Finite Group Databasebeta

← #11909797

Subgroups — #11909797

Order 1152.

2322 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596050C211yesmaximal, characteristic, complemented
2C3×#5585C211yesmaximal, characteristic, complemented
3C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
4#10595401C212yesmaximal, complemented
5#10595395C212yesmaximal, complemented
6#10594515C212yesmaximal, complemented
7#10594513C214yesmaximal, complemented
8#10594419C214yesmaximal, complemented
9#10594361C212yesmaximal, complemented
10#10593968C212yesmaximal, complemented
11#10593939C212yesmaximal, complemented
12#10593929C212yesmaximal, complemented
13#10593921C212yesmaximal, complemented
14#10593900C211yesmaximal, characteristic, complemented
15#10593897C211yesmaximal, characteristic, complemented
16#10593870C211yesmaximal, characteristic, complemented
17Dic62C211yesmaximal, characteristic, complemented
18#87055—31nomaximal
19#85821—31nomaximal
20C2×C3×D3×Q8C2211yescharacteristic
21C2×#3798C2214yes—
22C2×#3796C2212yes—
23C2×#3795C2212yes—
24C32×C4×Q8C2211yescharacteristic
25#64155C2212yes—
26#64105C2214yes—
27C4⋊C4×C3⋊D3C2212yes—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×C4⋊(C3⋊D3)C2212yes—
30#64079C2212yes—
31#64078C2211yescharacteristic
32C3×#947C2212yes—
33C3×Q8×Dic3C2211yescharacteristic
34C3×#894C2214yes—
35C3×#893C2212yes—
36C3×D3×C4⋊C4C2212yes—
37C3×D3×C4⋊C4C2211yescharacteristic
38C3×#887C2211yescharacteristic
39C3×#887C2212yes—
40C3×#875C2212yes—
41C3×#874C2211yescharacteristic
42C3×C4×D12C2212yes—
43C3×C42×D3C2211yescharacteristic
44C3×C42×D3C2212yes—
45C3×C4×Dic6C2211yescharacteristic
46C3×C4×Dic6C2211yescharacteristic
47C3×C4×Dic6C2212yes—
48#63918C2212yes—
49#63918C2212yes—
50#63916C2212yes—
51#63911C2212yes—
52#63909C2211yescharacteristic
53#63908C2212yes—
54#63908C2212yes—
55#63907C2214yes—
56#63906C2214yes—
57#63905C2214yes—
58C4×#626C2214yes—
59C4×#626C2212yes—
60#63899C2214yes—
61Dic3×D12C2212yes—
62Dic3×D12C2212yes—
63Dic3×D12C2212yes—
64#63890C2214yes—
65#63887C2214yes—
66#63886C2214yes—
67#63881C2214yes—
68#63879C2214yes—
69#63877C2214yes—
70D3×Dic3⋊C4C2214yes—
71#63874C2212yes—
72#63869C2211yescharacteristic
73#63868C2212yes—
74#63864C2211yescharacteristic
75#63860C2212yes—
76#63859C2214yes—
77#63856C2211yescharacteristic
78#63853C2214yes—
79#63852C2214yes—
80#63851C2214yes—
81#63850C2212yes—
82Dic3×Dic6C2212yes—
83Dic3×Dic6C2212yes—
84#63840C2214yes—
85C3×#559—31no—
86C2×C3×C4×Q8—31no—
87#5817—32no—
88#5718—31no—
89#5716—31no—
90#5682—32no—
91#5681—32no—
92#5680—32no—
93#5677—32no—
94#5662—34no—
95#5655—34no—
96#5585—32no—
97#5585D311yescharacteristic, complemented
98#5582—32no—
99#5582—34no—
100#5580—31no—
101#5579—31no—
102#5579—31no—
103#5579—32no—
104#5579—61no—
105#5577—31no—
106#5574—32no—
107C4×D3×Q8D311yescharacteristic, complemented
108Q8×Dic6—31no—
109Q8×Dic6—31no—
110#5551—32no—
111#5548—32no—
112#5546—32no—
113#5539—32no—
114#5507—34no—
115#5507—32no—
116#5479—32no—
117#5479—31no—
118#5477—31no—
119#5477—32no—
120C2×C32×Q8C2311yescharacteristic
121C2×C4⋊(C3⋊D3)C2311yescharacteristic
122C2×C4×C3⋊D3C2312yes—
123C2×C4×C3⋊D3C2314yes—
124C2×#634C2312yes—
125C3×D3×Q8—24no—
126C2×C3×D12C2312yes—
127C2×C3×D12C2312yes—
128C2×C3×D12C2312yes—
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×C4×D3C2314yes—
135C2×C3×Dic6C2312yes—
136C2×C3×Dic6C2311yescharacteristic
137C2×C3×Dic6C2311yescharacteristic
138C2×#627C2314yes—
139C2×#626C2314yes—
140C2×#626C2312yes—
141C2×#626C2314yes—
142C2×#625C2314yes—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2314yes—
145#3798—48no—
146#3796—28no—
147#3795—44no—
148C32×C4⋊C4C2311yescharacteristic
149C32×C4⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151C32×C42C2312yes—
152#3752C2312yes—
153#3752C2314yes—
154C4⋊(C3⋊Dic3)C2312yes—
155C4⋊(C3⋊Dic3)C2312yes—
156C4⋊(C3⋊Dic3)C2311yescharacteristic
157#3750C2314yes—
158#3750C2314yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2314yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2311yescharacteristic
164C3×C4⋊Dic3C2311yescharacteristic
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2312yes—
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2312yes—
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2312yes—
174C3×C4×Dic3C2312yes—
175C3×C4×Dic3C2311yescharacteristic
176#3724C2312yes—
177#3724C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2312yes—
181#3722C2312yes—
182#3722C2312yes—
183#3722C2312yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2314yes—
188Dic32C2314yes—
189#3522—91noSylow
190C22×C3×Q8—31no—
191C2×#239—32no—
192C2×D3×Q8C2×D311yescharacteristic
193C2×#237—32no—
194C2×#237—32no—
195C2×#235—32no—
196C2×#235—34no—
197C2×#235—34no—
198C3×#127—31no—
199C3×#124—32no—
200C3×#124—32no—
201C3×#123—34no—
202C3×C4×Q8—21no—
203C3×C4×Q8—31no—
204C3×C4×Q8—31no—
205C3×C4×Q8—32no—
206C3×C4×Q8—31no—
207C3×C4×Q8—31no—
208C3×C4×Q8—32no—
209C3×C4×Q8C2×D311yescharacteristic
210C3×C4×Q8C2×D311yescharacteristic
211C3×C4×D4—32no—
212C3×C4×D4—32no—
213C2×C3×C4⋊C4—32no—
214C2×C3×C4⋊C4—31no—
215C2×C3×C42—32no—
216C2×C3×C42—31no—
217#947—34no—
218#947—31no—
219#947C2×D312yes—
220#946—32no—
221#946—32no—
222#946—31no—
223#946—34no—
224#946—62no—
225Q8×Dic3—32no—
226Q8×Dic3—32no—
227Q8×Dic3C2×D311yescharacteristic
228#940—32no—
229#939—34no—
230#938—32no—
231#938—32no—
232#938—32no—
233#936—32no—
234D4×Dic3—32no—
235D4×Dic3—32no—
236D4×Dic3—32no—
237#930—32no—
238#930—32no—
239#930—34no—
240#930—31no—
241#929—34no—
242#929—32no—
243C4×#67—34no—
244C4×#67—34no—
245C4×#67—32no—
246#924—31no—
247#924—34no—
248C2×Dic3⋊C4—34no—
249#898—32no—
250#896—34no—
251#896—34no—
252#896—34no—
253#896—34no—
254#896—64no—
255#895—34no—
256#895—32no—
257#895—31no—
258#894—32no—
259#894—34no—
260#894—34no—
261#894C2×D314yes—
262#893—34no—
263#893C2×D312yes—
264D3×C4⋊C4—34no—
265D3×C4⋊C4—32no—
266D3×C4⋊C4—32no—
267D3×C4⋊C4—62no—
268D3×C4⋊C4C2×D312yes—
269D3×C4⋊C4C2×D311yescharacteristic
270#890—31no—
271#888—34no—
272#888—34no—
273#888—32no—
274#888—32no—
275#887C2×D312yes—
276#887C2×D311yescharacteristic
277#886—34no—
278#885—34no—
279#885—34no—
280#884—34no—
281#883—34no—
282#883—34no—
283#67⋊C4—34no—
284#67⋊C4—34no—
285#879—34no—
286#878—34no—
287#878—34no—
288#877—34no—
289#876—34no—
290#876—32no—
291#875—32no—
292#875—31no—
293#875—34no—
294#875C2×D312yes—
295#874—32no—
296#874C2×D311yescharacteristic
297C4×D12—32no—
298C4×D12—32no—
299C4×D12—32no—
300C4×D12—32no—
301C4×D12—34no—
302C4×D12—32no—
303C4×D12—31no—
304C4×D12—32no—
305C4×D12—31no—
306C4×D12—61no—
307C4×D12—62no—
308C4×D12C2×D312yes—
309#872—34no—
310#872—32no—
311#872—32no—
312C42×D3C2×D312yes—
313C42×D3C2×D311yescharacteristic
314#870—32no—
315#870—32no—
316#870—31no—
317#870—62no—
318#869—31no—
319#869—31no—
320#869—32no—
321#869—32no—
322#869—61no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6C2×D312yes—
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D311yescharacteristic
328C22×C3⋊D3C2412yes—
329C22×C3×D3C2414yes—
330C22×C3×D3C2411yescharacteristic
331C32×Q8—22no—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2412yes—
334C2×C32×C4C2412yes—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C3⋊Dic3C2414yes—
338C2×C3⋊Dic3C2412yes—
339C4⋊(C3⋊D3)—22no—
340C4×C3⋊D3—24no—
341C4×C3⋊D3—44no—
342#634—42no—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2411yescharacteristic
345C2×C3×Dic3C2411yescharacteristic
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C3×D12—24no—
351C3×D12—24no—
352C3×D12—42no—
353C3×C4×D3—22no—
354C3×C4×D3—24no—
355C3×C4×D3—22no—
356C3×C4×D3—22no—
357C3×C4×D3—24no—
358C3×C4×D3—44no—
359C3×Dic6—22no—
360C3×Dic6—24no—
361C3×Dic6#4114yescomplemented
362#627—44no—
363#626—24no—
364#626—28no—
365#626—44no—
366#625—28no—
367D3×Dic3—28no—
368D3×Dic3—44no—
369#559—31no—
370#559—92no—
371Q82—91no—
372#554—92no—
373#554—91no—
374#550—91no—
375#548—92no—
376#547—92no—
377#547—94no—
378#542—94no—
379#542—92no—
380#532—92no—
381#532—91no—
382#529—91no—
383#529—92no—
384#520—92no—
385C2×C4×Q8—31no—
386C2×C3×Q8—21no—
387C2×C3×Q8—31no—
388C2×C3×Q8—31no—
389C2×C3×Q8—32no—
390C2×C3×Q8—64no—
391C2×C3×Q8C22×D311yescharacteristic
392C2×C3×Q8C22×D311yescharacteristic
393C2×C3×D4—32no—
394C2×C3×D4—32no—
395C2×C3×D4—32no—
396C22×C3×C4—31no—
397C22×C3×C4—32no—
398C22×C3×C4—31no—
399C22×C3×C4—32no—
400C22×C3×C4—31no—
401C22×C3×C4—34no—
402C2×#67—34no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—32no—
406C2×#67—34no—
407C22×Dic3—34no—
408C22×Dic3—34no—
409#239—68no—
410D3×Q8—24no—
411#237—68no—
412#237—124no—
413#235—128no—
414#235—128no—
415#235—124no—
416C2×D12—34no—
417C2×D12—32no—
418C2×D12—31no—
419C2×D12—31no—
420C2×D12—34no—
421C2×D12—61no—
422C2×D12C22×D312yes—
423C2×D12C22×D312yes—
424C2×D12C22×D312yes—
425C2×C4×D3—34no—
426C2×C4×D3—32no—
427C2×C4×D3—32no—
428C2×C4×D3—34no—
429C2×C4×D3—34no—
430C2×C4×D3—34no—
431C2×C4×D3—62no—
432C2×C4×D3—64no—
433C2×C4×D3C22×D311yescharacteristic
434C2×C4×D3C22×D311yescharacteristic
435C2×C4×D3C22×D312yes—
436C2×C4×D3C22×D312yes—
437C2×C4×D3C22×D311yescharacteristic
438C2×C4×D3C22×D314yes—
439C2×Dic6—32no—
440C2×Dic6—32no—
441C2×Dic6—34no—
442C2×Dic6—34no—
443C2×Dic6—62no—
444C2×Dic6C22×D311yescharacteristic
445C2×Dic6C22×D312yes—
446C2×Dic6C22×D311yescharacteristic
447C3×C4⋊C4—21no—
448C3×C4⋊C4—22no—
449C3×C4⋊C4—31no—
450C3×C4⋊C4—32no—
451C3×C4⋊C4—32no—
452C3×C4⋊C4—31no—
453C3×C4⋊C4—32no—
454C3×C4⋊C4—32no—
455C3×C4⋊C4—32no—
456C3×C4⋊C4C22×D311yescharacteristic
457C3×C4⋊C4C22×D312yes—
458C3×C4⋊C4C22×D311yescharacteristic
459C3×C4⋊C4C22×D312yes—
460C3×C22⋊C4—34no—
461C3×C22⋊C4—34no—
462C3×C22⋊C4—34no—
463C3×C42—21no—
464C3×C42—22no—
465C3×C42—32no—
466C3×C42—32no—
467C3×C42—31no—
468C3×C42—32no—
469C3×C42—31no—
470C3×C42—31no—
471C3×C42—32no—
472C3×C42C22×D311yescharacteristic
473C3×C42C22×D311yescharacteristic
474C3×C42C22×D312yes—
475C3×C42C22×D312yes—
476#217—34no—
477#217—34no—
478#217—34no—
479#217—32no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—32no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—32no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4—32no—
492(C2×D3)⋊C4—32no—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—62no—
495(C2×D3)⋊C4—64no—
496(C2×D3)⋊C4C22×D314yes—
497(C2×D3)⋊C4C22×D314yes—
498(C2×D3)⋊C4C22×D314yes—
499C4⋊Dic3—32no—
500C4⋊Dic3—32no—
501C4⋊Dic3—32no—
502C4⋊Dic3—32no—
503C4⋊Dic3—31no—
504C4⋊Dic3—31no—
505C4⋊Dic3—34no—
506C4⋊Dic3—34no—
507C4⋊Dic3—32no—
508C4⋊Dic3—62no—
509C4⋊Dic3—62no—
510C4⋊Dic3—61no—
511C4⋊Dic3C22×D311yescharacteristic
512C4⋊Dic3C22×D311yescharacteristic
513C4⋊Dic3C22×D312yes—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—32no—
521Dic3⋊C4—32no—
522Dic3⋊C4—32no—
523Dic3⋊C4—32no—
524Dic3⋊C4—32no—
525Dic3⋊C4—64no—
526Dic3⋊C4—64no—
527Dic3⋊C4C22×D312yes—
528Dic3⋊C4C22×D312yes—
529Dic3⋊C4C22×D312yes—
530Dic3⋊C4C22×D312yes—
531C4×Dic3—34no—
532C4×Dic3—34no—
533C4×Dic3C22×D312yes—
534C4×Dic3C22×D311yescharacteristic
535C4×Dic3C22×D312yes—
536C4×Dic3C22×D311yescharacteristic
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D312yes—
539C4×Dic3C22×D311yescharacteristic
540C22×C32C2511yescharacteristic
541C2×C3⋊D3—22no—
542C2×C3⋊D3—22no—
543C2×C3⋊D3—22no—
544C2×C3×D3—21no—
545C2×C3×D3—21no—
546C2×C3×D3—24no—
547C2×C3×D3—24no—
548C2×C3×D3—24no—
549C2×C3×D3H(5,𝔽2)12yes—
550C32×C4—22no—
551C32×C4—22no—
552C32×C4—21no—
553C32×C4C2×#4112yes—
554C32×C42−1+412yes—
555C3⋊Dic3—22no—
556C3⋊Dic3—24no—
557C3×Dic3—21no—
558C3×Dic3—21no—
559C3×Dic3—22no—
560C3×Dic3—22no—
561C3×Dic3—22no—
562C3×Dic3—21no—
563C3×Dic3C2×#4114yes—
564C2×#41—94no—
565C2×#41—92no—
566C2×#41—92no—
567C22×Q8—31no—
568C4⋊Q8—92no—
569C4⋊Q8—92no—
570C4⋊Q8—94no—
571C4⋊Q8—91no—
572#127—31no—
573#127—92no—
574#126—94no—
575#126—92no—
576#125—91no—
577#125—92no—
578#124—32no—
579#124—32no—
580#124—94no—
581#124—92no—
582#124—91no—
583#124—94no—
584#123—34no—
585#123—94no—
586#123—94no—
587#123—94no—
588#123—92no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—91no—
593C22⋊Q8—92no—
594C22⋊Q8—94no—
595#121—94no—
596#121—91no—
597#121—92no—
598#121—94no—
599#121—92no—
600#121—92no—
601C4×Q8—31no—
602C4×Q8—31no—
603C4×Q8—32no—
604C4×Q8—31no—
605C4×Q8—32no—
606C4×Q8—31no—
607C4×Q8—92no—
608C4×Q8—92no—
609C4×Q8D3211yescharacteristic
610C4×D4—32no—
611C4×D4—32no—
612C4×D4—94no—
613C4×D4—92no—
614C4×D4—92no—
615C4×D4—92no—
616C4×D4—92no—
617C4×D4—94no—
618C4×D4—94no—
619C4×D4—91no—
620C4×D4—92no—
621#117—92no—
622#117—94no—
623C2×C4⋊C4—32no—
624C2×C4⋊C4—31no—
625C2×C4⋊C4—94no—
626C2×C4⋊C4—92no—
627C2×C42—31no—
628C2×C42—32no—
629C23×C3—31no—
630C23×C3—34no—
631C22×D3—32no—
632C22×D3—32no—
633C22×D3—62no—
634C22×D3C23×D314yes—
635C22×D3C23×D311yescharacteristic
636C3×Q8—22no—
637C3×Q8—22no—
638C3×Q8—34no—
639C3×Q8—42no—
640C3×Q8—64no—
641C3×Q8—62no—
642C3×D4—64no—
643C3×D4—64no—
644C3×D4—122no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—21no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—31no—
654C2×C3×C4—31no—
655C2×C3×C4—32no—
656C2×C3×C4—31no—
657C2×C3×C4—64no—
658C2×C3×C4—62no—
659C2×C3×C4—64no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—124no—
663C2×C3×C4C23×D312yes—
664C2×C3×C4C23×D312yes—
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D312yes—
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D311yescharacteristic
672C2×C3×C4C23×D311yescharacteristic
673#67—64no—
674#67—68no—
675#67—68no—
676#67—68no—
677#67—124no—
678C2×Dic3—34no—
679C2×Dic3—34no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—62no—
683C2×Dic3—64no—
684C2×Dic3—68no—
685C2×Dic3—124no—
686C2×Dic3C23×D312yes—
687C2×Dic3C23×D311yescharacteristic
688C2×Dic3C23×D311yescharacteristic
689C2×Dic3C23×D312yes—
690C2×Dic3C23×D311yescharacteristic
691C2×Dic3C23×D312yes—
692C2×Dic3C23×D312yes—
693D12—24no—
694D12—24no—
695D12—42no—
696D12—64no—
697D12—68no—
698D12—64no—
699D12—62no—
700D12—62no—
701D12—124no—
702C4×D3—24no—
703C4×D3—22no—
704C4×D3—22no—
705C4×D3—22no—
706C4×D3—24no—
707C4×D3—44no—
708C4×D3—68no—
709C4×D3—64no—
710C4×D3—64no—
711C4×D3—124no—
712C4×D3—124no—
713C4×D3—124no—
714C4×D3—124no—
715C4×D3—244no—
716Dic6—22no—
717Dic6—24no—
718Dic6—124no—
719Dic6—124no—
720Dic6—122no—
721Dic6—122no—
722Dic6—242no—
723Dic6#23514yescomplemented
724C2×C32C22×#4111yescharacteristic
725C2×C32C2×H(5,𝔽2)11yescharacteristic
726C2×C32C2×2−1+411yescharacteristic
727C3⋊D3—42no—
728C3×D3—22no—
729C3×D3—44no—
730#41—188no—
731#41—368no—
732#41—364no—
733C2×Q8—31no—
734C2×Q8—32no—
735C2×Q8—31no—
736C2×Q8—64no—
737C2×Q8—94no—
738C2×Q8—92no—
739C2×Q8C2×D3211yescharacteristic
740C2×D4—32no—
741C2×D4—32no—
742C2×D4—32no—
743C2×D4—94no—
744C2×D4—92no—
745C2×D4—94no—
746C2×D4—94no—
747C2×D4—91no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—32no—
751C22×C4—32no—
752C22×C4—31no—
753C22×C4—34no—
754C22×C4—94no—
755C22×C4—94no—
756C22×C4—92no—
757C22×C4—94no—
758C4⋊C4—32no—
759C4⋊C4—32no—
760C4⋊C4—31no—
761C4⋊C4—32no—
762C4⋊C4—32no—
763C4⋊C4—31no—
764C4⋊C4—32no—
765C4⋊C4—92no—
766C4⋊C4—94no—
767C4⋊C4—92no—
768C4⋊C4—92no—
769C4⋊C4—94no—
770C4⋊C4—94no—
771C4⋊C4—92no—
772C4⋊C4—91no—
773C4⋊C4—92no—
774C4⋊C4—94no—
775C4⋊C4C2×D3211yescharacteristic
776C4⋊C4C2×D3212yes—
777C22⋊C4—34no—
778C22⋊C4—34no—
779C22⋊C4—34no—
780C22⋊C4—92no—
781C22⋊C4—92no—
782C22⋊C4—92no—
783C22⋊C4—94no—
784C22⋊C4—92no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—92no—
788C22⋊C4—94no—
789C42—32no—
790C42—31no—
791C42—31no—
792C42—32no—
793C42—31no—
794C42—32no—
795C42—32no—
796C42—94no—
797C42C2×D3212yes—
798C42C2×D3211yescharacteristic
799C22×C3—21no—
800C22×C3—32no—
801C22×C3—61no—
802C22×C3—61no—
803C22×C3—64no—
804C22×C3—64no—
805C22×C3—64no—
806C22×C3C24×D311yescharacteristic
807C22×C3C24×D311yescharacteristic
808C2×D3—21no—
809C2×D3—21no—
810C2×D3—24no—
811C2×D3—24no—
812C2×D3—24no—
813C2×D3—64no—
814C2×D3—62no—
815C2×D3—62no—
816C2×D3—62no—
817C2×D3—62no—
818C2×D3—62no—
819C2×D3—62no—
820C2×D3—122no—
821C2×D3—122no—
822C2×D3#100912yes—
823C3×C4—22no—
824C3×C4—22no—
825C3×C4—21no—
826C3×C4—22no—
827C3×C4—21no—
828C3×C4—22no—
829C3×C4—22no—
830C3×C4—22no—
831C3×C4—34no—
832C3×C4—41no—
833C3×C4—42no—
834C3×C4—42no—
835C3×C4—62no—
836C3×C4—61no—
837C3×C4—62no—
838C3×C4—61no—
839C3×C4—62no—
840C3×C4—61no—
841C3×C4C2×#23512yes—
842C3×C4#100712yes—
843C3×C4D3×#4112yes—
844C3×C4#101012yes—
845Dic3—21no—
846Dic3—21no—
847Dic3—22no—
848Dic3—21no—
849Dic3—22no—
850Dic3—22no—
851Dic3—62no—
852Dic3—62no—
853Dic3—64no—
854Dic3—64no—
855Dic3—124no—
856Dic3—122no—
857Dic3C2×#23514yes—
858C32#352211yescharacteristic, complemented, Sylow
859C23—31no—
860C23—34no—
861C23—92no—
862Q8—22no—
863Q8—34no—
864Q8—64no—
865Q8—62no—
866Q8—362no—
867Q8—364no—
868D4—64no—
869D4—64no—
870D4—122no—
871D4—188no—
872D4—184no—
873D4—188no—
874D4—182no—
875D4—364no—
876C2×C4—32no—
877C2×C4—31no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—32no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—64no—
884C2×C4—64no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—94no—
889C2×C4—92no—
890C2×C4—124no—
891C2×C4—188no—
892C2×C4—184no—
893C2×C4—364no—
894C2×C4—364no—
895C2×C4C22×D3212yes—
896C2×C4C22×D3212yes—
897C2×C4C22×D3211yescharacteristic
898C2×C4C22×D3211yescharacteristic
899C2×C4C22×D3211yescharacteristic
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—62no—
904C2×C3—124no—
905C2×C3C22×#23511yescharacteristic
906C2×C3C2×#100711yescharacteristic
907C2×C3C2×D3×#4111yescharacteristic
908C2×C3C2×#100911yescharacteristic
909C2×C3C2×#101011yescharacteristic
910C2×C3D3×H(5,𝔽2)11yescharacteristic
911D3—22no—
912D3—44no—
913D3—124no—
914D3—122no—
915D3—122no—
916C22—32no—
917C22—61no—
918C22—61no—
919C22—64no—
920C22—64no—
921C22—64no—
922C22—182no—
923C22—182no—
924C22—182no—
925C22C23×D3211yescharacteristic
926C4—22no—
927C4—22no—
928C4—21no—
929C4—34no—
930C4—61no—
931C4—61no—
932C4—62no—
933C4—61no—
934C4—62no—
935C4—62no—
936C4—182no—
937C4—184no—
938C4D3×#23512yes—
939C4#6431512yes—
940C3—21no—
941C3#8582111yescharacteristic, complemented
942C3#8705511yescharacteristic, complemented
943C2—62no—
944C2—124no—
945C2—362no—
946C2C2×D3×#23511yescharacteristic
947C2C2×#6431511yescharacteristic
948C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596050C2semidirect
2. C3×#5585C2semidirect
3. C3×C4×D3×Q8C2semidirect
4. #10595401C2semidirect
5. #10595395C2semidirect
6. #10594515C2semidirect
7. #10594513C2semidirect
8. #10594419C2semidirect
9. #10594361C2semidirect
10. #10593968C2semidirect
11. #10593939C2semidirect
12. #10593929C2semidirect
13. #10593921C2semidirect
14. #10593900C2semidirect
15. #10593897C2semidirect
16. #10593870C2semidirect
17. Dic62C2semidirect
97. #5585D3semidirect
107. C4×D3×Q8D3semidirect
361. C3×Dic6#41semidirect
723. Dic6#235semidirect
858. C32#3522semidirect
941. C3#85821semidirect
942. C3#87055semidirect

Maximal subgroups

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

subgroupindex
#105960502
C3×#55852
C3×C4×D3×Q82
#105954012
#105953952
#105945152
#105945132
#105944192
#105943612
#105939682
#105939392
#105939292
#105939212
#105939002
#105938972
#105938702
Dic622
#870553
#858213