Finite Group Databasebeta

← #11902005

Subgroups — #11902005

Order 1152.

2493 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595964C211yesmaximal, characteristic, complemented
2C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
3C3×#5483C211yesmaximal, characteristic, complemented
4#10595519C212yesmaximal, complemented
5C2×#63952C212yesmaximal, complemented
6#10595038C212yesmaximal, complemented
7#10595005C212yesmaximal, complemented
8#10594980C212yesmaximal, complemented
9#10594955C212yesmaximal, complemented
10#10594243C214yesmaximal, complemented
11#10594241C214yesmaximal, complemented
12#10594216C214yesmaximal, complemented
13#10594066C214yesmaximal, complemented
14#86572—31nomaximal
15#85776—31nomaximal
16C22×#638C2212yes—
17C22×C3×#67C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic, complemented
20C22×#624C2212yescomplemented
21C2×#3799C2212yescomplemented
22C2×C32×C22⋊C4C2211yescharacteristic
23#64139C2212yes—
24#64139C2212yes—
25#64095C2214yescomplemented
26#64091C2214yescomplemented
27C2×C3×#217C2212yes—
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
29C3×#924C2212yescomplemented
30C3×#924C2212yescomplemented
31C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
32C2×C3×C4×Dic3C2211yescharacteristic, complemented
33C3×#67⋊C4C2214yescomplemented
34C3×#67⋊C4C2214yescomplemented
35C3×#878C2214yescomplemented
36C3×#878C2214yescomplemented
37#63981C2214yescomplemented
38#63978C2214yes—
39#63978C2214yes—
40#63977C2214yescomplemented
41C2×#3724C2212yescomplemented
42#63966C2214yescomplemented
43C2×#3722C2212yescomplemented
44#63962C2214yescomplemented
45C2×Dic32C2212yescomplemented
46#63952C2214yescomplemented
47#63952C2214yescomplemented
48#63952C2214yescomplemented
49#63952C2214yescomplemented
50#63910C2214yescomplemented
51#63909C2212yescomplemented
52#63907C2214yescomplemented
53#63904C2214yescomplemented
54#63897C2214yescomplemented
55#63894C2212yescomplemented
56#63888C2214yescomplemented
57#63869C2212yescomplemented
58#63868C2214yescomplemented
59#63864C2212yescomplemented
60#63861C2214yescomplemented
61#63856C2212yescomplemented
62#63854C2214yescomplemented
63#63850C2214yescomplemented
64#63848C2214yescomplemented
65#63845C2214yescomplemented
66Dic3×Dic6C2212yescomplemented
67#63841C2212yescomplemented
68#63836C2214yescomplemented
69C3×#543—31no—
70C2×C3×C4×D4—31no—
71#5804—32no—
72#5791—32no—
73C2×C4×#67—32no—
74#5645—32no—
75#5645—34no—
76#5644—32no—
77#5644—34no—
78#5627—32no—
79#5627—34no—
80#5624—32no—
81#5624—34no—
82#5564—34no—
83#5560—34no—
84#5547—34no—
85#5538—34no—
86#5515—32no—
87#5494—32no—
88#5493—32no—
89#5493—31no—
90#5493—31no—
91#5493—61no—
92C2×#67⋊C4—32no—
93C2×#67⋊C4D311yescharacteristic, complemented
94#5483D311yescharacteristic, complemented
95#5479—32no—
96C24×C32C2311yescharacteristic
97C23×C3⋊D3C2312yes—
98C23×C3×D3C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×#638—28no—
102C2×#638C2314yes—
103C2×#638C2314yes—
104C22×C3⋊Dic3C2312yes—
105C2×C4⋊(C3⋊D3)C2312yes—
106C2×C4⋊(C3⋊D3)C2312yes—
107C2×C3×#67—24no—
108C2×C3×#67C2314yes—
109C22×C3×Dic3—42no—
110C22×C3×Dic3C2312yes—
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2312yes—
114C22×C3×Dic3C2312yes—
115C22×C3×Dic3C2312yes—
116C22×C3×Dic3C2311yescharacteristic
117C2×C3×C4×D3—42no—
118C2×C3×C4×D3C2312yes—
119C2×C3×C4×D3C2312yes—
120C2×C3×Dic6C2312yes—
121C2×C3×Dic6C2312yes—
122C2×#626C2314yes—
123C2×#626C2314yes—
124C2×#624—44no—
125C2×#624C2314yes—
126C2×#624C2314yes—
127#3799—44no—
128C32×C22⋊C4C2314yes—
129#3752C2314yes—
130#3752C2314yes—
131C4⋊(C3⋊Dic3)C2312yes—
132C4⋊(C3⋊Dic3)C2312yes—
133C3×#217C2314yes—
134C3×#217C2314yes—
135C3×(C2×D3)⋊C4C2314yes—
136C3×C4⋊Dic3C2312yes—
137C3×C4⋊Dic3C2312yes—
138C3×Dic3⋊C4C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×C4×Dic3C2312yes—
142C3×C4×Dic3C2312yes—
143#3724C2314yes—
144#3724C2314yes—
145Dic3⋊Dic3C2314yes—
146Dic3⋊Dic3C2314yes—
147#3722C2314yes—
148#3722C2314yes—
149#3722C2314yes—
150#3722C2314yes—
151(C2×D3)⋊Dic3C2314yes—
152(C2×D3)⋊Dic3C2314yes—
153Dic32C2314yes—
154Dic32C2314yes—
155#3459—91noSylow
156C22×C3×D4—31no—
157C23×C3×C4—31no—
158C23×C3×C4—31no—
159C22×#67—32no—
160C22×#67—32no—
161C22×#67—62no—
162C22×#67C2×D311yescharacteristic
163C23×Dic3C2×D311yescharacteristic
164C2×#239—32no—
165C2×#235—32no—
166C22×C4×D3—32no—
167C22×C4×D3—32no—
168C22×C4×D3C2×D311yescharacteristic, complemented
169C3×C22⋊Q8—32no—
170C3×C22⋊Q8—32no—
171C3×C22⋊Q8—34no—
172C3×C22⋊Q8—34no—
173C3×C4×D4—34no—
174C3×C4×D4—34no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C22⋊C4—21no—
177C2×C3×C22⋊C4—32no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4C2×D311yescharacteristic
180C2×C3×C22⋊C4C2×D311yescharacteristic
181C2×C3×C42—31no—
182#953—34no—
183C2×#217C2×D312yes—
184#947—34no—
185#947—32no—
186#946—32no—
187#946—34no—
188Q8×Dic3—32no—
189#939—34no—
190#939—34no—
191#937—34no—
192#935—34no—
193#930—32no—
194#930—32no—
195#930—32no—
196#930—32no—
197#930—34no—
198#930—34no—
199#930—32no—
200#930—62no—
201#930—62no—
202#929—34no—
203#929—34no—
204C4×#67—34no—
205C4×#67—34no—
206C4×#67—34no—
207C4×#67—34no—
208C4×#67—34no—
209C2×(C2×D3)⋊C4—32no—
210C2×(C2×D3)⋊C4—32no—
211C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
212#926—32no—
213#924—32no—
214#924C2×D312yescomplemented
215#924C2×D312yescomplemented
216C2×Dic3⋊C4—32no—
217C2×Dic3⋊C4—32no—
218C2×Dic3⋊C4C2×D311yescharacteristic, complemented
219C2×C4×Dic3—32no—
220C2×C4×Dic3—32no—
221C2×C4×Dic3C2×D311yescharacteristic, complemented
222#898—34no—
223#898—34no—
224#898—34no—
225#898—34no—
226#896—34no—
227#895—32no—
228#895—34no—
229#894—34no—
230#894—34no—
231#894—34no—
232#894—34no—
233#893—34no—
234#893—32no—
235#892—32no—
236#892—34no—
237#890—34no—
238#890—32no—
239#889—34no—
240#886—34no—
241#886—34no—
242#886—34no—
243#886—34no—
244#886—64no—
245#885—34no—
246#884—34no—
247#883—34no—
248#882—34no—
249#882—34no—
250#882—34no—
251#882—34no—
252#882—64no—
253#67⋊C4—34no—
254#67⋊C4—34no—
255#67⋊C4—34no—
256#67⋊C4—34no—
257#67⋊C4C2×D314yescomplemented
258#67⋊C4C2×D314yescomplemented
259#879—34no—
260#878C2×D314yescomplemented
261#878C2×D314yescomplemented
262#876—34no—
263#875—32no—
264C4×D12—32no—
265#872—34no—
266#870—32no—
267C4×Dic6—32no—
268C23×C32—41no—
269C23×C32—41no—
270C23×C32#4114yescomplemented
271C23×C32C2411yescharacteristic
272C23×C32C2412yes—
273C22×C3⋊D3—24no—
274C22×C3⋊D3—42no—
275C22×C3⋊D3—42no—
276C22×C3⋊D3C2414yes—
277C22×C3×D3—22no—
278C22×C3×D3—41no—
279C22×C3×D3—41no—
280C22×C3×D3C2412yes—
281C2×C32×C4—41no—
282C2×C32×C4—41no—
283C2×C32×C4C2412yes—
284C2×C32×C4C2412yes—
285#638—28no—
286#638—28no—
287C2×C3⋊Dic3—24no—
288C2×C3⋊Dic3C2414yes—
289C4⋊(C3⋊D3)—42no—
290C4⋊(C3⋊D3)—42no—
291C3×#67—28no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—24no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—42no—
296C2×C3×Dic3—41no—
297C2×C3×Dic3—42no—
298C2×C3×Dic3—42no—
299C2×C3×Dic3C2414yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2414yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2411yescharacteristic
304C2×C3×Dic3C2411yescharacteristic
305C3×C4×D3—24no—
306C3×C4×D3—42no—
307C3×Dic6—42no—
308C3×Dic6—42no—
309#626—44no—
310#626—44no—
311#624—28no—
312#624—44no—
313#543—31no—
314#539—92no—
315#539—94no—
316#538—92no—
317#538—94no—
318#534—92no—
319#534—91no—
320#529—92no—
321#529—94no—
322#525—94no—
323#525—92no—
324C2×C4×D4—31no—
325C2×C4×D4—92no—
326C24×C3—21no—
327C24×C3—31no—
328C24×C3C22×D311yescharacteristic
329C24×C3C22×D311yescharacteristic
330C23×D3—32no—
331C23×D3—32no—
332C23×D3—62no—
333C23×D3C22×D311yescharacteristic
334C2×C3×Q8—32no—
335C2×C3×Q8—32no—
336C2×C3×D4—34no—
337C2×C3×D4—64no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—32no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—32no—
344C22×C3×C4—32no—
345C22×C3×C4—32no—
346C22×C3×C4—31no—
347C22×C3×C4—32no—
348C22×C3×C4—32no—
349C22×C3×C4—122no—
350C22×C3×C4—122no—
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C2×#67—24no—
356C2×#67—34no—
357C2×#67—34no—
358C2×#67—34no—
359C2×#67—34no—
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—64no—
363C2×#67—64no—
364C2×#67—68no—
365C2×#67—68no—
366C2×#67—128no—
367C2×#67C22×D314yes—
368C22×Dic3—32no—
369C22×Dic3—32no—
370C22×Dic3—42no—
371C22×Dic3—62no—
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D312yes—
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D312yes—
376C22×Dic3C22×D312yes—
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D312yes—
379#239—124no—
380#235—124no—
381C2×D12—34no—
382C2×D12—34no—
383C2×D12—32no—
384C2×D12—32no—
385C2×D12—32no—
386C2×D12—32no—
387C2×D12—62no—
388C2×D12—62no—
389C2×C4×D3—34no—
390C2×C4×D3—34no—
391C2×C4×D3—34no—
392C2×C4×D3—34no—
393C2×C4×D3—42no—
394C2×C4×D3—124no—
395C2×C4×D3—124no—
396C2×C4×D3C22×D312yes—
397C2×C4×D3C22×D312yes—
398C2×Dic6C22×D312yes—
399C2×Dic6C22×D312yes—
400C3×C4⋊C4—34no—
401C3×C4⋊C4—34no—
402C3×C4⋊C4—32no—
403C3×C4⋊C4—34no—
404C3×C4⋊C4—32no—
405C3×C22⋊C4—24no—
406C3×C22⋊C4—34no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4C22×D314yes—
410C3×C22⋊C4C22×D314yes—
411C3×C42—32no—
412C3×C42—32no—
413#217—34no—
414#217—34no—
415#217C22×D314yes—
416#217C22×D314yes—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—34no—
419(C2×D3)⋊C4—34no—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4—34no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—34no—
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—64no—
432(C2×D3)⋊C4—64no—
433(C2×D3)⋊C4C22×D314yes—
434C4⋊Dic3—32no—
435C4⋊Dic3—32no—
436C4⋊Dic3—32no—
437C4⋊Dic3—32no—
438C4⋊Dic3—34no—
439C4⋊Dic3—34no—
440C4⋊Dic3—62no—
441C4⋊Dic3—62no—
442C4⋊Dic3C22×D312yes—
443C4⋊Dic3C22×D312yes—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4C22×D314yes—
451Dic3⋊C4C22×D314yes—
452Dic3⋊C4C22×D314yes—
453C4×Dic3—34no—
454C4×Dic3—34no—
455C4×Dic3—34no—
456C4×Dic3—34no—
457C4×Dic3C22×D312yes—
458C4×Dic3C22×D312yes—
459C22×C32—22no—
460C22×C32—21no—
461C22×C32—22no—
462C22×C32—21no—
463C22×C32—44no—
464C22×C32C2×#4112yes—
465C22×C32C2×#4114yes—
466C22×C32C2511yescharacteristic
467C2×C3⋊D3—24no—
468C2×C3⋊D3—24no—
469C2×C3⋊D3—24no—
470C2×C3⋊D3—48no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—44no—
475C32×C4—22no—
476C32×C4—22no—
477C3⋊Dic3—24no—
478C3×Dic3—22no—
479C3×Dic3—24no—
480C3×Dic3—22no—
481C3×Dic3—21no—
482C3×Dic3—24no—
483C3×Dic3H(5,𝔽2)12yes—
484C2×#41—92no—
485C22×D4—31no—
486C22×D4—92no—
487C23×C4—31no—
488C23×C4—31no—
489C23×C4—92no—
490#126—94no—
491#126—94no—
492#126—94no—
493#125—92no—
494#125—94no—
495#124—92no—
496#124—94no—
497#123—94no—
498#123—94no—
499#123—94no—
500#123—94no—
501#123—94no—
502#123—94no—
503C22⋊Q8—32no—
504C22⋊Q8—32no—
505C22⋊Q8—34no—
506C22⋊Q8—34no—
507C22⋊Q8—94no—
508C22⋊Q8—92no—
509#121—94no—
510#121—92no—
511#121—94no—
512#121—94no—
513#121—92no—
514#121—92no—
515#120—94no—
516#120—94no—
517#120—94no—
518C4×Q8—92no—
519C4×D4—34no—
520C4×D4—34no—
521C4×D4—92no—
522C4×D4—94no—
523C4×D4—94no—
524C4×D4—94no—
525C4×D4—94no—
526C4×D4—94no—
527#117—94no—
528#117—92no—
529C2×C4⋊C4—31no—
530C2×C4⋊C4—92no—
531C2×C22⋊C4—32no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—92no—
534C2×C22⋊C4D3211yescharacteristic
535C2×C42—31no—
536C2×C42—92no—
537C23×C3—22no—
538C23×C3—21no—
539C23×C3—24no—
540C23×C3—32no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—62no—
546C23×C3—81no—
547C23×C3—81no—
548C23×C3—121no—
549C23×C3—121no—
550C23×C3#23514yescomplemented
551C23×C3#23914yescomplemented
552C23×C3C23×D311yescharacteristic
553C23×C3C23×D312yes—
554C23×C3C23×D311yescharacteristic
555C23×C3C23×D312yes—
556C22×D3—22no—
557C22×D3—34no—
558C22×D3—34no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3—64no—
562C22×D3—64no—
563C22×D3—64no—
564C22×D3—124no—
565C22×D3—122no—
566C22×D3—122no—
567C22×D3—122no—
568C22×D3—122no—
569C22×D3—242no—
570C22×D3—242no—
571C22×D3C23×D312yes—
572C3×Q8—122no—
573C3×Q8—122no—
574C3×D4—68no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—31no—
578C2×C3×C4—32no—
579C2×C3×C4—34no—
580C2×C3×C4—32no—
581C2×C3×C4—31no—
582C2×C3×C4—34no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—64no—
588C2×C3×C4—64no—
589C2×C3×C4—62no—
590C2×C3×C4—62no—
591C2×C3×C4—81no—
592C2×C3×C4—81no—
593C2×C3×C4—122no—
594C2×C3×C4—122no—
595C2×C3×C4—122no—
596C2×C3×C4—121no—
597C2×C3×C4—122no—
598C2×C3×C4C23×D312yes—
599C2×C3×C4C23×D312yes—
600C2×C3×C4C23×D312yes—
601C2×C3×C4C23×D312yes—
602#67—28no—
603#67—68no—
604#67—68no—
605#67—68no—
606#67—68no—
607#67—128no—
608#67—128no—
609#67—124no—
610#67—124no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—24no—
614C2×Dic3—34no—
615C2×Dic3—34no—
616C2×Dic3—42no—
617C2×Dic3—42no—
618C2×Dic3—41no—
619C2×Dic3—42no—
620C2×Dic3—64no—
621C2×Dic3—64no—
622C2×Dic3—64no—
623C2×Dic3—124no—
624C2×Dic3C23×D312yes—
625C2×Dic3C23×D314yes—
626C2×Dic3C23×D311yescharacteristic
627C2×Dic3C23×D312yes—
628C2×Dic3C23×D314yes—
629C2×Dic3C23×D311yescharacteristic
630D12—122no—
631D12—122no—
632D12—122no—
633D12—122no—
634D12—124no—
635D12—124no—
636D12—242no—
637D12—242no—
638C4×D3—24no—
639C4×D3—42no—
640C4×D3—68no—
641C4×D3—68no—
642C4×D3—124no—
643C4×D3—124no—
644Dic6—42no—
645Dic6—42no—
646C2×C32—22no—
647C2×C32—24no—
648C2×C32C22×#4111yescharacteristic
649C2×C32C2×H(5,𝔽2)11yescharacteristic
650C2×C32#58511yescharacteristic
651C3⋊D3—44no—
652C3×D3—42no—
653C24—31no—
654C24—92no—
655C24C2×D3211yescharacteristic
656#41—364no—
657C2×Q8—32no—
658C2×Q8—32no—
659C2×D4—34no—
660C2×D4—64no—
661C2×D4—94no—
662C2×D4—94no—
663C2×D4—94no—
664C2×D4—94no—
665C2×D4—92no—
666C2×D4—92no—
667C2×D4—188no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—32no—
671C22×C4—32no—
672C22×C4—31no—
673C22×C4—32no—
674C22×C4—32no—
675C22×C4—32no—
676C22×C4—32no—
677C22×C4—94no—
678C22×C4—94no—
679C22×C4—92no—
680C22×C4—122no—
681C22×C4—122no—
682C22×C4—364no—
683C22×C4C2×D3211yescharacteristic
684C22×C4C2×D3211yescharacteristic
685C4⋊C4—34no—
686C4⋊C4—34no—
687C4⋊C4—32no—
688C4⋊C4—34no—
689C4⋊C4—32no—
690C4⋊C4—94no—
691C4⋊C4—94no—
692C4⋊C4—94no—
693C4⋊C4—94no—
694C4⋊C4—92no—
695C4⋊C4—92no—
696C22⋊C4—34no—
697C22⋊C4—34no—
698C22⋊C4—34no—
699C22⋊C4—94no—
700C22⋊C4—94no—
701C22⋊C4—94no—
702C22⋊C4—94no—
703C22⋊C4—94no—
704C22⋊C4—94no—
705C22⋊C4—94no—
706C22⋊C4—94no—
707C22⋊C4C2×D3214yes—
708C42—32no—
709C42—32no—
710C42—94no—
711C42—94no—
712C22×C3—21no—
713C22×C3—22no—
714C22×C3—21no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—21no—
718C22×C3—22no—
719C22×C3—21no—
720C22×C3—24no—
721C22×C3—22no—
722C22×C3—21no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—42no—
726C22×C3—42no—
727C22×C3—44no—
728C22×C3—44no—
729C22×C3—62no—
730C22×C3—62no—
731C22×C3—62no—
732C22×C3—84no—
733C22×C3—124no—
734C22×C3C2×#23512yes—
735C22×C3C2×#23514yes—
736C22×C3C2×#23914yes—
737C22×C3C2×#23912yes—
738C22×C3C24×D311yescharacteristic
739C22×C3C24×D311yescharacteristic
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—44no—
744C2×D3—64no—
745C2×D3—64no—
746C2×D3—64no—
747C2×D3—64no—
748C2×D3—64no—
749C2×D3—64no—
750C2×D3—124no—
751C2×D3—124no—
752C2×D3—124no—
753C2×D3—128no—
754C2×D3—128no—
755C2×D3—248no—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—32no—
761C3×C4—42no—
762C3×C4—42no—
763C3×C4—64no—
764C3×C4—62no—
765C3×C4—64no—
766C3×C4—62no—
767C3×C4—61no—
768Dic3—22no—
769Dic3—21no—
770Dic3—22no—
771Dic3—24no—
772Dic3—24no—
773Dic3—64no—
774Dic3—64no—
775Dic3—124no—
776Dic3#100412yes—
777C32#345911yescharacteristic, complemented, Sylow
778C23—32no—
779C23—41no—
780C23—41no—
781C23—62no—
782C23—94no—
783C23—121no—
784C23—121no—
785C23—184no—
786C23—362no—
787C23—362no—
788C23#379914yescomplemented
789C23C22×D3211yescharacteristic
790C23C22×D3212yes—
791Q8—122no—
792Q8—122no—
793D4—68no—
794D4—188no—
795D4—188no—
796D4—362no—
797D4—362no—
798D4—364no—
799D4—364no—
800C2×C4—31no—
801C2×C4—32no—
802C2×C4—31no—
803C2×C4—34no—
804C2×C4—32no—
805C2×C4—34no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—64no—
809C2×C4—62no—
810C2×C4—64no—
811C2×C4—62no—
812C2×C4—94no—
813C2×C4—122no—
814C2×C4—122no—
815C2×C4—121no—
816C2×C4—122no—
817C2×C4—122no—
818C2×C4—188no—
819C2×C4—184no—
820C2×C4—364no—
821C2×C4C22×D3212yes—
822C2×C4C22×D3212yes—
823C2×C3—22no—
824C2×C3—24no—
825C2×C3—24no—
826C2×C3—22no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—44no—
831C2×C3—42no—
832C2×C3—122no—
833C2×C3C22×#23511yescharacteristic
834C2×C3C2×#100411yescharacteristic
835C2×C3C22×#23911yescharacteristic
836C2×C3#596411yescharacteristic
837C2×C3D3×H(5,𝔽2)11yescharacteristic
838C2×C3#596611yescharacteristic
839D3—42no—
840D3—124no—
841D3—124no—
842D3—244no—
843C22—21no—
844C22—22no—
845C22—21no—
846C22—22no—
847C22—44no—
848C22—62no—
849C22—62no—
850C22—62no—
851C22—124no—
852C22—184no—
853C22—184no—
854C22—184no—
855C22—368no—
856C22C2×#379912yes—
857C22C2×#379914yes—
858C22C23×D3211yescharacteristic
859C4—22no—
860C4—22no—
861C4—32no—
862C4—62no—
863C4—61no—
864C4—62no—
865C4—64no—
866C4—64no—
867C4—184no—
868C3—21no—
869C3#8577611yescharacteristic, complemented
870C3#8657211yescharacteristic, complemented
871C2—22no—
872C2—24no—
873C2—122no—
874C2—364no—
875C2C22×#379911yescharacteristic
876C2D3×#100411yescharacteristic
877C2#1059667811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3459
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595964C2semidirect
2. C2×C3×#67⋊C4C2semidirect
3. C3×#5483C2semidirect
4. #10595519C2semidirect
5. C2×#63952C2semidirect
6. #10595038C2semidirect
7. #10595005C2semidirect
8. #10594980C2semidirect
9. #10594955C2semidirect
10. #10594243C2semidirect
11. #10594241C2semidirect
12. #10594216C2semidirect
13. #10594066C2semidirect
19. C22×C3×C4×D3C22semidirect
20. C22×#624C22semidirect
21. C2×#3799C22semidirect
25. #64095C22semidirect
26. #64091C22semidirect
28. C2×C3×(C2×D3)⋊C4C22semidirect
29. C3×#924C22semidirect
30. C3×#924C22semidirect
31. C2×C3×Dic3⋊C4C22semidirect
32. C2×C3×C4×Dic3C22semidirect
33. C3×#67⋊C4C22semidirect
34. C3×#67⋊C4C22semidirect
35. C3×#878C22semidirect
36. C3×#878C22semidirect
37. #63981C22semidirect
40. #63977C22semidirect
41. C2×#3724C22semidirect
42. #63966C22semidirect
43. C2×#3722C22semidirect
44. #63962C22semidirect
45. C2×Dic32C22semidirect
46. #63952C22semidirect
47. #63952C22semidirect
48. #63952C22semidirect
49. #63952C22semidirect
50. #63910C22semidirect
51. #63909C22semidirect
52. #63907C22semidirect
53. #63904C22semidirect
54. #63897C22semidirect
55. #63894C22semidirect
56. #63888C22semidirect
57. #63869C22semidirect
58. #63868C22semidirect
59. #63864C22semidirect
60. #63861C22semidirect
61. #63856C22semidirect
62. #63854C22semidirect
63. #63850C22semidirect
64. #63848C22semidirect
65. #63845C22semidirect
66. Dic3×Dic6C22semidirect
67. #63841C22semidirect
68. #63836C22semidirect
93. C2×#67⋊C4D3semidirect
94. #5483D3semidirect
168. C22×C4×D3C2×D3semidirect
211. C2×(C2×D3)⋊C4C2×D3semidirect
214. #924C2×D3semidirect
215. #924C2×D3semidirect
218. C2×Dic3⋊C4C2×D3semidirect
221. C2×C4×Dic3C2×D3semidirect
257. #67⋊C4C2×D3semidirect
258. #67⋊C4C2×D3semidirect
260. #878C2×D3semidirect
261. #878C2×D3semidirect
270. C23×C32#41semidirect
550. C23×C3#235semidirect
551. C23×C3#239semidirect
777. C32#3459semidirect
788. C23#3799semidirect
869. C3#85776semidirect
870. C3#86572semidirect

Maximal subgroups

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

subgroupindex
#105959642
C2×C3×#67⋊C42
C3×#54832
#105955192
C2×#639522
#105950382
#105950052
#105949802
#105949552
#105942432
#105942412
#105942162
#105940662
#865723
#857763