Finite Group Databasebeta

← #11904900

Subgroups — #11904900

Order 1152.

2993 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic, complemented
2C3×#5791C212yesmaximal, complemented
3#10595527C212yesmaximal, complemented
4#10595501C212yesmaximal, complemented
5#10595084C211yesmaximal, characteristic, complemented
6#10595075C214yesmaximal, complemented
7#10595068C214yesmaximal, complemented
8#10595058C212yesmaximal, complemented
9#10595039C212yesmaximal, complemented
10#10595035C214yesmaximal, complemented
11#10594981C211yesmaximal, characteristic, complemented
12#10594979C212yesmaximal, complemented
13#10594966C214yesmaximal, complemented
14#86043—32nomaximal
15C24×C3⋊D3C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic, complemented
17C23×C3⋊Dic3C2211yescharacteristic, complemented
18C2×C3×#235C2212yescomplemented
19C2×#3811C2212yes—
20C2×#3811C2212yescomplemented
21C2×#3811C2212yescomplemented
22C2×#3805C2212yescomplemented
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2214yescomplemented
26C2×#3752C2214yescomplemented
27C2×#3752C2211yescharacteristic, complemented
28C2×#3752C2211yescharacteristic, complemented
29C3×#953C2214yescomplemented
30C3×#930C2212yescomplemented
31C3×#930C2212yescomplemented
32C3×#929C2214yescomplemented
33C3×C4×#67C2214yescomplemented
34C3×C4×#67C2214yescomplemented
35C3×#926C2212yescomplemented
36C3×#924C2212yescomplemented
37C3×#924C2212yescomplemented
38#63982C2212yescomplemented
39#63982C2212yescomplemented
40#63981C2214yes—
41#63981C2214yes—
42#63981C2214yescomplemented
43#63980C2212yescomplemented
44#63980C2212yescomplemented
45#63974C2212yes—
46#63974C2212yescomplemented
47#63974C2212yescomplemented
48#67⋊Dic3C2214yescomplemented
49#67⋊Dic3C2214yescomplemented
50#63962C2214yescomplemented
51#63957C2212yescomplemented
52#63922C2214yescomplemented
53D3×(C2×D3)⋊C4C2214yescomplemented
54#63907C2214yescomplemented
55#63906C2214yescomplemented
56#63904C2214yescomplemented
57#63895C2214yescomplemented
58#63890C2214yescomplemented
59#63888C2214yescomplemented
60#63886C2214yescomplemented
61#63880C2214yescomplemented
62#63868C2214yescomplemented
63#63854C2214yescomplemented
64#63852C2214yescomplemented
65#63850C2214yescomplemented
66#63848C2214yescomplemented
67#63836C2214yescomplemented
68C3×#525—32no—
69#5829—34no—
70#5791D312yescomplemented
71C22×(C2×D3)⋊C4—32no—
72C22×(C2×D3)⋊C4—61no—
73#5658—34no—
74#5654—34no—
75#5644—32no—
76#5637—34no—
77#5634—32no—
78#5617—32no—
79#5610—34no—
80#5605—32no—
81D3×#120—34no—
82#5586—34no—
83#5560—34no—
84#5556—34no—
85#5554—34no—
86#5545—34no—
87#5527—34no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3—24no—
90C23×C3⋊D3—42no—
91C23×C3⋊D3—42no—
92C23×C3⋊D3C2312yes—
93C23×C3⋊D3C2312yes—
94C23×C3⋊D3C2311yescharacteristic
95C23×C3⋊D3C2311yescharacteristic
96C22×D32C2312yes—
97C22×C32×C4—42no—
98C22×C32×C4C2312yes—
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2312yes—
101C22×C32×C4C2311yescharacteristic
102C22×C3⋊Dic3—42no—
103C22×C3⋊Dic3C2312yes—
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2312yes—
107C2×C3×#67C2314yes—
108C2×C3×#67C2314yes—
109C2×C3×#67C2314yes—
110C3×#235—44no—
111C2×C3×D12C2312yescomplemented
112C2×C3×C4×D3C2314yescomplemented
113C2×C3×Dic6C2312yescomplemented
114#3811—28no—
115#3811—44no—
116#3811—44no—
117C2×#627C2312yescomplemented
118C2×#626C2314yes—
119C2×#626C2314yes—
120C2×#626C2314yes—
121C2×#625C2312yescomplemented
122C2×#624C2312yes—
123C2×#624C2312yes—
124C2×#624C2312yes—
125#3805—44no—
126C2×D3×Dic3C2314yescomplemented
127#3752C2314yes—
128#3752C2314yes—
129#3752C2314yes—
130#3752C2314yes—
131C3×#217C2314yes—
132C3×#217C2314yes—
133C3×#217C2314yes—
134C3×(C2×D3)⋊C4C2314yescomplemented
135C3×(C2×D3)⋊C4C2314yescomplemented
136C3×C4⋊Dic3C2312yescomplemented
137C3×C4⋊Dic3C2312yescomplemented
138C3×Dic3⋊C4C2314yescomplemented
139C3×Dic3⋊C4C2314yescomplemented
140C3×C4×Dic3C2314yescomplemented
141#3724C2312yescomplemented
142#3724C2312yescomplemented
143Dic3⋊Dic3C2314yescomplemented
144Dic3⋊Dic3C2314yescomplemented
145#3722C2314yes—
146#3722C2314yes—
147#3722C2314yes—
148(C2×D3)⋊Dic3C2314yescomplemented
149(C2×D3)⋊Dic3C2314yescomplemented
150Dic32C2314yescomplemented
151#3490—91noSylow
152C24×D3—32no—
153C24×D3—61no—
154C2×C3×#41—32no—
155C23×C3×C4—21no—
156C23×C3×C4C2×D312yescomplemented
157C23×Dic3—32no—
158C23×Dic3—61no—
159C2×#237—34no—
160C2×D3×D4—34no—
161C2×D3×D4—34no—
162C2×D3×D4—34no—
163C2×#235C2×D312yescomplemented
164C3×#123—34no—
165C3×C22⋊Q8—32no—
166C3×C22⋊Q8—32no—
167C3×#121—32no—
168C3×#121—32no—
169C3×#120—34no—
170C3×C4×D4—34no—
171C3×C4×D4—34no—
172C3×#117—32no—
173#953C2×D314yescomplemented
174#947—34no—
175#946—34no—
176#939—34no—
177#939—34no—
178#939—34no—
179#937—34no—
180#937—34no—
181#937—34no—
182#937—34no—
183#935—34no—
184D4×Dic3—34no—
185D4×Dic3—34no—
186#930—34no—
187#930C2×D312yescomplemented
188#930C2×D312yescomplemented
189#929—34no—
190#929C2×D314yescomplemented
191C4×#67—34no—
192C4×#67C2×D314yescomplemented
193C4×#67C2×D314yescomplemented
194C2×(C2×D3)⋊C4—32no—
195C2×(C2×D3)⋊C4—34no—
196C2×(C2×D3)⋊C4—32no—
197C2×(C2×D3)⋊C4—34no—
198C2×(C2×D3)⋊C4—32no—
199C2×(C2×D3)⋊C4—34no—
200C2×(C2×D3)⋊C4—34no—
201C2×(C2×D3)⋊C4—32no—
202C2×(C2×D3)⋊C4—34no—
203C2×(C2×D3)⋊C4—61no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4—61no—
206C2×(C2×D3)⋊C4—61no—
207C2×(C2×D3)⋊C4—64no—
208C2×(C2×D3)⋊C4—64no—
209#926C2×D312yescomplemented
210#924C2×D312yescomplemented
211#924C2×D312yescomplemented
212#898—34no—
213#898—34no—
214#898—34no—
215#897—34no—
216#896—34no—
217#896—34no—
218#895—34no—
219#894—34no—
220#894—34no—
221#894—34no—
222#893—34no—
223#892—34no—
224#886—34no—
225#886—34no—
226#885—34no—
227#885—34no—
228#884—34no—
229#883—34no—
230#882—34no—
231#882—34no—
232#882—34no—
233#882—34no—
234#67⋊C4—34no—
235#67⋊C4—34no—
236#67⋊C4—34no—
237D3×C22⋊C4—34no—
238D3×C22⋊C4—34no—
239D3×C22⋊C4—34no—
240D3×C22⋊C4—34no—
241#878—34no—
242#878—34no—
243#877—34no—
244#876—34no—
245#875—34no—
246C4×D12—34no—
247#872—34no—
248C23×C32—22no—
249C23×C32—22no—
250C23×C32—22no—
251C23×C32C2411yescharacteristic
252C23×C32C2411yescharacteristic
253C23×C32C2411yescharacteristic
254C22×C3⋊D3—22no—
255C22×C3⋊D3—24no—
256C22×C3⋊D3—24no—
257C22×C3⋊D3—24no—
258C22×C3⋊D3—24no—
259C22×C3⋊D3—41no—
260C22×C3⋊D3—41no—
261C22×C3⋊D3—42no—
262C22×C3⋊D3—42no—
263C22×C3⋊D3—41no—
264C22×C3⋊D3—41no—
265C22×C3⋊D3—416no—
266C22×C3⋊D3#4114yescomplemented
267C22×C3⋊D3C2412yes—
268C22×C3⋊D3C2412yes—
269C22×C3×D3C2414yes—
270C2×D32—24no—
271C2×D32—42no—
272C2×D32—42no—
273C2×C32×C4—24no—
274C2×C32×C4—41no—
275C2×C32×C4—42no—
276C2×C32×C4—41no—
277C2×C32×C4C2412yes—
278C2×C32×C4C2412yes—
279C2×C3⋊Dic3—24no—
280C2×C3⋊Dic3—41no—
281C2×C3⋊Dic3—42no—
282C2×C3⋊Dic3—41no—
283C2×C3⋊Dic3C2412yes—
284C2×C3⋊Dic3C2412yes—
285C3×#67—28no—
286C3×#67—28no—
287C3×#67—28no—
288C2×C3×Dic3C2414yes—
289C2×C3×Dic3C2414yes—
290C2×C3×Dic3C2414yes—
291C3×D12—42no—
292C3×C4×D3—44no—
293C3×Dic6—42no—
294#627—42no—
295#626—28no—
296#626—44no—
297#626—44no—
298#625—42no—
299#624—24no—
300#624—42no—
301#624—42no—
302D3×Dic3—44no—
303#551—94no—
304#551—94no—
305#546—94no—
306#546—94no—
307#543—91no—
308#538—92no—
309#538—92no—
310#534—91no—
311#525—32no—
312#525—92no—
313C2×#120—92no—
314#518—92no—
315C22×C22⋊C4—91no—
316C24×C3—21no—
317C24×C3C22×D312yes—
318C23×D3—32no—
319C23×D3—34no—
320C23×D3—34no—
321C23×D3—32no—
322C23×D3—34no—
323C23×D3—61no—
324C23×D3—62no—
325C23×D3—62no—
326C23×D3—61no—
327C23×D3—68no—
328C23×D3—68no—
329C23×D3—124no—
330C23×D3—124no—
331C23×D3—124no—
332C23×D3—124no—
333C3×#41—124no—
334C2×C3×Q8—32no—
335C2×C3×D4—34no—
336C2×C3×D4—34no—
337C2×C3×D4—34no—
338C2×C3×D4—32no—
339C22×C3×C4—22no—
340C22×C3×C4—21no—
341C22×C3×C4—22no—
342C22×C3×C4—21no—
343C22×C3×C4—34no—
344C22×C3×C4—44no—
345C22×C3×C4—44no—
346C22×C3×C4C22×D312yes—
347C22×C3×C4C22×D312yes—
348C22×C3×C4C22×D312yes—
349C22×C3×C4C22×D312yes—
350C22×C3×C4C22×D312yes—
351C22×C3×C4C22×D312yes—
352C2×#67—34no—
353C2×#67—34no—
354C2×#67—34no—
355C2×#67—34no—
356C2×#67C22×D314yes—
357C2×#67C22×D314yes—
358C2×#67C22×D314yes—
359C22×Dic3—34no—
360C22×Dic3—32no—
361C22×Dic3—34no—
362C22×Dic3—32no—
363C22×Dic3—34no—
364C22×Dic3—62no—
365C22×Dic3—61no—
366C22×Dic3—62no—
367C22×Dic3—61no—
368C22×Dic3—124no—
369C22×Dic3—124no—
370#237—128no—
371D3×D4—616no—
372D3×D4—128no—
373D3×D4—128no—
374#235—44no—
375C2×D12—34no—
376C2×D12—34no—
377C2×D12—34no—
378C2×D12C22×D312yescomplemented
379C2×C4×D3—34no—
380C2×C4×D3—34no—
381C2×C4×D3—34no—
382C2×C4×D3—34no—
383C2×C4×D3C22×D314yescomplemented
384C2×Dic6—34no—
385C2×Dic6C22×D312yescomplemented
386C3×C4⋊C4—34no—
387C3×C4⋊C4—32no—
388C3×C4⋊C4—32no—
389C3×C4⋊C4—34no—
390C3×C22⋊C4—34no—
391C3×C22⋊C4—34no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—34no—
394C3×C22⋊C4—34no—
395C3×C42—34no—
396#217—34no—
397#217—34no—
398#217C22×D314yes—
399#217C22×D314yes—
400#217C22×D314yes—
401(C2×D3)⋊C4—34no—
402(C2×D3)⋊C4—34no—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4—34no—
409(C2×D3)⋊C4—34no—
410(C2×D3)⋊C4—34no—
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—34no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—34no—
417(C2×D3)⋊C4—64no—
418(C2×D3)⋊C4—64no—
419(C2×D3)⋊C4—64no—
420(C2×D3)⋊C4—64no—
421(C2×D3)⋊C4C22×D314yescomplemented
422(C2×D3)⋊C4C22×D314yescomplemented
423C4⋊Dic3—34no—
424C4⋊Dic3—34no—
425C4⋊Dic3C22×D312yescomplemented
426C4⋊Dic3C22×D312yescomplemented
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4C22×D314yescomplemented
432Dic3⋊C4C22×D314yescomplemented
433C4×Dic3—34no—
434C4×Dic3—34no—
435C4×Dic3C22×D314yescomplemented
436C22×C32—28no—
437C22×C32—21no—
438C22×C32—21no—
439C22×C32—21no—
440C22×C32—21no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32C2×#4112yes—
444C22×C32H(5,𝔽2)12yes—
445C22×C32H(5,𝔽2)12yes—
446C22×C32C2511yescharacteristic
447C2×C3⋊D3—22no—
448C2×C3⋊D3—22no—
449C2×C3⋊D3—22no—
450C2×C3⋊D3—22no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—44no—
453C2×C3⋊D3—48no—
454C2×C3⋊D3—48no—
455C2×C3⋊D3—44no—
456C2×C3⋊D3C2×#4114yes—
457C2×C3×D3—24no—
458C2×C3×D3—24no—
459C2×C3×D3—24no—
460D32—84no—
461C32×C4—22no—
462C32×C4—22no—
463C3⋊Dic3—22no—
464C3⋊Dic3—22no—
465C3×Dic3—24no—
466C3×Dic3—24no—
467C3×Dic3—24no—
468C25—91no—
469C2×#41—32no—
470C2×#41—92no—
471C22×D4—92no—
472C22×D4—92no—
473C22×D4—92no—
474C23×C4—91no—
475C23×C4D3211yescharacteristic, complemented
476#126—94no—
477#126—94no—
478#124—94no—
479#124—94no—
480#123—34no—
481#123—94no—
482#123—94no—
483#123—94no—
484#123—94no—
485C22⋊Q8—32no—
486C22⋊Q8—32no—
487C22⋊Q8—92no—
488C22⋊Q8—92no—
489C22⋊Q8—94no—
490C22⋊Q8—94no—
491#121—32no—
492#121—32no—
493#121—94no—
494#121—94no—
495#121—92no—
496#121—92no—
497#120—34no—
498#120—94no—
499#120—94no—
500#120—94no—
501#120—94no—
502C4×D4—34no—
503C4×D4—34no—
504C4×D4—94no—
505C4×D4—94no—
506C4×D4—94no—
507C4×D4—94no—
508#117—32no—
509#117—94no—
510#117—92no—
511C2×C22⋊C4—92no—
512C2×C22⋊C4—92no—
513C2×C22⋊C4—92no—
514C2×C22⋊C4—94no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4—91no—
517C2×C22⋊C4—91no—
518C2×C22⋊C4—91no—
519C2×C22⋊C4—94no—
520C2×C22⋊C4—94no—
521C23×C3—24no—
522C23×C3—24no—
523C23×C3—24no—
524C23×C3—24no—
525C23×C3—24no—
526C23×C3—24no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—34no—
531C23×C3C23×D312yes—
532C23×C3C23×D312yes—
533C23×C3C23×D312yes—
534C22×D3—34no—
535C22×D3—38no—
536C22×D3—34no—
537C22×D3—64no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—68no—
541C22×D3—68no—
542C22×D3—68no—
543C22×D3—68no—
544C22×D3—68no—
545C22×D3—64no—
546C22×D3—68no—
547C22×D3—64no—
548C22×D3—68no—
549C22×D3—124no—
550C22×D3—124no—
551C22×D3—124no—
552C22×D3—124no—
553C22×D3—122no—
554C22×D3—124no—
555C22×D3—122no—
556C22×D3—124no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—124no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—124no—
564C22×D3—122no—
565C22×D3—1232no—
566C22×D3—1232no—
567C22×D3C23×D314yes—
568C3×Q8—122no—
569C3×D4—68no—
570C3×D4—68no—
571C3×D4—68no—
572C3×D4—122no—
573C2×C3×C4—24no—
574C2×C3×C4—24no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—34no—
578C2×C3×C4—34no—
579C2×C3×C4—34no—
580C2×C3×C4—44no—
581C2×C3×C4—42no—
582C2×C3×C4—42no—
583C2×C3×C4—42no—
584C2×C3×C4—42no—
585C2×C3×C4—42no—
586C2×C3×C4—44no—
587C2×C3×C4—42no—
588C2×C3×C4—124no—
589C2×C3×C4C23×D312yes—
590C2×C3×C4C23×D312yes—
591C2×C3×C4C23×D312yes—
592C2×C3×C4C23×D312yes—
593#67—28no—
594#67—28no—
595#67—28no—
596#67—68no—
597#67—124no—
598#67—124no—
599#67—124no—
600C2×Dic3—34no—
601C2×Dic3—34no—
602C2×Dic3—62no—
603C2×Dic3—62no—
604C2×Dic3—68no—
605C2×Dic3—124no—
606C2×Dic3—124no—
607C2×Dic3—122no—
608C2×Dic3—124no—
609C2×Dic3—122no—
610C2×Dic3—122no—
611C2×Dic3—124no—
612C2×Dic3—122no—
613C2×Dic3C23×D314yes—
614C2×Dic3C23×D314yes—
615C2×Dic3C23×D314yes—
616D12—42no—
617D12—68no—
618D12—124no—
619D12—124no—
620C4×D3—44no—
621C4×D3—68no—
622C4×D3—124no—
623C4×D3—124no—
624C4×D3—124no—
625Dic6—42no—
626Dic6—124no—
627C2×C32—22no—
628C2×C32—22no—
629C2×C32—22no—
630C2×C32C22×#4111yescharacteristic
631C2×C32C2×H(5,𝔽2)11yescharacteristic
632C2×C32C2×H(5,𝔽2)11yescharacteristic
633C3⋊D3—24no—
634C3⋊D3—42no—
635C3×D3—44no—
636C24—92no—
637C24—91no—
638C24—92no—
639C24—92no—
640C24—91no—
641C24—184no—
642C24—362no—
643C24—362no—
644C24C2×D3211yescharacteristic
645#41—124no—
646#41—364no—
647C2×Q8—32no—
648C2×Q8—92no—
649C2×D4—34no—
650C2×D4—34no—
651C2×D4—34no—
652C2×D4—32no—
653C2×D4—94no—
654C2×D4—94no—
655C2×D4—94no—
656C2×D4—92no—
657C2×D4—188no—
658C2×D4—364no—
659C2×D4—364no—
660C22×C4—34no—
661C22×C4—42no—
662C22×C4—92no—
663C22×C4—92no—
664C22×C4—92no—
665C22×C4—94no—
666C22×C4—92no—
667C22×C4—91no—
668C22×C4—92no—
669C22×C4—91no—
670C22×C4—362no—
671C22×C4C2×D3212yes—
672C22×C4C2×D3211yescharacteristic
673C22×C4C2×D3212yes—
674C22×C4C2×D3211yescharacteristic
675C4⋊C4—32no—
676C4⋊C4—32no—
677C4⋊C4—34no—
678C4⋊C4—34no—
679C4⋊C4—94no—
680C4⋊C4—92no—
681C4⋊C4—92no—
682C4⋊C4—94no—
683C22⋊C4—34no—
684C22⋊C4—34no—
685C22⋊C4—34no—
686C22⋊C4—34no—
687C22⋊C4—34no—
688C22⋊C4—94no—
689C22⋊C4—94no—
690C22⋊C4—94no—
691C22⋊C4—94no—
692C22⋊C4—94no—
693C22⋊C4—94no—
694C22⋊C4—94no—
695C22⋊C4—94no—
696C22⋊C4—94no—
697C42—34no—
698C42—94no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—216no—
706C22×C3—216no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—22no—
715C22×C3—22no—
716C22×C3—21no—
717C22×C3—64no—
718C22×C3—64no—
719C22×C3—64no—
720C22×C3#100414yes—
721C22×C3D3×#4114yes—
722C22×C3#100914yes—
723C22×C3C24×D312yes—
724C2×D3—24no—
725C2×D3—24no—
726C2×D3—24no—
727C2×D3—38no—
728C2×D3—64no—
729C2×D3—64no—
730C2×D3—64no—
731C2×D3—64no—
732C2×D3—64no—
733C2×D3—64no—
734C2×D3—64no—
735C2×D3—122no—
736C2×D3—122no—
737C2×D3—122no—
738C2×D3—122no—
739C2×D3—128no—
740C2×D3—1216no—
741C2×D3—1216no—
742C2×D3—128no—
743C2×D3—1216no—
744C2×D3—1216no—
745C2×D3—128no—
746C2×D3—128no—
747C2×D3—248no—
748C3×C4—22no—
749C3×C4—22no—
750C3×C4—22no—
751C3×C4—22no—
752C3×C4—42no—
753C3×C4—42no—
754C3×C4—64no—
755C3×C4—64no—
756C3×C4—64no—
757Dic3—24no—
758Dic3—24no—
759Dic3—24no—
760Dic3—64no—
761Dic3—64no—
762Dic3—122no—
763Dic3—122no—
764C32#349011yescharacteristic, complemented, Sylow
765C23—22no—
766C23—22no—
767C23—22no—
768C23—34no—
769C23—92no—
770C23—94no—
771C23—92no—
772C23—184no—
773C23—184no—
774C23—184no—
775C23—182no—
776C23—184no—
777C23—184no—
778C23—361no—
779C23—362no—
780C23—361no—
781C23—361no—
782C23—362no—
783C23—361no—
784C23—3616no—
785C23—362no—
786C23—362no—
787C23C22×D3211yescharacteristic
788C23C22×D3211yescharacteristic
789C23C22×D3211yescharacteristic
790Q8—122no—
791Q8—362no—
792D4—68no—
793D4—68no—
794D4—68no—
795D4—122no—
796D4—188no—
797D4—364no—
798D4—364no—
799D4—362no—
800C2×C4—24no—
801C2×C4—34no—
802C2×C4—34no—
803C2×C4—34no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—92no—
808C2×C4—92no—
809C2×C4—124no—
810C2×C4—184no—
811C2×C4—184no—
812C2×C4—362no—
813C2×C4—362no—
814C2×C4—364no—
815C2×C4—361no—
816C2×C4—362no—
817C2×C4—361no—
818C2×C4C22×D3212yes—
819C2×C4C22×D3212yes—
820C2×C3—24no—
821C2×C3—24no—
822C2×C3—24no—
823C2×C3—24no—
824C2×C3—24no—
825C2×C3—24no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—124no—
830C2×C3C2×#100412yes—
831C2×C3C2×D3×#4112yes—
832C2×C3C2×#100912yes—
833D3—44no—
834D3—68no—
835D3—124no—
836D3—124no—
837D3—124no—
838C22—28no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—64no—
846C22—64no—
847C22—64no—
848C22—94no—
849C22—182no—
850C22—182no—
851C22—182no—
852C22—182no—
853C22—182no—
854C22—364no—
855C22—368no—
856C22—368no—
857C22—364no—
858C22—724no—
859C22#6430612yes—
860C22#6430812yes—
861C22#6433012yes—
862C22C23×D3211yescharacteristic
863C4—22no—
864C4—22no—
865C4—64no—
866C4—64no—
867C4—64no—
868C4—182no—
869C4—182no—
870C3—21no—
871C3#8604312yescomplemented
872C2—22no—
873C2—22no—
874C2—22no—
875C2—124no—
876C2—184no—
877C2—362no—
878C2C2×#6430611yescharacteristic
879C2C2×#6430811yescharacteristic
880C2C2×#6433011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3490
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3752C2semidirect
2. C3×#5791C2semidirect
3. #10595527C2semidirect
4. #10595501C2semidirect
5. #10595084C2semidirect
6. #10595075C2semidirect
7. #10595068C2semidirect
8. #10595058C2semidirect
9. #10595039C2semidirect
10. #10595035C2semidirect
11. #10594981C2semidirect
12. #10594979C2semidirect
13. #10594966C2semidirect
16. C23×C32×C4C22semidirect
17. C23×C3⋊Dic3C22semidirect
18. C2×C3×#235C22semidirect
20. C2×#3811C22semidirect
21. C2×#3811C22semidirect
22. C2×#3805C22semidirect
25. C2×#3752C22semidirect
26. C2×#3752C22semidirect
27. C2×#3752C22semidirect
28. C2×#3752C22semidirect
29. C3×#953C22semidirect
30. C3×#930C22semidirect
31. C3×#930C22semidirect
32. C3×#929C22semidirect
33. C3×C4×#67C22semidirect
34. C3×C4×#67C22semidirect
35. C3×#926C22semidirect
36. C3×#924C22semidirect
37. C3×#924C22semidirect
38. #63982C22semidirect
39. #63982C22semidirect
42. #63981C22semidirect
43. #63980C22semidirect
44. #63980C22semidirect
46. #63974C22semidirect
47. #63974C22semidirect
48. #67⋊Dic3C22semidirect
49. #67⋊Dic3C22semidirect
50. #63962C22semidirect
51. #63957C22semidirect
52. #63922C22semidirect
53. D3×(C2×D3)⋊C4C22semidirect
54. #63907C22semidirect
55. #63906C22semidirect
56. #63904C22semidirect
57. #63895C22semidirect
58. #63890C22semidirect
59. #63888C22semidirect
60. #63886C22semidirect
61. #63880C22semidirect
62. #63868C22semidirect
63. #63854C22semidirect
64. #63852C22semidirect
65. #63850C22semidirect
66. #63848C22semidirect
67. #63836C22semidirect
70. #5791D3semidirect
111. C2×C3×D12C23semidirect
112. C2×C3×C4×D3C23semidirect
113. C2×C3×Dic6C23semidirect
117. C2×#627C23semidirect
121. C2×#625C23semidirect
126. C2×D3×Dic3C23semidirect
134. C3×(C2×D3)⋊C4C23semidirect
135. C3×(C2×D3)⋊C4C23semidirect
136. C3×C4⋊Dic3C23semidirect
137. C3×C4⋊Dic3C23semidirect
138. C3×Dic3⋊C4C23semidirect
139. C3×Dic3⋊C4C23semidirect
140. C3×C4×Dic3C23semidirect
141. #3724C23semidirect
142. #3724C23semidirect
143. Dic3⋊Dic3C23semidirect
144. Dic3⋊Dic3C23semidirect
148. (C2×D3)⋊Dic3C23semidirect
149. (C2×D3)⋊Dic3C23semidirect
150. Dic32C23semidirect
156. C23×C3×C4C2×D3semidirect
163. C2×#235C2×D3semidirect
173. #953C2×D3semidirect
187. #930C2×D3semidirect
188. #930C2×D3semidirect
190. #929C2×D3semidirect
192. C4×#67C2×D3semidirect
193. C4×#67C2×D3semidirect
209. #926C2×D3semidirect
210. #924C2×D3semidirect
211. #924C2×D3semidirect
266. C22×C3⋊D3#41semidirect
378. C2×D12C22×D3semidirect
383. C2×C4×D3C22×D3semidirect
385. C2×Dic6C22×D3semidirect
421. (C2×D3)⋊C4C22×D3semidirect
422. (C2×D3)⋊C4C22×D3semidirect
425. C4⋊Dic3C22×D3semidirect
426. C4⋊Dic3C22×D3semidirect
431. Dic3⋊C4C22×D3semidirect
432. Dic3⋊C4C22×D3semidirect
435. C4×Dic3C22×D3semidirect
475. C23×C4D32semidirect
764. C32#3490semidirect
871. C3#86043semidirect

Maximal subgroups

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

subgroupindex
C22×#37522
C3×#57912
#105955272
#105955012
#105950842
#105950752
#105950682
#105950582
#105950392
#105950352
#105949812
#105949792
#105949662
#860433