Finite Group Databasebeta

← #11909309

Subgroups — #11909309

Order 1152.

2359 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic, complemented
2C3×#5732C211yesmaximal, characteristic, complemented
3C3×#5726C211yesmaximal, characteristic, complemented
4#10595428C212yesmaximal, complemented
5#10595396C212yesmaximal, complemented
6#10595394C212yesmaximal, complemented
7#10595371C212yesmaximal, complemented
8#10594648C214yesmaximal, complemented
9#10594626C212yesmaximal, complemented
10D3×#897C212yesmaximal, complemented
11#10594550C212yesmaximal, complemented
12#10594525C212yesmaximal, complemented
13#10594436C214yesmaximal, complemented
14C4×#3802C211yesmaximal, characteristic, complemented
15Dic6×D12C211yesmaximal, characteristic, complemented
16#10593895C211yesmaximal, characteristic, complemented
17#10593875C211yesmaximal, characteristic, complemented
18#86990—31nomaximal
19#86685—31nomaximal
20C2×C3×#239C2212yes—
21C2×#3802C2211yescharacteristic
22C2×C4×D32C2212yes—
23C2×#3795C2212yescomplemented
24C2×D3×Dic6C2212yescomplemented
25C32×C4⋊Q8C2211yescharacteristic, complemented
26#64155C2212yes—
27Q8×C3⋊Dic3C2212yescomplemented
28#64106C2212yes—
29#64101C2212yes—
30#64099C2212yescomplemented
31#64096C2212yescomplemented
32C42×C3⋊D3C2211yescharacteristic
33#64078C2211yescharacteristic, complemented
34C3×#947C2212yes—
35C3×#946C2212yescomplemented
36C3×Q8×Dic3C2212yescomplemented
37C3×#898C2214yescomplemented
38C3×#897C2212yescomplemented
39C3×#895C2212yescomplemented
40C3×#894C2214yescomplemented
41C3×#892C2212yescomplemented
42C3×D3×C4⋊C4C2212yescomplemented
43C3×C4×D12C2211yescharacteristic
44C3×C4×D12C2211yescharacteristic
45C3×C4×D12C2211yescharacteristic, complemented
46C3×C4×Dic6C2211yescharacteristic, complemented
47#63922C2214yes—
48#63921C2212yes—
49D3×(C2×D3)⋊C4C2214yes—
50#63918C2212yescomplemented
51#63916C2211yescharacteristic
52#63915C2214yescomplemented
53#63908C2212yes—
54#63905C2214yes—
55C4×#626C2212yes—
56#63902C2212yes—
57C4×#625C2212yes—
58#63900C2211yescharacteristic
59#63899C2214yescomplemented
60#63898C2211yescharacteristic
61#63898C2211yescharacteristic
62#63898C2214yescomplemented
63#63895C2214yes—
64#63893C2214yescomplemented
65#63893C2214yescomplemented
66Dic3×D12C2212yes—
67Dic3×D12C2214yescomplemented
68#63891C2214yescomplemented
69#63891C2214yescomplemented
70D3×C4⋊Dic3C2212yescomplemented
71D3×C4⋊Dic3C2214yescomplemented
72#63885C2214yes—
73#63880C2214yes—
74#63872C2211yescharacteristic, complemented
75#63871C2211yescharacteristic
76#63867C2214yescomplemented
77#63863C2211yescharacteristic, complemented
78#63862C2214yescomplemented
79#63862C2212yescomplemented
80#63857C2212yescomplemented
81#63857C2212yescomplemented
82#63855C2212yescomplemented
83#63855C2214yescomplemented
84#63853C2212yes—
85C3×#556—31no—
86C3×#547—31no—
87#5829—32no—
88#5827—32no—
89#5732D311yescharacteristic, complemented
90#5728—31no—
91#5728—31no—
92#5728—61no—
93#5726D311yescharacteristic, complemented
94#5707—34no—
95#5705—34no—
96#5682—32no—
97#5676—32no—
98#5665—34no—
99#5658—34no—
100#5643—32no—
101#5635—32no—
102#5633—32no—
103D3×C22⋊Q8—32no—
104#5606—32no—
105#5598—32no—
106#5580—31no—
107#5579—32no—
108Q8×D12—31no—
109#5574—32no—
110#5557—31no—
111#5555—31no—
112#5551—31no—
113C4×D3×D4—31no—
114C4×D3×D4—31no—
115D4×Dic6—31no—
116#5529—32no—
117#5524—32no—
118#5513—32no—
119C2×#897—32no—
120C22×D32C2312yes—
121C2×C32×Q8C2312yes—
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×#634C2312yes—
126C3×#239—28no—
127C2×C3×D12C2314yes—
128C2×C3×D12C2311yescharacteristic
129C2×C3×D12C2311yescharacteristic
130C2×C3×D12C2311yescharacteristic
131C2×C3×C4×D3C2314yes—
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2312yes—
134C2×C3×C4×D3C2312yes—
135C2×C3×Dic6C2311yescharacteristic
136C2×#627C2314yes—
137C2×#626C2312yes—
138C2×#625C2312yes—
139C2×#625C2314yes—
140C2×#624C2312yes—
141C2×D3×Dic3C2314yes—
142C2×D3×Dic3C2314yes—
143C2×D3×Dic3C2312yes—
144C2×D3×Dic3C2312yes—
145#3802—24no—
146C4×D32—44no—
147#3795—44no—
148D3×Dic6—44no—
149C32×C4⋊C4C2312yes—
150C32×C4⋊C4C2312yes—
151C32×C42C2311yescharacteristic
152#3752C2314yes—
153C4⋊(C3⋊Dic3)C2312yes—
154C4⋊(C3⋊Dic3)C2312yes—
155C4⋊(C3⋊Dic3)C2314yes—
156#3750C2314yes—
157C4×C3⋊Dic3C2311yescharacteristic
158C4×C3⋊Dic3C2311yescharacteristic
159C4×C3⋊Dic3C2311yescharacteristic
160C4×C3⋊Dic3C2314yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×(C2×D3)⋊C4C2312yes—
163C3×(C2×D3)⋊C4C2312yes—
164C3×(C2×D3)⋊C4C2314yes—
165C3×(C2×D3)⋊C4C2314yes—
166C3×(C2×D3)⋊C4C2312yes—
167C3×C4⋊Dic3C2311yescharacteristic
168C3×C4⋊Dic3C2311yescharacteristic
169C3×C4⋊Dic3C2314yes—
170C3×C4⋊Dic3C2311yescharacteristic
171C3×C4⋊Dic3C2311yescharacteristic
172C3×Dic3⋊C4C2314yes—
173C3×Dic3⋊C4C2312yes—
174C3×C4×Dic3C2314yes—
175C3×C4×Dic3C2312yes—
176#3724C2312yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2312yes—
182#3722C2312yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2312yes—
187(C2×D3)⋊Dic3C2314yes—
188(C2×D3)⋊Dic3C2312yes—
189(C2×D3)⋊Dic3C2312yes—
190#3520—91noSylow
191C2×C3×#41—32no—
192C2×#239C2×D312yes—
193C2×D3×Q8—32no—
194C2×#237—32no—
195C2×D3×D4—31no—
196C2×D3×D4—31no—
197C2×#235—32no—
198C22×C4×D3—32no—
199C22×C4×D3—32no—
200C22×Dic6—32no—
201C3×C4⋊Q8—21no—
202C3×C4⋊Q8C2×D311yescharacteristic, complemented
203C3×C4⋊Q8C2×D311yescharacteristic, complemented
204C3×#126—34no—
205C3×#124—32no—
206C3×#123—34no—
207C3×C22⋊Q8—32no—
208C3×C22⋊Q8—32no—
209C3×#121—32no—
210C3×C4×Q8—32no—
211C3×C4×Q8—31no—
212C3×C4×D4—31no—
213C3×C4×D4—31no—
214C3×C4×D4—31no—
215C3×#117—32no—
216C2×C3×C4⋊C4—32no—
217#947—31no—
218#947C2×D312yes—
219#946—32no—
220#946—32no—
221#946—31no—
222#946—62no—
223#946C2×D312yescomplemented
224Q8×Dic3—32no—
225Q8×Dic3—32no—
226Q8×Dic3—62no—
227Q8×Dic3C2×D312yescomplemented
228#939—34no—
229#938—32no—
230#938—31no—
231#937—34no—
232#936—31no—
233D4×Dic3—34no—
234D4×Dic3—31no—
235D4×Dic3—31no—
236D4×Dic3—34no—
237D4×Dic3—32no—
238#930—32no—
239#929—34no—
240C4×#67—32no—
241C4×#67—32no—
242C4×#67—32no—
243C2×(C2×D3)⋊C4—34no—
244#926—32no—
245#926—34no—
246C2×C4⋊Dic3—32no—
247C2×C4⋊Dic3—34no—
248#924—32no—
249#924—32no—
250#898—34no—
251#898—32no—
252#898C2×D314yescomplemented
253#897—32no—
254#897—32no—
255#897—31no—
256#897—32no—
257#897—32no—
258#897—34no—
259#897—34no—
260#897—34no—
261#897—62no—
262#897C2×D312yescomplemented
263#896—34no—
264#896—34no—
265#895—31no—
266#895C2×D312yescomplemented
267#894—32no—
268#894C2×D314yescomplemented
269#893—34no—
270#893—31no—
271#893—31no—
272#892—32no—
273#892—32no—
274#892—62no—
275#892C2×D312yescomplemented
276D3×C4⋊C4—34no—
277D3×C4⋊C4—32no—
278D3×C4⋊C4—31no—
279D3×C4⋊C4—31no—
280D3×C4⋊C4C2×D312yescomplemented
281#890—32no—
282#890—32no—
283#890—31no—
284#890—31no—
285#890—62no—
286#889—34no—
287#888—32no—
288#887—32no—
289#887—32no—
290#887—62no—
291#886—34no—
292#886—34no—
293#885—34no—
294#885—34no—
295#884—34no—
296#883—34no—
297#883—34no—
298#883—34no—
299#883—32no—
300#882—34no—
301#67⋊C4—32no—
302#67⋊C4—32no—
303#67⋊C4—34no—
304D3×C22⋊C4—34no—
305D3×C22⋊C4—32no—
306D3×C22⋊C4—32no—
307#879—32no—
308#879—34no—
309#878—34no—
310#878—34no—
311#878—34no—
312C4×D12—32no—
313C4×D12—34no—
314C4×D12—32no—
315C4×D12—34no—
316C4×D12C2×D311yescharacteristic
317C4×D12C2×D311yescharacteristic
318C4×D12C2×D311yescharacteristic, complemented
319#872—32no—
320#872—34no—
321C42×D3—31no—
322C42×D3—31no—
323C42×D3—61no—
324#870—34no—
325#869—31no—
326#869—31no—
327#869—32no—
328#869—61no—
329C4×Dic6C2×D311yescharacteristic, complemented
330C22×C3⋊D3C2411yescharacteristic
331C22×C3×D3C2412yes—
332C22×C3×D3C2412yes—
333C22×C3×D3C2412yes—
334C2×D32—24no—
335C2×D32—24no—
336C2×D32—42no—
337C32×Q8—24no—
338C2×C32×C4C2414yes—
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2411yescharacteristic
341C2×C32×C4C2411yescharacteristic
342C2×C3⋊Dic3C2411yescharacteristic
343C2×C3⋊Dic3C2411yescharacteristic
344C2×C3⋊Dic3C2411yescharacteristic
345C2×C3⋊Dic3C2414yes—
346C4×C3⋊D3—22no—
347C4×C3⋊D3—22no—
348C4×C3⋊D3—22no—
349#634—24no—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2412yes—
355C3×D12—28no—
356C3×D12—22no—
357C3×D12—22no—
358C3×D12#4114yescomplemented
359C3×C4×D3—28no—
360C3×C4×D3—24no—
361C3×C4×D3—24no—
362C3×C4×D3—24no—
363C3×Dic6—22no—
364#627—44no—
365#626—24no—
366#625—24no—
367#625—44no—
368#624—42no—
369D3×Dic3—44no—
370D3×Dic3—44no—
371D3×Dic3—42no—
372D3×Dic3—42no—
373#556—31no—
374#554—92no—
375#552—92no—
376#551—94no—
377D4×Q8—91no—
378#548—92no—
379#547—31no—
380#547—91no—
381#546—92no—
382#542—92no—
383#539—94no—
384#533—91no—
385#529—91no—
386#525—92no—
387C2×C22⋊Q8—92no—
388#520—92no—
389C2×C4×D4—91no—
390C23×D3—32no—
391C23×D3—32no—
392C3×#41—68no—
393C2×C3×Q8—22no—
394C2×C3×Q8—31no—
395C2×C3×Q8C22×D312yes—
396C2×C3×Q8C22×D312yes—
397C2×C3×D4—31no—
398C2×C3×D4—34no—
399C2×C3×D4—31no—
400C2×C3×D4—31no—
401C22×C3×C4—32no—
402C22×C3×C4—32no—
403C22×C3×C4—34no—
404C22×C3×C4—32no—
405C2×#67—32no—
406C2×#67—32no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—32no—
410C22×Dic3—32no—
411C22×Dic3—34no—
412C22×Dic3—34no—
413C22×Dic3—32no—
414#239—28no—
415D3×Q8—124no—
416#237—124no—
417D3×D4—64no—
418D3×D4—64no—
419#235—124no—
420C2×D12—32no—
421C2×D12C22×D314yes—
422C2×D12C22×D311yescharacteristic
423C2×D12C22×D311yescharacteristic
424C2×D12C22×D311yescharacteristic
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—32no—
432C2×C4×D3—34no—
433C2×C4×D3—34no—
434C2×C4×D3—32no—
435C2×C4×D3—32no—
436C2×C4×D3—32no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—124no—
441C2×C4×D3—124no—
442C2×C4×D3C22×D312yes—
443C2×C4×D3C22×D314yes—
444C2×C4×D3C22×D312yes—
445C2×C4×D3C22×D312yes—
446C2×Dic6—32no—
447C2×Dic6—32no—
448C2×Dic6—34no—
449C2×Dic6—34no—
450C2×Dic6—62no—
451C2×Dic6—124no—
452C2×Dic6C22×D311yescharacteristic
453C3×C4⋊C4—22no—
454C3×C4⋊C4—22no—
455C3×C4⋊C4—31no—
456C3×C4⋊C4—34no—
457C3×C4⋊C4—31no—
458C3×C4⋊C4—31no—
459C3×C4⋊C4—31no—
460C3×C4⋊C4—34no—
461C3×C4⋊C4—32no—
462C3×C4⋊C4C22×D312yes—
463C3×C4⋊C4C22×D312yes—
464C3×C4⋊C4C22×D312yes—
465C3×C4⋊C4C22×D312yes—
466C3×C22⋊C4—32no—
467C3×C22⋊C4—34no—
468C3×C22⋊C4—34no—
469C3×C22⋊C4—34no—
470C3×C22⋊C4—32no—
471C3×C22⋊C4—32no—
472C3×C42—21no—
473C3×C42—32no—
474C3×C42—34no—
475C3×C42C22×D311yescharacteristic
476C3×C42C22×D311yescharacteristic
477#217—32no—
478#217—34no—
479#217—34no—
480#217—32no—
481#217—32no—
482#217—32no—
483#217—32no—
484(C2×D3)⋊C4—32no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—32no—
495(C2×D3)⋊C4—64no—
496(C2×D3)⋊C4C22×D314yes—
497(C2×D3)⋊C4C22×D312yes—
498(C2×D3)⋊C4C22×D312yes—
499(C2×D3)⋊C4C22×D312yes—
500(C2×D3)⋊C4C22×D314yes—
501(C2×D3)⋊C4C22×D314yes—
502C4⋊Dic3—32no—
503C4⋊Dic3—32no—
504C4⋊Dic3—32no—
505C4⋊Dic3—32no—
506C4⋊Dic3—34no—
507C4⋊Dic3—34no—
508C4⋊Dic3—34no—
509C4⋊Dic3—32no—
510C4⋊Dic3—32no—
511C4⋊Dic3—32no—
512C4⋊Dic3—34no—
513C4⋊Dic3—62no—
514C4⋊Dic3—62no—
515C4⋊Dic3—64no—
516C4⋊Dic3C22×D311yescharacteristic
517C4⋊Dic3C22×D311yescharacteristic
518C4⋊Dic3C22×D311yescharacteristic
519C4⋊Dic3C22×D311yescharacteristic
520C4⋊Dic3C22×D314yes—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—32no—
524Dic3⋊C4—34no—
525Dic3⋊C4—32no—
526Dic3⋊C4—32no—
527Dic3⋊C4—32no—
528Dic3⋊C4—34no—
529Dic3⋊C4—32no—
530Dic3⋊C4—64no—
531Dic3⋊C4C22×D312yes—
532Dic3⋊C4C22×D314yes—
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—31no—
539C4×Dic3—34no—
540C4×Dic3—34no—
541C4×Dic3—61no—
542C4×Dic3—61no—
543C4×Dic3—61no—
544C4×Dic3—64no—
545C4×Dic3C22×D312yes—
546C4×Dic3C22×D314yes—
547C22×C32C2511yescharacteristic
548C2×C3⋊D3—21no—
549C2×C3⋊D3—21no—
550C2×C3⋊D32−1+412yes—
551C2×C3×D3—22no—
552C2×C3×D3—22no—
553C2×C3×D3—22no—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C2×C3×D3C2×#4114yes—
560D32—48no—
561C32×C4—21no—
562C32×C4—24no—
563C32×C4C2×#4112yes—
564C32×C4H(5,𝔽2)12yes—
565C3⋊Dic3—21no—
566C3⋊Dic3—21no—
567C3⋊Dic3—21no—
568C3⋊Dic3—24no—
569C3×Dic3—22no—
570C3×Dic3—22no—
571C3×Dic3—22no—
572C3×Dic3—22no—
573C3×Dic3—22no—
574C2×#41—32no—
575C2×#41—92no—
576C22×Q8—92no—
577C22×D4—91no—
578C23×C4—92no—
579C4⋊Q8—92no—
580C4⋊Q8—91no—
581C4⋊Q8D3211yescharacteristic, complemented
582#126—34no—
583#126—92no—
584#126—94no—
585#125—94no—
586#125—91no—
587#125—92no—
588#124—32no—
589#124—94no—
590#124—91no—
591#123—34no—
592#123—94no—
593#123—94no—
594#123—92no—
595#123—94no—
596C22⋊Q8—32no—
597C22⋊Q8—32no—
598C22⋊Q8—94no—
599C22⋊Q8—94no—
600C22⋊Q8—94no—
601C22⋊Q8—94no—
602C22⋊Q8—92no—
603C22⋊Q8—92no—
604C22⋊Q8—91no—
605C22⋊Q8—92no—
606C22⋊Q8—92no—
607#121—32no—
608#121—94no—
609#121—91no—
610#121—92no—
611#120—94no—
612C4×Q8—32no—
613C4×Q8—31no—
614C4×Q8—92no—
615C4×Q8—92no—
616C4×D4—31no—
617C4×D4—31no—
618C4×D4—31no—
619C4×D4—94no—
620C4×D4—92no—
621C4×D4—94no—
622C4×D4—92no—
623C4×D4—92no—
624C4×D4—91no—
625C4×D4—91no—
626C4×D4—94no—
627C4×D4—92no—
628#117—32no—
629#117—92no—
630#117—94no—
631#117—92no—
632C2×C4⋊C4—32no—
633C2×C4⋊C4—91no—
634C2×C4⋊C4—94no—
635C2×C4⋊C4—92no—
636C2×C22⋊C4—92no—
637C2×C22⋊C4—94no—
638C2×C42—91no—
639C23×C3—32no—
640C23×C3—32no—
641C23×C3—32no—
642C22×D3—31no—
643C22×D3—31no—
644C22×D3—61no—
645C22×D3—64no—
646C22×D3—64no—
647C22×D3—64no—
648C22×D3—64no—
649C22×D3—122no—
650C22×D3—122no—
651C22×D3C23×D312yes—
652C22×D3C23×D312yes—
653C22×D3C23×D312yes—
654C3×Q8—24no—
655C3×Q8—24no—
656C3×Q8—44no—
657C3×Q8—62no—
658C3×D4—34no—
659C3×D4—68no—
660C3×D4—62no—
661C3×D4—62no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—24no—
666C2×C3×C4—32no—
667C2×C3×C4—32no—
668C2×C3×C4—32no—
669C2×C3×C4—32no—
670C2×C3×C4—32no—
671C2×C3×C4—68no—
672C2×C3×C4—64no—
673C2×C3×C4—64no—
674C2×C3×C4—64no—
675C2×C3×C4C23×D314yes—
676C2×C3×C4C23×D314yes—
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—64no—
684#67—64no—
685#67—64no—
686#67—124no—
687#67—124no—
688C2×Dic3—31no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—34no—
695C2×Dic3—34no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—64no—
700C2×Dic3—124no—
701C2×Dic3—122no—
702C2×Dic3—122no—
703C2×Dic3—124no—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D312yes—
709D12—28no—
710D12—22no—
711D12—22no—
712D12—64no—
713D12#23714yescomplemented
714C4×D3—28no—
715C4×D3—24no—
716C4×D3—24no—
717C4×D3—24no—
718C4×D3—62no—
719C4×D3—62no—
720C4×D3—64no—
721C4×D3—62no—
722C4×D3—62no—
723C4×D3—62no—
724C4×D3—62no—
725C4×D3—122no—
726C4×D3—122no—
727C4×D3—122no—
728C4×D3—122no—
729C4×D3—122no—
730C4×D3—122no—
731C4×D3—124no—
732C4×D3—124no—
733Dic6—22no—
734Dic6—64no—
735Dic6—64no—
736Dic6—124no—
737Dic6—124no—
738Dic6—124no—
739C2×C32C22×#4111yescharacteristic
740C2×C32C2×H(5,𝔽2)11yescharacteristic
741C2×C32C2×2−1+411yescharacteristic
742C3⋊D3—22no—
743C3×D3—24no—
744C3×D3—42no—
745C3×D3—42no—
746C24—92no—
747#41—68no—
748#41—364no—
749C2×Q8—31no—
750C2×Q8—94no—
751C2×Q8—92no—
752C2×Q8—364no—
753C2×Q8C2×D3212yes—
754C2×D4—31no—
755C2×D4—31no—
756C2×D4—31no—
757C2×D4—34no—
758C2×D4—92no—
759C2×D4—92no—
760C2×D4—94no—
761C2×D4—184no—
762C22×C4—34no—
763C22×C4—32no—
764C22×C4—32no—
765C22×C4—32no—
766C22×C4—92no—
767C22×C4—94no—
768C22×C4—92no—
769C22×C4—94no—
770C22×C4—92no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—91no—
774C22×C4—364no—
775C4⋊C4—31no—
776C4⋊C4—34no—
777C4⋊C4—31no—
778C4⋊C4—31no—
779C4⋊C4—34no—
780C4⋊C4—31no—
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—94no—
790C4⋊C4—92no—
791C4⋊C4—94no—
792C4⋊C4C2×D3212yes—
793C4⋊C4C2×D3212yes—
794C22⋊C4—32no—
795C22⋊C4—32no—
796C22⋊C4—34no—
797C22⋊C4—34no—
798C22⋊C4—32no—
799C22⋊C4—34no—
800C22⋊C4—92no—
801C22⋊C4—92no—
802C22⋊C4—92no—
803C22⋊C4—94no—
804C22⋊C4—94no—
805C22⋊C4—92no—
806C22⋊C4—92no—
807C22⋊C4—92no—
808C22⋊C4—94no—
809C42—34no—
810C42—32no—
811C42—91no—
812C42—91no—
813C42—91no—
814C42—94no—
815C42C2×D3211yescharacteristic
816C22×C3—21no—
817C22×C3—34no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3C24×D311yescharacteristic
827C22×C3C24×D311yescharacteristic
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—32no—
837C2×D3—32no—
838C2×D3—62no—
839C2×D3—61no—
840C2×D3—61no—
841C2×D3—61no—
842C2×D3—61no—
843C2×D3—121no—
844C2×D3—121no—
845C2×D3—128no—
846C2×D3—128no—
847C2×D3C2×#23714yes—
848C3×C4—22no—
849C3×C4—24no—
850C3×C4—24no—
851C3×C4—21no—
852C3×C4—21no—
853C3×C4—22no—
854C3×C4—22no—
855C3×C4—44no—
856C3×C4—62no—
857C3×C4—62no—
858C3×C4—62no—
859C3×C4—62no—
860C3×C4—62no—
861C3×C4C2×#23712yes—
862C3×C4D3×#4112yes—
863C3×C4#100912yes—
864C3×C4#100912yes—
865Dic3—22no—
866Dic3—22no—
867Dic3—22no—
868Dic3—22no—
869Dic3—22no—
870Dic3—62no—
871Dic3—61no—
872Dic3—61no—
873Dic3—64no—
874Dic3—64no—
875Dic3—61no—
876Dic3—61no—
877Dic3—61no—
878Dic3—61no—
879Dic3—124no—
880Dic3—121no—
881Dic3—121no—
882C32#352011yescharacteristic, complemented, Sylow
883C23—32no—
884C23—32no—
885C23—32no—
886C23—91no—
887C23—184no—
888C23—184no—
889C23—362no—
890Q8—24no—
891Q8—62no—
892Q8—184no—
893Q8—364no—
894D4—34no—
895D4—68no—
896D4—62no—
897D4—62no—
898D4—184no—
899D4—184no—
900D4—364no—
901C2×C4—32no—
902C2×C4—32no—
903C2×C4—32no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—68no—
907C2×C4—64no—
908C2×C4—64no—
909C2×C4—64no—
910C2×C4—91no—
911C2×C4—91no—
912C2×C4—91no—
913C2×C4—94no—
914C2×C4—182no—
915C2×C4—182no—
916C2×C4—182no—
917C2×C4—362no—
918C2×C4—362no—
919C2×C4—362no—
920C2×C4—364no—
921C2×C4—364no—
922C2×C4C22×D3214yes—
923C2×C4C22×D3211yescharacteristic
924C2×C4C22×D3211yescharacteristic
925C2×C4C22×D3211yescharacteristic
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—64no—
930C2×C3—122no—
931C2×C3—122no—
932C2×C3C22×#23711yescharacteristic
933C2×C3C2×D3×#4111yescharacteristic
934C2×C3C2×#100911yescharacteristic
935C2×C3C2×#100911yescharacteristic
936C2×C3D3×2−1+411yescharacteristic
937C2×C3D3×2−1+411yescharacteristic
938D3—24no—
939D3—42no—
940D3—42no—
941D3—62no—
942D3—62no—
943D3—122no—
944C22—34no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—62no—
949C22—62no—
950C22—62no—
951C22—62no—
952C22—62no—
953C22—92no—
954C22—181no—
955C22—181no—
956C22—368no—
957C22C23×D3211yescharacteristic
958C4—24no—
959C4—21no—
960C4—62no—
961C4—62no—
962C4—62no—
963C4—62no—
964C4—62no—
965C4—181no—
966C4—181no—
967C4—184no—
968C4—181no—
969C4D3×#23712yes—
970C4#6432012yes—
971C3—21no—
972C3#8668511yescharacteristic, complemented
973C3#8699011yescharacteristic, complemented
974C2—64no—
975C2—122no—
976C2—122no—
977C2—182no—
978C2C2×D3×#23711yescharacteristic
979C2C2×#6432011yescharacteristic
980C2#1059668711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
hypercenterC4⋊Q8D32
hypocenterC32#3520
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
2. C3×#5732C2semidirect
3. C3×#5726C2semidirect
4. #10595428C2semidirect
5. #10595396C2semidirect
6. #10595394C2semidirect
7. #10595371C2semidirect
8. #10594648C2semidirect
9. #10594626C2semidirect
10. D3×#897C2semidirect
11. #10594550C2semidirect
12. #10594525C2semidirect
13. #10594436C2semidirect
14. C4×#3802C2semidirect
15. Dic6×D12C2semidirect
16. #10593895C2semidirect
17. #10593875C2semidirect
23. C2×#3795C22semidirect
24. C2×D3×Dic6C22semidirect
25. C32×C4⋊Q8C22semidirect
27. Q8×C3⋊Dic3C22semidirect
30. #64099C22semidirect
31. #64096C22semidirect
33. #64078C22semidirect
35. C3×#946C22semidirect
36. C3×Q8×Dic3C22semidirect
37. C3×#898C22semidirect
38. C3×#897C22semidirect
39. C3×#895C22semidirect
40. C3×#894C22semidirect
41. C3×#892C22semidirect
42. C3×D3×C4⋊C4C22semidirect
45. C3×C4×D12C22semidirect
46. C3×C4×Dic6C22semidirect
50. #63918C22semidirect
52. #63915C22semidirect
59. #63899C22semidirect
62. #63898C22semidirect
64. #63893C22semidirect
65. #63893C22semidirect
67. Dic3×D12C22semidirect
68. #63891C22semidirect
69. #63891C22semidirect
70. D3×C4⋊Dic3C22semidirect
71. D3×C4⋊Dic3C22semidirect
74. #63872C22semidirect
76. #63867C22semidirect
77. #63863C22semidirect
78. #63862C22semidirect
79. #63862C22semidirect
80. #63857C22semidirect
81. #63857C22semidirect
82. #63855C22semidirect
83. #63855C22semidirect
89. #5732D3semidirect
93. #5726D3semidirect
202. C3×C4⋊Q8C2×D3semidirect
203. C3×C4⋊Q8C2×D3semidirect
223. #946C2×D3semidirect
227. Q8×Dic3C2×D3semidirect
252. #898C2×D3semidirect
262. #897C2×D3semidirect
266. #895C2×D3semidirect
268. #894C2×D3semidirect
275. #892C2×D3semidirect
280. D3×C4⋊C4C2×D3semidirect
318. C4×D12C2×D3semidirect
329. C4×Dic6C2×D3semidirect
358. C3×D12#41semidirect
581. C4⋊Q8D32semidirect
713. D12#237semidirect
882. C32#3520semidirect
972. C3#86685semidirect
973. C3#86990semidirect

Maximal subgroups

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

subgroupindex
#105961992
C3×#57322
C3×#57262
#105954282
#105953962
#105953942
#105953712
#105946482
#105946262
D3×#8972
#105945502
#105945252
#105944362
C4×#38022
Dic6×D122
#105938952
#105938752
#869903
#866853