Finite Group Databasebeta

← #11909798

Subgroups — #11909798

Order 1152.

2357 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5585C211yesmaximal, characteristic, complemented
3C3×#5579C211yesmaximal, characteristic, complemented
4#10595396C212yesmaximal, complemented
5#10595362C212yesmaximal, complemented
6#10594567C214yesmaximal, complemented
7#10594515C212yesmaximal, complemented
8#10594371C214yesmaximal, complemented
9#10594359C212yesmaximal, complemented
10#10593981C212yesmaximal, complemented
11#10593972C212yesmaximal, complemented
12#10593943C212yesmaximal, complemented
13#10593941C212yesmaximal, complemented
14#10593907C211yesmaximal, characteristic, complemented
15#10593906C211yesmaximal, characteristic, complemented
16#10593875C211yesmaximal, characteristic, complemented
17#10593856C211yesmaximal, characteristic, complemented
18#87055—31nomaximal
19#86936—31nomaximal
20C2×Q8×C3⋊D3C2211yescharacteristic
21C2×#3798C2214yes—
22C2×#3796C2212yes—
23C2×#3795C2212yes—
24C32×C4×Q8C2211yescharacteristic
25Q8×C3⋊Dic3C2211yescharacteristic
26C4⋊C4×C3⋊D3C2212yes—
27C4⋊C4×C3⋊D3C2211yescharacteristic
28#64096C2212yes—
29#64096C2211yescharacteristic
30C42×C3⋊D3C2211yescharacteristic
31C42×C3⋊D3C2212yes—
32C4×#634C2211yescharacteristic
33C4×#634C2212yes—
34C3×#947C2212yes—
35C3×#946C2212yes—
36C3×#896C2214yes—
37C3×#894C2214yes—
38C3×#893C2212yes—
39C3×D3×C4⋊C4C2212yes—
40C3×#875C2212yes—
41C3×#874C2211yescharacteristic
42C3×C4×D12C2211yescharacteristic
43C3×C4×D12C2212yes—
44C3×C4×D12C2212yes—
45C3×#870C2212yes—
46C3×#869C2211yescharacteristic
47C3×C4×Dic6C2211yescharacteristic
48#63919C2212yes—
49#63918C2212yes—
50#63916C2212yes—
51#63916C2211yescharacteristic
52#63916C2212yes—
53#63915C2214yes—
54#63914C2212yes—
55#63913C2214yes—
56#63912C2214yes—
57#63908C2212yes—
58#63905C2214yes—
59C4×#626C2212yes—
60C4×#625C2214yes—
61#63898C2212yes—
62#63898C2212yes—
63#63898C2212yes—
64#63896C2214yes—
65#63893C2214yes—
66#63891C2214yes—
67#63885C2214yes—
68#63881C2214yes—
69#63879C2214yes—
70#63878C2214yes—
71D3×Dic3⋊C4C2214yes—
72#63872C2211yescharacteristic
73#63871C2211yescharacteristic
74#63863C2212yes—
75#63863C2211yescharacteristic
76#63862C2212yes—
77#63862C2214yes—
78#63855C2212yes—
79#63853C2212yes—
80#63853C2214yes—
81#63851C2214yes—
82#63844C2212yes—
83#63843C2212yes—
84#63839C2214yes—
85C3×#559—31no—
86C3×#554—31no—
87#5725—31no—
88#5722—31no—
89#5718—31no—
90#5716—31no—
91#5691—32no—
92#5690—32no—
93#5682—32no—
94#5681—32no—
95#5680—32no—
96#5677—32no—
97#5662—34no—
98#5655—34no—
99#5643—32no—
100#5640—34no—
101#5633—32no—
102#5631—34no—
103#5585D311yescharacteristic, complemented
104#5580—31no—
105#5579D311yescharacteristic, complemented
106C4×D3×Q8—31no—
107C4×D3×Q8—31no—
108C4×D3×Q8—61no—
109Q8×Dic6—31no—
110#5559—32no—
111#5557—31no—
112#5553—31no—
113#5551—32no—
114#5548—32no—
115#5548—32no—
116#5546—32no—
117#5539—32no—
118#5507—32no—
119#5504—32no—
120C2×C32×Q8C2311yescharacteristic
121Q8×C3⋊D3—24no—
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2312yes—
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×C4×C3⋊D3C2312yes—
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×#634C2312yes—
128C2×#634C2311yescharacteristic
129C2×C3×D12C2312yes—
130C2×C3×D12C2311yescharacteristic
131C2×C3×D12C2312yes—
132C2×C3×D12C2312yes—
133C2×C3×C4×D3C2312yes—
134C2×C3×C4×D3C2314yes—
135C2×C3×C4×D3C2314yes—
136C2×C3×Dic6C2311yescharacteristic
137C2×C3×Dic6C2312yes—
138C2×#627C2314yes—
139C2×#626C2314yes—
140C2×#626C2312yes—
141C2×#625C2314yes—
142C2×#625C2314yes—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2314yes—
145#3798—48no—
146#3796—44no—
147#3795—28no—
148C32×C4⋊C4C2311yescharacteristic
149C32×C4⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151C32×C42C2312yes—
152C4⋊(C3⋊Dic3)C2312yes—
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154#3750C2312yes—
155#3750C2312yes—
156#3750C2312yes—
157C4×C3⋊Dic3C2312yes—
158C4×C3⋊Dic3C2311yescharacteristic
159C4×C3⋊Dic3C2311yescharacteristic
160C4×C3⋊Dic3C2312yes—
161C4×C3⋊Dic3C2311yescharacteristic
162C4×C3⋊Dic3C2312yes—
163C3×(C2×D3)⋊C4C2314yes—
164C3×(C2×D3)⋊C4C2314yes—
165C3×(C2×D3)⋊C4C2314yes—
166C3×(C2×D3)⋊C4C2312yes—
167C3×(C2×D3)⋊C4C2314yes—
168C3×C4⋊Dic3C2312yes—
169C3×C4⋊Dic3C2312yes—
170C3×C4⋊Dic3C2311yescharacteristic
171C3×C4⋊Dic3C2311yescharacteristic
172C3×Dic3⋊C4C2314yes—
173C3×Dic3⋊C4C2312yes—
174C3×Dic3⋊C4C2314yes—
175C3×C4×Dic3C2312yes—
176#3724C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2312yes—
181#3722C2312yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2312yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2312yes—
188Dic32C2314yes—
189#3522—91noSylow
190C2×#239—32no—
191C2×D3×Q8—31no—
192C2×D3×Q8—31no—
193C2×D3×Q8—61no—
194C2×#237—32no—
195C2×#237—32no—
196C2×#235—32no—
197C2×#235—34no—
198C2×#235—34no—
199C3×C4⋊Q8—31no—
200C3×#127—31no—
201C3×#125—32no—
202C3×#124—32no—
203C3×#124—32no—
204C3×#123—34no—
205C3×C22⋊Q8—32no—
206C3×C22⋊Q8—34no—
207C3×C4×Q8—21no—
208C3×C4×Q8—31no—
209C3×C4×Q8C2×D311yescharacteristic
210C3×C4×Q8C2×D311yescharacteristic
211C3×C4×D4—32no—
212C3×C4×D4—32no—
213C3×C4×D4—32no—
214C3×C4×D4—31no—
215C2×C3×C4⋊C4—32no—
216#947—32no—
217#947—31no—
218#947C2×D312yes—
219#946—31no—
220#946C2×D312yes—
221Q8×Dic3—31no—
222Q8×Dic3—31no—
223Q8×Dic3—32no—
224Q8×Dic3—61no—
225#944—34no—
226#940—32no—
227#940—32no—
228#939—34no—
229#938—32no—
230#938—32no—
231#938—32no—
232#938—31no—
233#936—32no—
234#936—31no—
235D4×Dic3—32no—
236D4×Dic3—32no—
237D4×Dic3—32no—
238#930—32no—
239#929—34no—
240C4×#67—34no—
241C4×#67—34no—
242C4×#67—34no—
243C4×#67—32no—
244#926—32no—
245#924—34no—
246C2×Dic3⋊C4—34no—
247#898—34no—
248#898—32no—
249#897—31no—
250#897—34no—
251#896—34no—
252#896—34no—
253#896C2×D314yes—
254#895—32no—
255#895—32no—
256#895—31no—
257#894—32no—
258#894—34no—
259#894C2×D314yes—
260#893—32no—
261#893—32no—
262#893—32no—
263#893—34no—
264#893C2×D312yes—
265#892—34no—
266D3×C4⋊C4—34no—
267D3×C4⋊C4—32no—
268D3×C4⋊C4—31no—
269D3×C4⋊C4—31no—
270D3×C4⋊C4—32no—
271D3×C4⋊C4—62no—
272D3×C4⋊C4—61no—
273D3×C4⋊C4C2×D312yes—
274#890—31no—
275#890—31no—
276#888—34no—
277#888—32no—
278#888—32no—
279#888—32no—
280#887—32no—
281#887—32no—
282#887—32no—
283#887—31no—
284#887—31no—
285#887—32no—
286#887—61no—
287#887—62no—
288#886—34no—
289#885—34no—
290#885—34no—
291#885—34no—
292#885—34no—
293#884—34no—
294#884—34no—
295#884—34no—
296#883—34no—
297#883—34no—
298#883—34no—
299#883—32no—
300#67⋊C4—34no—
301#67⋊C4—34no—
302#879—32no—
303#879—34no—
304#878—34no—
305#878—34no—
306#877—34no—
307#875C2×D312yes—
308#874C2×D311yescharacteristic
309C4×D12—32no—
310C4×D12C2×D312yes—
311C4×D12C2×D312yes—
312C4×D12C2×D311yescharacteristic
313#872—32no—
314C42×D3—32no—
315C42×D3—32no—
316C42×D3—31no—
317C42×D3—31no—
318C42×D3—61no—
319C42×D3—62no—
320#870C2×D312yes—
321#869—32no—
322#869C2×D311yescharacteristic
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—31no—
326C4×Dic6—31no—
327C4×Dic6—32no—
328C4×Dic6—61no—
329C4×Dic6—62no—
330C4×Dic6C2×D311yescharacteristic
331C22×C3⋊D3C2411yescharacteristic
332C22×C3×D3C2414yes—
333C22×C3×D3C2412yes—
334C32×Q8—22no—
335C2×C32×C4C2412yes—
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2412yes—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C3⋊Dic3C2411yescharacteristic
341C2×C3⋊Dic3C2411yescharacteristic
342C2×C3⋊Dic3C2411yescharacteristic
343C2×C3⋊Dic3C2412yes—
344C2×C3⋊Dic3C2412yes—
345C4×C3⋊D3—22no—
346C4×C3⋊D3—22no—
347C4×C3⋊D3—24no—
348C4×C3⋊D3—22no—
349C4×C3⋊D3—24no—
350#634—24no—
351#634#4114yescomplemented
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2414yes—
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2412yes—
356C3×D12—24no—
357C3×D12—22no—
358C3×D12—24no—
359C3×D12—42no—
360C3×C4×D3—24no—
361C3×C4×D3—44no—
362C3×C4×D3—44no—
363C3×Dic6—22no—
364C3×Dic6—42no—
365#627—44no—
366#626—28no—
367#626—24no—
368#625—28no—
369#625—44no—
370D3×Dic3—28no—
371D3×Dic3—44no—
372#559—31no—
373#559—92no—
374Q82—91no—
375#554—31no—
376#554—92no—
377#550—91no—
378#548—92no—
379#547—92no—
380#547—94no—
381#542—94no—
382#542—92no—
383#532—92no—
384#532—91no—
385#529—91no—
386#529—92no—
387#520—92no—
388C2×C4×Q8—91no—
389C2×C3×Q8—21no—
390C2×C3×Q8—31no—
391C2×C3×Q8—32no—
392C2×C3×Q8C22×D311yescharacteristic
393C2×C3×Q8C22×D311yescharacteristic
394C2×C3×D4—32no—
395C2×C3×D4—32no—
396C2×C3×D4—31no—
397C2×C3×D4—32no—
398C22×C3×C4—32no—
399C22×C3×C4—34no—
400C22×C3×C4—34no—
401C2×#67—34no—
402C2×#67—34no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—34no—
406C2×#67—32no—
407C22×Dic3—34no—
408C22×Dic3—34no—
409#239—124no—
410D3×Q8—64no—
411D3×Q8—64no—
412D3×Q8—68no—
413#237—68no—
414#237—124no—
415#235—68no—
416#235—128no—
417#235—128no—
418C2×D12—32no—
419C2×D12—34no—
420C2×D12C22×D311yescharacteristic
421C2×D12C22×D312yes—
422C2×D12C22×D312yes—
423C2×D12C22×D312yes—
424C2×C4×D3—34no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—32no—
429C2×C4×D3—32no—
430C2×C4×D3—31no—
431C2×C4×D3—32no—
432C2×C4×D3—32no—
433C2×C4×D3—31no—
434C2×C4×D3—31no—
435C2×C4×D3—34no—
436C2×C4×D3—61no—
437C2×C4×D3—62no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—62no—
441C2×C4×D3C22×D312yes—
442C2×C4×D3C22×D314yes—
443C2×C4×D3C22×D314yes—
444C2×Dic6—31no—
445C2×Dic6—31no—
446C2×Dic6—32no—
447C2×Dic6—32no—
448C2×Dic6—34no—
449C2×Dic6—34no—
450C2×Dic6—61no—
451C2×Dic6—62no—
452C2×Dic6C22×D311yescharacteristic
453C2×Dic6C22×D312yes—
454C3×C4⋊C4—21no—
455C3×C4⋊C4—22no—
456C3×C4⋊C4—32no—
457C3×C4⋊C4—32no—
458C3×C4⋊C4—31no—
459C3×C4⋊C4—32no—
460C3×C4⋊C4—31no—
461C3×C4⋊C4—34no—
462C3×C4⋊C4—34no—
463C3×C4⋊C4C22×D311yescharacteristic
464C3×C4⋊C4C22×D311yescharacteristic
465C3×C4⋊C4C22×D312yes—
466C3×C4⋊C4C22×D312yes—
467C3×C22⋊C4—34no—
468C3×C22⋊C4—34no—
469C3×C22⋊C4—34no—
470C3×C22⋊C4—32no—
471C3×C22⋊C4—34no—
472C3×C42—22no—
473C3×C42—21no—
474C3×C42—32no—
475C3×C42C22×D311yescharacteristic
476C3×C42C22×D311yescharacteristic
477C3×C42C22×D312yes—
478C3×C42C22×D312yes—
479#217—34no—
480#217—34no—
481#217—34no—
482#217—32no—
483#217—32no—
484#217—32no—
485(C2×D3)⋊C4—32no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—32no—
492(C2×D3)⋊C4—32no—
493(C2×D3)⋊C4C22×D314yes—
494(C2×D3)⋊C4C22×D314yes—
495(C2×D3)⋊C4C22×D312yes—
496(C2×D3)⋊C4C22×D314yes—
497(C2×D3)⋊C4C22×D314yes—
498C4⋊Dic3—31no—
499C4⋊Dic3—32no—
500C4⋊Dic3—32no—
501C4⋊Dic3—31no—
502C4⋊Dic3—34no—
503C4⋊Dic3—32no—
504C4⋊Dic3—32no—
505C4⋊Dic3—32no—
506C4⋊Dic3—61no—
507C4⋊Dic3—62no—
508C4⋊Dic3C22×D312yes—
509C4⋊Dic3C22×D311yescharacteristic
510C4⋊Dic3C22×D312yes—
511C4⋊Dic3C22×D311yescharacteristic
512Dic3⋊C4—32no—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—32no—
516Dic3⋊C4—32no—
517Dic3⋊C4—32no—
518Dic3⋊C4—34no—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—32no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—62no—
525Dic3⋊C4—62no—
526Dic3⋊C4—62no—
527Dic3⋊C4C22×D312yes—
528Dic3⋊C4C22×D314yes—
529Dic3⋊C4C22×D314yes—
530C4×Dic3—32no—
531C4×Dic3—32no—
532C4×Dic3—31no—
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—32no—
536C4×Dic3—32no—
537C4×Dic3—31no—
538C4×Dic3—32no—
539C4×Dic3—32no—
540C4×Dic3—31no—
541C4×Dic3—31no—
542C4×Dic3—34no—
543C4×Dic3—34no—
544C4×Dic3—61no—
545C4×Dic3—62no—
546C4×Dic3—62no—
547C4×Dic3—61no—
548C4×Dic3—61no—
549C4×Dic3—62no—
550C4×Dic3C22×D312yes—
551C22×C32C2511yescharacteristic
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3H(5,𝔽2)12yes—
555C2×C3×D3—24no—
556C2×C3×D3—22no—
557C2×C3×D3—24no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—24no—
561C32×C4—22no—
562C32×C4—21no—
563C32×C4—22no—
564C32×C4C2×#4112yes—
565C32×C42−1+412yes—
566C3⋊Dic3—21no—
567C3⋊Dic3—21no—
568C3⋊Dic3—21no—
569C3⋊Dic3—22no—
570C3⋊Dic3C2×#4114yes—
571C3×Dic3—22no—
572C3×Dic3—24no—
573C3×Dic3—22no—
574C3×Dic3—22no—
575C2×#41—94no—
576C2×#41—92no—
577C2×#41—92no—
578C22×Q8—91no—
579C4⋊Q8—31no—
580C4⋊Q8—92no—
581C4⋊Q8—92no—
582C4⋊Q8—94no—
583#127—31no—
584#127—92no—
585#126—92no—
586#126—94no—
587#125—32no—
588#125—91no—
589#124—32no—
590#124—32no—
591#124—94no—
592#124—94no—
593#124—91no—
594#124—92no—
595#123—34no—
596#123—94no—
597#123—94no—
598#123—92no—
599#123—94no—
600C22⋊Q8—32no—
601C22⋊Q8—34no—
602C22⋊Q8—94no—
603C22⋊Q8—94no—
604C22⋊Q8—94no—
605C22⋊Q8—91no—
606#121—94no—
607#121—94no—
608#121—91no—
609#121—92no—
610#121—92no—
611#121—92no—
612C4×Q8—31no—
613C4×Q8—92no—
614C4×Q8—92no—
615C4×Q8—91no—
616C4×Q8—91no—
617C4×Q8—92no—
618C4×Q8—91no—
619C4×Q8—92no—
620C4×Q8D3211yescharacteristic
621C4×D4—32no—
622C4×D4—31no—
623C4×D4—32no—
624C4×D4—32no—
625C4×D4—92no—
626C4×D4—94no—
627C4×D4—94no—
628C4×D4—92no—
629C4×D4—92no—
630C4×D4—92no—
631C4×D4—94no—
632#117—92no—
633#117—94no—
634C2×C4⋊C4—32no—
635C2×C4⋊C4—94no—
636C2×C4⋊C4—92no—
637C2×C4⋊C4—91no—
638C2×C42—91no—
639C2×C42—92no—
640C23×C3—34no—
641C23×C3—32no—
642C22×D3—31no—
643C22×D3—31no—
644C22×D3—61no—
645C22×D3C23×D314yes—
646C22×D3C23×D312yes—
647C3×Q8—24no—
648C3×Q8—22no—
649C3×Q8—22no—
650C3×Q8—62no—
651C3×Q8—122no—
652C3×D4—64no—
653C3×D4—64no—
654C3×D4—62no—
655C3×D4—122no—
656C2×C3×C4—21no—
657C2×C3×C4—22no—
658C2×C3×C4—21no—
659C2×C3×C4—22no—
660C2×C3×C4—21no—
661C2×C3×C4—32no—
662C2×C3×C4—34no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—64no—
666C2×C3×C4—124no—
667C2×C3×C4—124no—
668C2×C3×C4C23×D312yes—
669C2×C3×C4C23×D311yescharacteristic
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D312yes—
672C2×C3×C4C23×D312yes—
673C2×C3×C4C23×D312yes—
674C2×C3×C4C23×D311yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D311yescharacteristic
678#67—64no—
679#67—68no—
680#67—68no—
681#67—68no—
682#67—124no—
683#67—124no—
684C2×Dic3—32no—
685C2×Dic3—32no—
686C2×Dic3—31no—
687C2×Dic3—31no—
688C2×Dic3—32no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—32no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—61no—
695C2×Dic3—62no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—62no—
699C2×Dic3—68no—
700C2×Dic3—124no—
701C2×Dic3C23×D312yes—
702C2×Dic3C23×D314yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705D12—22no—
706D12—24no—
707D12—24no—
708D12—42no—
709D12—64no—
710D12—68no—
711C4×D3—24no—
712C4×D3—44no—
713C4×D3—44no—
714C4×D3—64no—
715C4×D3—64no—
716C4×D3—68no—
717C4×D3—64no—
718C4×D3—64no—
719C4×D3—62no—
720C4×D3—62no—
721C4×D3—64no—
722C4×D3—68no—
723C4×D3—64no—
724C4×D3—62no—
725C4×D3—62no—
726C4×D3—62no—
727C4×D3—62no—
728C4×D3—122no—
729C4×D3—124no—
730C4×D3—124no—
731Dic6—22no—
732Dic6—34no—
733Dic6—34no—
734Dic6—42no—
735Dic6—64no—
736Dic6—64no—
737Dic6—64no—
738Dic6—68no—
739Dic6—124no—
740Dic6—124no—
741C2×C32C22×#4111yescharacteristic
742C2×C32C2×H(5,𝔽2)11yescharacteristic
743C2×C32C2×2−1+411yescharacteristic
744C3⋊D3—22no—
745C3×D3—44no—
746C3×D3—42no—
747#41—188no—
748#41—368no—
749#41—364no—
750C2×Q8—31no—
751C2×Q8—32no—
752C2×Q8—94no—
753C2×Q8—91no—
754C2×Q8—92no—
755C2×Q8—184no—
756C2×Q8C2×D3211yescharacteristic
757C2×D4—31no—
758C2×D4—32no—
759C2×D4—32no—
760C2×D4—32no—
761C2×D4—92no—
762C2×D4—94no—
763C2×D4—94no—
764C2×D4—94no—
765C22×C4—32no—
766C22×C4—34no—
767C22×C4—34no—
768C22×C4—94no—
769C22×C4—94no—
770C22×C4—91no—
771C22×C4—91no—
772C22×C4—92no—
773C22×C4—92no—
774C22×C4—91no—
775C4⋊C4—34no—
776C4⋊C4—32no—
777C4⋊C4—31no—
778C4⋊C4—31no—
779C4⋊C4—32no—
780C4⋊C4—34no—
781C4⋊C4—32no—
782C4⋊C4—92no—
783C4⋊C4—94no—
784C4⋊C4—92no—
785C4⋊C4—92no—
786C4⋊C4—94no—
787C4⋊C4—92no—
788C4⋊C4—92no—
789C4⋊C4—91no—
790C4⋊C4—92no—
791C4⋊C4—92no—
792C4⋊C4C2×D3211yescharacteristic
793C4⋊C4C2×D3212yes—
794C22⋊C4—34no—
795C22⋊C4—32no—
796C22⋊C4—34no—
797C22⋊C4—34no—
798C22⋊C4—34no—
799C22⋊C4—92no—
800C22⋊C4—92no—
801C22⋊C4—94no—
802C22⋊C4—92no—
803C22⋊C4—94no—
804C22⋊C4—94no—
805C22⋊C4—92no—
806C42—32no—
807C42—94no—
808C42—92no—
809C42—91no—
810C42—91no—
811C42—92no—
812C42—91no—
813C42—92no—
814C42C2×D3212yes—
815C42C2×D3211yescharacteristic
816C22×C3—21no—
817C22×C3—64no—
818C22×C3—64no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—64no—
822C22×C3—62no—
823C22×C3C24×D311yescharacteristic
824C22×C3C24×D311yescharacteristic
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—24no—
828C2×D3—24no—
829C2×D3—22no—
830C2×D3—24no—
831C2×D3—32no—
832C2×D3—32no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—61no—
840C3×C4—24no—
841C3×C4—22no—
842C3×C4—22no—
843C3×C4—21no—
844C3×C4—22no—
845C3×C4—22no—
846C3×C4—21no—
847C3×C4—22no—
848C3×C4—22no—
849C3×C4—42no—
850C3×C4—41no—
851C3×C4—62no—
852C3×C4—62no—
853C3×C4—62no—
854C3×C4—64no—
855C3×C4#100712yes—
856C3×C4D3×#4112yes—
857C3×C4D3×#4112yes—
858C3×C4#101012yes—
859Dic3—22no—
860Dic3—22no—
861Dic3—24no—
862Dic3—22no—
863Dic3—34no—
864Dic3—34no—
865Dic3—64no—
866Dic3—62no—
867Dic3—62no—
868Dic3—61no—
869Dic3—61no—
870Dic3—61no—
871Dic3—61no—
872Dic3—62no—
873Dic3—62no—
874Dic3—61no—
875Dic3—61no—
876Dic3—121no—
877Dic3—122no—
878C32#352211yescharacteristic, complemented, Sylow
879C23—32no—
880C23—34no—
881C23—91no—
882Q8—22no—
883Q8—62no—
884Q8—94no—
885Q8—122no—
886Q8—184no—
887Q8—364no—
888D4—64no—
889D4—62no—
890D4—64no—
891D4—122no—
892D4—184no—
893D4—188no—
894D4—188no—
895D4—364no—
896C2×C4—32no—
897C2×C4—32no—
898C2×C4—34no—
899C2×C4—32no—
900C2×C4—64no—
901C2×C4—92no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—91no—
905C2×C4—92no—
906C2×C4—124no—
907C2×C4—124no—
908C2×C4—184no—
909C2×C4—184no—
910C2×C4—182no—
911C2×C4—188no—
912C2×C4—182no—
913C2×C4—182no—
914C2×C4—364no—
915C2×C4C22×D3212yes—
916C2×C4C22×D3212yes—
917C2×C4C22×D3211yescharacteristic
918C2×C4C22×D3211yescharacteristic
919C2×C4C22×D3211yescharacteristic
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—122no—
924C2×C3—124no—
925C2×C3C2×#100711yescharacteristic
926C2×C3C2×D3×#4111yescharacteristic
927C2×C3C2×D3×#4111yescharacteristic
928C2×C3C2×#101011yescharacteristic
929C2×C3D3×H(5,𝔽2)11yescharacteristic
930C2×C3D3×H(5,𝔽2)11yescharacteristic
931D3—44no—
932D3—42no—
933D3—64no—
934D3—62no—
935D3—62no—
936C22—62no—
937C22—64no—
938C22—62no—
939C22—64no—
940C22—62no—
941C22—64no—
942C22—92no—
943C22—181no—
944C22—181no—
945C22C23×D3211yescharacteristic
946C4—22no—
947C4—22no—
948C4—21no—
949C4—62no—
950C4—62no—
951C4—62no—
952C4—64no—
953C4—94no—
954C4—181no—
955C4—181no—
956C4—181no—
957C4—182no—
958C4#6430612yes—
959C4#6431512yes—
960C3—21no—
961C3#8693611yescharacteristic, complemented
962C3#8705511yescharacteristic, complemented
963C2—122no—
964C2—124no—
965C2—182no—
966C2C2×#6430611yescharacteristic
967C2C2×#6431511yescharacteristic
968C2#1059669211yescharacteristic
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. C4×Q8×C3⋊D3C2semidirect
2. C3×#5585C2semidirect
3. C3×#5579C2semidirect
4. #10595396C2semidirect
5. #10595362C2semidirect
6. #10594567C2semidirect
7. #10594515C2semidirect
8. #10594371C2semidirect
9. #10594359C2semidirect
10. #10593981C2semidirect
11. #10593972C2semidirect
12. #10593943C2semidirect
13. #10593941C2semidirect
14. #10593907C2semidirect
15. #10593906C2semidirect
16. #10593875C2semidirect
17. #10593856C2semidirect
103. #5585D3semidirect
105. #5579D3semidirect
351. #634#41semidirect
878. C32#3522semidirect
961. C3#86936semidirect
962. C3#87055semidirect

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×#55852
C3×#55792
#105953962
#105953622
#105945672
#105945152
#105943712
#105943592
#105939812
#105939722
#105939432
#105939412
#105939072
#105939062
#105938752
#105938562
#870553
#869363