic3C2×D3semidirect
326. #930C2×D3semidirect
339. C2×(C2×D3)⋊C4C2×D3semidirect
342. #924C2×D3semidirect
344. C2×Dic3⋊C4C2×D3semidirect
350. #898C2×D3semidirect
354. #896C2×D3semidirect
383. #886C2×D3semidirect
385. #885C2×D3semidirect
393. #884C2×D3semidirect
423. #878C2×D3semidirect
830. #121D32semidirect
1232. C32#3534semidirect
1369. C3#86383semidirect
1370. C3#86420semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1212
C3×#56172
C3×#55972
#105953082
#105953042
#105952922
#105952542
#105951972
#105951962
#105950722
#105949802
#105949222
C2×#638532
#105946522
#105945732
#105943082
#105942852
#105941782
#105941642
#864203
#863833