Finite Group Databasebeta

← #11909817

Subgroups — #11909817

Order 1152.

2363 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic, complemented
2C3×#5479C211yesmaximal, characteristic, complemented
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4#10594955C212yesmaximal, complemented
5#10594917C214yesmaximal, complemented
6#10594910C212yesmaximal, complemented
7#10594906C212yesmaximal, complemented
8#10594902C212yesmaximal, complemented
9#10593963C211yesmaximal, characteristic, complemented
10#10593960C211yesmaximal, characteristic, complemented
11#10593939C212yesmaximal, complemented
12#10593938C212yesmaximal, complemented
13#10593936C214yesmaximal, complemented
14#10593902C211yesmaximal, characteristic, complemented
15#10593890C212yesmaximal, complemented
16#10593878C212yesmaximal, complemented
17Dic62C211yesmaximal, characteristic, complemented
18#86128—31nomaximal
19#85821—31nomaximal
20C2×#3828C2212yes—
21C22×C3×Dic6C2211yescharacteristic
22C2×#3804C2214yes—
23C2×#3799C2212yes—
24C2×C32×C42C2211yescharacteristic
25#64139C2212yes—
26#64139C2212yes—
27#64084C2212yes—
28#64083C2211yescharacteristic
29C4×C4⋊(C3⋊D3)C2212yes—
30C4×C4⋊(C3⋊D3)C2212yes—
31#64078C2211yescharacteristic
32C3×#930C2211yescharacteristic
33C3×#929C2212yes—
34C3×C4×#67C2212yes—
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C3×#924C2211yescharacteristic
37C2×C3×Dic3⋊C4C2212yes—
38C2×C3×C4×Dic3C2212yes—
39C3×#876C2212yes—
40C3×#875C2211yescharacteristic
41C3×C4×D12C2211yescharacteristic
42C3×#872C2212yes—
43C3×#870C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46C3×C4×Dic6C2211yescharacteristic
47C3×C4×Dic6C2211yescharacteristic
48C3×C4×Dic6C2212yes—
49C3×C4×Dic6C2212yes—
50C3×C4×Dic6C2211yescharacteristic
51#63978C2214yes—
52#63966C2214yes—
53#63952C2214yes—
54#63918C2212yes—
55#63918C2212yes—
56#63911C2212yes—
57#63910C2214yes—
58#63909C2212yes—
59#63907C2214yes—
60#63897C2214yes—
61#63896C2214yes—
62#63895C2214yes—
63#63894C2212yes—
64#63894C2212yes—
65#63894C2212yes—
66Dic3×D12C2212yes—
67#63890C2214yes—
68D3×C4⋊Dic3C2212yes—
69#63888C2214yes—
70#63883C2214yes—
71#63881C2214yes—
72#63880C2214yes—
73#63869C2212yes—
74#63868C2214yes—
75#63865C2214yes—
76#63864C2212yes—
77#63864C2212yes—
78#63856C2212yes—
79#63853C2214yes—
80#63852C2214yes—
81Dic3×Dic6C2212yes—
82Dic3×Dic6C2212yes—
83#63840C2214yes—
84#63836C2214yes—
85C3×#529—31no—
86C2×C3×C4×Q8—31no—
87#5817—32no—
88#5710—34no—
89#5690—32no—
90#5681—32no—
91#5655—34no—
92#5624—32no—
93#5596—32no—
94#5585—32no—
95#5585—31no—
96#5585—31no—
97#5582—34no—
98#5582—32no—
99#5579—31no—
100#5579—32no—
101#5577—31no—
102#5574—32no—
103Q8×Dic6—31no—
104Q8×Dic6—31no—
105#5555—32no—
106#5553—31no—
107#5552—32no—
108#5543—31no—
109#5534—32no—
110#5523—32no—
111#5507—34no—
112#5507—32no—
113#5479—32no—
114#5479D311yescharacteristic, complemented
115#5477—31no—
116#5477—31no—
117#5477—32no—
118#5477—61no—
119C2×C4×Dic6D311yescharacteristic, complemented
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2311yescharacteristic
122C22×C32×C4C2311yescharacteristic
123C2×#638C2314yes—
124#3828—44no—
125C2×C4⋊(C3⋊D3)C2312yes—
126C2×C4⋊(C3⋊D3)C2312yes—
127C2×C4⋊(C3⋊D3)C2312yes—
128C2×C4×C3⋊D3C2314yes—
129C2×#634C2312yes—
130C2×C3×#67C2312yes—
131C22×C3×Dic3C2312yes—
132C22×C3×Dic3C2312yes—
133C2×C3×D12C2311yescharacteristic
134C2×C3×C4×D3C2312yes—
135C2×C3×Dic6—24no—
136C2×C3×Dic6C2311yescharacteristic
137C2×C3×Dic6C2311yescharacteristic
138C2×C3×Dic6C2312yes—
139C2×C3×Dic6C2311yescharacteristic
140C2×#627C2314yes—
141C2×#626C2314yes—
142C2×#626C2314yes—
143C2×#624C2314yes—
144C2×#624C2314yes—
145#3804—48no—
146C2×D3×Dic3C2314yes—
147#3799—28no—
148C32×C42C2311yescharacteristic
149C32×C42C2311yescharacteristic
150C32×C42C2311yescharacteristic
151C32×C42C2311yescharacteristic
152#3752C2314yes—
153#3752C2314yes—
154C4⋊(C3⋊Dic3)C2312yes—
155C4⋊(C3⋊Dic3)C2312yes—
156C3×#217C2312yes—
157C3×(C2×D3)⋊C4C2312yes—
158C3×(C2×D3)⋊C4C2312yes—
159C3×(C2×D3)⋊C4C2312yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4⋊Dic3C2311yescharacteristic
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2311yescharacteristic
165C3×C4⋊Dic3C2311yescharacteristic
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2312yes—
169C3×Dic3⋊C4C2312yes—
170C3×Dic3⋊C4C2312yes—
171C3×Dic3⋊C4C2312yes—
172C3×Dic3⋊C4C2312yes—
173C3×Dic3⋊C4C2312yes—
174C3×C4×Dic3C2312yes—
175C3×C4×Dic3C2312yes—
176C3×C4×Dic3C2312yes—
177C3×C4×Dic3C2312yes—
178C3×C4×Dic3C2312yes—
179#3724C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2314yes—
183#3722C2314yes—
184#3722C2314yes—
185#3722C2314yes—
186#3722C2314yes—
187(C2×D3)⋊Dic3C2314yes—
188Dic32C2314yes—
189#3522—91noSylow
190C22×C3×Q8—31no—
191C2×#239—32no—
192C2×#237—34no—
193C2×#235—32no—
194C2×#235—32no—
195C2×#235—34no—
196C2×#235—32no—
197C2×#235—62no—
198C22×Dic6C2×D311yescharacteristic
199C3×#126—32no—
200C3×#125—31no—
201C3×#124—31no—
202C3×#123—32no—
203C3×C22⋊Q8—31no—
204C3×#121—31no—
205C3×C4×Q8—31no—
206C3×C4×Q8—31no—
207C3×C4×Q8—31no—
208C3×C4×Q8—32no—
209C3×C4×Q8—31no—
210C3×C4×Q8—32no—
211C3×C4×Q8—31no—
212C3×C4×D4—32no—
213C3×C4×D4—31no—
214C3×#117—32no—
215C2×C3×C4⋊C4—32no—
216C2×C3×C4⋊C4—31no—
217C2×C3×C42—21no—
218C2×C3×C42—32no—
219C2×C3×C42C2×D311yescharacteristic
220C2×C3×C42C2×D311yescharacteristic
221#947—34no—
222#947—32no—
223#947—32no—
224#946—32no—
225#946—34no—
226Q8×Dic3—32no—
227Q8×Dic3—32no—
228#940—32no—
229#939—34no—
230D4×Dic3—32no—
231#930—32no—
232#930—32no—
233#930—32no—
234#930—32no—
235#930—34no—
236#930—32no—
237#930—62no—
238#930—62no—
239#930C2×D311yescharacteristic
240#929—34no—
241#929C2×D312yes—
242C4×#67—34no—
243C4×#67C2×D312yes—
244C2×C4⋊Dic3—32no—
245C2×C4⋊Dic3C2×D311yescharacteristic
246#924—32no—
247#924C2×D311yescharacteristic
248C2×Dic3⋊C4C2×D312yes—
249C2×C4×Dic3C2×D312yes—
250#898—34no—
251#897—34no—
252#896—34no—
253#896—34no—
254#896—34no—
255#896—34no—
256#896—34no—
257#895—32no—
258#895—34no—
259#894—34no—
260#894—34no—
261#894—34no—
262#894—34no—
263#893—34no—
264#893—32no—
265#893—32no—
266#893—32no—
267#892—34no—
268D3×C4⋊C4—32no—
269D3×C4⋊C4—34no—
270D3×C4⋊C4—34no—
271#890—32no—
272#888—34no—
273#888—34no—
274#888—32no—
275#888—32no—
276#886—34no—
277#886—34no—
278#885—34no—
279#885—34no—
280#884—34no—
281#883—34no—
282#67⋊C4—34no—
283#67⋊C4—34no—
284#67⋊C4—34no—
285#878—34no—
286#876—34no—
287#876C2×D312yes—
288#875—32no—
289#875—32no—
290#875—32no—
291#875—32no—
292#875—34no—
293#875—62no—
294#875C2×D311yescharacteristic
295#874—32no—
296#874—31no—
297#874—31no—
298#874—61no—
299C4×D12—32no—
300C4×D12—32no—
301C4×D12—32no—
302C4×D12—32no—
303C4×D12—32no—
304C4×D12—34no—
305C4×D12—32no—
306C4×D12—32no—
307C4×D12—32no—
308C4×D12—62no—
309C4×D12—62no—
310C4×D12C2×D311yescharacteristic
311#872—34no—
312#872C2×D312yes—
313#870—32no—
314#870C2×D311yescharacteristic
315#869—31no—
316#869—31no—
317#869—32no—
318#869—32no—
319#869—61no—
320C4×Dic6—32no—
321C4×Dic6—32no—
322C4×Dic6C2×D312yes—
323C4×Dic6C2×D312yes—
324C4×Dic6C2×D311yescharacteristic
325C4×Dic6C2×D311yescharacteristic
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D311yescharacteristic
328C4×Dic6C2×D311yescharacteristic
329C23×C32C2411yescharacteristic
330C22×C3⋊D3C2414yes—
331C22×C3×D3C2412yes—
332C2×C32×C4—22no—
333C2×C32×C4—22no—
334C2×C32×C4—22no—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2411yescharacteristic
341#638—28no—
342C2×C3⋊Dic3C2414yes—
343C4⋊(C3⋊D3)—24no—
344C4⋊(C3⋊D3)—24no—
345C4⋊(C3⋊D3)—42no—
346C4×C3⋊D3—44no—
347#634—42no—
348C3×#67—24no—
349C2×C3×Dic3—24no—
350C2×C3×Dic3—24no—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2412yes—
356C2×C3×Dic3C2412yes—
357C2×C3×Dic3C2412yes—
358C3×D12—22no—
359C3×C4×D3—24no—
360C3×Dic6—22no—
361C3×Dic6—22no—
362C3×Dic6—24no—
363C3×Dic6#4114yescomplemented
364#627—44no—
365#626—28no—
366#626—44no—
367#624—28no—
368#624—44no—
369D3×Dic3—44no—
370#559—91no—
371#559—92no—
372Q82—91no—
373#554—91no—
374#554—92no—
375#550—91no—
376#548—92no—
377#547—92no—
378#547—94no—
379#542—92no—
380#542—94no—
381#532—92no—
382#532—91no—
383#529—31no—
384#529—92no—
385#520—92no—
386C2×C4×Q8—31no—
387C2×C3×Q8—31no—
388C2×C3×Q8—31no—
389C2×C3×Q8—32no—
390C2×C3×Q8—31no—
391C2×C3×Q8—64no—
392C2×C3×D4—32no—
393C2×C3×D4—31no—
394C22×C3×C4—21no—
395C22×C3×C4—21no—
396C22×C3×C4—21no—
397C22×C3×C4—32no—
398C22×C3×C4—32no—
399C22×C3×C4—32no—
400C22×C3×C4C22×D311yescharacteristic
401C22×C3×C4C22×D311yescharacteristic
402C22×C3×C4C22×D311yescharacteristic
403C22×C3×C4C22×D311yescharacteristic
404C22×C3×C4C22×D311yescharacteristic
405C22×C3×C4C22×D311yescharacteristic
406C2×#67—34no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—64no—
411C2×#67C22×D312yes—
412C22×Dic3—34no—
413C22×Dic3C22×D312yes—
414C22×Dic3C22×D312yes—
415#239—68no—
416#237—128no—
417#235—68no—
418#235—128no—
419#235—124no—
420#235—124no—
421#235—128no—
422C2×D12—34no—
423C2×D12—32no—
424C2×D12—32no—
425C2×D12—32no—
426C2×D12—32no—
427C2×D12—34no—
428C2×D12—32no—
429C2×D12—32no—
430C2×D12—62no—
431C2×D12—62no—
432C2×D12—62no—
433C2×D12C22×D311yescharacteristic
434C2×C4×D3—34no—
435C2×C4×D3—34no—
436C2×C4×D3—34no—
437C2×C4×D3—34no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—64no—
442C2×C4×D3C22×D312yes—
443C2×Dic6—24no—
444C2×Dic6—32no—
445C2×Dic6—32no—
446C2×Dic6—34no—
447C2×Dic6—34no—
448C2×Dic6—62no—
449C2×Dic6C22×D311yescharacteristic
450C2×Dic6C22×D311yescharacteristic
451C2×Dic6C22×D312yes—
452C2×Dic6C22×D311yescharacteristic
453C3×C4⋊C4—31no—
454C3×C4⋊C4—32no—
455C3×C4⋊C4—32no—
456C3×C4⋊C4—31no—
457C3×C4⋊C4—31no—
458C3×C4⋊C4—32no—
459C3×C4⋊C4—31no—
460C3×C4⋊C4—32no—
461C3×C4⋊C4—32no—
462C3×C4⋊C4—32no—
463C3×C4⋊C4—32no—
464C3×C4⋊C4—32no—
465C3×C4⋊C4—32no—
466C3×C22⋊C4—32no—
467C3×C22⋊C4—32no—
468C3×C22⋊C4—32no—
469C3×C22⋊C4—32no—
470C3×C22⋊C4—32no—
471C3×C42—21no—
472C3×C42—21no—
473C3×C42—21no—
474C3×C42—21no—
475C3×C42—32no—
476C3×C42—32no—
477C3×C42—32no—
478C3×C42—32no—
479C3×C42—32no—
480C3×C42C22×D311yescharacteristic
481C3×C42C22×D311yescharacteristic
482C3×C42C22×D311yescharacteristic
483C3×C42C22×D311yescharacteristic
484C3×C42C22×D311yescharacteristic
485C3×C42C22×D311yescharacteristic
486C3×C42C22×D311yescharacteristic
487C3×C42C22×D311yescharacteristic
488#217—34no—
489#217C22×D312yes—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4—34no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—34no—
498(C2×D3)⋊C4—34no—
499(C2×D3)⋊C4—34no—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—64no—
504(C2×D3)⋊C4—64no—
505(C2×D3)⋊C4C22×D312yes—
506(C2×D3)⋊C4C22×D312yes—
507(C2×D3)⋊C4C22×D312yes—
508(C2×D3)⋊C4C22×D312yes—
509C4⋊Dic3—32no—
510C4⋊Dic3—32no—
511C4⋊Dic3—32no—
512C4⋊Dic3—32no—
513C4⋊Dic3—34no—
514C4⋊Dic3—34no—
515C4⋊Dic3—34no—
516C4⋊Dic3—62no—
517C4⋊Dic3—62no—
518C4⋊Dic3C22×D311yescharacteristic
519C4⋊Dic3C22×D311yescharacteristic
520C4⋊Dic3C22×D312yes—
521C4⋊Dic3C22×D311yescharacteristic
522C4⋊Dic3C22×D311yescharacteristic
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—34no—
526Dic3⋊C4—34no—
527Dic3⋊C4—34no—
528Dic3⋊C4C22×D312yes—
529Dic3⋊C4C22×D312yes—
530Dic3⋊C4C22×D312yes—
531Dic3⋊C4C22×D312yes—
532Dic3⋊C4C22×D312yes—
533Dic3⋊C4C22×D312yes—
534Dic3⋊C4C22×D312yes—
535Dic3⋊C4C22×D312yes—
536C4×Dic3—34no—
537C4×Dic3—34no—
538C4×Dic3C22×D312yes—
539C4×Dic3C22×D312yes—
540C4×Dic3C22×D312yes—
541C4×Dic3C22×D312yes—
542C4×Dic3C22×D312yes—
543C22×C32—21no—
544C22×C32—21no—
545C22×C32H(5,𝔽2)12yes—
546C22×C32C2511yescharacteristic
547C2×C3⋊D3—24no—
548C2×C3⋊D3—24no—
549C2×C3⋊D3—24no—
550C2×C3×D3—22no—
551C2×C3×D3—22no—
552C2×C3×D3—22no—
553C32×C4—21no—
554C32×C4—21no—
555C32×C4—21no—
556C32×C4—21no—
557C32×C4C2×#4112yes—
558C32×C42−1+412yes—
559C3⋊Dic3—24no—
560C3×Dic3—22no—
561C3×Dic3—22no—
562C3×Dic3—22no—
563C3×Dic3—22no—
564C3×Dic3—22no—
565C3×Dic3—22no—
566C3×Dic3C2×#4114yes—
567C2×#41—94no—
568C2×#41—92no—
569C2×#41—92no—
570C22×Q8—31no—
571C4⋊Q8—92no—
572C4⋊Q8—92no—
573C4⋊Q8—94no—
574C4⋊Q8—91no—
575#127—92no—
576#127—91no—
577#126—32no—
578#126—94no—
579#125—31no—
580#125—92no—
581#124—31no—
582#124—94no—
583#124—92no—
584#124—92no—
585#124—94no—
586#124—92no—
587#123—32no—
588#123—94no—
589#123—94no—
590#123—94no—
591#123—94no—
592C22⋊Q8—31no—
593C22⋊Q8—94no—
594C22⋊Q8—94no—
595C22⋊Q8—94no—
596C22⋊Q8—94no—
597C22⋊Q8—92no—
598#121—31no—
599#121—94no—
600#121—92no—
601#121—94no—
602#121—92no—
603#121—92no—
604C4×Q8—31no—
605C4×Q8—32no—
606C4×Q8—31no—
607C4×Q8—31no—
608C4×Q8—31no—
609C4×Q8—32no—
610C4×Q8—31no—
611C4×Q8—92no—
612C4×Q8—92no—
613C4×D4—32no—
614C4×D4—31no—
615C4×D4—94no—
616C4×D4—92no—
617C4×D4—92no—
618C4×D4—92no—
619C4×D4—92no—
620C4×D4—94no—
621C4×D4—94no—
622C4×D4—92no—
623C4×D4—92no—
624#117—32no—
625#117—94no—
626C2×C4⋊C4—32no—
627C2×C4⋊C4—31no—
628C2×C4⋊C4—94no—
629C2×C4⋊C4—92no—
630C2×C42—32no—
631C2×C42D3211yescharacteristic
632C23×C3—21no—
633C23×C3—32no—
634C23×C3C23×D311yescharacteristic
635C23×C3C23×D311yescharacteristic
636C22×D3—34no—
637C22×D3—34no—
638C22×D3—64no—
639C22×D3C23×D312yes—
640C3×Q8—34no—
641C3×Q8—64no—
642C3×Q8—62no—
643C3×Q8—62no—
644C3×D4—64no—
645C3×D4—62no—
646C2×C3×C4—24no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—32no—
660C2×C3×C4—32no—
661C2×C3×C4—32no—
662C2×C3×C4—32no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—32no—
666C2×C3×C4—42no—
667C2×C3×C4—42no—
668C2×C3×C4—64no—
669C2×C3×C4—64no—
670C2×C3×C4—64no—
671C2×C3×C4C23×D311yescharacteristic
672C2×C3×C4C23×D311yescharacteristic
673C2×C3×C4C23×D311yescharacteristic
674C2×C3×C4C23×D311yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D311yescharacteristic
678C2×C3×C4C23×D311yescharacteristic
679C2×C3×C4C23×D311yescharacteristic
680C2×C3×C4C23×D311yescharacteristic
681C2×C3×C4C23×D311yescharacteristic
682C2×C3×C4C23×D311yescharacteristic
683#67—24no—
684#67—68no—
685#67—68no—
686#67—68no—
687#67—128no—
688#67—124no—
689C2×Dic3—24no—
690C2×Dic3—24no—
691C2×Dic3—34no—
692C2×Dic3—34no—
693C2×Dic3—64no—
694C2×Dic3—124no—
695C2×Dic3C23×D312yes—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D312yes—
698C2×Dic3C23×D312yes—
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D312yes—
701C2×Dic3C23×D312yes—
702D12—22no—
703D12—68no—
704D12—64no—
705D12—64no—
706D12—64no—
707D12—64no—
708D12—124no—
709D12—124no—
710D12—122no—
711D12—122no—
712D12—124no—
713D12—124no—
714C4×D3—24no—
715C4×D3—68no—
716C4×D3—68no—
717C4×D3—124no—
718C4×D3—124no—
719C4×D3—124no—
720C4×D3—124no—
721C4×D3—124no—
722C4×D3—128no—
723Dic6—22no—
724Dic6—22no—
725Dic6—24no—
726Dic6—124no—
727Dic6—124no—
728Dic6—122no—
729Dic6—122no—
730Dic6—124no—
731Dic6#23514yescomplemented
732C2×C32—22no—
733C2×C32C22×#4111yescharacteristic
734C2×C32C2×H(5,𝔽2)11yescharacteristic
735C2×C32C2×2−1+411yescharacteristic
736C3⋊D3—44no—
737C3×D3—42no—
738#41—188no—
739#41—364no—
740#41—368no—
741C2×Q8—31no—
742C2×Q8—32no—
743C2×Q8—31no—
744C2×Q8—31no—
745C2×Q8—64no—
746C2×Q8—94no—
747C2×Q8—92no—
748C2×D4—32no—
749C2×D4—31no—
750C2×D4—94no—
751C2×D4—94no—
752C2×D4—94no—
753C2×D4—92no—
754C2×D4—92no—
755C2×D4—92no—
756C22×C4—32no—
757C22×C4—32no—
758C22×C4—32no—
759C22×C4—94no—
760C22×C4—94no—
761C22×C4—94no—
762C22×C4—94no—
763C22×C4C2×D3211yescharacteristic
764C22×C4C2×D3211yescharacteristic
765C22×C4C2×D3211yescharacteristic
766C4⋊C4—32no—
767C4⋊C4—31no—
768C4⋊C4—32no—
769C4⋊C4—31no—
770C4⋊C4—32no—
771C4⋊C4—32no—
772C4⋊C4—32no—
773C4⋊C4—32no—
774C4⋊C4—32no—
775C4⋊C4—31no—
776C4⋊C4—32no—
777C4⋊C4—31no—
778C4⋊C4—32no—
779C4⋊C4—94no—
780C4⋊C4—94no—
781C4⋊C4—94no—
782C4⋊C4—94no—
783C4⋊C4—92no—
784C4⋊C4—92no—
785C22⋊C4—32no—
786C22⋊C4—32no—
787C22⋊C4—32no—
788C22⋊C4—32no—
789C22⋊C4—32no—
790C22⋊C4—94no—
791C22⋊C4—94no—
792C22⋊C4—94no—
793C22⋊C4—94no—
794C22⋊C4—94no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C42—32no—
798C42—32no—
799C42—32no—
800C42—32no—
801C42—32no—
802C42—94no—
803C42C2×D3211yescharacteristic
804C42C2×D3211yescharacteristic
805C42C2×D3211yescharacteristic
806C42C2×D3211yescharacteristic
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—22no—
812C22×C3—21no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3#100912yes—
819C22×C3#100912yes—
820C22×C3C24×D311yescharacteristic
821C22×C3C24×D311yescharacteristic
822C2×D3—22no—
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—64no—
826C2×D3—64no—
827C2×D3—64no—
828C2×D3—64no—
829C2×D3—64no—
830C2×D3—64no—
831C2×D3—124no—
832C2×D3—124no—
833C2×D3—124no—
834C3×C4—22no—
835C3×C4—22no—
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—21no—
839C3×C4—21no—
840C3×C4—21no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—22no—
845C3×C4—22no—
846C3×C4—34no—
847C3×C4—41no—
848C3×C4—41no—
849C3×C4—62no—
850C3×C4—62no—
851C3×C4—62no—
852C3×C4—62no—
853C3×C4—62no—
854C3×C4—62no—
855C3×C4C2×#23512yes—
856C3×C4#100712yes—
857C3×C4D3×#4112yes—
858C3×C4#101012yes—
859Dic3—22no—
860Dic3—22no—
861Dic3—22no—
862Dic3—22no—
863Dic3—22no—
864Dic3—22no—
865Dic3—64no—
866Dic3—64no—
867Dic3—124no—
868Dic3C2×#23514yes—
869C32#352211yescharacteristic, complemented, Sylow
870C23—32no—
871C23—94no—
872C23C22×D3211yescharacteristic
873Q8—34no—
874Q8—64no—
875Q8—62no—
876Q8—62no—
877Q8—362no—
878Q8—364no—
879D4—64no—
880D4—62no—
881D4—188no—
882D4—188no—
883D4—184no—
884D4—184no—
885D4—362no—
886D4—364no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—32no—
891C2×C4—32no—
892C2×C4—32no—
893C2×C4—32no—
894C2×C4—32no—
895C2×C4—32no—
896C2×C4—32no—
897C2×C4—64no—
898C2×C4—64no—
899C2×C4—64no—
900C2×C4—94no—
901C2×C4—188no—
902C2×C4—364no—
903C2×C4—364no—
904C2×C4—364no—
905C2×C4C22×D3211yescharacteristic
906C2×C4C22×D3211yescharacteristic
907C2×C4C22×D3211yescharacteristic
908C2×C4C22×D3211yescharacteristic
909C2×C4C22×D3211yescharacteristic
910C2×C4C22×D3211yescharacteristic
911C2×C3—22no—
912C2×C3—22no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—42no—
917C2×C3—122no—
918C2×C3C22×#23511yescharacteristic
919C2×C3C2×#100711yescharacteristic
920C2×C3C2×D3×#4111yescharacteristic
921C2×C3C2×#100911yescharacteristic
922C2×C3C2×#100911yescharacteristic
923C2×C3C2×#101011yescharacteristic
924D3—42no—
925D3—124no—
926D3—124no—
927D3—244no—
928C22—21no—
929C22—21no—
930C22—62no—
931C22—62no—
932C22—62no—
933C22—184no—
934C22—184no—
935C22—184no—
936C22#6430812yes—
937C22C23×D3211yescharacteristic
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—34no—
943C4—62no—
944C4—62no—
945C4—62no—
946C4—62no—
947C4—62no—
948C4—62no—
949C4—184no—
950C4#6429712yes—
951C4D3×#23512yes—
952C3—21no—
953C3#8582111yescharacteristic, complemented
954C3#8612811yescharacteristic, complemented
955C2—22no—
956C2—122no—
957C2—364no—
958C2C2×#6429711yescharacteristic
959C2C2×D3×#23511yescharacteristic
960C2C2×#6430811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595948C2semidirect
2. C3×#5479C2semidirect
3. C2×C3×C4×Dic6C2semidirect
4. #10594955C2semidirect
5. #10594917C2semidirect
6. #10594910C2semidirect
7. #10594906C2semidirect
8. #10594902C2semidirect
9. #10593963C2semidirect
10. #10593960C2semidirect
11. #10593939C2semidirect
12. #10593938C2semidirect
13. #10593936C2semidirect
14. #10593902C2semidirect
15. #10593890C2semidirect
16. #10593878C2semidirect
17. Dic62C2semidirect
114. #5479D3semidirect
119. C2×C4×Dic6D3semidirect
363. C3×Dic6#41semidirect
731. Dic6#235semidirect
869. C32#3522semidirect
953. C3#85821semidirect
954. C3#86128semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×#54792
C2×C3×C4×Dic62
#105949552
#105949172
#105949102
#105949062
#105949022
#105939632
#105939602
#105939392
#105939382
#105939362
#105939022
#105938902
#105938782
Dic622
#861283
#858213