Finite Group Databasebeta

← #11906200

Subgroups — #11906200

Order 1152.

2413 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×C3⋊D3C211yesmaximal, characteristic
2C3×#5543C211yesmaximal, characteristic, complemented
3C3×D4×Dic6C211yesmaximal, characteristic, complemented
4#10595272C212yesmaximal, complemented
5#10595223C212yesmaximal
6#10594991C212yesmaximal, complemented
7#10594925C212yesmaximal, complemented
8C2×#63871C212yesmaximal, complemented
9#10594803C212yesmaximal, complemented
10#10594470C212yesmaximal, complemented
11#10594325C212yesmaximal, complemented
12#10594180C214yesmaximal, complemented
13#10594141C214yesmaximal, complemented
14#10593958C211yesmaximal, characteristic, complemented
15#10593903C211yesmaximal, characteristic, complemented
16#10593882C211yesmaximal, characteristic, complemented
17#10593866C211yesmaximal, characteristic, complemented
18#86948—31nomaximal
19#86761—31nomaximal
20C2×D4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2212yes—
22C22×C3×Dic6C2212yescomplemented
23C2×#3797C2212yescomplemented
24C32×C4×D4C2211yescharacteristic
25D4×C3⋊Dic3C2211yescharacteristic
26C4×#638C2212yes—
27#64102C2211yescharacteristic
28C4⋊C4×C3⋊D3C2211yescharacteristic
29#64090C2212yes—
30C22⋊C4×C3⋊D3C2212yes—
31C4×C4⋊(C3⋊D3)C2211yescharacteristic
32C42×C3⋊D3C2211yescharacteristic
33C3×D4×Dic3C2212yes—
34C3×D4×Dic3C2212yes—
35C2×C3×C4⋊Dic3C2212yescomplemented
36C3×#924C2212yescomplemented
37C3×#924C2212yescomplemented
38C3×#890C2212yescomplemented
39C3×#888C2212yescomplemented
40C3×#878C2214yescomplemented
41C3×#878C2214yescomplemented
42C3×#869C2211yescharacteristic, complemented
43C3×#869C2211yescharacteristic, complemented
44C3×C4×Dic6C2211yescharacteristic, complemented
45C3×C4×Dic6C2211yescharacteristic, complemented
46#63982C2214yescomplemented
47#63974C2214yes—
48C2×Dic3⋊Dic3C2214yescomplemented
49#63964C2214yescomplemented
50#63964C2214yescomplemented
51C2×#3722C2214yes—
52#63952C2214yes—
53#63952C2214yes—
54#63919C2211yescharacteristic, complemented
55#63918C2212yescomplemented
56C4×#627C2212yescomplemented
57#63900C2212yescomplemented
58#63895C2214yescomplemented
59#63895C2214yescomplemented
60#63894C2212yes—
61#63894C2212yes—
62#63888C2214yescomplemented
63#63888C2214yescomplemented
64#63883C2214yescomplemented
65#63874C2212yes—
66#63873C2211yescharacteristic, complemented
67#63872C2212yescomplemented
68#63871C2214yes—
69#63871C2211yescharacteristic
70#63871C2212yes—
71#63871C2212yes—
72#63871C2211yescharacteristic
73#63871C2214yescomplemented
74#63871C2212yescomplemented
75#63871C2212yescomplemented
76#63870C2212yescomplemented
77#63869C2212yescomplemented
78#63865C2214yes—
79#63865C2212yes—
80#63849C2212yes—
81#63847C2214yescomplemented
82#63843C2212yescomplemented
83#63843C2212yescomplemented
84#63839C2214yescomplemented
85C3×#554—31no—
86C3×D4×Q8—31no—
87Q8×#67—32no—
88C2×#946—32no—
89#5730—32no—
90#5730—31no—
91#5729—32no—
92#5728—31no—
93#5728—31no—
94#5727—31no—
95#5690—32no—
96#5689—32no—
97#5636—34no—
98#5635—32no—
99#5635—34no—
100#5634—34no—
101#5634—34no—
102#5632—32no—
103D3×C22⋊Q8—32no—
104D3×C22⋊Q8—32no—
105#5579—31no—
106#5578—31no—
107#5578—31no—
108Q8×D12—31no—
109#5545—32no—
110#5545—32no—
111C4×D3×D4—31no—
112C4×D3×D4—31no—
113C4×D3×D4—61no—
114#5543—32no—
115#5543D311yescharacteristic, complemented
116#5539—32no—
117D4×Dic6D311yescharacteristic, complemented
118#5511—32no—
119C2×#897—32no—
120C23×C3⋊D3C2312yes—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C2×#638C2312yes—
124C22×C3⋊Dic3C2312yes—
125D4×C3⋊D3Q818yescomplemented
126C2×C4⋊(C3⋊D3)C2311yescharacteristic
127C2×C4×C3⋊D3—44no—
128C2×C4×C3⋊D3C2312yes—
129C2×C4×C3⋊D3C2311yescharacteristic
130C2×C4×C3⋊D3C2311yescharacteristic
131C2×C4×C3⋊D3C2312yes—
132C2×C4×C3⋊D3C2312yes—
133C2×C4×C3⋊D3C2311yescharacteristic
134C22×C3×Dic3C2314yes—
135C22×C3×Dic3C2314yes—
136C2×C3×Dic6—44no—
137C2×C3×Dic6C2311yescharacteristic
138C2×C3×Dic6C2312yes—
139C2×C3×Dic6C2311yescharacteristic
140C2×C3×Dic6C2312yes—
141C2×C3×Dic6C2314yes—
142C2×#627C2314yes—
143C2×#627C2312yes—
144C2×#624C2314yes—
145C2×#624C2314yes—
146#3797—44no—
147C32×C4⋊C4C2311yescharacteristic
148C32×C22⋊C4C2312yes—
149C32×C42C2311yescharacteristic
150#3757C2312yes—
151#3752C2312yes—
152#3752C2312yes—
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154#3750C2312yes—
155C4×C3⋊Dic3C2311yescharacteristic
156C4×C3⋊Dic3C2311yescharacteristic
157C4×C3⋊Dic3C2311yescharacteristic
158C3×#217C2314yes—
159C3×#217C2314yes—
160C3×C4⋊Dic3C2312yes—
161C3×C4⋊Dic3C2314yes—
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2311yescharacteristic
165C3×C4⋊Dic3C2312yes—
166C3×C4⋊Dic3C2311yescharacteristic
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2312yes—
169C3×Dic3⋊C4C2314yes—
170C3×Dic3⋊C4C2314yes—
171C3×C4×Dic3C2312yes—
172C3×C4×Dic3C2312yes—
173#3724C2312yes—
174#3724C2312yes—
175#3724C2314yes—
176#3724C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2312yes—
182Dic3⋊Dic3C2312yes—
183#3722C2314yes—
184#3722C2312yes—
185#3722C2312yes—
186#3722C2314yes—
187#3722C2314yes—
188Dic32C2314yes—
189#3501—91noSylow
190C22×C3×Q8—32no—
191C2×D3×Q8—32no—
192C2×D3×Q8—32no—
193C2×D3×D4—31no—
194C2×D3×D4—31no—
195C2×D3×D4—61no—
196C22×C4×D3—32no—
197C22×C4×D3—32no—
198C22×C4×D3—62no—
199C22×Dic6C2×D312yescomplemented
200C3×C4⋊Q8—32no—
201C3×C4⋊Q8—31no—
202C3×C4⋊Q8—31no—
203C3×#125—32no—
204C3×C22⋊Q8—32no—
205C3×C22⋊Q8—32no—
206C3×C22⋊Q8—34no—
207C3×C22⋊Q8—34no—
208C3×C4×Q8—31no—
209C3×C4×Q8—31no—
210C3×C4×D4—21no—
211C3×C4×D4—32no—
212C3×C4×D4—32no—
213C3×C4×D4C2×D311yescharacteristic
214C3×C4×D4C2×D311yescharacteristic
215C2×C3×C4⋊C4—32no—
216#946—32no—
217#946—34no—
218#946—32no—
219#946—34no—
220#946—32no—
221#946—31no—
222#946—31no—
223#946—32no—
224#946—34no—
225#946—34no—
226Q8×Dic3—32no—
227Q8×Dic3—32no—
228#944—31no—
229#944—31no—
230#944—34no—
231D4×Dic3—31no—
232D4×Dic3—31no—
233D4×Dic3—61no—
234D4×Dic3C2×D312yes—
235D4×Dic3C2×D312yes—
236C4×#67—32no—
237C4×#67—32no—
238C4×#67—34no—
239C4×#67—34no—
240C4×#67—62no—
241C2×(C2×D3)⋊C4—34no—
242C2×(C2×D3)⋊C4—34no—
243C2×C4⋊Dic3—34no—
244C2×C4⋊Dic3C2×D312yescomplemented
245#924—34no—
246#924—34no—
247#924C2×D312yescomplemented
248#924C2×D312yescomplemented
249C2×Dic3⋊C4—34no—
250#897—32no—
251#897—32no—
252#897—34no—
253#897—34no—
254#897—32no—
255#897—31no—
256#897—31no—
257#897—32no—
258#897—34no—
259#897—34no—
260#896—34no—
261#896—34no—
262#896—32no—
263#896—32no—
264#896—34no—
265#896—34no—
266#896—34no—
267#896—34no—
268#893—31no—
269#893—31no—
270#893—32no—
271#893—32no—
272#893—61no—
273#892—32no—
274#892—32no—
275D3×C4⋊C4—31no—
276D3×C4⋊C4—31no—
277D3×C4⋊C4—32no—
278D3×C4⋊C4—32no—
279D3×C4⋊C4—34no—
280D3×C4⋊C4—34no—
281D3×C4⋊C4—61no—
282#890—32no—
283#890—32no—
284#890—32no—
285#890C2×D312yescomplemented
286#889—34no—
287#889—32no—
288#889—34no—
289#889—32no—
290#888—34no—
291#888—31no—
292#888—31no—
293#888—32no—
294#888C2×D312yescomplemented
295#887—32no—
296#887—32no—
297#67⋊C4—34no—
298#67⋊C4—34no—
299#67⋊C4—32no—
300#67⋊C4—32no—
301#67⋊C4—62no—
302D3×C22⋊C4—32no—
303D3×C22⋊C4—32no—
304D3×C22⋊C4—34no—
305D3×C22⋊C4—34no—
306D3×C22⋊C4—62no—
307#878—34no—
308#878—34no—
309#878—34no—
310#878—34no—
311#878C2×D314yescomplemented
312#878C2×D314yescomplemented
313C4×D12—31no—
314C4×D12—31no—
315C4×D12—32no—
316C4×D12—32no—
317C4×D12—61no—
318#872—32no—
319#872—32no—
320C42×D3—31no—
321C42×D3—31no—
322C42×D3—61no—
323#870—32no—
324#869—32no—
325#869C2×D311yescharacteristic, complemented
326#869C2×D311yescharacteristic, complemented
327C4×Dic6—32no—
328C4×Dic6—32no—
329C4×Dic6C2×D311yescharacteristic, complemented
330C4×Dic6C2×D311yescharacteristic, complemented
331C23×C32C2412yes—
332C22×C3⋊D3—42no—
333C22×C3⋊D3—42no—
334C22×C3⋊D3C2×Q818yescomplemented
335C22×C3⋊D3C2411yescharacteristic
336C22×C3⋊D3C2412yes—
337C32×D4C2×Q814yescomplemented
338C2×C32×C4—24no—
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2412yes—
341C2×C32×C4C2411yescharacteristic
342C2×C32×C4C2411yescharacteristic
343#638C2×Q818yescomplemented
344C2×C3⋊Dic3—42no—
345C2×C3⋊Dic3C2411yescharacteristic
346C2×C3⋊Dic3C2411yescharacteristic
347C2×C3⋊Dic3C2412yes—
348C2×C3⋊Dic3C2411yescharacteristic
349C4⋊(C3⋊D3)C2×Q814yescomplemented
350C4×C3⋊D3—22no—
351C4×C3⋊D3—24no—
352C4×C3⋊D3—42no—
353C4×C3⋊D3—42no—
354C4×C3⋊D3—41no—
355C4×C3⋊D3C2×Q814yescomplemented
356C2×C3×Dic3—44no—
357C2×C3×Dic3—44no—
358C2×C3×Dic3C2414yes—
359C2×C3×Dic3C2414yes—
360C2×C3×Dic3C2412yes—
361C2×C3×Dic3C2412yes—
362C2×C3×Dic3C2412yes—
363C2×C3×Dic3C2412yes—
364C3×Dic6—22no—
365C3×Dic6—24no—
366C3×Dic6—22no—
367C3×Dic6—44no—
368C3×Dic6—42no—
369#627—44no—
370#627—42no—
371#624—44no—
372#624—44no—
373#554—31no—
374#554—92no—
375#554—92no—
376#554—91no—
377#554—94no—
378#554—92no—
379D4×Q8—31no—
380D4×Q8—91no—
381D4×Q8—92no—
382#544—92no—
383#543—94no—
384#533—91no—
385#533—91no—
386C2×C22⋊Q8—92no—
387C2×C22⋊Q8—92no—
388#518—92no—
389C2×C4×D4—91no—
390C23×D3—32no—
391C23×D3—32no—
392C23×D3—62no—
393C2×C3×Q8—31no—
394C2×C3×Q8—31no—
395C2×C3×Q8—32no—
396C2×C3×Q8—34no—
397C2×C3×Q8—32no—
398C2×C3×Q8—124no—
399C2×C3×D4—21no—
400C2×C3×D4C22×D311yescharacteristic
401C2×C3×D4C22×D311yescharacteristic
402C22×C3×C4—22no—
403C22×C3×C4—34no—
404C22×C3×C4—34no—
405C22×C3×C4C22×D312yes—
406C22×C3×C4C22×D312yes—
407C2×#67—32no—
408C2×#67—32no—
409C2×#67—62no—
410C22×Dic3—32no—
411C22×Dic3—32no—
412C22×Dic3—62no—
413C22×Dic3C22×D314yes—
414C22×Dic3C22×D314yes—
415D3×Q8—124no—
416D3×Q8—124no—
417D3×D4—38no—
418D3×D4—38no—
419D3×D4—68no—
420C2×D12—31no—
421C2×D12—31no—
422C2×D12—61no—
423C2×C4×D3—31no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—32no—
428C2×C4×D3—32no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—32no—
432C2×C4×D3—32no—
433C2×C4×D3—32no—
434C2×C4×D3—32no—
435C2×C4×D3—34no—
436C2×C4×D3—34no—
437C2×C4×D3—34no—
438C2×C4×D3—34no—
439C2×C4×D3—61no—
440C2×C4×D3—61no—
441C2×C4×D3—61no—
442C2×C4×D3—62no—
443C2×C4×D3—62no—
444C2×C4×D3—62no—
445C2×C4×D3—124no—
446C2×C4×D3—124no—
447C2×C4×D3—128no—
448C2×Dic6—32no—
449C2×Dic6—32no—
450C2×Dic6—34no—
451C2×Dic6—34no—
452C2×Dic6—44no—
453C2×Dic6C22×D311yescharacteristic
454C2×Dic6C22×D311yescharacteristic
455C2×Dic6C22×D312yes—
456C2×Dic6C22×D312yes—
457C2×Dic6C22×D314yes—
458C3×C4⋊C4—21no—
459C3×C4⋊C4—32no—
460C3×C4⋊C4—32no—
461C3×C4⋊C4—32no—
462C3×C4⋊C4—31no—
463C3×C4⋊C4—34no—
464C3×C4⋊C4—31no—
465C3×C4⋊C4—34no—
466C3×C4⋊C4—32no—
467C3×C4⋊C4—32no—
468C3×C4⋊C4—34no—
469C3×C4⋊C4—32no—
470C3×C4⋊C4C22×D311yescharacteristic
471C3×C4⋊C4C22×D311yescharacteristic
472C3×C22⋊C4—22no—
473C3×C22⋊C4—34no—
474C3×C22⋊C4—34no—
475C3×C22⋊C4C22×D312yes—
476C3×C22⋊C4C22×D312yes—
477C3×C42—21no—
478C3×C42—32no—
479C3×C42—32no—
480C3×C42C22×D311yescharacteristic
481C3×C42C22×D311yescharacteristic
482#217—32no—
483#217—32no—
484#217—62no—
485#217C22×D314yes—
486#217C22×D314yes—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4—32no—
492(C2×D3)⋊C4—32no—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—32no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—34no—
498(C2×D3)⋊C4—34no—
499(C2×D3)⋊C4—34no—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—62no—
502(C2×D3)⋊C4—62no—
503C4⋊Dic3—31no—
504C4⋊Dic3—31no—
505C4⋊Dic3—32no—
506C4⋊Dic3—32no—
507C4⋊Dic3—34no—
508C4⋊Dic3—34no—
509C4⋊Dic3—34no—
510C4⋊Dic3—34no—
511C4⋊Dic3—61no—
512C4⋊Dic3C22×D311yescharacteristic
513C4⋊Dic3C22×D311yescharacteristic
514C4⋊Dic3C22×D312yes—
515C4⋊Dic3C22×D312yes—
516C4⋊Dic3C22×D312yes—
517C4⋊Dic3C22×D312yes—
518C4⋊Dic3C22×D314yes—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—32no—
522Dic3⋊C4—32no—
523Dic3⋊C4—32no—
524Dic3⋊C4—32no—
525Dic3⋊C4—34no—
526Dic3⋊C4—34no—
527Dic3⋊C4—32no—
528Dic3⋊C4—32no—
529Dic3⋊C4—32no—
530Dic3⋊C4—32no—
531Dic3⋊C4—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4—34no—
534Dic3⋊C4—34no—
535Dic3⋊C4—62no—
536Dic3⋊C4C22×D312yes—
537Dic3⋊C4C22×D312yes—
538Dic3⋊C4C22×D314yes—
539Dic3⋊C4C22×D314yes—
540C4×Dic3—31no—
541C4×Dic3—31no—
542C4×Dic3—31no—
543C4×Dic3—31no—
544C4×Dic3—31no—
545C4×Dic3—31no—
546C4×Dic3—34no—
547C4×Dic3—34no—
548C4×Dic3—61no—
549C4×Dic3—61no—
550C4×Dic3—61no—
551C4×Dic3C22×D312yes—
552C4×Dic3C22×D312yes—
553C22×C32—22no—
554C22×C32—22no—
555C22×C32C22×Q814yes—
556C22×C32C2511yescharacteristic
557C2×C3⋊D3—21no—
558C2×C3⋊D3—21no—
559C2×C3⋊D3—22no—
560C2×C3⋊D3—22no—
561C2×C3⋊D3—48no—
562C2×C3⋊D3C22×Q812yes—
563C2×C3⋊D3C22×Q814yes—
564C32×C4—22no—
565C32×C4—21no—
566C32×C4C22×Q812yes—
567C32×C4H(5,𝔽2)12yes—
568C3⋊Dic3—21no—
569C3⋊Dic3—22no—
570C3⋊Dic3—21no—
571C3⋊Dic3C22×Q812yes—
572C3×Dic3—22no—
573C3×Dic3—24no—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—24no—
577C3×Dic3—22no—
578C22×Q8—32no—
579C22×Q8—92no—
580C22×D4—91no—
581C23×C4—92no—
582C4⋊Q8—32no—
583C4⋊Q8—31no—
584C4⋊Q8—31no—
585C4⋊Q8—92no—
586C4⋊Q8—91no—
587C4⋊Q8—94no—
588C4⋊Q8—91no—
589#125—32no—
590#125—92no—
591#125—92no—
592#125—92no—
593#125—94no—
594C22⋊Q8—32no—
595C22⋊Q8—32no—
596C22⋊Q8—34no—
597C22⋊Q8—34no—
598C22⋊Q8—94no—
599C22⋊Q8—94no—
600C22⋊Q8—94no—
601C22⋊Q8—94no—
602C22⋊Q8—92no—
603C22⋊Q8—94no—
604C22⋊Q8—94no—
605C22⋊Q8—91no—
606C22⋊Q8—92no—
607C22⋊Q8—91no—
608C22⋊Q8—94no—
609C22⋊Q8—92no—
610C22⋊Q8—92no—
611C22⋊Q8—94no—
612C22⋊Q8—92no—
613C22⋊Q8—94no—
614C22⋊Q8—94no—
615C4×Q8—31no—
616C4×Q8—31no—
617C4×Q8—92no—
618C4×Q8—92no—
619C4×Q8—92no—
620C4×D4—32no—
621C4×D4—32no—
622C4×D4—92no—
623C4×D4—92no—
624C4×D4—94no—
625C4×D4—94no—
626C4×D4—91no—
627C4×D4—92no—
628C4×D4—91no—
629C4×D4—92no—
630C4×D4—91no—
631C4×D4D3211yescharacteristic
632#117—92no—
633#117—92no—
634C2×C4⋊C4—32no—
635C2×C4⋊C4—92no—
636C2×C4⋊C4—94no—
637C2×C4⋊C4—94no—
638C2×C4⋊C4—91no—
639C2×C22⋊C4—94no—
640C2×C22⋊C4—94no—
641C2×C22⋊C4—92no—
642C2×C42—91no—
643C23×C3—22no—
644C23×C3C23×D312yes—
645C23×C3C23×D312yes—
646C22×D3—31no—
647C22×D3—31no—
648C22×D3—32no—
649C22×D3—32no—
650C22×D3—38no—
651C22×D3—38no—
652C22×D3—61no—
653C22×D3—68no—
654C22×D3—62no—
655C22×D3—122no—
656C22×D3—122no—
657C22×D3—122no—
658C22×D3—122no—
659C22×D3—124no—
660C22×D3—124no—
661C3×Q8—62no—
662C3×Q8—64no—
663C3×Q8—62no—
664C3×Q8—122no—
665C3×Q8—124no—
666C3×D4—24no—
667C3×D4D3×Q814yescomplemented
668C3×D4D3×Q814yescomplemented
669C2×C3×C4—24no—
670C2×C3×C4—24no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—22no—
675C2×C3×C4—34no—
676C2×C3×C4—34no—
677C2×C3×C4—32no—
678C2×C3×C4—32no—
679C2×C3×C4—32no—
680C2×C3×C4—32no—
681C2×C3×C4—44no—
682C2×C3×C4—124no—
683C2×C3×C4—124no—
684C2×C3×C4C23×D311yescharacteristic
685C2×C3×C4C23×D311yescharacteristic
686C2×C3×C4C23×D312yes—
687C2×C3×C4C23×D312yes—
688C2×C3×C4C23×D311yescharacteristic
689C2×C3×C4C23×D311yescharacteristic
690C2×C3×C4C23×D311yescharacteristic
691C2×C3×C4C23×D311yescharacteristic
692#67—38no—
693#67—38no—
694#67—68no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—31no—
698C2×Dic3—31no—
699C2×Dic3—31no—
700C2×Dic3—31no—
701C2×Dic3—32no—
702C2×Dic3—32no—
703C2×Dic3—44no—
704C2×Dic3—44no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—62no—
709C2×Dic3—122no—
710C2×Dic3—122no—
711C2×Dic3—124no—
712C2×Dic3C23×D314yes—
713C2×Dic3C23×D314yes—
714C2×Dic3C23×D312yes—
715C2×Dic3C23×D312yes—
716C2×Dic3C23×D312yes—
717C2×Dic3C23×D312yes—
718D12—34no—
719D12—34no—
720D12—64no—
721C4×D3—34no—
722C4×D3—34no—
723C4×D3—64no—
724C4×D3—64no—
725C4×D3—62no—
726C4×D3—64no—
727C4×D3—62no—
728C4×D3—64no—
729C4×D3—124no—
730C4×D3—124no—
731C4×D3—124no—
732C4×D3—124no—
733C4×D3—124no—
734C4×D3—121no—
735C4×D3—121no—
736C4×D3—122no—
737C4×D3—122no—
738C4×D3—122no—
739C4×D3—122no—
740C4×D3—124no—
741C4×D3—122no—
742C4×D3—124no—
743Dic6—22no—
744Dic6—24no—
745Dic6—22no—
746Dic6—44no—
747Dic6—42no—
748Dic6—122no—
749Dic6—122no—
750Dic6—124no—
751Dic6—124no—
752C2×C32—24no—
753C2×C32C23×Q811yescharacteristic
754C2×C32C2×H(5,𝔽2)11yescharacteristic
755C2×C32#58511yescharacteristic
756C3⋊D3—22no—
757C3⋊D3—24no—
758C24—92no—
759C2×Q8—31no—
760C2×Q8—31no—
761C2×Q8—32no—
762C2×Q8—32no—
763C2×Q8—34no—
764C2×Q8—92no—
765C2×Q8—94no—
766C2×Q8—124no—
767C2×Q8—364no—
768C2×D4—92no—
769C2×D4—98no—
770C2×D4—91no—
771C2×D4C2×D3211yescharacteristic
772C22×C4—34no—
773C22×C4—34no—
774C22×C4—94no—
775C22×C4—94no—
776C22×C4—91no—
777C22×C4—92no—
778C22×C4—91no—
779C22×C4—92no—
780C22×C4—91no—
781C22×C4—92no—
782C22×C4—92no—
783C22×C4—364no—
784C22×C4C2×D3212yes—
785C4⋊C4—31no—
786C4⋊C4—32no—
787C4⋊C4—34no—
788C4⋊C4—31no—
789C4⋊C4—34no—
790C4⋊C4—34no—
791C4⋊C4—32no—
792C4⋊C4—32no—
793C4⋊C4—32no—
794C4⋊C4—32no—
795C4⋊C4—32no—
796C4⋊C4—92no—
797C4⋊C4—92no—
798C4⋊C4—94no—
799C4⋊C4—94no—
800C4⋊C4—94no—
801C4⋊C4—94no—
802C4⋊C4—92no—
803C4⋊C4—92no—
804C4⋊C4—94no—
805C4⋊C4—92no—
806C4⋊C4—92no—
807C4⋊C4—91no—
808C4⋊C4C2×D3211yescharacteristic
809C22⋊C4—34no—
810C22⋊C4—34no—
811C22⋊C4—92no—
812C22⋊C4—92no—
813C22⋊C4—94no—
814C22⋊C4—94no—
815C22⋊C4—94no—
816C22⋊C4—92no—
817C22⋊C4—92no—
818C22⋊C4—92no—
819C22⋊C4C2×D3212yes—
820C42—32no—
821C42—32no—
822C42—94no—
823C42—91no—
824C42—91no—
825C42—91no—
826C42C2×D3211yescharacteristic
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—24no—
832C22×C3—21no—
833C22×C3—42no—
834C22×C3—42no—
835C22×C3C2×D3×Q814yes—
836C22×C3C2×D3×Q814yes—
837C22×C3C24×D311yescharacteristic
838C22×C3C24×D311yescharacteristic
839C2×D3—32no—
840C2×D3—32no—
841C2×D3—34no—
842C2×D3—34no—
843C2×D3—62no—
844C2×D3—64no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—61no—
849C2×D3—62no—
850C2×D3—61no—
851C2×D3—62no—
852C2×D3—61no—
853C2×D3—62no—
854C2×D3—61no—
855C2×D3—122no—
856C2×D3—122no—
857C2×D3—128no—
858C2×D3—128no—
859C2×D3—1216no—
860C3×C4—22no—
861C3×C4—22no—
862C3×C4—21no—
863C3×C4—21no—
864C3×C4—22no—
865C3×C4—22no—
866C3×C4—42no—
867C3×C4—41no—
868C3×C4—62no—
869C3×C4—64no—
870C3×C4—62no—
871C3×C4—62no—
872C3×C4—62no—
873C3×C4—64no—
874C3×C4#100412yes—
875C3×C4C2×D3×Q812yes—
876C3×C4C2×D3×Q812yes—
877C3×C4#100912yes—
878Dic3—22no—
879Dic3—24no—
880Dic3—22no—
881Dic3—24no—
882Dic3—22no—
883Dic3—22no—
884Dic3—32no—
885Dic3—32no—
886Dic3—62no—
887Dic3—62no—
888Dic3—62no—
889Dic3—61no—
890Dic3—62no—
891Dic3—61no—
892Dic3—61no—
893Dic3—61no—
894Dic3—122no—
895Dic3—121no—
896C32#350111yescharacteristic, complemented, Sylow
897C23—91no—
898C23—92no—
899C23—98no—
900C23—362no—
901C23—362no—
902C23C22×D3212yes—
903Q8—62no—
904Q8—64no—
905Q8—62no—
906Q8—124no—
907Q8—122no—
908Q8—364no—
909Q8—362no—
910D4—98no—
911D4—94no—
912D4#379714yescomplemented
913C2×C4—24no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—32no—
918C2×C4—34no—
919C2×C4—34no—
920C2×C4—91no—
921C2×C4—94no—
922C2×C4—91no—
923C2×C4—91no—
924C2×C4—92no—
925C2×C4—124no—
926C2×C4—124no—
927C2×C4—182no—
928C2×C4—184no—
929C2×C4—362no—
930C2×C4—362no—
931C2×C4—361no—
932C2×C4—364no—
933C2×C4—364no—
934C2×C4—362no—
935C2×C4C22×D3211yescharacteristic
936C2×C4C22×D3212yes—
937C2×C4C22×D3211yescharacteristic
938C2×C4C22×D3211yescharacteristic
939C2×C3—24no—
940C2×C3—24no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—21no—
944C2×C3—44no—
945C2×C3C2×#100411yescharacteristic
946C2×C3C22×D3×Q811yescharacteristic
947C2×C3C22×D3×Q811yescharacteristic
948C2×C3C2×#100911yescharacteristic
949C2×C3#596611yescharacteristic
950C2×C3#596811yescharacteristic
951D3—64no—
952D3—62no—
953D3—64no—
954D3—62no—
955D3—64no—
956D3—124no—
957C22—22no—
958C22—22no—
959C22—92no—
960C22—94no—
961C22—182no—
962C22—181no—
963C22—182no—
964C22—181no—
965C22—368no—
966C22C2×#379714yes—
967C22C23×D3211yescharacteristic
968C4—22no—
969C4—21no—
970C4—62no—
971C4—64no—
972C4—62no—
973C4—62no—
974C4—64no—
975C4—62no—
976C4—92no—
977C4—181no—
978C4—182no—
979C4—181no—
980C4C2×#379712yes—
981C4#6431412yes—
982C3—21no—
983C3#8676111yescharacteristic, complemented
984C3#8694811yescharacteristic, complemented
985C2—24no—
986C2—182no—
987C2—184no—
988C2C22×#379711yescharacteristic
989C2C2×#6431411yescharacteristic
990C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
prime radicalC2×D4×C3⋊D3C22
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
2. C3×#5543C2semidirect
3. C3×D4×Dic6C2semidirect
4. #10595272C2semidirect
6. #10594991C2semidirect
7. #10594925C2semidirect
8. C2×#63871C2semidirect
9. #10594803C2semidirect
10. #10594470C2semidirect
11. #10594325C2semidirect
12. #10594180C2semidirect
13. #10594141C2semidirect
14. #10593958C2semidirect
15. #10593903C2semidirect
16. #10593882C2semidirect
17. #10593866C2semidirect
22. C22×C3×Dic6C22semidirect
23. C2×#3797C22semidirect
35. C2×C3×C4⋊Dic3C22semidirect
36. C3×#924C22semidirect
37. C3×#924C22semidirect
38. C3×#890C22semidirect
39. C3×#888C22semidirect
40. C3×#878C22semidirect
41. C3×#878C22semidirect
42. C3×#869C22semidirect
43. C3×#869C22semidirect
44. C3×C4×Dic6C22semidirect
45. C3×C4×Dic6C22semidirect
46. #63982C22semidirect
48. C2×Dic3⋊Dic3C22semidirect
49. #63964C22semidirect
50. #63964C22semidirect
54. #63919C22semidirect
55. #63918C22semidirect
56. C4×#627C22semidirect
57. #63900C22semidirect
58. #63895C22semidirect
59. #63895C22semidirect
62. #63888C22semidirect
63. #63888C22semidirect
64. #63883C22semidirect
66. #63873C22semidirect
67. #63872C22semidirect
73. #63871C22semidirect
74. #63871C22semidirect
75. #63871C22semidirect
76. #63870C22semidirect
77. #63869C22semidirect
81. #63847C22semidirect
82. #63843C22semidirect
83. #63843C22semidirect
84. #63839C22semidirect
115. #5543D3semidirect
117. D4×Dic6D3semidirect
125. D4×C3⋊D3Q8semidirect
199. C22×Dic6C2×D3semidirect
244. C2×C4⋊Dic3C2×D3semidirect
247. #924C2×D3semidirect
248. #924C2×D3semidirect
285. #890C2×D3semidirect
294. #888C2×D3semidirect
311. #878C2×D3semidirect
312. #878C2×D3semidirect
325. #869C2×D3semidirect
326. #869C2×D3semidirect
329. C4×Dic6C2×D3semidirect
330. C4×Dic6C2×D3semidirect
334. C22×C3⋊D3C2×Q8semidirect
337. C32×D4C2×Q8semidirect
343. #638C2×Q8semidirect
349. C4⋊(C3⋊D3)C2×Q8semidirect
355. C4×C3⋊D3C2×Q8semidirect
667. C3×D4D3×Q8semidirect
668. C3×D4D3×Q8semidirect
896. C32#3501semidirect
912. D4#3797semidirect
983. C3#86761semidirect
984. C3#86948semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
C3×#55432
C3×D4×Dic62
#105952722
#105952232
#105949912
#105949252
C2×#638712
#105948032
#105944702
#105943252
#105941802
#105941412
#105939582
#105939032
#105938822
#105938662
#869483
#867613