Finite Group Databasebeta

← #11903770

Subgroups — #11903770

Order 1152.

2285 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5579C211yesmaximal, characteristic, complemented
3C3×#5567C211yesmaximal, characteristic, complemented
4#10595368C212yesmaximal, complemented
5#10595361C212yesmaximal, complemented
6#10594536C212yesmaximal, complemented
7#10594394C214yesmaximal, complemented
8#10594388C214yesmaximal, complemented
9D3×#887C212yesmaximal, complemented
10#10593941C212yesmaximal, complemented
11#10593904C211yesmaximal, characteristic, complemented
12C4×#3796C212yesmaximal
13C4×#3796C211yesmaximal, characteristic
14#10593866C211yesmaximal, characteristic, complemented
15#10593856C211yesmaximal, characteristic, complemented
16#10593854C212yesmaximal, complemented
17#10593853C212yesmaximal, complemented
18#87015—31nomaximal
19#86923—31nomaximal
20C2×Q8×C3⋊D3C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22C2×D3×Dic6C2212yes—
23C32×C4×Q8C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic
25C4⋊C4×C3⋊D3C2212yes—
26C4⋊C4×C3⋊D3C2211yescharacteristic
27#64096C2211yescharacteristic
28#64096C2212yes—
29C42×C3⋊D3C2212yes—
30C42×C3⋊D3C2211yescharacteristic
31C4×#634C2212yes—
32C4×#634C2211yescharacteristic
33C3×#946C2212yes—
34C3×#944C2212yes—
35C3×#896C2214yes—
36C3×D3×C4⋊C4C2212yes—
37C3×#889C2214yes—
38C3×#887C2212yes—
39C3×C4×D12C2211yescharacteristic
40C3×C4×D12C2212yes—
41C3×#870C2212yes—
42C3×#870C2212yes—
43C3×#869C2211yescharacteristic
44C3×#869C2211yescharacteristic
45C3×C4×Dic6C2212yes—
46C3×C4×Dic6C2211yescharacteristic
47#63919C2212yes—
48#63919C2212yes—
49#63918C2212yes—
50C4×#626C2212yes—
51C4×#626C2214yes—
52#63899C2214yes—
53#63898C2212yes—
54#63898C2211yescharacteristic
55#63896C2214yes—
56#63893C2214yes—
57#63881C2214yes—
58#63881C2212yes—
59#63878C2214yes—
60#63878C2212yes—
61D3×Dic3⋊C4C2214yes—
62C4×D3×Dic3C2212yes—
63C4×D3×Dic3C2214yes—
64#63872C2212yes—
65#63871C2212yes—
66#63871C2212yes—
67#63867C2214yes—
68#63865C2214yes—
69#63865C2214yes—
70#63856C2212yes—
71#63851C2214yes—
72#63849C2211yescharacteristic
73#63849C2212yes—
74#63845C2214yes—
75#63844C2212yes—
76#63843C2212yes—
77#63843C2211yescharacteristic
78#63843C2212yes—
79#63843C2212yes—
80#63840C2214yes—
81#63839C2214yes—
82#63838C2214yes—
83#63838C2214yes—
84#63837C2214yes—
85C3×#557—31no—
86C3×#554—31no—
87#5728—32no—
88#5728—31no—
89#5728—31no—
90#5727—32no—
91#5727—31no—
92#5722—31no—
93#5690—34no—
94#5690—32no—
95#5688—34no—
96#5688—32no—
97#5688—32no—
98#5685—32no—
99#5636—34no—
100#5632—32no—
101#5622—32no—
102#5622—34no—
103#5579—32no—
104#5579D311yescharacteristic, complemented
105C4×#239—32no—
106C4×#239—31no—
107C4×D3×Q8—31no—
108C4×D3×Q8—31no—
109C4×D3×Q8—32no—
110C4×D3×Q8—61no—
111#5569—32no—
112#5567D311yescharacteristic, complemented
113Q8×Dic6—31no—
114#5539—32no—
115D4×Dic6—31no—
116C4×#237—32no—
117C4×#237—31no—
118#5511—32no—
119C2×#887—32no—
120C2×C32×Q8C2311yescharacteristic
121Q8×C3⋊D3—24no—
122C2×C4×C3⋊D3C2312yes—
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2312yes—
125C2×C4×C3⋊D3C2311yescharacteristic
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×#634C2312yes—
128C2×#634C2311yescharacteristic
129C2×C3×D12C2311yescharacteristic
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2314yes—
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2312yes—
134C2×C3×Dic6C2311yescharacteristic
135C2×#627C2314yes—
136C2×#627C2314yes—
137C2×#626C2312yes—
138C2×D3×Dic3C2314yes—
139C2×D3×Dic3C2312yes—
140C2×D3×Dic3C2312yes—
141#3796Q818yescomplemented
142D3×Dic6—28no—
143C32×C4⋊C4C2311yescharacteristic
144C32×C4⋊C4C2312yes—
145C32×C42C2311yescharacteristic
146C32×C42C2312yes—
147C4⋊(C3⋊Dic3)C2312yes—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149#3750C2312yes—
150#3750C2312yes—
151#3750C2312yes—
152C4×C3⋊Dic3C2311yescharacteristic
153C4×C3⋊Dic3C2312yes—
154C4×C3⋊Dic3C2312yes—
155C4×C3⋊Dic3C2312yes—
156C4×C3⋊Dic3C2311yescharacteristic
157C4×C3⋊Dic3C2311yescharacteristic
158C3×(C2×D3)⋊C4C2312yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×C4⋊Dic3C2312yes—
161C3×C4⋊Dic3C2312yes—
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2311yescharacteristic
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×Dic3⋊C4C2314yes—
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2314yes—
169C3×Dic3⋊C4C2314yes—
170C3×Dic3⋊C4C2314yes—
171C3×Dic3⋊C4C2314yes—
172C3×C4×Dic3C2314yes—
173C3×C4×Dic3C2312yes—
174#3724C2314yes—
175#3724C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
180#3722C2312yes—
181#3722C2314yes—
182(C2×D3)⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2314yes—
184Dic32C2312yes—
185Dic32C2314yes—
186Dic32C2312yes—
187Dic32C2314yes—
188Q8×#41—91noSylow
189C2×#239—31no—
190C2×D3×Q8—31no—
191C2×D3×Q8—31no—
192C2×D3×Q8—32no—
193C2×D3×Q8—61no—
194C2×#237—31no—
195C22×Dic6—32no—
196C3×C4⋊Q8—32no—
197C3×C4⋊Q8—31no—
198C3×C4⋊Q8—31no—
199C3×#125—34no—
200C3×#125—32no—
201C3×#125—32no—
202C3×C22⋊Q8—32no—
203C3×C22⋊Q8—34no—
204C3×C4×Q8—21no—
205C3×C4×Q8—32no—
206C3×C4×Q8—31no—
207C3×C4×Q8—32no—
208C3×C4×Q8C2×D311yescharacteristic
209C3×C4×Q8C2×D311yescharacteristic
210C3×C4×D4—31no—
211C3×C4×D4—32no—
212C2×C3×C4⋊C4—32no—
213#946—32no—
214#946—32no—
215#946—32no—
216#946C2×D312yes—
217Q8×Dic3—31no—
218Q8×Dic3—31no—
219Q8×Dic3—32no—
220Q8×Dic3—32no—
221Q8×Dic3—32no—
222Q8×Dic3—31no—
223Q8×Dic3—61no—
224#944—34no—
225#944C2×D312yes—
226D4×Dic3—32no—
227D4×Dic3—31no—
228C4×#67—32no—
229C4×#67—34no—
230#924—32no—
231#924—34no—
232C2×Dic3⋊C4—34no—
233C2×C4×Dic3—34no—
234C2×C4×Dic3—32no—
235#897—32no—
236#897—32no—
237#897—34no—
238#896—34no—
239#896—34no—
240#896—34no—
241#896—34no—
242#896—34no—
243#896—34no—
244#896—34no—
245#896C2×D314yes—
246#893—31no—
247#893—32no—
248#893—32no—
249#893—34no—
250#892—32no—
251#892—34no—
252#892—31no—
253#892—31no—
254#892—32no—
255#892—32no—
256D3×C4⋊C4—34no—
257D3×C4⋊C4—32no—
258D3×C4⋊C4—32no—
259D3×C4⋊C4—31no—
260D3×C4⋊C4—31no—
261D3×C4⋊C4—62no—
262D3×C4⋊C4—61no—
263D3×C4⋊C4C2×D312yes—
264#890—32no—
265#890—32no—
266#890—34no—
267#889—34no—
268#889—34no—
269#889C2×D314yes—
270#888—34no—
271#888—32no—
272#888—32no—
273#888—32no—
274#888—32no—
275#888—34no—
276#888—34no—
277#888—32no—
278#887—31no—
279#887—32no—
280#887—32no—
281#887—32no—
282#887—32no—
283#887—31no—
284#887—31no—
285#887—32no—
286#887—34no—
287#887—34no—
288#887—34no—
289#887—34no—
290#887—32no—
291#887—34no—
292#887—61no—
293#887—62no—
294#887C2×D312yes—
295#67⋊C4—34no—
296#67⋊C4—32no—
297#878—34no—
298#878—34no—
299#878—34no—
300#877—34no—
301#877—32no—
302C4×D12—34no—
303C4×D12—32no—
304C4×D12C2×D312yes—
305C4×D12C2×D311yescharacteristic
306C42×D3—34no—
307C42×D3—32no—
308C42×D3—32no—
309C42×D3—32no—
310C42×D3—31no—
311C42×D3—31no—
312C42×D3—62no—
313C42×D3—61no—
314#870—34no—
315#870C2×D312yes—
316#870C2×D312yes—
317#869—32no—
318#869C2×D311yescharacteristic
319#869C2×D311yescharacteristic
320C4×Dic6—32no—
321C4×Dic6—32no—
322C4×Dic6—31no—
323C4×Dic6—31no—
324C4×Dic6—32no—
325C4×Dic6—34no—
326C4×Dic6—61no—
327C4×Dic6—62no—
328C4×Dic6C2×D312yes—
329C4×Dic6C2×D311yescharacteristic
330C22×C3⋊D3C2411yescharacteristic
331C22×C3×D3C2412yes—
332C32×Q8—22no—
333C2×C32×C4C2412yes—
334C2×C32×C4C2412yes—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2411yescharacteristic
338C2×C3⋊Dic3C2411yescharacteristic
339C2×C3⋊Dic3C2411yescharacteristic
340C2×C3⋊Dic3C2412yes—
341C2×C3⋊Dic3C2411yescharacteristic
342C2×C3⋊Dic3C2412yes—
343C4×C3⋊D3—22no—
344C4×C3⋊D3—24no—
345C4×C3⋊D3—41no—
346C4×C3⋊D3—42no—
347C4×C3⋊D3C2×Q814yescomplemented
348#634—24no—
349#634#4114yescomplemented
350C2×C3×Dic3C2414yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2414yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2412yes—
355C3×D12C2×Q814yescomplemented
356C3×C4×D3—24no—
357C3×C4×D3—44no—
358C3×Dic6—24no—
359C3×Dic6—42no—
360C3×Dic6C2×Q814yescomplemented
361#627—28no—
362#627—44no—
363#626C2×Q818yescomplemented
364D3×Dic3—28no—
365D3×Dic3—42no—
366D3×Dic3C2×Q818yescomplemented
367Q82—91no—
368#557—31no—
369#557—92no—
370#554—31no—
371#554—92no—
372#554—92no—
373#554—94no—
374D4×Q8—91no—
375D4×Q8—92no—
376#533—94no—
377#533—92no—
378#533—92no—
379#533—91no—
380C4×#41—91no—
381C4×#41—92no—
382C2×C4×Q8—92no—
383C2×C4×Q8—91no—
384C2×C3×Q8—21no—
385C2×C3×Q8—31no—
386C2×C3×Q8—32no—
387C2×C3×Q8—32no—
388C2×C3×Q8C22×D311yescharacteristic
389C2×C3×Q8C22×D311yescharacteristic
390C2×C3×D4—31no—
391C22×C3×C4—32no—
392C22×C3×C4—34no—
393C2×#67—32no—
394C22×Dic3—32no—
395C22×Dic3—34no—
396C22×Dic3—32no—
397#239—38no—
398D3×Q8—68no—
399D3×Q8—64no—
400D3×Q8—64no—
401D3×Q8—68no—
402#237—38no—
403C2×D12—32no—
404C2×D12C22×D311yescharacteristic
405C2×C4×D3—32no—
406C2×C4×D3—31no—
407C2×C4×D3—31no—
408C2×C4×D3—34no—
409C2×C4×D3—31no—
410C2×C4×D3—32no—
411C2×C4×D3—32no—
412C2×C4×D3—31no—
413C2×C4×D3—32no—
414C2×C4×D3—32no—
415C2×C4×D3—31no—
416C2×C4×D3—31no—
417C2×C4×D3—32no—
418C2×C4×D3—61no—
419C2×C4×D3—62no—
420C2×C4×D3—61no—
421C2×C4×D3—62no—
422C2×C4×D3—61no—
423C2×C4×D3C22×D312yes—
424C2×C4×D3C22×D314yes—
425C2×Dic6—31no—
426C2×Dic6—31no—
427C2×Dic6—32no—
428C2×Dic6—32no—
429C2×Dic6—34no—
430C2×Dic6—34no—
431C2×Dic6—34no—
432C2×Dic6—34no—
433C2×Dic6—61no—
434C2×Dic6—62no—
435C2×Dic6—68no—
436C2×Dic6C22×D312yes—
437C2×Dic6C22×D312yes—
438C2×Dic6C22×D311yescharacteristic
439C3×C4⋊C4—21no—
440C3×C4⋊C4—22no—
441C3×C4⋊C4—32no—
442C3×C4⋊C4—34no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—34no—
445C3×C4⋊C4—32no—
446C3×C4⋊C4—34no—
447C3×C4⋊C4—34no—
448C3×C4⋊C4—32no—
449C3×C4⋊C4—32no—
450C3×C4⋊C4—31no—
451C3×C4⋊C4—34no—
452C3×C4⋊C4—32no—
453C3×C4⋊C4C22×D311yescharacteristic
454C3×C4⋊C4C22×D312yes—
455C3×C4⋊C4C22×D311yescharacteristic
456C3×C4⋊C4C22×D312yes—
457C3×C22⋊C4—34no—
458C3×C22⋊C4—32no—
459C3×C42—22no—
460C3×C42—21no—
461C3×C42—32no—
462C3×C42—34no—
463C3×C42C22×D311yescharacteristic
464C3×C42C22×D312yes—
465C3×C42C22×D311yescharacteristic
466C3×C42C22×D312yes—
467#217—34no—
468#217—32no—
469(C2×D3)⋊C4—32no—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—32no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—32no—
474(C2×D3)⋊C4—34no—
475(C2×D3)⋊C4C22×D312yes—
476(C2×D3)⋊C4C22×D314yes—
477C4⋊Dic3—31no—
478C4⋊Dic3—32no—
479C4⋊Dic3—31no—
480C4⋊Dic3—32no—
481C4⋊Dic3—34no—
482C4⋊Dic3—34no—
483C4⋊Dic3—32no—
484C4⋊Dic3—34no—
485C4⋊Dic3—62no—
486C4⋊Dic3—61no—
487C4⋊Dic3C22×D312yes—
488C4⋊Dic3C22×D312yes—
489C4⋊Dic3C22×D311yescharacteristic
490C4⋊Dic3C22×D312yes—
491C4⋊Dic3C22×D312yes—
492C4⋊Dic3C22×D311yescharacteristic
493Dic3⋊C4—32no—
494Dic3⋊C4—32no—
495Dic3⋊C4—32no—
496Dic3⋊C4—32no—
497Dic3⋊C4—32no—
498Dic3⋊C4—32no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—32no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—62no—
508Dic3⋊C4—62no—
509Dic3⋊C4—62no—
510Dic3⋊C4C22×D314yes—
511Dic3⋊C4C22×D314yes—
512Dic3⋊C4C22×D312yes—
513Dic3⋊C4C22×D314yes—
514Dic3⋊C4C22×D314yes—
515Dic3⋊C4C22×D314yes—
516C4×Dic3—32no—
517C4×Dic3—31no—
518C4×Dic3—32no—
519C4×Dic3—31no—
520C4×Dic3—32no—
521C4×Dic3—31no—
522C4×Dic3—32no—
523C4×Dic3—31no—
524C4×Dic3—31no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—31no—
528C4×Dic3—34no—
529C4×Dic3—32no—
530C4×Dic3—32no—
531C4×Dic3—34no—
532C4×Dic3—32no—
533C4×Dic3—34no—
534C4×Dic3—34no—
535C4×Dic3—32no—
536C4×Dic3—61no—
537C4×Dic3—62no—
538C4×Dic3—62no—
539C4×Dic3—61no—
540C4×Dic3—61no—
541C4×Dic3—62no—
542C4×Dic3C22×D312yes—
543C4×Dic3C22×D314yes—
544C22×C32C2511yescharacteristic
545C2×C3⋊D3—21no—
546C2×C3⋊D3—21no—
547C2×C3⋊D3C22×Q812yes—
548C2×C3×D3—22no—
549C2×C3×D3—22no—
550C2×C3×D3C22×Q814yes—
551C32×C4—22no—
552C32×C4—21no—
553C32×C4—22no—
554C32×C4C22×Q812yes—
555C32×C4C2×#4112yes—
556C3⋊Dic3—21no—
557C3⋊Dic3—21no—
558C3⋊Dic3—22no—
559C3⋊Dic3C22×Q812yes—
560C3⋊Dic3C2×#4114yes—
561C3×Dic3—24no—
562C3×Dic3—22no—
563C3×Dic3—22no—
564C3×Dic3—24no—
565C3×Dic3C22×Q814yes—
566C2×#41—91no—
567C22×Q8—92no—
568C22×Q8—91no—
569C4⋊Q8—32no—
570C4⋊Q8—31no—
571C4⋊Q8—31no—
572C4⋊Q8—92no—
573C4⋊Q8—94no—
574C4⋊Q8—92no—
575C4⋊Q8—92no—
576C4⋊Q8—94no—
577#125—34no—
578#125—32no—
579#125—32no—
580#125—94no—
581#125—94no—
582#125—92no—
583C22⋊Q8—32no—
584C22⋊Q8—34no—
585C22⋊Q8—94no—
586C22⋊Q8—94no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—92no—
592C22⋊Q8—92no—
593C22⋊Q8—92no—
594C4×Q8—32no—
595C4×Q8—32no—
596C4×Q8—31no—
597C4×Q8—92no—
598C4×Q8—94no—
599C4×Q8—94no—
600C4×Q8—94no—
601C4×Q8—92no—
602C4×Q8—91no—
603C4×Q8—92no—
604C4×Q8—92no—
605C4×Q8—91no—
606C4×Q8—91no—
607C4×Q8—92no—
608C4×Q8—91no—
609C4×Q8—92no—
610C4×Q8D3211yescharacteristic
611C4×D4—31no—
612C4×D4—32no—
613C4×D4—92no—
614C4×D4—94no—
615C4×D4—94no—
616C4×D4—92no—
617C4×D4—92no—
618C4×D4—91no—
619#117—92no—
620#117—94no—
621#117—91no—
622#117—92no—
623C2×C4⋊C4—32no—
624C2×C4⋊C4—94no—
625C2×C4⋊C4—92no—
626C2×C4⋊C4—91no—
627C2×C42—94no—
628C2×C42—92no—
629C2×C42—91no—
630C2×C42—92no—
631C23×C3—32no—
632C22×D3—31no—
633C22×D3—31no—
634C22×D3—61no—
635C22×D3C23×D312yes—
636C3×Q8—24no—
637C3×Q8—22no—
638C3×Q8—22no—
639C3×Q8—34no—
640C3×Q8—64no—
641C3×Q8—122no—
642C3×D4—34no—
643C2×C3×C4—21no—
644C2×C3×C4—22no—
645C2×C3×C4—21no—
646C2×C3×C4—22no—
647C2×C3×C4—21no—
648C2×C3×C4—32no—
649C2×C3×C4—34no—
650C2×C3×C4—32no—
651C2×C3×C4—34no—
652C2×C3×C4—32no—
653C2×C3×C4—64no—
654C2×C3×C4—124no—
655C2×C3×C4C23×D312yes—
656C2×C3×C4C23×D311yescharacteristic
657C2×C3×C4C23×D312yes—
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D312yes—
660C2×C3×C4C23×D312yes—
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664C2×C3×C4C23×D311yescharacteristic
665#67—38no—
666C2×Dic3—31no—
667C2×Dic3—31no—
668C2×Dic3—32no—
669C2×Dic3—32no—
670C2×Dic3—38no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—31no—
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—31no—
677C2×Dic3—61no—
678C2×Dic3—62no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—62no—
682C2×Dic3—68no—
683C2×Dic3—122no—
684C2×Dic3C23×D312yes—
685C2×Dic3C23×D314yes—
686C2×Dic3C23×D312yes—
687C2×Dic3C23×D314yes—
688C2×Dic3C23×D312yes—
689D12—38no—
690D12D3×Q814yescomplemented
691C4×D3—24no—
692C4×D3—38no—
693C4×D3—34no—
694C4×D3—34no—
695C4×D3—44no—
696C4×D3—64no—
697C4×D3—64no—
698C4×D3—64no—
699C4×D3—68no—
700C4×D3—68no—
701C4×D3—64no—
702C4×D3—62no—
703C4×D3—62no—
704C4×D3—122no—
705C4×D3—121no—
706C4×D3—122no—
707C4×D3—121no—
708C4×D3—122no—
709C4×D3—124no—
710C4×D3—122no—
711Dic6—24no—
712Dic6—34no—
713Dic6—34no—
714Dic6—42no—
715Dic6—64no—
716Dic6—68no—
717Dic6—68no—
718Dic6—64no—
719Dic6—64no—
720Dic6—68no—
721Dic6—124no—
722Dic6—124no—
723Dic6D3×Q814yescomplemented
724C2×C32C23×Q811yescharacteristic
725C2×C32C22×#4111yescharacteristic
726C2×C32#58511yescharacteristic
727C3⋊D3—22no—
728C3×D3—24no—
729#41—98no—
730C2×Q8—31no—
731C2×Q8—32no—
732C2×Q8—32no—
733C2×Q8—94no—
734C2×Q8—94no—
735C2×Q8—91no—
736C2×Q8—92no—
737C2×Q8—188no—
738C2×Q8—184no—
739C2×Q8C2×D3211yescharacteristic
740C2×D4—31no—
741C2×D4—92no—
742C22×C4—32no—
743C22×C4—34no—
744C22×C4—92no—
745C22×C4—94no—
746C22×C4—92no—
747C22×C4—91no—
748C22×C4—92no—
749C22×C4—91no—
750C22×C4—91no—
751C22×C4—92no—
752C4⋊C4—34no—
753C4⋊C4—32no—
754C4⋊C4—34no—
755C4⋊C4—31no—
756C4⋊C4—32no—
757C4⋊C4—32no—
758C4⋊C4—31no—
759C4⋊C4—34no—
760C4⋊C4—32no—
761C4⋊C4—34no—
762C4⋊C4—34no—
763C4⋊C4—32no—
764C4⋊C4—94no—
765C4⋊C4—94no—
766C4⋊C4—92no—
767C4⋊C4—94no—
768C4⋊C4—94no—
769C4⋊C4—94no—
770C4⋊C4—92no—
771C4⋊C4—92no—
772C4⋊C4—92no—
773C4⋊C4—92no—
774C4⋊C4—91no—
775C4⋊C4C2×D3211yescharacteristic
776C4⋊C4C2×D3212yes—
777C22⋊C4—32no—
778C22⋊C4—34no—
779C22⋊C4—92no—
780C22⋊C4—94no—
781C22⋊C4—92no—
782C22⋊C4—94no—
783C42—34no—
784C42—32no—
785C42—92no—
786C42—94no—
787C42—92no—
788C42—94no—
789C42—92no—
790C42—91no—
791C42—92no—
792C42—91no—
793C42—91no—
794C42—92no—
795C42C2×D3212yes—
796C42C2×D3211yescharacteristic
797C22×C3—21no—
798C22×C3—34no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3C24×D311yescharacteristic
802C22×C3C24×D311yescharacteristic
803C2×D3—22no—
804C2×D3—22no—
805C2×D3—32no—
806C2×D3—32no—
807C2×D3—62no—
808C2×D3—62no—
809C2×D3—62no—
810C2×D3—61no—
811C2×D3—61no—
812C2×D3—61no—
813C2×D3—61no—
814C2×D3C2×D3×Q814yes—
815C3×C4—24no—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—21no—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—21no—
822C3×C4—22no—
823C3×C4—22no—
824C3×C4—34no—
825C3×C4—42no—
826C3×C4—41no—
827C3×C4—62no—
828C3×C4—64no—
829C3×C4—62no—
830C3×C4—64no—
831C3×C4C2×D3×Q812yes—
832C3×C4C2×D3×Q812yes—
833C3×C4D3×#4112yes—
834C3×C4D3×#4112yes—
835Dic3—24no—
836Dic3—22no—
837Dic3—24no—
838Dic3—22no—
839Dic3—32no—
840Dic3—32no—
841Dic3—34no—
842Dic3—34no—
843Dic3—64no—
844Dic3—62no—
845Dic3—62no—
846Dic3—61no—
847Dic3—61no—
848Dic3—62no—
849Dic3—61no—
850Dic3—62no—
851Dic3—61no—
852Dic3—121no—
853Dic3—122no—
854Dic3C2×D3×Q814yes—
855C32Q8×#4111yescharacteristic, complemented, Sylow
856C23—32no—
857C23—91no—
858Q8—22no—
859Q8—34no—
860Q8—64no—
861Q8—94no—
862Q8—122no—
863Q8—184no—
864Q8—188no—
865Q8—364no—
866D4—34no—
867D4—98no—
868C2×C4—32no—
869C2×C4—32no—
870C2×C4—34no—
871C2×C4—32no—
872C2×C4—34no—
873C2×C4—64no—
874C2×C4—98no—
875C2×C4—91no—
876C2×C4—92no—
877C2×C4—94no—
878C2×C4—91no—
879C2×C4—91no—
880C2×C4—92no—
881C2×C4—124no—
882C2×C4—184no—
883C2×C4—188no—
884C2×C4—182no—
885C2×C4—362no—
886C2×C4—361no—
887C2×C4—362no—
888C2×C4C22×D3212yes—
889C2×C4C22×D3212yes—
890C2×C4C22×D3211yescharacteristic
891C2×C4C22×D3211yescharacteristic
892C2×C4C22×D3211yescharacteristic
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—64no—
897C2×C3C22×D3×Q811yescharacteristic
898C2×C3C22×D3×Q811yescharacteristic
899C2×C3C2×D3×#4111yescharacteristic
900C2×C3C2×D3×#4111yescharacteristic
901C2×C3#596611yescharacteristic
902C2×C3#596811yescharacteristic
903D3—24no—
904D3—64no—
905D3—62no—
906D3—62no—
907C22—34no—
908C22—62no—
909C22—62no—
910C22—92no—
911C22—181no—
912C22—181no—
913C22C23×D3211yescharacteristic
914C4—22no—
915C4—22no—
916C4—21no—
917C4—34no—
918C4—62no—
919C4—64no—
920C4—64no—
921C4—62no—
922C4—94no—
923C4—92no—
924C4—181no—
925C4—181no—
926C4—182no—
927C4#6430612yes—
928C4D32×Q812yes—
929C3—21no—
930C3#8692311yescharacteristic, complemented
931C3#8701511yescharacteristic, complemented
932C2—64no—
933C2—182no—
934C2C2×#6430611yescharacteristic
935C2C2×D32×Q811yescharacteristic
936C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×#3796C22
hypercenterC4×Q8D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×Q8×C3⋊D3C2semidirect
2. C3×#5579C2semidirect
3. C3×#5567C2semidirect
4. #10595368C2semidirect
5. #10595361C2semidirect
6. #10594536C2semidirect
7. #10594394C2semidirect
8. #10594388C2semidirect
9. D3×#887C2semidirect
10. #10593941C2semidirect
11. #10593904C2semidirect
14. #10593866C2semidirect
15. #10593856C2semidirect
16. #10593854C2semidirect
17. #10593853C2semidirect
104. #5579D3semidirect
112. #5567D3semidirect
141. #3796Q8semidirect
347. C4×C3⋊D3C2×Q8semidirect
349. #634#41semidirect
355. C3×D12C2×Q8semidirect
360. C3×Dic6C2×Q8semidirect
363. #626C2×Q8semidirect
366. D3×Dic3C2×Q8semidirect
690. D12D3×Q8semidirect
723. Dic6D3×Q8semidirect
855. C32Q8×#41semidirect
930. C3#86923semidirect
931. C3#87015semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C3×#55792
C3×#55672
#105953682
#105953612
#105945362
#105943942
#105943882
D3×#8872
#105939412
#105939042
C4×#37962
#105938662
#105938562
#105938542
#105938532
#870153
#869233