Finite Group Databasebeta

← #11901007

Subgroups — #11901007

Order 1152.

4005 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×D4C211yesmaximal, characteristic, complemented
2C2×#64306C211yesmaximal, characteristic, complemented
3C3⋊D3×#121C211yesmaximal, characteristic, complemented
4C3×#5607C212yesmaximal, complemented
5#10595300C212yesmaximal, complemented
6#10595286C214yesmaximal, complemented
7#10595282C211yesmaximal, characteristic, complemented
8#10595278C212yesmaximal, complemented
9#10595231C212yesmaximal, complemented
10#10595081C211yesmaximal, characteristic, complemented
11#10595064C212yesmaximal, complemented
12#10594628C212yesmaximal, complemented
13#10594612C211yesmaximal, characteristic, complemented
14#10594602C211yesmaximal, characteristic, complemented
15#10594288C212yesmaximal, complemented
16#10594270C214yesmaximal, complemented
17#10594258C212yesmaximal, complemented
18D3×#535—32nomaximal
19C23×D32C2212yes—
20C2×D4×C3⋊D3C2211yescharacteristic
21C2×D4×C3⋊D3C2212yescomplemented
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C3×D3×D4C2212yescomplemented
24C2×C3×#235C2212yescomplemented
25C2×#3811C2211yescharacteristic
26C2×#3811C2212yes—
27C2×#3811C2211yescharacteristic, complemented
28C2×#3811C2212yescomplemented
29C2×#3811C2212yescomplemented
30C2×D3×#67C2214yescomplemented
31C2×#3805C2212yescomplemented
32D32×D4—28no—
33#64306—28no—
34C2×#3802C2211yescharacteristic
35C2×#3802C2211yescharacteristic
36C2×#3802C2212yescomplemented
37C2×D3×D12C2212yescomplemented
38C2×C4×D32C2211yescharacteristic
39C2×C4×D32C2211yescharacteristic, complemented
40C2×#3798C2212yescomplemented
41C2×#3797C2211yescharacteristic, complemented
42C2×#3796C2212yescomplemented
43C32×#121C2211yescharacteristic, complemented
44#64148C2212yescomplemented
45#64147C2211yescharacteristic, complemented
46#64139C2211yescharacteristic, complemented
47#64104C2211yescharacteristic, complemented
48C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
49#64093C2212yescomplemented
50C22⋊C4×C3⋊D3C2212yescomplemented
51C3×#940C2214yescomplemented
52C3×#938C2212yescomplemented
53C3×#937C2214yescomplemented
54C3×#930C2212yescomplemented
55C3×#895C2212yescomplemented
56C3×#892C2212yescomplemented
57C3×#885C2214yescomplemented
58C3×#882C2214yescomplemented
59#63983C2214yescomplemented
60#63980C2212yescomplemented
61#63979C2214yescomplemented
62#63979C2214yescomplemented
63#63977C2214yescomplemented
64#63976C2214yescomplemented
65#63974C2212yescomplemented
66#63971C2214yescomplemented
67#63959C2214yescomplemented
68#63923C2214yescomplemented
69#63922C2214yescomplemented
70#63922C2214yescomplemented
71#63921C2212yes—
72#63921C2212yescomplemented
73#63921C2212yescomplemented
74#63916C2212yescomplemented
75#63912C2212yescomplemented
76#63911C2214yescomplemented
77#63909C2212yescomplemented
78#63908C2212yescomplemented
79#63907C2214yescomplemented
80#63900C2211yescharacteristic, complemented
81#63885C2214yescomplemented
82C4×#624C2212yescomplemented
83#63877C2214yescomplemented
84#63852C2214yescomplemented
85#63841C2212yescomplemented
86C2×D3×#41—32no—
87C22×D3×D4—32no—
88C3×#535—32no—
89#5830—32no—
90#5805—32no—
91#5715—34no—
92D3×#127—34no—
93#5674—34no—
94D3×#124—34no—
95#5607—32no—
96#5607—32no—
97#5607—32no—
98#5607D312yescomplemented
99D3×#121—32no—
100D3×#121—32no—
101D3×#121—32no—
102D3×#121—32no—
103D3×#121—61no—
104#5592—34no—
105#5592—34no—
106D3×#120—34no—
107D3×#120—34no—
108#5525—32no—
109D3×#117—32no—
110C23×C3⋊D3C2311yescharacteristic
111C23×C3⋊D3C2312yes—
112C23×C3×D3C2314yes—
113C22×D32—28no—
114C22×D32—44no—
115C22×D32—44no—
116C22×D32C2311yescharacteristic
117C22×D32C2312yes—
118C22×D32C2311yescharacteristic
119C22×D32C2314yes—
120C2×C32×D4C2311yescharacteristic
121C2×C32×D4C2312yescomplemented
122C22×C32×C4C2311yescharacteristic, complemented
123C2×#638C2312yes—
124C2×#638C2312yescomplemented
125C2×#638C2312yescomplemented
126C22×C3⋊Dic3C2311yescharacteristic, complemented
127D4×C3⋊D3—24no—
128D4×C3⋊D3—44no—
129C2×C4⋊(C3⋊D3)C2311yescharacteristic
130C2×C4⋊(C3⋊D3)C2312yescomplemented
131C2×C4×C3⋊D3—24no—
132C2×C4×C3⋊D3C2311yescharacteristic
133C2×C4×C3⋊D3C2312yes—
134C2×C4×C3⋊D3C2311yescharacteristic
135C2×C4×C3⋊D3C2311yescharacteristic, complemented
136C2×C4×C3⋊D3C2311yescharacteristic, complemented
137C2×C3×#67C2314yes—
138C2×C3×#67C2312yes—
139C2×C3×#67C2312yescomplemented
140C2×C3×#67C2314yescomplemented
141C2×C3×#67C2314yescomplemented
142C3×D3×D4—28no—
143C3×#235—28no—
144C2×C3×D12C2312yes—
145C2×C3×D12C2312yes—
146C2×C3×D12C2314yescomplemented
147C2×C3×C4×D3C2312yes—
148C2×C3×C4×D3C2312yescomplemented
149C2×C3×Dic6C2312yescomplemented
150#3811—24no—
151#3811—24no—
152#3811—28no—
153#3811—44no—
154#3811—44no—
155D3×#67—216no—
156C2×#627C2312yescomplemented
157C2×#626C2312yes—
158C2×#626C2314yes—
159C2×#626C2312yescomplemented
160C2×#626C2314yescomplemented
161C2×#626C2314yescomplemented
162C2×#625C2312yes—
163C2×#625C2312yes—
164C2×#625C2314yescomplemented
165C2×#624C2311yescharacteristic
166C2×#624C2312yes—
167C2×#624C2311yescharacteristic
168#3805—28no—
169C2×D3×Dic3C2312yes—
170C2×D3×Dic3C2312yescomplemented
171#3802—24no—
172#3802—24no—
173#3802—44no—
174D3×D12—28no—
175C4×D32—24no—
176C4×D32D418yescomplemented
177#3798—28no—
178#3797—24no—
179#3796—28no—
180C32×C4⋊C4C2311yescharacteristic, complemented
181C32×C22⋊C4C2312yescomplemented
182#3757C2312yescomplemented
183#3752C2312yescomplemented
184#3752C2312yescomplemented
185C4⋊(C3⋊Dic3)C2311yescharacteristic, complemented
186#3750C2312yescomplemented
187C3×#217C2314yescomplemented
188C3×(C2×D3)⋊C4C2314yes—
189C3×(C2×D3)⋊C4C2314yescomplemented
190C3×(C2×D3)⋊C4C2314yescomplemented
191C3×C4⋊Dic3C2312yescomplemented
192C3×C4×Dic3C2314yescomplemented
193#3724C2312yescomplemented
194#3722C2314yescomplemented
195(C2×D3)⋊Dic3C2314yes—
196(C2×D3)⋊Dic3C2314yescomplemented
197(C2×D3)⋊Dic3C2314yescomplemented
198Dic32C2314yescomplemented
199C2×#535—91noSylow
200C24×D3—34no—
201C2×C3×#41—32no—
202C22×C3×D4—32no—
203C22×#67—34no—
204D3×#41—616no—
205C2×#239—32no—
206C2×D3×Q8—32no—
207C2×#237—32no—
208C2×#237—32no—
209C2×#237—32no—
210C2×D3×D4—34no—
211C2×D3×D4—32no—
212C2×D3×D4—34no—
213C2×D3×D4—32no—
214C2×D3×D4—32no—
215C2×D3×D4—34no—
216C2×D3×D4—34no—
217C2×D3×D4—34no—
218C2×D3×D4—32no—
219C2×D3×D4—32no—
220C2×D3×D4—34no—
221C2×D3×D4—32no—
222C2×D3×D4—61no—
223C2×D3×D4—62no—
224C2×D3×D4—616no—
225C2×D3×D4C2×D312yescomplemented
226C2×#235—32no—
227C2×#235—32no—
228C2×#235C2×D312yescomplemented
229C22×D12—32no—
230C22×C4×D3—32no—
231C22×C4×D3—32no—
232C22×C4×D3—32no—
233C22×C4×D3—61no—
234C3×#127—34no—
235C3×#124—34no—
236C3×#121—21no—
237C3×#121—32no—
238C3×#121—32no—
239C3×#121—32no—
240C3×#121C2×D312yescomplemented
241C3×#120—34no—
242C3×#120—34no—
243C3×#117—32no—
244#953—34no—
245#953—34no—
246#947—34no—
247#940—34no—
248#940—34no—
249#940—34no—
250#940—34no—
251#940—34no—
252#940C2×D314yescomplemented
253#939—34no—
254#939—34no—
255#939—34no—
256#939—34no—
257#939—62no—
258#938—32no—
259#938—32no—
260#938—32no—
261#938—61no—
262#938C2×D312yescomplemented
263#937—34no—
264#937—34no—
265#937—34no—
266#937—34no—
267#937—34no—
268#937C2×D314yescomplemented
269#936—34no—
270#930—32no—
271#930—32no—
272#930—32no—
273#930—61no—
274#930C2×D312yescomplemented
275#926—32no—
276#895—32no—
277#895—32no—
278#895—32no—
279#895—61no—
280#895C2×D312yescomplemented
281#892—32no—
282#892C2×D312yescomplemented
283D3×C4⋊C4—32no—
284D3×C4⋊C4—32no—
285D3×C4⋊C4—61no—
286#885—34no—
287#885—34no—
288#885—34no—
289#885C2×D314yescomplemented
290#884—34no—
291#884—34no—
292#884—34no—
293#884—34no—
294#884—62no—
295#882—34no—
296#882—34no—
297#882—34no—
298#882—34no—
299#882—34no—
300#882C2×D314yescomplemented
301D3×C22⋊C4—34no—
302D3×C22⋊C4—34no—
303D3×C22⋊C4—34no—
304D3×C22⋊C4—34no—
305D3×C22⋊C4—34no—
306D3×C22⋊C4—62no—
307#877—34no—
308#875—34no—
309#874—34no—
310#872—34no—
311C42×D3—34no—
312C23×C32C2412yes—
313C23×C32C2411yescharacteristic
314C22×C3⋊D3—22no—
315C22×C3⋊D3—24no—
316C22×C3⋊D3—22no—
317C22×C3⋊D3—24no—
318C22×C3⋊D3—24no—
319C22×C3⋊D3—22no—
320C22×C3⋊D3C2412yes—
321C22×C3⋊D3C2411yescharacteristic
322C22×C3⋊D3C2411yescharacteristic
323C22×C3×D3—28no—
324C22×C3×D3—44no—
325C22×C3×D3—44no—
326C22×C3×D3C2414yes—
327C22×C3×D3C2412yes—
328C22×C3×D3C2412yes—
329C2×D32—22no—
330C2×D32—22no—
331C2×D32—24no—
332C2×D32—22no—
333C2×D32—24no—
334C2×D32—24no—
335C2×D32—22no—
336C2×D32—22no—
337C2×D32—28no—
338C2×D32—432no—
339C2×D32—44no—
340C2×D32—44no—
341C2×D32C2×D414yes—
342C32×D4—22no—
343C32×D4—42no—
344C2×C32×C4—22no—
345C2×C32×C4C2412yes—
346C2×C32×C4C2411yescharacteristic
347C2×C32×C4C2411yescharacteristic
348#638—24no—
349#638—42no—
350#638—42no—
351C2×C3⋊Dic3—22no—
352C2×C3⋊Dic3C2412yes—
353C2×C3⋊Dic3C2411yescharacteristic
354C2×C3⋊Dic3C2411yescharacteristic
355C4⋊(C3⋊D3)—22no—
356C4⋊(C3⋊D3)—42no—
357C4×C3⋊D3—22no—
358C4×C3⋊D3—24no—
359C4×C3⋊D3—22no—
360C4×C3⋊D3—22no—
361C4×C3⋊D3C2×D414yes—
362C3×#67—24no—
363C3×#67—24no—
364C3×#67—28no—
365C3×#67—44no—
366C3×#67—44no—
367C2×C3×Dic3C2414yes—
368C2×C3×Dic3C2412yes—
369C2×C3×Dic3C2412yes—
370C3×D12—24no—
371C3×D12—24no—
372C3×D12—44no—
373C3×C4×D3—24no—
374C3×C4×D3C2×D418yescomplemented
375C3×Dic6—24no—
376#627—24no—
377#626—24no—
378#626—24no—
379#626—28no—
380#626—44no—
381#626—44no—
382#625—24no—
383#625—24no—
384#625—44no—
385#624—22no—
386#624—24no—
387#624C2×D414yes—
388D3×Dic3—24no—
389D3×Dic3C2×D418yescomplemented
390C22×#41—91no—
391C23×D4—91no—
392#535—32no—
393#535—92no—
394#535—94no—
395#535—94no—
396#535—92no—
397#535—92no—
398C2×#127—92no—
399C2×#124—92no—
400C2×#121—91no—
401C2×#121—91no—
402C2×#121—91no—
403C2×#121—91no—
404C2×#120—92no—
405C2×#120—92no—
406C2×#117—91no—
407C24×C3—34no—
408C23×D3—32no—
409C23×D3—34no—
410C23×D3—32no—
411C23×D3—34no—
412C23×D3—32no—
413C23×D3—34no—
414C23×D3—34no—
415C23×D3—61no—
416C23×D3—62no—
417C23×D3—616no—
418C23×D3—128no—
419C23×D3—128no—
420C23×D3C22×D314yes—
421C3×#41—68no—
422C2×C3×Q8—32no—
423C2×C3×D4—21no—
424C2×C3×D4—22no—
425C2×C3×D4—34no—
426C2×C3×D4—32no—
427C2×C3×D4—32no—
428C2×C3×D4—34no—
429C2×C3×D4—34no—
430C2×C3×D4—32no—
431C2×C3×D4—32no—
432C2×C3×D4—34no—
433C2×C3×D4—68no—
434C2×C3×D4C22×D312yes—
435C2×C3×D4C22×D314yescomplemented
436C22×C3×C4—21no—
437C22×C3×C4—32no—
438C22×C3×C4—32no—
439C22×C3×C4C22×D312yescomplemented
440C2×#67—34no—
441C2×#67—32no—
442C2×#67—34no—
443C2×#67—32no—
444C2×#67—34no—
445C2×#67—34no—
446C2×#67—34no—
447C2×#67—34no—
448C2×#67—32no—
449C2×#67—34no—
450C2×#67—32no—
451C2×#67—34no—
452C2×#67—34no—
453C2×#67—62no—
454C2×#67—62no—
455C2×#67—62no—
456C2×#67—616no—
457C2×#67C22×D314yes—
458C2×#67C22×D312yes—
459C2×#67C22×D312yescomplemented
460C2×#67C22×D314yescomplemented
461C2×#67C22×D314yescomplemented
462C22×Dic3—32no—
463C22×Dic3—32no—
464C22×Dic3—32no—
465C22×Dic3—61no—
466#239—68no—
467D3×Q8—68no—
468#237—68no—
469#237—68no—
470#237—68no—
471D3×D4—28no—
472D3×D4—68no—
473D3×D4—616no—
474D3×D4—68no—
475D3×D4—68no—
476D3×D4—616no—
477D3×D4—68no—
478D3×D4—68no—
479D3×D4—68no—
480D3×D4—124no—
481D3×D4—128no—
482D3×D4—128no—
483D3×D4—128no—
484D3×D4—128no—
485D3×D4—128no—
486#235—28no—
487#235—68no—
488#235—68no—
489C2×D12—32no—
490C2×D12—34no—
491C2×D12—32no—
492C2×D12—32no—
493C2×D12—34no—
494C2×D12—34no—
495C2×D12—34no—
496C2×D12—62no—
497C2×D12—61no—
498C2×D12—68no—
499C2×D12C22×D312yes—
500C2×D12C22×D312yes—
501C2×D12C22×D314yescomplemented
502C2×C4×D3—32no—
503C2×C4×D3—32no—
504C2×C4×D3—32no—
505C2×C4×D3—316no—
506C2×C4×D3—32no—
507C2×C4×D3—34no—
508C2×C4×D3—32no—
509C2×C4×D3—32no—
510C2×C4×D3—32no—
511C2×C4×D3—34no—
512C2×C4×D3—32no—
513C2×C4×D3—61no—
514C2×C4×D3—61no—
515C2×C4×D3—62no—
516C2×C4×D3—61no—
517C2×C4×D3—61no—
518C2×C4×D3—68no—
519C2×C4×D3—68no—
520C2×C4×D3—124no—
521C2×C4×D3C22×D312yes—
522C2×C4×D3C22×D312yescomplemented
523C2×Dic6—32no—
524C2×Dic6—32no—
525C2×Dic6C22×D312yescomplemented
526C3×C4⋊C4—21no—
527C3×C4⋊C4—32no—
528C3×C4⋊C4C22×D312yescomplemented
529C3×C22⋊C4—22no—
530C3×C22⋊C4—34no—
531C3×C22⋊C4—34no—
532C3×C22⋊C4—34no—
533C3×C22⋊C4—34no—
534C3×C22⋊C4C22×D314yescomplemented
535C3×C42—34no—
536#217—34no—
537#217—34no—
538#217—34no—
539#217—34no—
540#217—62no—
541#217C22×D314yescomplemented
542(C2×D3)⋊C4—34no—
543(C2×D3)⋊C4—34no—
544(C2×D3)⋊C4—34no—
545(C2×D3)⋊C4—34no—
546(C2×D3)⋊C4—34no—
547(C2×D3)⋊C4—34no—
548(C2×D3)⋊C4—34no—
549(C2×D3)⋊C4—62no—
550(C2×D3)⋊C4—62no—
551(C2×D3)⋊C4C22×D314yes—
552(C2×D3)⋊C4C22×D314yescomplemented
553(C2×D3)⋊C4C22×D314yescomplemented
554C4⋊Dic3—32no—
555C4⋊Dic3—61no—
556C4⋊Dic3C22×D312yescomplemented
557Dic3⋊C4—34no—
558Dic3⋊C4—34no—
559Dic3⋊C4—62no—
560C4×Dic3—34no—
561C4×Dic3—34no—
562C4×Dic3C22×D314yescomplemented
563C22×C32—21no—
564C22×C32—21no—
565C22×C32—22no—
566C22×C32—21no—
567C22×C32—22no—
568C22×C32—22no—
569C22×C32C2511yescharacteristic
570C2×C3⋊D3—21no—
571C2×C3⋊D3—21no—
572C2×C3⋊D3—22no—
573C2×C3⋊D3—21no—
574C2×C3⋊D3—22no—
575C2×C3⋊D3—22no—
576C2×C3⋊D3—44no—
577C2×C3⋊D3—48no—
578C2×C3⋊D3C22×D412yes—
579C2×C3⋊D3H(5,𝔽2)12yes—
580C2×C3⋊D3H(5,𝔽2)12yes—
581C2×C3×D3—22no—
582C2×C3×D3—22no—
583C2×C3×D3—22no—
584C2×C3×D3—24no—
585C2×C3×D3—22no—
586C2×C3×D3—24no—
587C2×C3×D3—22no—
588C2×C3×D3—24no—
589C2×C3×D3—416no—
590C2×C3×D3C22×D414yes—
591D32—28no—
592D32—416no—
593D32—44no—
594D32—48no—
595C32×C4—21no—
596C32×C4—22no—
597C32×C4C22×D412yes—
598C3⋊Dic3—21no—
599C3⋊Dic3—22no—
600C3⋊Dic3C22×D412yes—
601C3×Dic3—22no—
602C3×Dic3—24no—
603C3×Dic3C22×D414yes—
604C25—92no—
605C2×#41—32no—
606C2×#41—92no—
607C2×#41—92no—
608C2×#41—92no—
609C2×#41—188no—
610C22×Q8—91no—
611C22×D4—32no—
612C22×D4—92no—
613C22×D4—91no—
614C22×D4—91no—
615C22×D4—91no—
616C22×D4—92no—
617C22×D4—91no—
618C22×D4—92no—
619C22×D4—92no—
620C22×D4—92no—
621C22×D4—94no—
622C22×D4—91no—
623C22×D4—92no—
624C22×D4—188no—
625C23×C4—91no—
626C23×C4—91no—
627C23×C4—91no—
628#127—34no—
629#127—94no—
630#127—94no—
631#127—94no—
632#124—34no—
633#124—94no—
634#124—94no—
635#124—94no—
636#121—32no—
637#121—32no—
638#121—32no—
639#121—92no—
640#121—94no—
641#121—94no—
642#121—92no—
643#121—92no—
644#121—92no—
645#121—92no—
646#121—91no—
647#121—92no—
648#121—91no—
649#121—91no—
650#121—92no—
651#121D3211yescharacteristic, complemented
652#120—34no—
653#120—34no—
654#120—94no—
655#120—94no—
656#120—94no—
657#120—94no—
658#120—94no—
659#120—94no—
660#117—32no—
661#117—94no—
662#117—92no—
663C2×C4⋊C4—91no—
664C2×C4⋊C4—91no—
665C2×C22⋊C4—92no—
666C2×C22⋊C4—92no—
667C2×C22⋊C4—92no—
668C2×C22⋊C4—92no—
669C2×C22⋊C4—92no—
670C2×C42—92no—
671C23×C3—21no—
672C23×C3—22no—
673C23×C3—32no—
674C23×C3—34no—
675C23×C3—32no—
676C23×C3—68no—
677C23×C3—124no—
678C23×C3—124no—
679C23×C3C23×D314yes—
680C23×C3C23×D312yes—
681C22×D3—28no—
682C22×D3—32no—
683C22×D3—38no—
684C22×D3—34no—
685C22×D3—32no—
686C22×D3—44no—
687C22×D3—44no—
688C22×D3—61no—
689C22×D3—61no—
690C22×D3—62no—
691C22×D3—64no—
692C22×D3—64no—
693C22×D3—64no—
694C22×D3—68no—
695C22×D3—64no—
696C22×D3—64no—
697C22×D3—68no—
698C22×D3—68no—
699C22×D3—68no—
700C22×D3—64no—
701C22×D3—68no—
702C22×D3—64no—
703C22×D3—64no—
704C22×D3—68no—
705C22×D3—68no—
706C22×D3—64no—
707C22×D3—68no—
708C22×D3—122no—
709C22×D3—122no—
710C22×D3—124no—
711C22×D3—124no—
712C22×D3—124no—
713C22×D3—124no—
714C22×D3—124no—
715C22×D3—124no—
716C22×D3—124no—
717C22×D3—1264no—
718C22×D3C23×D314yes—
719C22×D3C23×D312yes—
720C22×D3C23×D312yes—
721C3×Q8—64no—
722C3×D4—24no—
723C3×D4—42no—
724C3×D4—44no—
725C3×D4—44no—
726C3×D4—64no—
727C3×D4—68no—
728C3×D4—64no—
729C3×D4—64no—
730C3×D4—64no—
731C3×D4—124no—
732C3×D4—124no—
733C3×D4—124no—
734C2×C3×C4—24no—
735C2×C3×C4—21no—
736C2×C3×C4—22no—
737C2×C3×C4—21no—
738C2×C3×C4—32no—
739C2×C3×C4—38no—
740C2×C3×C4—34no—
741C2×C3×C4—32no—
742C2×C3×C4—42no—
743C2×C3×C4—64no—
744C2×C3×C4C23×D314yes—
745C2×C3×C4C23×D312yes—
746C2×C3×C4C23×D312yes—
747#67—24no—
748#67—24no—
749#67—28no—
750#67—44no—
751#67—44no—
752#67—64no—
753#67—68no—
754#67—68no—
755#67—64no—
756#67—64no—
757#67—64no—
758#67—68no—
759#67—124no—
760#67—124no—
761#67—124no—
762#67—124no—
763#67—124no—
764#67—124no—
765#67—124no—
766#67—124no—
767#67—124no—
768C2×Dic3—32no—
769C2×Dic3—38no—
770C2×Dic3—34no—
771C2×Dic3—32no—
772C2×Dic3—61no—
773C2×Dic3—62no—
774C2×Dic3—61no—
775C2×Dic3—64no—
776C2×Dic3—64no—
777C2×Dic3—122no—
778C2×Dic3C23×D314yes—
779C2×Dic3C23×D312yes—
780C2×Dic3C23×D312yes—
781D12—24no—
782D12—24no—
783D12—44no—
784D12—68no—
785D12—64no—
786D12—64no—
787D12—64no—
788D12—122no—
789D12—124no—
790D12—124no—
791D12—124no—
792D12—124no—
793C4×D3—24no—
794C4×D3—38no—
795C4×D3—38no—
796C4×D3—38no—
797C4×D3—64no—
798C4×D3—64no—
799C4×D3—68no—
800C4×D3—64no—
801C4×D3—64no—
802C4×D3—64no—
803C4×D3—68no—
804C4×D3—64no—
805C4×D3—122no—
806C4×D3—122no—
807C4×D3—122no—
808C4×D3—124no—
809C4×D3D3×D418yescomplemented
810Dic6—24no—
811Dic6—64no—
812Dic6—64no—
813C2×C32—41no—
814C2×C32—42no—
815C2×C32C23×D411yescharacteristic
816C2×C32C2×H(5,𝔽2)11yescharacteristic
817C2×C32C2×H(5,𝔽2)11yescharacteristic
818C3⋊D3—41no—
819C3⋊D3—42no—
820C3⋊D3#53514yescomplemented
821C3×D3—24no—
822C3×D3—44no—
823C3×D3—42no—
824C24—34no—
825C24—91no—
826C24—92no—
827C24—91no—
828C24—94no—
829C24—92no—
830C24—91no—
831C24—188no—
832C24—364no—
833C24—364no—
834#41—68no—
835#41—188no—
836#41—188no—
837#41—188no—
838C2×Q8—32no—
839C2×Q8—92no—
840C2×Q8—184no—
841C2×D4—32no—
842C2×D4—34no—
843C2×D4—32no—
844C2×D4—34no—
845C2×D4—34no—
846C2×D4—32no—
847C2×D4—32no—
848C2×D4—34no—
849C2×D4—68no—
850C2×D4—92no—
851C2×D4—94no—
852C2×D4—92no—
853C2×D4—94no—
854C2×D4—94no—
855C2×D4—92no—
856C2×D4—92no—
857C2×D4—92no—
858C2×D4—94no—
859C2×D4—92no—
860C2×D4—92no—
861C2×D4—91no—
862C2×D4—92no—
863C2×D4—188no—
864C2×D4—184no—
865C2×D4—188no—
866C2×D4—184no—
867C2×D4—184no—
868C2×D4—1816no—
869C2×D4—184no—
870C2×D4—184no—
871C2×D4—364no—
872C2×D4—364no—
873C2×D4—364no—
874C2×D4—364no—
875C2×D4C2×D3211yescharacteristic
876C2×D4C2×D3212yescomplemented
877C22×C4—32no—
878C22×C4—32no—
879C22×C4—91no—
880C22×C4—98no—
881C22×C4—92no—
882C22×C4—91no—
883C22×C4—92no—
884C22×C4—92no—
885C22×C4—91no—
886C22×C4—91no—
887C22×C4—92no—
888C22×C4—91no—
889C22×C4—91no—
890C22×C4—91no—
891C22×C4—184no—
892C22×C4—184no—
893C22×C4C2×D3211yescharacteristic, complemented
894C4⋊C4—32no—
895C4⋊C4—92no—
896C4⋊C4—92no—
897C4⋊C4—91no—
898C4⋊C4C2×D3211yescharacteristic, complemented
899C22⋊C4—34no—
900C22⋊C4—34no—
901C22⋊C4—34no—
902C22⋊C4—34no—
903C22⋊C4—94no—
904C22⋊C4—94no—
905C22⋊C4—94no—
906C22⋊C4—94no—
907C22⋊C4—92no—
908C22⋊C4—92no—
909C22⋊C4—92no—
910C22⋊C4C2×D3212yescomplemented
911C42—34no—
912C42—94no—
913C22×C3—22no—
914C22×C3—22no—
915C22×C3—24no—
916C22×C3—22no—
917C22×C3—24no—
918C22×C3—22no—
919C22×C3—24no—
920C22×C3—21no—
921C22×C3—34no—
922C22×C3—41no—
923C22×C3—41no—
924C22×C3—42no—
925C22×C3—42no—
926C22×C3—42no—
927C22×C3—62no—
928C22×C3—62no—
929C22×C3—62no—
930C22×C3—64no—
931C22×C3—62no—
932C22×C3—62no—
933C22×C3—64no—
934C22×C3—64no—
935C22×C3—1216no—
936C22×C3C24×D312yes—
937C2×D3—22no—
938C2×D3—22no—
939C2×D3—22no—
940C2×D3—24no—
941C2×D3—22no—
942C2×D3—24no—
943C2×D3—22no—
944C2×D3—24no—
945C2×D3—34no—
946C2×D3—34no—
947C2×D3—34no—
948C2×D3—416no—
949C2×D3—62no—
950C2×D3—62no—
951C2×D3—62no—
952C2×D3—616no—
953C2×D3—62no—
954C2×D3—62no—
955C2×D3—64no—
956C2×D3—62no—
957C2×D3—62no—
958C2×D3—64no—
959C2×D3—64no—
960C2×D3—121no—
961C2×D3—121no—
962C2×D3—122no—
963C2×D3—122no—
964C2×D3—122no—
965C2×D3—1216no—
966C2×D3—1216no—
967C2×D3—128no—
968C2×D3—1216no—
969C2×D3—128no—
970C2×D3—1216no—
971C2×D3—128no—
972C2×D3—248no—
973C2×D3C2×D3×D414yes—
974C3×C4—22no—
975C3×C4—24no—
976C3×C4—22no—
977C3×C4—34no—
978C3×C4—41no—
979C3×C4—42no—
980C3×C4—62no—
981C3×C4—64no—
982C3×C4C2×D3×D414yes—
983Dic3—22no—
984Dic3—24no—
985Dic3—34no—
986Dic3—62no—
987Dic3—62no—
988Dic3—64no—
989Dic3—121no—
990Dic3—122no—
991Dic3C2×D3×D414yes—
992C32C2×#53511yescharacteristic, complemented, Sylow
993C23—32no—
994C23—34no—
995C23—32no—
996C23—68no—
997C23—94no—
998C23—91no—
999C23—92no—
1000C23—91no—
1001C23—124no—
1002C23—124no—
1003C23—182no—
1004C23—184no—
1005C23—182no—
1006C23—182no—
1007C23—184no—
1008C23—184no—
1009C23—188no—
1010C23—182no—
1011C23—182no—
1012C23—182no—
1013C23—184no—
1014C23—182no—
1015C23—182no—
1016C23—184no—
1017C23—184no—
1018C23—364no—
1019C23—364no—
1020C23—3632no—
1021C23C22×D3212yes—
1022C23C22×D3211yescharacteristic
1023Q8—64no—
1024Q8—184no—
1025D4—22no—
1026D4—42no—
1027D4—64no—
1028D4—68no—
1029D4—64no—
1030D4—64no—
1031D4—64no—
1032D4—124no—
1033D4—124no—
1034D4—124no—
1035D4—188no—
1036D4—184no—
1037D4—184no—
1038D4—184no—
1039D4—184no—
1040D4—184no—
1041D4—182no—
1042D4—362no—
1043D4—364no—
1044D4—364no—
1045D4—362no—
1046D4—362no—
1047D4—364no—
1048C2×C4—22no—
1049C2×C4—32no—
1050C2×C4—38no—
1051C2×C4—34no—
1052C2×C4—32no—
1053C2×C4—64no—
1054C2×C4—94no—
1055C2×C4—98no—
1056C2×C4—91no—
1057C2×C4—94no—
1058C2×C4—92no—
1059C2×C4—91no—
1060C2×C4—182no—
1061C2×C4—182no—
1062C2×C4—184no—
1063C2×C4—182no—
1064C2×C4—184no—
1065C2×C4—184no—
1066C2×C4—182no—
1067C2×C4—182no—
1068C2×C4C22×D3212yes—
1069C2×C4C22×D3211yescharacteristic
1070C2×C4C22×D3211yescharacteristic
1071C2×C3—21no—
1072C2×C3—21no—
1073C2×C3—21no—
1074C2×C3—42no—
1075C2×C3—44no—
1076C2×C3—42no—
1077C2×C3—64no—
1078C2×C3—82no—
1079C2×C3—124no—
1080C2×C3—122no—
1081C2×C3C22×D3×D412yes—
1082C2×C3D3×H(5,𝔽2)12yes—
1083C2×C3D3×H(5,𝔽2)12yes—
1084D3—24no—
1085D3—38no—
1086D3—44no—
1087D3—42no—
1088D3—64no—
1089D3—122no—
1090D3—124no—
1091D3—122no—
1092D3—242no—
1093C22—21no—
1094C22—22no—
1095C22—21no—
1096C22—22no—
1097C22—21no—
1098C22—22no—
1099C22—34no—
1100C22—62no—
1101C22—62no—
1102C22—62no—
1103C22—64no—
1104C22—62no—
1105C22—64no—
1106C22—62no—
1107C22—64no—
1108C22—92no—
1109C22—92no—
1110C22—92no—
1111C22—1216no—
1112C22—188no—
1113C22—181no—
1114C22—182no—
1115C22—181no—
1116C22—182no—
1117C22—181no—
1118C22—182no—
1119C22—368no—
1120C22—364no—
1121C22—3616no—
1122C22—368no—
1123C22—364no—
1124C22C23×D3211yescharacteristic
1125C4—21no—
1126C4—22no—
1127C4—34no—
1128C4—62no—
1129C4—64no—
1130C4—92no—
1131C4—181no—
1132C4—182no—
1133C4D32×D412yes—
1134C3—21no—
1135C3D3×#53512yescomplemented
1136C2—42no—
1137C2—41no—
1138C2—64no—
1139C2—94no—
1140C2—124no—
1141C2—122no—
1142C2—362no—
1143C2—361no—
1144C2C2×D32×D411yescharacteristic
1145C2#1059667511yescharacteristic
1146C2#1059669211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#121C22
hypercenter#121D32
hypocenterC32C2×#535
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D32×D4C2semidirect
2. C2×#64306C2semidirect
3. C3⋊D3×#121C2semidirect
4. C3×#5607C2semidirect
5. #10595300C2semidirect
6. #10595286C2semidirect
7. #10595282C2semidirect
8. #10595278C2semidirect
9. #10595231C2semidirect
10. #10595081C2semidirect
11. #10595064C2semidirect
12. #10594628C2semidirect
13. #10594612C2semidirect
14. #10594602C2semidirect
15. #10594288C2semidirect
16. #10594270C2semidirect
17. #10594258C2semidirect
21. C2×D4×C3⋊D3C22semidirect
22. C22×C4×C3⋊D3C22semidirect
23. C2×C3×D3×D4C22semidirect
24. C2×C3×#235C22semidirect
27. C2×#3811C22semidirect
28. C2×#3811C22semidirect
29. C2×#3811C22semidirect
30. C2×D3×#67C22semidirect
31. C2×#3805C22semidirect
36. C2×#3802C22semidirect
37. C2×D3×D12C22semidirect
39. C2×C4×D32C22semidirect
40. C2×#3798C22semidirect
41. C2×#3797C22semidirect
42. C2×#3796C22semidirect
43. C32×#121C22semidirect
44. #64148C22semidirect
45. #64147C22semidirect
46. #64139C22semidirect
47. #64104C22semidirect
48. C4⋊C4×C3⋊D3C22semidirect
49. #64093C22semidirect
50. C22⋊C4×C3⋊D3C22semidirect
51. C3×#940C22semidirect
52. C3×#938C22semidirect
53. C3×#937C22semidirect
54. C3×#930C22semidirect
55. C3×#895C22semidirect
56. C3×#892C22semidirect
57. C3×#885C22semidirect
58. C3×#882C22semidirect
59. #63983C22semidirect
60. #63980C22semidirect
61. #63979C22semidirect
62. #63979C22semidirect
63. #63977C22semidirect
64. #63976C22semidirect
65. #63974C22semidirect
66. #63971C22semidirect
67. #63959C22semidirect
68. #63923C22semidirect
69. #63922C22semidirect
70. #63922C22semidirect
72. #63921C22semidirect
73. #63921C22semidirect
74. #63916C22semidirect
75. #63912C22semidirect
76. #63911C22semidirect
77. #63909C22semidirect
78. #63908C22semidirect
79. #63907C22semidirect
80. #63900C22semidirect
81. #63885C22semidirect
82. C4×#624C22semidirect
83. #63877C22semidirect
84. #63852C22semidirect
85. #63841C22semidirect
98. #5607D3semidirect
121. C2×C32×D4C23semidirect
122. C22×C32×C4C23semidirect
124. C2×#638C23semidirect
125. C2×#638C23semidirect
126. C22×C3⋊Dic3C23semidirect
130. C2×C4⋊(C3⋊D3)C23semidirect
135. C2×C4×C3⋊D3C23semidirect
136. C2×C4×C3⋊D3C23semidirect
139. C2×C3×#67C23semidirect
140. C2×C3×#67C23semidirect
141. C2×C3×#67C23semidirect
146. C2×C3×D12C23semidirect
148. C2×C3×C4×D3C23semidirect
149. C2×C3×Dic6C23semidirect
156. C2×#627C23semidirect
159. C2×#626C23semidirect
160. C2×#626C23semidirect
161. C2×#626C23semidirect
164. C2×#625C23semidirect
170. C2×D3×Dic3C23semidirect
176. C4×D32D4semidirect
180. C32×C4⋊C4C23semidirect
181. C32×C22⋊C4C23semidirect
182. #3757C23semidirect
183. #3752C23semidirect
184. #3752C23semidirect
185. C4⋊(C3⋊Dic3)C23semidirect
186. #3750C23semidirect
187. C3×#217C23semidirect
189. C3×(C2×D3)⋊C4C23semidirect
190. C3×(C2×D3)⋊C4C23semidirect
191. C3×C4⋊Dic3C23semidirect
192. C3×C4×Dic3C23semidirect
193. #3724C23semidirect
194. #3722C23semidirect
196. (C2×D3)⋊Dic3C23semidirect
197. (C2×D3)⋊Dic3C23semidirect
198. Dic32C23semidirect
225. C2×D3×D4C2×D3semidirect
228. C2×#235C2×D3semidirect
240. C3×#121C2×D3semidirect
252. #940C2×D3semidirect
262. #938C2×D3semidirect
268. #937C2×D3semidirect
274. #930C2×D3semidirect
280. #895C2×D3semidirect
282. #892C2×D3semidirect
289. #885C2×D3semidirect
300. #882C2×D3semidirect
374. C3×C4×D3C2×D4semidirect
389. D3×Dic3C2×D4semidirect
435. C2×C3×D4C22×D3semidirect
439. C22×C3×C4C22×D3semidirect
459. C2×#67C22×D3semidirect
460. C2×#67C22×D3semidirect
461. C2×#67C22×D3semidirect
501. C2×D12C22×D3semidirect
522. C2×C4×D3C22×D3semidirect
525. C2×Dic6C22×D3semidirect
528. C3×C4⋊C4C22×D3semidirect
534. C3×C22⋊C4C22×D3semidirect
541. #217C22×D3semidirect
552. (C2×D3)⋊C4C22×D3semidirect
553. (C2×D3)⋊C4C22×D3semidirect
556. C4⋊Dic3C22×D3semidirect
562. C4×Dic3C22×D3semidirect
651. #121D32semidirect
809. C4×D3D3×D4semidirect
820. C3⋊D3#535semidirect
876. C2×D4C2×D32semidirect
893. C22×C4C2×D32semidirect
898. C4⋊C4C2×D32semidirect
910. C22⋊C4C2×D32semidirect
992. C32C2×#535semidirect
1135. C3D3×#535semidirect

Maximal subgroups

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

subgroupindex
C2×D32×D42
C2×#643062
C3⋊D3×#1212
C3×#56072
#105953002
#105952862
#105952822
#105952782
#105952312
#105950812
#105950642
#105946282
#105946122
#105946022
#105942882
#105942702
#105942582
D3×#5353