Finite Group Databasebeta

← #11906201

Subgroups — #11906201

Order 1152.

2314 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596014C211yesmaximal, characteristic, complemented
2C3×C4×D3×D4C211yesmaximal, characteristic
3C3×D4×Dic6C211yesmaximal, characteristic, complemented
4#10595274C212yesmaximal, complemented
5#10595215C212yesmaximal
6#10594993C212yesmaximal, complemented
7Dic6×#67C212yesmaximal, complemented
8D3×#924C212yesmaximal, complemented
9C2×#63856C212yesmaximal, complemented
10#10594460C212yesmaximal, complemented
11#10594342C212yesmaximal, complemented
12#10594170C214yesmaximal, complemented
13#10594156C214yesmaximal, complemented
14#10593960C211yesmaximal, characteristic, complemented
15#10593904C211yesmaximal, characteristic, complemented
16#10593873C211yesmaximal, characteristic, complemented
17#10593859C211yesmaximal, characteristic, complemented
18#86761—31nomaximal
19#85766—31nomaximal
20C2×C3×D3×D4C2211yescharacteristic
21C22×C3×C4×D3C2212yes—
22C22×C3×Dic6C2212yescomplemented
23C2×D3×Dic6C2212yescomplemented
24C32×C4×D4C2211yescharacteristic
25D4×C3⋊Dic3C2212yes—
26C2×C4⋊(C3⋊Dic3)C2212yescomplemented
27#64133C2212yescomplemented
28#64099C2212yescomplemented
29#64087C2214yescomplemented
30#64078C2211yescharacteristic, complemented
31C4×#634C2211yescharacteristic, complemented
32C3×D4×Dic3C2212yes—
33C3×D4×Dic3C2211yescharacteristic
34C3×C4×#67C2212yes—
35C3×#924C2212yescomplemented
36C3×#893C2211yescharacteristic
37C3×D3×C4⋊C4C2211yescharacteristic
38C3×#888C2212yescomplemented
39C3×#67⋊C4C2212yes—
40C3×D3×C22⋊C4C2212yes—
41C3×#878C2214yescomplemented
42C3×C4×D12C2211yescharacteristic
43C3×C42×D3C2211yescharacteristic
44C3×#869C2211yescharacteristic, complemented
45C3×C4×Dic6C2211yescharacteristic, complemented
46#63982C2214yescomplemented
47#67⋊Dic3C2214yes—
48Dic3×#67C2214yes—
49D3×#217C2214yes—
50C2×#3724C2214yescomplemented
51#63964C2214yescomplemented
52#63964C2214yescomplemented
53C2×(C2×D3)⋊Dic3C2214yes—
54#63919C2212yescomplemented
55#63918C2211yescharacteristic, complemented
56C4×#627C2212yescomplemented
57#63899C2214yescomplemented
58#63898C2212yes—
59#63896C2214yescomplemented
60#63893C2214yescomplemented
61Dic3×D12C2212yes—
62D3×C4⋊Dic3C2212yescomplemented
63#63887C2214yescomplemented
64D3×Dic3⋊C4C2214yescomplemented
65#63869C2212yescomplemented
66#63869C2212yescomplemented
67#63867C2212yescomplemented
68#63866C2211yescharacteristic, complemented
69#63857C2212yes—
70#63857C2211yescharacteristic
71#63856C2211yescharacteristic
72#63856C2214yes—
73#63856C2212yes—
74#63856C2212yescomplemented
75#63856C2214yescomplemented
76#63856C2212yescomplemented
77#63855C2212yes—
78#63851C2214yes—
79#63851C2212yes—
80#63845C2214yescomplemented
81#63844C2212yescomplemented
82Dic3×Dic6C2212yescomplemented
83#63841C2212yes—
84#63839C2214yescomplemented
85C3×D4×Q8—31no—
86C2×C3×C4×D4—31no—
87Q8×#67—32no—
88C2×#946—32no—
89#5798—32no—
90C2×#924—32no—
91C2×#924—32no—
92#5730—32no—
93#5729—32no—
94#5728—31no—
95#5727—31no—
96#5636—34no—
97#5635—32no—
98#5634—34no—
99D3×C22⋊Q8—32no—
100#5579—31no—
101#5578—31no—
102#5545—32no—
103C4×D3×D4D311yescharacteristic
104#5543—31no—
105#5543—31no—
106#5543—32no—
107#5543—31no—
108#5543—61no—
109#5539—32no—
110#5539—32no—
111#5539—32no—
112#5539—34no—
113D4×Dic6—32no—
114D4×Dic6—31no—
115D4×Dic6D311yescharacteristic, complemented
116#5500—32no—
117#5483—34no—
118#5470—31no—
119#5470—31no—
120C23×C3×D3C2312yes—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C22×C3⋊Dic3C2314yes—
124C2×#634C2311yescharacteristic
125C2×#634C2312yes—
126C2×C3×#67C2312yes—
127C22×C3×Dic3C2314yes—
128C22×C3×Dic3C2312yes—
129C3×D3×D4Q818yescomplemented
130C2×C3×D12C2311yescharacteristic
131C2×C3×C4×D3—44no—
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2312yes—
136C2×C3×C4×D3C2312yes—
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×Dic6—44no—
139C2×C3×Dic6C2312yes—
140C2×C3×Dic6C2311yescharacteristic
141C2×C3×Dic6C2314yes—
142C2×#627C2314yes—
143C2×#627C2312yes—
144C2×D3×Dic3C2314yes—
145C2×D3×Dic3C2314yes—
146D3×Dic6—44no—
147C32×C4⋊C4C2311yescharacteristic
148C32×C22⋊C4C2312yes—
149C32×C42C2311yescharacteristic
150#3757C2314yes—
151C4⋊(C3⋊Dic3)C2311yescharacteristic
152C4⋊(C3⋊Dic3)C2312yes—
153C4⋊(C3⋊Dic3)C2312yes—
154C4⋊(C3⋊Dic3)C2314yes—
155#3750C2312yes—
156#3750C2314yes—
157C4×C3⋊Dic3C2312yes—
158C3×#217C2314yes—
159C3×#217C2312yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×(C2×D3)⋊C4C2312yes—
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2311yescharacteristic
165C3×C4⋊Dic3C2311yescharacteristic
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2314yes—
168C3×Dic3⋊C4C2312yes—
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2311yescharacteristic
173#3724C2314yes—
174#3724C2314yes—
175#3724C2314yes—
176#3724C2312yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2312yes—
182Dic3⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2312yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2314yes—
188Dic32C2314yes—
189#3501—91noSylow
190C22×C3×Q8—32no—
191C22×C3×D4—31no—
192C23×C3×C4—32no—
193C2×D3×Q8—32no—
194C2×D3×D4C2×D311yescharacteristic
195C22×C4×D3C2×D312yes—
196C22×Dic6—32no—
197C22×Dic6C2×D312yescomplemented
198C3×C4⋊Q8—32no—
199C3×C4⋊Q8—31no—
200C3×C22⋊Q8—32no—
201C3×C22⋊Q8—34no—
202C3×C4×Q8—31no—
203C3×C4×D4—21no—
204C3×C4×D4—31no—
205C3×C4×D4—32no—
206C3×C4×D4—32no—
207C3×C4×D4—31no—
208C3×C4×D4—32no—
209C3×C4×D4—31no—
210C3×C4×D4C2×D311yescharacteristic
211C3×C4×D4C2×D311yescharacteristic
212C2×C3×C4⋊C4—31no—
213C2×C3×C22⋊C4—32no—
214C2×C3×C42—31no—
215C2×#217—34no—
216C2×#217—34no—
217#946—34no—
218#946—32no—
219#946—34no—
220#946—32no—
221#946—31no—
222#946—32no—
223#946—34no—
224Q8×Dic3—32no—
225#944—34no—
226#944—31no—
227D4×Dic3—32no—
228D4×Dic3—32no—
229D4×Dic3—34no—
230D4×Dic3—34no—
231D4×Dic3—32no—
232D4×Dic3—32no—
233D4×Dic3—62no—
234D4×Dic3C2×D312yes—
235D4×Dic3C2×D311yescharacteristic
236C4×#67—34no—
237C4×#67C2×D312yes—
238C2×(C2×D3)⋊C4—34no—
239#926—32no—
240#926—32no—
241C2×C4⋊Dic3—32no—
242C2×C4⋊Dic3—32no—
243C2×C4⋊Dic3—32no—
244C2×C4⋊Dic3—62no—
245#924—32no—
246#924—32no—
247#924—32no—
248#924—31no—
249#924—34no—
250#924—32no—
251#924—32no—
252#924—34no—
253#924—34no—
254#924—34no—
255#924—32no—
256#924—31no—
257#924—32no—
258#924—34no—
259#924—62no—
260#924C2×D312yescomplemented
261C2×Dic3⋊C4—34no—
262C2×Dic3⋊C4—34no—
263C2×Dic3⋊C4—34no—
264#897—32no—
265#897—31no—
266#897—34no—
267#896—32no—
268#896—34no—
269#896—34no—
270#896—34no—
271#893—32no—
272#893C2×D311yescharacteristic
273#892—32no—
274D3×C4⋊C4—32no—
275D3×C4⋊C4—34no—
276D3×C4⋊C4C2×D311yescharacteristic
277#890—32no—
278#890—32no—
279#890—34no—
280#890—32no—
281#890—32no—
282#890—62no—
283#889—34no—
284#889—32no—
285#888—34no—
286#888—32no—
287#888—32no—
288#888—31no—
289#888C2×D312yescomplemented
290#887—32no—
291#67⋊C4—34no—
292#67⋊C4C2×D312yes—
293D3×C22⋊C4—34no—
294D3×C22⋊C4C2×D312yes—
295#878—34no—
296#878—34no—
297#878—34no—
298#878—34no—
299#878—34no—
300#878—34no—
301#878—34no—
302#878—34no—
303#878—34no—
304#878—34no—
305#878—64no—
306#878C2×D314yescomplemented
307C4×D12—32no—
308C4×D12C2×D311yescharacteristic
309#872—32no—
310C42×D3C2×D311yescharacteristic
311#870—32no—
312#870—32no—
313#870—32no—
314#869—31no—
315#869—31no—
316#869—31no—
317#869—31no—
318#869—61no—
319#869C2×D311yescharacteristic, complemented
320C4×Dic6—32no—
321C4×Dic6—31no—
322C4×Dic6—31no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6—61no—
327C4×Dic6C2×D311yescharacteristic, complemented
328C23×C32C2412yes—
329C22×C3×D3—42no—
330C22×C3×D3—42no—
331C22×C3×D3C2×Q818yescomplemented
332C22×C3×D3C2411yescharacteristic
333C22×C3×D3C2412yes—
334C32×D4C2×Q814yescomplemented
335C2×C32×C4—24no—
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2412yes—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C3⋊Dic3—44no—
341C2×C3⋊Dic3C2414yes—
342C2×C3⋊Dic3C2412yes—
343C2×C3⋊Dic3C2412yes—
344#634—22no—
345#634—42no—
346C3×#67C2×Q818yescomplemented
347C2×C3×Dic3—44no—
348C2×C3×Dic3—42no—
349C2×C3×Dic3C2414yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2411yescharacteristic
353C2×C3×Dic3C2411yescharacteristic
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2411yescharacteristic
356C3×D12C2×Q814yescomplemented
357C3×C4×D3—24no—
358C3×C4×D3—22no—
359C3×C4×D3—42no—
360C3×C4×D3—42no—
361C3×C4×D3—41no—
362C3×C4×D3C2×Q814yescomplemented
363C3×Dic6—24no—
364C3×Dic6—22no—
365C3×Dic6—44no—
366#627—44no—
367#627—42no—
368D3×Dic3—44no—
369D3×Dic3—44no—
370#554—92no—
371#554—91no—
372#554—92no—
373#554—94no—
374#554—92no—
375#554—91no—
376D4×Q8—31no—
377D4×Q8—91no—
378D4×Q8—92no—
379#544—92no—
380#543—94no—
381#533—91no—
382#533—91no—
383C2×C22⋊Q8—92no—
384C2×C22⋊Q8—92no—
385#518—92no—
386C2×C4×D4—31no—
387C24×C3—32no—
388C23×D3C22×D312yes—
389C2×C3×Q8—31no—
390C2×C3×Q8—32no—
391C2×C3×Q8—34no—
392C2×C3×Q8—124no—
393C2×C3×D4—21no—
394C2×C3×D4—32no—
395C2×C3×D4—38no—
396C2×C3×D4—31no—
397C2×C3×D4C22×D311yescharacteristic
398C2×C3×D4C22×D311yescharacteristic
399C22×C3×C4—22no—
400C22×C3×C4—31no—
401C22×C3×C4—32no—
402C22×C3×C4—34no—
403C22×C3×C4—31no—
404C22×C3×C4—32no—
405C22×C3×C4—32no—
406C22×C3×C4—31no—
407C22×C3×C4—32no—
408C22×C3×C4—124no—
409C22×C3×C4C22×D312yes—
410C22×C3×C4C22×D312yes—
411C2×#67C22×D312yes—
412C22×Dic3—34no—
413C22×Dic3—34no—
414C22×Dic3—34no—
415C22×Dic3—34no—
416C22×Dic3—64no—
417C22×Dic3C22×D312yes—
418C22×Dic3C22×D314yes—
419D3×Q8—124no—
420D3×D4Dic618yescomplemented
421C2×D12C22×D311yescharacteristic
422C2×C4×D3—34no—
423C2×C4×D3—34no—
424C2×C4×D3—44no—
425C2×C4×D3C22×D311yescharacteristic
426C2×C4×D3C22×D312yes—
427C2×C4×D3C22×D311yescharacteristic
428C2×C4×D3C22×D312yes—
429C2×C4×D3C22×D312yes—
430C2×C4×D3C22×D311yescharacteristic
431C2×Dic6—31no—
432C2×Dic6—31no—
433C2×Dic6—32no—
434C2×Dic6—32no—
435C2×Dic6—32no—
436C2×Dic6—32no—
437C2×Dic6—34no—
438C2×Dic6—34no—
439C2×Dic6—44no—
440C2×Dic6—61no—
441C2×Dic6—62no—
442C2×Dic6—124no—
443C2×Dic6C22×D312yes—
444C2×Dic6C22×D311yescharacteristic
445C2×Dic6C22×D314yes—
446C3×C4⋊C4—21no—
447C3×C4⋊C4—32no—
448C3×C4⋊C4—32no—
449C3×C4⋊C4—31no—
450C3×C4⋊C4—32no—
451C3×C4⋊C4—31no—
452C3×C4⋊C4—34no—
453C3×C4⋊C4—32no—
454C3×C4⋊C4C22×D311yescharacteristic
455C3×C4⋊C4C22×D311yescharacteristic
456C3×C22⋊C4—22no—
457C3×C22⋊C4—32no—
458C3×C22⋊C4—34no—
459C3×C22⋊C4—32no—
460C3×C22⋊C4—32no—
461C3×C22⋊C4C22×D312yes—
462C3×C22⋊C4C22×D312yes—
463C3×C42—21no—
464C3×C42—31no—
465C3×C42—31no—
466C3×C42—31no—
467C3×C42—32no—
468C3×C42C22×D311yescharacteristic
469C3×C42C22×D311yescharacteristic
470#217—34no—
471#217—34no—
472#217—34no—
473#217—34no—
474#217—34no—
475#217—32no—
476#217—32no—
477#217—64no—
478#217C22×D312yes—
479#217C22×D314yes—
480(C2×D3)⋊C4—32no—
481(C2×D3)⋊C4—32no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4C22×D312yes—
486(C2×D3)⋊C4C22×D312yes—
487C4⋊Dic3—32no—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—32no—
491C4⋊Dic3—32no—
492C4⋊Dic3—32no—
493C4⋊Dic3—34no—
494C4⋊Dic3—34no—
495C4⋊Dic3—32no—
496C4⋊Dic3—32no—
497C4⋊Dic3—32no—
498C4⋊Dic3—32no—
499C4⋊Dic3—34no—
500C4⋊Dic3—34no—
501C4⋊Dic3—61no—
502C4⋊Dic3—62no—
503C4⋊Dic3—62no—
504C4⋊Dic3—64no—
505C4⋊Dic3C22×D312yes—
506C4⋊Dic3C22×D311yescharacteristic
507C4⋊Dic3C22×D312yes—
508C4⋊Dic3C22×D311yescharacteristic
509Dic3⋊C4—32no—
510Dic3⋊C4—32no—
511Dic3⋊C4—34no—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—32no—
515Dic3⋊C4—34no—
516Dic3⋊C4—32no—
517Dic3⋊C4—32no—
518Dic3⋊C4—32no—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—32no—
522Dic3⋊C4—32no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—34no—
526Dic3⋊C4—34no—
527Dic3⋊C4—62no—
528Dic3⋊C4—64no—
529Dic3⋊C4C22×D312yes—
530Dic3⋊C4C22×D314yes—
531Dic3⋊C4C22×D312yes—
532C4×Dic3—32no—
533C4×Dic3—32no—
534C4×Dic3—34no—
535C4×Dic3—34no—
536C4×Dic3—62no—
537C4×Dic3C22×D311yescharacteristic
538C4×Dic3C22×D312yes—
539C4×Dic3C22×D311yescharacteristic
540C4×Dic3C22×D311yescharacteristic
541C22×C32—22no—
542C22×C32—22no—
543C22×C32C22×Q814yes—
544C22×C32C2511yescharacteristic
545C2×C3×D3—22no—
546C2×C3×D3—21no—
547C2×C3×D3—22no—
548C2×C3×D3—21no—
549C2×C3×D3—48no—
550C2×C3×D3C22×Q812yes—
551C2×C3×D3C22×Q814yes—
552C32×C4—22no—
553C32×C4—21no—
554C32×C4C22×Q812yes—
555C32×C4H(5,𝔽2)12yes—
556C3⋊Dic3—22no—
557C3⋊Dic3—24no—
558C3⋊Dic3—22no—
559C3×Dic3—24no—
560C3×Dic3—22no—
561C3×Dic3—22no—
562C3×Dic3—21no—
563C3×Dic3—22no—
564C3×Dic3—21no—
565C3×Dic3C22×Q812yes—
566C22×Q8—32no—
567C22×Q8—92no—
568C22×D4—31no—
569C23×C4—32no—
570C4⋊Q8—32no—
571C4⋊Q8—31no—
572C4⋊Q8—91no—
573C4⋊Q8—91no—
574C4⋊Q8—92no—
575C4⋊Q8—94no—
576C4⋊Q8—91no—
577#125—92no—
578#125—92no—
579#125—92no—
580#125—94no—
581#125—92no—
582C22⋊Q8—32no—
583C22⋊Q8—34no—
584C22⋊Q8—94no—
585C22⋊Q8—94no—
586C22⋊Q8—94no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—91no—
592C22⋊Q8—94no—
593C22⋊Q8—92no—
594C22⋊Q8—92no—
595C22⋊Q8—91no—
596C22⋊Q8—92no—
597C22⋊Q8—94no—
598C22⋊Q8—92no—
599C22⋊Q8—92no—
600C22⋊Q8—94no—
601C22⋊Q8—92no—
602C22⋊Q8—94no—
603C4×Q8—31no—
604C4×Q8—92no—
605C4×Q8—92no—
606C4×Q8—92no—
607C4×Q8—91no—
608C4×D4—31no—
609C4×D4—32no—
610C4×D4—32no—
611C4×D4—31no—
612C4×D4—32no—
613C4×D4—31no—
614C4×D4—92no—
615C4×D4—94no—
616C4×D4—92no—
617C4×D4—94no—
618C4×D4—92no—
619C4×D4D3211yescharacteristic
620#117—92no—
621#117—92no—
622C2×C4⋊C4—31no—
623C2×C4⋊C4—94no—
624C2×C4⋊C4—92no—
625C2×C4⋊C4—94no—
626C2×C4⋊C4—92no—
627C2×C22⋊C4—32no—
628C2×C22⋊C4—94no—
629C2×C22⋊C4—94no—
630C2×C42—31no—
631C23×C3—22no—
632C23×C3—31no—
633C23×C3—32no—
634C23×C3—38no—
635C23×C3—122no—
636C23×C3—122no—
637C23×C3C23×D312yes—
638C23×C3C23×D312yes—
639C22×D3—42no—
640C22×D3—42no—
641C22×D3C2×Dic618yescomplemented
642C22×D3C23×D311yescharacteristic
643C22×D3C23×D312yes—
644C3×Q8—64no—
645C3×Q8—62no—
646C3×Q8—124no—
647C3×D4—24no—
648C3×D4—38no—
649C3×D4—34no—
650C3×D4C2×Dic614yescomplemented
651C3×D4D3×Q814yescomplemented
652C2×C3×C4—24no—
653C2×C3×C4—24no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—22no—
657C2×C3×C4—21no—
658C2×C3×C4—31no—
659C2×C3×C4—34no—
660C2×C3×C4—34no—
661C2×C3×C4—31no—
662C2×C3×C4—32no—
663C2×C3×C4—31no—
664C2×C3×C4—32no—
665C2×C3×C4—32no—
666C2×C3×C4—44no—
667C2×C3×C4—64no—
668C2×C3×C4—62no—
669C2×C3×C4—121no—
670C2×C3×C4—122no—
671C2×C3×C4—122no—
672C2×C3×C4—122no—
673C2×C3×C4—124no—
674C2×C3×C4C23×D311yescharacteristic
675C2×C3×C4C23×D312yes—
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D312yes—
678C2×C3×C4C23×D311yescharacteristic
679C2×C3×C4C23×D311yescharacteristic
680C2×C3×C4C23×D311yescharacteristic
681C2×C3×C4C23×D311yescharacteristic
682#67C2×Dic618yescomplemented
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—34no—
686C2×Dic3—34no—
687C2×Dic3—32no—
688C2×Dic3—32no—
689C2×Dic3—44no—
690C2×Dic3—42no—
691C2×Dic3—62no—
692C2×Dic3—62no—
693C2×Dic3—64no—
694C2×Dic3—124no—
695C2×Dic3—124no—
696C2×Dic3—124no—
697C2×Dic3—124no—
698C2×Dic3—244no—
699C2×Dic3C23×D314yes—
700C2×Dic3C23×D311yescharacteristic
701C2×Dic3C23×D311yescharacteristic
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D311yescharacteristic
706D12C2×Dic614yescomplemented
707C4×D3—22no—
708C4×D3—24no—
709C4×D3—42no—
710C4×D3—42no—
711C4×D3—41no—
712C4×D3—124no—
713C4×D3—124no—
714C4×D3C2×Dic614yescomplemented
715Dic6—22no—
716Dic6—24no—
717Dic6—44no—
718Dic6—62no—
719Dic6—62no—
720Dic6—122no—
721Dic6—122no—
722Dic6—122no—
723Dic6—124no—
724Dic6—124no—
725Dic6—122no—
726Dic6—122no—
727Dic6—242no—
728C2×C32—24no—
729C2×C32C23×Q811yescharacteristic
730C2×C32C2×H(5,𝔽2)11yescharacteristic
731C2×C32#58511yescharacteristic
732C3×D3—22no—
733C3×D3—24no—
734C24—32no—
735C2×Q8—31no—
736C2×Q8—32no—
737C2×Q8—34no—
738C2×Q8—92no—
739C2×Q8—94no—
740C2×Q8—91no—
741C2×Q8—92no—
742C2×Q8—124no—
743C2×Q8—364no—
744C2×D4—32no—
745C2×D4—38no—
746C2×D4—31no—
747C2×D4C2×D3211yescharacteristic
748C22×C4—31no—
749C22×C4—34no—
750C22×C4—32no—
751C22×C4—31no—
752C22×C4—32no—
753C22×C4—31no—
754C22×C4—32no—
755C22×C4—32no—
756C22×C4—94no—
757C22×C4—94no—
758C22×C4—94no—
759C22×C4—124no—
760C22×C4C2×D3212yes—
761C4⋊C4—32no—
762C4⋊C4—31no—
763C4⋊C4—31no—
764C4⋊C4—34no—
765C4⋊C4—32no—
766C4⋊C4—32no—
767C4⋊C4—32no—
768C4⋊C4—92no—
769C4⋊C4—94no—
770C4⋊C4—92no—
771C4⋊C4—94no—
772C4⋊C4—94no—
773C4⋊C4—94no—
774C4⋊C4—92no—
775C4⋊C4—92no—
776C4⋊C4—94no—
777C4⋊C4—92no—
778C4⋊C4—92no—
779C4⋊C4—91no—
780C4⋊C4—94no—
781C4⋊C4—94no—
782C4⋊C4—92no—
783C4⋊C4—92no—
784C4⋊C4C2×D3211yescharacteristic
785C22⋊C4—32no—
786C22⋊C4—34no—
787C22⋊C4—32no—
788C22⋊C4—32no—
789C22⋊C4—92no—
790C22⋊C4—92no—
791C22⋊C4—94no—
792C22⋊C4—94no—
793C22⋊C4—94no—
794C22⋊C4—94no—
795C22⋊C4C2×D3212yes—
796C42—31no—
797C42—31no—
798C42—31no—
799C42—32no—
800C42—94no—
801C42—92no—
802C42C2×D3211yescharacteristic
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—24no—
808C22×C3—21no—
809C22×C3—32no—
810C22×C3—34no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—62no—
814C22×C3—61no—
815C22×C3—62no—
816C22×C3—61no—
817C22×C3—128no—
818C22×C3C22×Dic614yes—
819C22×C3C2×D3×Q814yes—
820C22×C3C24×D311yescharacteristic
821C22×C3C24×D311yescharacteristic
822C2×D3—21no—
823C2×D3—22no—
824C2×D3—21no—
825C2×D3—22no—
826C2×D3—48no—
827C2×D3C22×Dic612yes—
828C2×D3C22×Dic614yes—
829C3×C4—22no—
830C3×C4—22no—
831C3×C4—21no—
832C3×C4—21no—
833C3×C4—22no—
834C3×C4—22no—
835C3×C4—32no—
836C3×C4—41no—
837C3×C4—42no—
838C3×C4—62no—
839C3×C4—64no—
840C3×C4—61no—
841C3×C4—62no—
842C3×C4—62no—
843C3×C4—61no—
844C3×C4C22×Dic612yes—
845C3×C4#100412yes—
846C3×C4#100412yes—
847C3×C4C2×D3×Q812yes—
848Dic3—22no—
849Dic3—24no—
850Dic3—22no—
851Dic3—21no—
852Dic3—21no—
853Dic3—22no—
854Dic3—62no—
855Dic3—62no—
856Dic3—64no—
857Dic3—62no—
858Dic3—62no—
859Dic3—64no—
860Dic3—122no—
861Dic3—124no—
862Dic3—122no—
863Dic3C22×Dic612yes—
864C32#350111yescharacteristic, complemented, Sylow
865C23—32no—
866C23—31no—
867C23—38no—
868C23—122no—
869C23—122no—
870C23C22×D3212yes—
871Q8—62no—
872Q8—64no—
873Q8—124no—
874Q8—182no—
875Q8—362no—
876Q8—364no—
877Q8—362no—
878D4—38no—
879D4—34no—
880D4D3×Dic614yescomplemented
881C2×C4—24no—
882C2×C4—31no—
883C2×C4—34no—
884C2×C4—31no—
885C2×C4—31no—
886C2×C4—32no—
887C2×C4—32no—
888C2×C4—34no—
889C2×C4—32no—
890C2×C4—62no—
891C2×C4—64no—
892C2×C4—94no—
893C2×C4—92no—
894C2×C4—92no—
895C2×C4—122no—
896C2×C4—122no—
897C2×C4—121no—
898C2×C4—122no—
899C2×C4—124no—
900C2×C4—364no—
901C2×C4—364no—
902C2×C4—364no—
903C2×C4C22×D3211yescharacteristic
904C2×C4C22×D3212yes—
905C2×C4C22×D3211yescharacteristic
906C2×C4C22×D3211yescharacteristic
907C2×C3—24no—
908C2×C3—24no—
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—21no—
912C2×C3—44no—
913C2×C3—62no—
914C2×C3—64no—
915C2×C3C23×Dic611yescharacteristic
916C2×C3C2×#100411yescharacteristic
917C2×C3C2×#100411yescharacteristic
918C2×C3C22×D3×Q811yescharacteristic
919C2×C3#596411yescharacteristic
920C2×C3#596811yescharacteristic
921D3—22no—
922D3—24no—
923C22—22no—
924C22—22no—
925C22—32no—
926C22—34no—
927C22—61no—
928C22—62no—
929C22—61no—
930C22—62no—
931C22—128no—
932C22C2×D3×Dic614yes—
933C22C23×D3211yescharacteristic
934C4—22no—
935C4—21no—
936C4—32no—
937C4—61no—
938C4—62no—
939C4—62no—
940C4—64no—
941C4—61no—
942C4—62no—
943C4—182no—
944C4—184no—
945C4—182no—
946C4C2×D3×Dic612yes—
947C4#6431312yes—
948C3—21no—
949C3#8576611yescharacteristic, complemented
950C3#8676111yescharacteristic, complemented
951C2—24no—
952C2—62no—
953C2—64no—
954C2C22×D3×Dic611yescharacteristic
955C2C2×#6431311yescharacteristic
956C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
prime radicalC2×C3×D3×D4C22
hypercenterC4×D4D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596014C2semidirect
3. C3×D4×Dic6C2semidirect
4. #10595274C2semidirect
6. #10594993C2semidirect
7. Dic6×#67C2semidirect
8. D3×#924C2semidirect
9. C2×#63856C2semidirect
10. #10594460C2semidirect
11. #10594342C2semidirect
12. #10594170C2semidirect
13. #10594156C2semidirect
14. #10593960C2semidirect
15. #10593904C2semidirect
16. #10593873C2semidirect
17. #10593859C2semidirect
22. C22×C3×Dic6C22semidirect
23. C2×D3×Dic6C22semidirect
26. C2×C4⋊(C3⋊Dic3)C22semidirect
27. #64133C22semidirect
28. #64099C22semidirect
29. #64087C22semidirect
30. #64078C22semidirect
31. C4×#634C22semidirect
35. C3×#924C22semidirect
38. C3×#888C22semidirect
41. C3×#878C22semidirect
44. C3×#869C22semidirect
45. C3×C4×Dic6C22semidirect
46. #63982C22semidirect
50. C2×#3724C22semidirect
51. #63964C22semidirect
52. #63964C22semidirect
54. #63919C22semidirect
55. #63918C22semidirect
56. C4×#627C22semidirect
57. #63899C22semidirect
59. #63896C22semidirect
60. #63893C22semidirect
62. D3×C4⋊Dic3C22semidirect
63. #63887C22semidirect
64. D3×Dic3⋊C4C22semidirect
65. #63869C22semidirect
66. #63869C22semidirect
67. #63867C22semidirect
68. #63866C22semidirect
74. #63856C22semidirect
75. #63856C22semidirect
76. #63856C22semidirect
80. #63845C22semidirect
81. #63844C22semidirect
82. Dic3×Dic6C22semidirect
84. #63839C22semidirect
115. D4×Dic6D3semidirect
129. C3×D3×D4Q8semidirect
197. C22×Dic6C2×D3semidirect
260. #924C2×D3semidirect
289. #888C2×D3semidirect
306. #878C2×D3semidirect
319. #869C2×D3semidirect
327. C4×Dic6C2×D3semidirect
331. C22×C3×D3C2×Q8semidirect
334. C32×D4C2×Q8semidirect
346. C3×#67C2×Q8semidirect
356. C3×D12C2×Q8semidirect
362. C3×C4×D3C2×Q8semidirect
420. D3×D4Dic6semidirect
641. C22×D3C2×Dic6semidirect
650. C3×D4C2×Dic6semidirect
651. C3×D4D3×Q8semidirect
682. #67C2×Dic6semidirect
706. D12C2×Dic6semidirect
714. C4×D3C2×Dic6semidirect
864. C32#3501semidirect
880. D4D3×Dic6semidirect
949. C3#85766semidirect
950. C3#86761semidirect

Maximal subgroups

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

subgroupindex
#105960142
C3×C4×D3×D42
C3×D4×Dic62
#105952742
#105952152
#105949932
Dic6×#672
D3×#9242
C2×#638562
#105944602
#105943422
#105941702
#105941562
#105939602
#105939042
#105938732
#105938592
#867613
#857663