Finite Group Databasebeta

← #11911153

Subgroups — #11911153

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×#64103C211yesmaximal, characteristic, complemented
2C3×#5515C211yesmaximal, characteristic, complemented
3C3×#5510C211yesmaximal, characteristic, complemented
4#10595084C211yesmaximal, characteristic, complemented
5#10595081C211yesmaximal, characteristic, complemented
6#10595074C212yesmaximal, complemented
7#10595068C212yesmaximal, complemented
8#10595068C212yesmaximal, complemented
9#10594979C211yesmaximal, characteristic, complemented
10#10594962C212yesmaximal, complemented
11#10594922C211yesmaximal, characteristic, complemented
12#10594661C212yesmaximal, complemented
13#10594654C212yesmaximal, complemented
14#10594650C212yesmaximal, complemented
15#10594622C212yesmaximal, complemented
16#10594611C212yesmaximal, complemented
17#10594588C212yesmaximal, complemented
18#10594563C212yesmaximal, complemented
19#10594338C212yesmaximal, complemented
20#86459—31nomaximal
21#86383—31nomaximal
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C3×#235C2212yescomplemented
25C2×#3811C2212yescomplemented
26C2×#3811C2212yescomplemented
27C2×#3802C2211yescharacteristic, complemented
28C2×D3×D12C2212yescomplemented
29C2×#3796C2211yescharacteristic, complemented
30C2×C32×C4⋊C4C2211yescharacteristic, complemented
31C2×#3752C2211yescharacteristic, complemented
32C2×#3752C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic, complemented
34C2×#3750C2211yescharacteristic, complemented
35#64103C2212yescomplemented
36#64103C2212yescomplemented
37#64103C2212yescomplemented
38#64103C2212yescomplemented
39C3×#930C2211yescharacteristic
40C3×#930C2212yescomplemented
41C3×#930C2211yescharacteristic, complemented
42C3×#930C2211yescharacteristic, complemented
43C3×#929C2212yescomplemented
44C3×C4×#67C2212yescomplemented
45C3×#924C2211yescharacteristic, complemented
46C3×#898C2212yescomplemented
47C3×#897C2212yescomplemented
48C3×#897C2212yescomplemented
49C3×#896C2212yescomplemented
50C3×#895C2212yescomplemented
51C3×#895C2212yescomplemented
52C3×#894C2212yescomplemented
53C3×#889C2212yescomplemented
54#63981C2212yescomplemented
55#63981C2212yescomplemented
56#63980C2212yescomplemented
57#63980C2212yescomplemented
58#67⋊Dic3C2212yescomplemented
59#67⋊Dic3C2212yescomplemented
60#63923C2212yes—
61#63923C2212yescomplemented
62#63922C2212yescomplemented
63#63922C2212yescomplemented
64#63922C2212yescomplemented
65#63922C2212yescomplemented
66#63921C2212yescomplemented
67D3×(C2×D3)⋊C4C2212yescomplemented
68D3×(C2×D3)⋊C4C2212yescomplemented
69#63916C2211yescharacteristic, complemented
70#63916C2211yescharacteristic, complemented
71#63916C2211yescharacteristic, complemented
72#63912C2212yescomplemented
73#63911C2212yescomplemented
74#63910C2212yes—
75#63910C2212yescomplemented
76#63909C2212yescomplemented
77#63907C2212yescomplemented
78#63907C2212yescomplemented
79#63907C2212yescomplemented
80#63906C2212yescomplemented
81#63906C2212yescomplemented
82#63905C2212yescomplemented
83#63904C2212yescomplemented
84#63904C2212yescomplemented
85#63900C2211yescharacteristic, complemented
86#63894C2212yescomplemented
87#63890C2212yescomplemented
88#63888C2212yescomplemented
89#63888C2212yescomplemented
90#63886C2212yescomplemented
91#63886C2212yescomplemented
92#63886C2212yescomplemented
93#63885C2212yescomplemented
94#63884C2212yescomplemented
95#63881C2212yescomplemented
96#63879C2212yescomplemented
97#63877C2212yescomplemented
98#63871C2211yescharacteristic, complemented
99#63859C2212yescomplemented
100#63858C2212yescomplemented
101#63854C2212yescomplemented
102#63854C2212yescomplemented
103#63853C2212yescomplemented
104#63850C2212yescomplemented
105#63850C2212yescomplemented
106#63849C2211yescharacteristic, complemented
107#63848C2212yescomplemented
108#63847C2212yescomplemented
109C3×#539—31no—
110C3×#537—31no—
111#5829—32no—
112#5829—32no—
113#5711—32no—
114#5705—32no—
115#5697—32no—
116#5692—32no—
117#5657—32no—
118#5654—32no—
119#5654—32no—
120#5653—32no—
121#5647—32no—
122#5647—32no—
123#5644—31no—
124#5644—32no—
125#5638—32no—
126#5637—32no—
127#5630—32no—
128#5627—31no—
129#5620—32no—
130#5617—31no—
131#5615—32no—
132#5610—32no—
133#5609—32no—
134#5606—31no—
135#5605—31no—
136#5605—31no—
137#5605—32no—
138D3×#121—31no—
139D3×#121—31no—
140#5601—32no—
141D4×D12—32no—
142#5540—32no—
143#5515D311yescharacteristic, complemented
144#5510D311yescharacteristic, complemented
145C2×#894—31no—
146C2×#894—31no—
147C2×#894—61no—
148C23×C3⋊D3C2311yescharacteristic
149C23×C3⋊D3C2311yescharacteristic
150C22×D32C2312yes—
151C22×D32C2312yes—
152C22×C32×C4C2311yescharacteristic
153C22×C32×C4C2311yescharacteristic
154C22×C32×C4C2311yescharacteristic
155C22×C3⋊Dic3C2311yescharacteristic
156C22×C3⋊Dic3C2311yescharacteristic
157C2×C4⋊(C3⋊D3)—42no—
158C2×C4⋊(C3⋊D3)C2312yes—
159C2×C4⋊(C3⋊D3)C2312yes—
160C2×C4×C3⋊D3—42no—
161C2×C4×C3⋊D3C2311yescharacteristic
162C2×C4×C3⋊D3C2311yescharacteristic
163C2×C4×C3⋊D3C2311yescharacteristic
164C2×C4×C3⋊D3C2311yescharacteristic
165C2×C3×#67C2312yes—
166C2×C3×#67C2312yes—
167C2×C3×#67C2312yes—
168C3×#235—44no—
169C2×C3×D12C2311yescharacteristic
170C2×C3×D12C2311yescharacteristic
171C2×C3×D12C2312yes—
172C2×C3×D12C2311yescharacteristic
173C2×C3×D12C2312yes—
174C2×C3×C4×D3C2312yes—
175C2×C3×C4×D3C2312yes—
176C2×C3×C4×D3C2312yes—
177C2×C3×Dic6C2311yescharacteristic
178C2×C3×Dic6C2312yes—
179#3811—44no—
180#3811—44no—
181C2×#626C2312yes—
182C2×#626C2312yes—
183C2×#626C2312yes—
184C2×#626C2312yes—
185C2×#626C2312yes—
186C2×#626C2312yes—
187C2×#626C2312yes—
188C2×#626C2312yes—
189C2×#625C2312yes—
190C2×#625C2312yes—
191C2×#624C2312yes—
192C2×#624C2312yes—
193C2×D3×Dic3C2312yes—
194C2×D3×Dic3C2312yes—
195#3802—42no—
196D3×D12—44no—
197#3796—42no—
198C32×C4⋊C4C2312yes—
199C32×C4⋊C4C2312yes—
200#3752C2312yes—
201#3752C2312yes—
202#3752C2312yes—
203#3752C2312yes—
204#3752C2312yes—
205#3752C2312yes—
206#3750C2312yes—
207#3750C2312yes—
208C3×#217C2312yes—
209C3×(C2×D3)⋊C4C2312yes—
210C3×(C2×D3)⋊C4C2312yes—
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⋊Dic3C2312yes—
219C3×C4⋊Dic3C2311yescharacteristic
220C3×C4⋊Dic3C2311yescharacteristic
221C3×C4⋊Dic3C2311yescharacteristic
222C3×Dic3⋊C4C2312yes—
223C3×Dic3⋊C4C2312yes—
224C3×Dic3⋊C4C2312yes—
225C3×Dic3⋊C4C2312yes—
226C3×C4×Dic3C2312yes—
227#3724C2312yes—
228#3724C2312yes—
229Dic3⋊Dic3C2312yes—
230Dic3⋊Dic3C2312yes—
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
244C2×C3×#41—32no—
245C2×#239—31no—
246C2×#237—31no—
247C2×D3×D4—32no—
248C2×D3×D4—32no—
249C2×D3×D4—32no—
250C2×D3×D4—32no—
251C2×D3×D4—31no—
252C2×D3×D4—31no—
253C2×D3×D4—32no—
254C2×#235C2×D312yescomplemented
255C22×D12—31no—
256C22×D12—31no—
257C22×D12—32no—
258C22×D12—61no—
259C22×C4×D3—31no—
260C22×C4×D3—31no—
261C22×C4×D3—61no—
262C3×#126—32no—
263C3×#125—32no—
264C3×#123—32no—
265C3×#123—32no—
266C3×C22⋊Q8—31no—
267C3×C22⋊Q8—32no—
268C3×C22⋊Q8—32no—
269C3×C22⋊Q8—32no—
270C3×#121—31no—
271C3×#121—32no—
272C3×#121—31no—
273C3×#121—31no—
274C3×#121—32no—
275C3×#121—32no—
276C3×C4×D4—32no—
277C2×C3×C4⋊C4—21no—
278C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
279C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
280#947—32no—
281#947—32no—
282#947—32no—
283#946—31no—
284#946—32no—
285#946—32no—
286#940—32no—
287#939—32no—
288#939—32no—
289#939—32no—
290#939—32no—
291#939—32no—
292#939—32no—
293#939—32no—
294#939—32no—
295#938—31no—
296#938—31no—
297#938—31no—
298#937—32no—
299#937—32no—
300#937—32no—
301#937—32no—
302#937—32no—
303#937—32no—
304#935—32no—
305D4×Dic3—32no—
306D4×Dic3—32no—
307#930—32no—
308#930—32no—
309#930—32no—
310#930C2×D311yescharacteristic
311#930C2×D311yescharacteristic, complemented
312#930C2×D312yescomplemented
313#930C2×D311yescharacteristic, complemented
314#929—32no—
315#929—32no—
316#929—32no—
317#929C2×D312yescomplemented
318C4×#67—32no—
319C4×#67—32no—
320C4×#67—32no—
321C4×#67C2×D312yescomplemented
322C2×(C2×D3)⋊C4—31no—
323C2×(C2×D3)⋊C4—31no—
324C2×(C2×D3)⋊C4—31no—
325C2×(C2×D3)⋊C4—31no—
326C2×(C2×D3)⋊C4—31no—
327C2×(C2×D3)⋊C4—31no—
328C2×(C2×D3)⋊C4—32no—
329C2×(C2×D3)⋊C4—32no—
330C2×(C2×D3)⋊C4—61no—
331C2×(C2×D3)⋊C4—61no—
332C2×(C2×D3)⋊C4—61no—
333#924C2×D311yescharacteristic, complemented
334C2×Dic3⋊C4—31no—
335C2×Dic3⋊C4—31no—
336C2×Dic3⋊C4—61no—
337#898—32no—
338#898—32no—
339#898—32no—
340#898C2×D312yescomplemented
341#897—31no—
342#897C2×D312yescomplemented
343#897C2×D312yescomplemented
344#896—32no—
345#896—32no—
346#896C2×D312yescomplemented
347#895—31no—
348#895—32no—
349#895—32no—
350#895—32no—
351#895—31no—
352#895—31no—
353#895—32no—
354#895—32no—
355#895—32no—
356#895C2×D312yescomplemented
357#895C2×D312yescomplemented
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#894—32no—
367#894—32no—
368#894—32no—
369#894—32no—
370#894—32no—
371#894—32no—
372#894—32no—
373#894—62no—
374#894—62no—
375#894—62no—
376#894—62no—
377#894C2×D312yescomplemented
378#893—32no—
379#893—32no—
380#893—32no—
381#893—32no—
382#892—31no—
383#892—31no—
384D3×C4⋊C4—31no—
385D3×C4⋊C4—31no—
386#889—32no—
387#889—32no—
388#889C2×D312yescomplemented
389#886—32no—
390#885—32no—
391#885—32no—
392#885—32no—
393#884—32no—
394#884—32no—
395#884—32no—
396#884—32no—
397#884—32no—
398#884—32no—
399#884—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#882—32no—
413#882—32no—
414#67⋊C4—32no—
415#67⋊C4—32no—
416#67⋊C4—32no—
417#67⋊C4—32no—
418D3×C22⋊C4—32no—
419D3×C22⋊C4—32no—
420D3×C22⋊C4—32no—
421D3×C22⋊C4—32no—
422#879—32no—
423#879—32no—
424#877—32no—
425#876—32no—
426#874—32no—
427C4×D12—32no—
428#872—32no—
429C23×C32C2411yescharacteristic
430C22×C3⋊D3—22no—
431C22×C3⋊D3—22no—
432C22×C3⋊D3—22no—
433C22×C3⋊D3—41no—
434C22×C3⋊D3—41no—
435C22×C3⋊D3—41no—
436C22×C3⋊D3C2412yes—
437C22×C3⋊D3C2411yescharacteristic
438C22×C3⋊D3C2411yescharacteristic
439C22×C3×D3C2412yes—
440C22×C3×D3C2412yes—
441C22×C3×D3C2412yes—
442C2×D32—24no—
443C2×D32—42no—
444C2×D32—42no—
445C2×D32—42no—
446C2×D32—42no—
447C2×D32—42no—
448C2×C32×C4—22no—
449C2×C32×C4—41no—
450C2×C32×C4—41no—
451C2×C32×C4C2412yes—
452C2×C32×C4C2411yescharacteristic
453C2×C32×C4C2412yes—
454C2×C32×C4C2411yescharacteristic
455C2×C3⋊Dic3—41no—
456C2×C3⋊Dic3—41no—
457C2×C3⋊Dic3C2411yescharacteristic
458C2×C3⋊Dic3C2412yes—
459C2×C3⋊Dic3C2411yescharacteristic
460C4⋊(C3⋊D3)—24no—
461C4⋊(C3⋊D3)—42no—
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—
469C2×C3×Dic3C2412yes—
470C2×C3×Dic3C2412yes—
471C2×C3×Dic3C2412yes—
472C2×C3×Dic3C2412yes—
473C2×C3×Dic3C2412yes—
474C3×D12—41no—
475C3×D12—42no—
476C3×D12—41no—
477C3×D12—41no—
478C3×D12—42no—
479C3×C4×D3—42no—
480C3×C4×D3—42no—
481C3×C4×D3—42no—
482C3×Dic6—41no—
483C3×Dic6—42no—
484#626—24no—
485#626—42no—
486#626—42no—
487#626—42no—
488#626—42no—
489#626—42no—
490#626—42no—
491#626—42no—
492#625—42no—
493#625—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—31no—
512#534—91no—
513#534—92no—
514#525—91no—
515C2×#123—91no—
516C2×#121—91no—
517C23×D3—31no—
518C23×D3—31no—
519C23×D3—31no—
520C23×D3—31no—
521C23×D3—32no—
522C23×D3—32no—
523C23×D3—32no—
524C23×D3—32no—
525C23×D3—61no—
526C23×D3—61no—
527C3×#41—124no—
528C2×C3×Q8—32no—
529C2×C3×Q8—31no—
530C2×C3×D4—32no—
531C2×C3×D4—32no—
532C2×C3×D4—32no—
533C2×C3×D4—32no—
534C2×C3×D4—31no—
535C2×C3×D4—31no—
536C2×C3×D4—32no—
537C2×C3×D4—31no—
538C22×C3×C4—21no—
539C22×C3×C4—21no—
540C22×C3×C4—21no—
541C22×C3×C4—32no—
542C22×C3×C4—32no—
543C22×C3×C4—32no—
544C22×C3×C4C22×D311yescharacteristic
545C22×C3×C4C22×D311yescharacteristic
546C22×C3×C4C22×D311yescharacteristic
547C22×C3×C4C22×D311yescharacteristic
548C22×C3×C4C22×D311yescharacteristic
549C22×C3×C4C22×D311yescharacteristic
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×#67C22×D312yes—
563C2×#67C22×D312yes—
564C2×#67C22×D312yes—
565C22×Dic3—31no—
566C22×Dic3—31no—
567C22×Dic3—31no—
568C22×Dic3—31no—
569C22×Dic3—32no—
570C22×Dic3—32no—
571C22×Dic3—61no—
572C22×Dic3—61no—
573#239—122no—
574#237—122no—
575D3×D4—124no—
576D3×D4—122no—
577D3×D4—122no—
578D3×D4—124no—
579D3×D4—124no—
580D3×D4—124no—
581D3×D4—124no—
582#235—44no—
583C2×D12—32no—
584C2×D12—32no—
585C2×D12—32no—
586C2×D12—32no—
587C2×D12—32no—
588C2×D12—32no—
589C2×D12—32no—
590C2×D12—32no—
591C2×D12—32no—
592C2×D12—32no—
593C2×D12—32no—
594C2×D12—32no—
595C2×D12—62no—
596C2×D12—62no—
597C2×D12—124no—
598C2×D12—122no—
599C2×D12—122no—
600C2×D12—124no—
601C2×D12C22×D312yes—
602C2×D12C22×D311yescharacteristic
603C2×D12C22×D312yes—
604C2×D12C22×D311yescharacteristic
605C2×D12C22×D311yescharacteristic
606C2×C4×D3—31no—
607C2×C4×D3—31no—
608C2×C4×D3—31no—
609C2×C4×D3—31no—
610C2×C4×D3—32no—
611C2×C4×D3—32no—
612C2×C4×D3—31no—
613C2×C4×D3—31no—
614C2×C4×D3—31no—
615C2×C4×D3—31no—
616C2×C4×D3—32no—
617C2×C4×D3—32no—
618C2×C4×D3—32no—
619C2×C4×D3—32no—
620C2×C4×D3—61no—
621C2×C4×D3—61no—
622C2×C4×D3—61no—
623C2×C4×D3—61no—
624C2×C4×D3—122no—
625C2×C4×D3—122no—
626C2×C4×D3—124no—
627C2×C4×D3C22×D312yes—
628C2×C4×D3C22×D312yes—
629C2×C4×D3C22×D312yes—
630C2×Dic6C22×D312yes—
631C2×Dic6C22×D311yescharacteristic
632C3×C4⋊C4—22no—
633C3×C4⋊C4—22no—
634C3×C4⋊C4—32no—
635C3×C4⋊C4—32no—
636C3×C4⋊C4—31no—
637C3×C4⋊C4—31no—
638C3×C4⋊C4—31no—
639C3×C4⋊C4—31no—
640C3×C4⋊C4—32no—
641C3×C4⋊C4—32no—
642C3×C4⋊C4—32no—
643C3×C4⋊C4C22×D312yes—
644C3×C4⋊C4C22×D312yes—
645C3×C4⋊C4C22×D312yes—
646C3×C4⋊C4C22×D312yes—
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×C42—32no—
657#217—32no—
658#217—32no—
659#217—32no—
660#217—32no—
661#217—32no—
662#217—32no—
663#217C22×D312yes—
664(C2×D3)⋊C4—32no—
665(C2×D3)⋊C4—32no—
666(C2×D3)⋊C4—32no—
667(C2×D3)⋊C4—32no—
668(C2×D3)⋊C4—32no—
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—62no—
691(C2×D3)⋊C4—62no—
692(C2×D3)⋊C4—62no—
693(C2×D3)⋊C4—62no—
694(C2×D3)⋊C4—62no—
695(C2×D3)⋊C4—62no—
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—
701(C2×D3)⋊C4C22×D312yes—
702(C2×D3)⋊C4C22×D312yes—
703(C2×D3)⋊C4C22×D312yes—
704C4⋊Dic3—32no—
705C4⋊Dic3—32no—
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—62no—
722Dic3⋊C4—62no—
723Dic3⋊C4C22×D312yes—
724Dic3⋊C4C22×D312yes—
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×C32H(5,𝔽2)12yes—
735C22×C32C2511yescharacteristic
736C2×C3⋊D3—21no—
737C2×C3⋊D3—21no—
738C2×C3⋊D3—21no—
739C2×C3⋊D3—22no—
740C2×C3⋊D3—21no—
741C2×C3⋊D3—22no—
742C2×C3⋊D3—21no—
743C2×C3⋊D3—22no—
744C2×C3⋊D3—44no—
745C2×C3⋊D3—82no—
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—
756D32—84no—
757D32—84no—
758C32×C4—22no—
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—
770C2×#41—32no—
771C2×#41—91no—
772C22×D4—92no—
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—32no—
784#125—92no—
785#124—92no—
786#124—92no—
787#124—92no—
788#123—32no—
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—
802C22⋊Q8—31no—
803C22⋊Q8—32no—
804C22⋊Q8—32no—
805C22⋊Q8—32no—
806C22⋊Q8—91no—
807C22⋊Q8—92no—
808C22⋊Q8—92no—
809#121—31no—
810#121—31no—
811#121—31no—
812#121—32no—
813#121—32no—
814#121—32no—
815#121—92no—
816#121—92no—
817#121—92no—
818#121—92no—
819#121—92no—
820#121—92no—
821#121—92no—
822#121—91no—
823#121—91no—
824#121—91no—
825#121—92no—
826#121—92no—
827#121—92no—
828#121—92no—
829#121—92no—
830#120—92no—
831#120—92no—
832#120—92no—
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—92no—
847#117—91no—
848C2×C4⋊C4—91no—
849C2×C4⋊C4—91no—
850C2×C4⋊C4D3211yescharacteristic, complemented
851C2×C22⋊C4—92no—
852C2×C22⋊C4—92no—
853C2×C22⋊C4—92no—
854C2×C22⋊C4—91no—
855C2×C22⋊C4—91no—
856C2×C22⋊C4—91no—
857C23×C3—21no—
858C23×C3—32no—
859C23×C3—32no—
860C23×C3—32no—
861C23×C3C23×D311yescharacteristic
862C23×C3C23×D311yescharacteristic
863C22×D3—31no—
864C22×D3—31no—
865C22×D3—32no—
866C22×D3—32no—
867C22×D3—31no—
868C22×D3—31no—
869C22×D3—61no—
870C22×D3—61no—
871C22×D3—62no—
872C22×D3—64no—
873C22×D3—64no—
874C22×D3—62no—
875C22×D3—62no—
876C22×D3—64no—
877C22×D3—62no—
878C22×D3—62no—
879C22×D3—62no—
880C22×D3—62no—
881C22×D3—122no—
882C22×D3—122no—
883C22×D3—122no—
884C22×D3—122no—
885C22×D3—122no—
886C22×D3—122no—
887C22×D3—122no—
888C22×D3—122no—
889C22×D3—122no—
890C22×D3—122no—
891C22×D3—122no—
892C22×D3—122no—
893C22×D3—121no—
894C22×D3—121no—
895C22×D3—121no—
896C22×D3—121no—
897C22×D3—121no—
898C22×D3—121no—
899C22×D3—122no—
900C22×D3—122no—
901C22×D3—122no—
902C22×D3C23×D312yes—
903C22×D3C23×D312yes—
904C22×D3C23×D312yes—
905C3×Q8—121no—
906C3×Q8—122no—
907C3×D4—64no—
908C3×D4—64no—
909C3×D4—64no—
910C3×D4—122no—
911C3×D4—121no—
912C3×D4—121no—
913C3×D4—121no—
914C3×D4—122no—
915C2×C3×C4—22no—
916C2×C3×C4—22no—
917C2×C3×C4—22no—
918C2×C3×C4—22no—
919C2×C3×C4—21no—
920C2×C3×C4—21no—
921C2×C3×C4—32no—
922C2×C3×C4—32no—
923C2×C3×C4—32no—
924C2×C3×C4—32no—
925C2×C3×C4—32no—
926C2×C3×C4—42no—
927C2×C3×C4—41no—
928C2×C3×C4—41no—
929C2×C3×C4—41no—
930C2×C3×C4—41no—
931C2×C3×C4—42no—
932C2×C3×C4—42no—
933C2×C3×C4—122no—
934C2×C3×C4—122no—
935C2×C3×C4—122no—
936C2×C3×C4C23×D312yes—
937C2×C3×C4C23×D312yes—
938C2×C3×C4C23×D311yescharacteristic
939C2×C3×C4C23×D312yes—
940C2×C3×C4C23×D311yescharacteristic
941C2×C3×C4C23×D311yescharacteristic
942C2×C3×C4C23×D311yescharacteristic
943C2×C3×C4C23×D312yes—
944#67—24no—
945#67—24no—
946#67—24no—
947#67—64no—
948#67—122no—
949#67—122no—
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—
959C2×Dic3—31no—
960C2×Dic3—31no—
961C2×Dic3—32no—
962C2×Dic3—32no—
963C2×Dic3—31no—
964C2×Dic3—31no—
965C2×Dic3—62no—
966C2×Dic3—61no—
967C2×Dic3—61no—
968C2×Dic3—122no—
969C2×Dic3—122no—
970C2×Dic3—121no—
971C2×Dic3—121no—
972C2×Dic3—121no—
973C2×Dic3—121no—
974C2×Dic3—122no—
975C2×Dic3—122no—
976C2×Dic3C23×D312yes—
977C2×Dic3C23×D312yes—
978C2×Dic3C23×D312yes—
979C2×Dic3C23×D312yes—
980C2×Dic3C23×D312yes—
981D12—42no—
982D12—42no—
983D12—41no—
984D12—41no—
985D12—41no—
986D12—64no—
987D12—64no—
988D12—64no—
989D12—124no—
990D12—122no—
991D12—122no—
992D12—124no—
993D12—122no—
994D12—122no—
995D12—122no—
996D12—122no—
997D12—122no—
998D12—122no—
999D12—122no—
1000C4×D3—42no—
1001C4×D3—42no—
1002C4×D3—42no—
1003C4×D3—62no—
1004C4×D3—62no—
1005C4×D3—62no—
1006C4×D3—62no—
1007C4×D3—122no—
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—
1021Dic6—42no—
1022Dic6—41no—
1023C2×C32—22no—
1024C2×C32C2×H(5,𝔽2)11yescharacteristic
1025C2×C32C2×H(5,𝔽2)11yescharacteristic
1026C2×C32#58511yescharacteristic
1027C3⋊D3—22no—
1028C3⋊D3—41no—
1029C3⋊D3—42no—
1030C3×D3—42no—
1031C3×D3—42no—
1032C3×D3—42no—
1033C24—92no—
1034C24—92no—
1035C24—91no—
1036C24—91no—
1037#41—124no—
1038#41—362no—
1039C2×Q8—31no—
1040C2×Q8—32no—
1041C2×D4—32no—
1042C2×D4—32no—
1043C2×D4—32no—
1044C2×D4—31no—
1045C2×D4—32no—
1046C2×D4—31no—
1047C2×D4—31no—
1048C2×D4—32no—
1049C2×D4—92no—
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—362no—
1062C2×D4—364no—
1063C2×D4—362no—
1064C2×D4—364no—
1065C2×D4—364no—
1066C22×C4—32no—
1067C22×C4—32no—
1068C22×C4—32no—
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—362no—
1080C22×C4C2×D3211yescharacteristic
1081C22×C4C2×D3211yescharacteristic
1082C22×C4C2×D3211yescharacteristic
1083C4⋊C4—31no—
1084C4⋊C4—31no—
1085C4⋊C4—31no—
1086C4⋊C4—31no—
1087C4⋊C4—32no—
1088C4⋊C4—32no—
1089C4⋊C4—32no—
1090C4⋊C4—32no—
1091C4⋊C4—32no—
1092C4⋊C4—92no—
1093C4⋊C4—92no—
1094C4⋊C4—92no—
1095C4⋊C4—92no—
1096C4⋊C4—92no—
1097C4⋊C4—92no—
1098C4⋊C4C2×D3212yes—
1099C4⋊C4C2×D3212yes—
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⋊C4—92no—
1124C22⋊C4—92no—
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—21no—
1136C22×C3—62no—
1137C22×C3—62no—
1138C22×C3—62no—
1139C22×C3—62no—
1140C22×C3—62no—
1141C22×C3—62no—
1142C22×C3—62no—
1143C22×C3—62no—
1144C22×C3—62no—
1145C22×C3#100412yes—
1146C22×C3#100912yes—
1147C22×C3C24×D311yescharacteristic
1148C22×C3C24×D311yescharacteristic
1149C2×D3—22no—
1150C2×D3—22no—
1151C2×D3—22no—
1152C2×D3—22no—
1153C2×D3—22no—
1154C2×D3—22no—
1155C2×D3—22no—
1156C2×D3—22no—
1157C2×D3—22no—
1158C2×D3—32no—
1159C2×D3—32no—
1160C2×D3—62no—
1161C2×D3—61no—
1162C2×D3—61no—
1163C2×D3—61no—
1164C2×D3—61no—
1165C2×D3—62no—
1166C2×D3—62no—
1167C2×D3—61no—
1168C2×D3—62no—
1169C2×D3—61no—
1170C2×D3—61no—
1171C2×D3—61no—
1172C2×D3—62no—
1173C2×D3—62no—
1174C2×D3—61no—
1175C2×D3—62no—
1176C2×D3—61no—
1177C2×D3—62no—
1178C2×D3—121no—
1179C2×D3—121no—
1180C2×D3—121no—
1181C2×D3—121no—
1182C2×D3—122no—
1183C2×D3—122no—
1184C2×D3—122no—
1185C2×D3—124no—
1186C2×D3—124no—
1187C2×D3—128no—
1188C2×D3—244no—
1189C2×D3—244no—
1190C2×D3—244no—
1191C2×D3—244no—
1192C2×D3—242no—
1193C2×D3—242no—
1194C2×D3—244no—
1195C3×C4—22no—
1196C3×C4—22no—
1197C3×C4—21no—
1198C3×C4—22no—
1199C3×C4—21no—
1200C3×C4—21no—
1201C3×C4—21no—
1202C3×C4—22no—
1203C3×C4—41no—
1204C3×C4—41no—
1205C3×C4—42no—
1206C3×C4—42no—
1207C3×C4—62no—
1208C3×C4—62no—
1209C3×C4—62no—
1210C3×C4—62no—
1211C3×C4—62no—
1212Dic3—22no—
1213Dic3—22no—
1214Dic3—22no—
1215Dic3—22no—
1216Dic3—22no—
1217Dic3—61no—
1218Dic3—61no—
1219Dic3—61no—
1220Dic3—61no—
1221Dic3—62no—
1222Dic3—62no—
1223Dic3—121no—
1224Dic3—121no—
1225Dic3—122no—
1226C32#353411yescharacteristic, complemented, Sylow
1227C23—32no—
1228C23—32no—
1229C23—32no—
1230C23—91no—
1231C23—92no—
1232C23—91no—
1233C23—182no—
1234C23—184no—
1235C23—182no—
1236C23—182no—
1237C23—361no—
1238C23—361no—
1239C23—361no—
1240C23—362no—
1241C23—362no—
1242C23—362no—
1243C23—362no—
1244C23—362no—
1245C23C22×D3211yescharacteristic
1246Q8—122no—
1247Q8—121no—
1248D4—64no—
1249D4—64no—
1250D4—64no—
1251D4—122no—
1252D4—121no—
1253D4—121no—
1254D4—122no—
1255D4—121no—
1256D4—184no—
1257D4—184no—
1258D4—362no—
1259D4—362no—
1260D4—362no—
1261D4—362no—
1262D4—362no—
1263D4—362no—
1264D4—362no—
1265D4—362no—
1266D4—362no—
1267D4—362no—
1268C2×C4—22no—
1269C2×C4—32no—
1270C2×C4—32no—
1271C2×C4—32no—
1272C2×C4—32no—
1273C2×C4—32no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—91no—
1277C2×C4—92no—
1278C2×C4—91no—
1279C2×C4—122no—
1280C2×C4—122no—
1281C2×C4—122no—
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—361no—
1291C2×C4—361no—
1292C2×C4C22×D3212yes—
1293C2×C4C22×D3211yescharacteristic
1294C2×C4C22×D3212yes—
1295C2×C4C22×D3211yescharacteristic
1296C2×C3—24no—
1297C2×C3—22no—
1298C2×C3—22no—
1299C2×C3—21no—
1300C2×C3—21no—
1301C2×C3—21no—
1302C2×C3—122no—
1303C2×C3—122no—
1304C2×C3—122no—
1305C2×C3C2×#100411yescharacteristic
1306C2×C3C2×#100911yescharacteristic
1307C2×C3D3×H(5,𝔽2)11yescharacteristic
1308C2×C3D3×H(5,𝔽2)11yescharacteristic
1309C2×C3#596811yescharacteristic
1310C2×C3#596811yescharacteristic
1311D3—42no—
1312D3—42no—
1313D3—42no—
1314D3—62no—
1315D3—62no—
1316D3—122no—
1317D3—122no—
1318D3—121no—
1319D3—122no—
1320D3—121no—
1321D3—122no—
1322D3—242no—
1323C22—21no—
1324C22—21no—
1325C22—62no—
1326C22—62no—
1327C22—62no—
1328C22—62no—
1329C22—62no—
1330C22—62no—
1331C22—62no—
1332C22—62no—
1333C22—62no—
1334C22—92no—
1335C22—181no—
1336C22—181no—
1337C22—182no—
1338C22—181no—
1339C22—181no—
1340C22—182no—
1341C22—181no—
1342C22—182no—
1343C22—364no—
1344C22—722no—
1345C22—724no—
1346C22—724no—
1347C22#6430712yes—
1348C22C23×D3211yescharacteristic
1349C4—22no—
1350C4—22no—
1351C4—21no—
1352C4—21no—
1353C4—62no—
1354C4—62no—
1355C4—62no—
1356C4—62no—
1357C4—62no—
1358C4—181no—
1359C4—181no—
1360C4—182no—
1361C3—21no—
1362C3#8638311yescharacteristic, complemented
1363C3#8645911yescharacteristic, complemented
1364C2—22no—
1365C2—122no—
1366C2—122no—
1367C2—122no—
1368C2—182no—
1369C2—361no—
1370C2—362no—
1371C2C2×#6430711yescharacteristic
1372C2#1059667511yescharacteristic
1373C2#1059668911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64103C2semidirect
2. C3×#5515C2semidirect
3. C3×#5510C2semidirect
4. #10595084C2semidirect
5. #10595081C2semidirect
6. #10595074C2semidirect
7. #10595068C2semidirect
8. #10595068C2semidirect
9. #10594979C2semidirect
10. #10594962C2semidirect
11. #10594922C2semidirect
12. #10594661C2semidirect
13. #10594654C2semidirect
14. #10594650C2semidirect
15. #10594622C2semidirect
16. #10594611C2semidirect
17. #10594588C2semidirect
18. #10594563C2semidirect
19. #10594338C2semidirect
23. C22×C4×C3⋊D3C22semidirect
24. C2×C3×#235C22semidirect
25. C2×#3811C22semidirect
26. C2×#3811C22semidirect
27. C2×#3802C22semidirect
28. C2×D3×D12C22semidirect
29. C2×#3796C22semidirect
30. C2×C32×C4⋊C4C22semidirect
31. C2×#3752C22semidirect
32. C2×#3752C22semidirect
33. C2×#3752C22semidirect
34. C2×#3750C22semidirect
35. #64103C22semidirect
36. #64103C22semidirect
37. #64103C22semidirect
38. #64103C22semidirect
40. C3×#930C22semidirect
41. C3×#930C22semidirect
42. C3×#930C22semidirect
43. C3×#929C22semidirect
44. C3×C4×#67C22semidirect
45. C3×#924C22semidirect
46. C3×#898C22semidirect
47. C3×#897C22semidirect
48. C3×#897C22semidirect
49. C3×#896C22semidirect
50. C3×#895C22semidirect
51. C3×#895C22semidirect
52. C3×#894C22semidirect
53. C3×#889C22semidirect
54. #63981C22semidirect
55. #63981C22semidirect
56. #63980C22semidirect
57. #63980C22semidirect
58. #67⋊Dic3C22semidirect
59. #67⋊Dic3C22semidirect
61. #63923C22semidirect
62. #63922C22semidirect
63. #63922C22semidirect
64. #63922C22semidirect
65. #63922C22semidirect
66. #63921C22semidirect
67. D3×(C2×D3)⋊C4C22semidirect
68. D3×(C2×D3)⋊C4C22semidirect
69. #63916C22semidirect
70. #63916C22semidirect
71. #63916C22semidirect
72. #63912C22semidirect
73. #63911C22semidirect
75. #63910C22semidirect
76. #63909C22semidirect
77. #63907C22semidirect
78. #63907C22semidirect
79. #63907C22semidirect
80. #63906C22semidirect
81. #63906C22semidirect
82. #63905C22semidirect
83. #63904C22semidirect
84. #63904C22semidirect
85. #63900C22semidirect
86. #63894C22semidirect
87. #63890C22semidirect
88. #63888C22semidirect
89. #63888C22semidirect
90. #63886C22semidirect
91. #63886C22semidirect
92. #63886C22semidirect
93. #63885C22semidirect
94. #63884C22semidirect
95. #63881C22semidirect
96. #63879C22semidirect
97. #63877C22semidirect
98. #63871C22semidirect
99. #63859C22semidirect
100. #63858C22semidirect
101. #63854C22semidirect
102. #63854C22semidirect
103. #63853C22semidirect
104. #63850C22semidirect
105. #63850C22semidirect
106. #63849C22semidirect
107. #63848C22semidirect
108. #63847C22semidirect
143. #5515D3semidirect
144. #5510D3semidirect
254. C2×#235C2×D3semidirect
278. C2×C3×C4⋊C4C2×D3semidirect
279. C2×C3×C4⋊C4C2×D3semidirect
311. #930C2×D3semidirect
312. #930C2×D3semidirect
313. #930C2×D3semidirect
317. #929C2×D3semidirect
321. C4×#67C2×D3semidirect
333. #924C2×D3semidirect
340. #898C2×D3semidirect
342. #897C2×D3semidirect
343. #897C2×D3semidirect
346. #896C2×D3semidirect
356. #895C2×D3semidirect
357. #895C2×D3semidirect
377. #894C2×D3semidirect
388. #889C2×D3semidirect
850. C2×C4⋊C4D32semidirect
1226. C32#3534semidirect
1362. C3#86383semidirect
1363. C3#86459semidirect

Maximal subgroups

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

subgroupindex
C2×#641032
C3×#55152
C3×#55102
#105950842
#105950812
#105950742
#105950682
#105949792
#105949622
#105949222
#105946612
#105946542
#105946502
#105946222
#105946112
#105945882
#105945632
#105943382
#864593
#863833