Finite Group Databasebeta

← #11906186

Subgroups — #11906186

Order 1152.

2340 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596198C211yesmaximal, characteristic, complemented
2C3×#5728C211yesmaximal, characteristic, complemented
3C3×#5727C211yesmaximal, characteristic, complemented
4#10595429C212yesmaximal, complemented
5D3×#946C212yesmaximal, complemented
6Q8×#626C212yesmaximal, complemented
7#10595371C212yesmaximal, complemented
8#10594635C214yesmaximal, complemented
9#10594604C212yesmaximal
10#10594502C212yesmaximal, complemented
11#10594485C212yesmaximal, complemented
12#10594470C212yesmaximal, complemented
13#10594392C214yesmaximal, complemented
14C4×D3×D12C211yesmaximal, characteristic
15#10593958C211yesmaximal, characteristic, complemented
16#10593956C211yesmaximal, characteristic, complemented
17#10593873C211yesmaximal, characteristic, complemented
18#86761—31nomaximal
19#86280—31nomaximal
20C2×Q8×C3⋊D3C2212yescomplemented
21C2×C3×D3×Q8C2212yescomplemented
22C2×D3×D12C2211yescharacteristic
23C2×C4×D32C2212yes—
24C32×C4⋊Q8C2211yescharacteristic, complemented
25#64155C2212yescomplemented
26#64105C2214yescomplemented
27#64102C2212yes—
28#64097C2212yescomplemented
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30C4×#634C2211yescharacteristic, complemented
31C3×#946C2212yes—
32C3×#946C2212yescomplemented
33C3×Q8×Dic3C2212yescomplemented
34C3×#897C2212yes—
35C3×#896C2214yescomplemented
36C3×#893C2212yes—
37C3×#892C2212yes—
38C3×#890C2212yescomplemented
39C3×#888C2212yescomplemented
40C3×#887C2212yescomplemented
41C3×C4×D12C2211yescharacteristic
42C3×C42×D3C2211yescharacteristic
43C3×#869C2211yescharacteristic, complemented
44C3×C4×Dic6C2211yescharacteristic, complemented
45#63921C2214yes—
46D3×(C2×D3)⋊C4C2214yes—
47D3×(C2×D3)⋊C4C2212yes—
48#63918C2211yescharacteristic, complemented
49C4×#627C2212yescomplemented
50C4×#626C2212yes—
51C4×#626C2214yes—
52#63900C2212yescomplemented
53#63899C2214yescomplemented
54#63898C2212yes—
55#63896C2214yes—
56#63896C2214yescomplemented
57#63895C2214yescomplemented
58#63894C2212yes—
59#63894C2211yescharacteristic
60Dic3×D12C2211yescharacteristic
61D3×C4⋊Dic3C2211yescharacteristic
62D3×C4⋊Dic3C2212yescomplemented
63#63888C2214yescomplemented
64#63888C2214yescomplemented
65#63887C2214yes—
66#63887C2214yescomplemented
67#63883C2214yescomplemented
68#63880C2214yes—
69#63880C2212yes—
70D3×Dic3⋊C4C2214yescomplemented
71#63872C2212yescomplemented
72#63871C2214yescomplemented
73#63871C2212yescomplemented
74#63869C2212yescomplemented
75#63867C2214yescomplemented
76#63867C2212yescomplemented
77#63866C2211yescharacteristic, complemented
78#63866C2214yescomplemented
79#63857C2211yescharacteristic
80#63857C2214yescomplemented
81#63857C2212yescomplemented
82#63856C2211yescharacteristic
83#63855C2212yes—
84#63851C2212yes—
85C3×D4×Q8—31no—
86C3×#533—31no—
87Q8×#67—32no—
88C2×#946—32no—
89#5730—32no—
90#5730—31no—
91#5730—31no—
92#5729—32no—
93#5728D311yescharacteristic, complemented
94#5727—31no—
95#5727—31no—
96#5727—61no—
97#5727D311yescharacteristic, complemented
98#5690—32no—
99#5690—32no—
100#5636—34no—
101#5635—32no—
102#5634—34no—
103#5634—34no—
104D3×C22⋊Q8—32no—
105D3×C22⋊Q8—32no—
106D3×C22⋊Q8—32no—
107#5579—32no—
108#5579—34no—
109#5579—31no—
110#5578—31no—
111Q8×D12—32no—
112#5545—32no—
113C4×D3×D4—31no—
114#5543—31no—
115#5539—32no—
116#5521—32no—
117#5519—32no—
118C2×C4×D12—31no—
119#5470—31no—
120C22×D32C2312yes—
121C2×C32×Q8C2312yes—
122Q8×C3⋊D3—44no—
123C2×C4⋊(C3⋊D3)C2311yescharacteristic
124C2×C4×C3⋊D3C2312yes—
125C2×C4×C3⋊D3C2314yes—
126C2×#634C2311yescharacteristic
127C2×#634C2314yes—
128C3×D3×Q8—44no—
129C2×C3×D12C2311yescharacteristic
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2314yes—
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×Dic6C2311yescharacteristic
136C2×C3×Dic6C2312yes—
137C2×C3×Dic6C2314yes—
138C2×#627C2312yes—
139C2×#626C2312yes—
140C2×#624C2312yes—
141C2×#624C2314yes—
142C2×D3×Dic3C2312yes—
143C2×D3×Dic3C2312yes—
144C2×D3×Dic3C2314yes—
145D3×D12Q818yescomplemented
146C4×D32—44no—
147C32×C4⋊C4C2312yes—
148C32×C4⋊C4C2312yes—
149C32×C42C2311yescharacteristic
150#3752C2312yes—
151#3752C2314yes—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154#3750C2312yes—
155#3750C2314yes—
156C4×C3⋊Dic3C2312yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2312yes—
160C3×C4⋊Dic3C2311yescharacteristic
161C3×C4⋊Dic3C2312yes—
162C3×C4⋊Dic3C2314yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2311yescharacteristic
165C3×Dic3⋊C4C2314yes—
166C3×Dic3⋊C4C2314yes—
167C3×Dic3⋊C4C2312yes—
168C3×C4×Dic3C2311yescharacteristic
169C3×C4×Dic3C2314yes—
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2311yescharacteristic
173#3724C2312yes—
174#3724C2314yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2312yes—
182Dic3⋊Dic3C2314yes—
183#3722C2314yes—
184#3722C2312yes—
185(C2×D3)⋊Dic3C2312yes—
186(C2×D3)⋊Dic3C2312yes—
187(C2×D3)⋊Dic3C2314yes—
188(C2×D3)⋊Dic3C2312yes—
189#3501—91noSylow
190C22×C3×Q8—32no—
191C2×D3×Q8—32no—
192C2×D3×Q8—32no—
193C2×D3×Q8—62no—
194C2×D3×Q8C2×D312yescomplemented
195C2×D3×D4—31no—
196C22×D12—31no—
197C22×C4×D3—32no—
198C22×C4×D3—32no—
199C3×C4⋊Q8—21no—
200C3×C4⋊Q8—32no—
201C3×C4⋊Q8—31no—
202C3×C4⋊Q8C2×D311yescharacteristic, complemented
203C3×C4⋊Q8C2×D311yescharacteristic, complemented
204C3×#125—32no—
205C3×C22⋊Q8—32no—
206C3×C22⋊Q8—32no—
207C3×C22⋊Q8—32no—
208C3×C22⋊Q8—34no—
209C3×C4×Q8—32no—
210C3×C4×Q8—32no—
211C3×C4×Q8—31no—
212C3×C4×D4—32no—
213C3×C4×D4—31no—
214C3×#117—32no—
215C2×C3×C42—31no—
216#946—32no—
217#946—32no—
218#946—31no—
219#946—34no—
220#946—34no—
221#946—34no—
222#946—32no—
223#946—34no—
224#946—34no—
225#946—62no—
226#946C2×D312yes—
227#946C2×D312yescomplemented
228Q8×Dic3C2×D312yescomplemented
229#944—34no—
230#944—31no—
231D4×Dic3—32no—
232D4×Dic3—31no—
233C4×#67—32no—
234C4×#67—34no—
235C2×(C2×D3)⋊C4—32no—
236C2×(C2×D3)⋊C4—34no—
237#926—32no—
238C2×C4⋊Dic3—32no—
239C2×C4⋊Dic3—31no—
240#924—31no—
241#924—34no—
242#924—31no—
243#924—32no—
244#924—32no—
245C2×Dic3⋊C4—34no—
246#897—34no—
247#897—32no—
248#897—31no—
249#897—34no—
250#897—32no—
251#897—34no—
252#897C2×D312yes—
253#896—32no—
254#896—34no—
255#896—34no—
256#896—34no—
257#896—34no—
258#896—34no—
259#896—34no—
260#896—34no—
261#896—34no—
262#896—64no—
263#896C2×D314yescomplemented
264#893—32no—
265#893—32no—
266#893—32no—
267#893—32no—
268#893—31no—
269#893—62no—
270#893C2×D312yes—
271#892C2×D312yes—
272D3×C4⋊C4—34no—
273D3×C4⋊C4—31no—
274D3×C4⋊C4—32no—
275D3×C4⋊C4—32no—
276D3×C4⋊C4—32no—
277D3×C4⋊C4—34no—
278D3×C4⋊C4—34no—
279#890—32no—
280#890—32no—
281#890—32no—
282#890C2×D312yescomplemented
283#889—34no—
284#889—32no—
285#888—32no—
286#888—32no—
287#888—31no—
288#888—62no—
289#888C2×D312yescomplemented
290#887C2×D312yescomplemented
291#67⋊C4—34no—
292#67⋊C4—32no—
293D3×C22⋊C4—32no—
294D3×C22⋊C4—34no—
295D3×C22⋊C4—34no—
296D3×C22⋊C4—34no—
297#878—34no—
298#878—34no—
299#878—34no—
300#878—34no—
301#878—34no—
302C4×D12—31no—
303C4×D12—32no—
304C4×D12—34no—
305C4×D12—31no—
306C4×D12—31no—
307C4×D12—32no—
308C4×D12—34no—
309C4×D12—31no—
310C4×D12—32no—
311C4×D12—61no—
312C4×D12C2×D311yescharacteristic
313#872—32no—
314C42×D3C2×D311yescharacteristic
315#870—32no—
316#870—32no—
317#870—34no—
318#869—31no—
319#869—34no—
320#869—31no—
321#869C2×D311yescharacteristic, complemented
322C4×Dic6—31no—
323C4×Dic6—31no—
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6—61no—
327C4×Dic6C2×D311yescharacteristic, complemented
328C22×C3⋊D3C2412yes—
329C22×C3×D3C2411yescharacteristic
330C22×C3×D3C2412yes—
331C2×D32—42no—
332C2×D32—42no—
333C2×D32C2×Q818yescomplemented
334C32×Q8—24no—
335C2×C32×C4C2414yes—
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C3⋊Dic3C2412yes—
340C2×C3⋊Dic3C2412yes—
341C2×C3⋊Dic3C2412yes—
342C4⋊(C3⋊D3)C2×Q814yescomplemented
343C4×C3⋊D3—24no—
344C4×C3⋊D3—44no—
345#634—22no—
346#634—44no—
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2414yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2411yescharacteristic
353C2×C3×Dic3C2411yescharacteristic
354C3×D12C2×Q814yescomplemented
355C3×C4×D3—22no—
356C3×C4×D3—24no—
357C3×C4×D3—41no—
358C3×C4×D3—44no—
359C3×C4×D3C2×Q814yescomplemented
360C3×Dic6—22no—
361C3×Dic6—42no—
362C3×Dic6—44no—
363#627—42no—
364#626C2×Q818yescomplemented
365#624—42no—
366#624—44no—
367D3×Dic3—42no—
368D3×Dic3—42no—
369D3×Dic3—44no—
370#554—92no—
371#554—91no—
372#554—92no—
373#554—94no—
374#554—91no—
375#554—92no—
376D4×Q8—31no—
377D4×Q8—92no—
378D4×Q8—91no—
379#544—92no—
380#543—94no—
381#533—31no—
382#533—91no—
383C2×C22⋊Q8—92no—
384C2×C22⋊Q8—92no—
385#518—92no—
386C2×C4×D4—91no—
387C23×D3—32no—
388C23×D3—32no—
389C2×C3×Q8—22no—
390C2×C3×Q8—31no—
391C2×C3×Q8—34no—
392C2×C3×Q8—32no—
393C2×C3×Q8—124no—
394C2×C3×Q8C22×D312yes—
395C2×C3×Q8C22×D312yes—
396C2×C3×D4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—32no—
400C22×C3×C4—34no—
401C22×C3×C4—31no—
402C2×#67—32no—
403C22×Dic3—32no—
404C22×Dic3—32no—
405C22×Dic3—34no—
406D3×Q8—44no—
407D3×Q8—124no—
408D3×Q8—124no—
409D3×Q8—128no—
410D3×D4—38no—
411C2×D12—32no—
412C2×D12—31no—
413C2×D12—31no—
414C2×D12—38no—
415C2×D12—61no—
416C2×D12C22×D311yescharacteristic
417C2×C4×D3—32no—
418C2×C4×D3—32no—
419C2×C4×D3—32no—
420C2×C4×D3—34no—
421C2×C4×D3—32no—
422C2×C4×D3—34no—
423C2×C4×D3—34no—
424C2×C4×D3—32no—
425C2×C4×D3—34no—
426C2×C4×D3—34no—
427C2×C4×D3—32no—
428C2×C4×D3—62no—
429C2×C4×D3—64no—
430C2×C4×D3—124no—
431C2×C4×D3—124no—
432C2×C4×D3C22×D311yescharacteristic
433C2×C4×D3C22×D312yes—
434C2×C4×D3C22×D311yescharacteristic
435C2×C4×D3C22×D314yes—
436C2×C4×D3C22×D311yescharacteristic
437C2×Dic6—31no—
438C2×Dic6—31no—
439C2×Dic6—34no—
440C2×Dic6—34no—
441C2×Dic6—32no—
442C2×Dic6—32no—
443C2×Dic6—61no—
444C2×Dic6—64no—
445C2×Dic6C22×D311yescharacteristic
446C2×Dic6C22×D314yes—
447C2×Dic6C22×D312yes—
448C3×C4⋊C4—22no—
449C3×C4⋊C4—22no—
450C3×C4⋊C4—31no—
451C3×C4⋊C4—34no—
452C3×C4⋊C4—32no—
453C3×C4⋊C4—31no—
454C3×C4⋊C4—32no—
455C3×C4⋊C4—34no—
456C3×C4⋊C4—32no—
457C3×C4⋊C4—34no—
458C3×C4⋊C4C22×D312yes—
459C3×C4⋊C4C22×D312yes—
460C3×C4⋊C4C22×D312yes—
461C3×C4⋊C4C22×D312yes—
462C3×C22⋊C4—34no—
463C3×C22⋊C4—32no—
464C3×C22⋊C4—34no—
465C3×C42—21no—
466C3×C42—31no—
467C3×C42—32no—
468C3×C42—31no—
469C3×C42—34no—
470C3×C42—31no—
471C3×C42C22×D311yescharacteristic
472C3×C42C22×D311yescharacteristic
473#217—32no—
474#217—32no—
475#217—34no—
476#217—32no—
477(C2×D3)⋊C4—32no—
478(C2×D3)⋊C4—32no—
479(C2×D3)⋊C4—32no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—32no—
482(C2×D3)⋊C4—32no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—32no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—62no—
490(C2×D3)⋊C4—64no—
491(C2×D3)⋊C4C22×D312yes—
492(C2×D3)⋊C4C22×D314yes—
493(C2×D3)⋊C4C22×D314yes—
494C4⋊Dic3—31no—
495C4⋊Dic3—31no—
496C4⋊Dic3—31no—
497C4⋊Dic3—31no—
498C4⋊Dic3—32no—
499C4⋊Dic3—32no—
500C4⋊Dic3—32no—
501C4⋊Dic3—32no—
502C4⋊Dic3—32no—
503C4⋊Dic3—34no—
504C4⋊Dic3—34no—
505C4⋊Dic3—34no—
506C4⋊Dic3—61no—
507C4⋊Dic3—61no—
508C4⋊Dic3C22×D311yescharacteristic
509C4⋊Dic3C22×D312yes—
510C4⋊Dic3C22×D312yes—
511C4⋊Dic3C22×D311yescharacteristic
512C4⋊Dic3C22×D314yes—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—32no—
518Dic3⋊C4—32no—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—32no—
526Dic3⋊C4—32no—
527Dic3⋊C4—34no—
528Dic3⋊C4—32no—
529Dic3⋊C4—62no—
530Dic3⋊C4—64no—
531Dic3⋊C4C22×D312yes—
532Dic3⋊C4C22×D314yes—
533Dic3⋊C4C22×D314yes—
534C4×Dic3—32no—
535C4×Dic3—32no—
536C4×Dic3—62no—
537C4×Dic3C22×D311yescharacteristic
538C4×Dic3C22×D312yes—
539C4×Dic3C22×D311yescharacteristic
540C4×Dic3C22×D311yescharacteristic
541C4×Dic3C22×D314yes—
542C22×C32C2511yescharacteristic
543C2×C3⋊D3—22no—
544C2×C3⋊D3—22no—
545C2×C3⋊D3C22×Q814yes—
546C2×C3×D3—21no—
547C2×C3×D3—22no—
548C2×C3×D3—22no—
549C2×C3×D3—21no—
550C2×C3×D3C22×Q814yes—
551C2×C3×D3C22×Q812yes—
552D32—48no—
553C32×C4—24no—
554C32×C4—21no—
555C32×C4C22×Q812yes—
556C32×C4H(5,𝔽2)12yes—
557C3⋊Dic3—22no—
558C3⋊Dic3—22no—
559C3⋊Dic3—22no—
560C3×Dic3—21no—
561C3×Dic3—22no—
562C3×Dic3—22no—
563C3×Dic3—24no—
564C3×Dic3—22no—
565C3×Dic3—21no—
566C3×Dic3C22×Q812yes—
567C22×Q8—32no—
568C22×Q8—92no—
569C22×D4—91no—
570C23×C4—92no—
571C4⋊Q8—32no—
572C4⋊Q8—31no—
573C4⋊Q8—91no—
574C4⋊Q8—91no—
575C4⋊Q8—94no—
576C4⋊Q8—92no—
577C4⋊Q8D3211yescharacteristic, complemented
578#125—32no—
579#125—92no—
580#125—94no—
581#125—92no—
582#125—92no—
583C22⋊Q8—32no—
584C22⋊Q8—32no—
585C22⋊Q8—32no—
586C22⋊Q8—34no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—91no—
594C22⋊Q8—92no—
595C22⋊Q8—92no—
596C22⋊Q8—94no—
597C22⋊Q8—92no—
598C22⋊Q8—94no—
599C22⋊Q8—94no—
600C22⋊Q8—94no—
601C22⋊Q8—91no—
602C22⋊Q8—92no—
603C22⋊Q8—94no—
604C4×Q8—32no—
605C4×Q8—32no—
606C4×Q8—31no—
607C4×Q8—92no—
608C4×Q8—91no—
609C4×D4—32no—
610C4×D4—31no—
611C4×D4—92no—
612C4×D4—94no—
613C4×D4—91no—
614C4×D4—92no—
615C4×D4—92no—
616C4×D4—94no—
617C4×D4—91no—
618C4×D4—92no—
619C4×D4—92no—
620C4×D4—91no—
621#117—32no—
622#117—92no—
623C2×C4⋊C4—92no—
624C2×C4⋊C4—94no—
625C2×C4⋊C4—91no—
626C2×C4⋊C4—94no—
627C2×C4⋊C4—92no—
628C2×C22⋊C4—94no—
629C2×C22⋊C4—92no—
630C2×C22⋊C4—94no—
631C2×C42—31no—
632C23×C3—31no—
633C23×C3—32no—
634C22×D3—32no—
635C22×D3—32no—
636C22×D3—38no—
637C22×D3—38no—
638C22×D3—62no—
639C22×D3—122no—
640C22×D3—122no—
641C22×D3—122no—
642C22×D3—122no—
643C22×D3C23×D311yescharacteristic
644C22×D3C23×D312yes—
645C3×Q8—24no—
646C3×Q8—24no—
647C3×Q8—44no—
648C3×Q8—62no—
649C3×Q8—122no—
650C3×Q8—124no—
651C3×D4—34no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—24no—
656C2×C3×C4—31no—
657C2×C3×C4—34no—
658C2×C3×C4—32no—
659C2×C3×C4—31no—
660C2×C3×C4—32no—
661C2×C3×C4—32no—
662C2×C3×C4—34no—
663C2×C3×C4—31no—
664C2×C3×C4—62no—
665C2×C3×C4—64no—
666C2×C3×C4—121no—
667C2×C3×C4—124no—
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D314yes—
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D314yes—
672C2×C3×C4C23×D311yescharacteristic
673C2×C3×C4C23×D311yescharacteristic
674C2×C3×C4C23×D311yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676#67—38no—
677C2×Dic3—32no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—62no—
684C2×Dic3—62no—
685C2×Dic3—62no—
686C2×Dic3—122no—
687C2×Dic3—122no—
688C2×Dic3—124no—
689C2×Dic3C23×D311yescharacteristic
690C2×Dic3C23×D311yescharacteristic
691C2×Dic3C23×D312yes—
692C2×Dic3C23×D314yes—
693C2×Dic3C23×D312yes—
694C2×Dic3C23×D312yes—
695C2×Dic3C23×D311yescharacteristic
696D12—38no—
697D12—34no—
698D12—34no—
699D12—64no—
700D12D3×Q814yescomplemented
701C4×D3—24no—
702C4×D3—22no—
703C4×D3—41no—
704C4×D3—44no—
705C4×D3—64no—
706C4×D3—64no—
707C4×D3—124no—
708C4×D3—124no—
709C4×D3—124no—
710C4×D3—122no—
711C4×D3—122no—
712C4×D3—124no—
713C4×D3—124no—
714C4×D3—128no—
715C4×D3—124no—
716C4×D3—122no—
717C4×D3—122no—
718C4×D3D3×Q814yescomplemented
719Dic6—22no—
720Dic6—42no—
721Dic6—44no—
722Dic6—64no—
723Dic6—62no—
724Dic6—62no—
725Dic6—122no—
726Dic6—122no—
727Dic6—124no—
728Dic6—124no—
729Dic6—128no—
730C2×C32C23×Q811yescharacteristic
731C2×C32C2×H(5,𝔽2)11yescharacteristic
732C2×C32#58511yescharacteristic
733C3⋊D3—24no—
734C3×D3—22no—
735C3×D3—24no—
736C24—92no—
737C2×Q8—31no—
738C2×Q8—32no—
739C2×Q8—34no—
740C2×Q8—92no—
741C2×Q8—91no—
742C2×Q8—94no—
743C2×Q8—124no—
744C2×Q8—364no—
745C2×Q8C2×D3212yes—
746C2×D4—31no—
747C2×D4—98no—
748C2×D4—92no—
749C2×D4—91no—
750C22×C4—31no—
751C22×C4—31no—
752C22×C4—32no—
753C22×C4—31no—
754C22×C4—34no—
755C22×C4—94no—
756C22×C4—92no—
757C22×C4—94no—
758C22×C4—92no—
759C22×C4—92no—
760C22×C4—92no—
761C22×C4—94no—
762C22×C4—364no—
763C4⋊C4—31no—
764C4⋊C4—34no—
765C4⋊C4—32no—
766C4⋊C4—31no—
767C4⋊C4—34no—
768C4⋊C4—32no—
769C4⋊C4—32no—
770C4⋊C4—34no—
771C4⋊C4—92no—
772C4⋊C4—92no—
773C4⋊C4—92no—
774C4⋊C4—94no—
775C4⋊C4—94no—
776C4⋊C4—94no—
777C4⋊C4—94no—
778C4⋊C4—92no—
779C4⋊C4—92no—
780C4⋊C4—92no—
781C4⋊C4—91no—
782C4⋊C4—91no—
783C4⋊C4—94no—
784C4⋊C4—92no—
785C4⋊C4C2×D3212yes—
786C4⋊C4C2×D3212yes—
787C22⋊C4—34no—
788C22⋊C4—34no—
789C22⋊C4—32no—
790C22⋊C4—92no—
791C22⋊C4—94no—
792C22⋊C4—92no—
793C22⋊C4—92no—
794C22⋊C4—92no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C22⋊C4—92no—
798C42—31no—
799C42—31no—
800C42—31no—
801C42—34no—
802C42—32no—
803C42—92no—
804C42C2×D3211yescharacteristic
805C22×C3—21no—
806C22×C3—34no—
807C22×C3—32no—
808C22×C3—61no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3—61no—
812C22×C3C24×D311yescharacteristic
813C22×C3C24×D311yescharacteristic
814C2×D3—22no—
815C2×D3—21no—
816C2×D3—21no—
817C2×D3—22no—
818C2×D3—34no—
819C2×D3—34no—
820C2×D3—64no—
821C2×D3—62no—
822C2×D3—62no—
823C2×D3—62no—
824C2×D3—62no—
825C2×D3—122no—
826C2×D3—122no—
827C2×D3—128no—
828C2×D3—128no—
829C2×D3C2×D3×Q812yes—
830C2×D3C2×D3×Q814yes—
831C3×C4—24no—
832C3×C4—24no—
833C3×C4—21no—
834C3×C4—21no—
835C3×C4—22no—
836C3×C4—22no—
837C3×C4—32no—
838C3×C4—44no—
839C3×C4—41no—
840C3×C4—61no—
841C3×C4—62no—
842C3×C4—62no—
843C3×C4—62no—
844C3×C4—61no—
845C3×C4—64no—
846C3×C4#100412yes—
847C3×C4C2×D3×Q812yes—
848C3×C4C2×D3×Q812yes—
849C3×C4#100912yes—
850Dic3—22no—
851Dic3—22no—
852Dic3—21no—
853Dic3—24no—
854Dic3—21no—
855Dic3—22no—
856Dic3—64no—
857Dic3—62no—
858Dic3—62no—
859Dic3—62no—
860Dic3—62no—
861Dic3—62no—
862Dic3—62no—
863Dic3—122no—
864Dic3—122no—
865Dic3C2×D3×Q812yes—
866C32#350111yescharacteristic, complemented, Sylow
867C23—31no—
868C23—32no—
869C23—98no—
870C23—92no—
871C23—362no—
872C23—362no—
873Q8—24no—
874Q8—62no—
875Q8—124no—
876Q8—122no—
877Q8—182no—
878Q8—364no—
879Q8—362no—
880D4—34no—
881D4—98no—
882D4—94no—
883C2×C4—31no—
884C2×C4—34no—
885C2×C4—31no—
886C2×C4—31no—
887C2×C4—32no—
888C2×C4—34no—
889C2×C4—32no—
890C2×C4—32no—
891C2×C4—62no—
892C2×C4—64no—
893C2×C4—92no—
894C2×C4—92no—
895C2×C4—92no—
896C2×C4—124no—
897C2×C4—121no—
898C2×C4—184no—
899C2×C4—364no—
900C2×C4—362no—
901C2×C4—364no—
902C2×C4—362no—
903C2×C4—362no—
904C2×C4—364no—
905C2×C4C22×D3211yescharacteristic
906C2×C4C22×D3214yes—
907C2×C4C22×D3211yescharacteristic
908C2×C4C22×D3211yescharacteristic
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—21no—
912C2×C3—64no—
913C2×C3—62no—
914C2×C3C2×#100411yescharacteristic
915C2×C3C22×D3×Q811yescharacteristic
916C2×C3C22×D3×Q811yescharacteristic
917C2×C3C2×#100911yescharacteristic
918C2×C3#596411yescharacteristic
919C2×C3#596811yescharacteristic
920D3—22no—
921D3—24no—
922D3—64no—
923D3—64no—
924D3—124no—
925C22—32no—
926C22—34no—
927C22—62no—
928C22—61no—
929C22—61no—
930C22—62no—
931C22—94no—
932C22—182no—
933C22—182no—
934C22—368no—
935C22C23×D3211yescharacteristic
936C4—24no—
937C4—21no—
938C4—32no—
939C4—61no—
940C4—62no—
941C4—62no—
942C4—61no—
943C4—64no—
944C4—62no—
945C4—182no—
946C4—182no—
947C4—182no—
948C4#6431412yes—
949C4D32×Q812yes—
950C3—21no—
951C3#8628011yescharacteristic, complemented
952C3#8676111yescharacteristic, complemented
953C2—62no—
954C2—64no—
955C2—184no—
956C2C2×#6431411yescharacteristic
957C2C2×D32×Q811yescharacteristic
958C2#1059668811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radicalC2×D3×D12C22
hypercenterC4⋊Q8D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596198C2semidirect
2. C3×#5728C2semidirect
3. C3×#5727C2semidirect
4. #10595429C2semidirect
5. D3×#946C2semidirect
6. Q8×#626C2semidirect
7. #10595371C2semidirect
8. #10594635C2semidirect
10. #10594502C2semidirect
11. #10594485C2semidirect
12. #10594470C2semidirect
13. #10594392C2semidirect
15. #10593958C2semidirect
16. #10593956C2semidirect
17. #10593873C2semidirect
20. C2×Q8×C3⋊D3C22semidirect
21. C2×C3×D3×Q8C22semidirect
24. C32×C4⋊Q8C22semidirect
25. #64155C22semidirect
26. #64105C22semidirect
28. #64097C22semidirect
30. C4×#634C22semidirect
32. C3×#946C22semidirect
33. C3×Q8×Dic3C22semidirect
35. C3×#896C22semidirect
38. C3×#890C22semidirect
39. C3×#888C22semidirect
40. C3×#887C22semidirect
43. C3×#869C22semidirect
44. C3×C4×Dic6C22semidirect
48. #63918C22semidirect
49. C4×#627C22semidirect
52. #63900C22semidirect
53. #63899C22semidirect
56. #63896C22semidirect
57. #63895C22semidirect
62. D3×C4⋊Dic3C22semidirect
63. #63888C22semidirect
64. #63888C22semidirect
66. #63887C22semidirect
67. #63883C22semidirect
70. D3×Dic3⋊C4C22semidirect
71. #63872C22semidirect
72. #63871C22semidirect
73. #63871C22semidirect
74. #63869C22semidirect
75. #63867C22semidirect
76. #63867C22semidirect
77. #63866C22semidirect
78. #63866C22semidirect
80. #63857C22semidirect
81. #63857C22semidirect
93. #5728D3semidirect
97. #5727D3semidirect
145. D3×D12Q8semidirect
194. C2×D3×Q8C2×D3semidirect
202. C3×C4⋊Q8C2×D3semidirect
203. C3×C4⋊Q8C2×D3semidirect
227. #946C2×D3semidirect
228. Q8×Dic3C2×D3semidirect
263. #896C2×D3semidirect
282. #890C2×D3semidirect
289. #888C2×D3semidirect
290. #887C2×D3semidirect
321. #869C2×D3semidirect
327. C4×Dic6C2×D3semidirect
333. C2×D32C2×Q8semidirect
342. C4⋊(C3⋊D3)C2×Q8semidirect
354. C3×D12C2×Q8semidirect
359. C3×C4×D3C2×Q8semidirect
364. #626C2×Q8semidirect
577. C4⋊Q8D32semidirect
700. D12D3×Q8semidirect
718. C4×D3D3×Q8semidirect
866. C32#3501semidirect
951. C3#86280semidirect
952. C3#86761semidirect

Maximal subgroups

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

subgroupindex
#105961982
C3×#57282
C3×#57272
#105954292
D3×#9462
Q8×#6262
#105953712
#105946352
#105946042
#105945022
#105944852
#105944702
#105943922
C4×D3×D122
#105939582
#105939562
#105938732
#867613
#862803