Finite Group Databasebeta

← #11909348

Subgroups — #11909348

Order 1152.

2461 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5551C211yesmaximal, characteristic, complemented
3C3×#5542C211yesmaximal, characteristic, complemented
4#10595243C212yesmaximal, complemented
5#10595126C212yesmaximal, complemented
6#10595034C212yesmaximal, complemented
7#10594970C212yesmaximal, complemented
8#10594925C212yesmaximal, complemented
9#10594830C212yesmaximal, complemented
10#10594536C212yesmaximal, complemented
11#10594327C212yesmaximal, complemented
12#10594228C214yesmaximal, complemented
13#10594227C214yesmaximal, complemented
14#10593903C211yesmaximal, characteristic, complemented
15#10593875C211yesmaximal, characteristic, complemented
16#10593869C211yesmaximal, characteristic, complemented
17#10593866C211yesmaximal, characteristic, complemented
18#86990—31nomaximal
19#86686—31nomaximal
20C2×D4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2212yes—
22C2×C3×#235C2212yescomplemented
23C2×#3799C2212yes—
24C2×#3797C2212yescomplemented
25C32×C4×D4C2211yescharacteristic
26D4×C3⋊Dic3C2211yescharacteristic
27C4×#638C2212yes—
28#64102C2211yescharacteristic
29C4⋊C4×C3⋊D3C2211yescharacteristic
30#64090C2212yes—
31C22⋊C4×C3⋊D3C2212yes—
32C4×C4⋊(C3⋊D3)C2211yescharacteristic
33C42×C3⋊D3C2211yescharacteristic
34C3×#938C2212yes—
35C3×#936C2212yes—
36C3×#926C2212yescomplemented
37C3×#924C2212yescomplemented
38C3×#924C2212yescomplemented
39C3×D3×C4⋊C4C2212yescomplemented
40C3×#887C2212yescomplemented
41C3×#883C2214yescomplemented
42C3×#879C2214yescomplemented
43C3×C4×D12C2211yescharacteristic, complemented
44C3×#869C2211yescharacteristic, complemented
45C3×#869C2211yescharacteristic, complemented
46C3×C4×Dic6C2211yescharacteristic, complemented
47#63982C2214yescomplemented
48#63981C2214yes—
49#63975C2214yes—
50#63974C2214yes—
51#63962C2214yescomplemented
52#63959C2214yescomplemented
53#63958C2214yes—
54#63956C2214yescomplemented
55#63918C2212yescomplemented
56#63916C2211yescharacteristic
57#63916C2212yescomplemented
58#63904C2214yescomplemented
59C4×#626C2212yes—
60C4×#626C2214yes—
61C4×#626C2214yescomplemented
62#63900C2212yescomplemented
63#63895C2214yescomplemented
64#63894C2212yes—
65#63883C2214yescomplemented
66#63872C2212yescomplemented
67#63872C2211yescharacteristic, complemented
68#63871C2212yes—
69#63871C2212yes—
70#63871C2211yescharacteristic
71#63871C2212yescomplemented
72#63867C2214yescomplemented
73#63865C2214yes—
74#63863C2211yescharacteristic, complemented
75#63862C2212yescomplemented
76#63856C2212yescomplemented
77#63855C2212yescomplemented
78#63854C2214yescomplemented
79#63853C2212yes—
80#63851C2214yescomplemented
81#63849C2212yes—
82#63843C2212yescomplemented
83#63843C2212yescomplemented
84#63836C2214yescomplemented
85C3×#556—31no—
86C3×#547—31no—
87#5831—32no—
88#5828—32no—
89#5728—31no—
90#5728—31no—
91#5727—31no—
92#5726—31no—
93#5707—34no—
94#5705—34no—
95#5682—32no—
96#5676—32no—
97#5660—34no—
98#5659—34no—
99#5639—32no—
100#5633—32no—
101D3×C22⋊Q8—32no—
102D3×C22⋊Q8—32no—
103#5612—32no—
104#5603—32no—
105#5580—31no—
106#5579—32no—
107Q8×D12—31no—
108#5574—32no—
109#5557—31no—
110#5551—31no—
111#5551D311yescharacteristic, complemented
112C4×D3×D4—31no—
113C4×D3×D4—31no—
114C4×D3×D4—61no—
115#5542D311yescharacteristic, complemented
116#5529—32no—
117#5524—32no—
118#5511—32no—
119#5504—32no—
120C23×C3⋊D3C2312yes—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C2×#638C2312yes—
124C22×C3⋊Dic3C2312yes—
125D4×C3⋊D3—24no—
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⋊D3C2311yescharacteristic
132C2×C4×C3⋊D3C2312yes—
133C2×C4×C3⋊D3C2312yes—
134C2×C3×#67C2314yes—
135C3×#235—44no—
136C2×C3×D12C2311yescharacteristic
137C2×C3×C4×D3C2312yes—
138C2×C3×C4×D3C2314yes—
139C2×C3×Dic6C2312yes—
140C2×C3×Dic6C2311yescharacteristic
141C2×C3×Dic6C2312yes—
142C2×#627C2314yes—
143C2×#626C2314yes—
144C2×#626C2312yes—
145C2×#624C2314yes—
146C2×#624C2314yes—
147#3799—28no—
148#3797—44no—
149C32×C4⋊C4C2311yescharacteristic
150C32×C22⋊C4C2312yes—
151C32×C42C2311yescharacteristic
152#3757C2312yes—
153#3752C2312yes—
154#3752C2312yes—
155C4⋊(C3⋊Dic3)C2311yescharacteristic
156#3750C2312yes—
157C4×C3⋊Dic3C2311yescharacteristic
158C4×C3⋊Dic3C2311yescharacteristic
159C4×C3⋊Dic3C2311yescharacteristic
160C3×#217C2314yes—
161C3×#217C2314yes—
162C3×#217C2314yes—
163C3×(C2×D3)⋊C4C2312yes—
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2312yes—
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2311yescharacteristic
168C3×C4⋊Dic3C2312yes—
169C3×C4⋊Dic3C2311yescharacteristic
170C3×Dic3⋊C4C2312yes—
171C3×Dic3⋊C4C2314yes—
172C3×Dic3⋊C4C2314yes—
173C3×C4×Dic3C2314yes—
174C3×C4×Dic3C2312yes—
175#3724C2314yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2312yes—
181Dic3⋊Dic3C2314yes—
182#3722C2314yes—
183#3722C2314yes—
184#3722C2312yes—
185(C2×D3)⋊Dic3C2312yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2312yes—
188(C2×D3)⋊Dic3C2312yes—
189Dic32C2314yes—
190#3520—91noSylow
191C2×C3×#41—32no—
192C2×#239—32no—
193C2×D3×Q8—32no—
194C2×D3×Q8—32no—
195C2×D3×D4—31no—
196C2×D3×D4—31no—
197C2×D3×D4—61no—
198C2×#235—32no—
199C2×#235C2×D312yescomplemented
200C22×C4×D3—32no—
201C22×C4×D3—32no—
202C22×C4×D3—62no—
203C3×C4⋊Q8—31no—
204C3×C4⋊Q8—31no—
205C3×#126—34no—
206C3×#124—32no—
207C3×#123—34no—
208C3×C22⋊Q8—32no—
209C3×C22⋊Q8—32no—
210C3×#121—32no—
211C3×C4×Q8—32no—
212C3×C4×Q8—31no—
213C3×C4×D4—21no—
214C3×C4×D4—31no—
215C3×C4×D4C2×D311yescharacteristic
216C3×C4×D4C2×D311yescharacteristic
217C3×#117—32no—
218C2×C3×C4⋊C4—32no—
219#947—31no—
220#946—32no—
221#946—32no—
222#946—32no—
223#946—32no—
224#946—31no—
225Q8×Dic3—32no—
226Q8×Dic3—32no—
227#938—34no—
228#938—31no—
229#938—32no—
230#938C2×D312yes—
231#937—34no—
232#936—31no—
233#936—34no—
234#936C2×D312yes—
235#935—34no—
236D4×Dic3—31no—
237D4×Dic3—31no—
238D4×Dic3—61no—
239C4×#67—32no—
240C4×#67—32no—
241C4×#67—34no—
242C4×#67—34no—
243C4×#67—34no—
244C4×#67—32no—
245C4×#67—62no—
246#926—32no—
247#926C2×D312yescomplemented
248#924—32no—
249#924—34no—
250#924C2×D312yescomplemented
251#924C2×D312yescomplemented
252#898—32no—
253#897—32no—
254#897—32no—
255#897—31no—
256#897—32no—
257#897—34no—
258#896—34no—
259#896—34no—
260#896—34no—
261#896—34no—
262#895—32no—
263#895—31no—
264#894—32no—
265#894—34no—
266#893—34no—
267#893—31no—
268#893—31no—
269#893—32no—
270#893—61no—
271#892—32no—
272#892—32no—
273#892—34no—
274D3×C4⋊C4—31no—
275D3×C4⋊C4—31no—
276D3×C4⋊C4—32no—
277D3×C4⋊C4—32no—
278D3×C4⋊C4—34no—
279D3×C4⋊C4—34no—
280D3×C4⋊C4—61no—
281D3×C4⋊C4C2×D312yescomplemented
282#890—31no—
283#890—32no—
284#890—32no—
285#890—31no—
286#889—34no—
287#888—32no—
288#887—32no—
289#887—32no—
290#887C2×D312yescomplemented
291#886—34no—
292#885—34no—
293#884—34no—
294#883—34no—
295#883—34no—
296#883—34no—
297#883—32no—
298#883C2×D314yescomplemented
299#882—34no—
300#67⋊C4—32no—
301#67⋊C4—32no—
302#67⋊C4—62no—
303D3×C22⋊C4—32no—
304D3×C22⋊C4—32no—
305D3×C22⋊C4—34no—
306D3×C22⋊C4—34no—
307D3×C22⋊C4—62no—
308#879—34no—
309#879—34no—
310#879—32no—
311#879C2×D314yescomplemented
312#878—34no—
313#878—34no—
314C4×D12—32no—
315C4×D12—34no—
316C4×D12—34no—
317C4×D12—31no—
318C4×D12—31no—
319C4×D12—32no—
320C4×D12—61no—
321C4×D12C2×D311yescharacteristic, complemented
322#872—32no—
323#872—34no—
324C42×D3—31no—
325C42×D3—31no—
326C42×D3—61no—
327#870—34no—
328#869—32no—
329#869C2×D311yescharacteristic, complemented
330#869C2×D311yescharacteristic, complemented
331C4×Dic6C2×D311yescharacteristic, complemented
332C23×C32C2412yes—
333C22×C3⋊D3—24no—
334C22×C3⋊D3—24no—
335C22×C3⋊D3—42no—
336C22×C3⋊D3C2412yes—
337C22×C3⋊D3C2411yescharacteristic
338C22×C3×D3C2412yes—
339C32×D4—22no—
340C2×C32×C4—24no—
341C2×C32×C4C2412yes—
342C2×C32×C4C2411yescharacteristic
343C2×C32×C4C2411yescharacteristic
344C2×C32×C4C2411yescharacteristic
345#638—24no—
346C2×C3⋊Dic3—42no—
347C2×C3⋊Dic3C2411yescharacteristic
348C2×C3⋊Dic3C2411yescharacteristic
349C2×C3⋊Dic3C2411yescharacteristic
350C2×C3⋊Dic3C2412yes—
351C4⋊(C3⋊D3)#4114yescomplemented
352C4×C3⋊D3—22no—
353C4×C3⋊D3—22no—
354C4×C3⋊D3—22no—
355C4×C3⋊D3—24no—
356C4×C3⋊D3—42no—
357C4×C3⋊D3—42no—
358C3×#67—44no—
359C2×C3×Dic3C2414yes—
360C2×C3×Dic3C2414yes—
361C2×C3×Dic3C2412yes—
362C2×C3×Dic3C2412yes—
363C2×C3×Dic3C2412yes—
364C3×D12—22no—
365C3×C4×D3—24no—
366C3×C4×D3—44no—
367C3×Dic6—24no—
368C3×Dic6—22no—
369C3×Dic6—24no—
370#627—44no—
371#626—28no—
372#626—24no—
373#624—28no—
374#624—44no—
375#556—31no—
376#554—92no—
377#552—92no—
378#551—94no—
379D4×Q8—91no—
380#548—92no—
381#547—31no—
382#547—91no—
383#546—92no—
384#542—92no—
385#539—94no—
386#533—91no—
387#529—91no—
388#525—92no—
389C2×C22⋊Q8—92no—
390#520—92no—
391C2×C4×D4—91no—
392C23×D3—32no—
393C23×D3—32no—
394C23×D3—62no—
395C3×#41—124no—
396C2×C3×Q8—32no—
397C2×C3×Q8—32no—
398C2×C3×Q8—31no—
399C2×C3×D4—21no—
400C2×C3×D4—34no—
401C2×C3×D4—31no—
402C2×C3×D4C22×D311yescharacteristic
403C2×C3×D4C22×D311yescharacteristic
404C22×C3×C4—22no—
405C22×C3×C4—32no—
406C22×C3×C4—34no—
407C22×C3×C4C22×D312yes—
408C22×C3×C4C22×D312yes—
409C2×#67—32no—
410C2×#67—32no—
411C2×#67—32no—
412C2×#67—34no—
413C2×#67—62no—
414C2×#67C22×D314yes—
415C22×Dic3—32no—
416C22×Dic3—32no—
417C22×Dic3—62no—
418#239—68no—
419D3×Q8—124no—
420D3×Q8—124no—
421D3×D4—64no—
422D3×D4—64no—
423D3×D4—68no—
424#235—44no—
425#235—68no—
426C2×D12—31no—
427C2×D12—31no—
428C2×D12—32no—
429C2×D12—34no—
430C2×D12—61no—
431C2×D12C22×D311yescharacteristic
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—31no—
435C2×C4×D3—31no—
436C2×C4×D3—31no—
437C2×C4×D3—31no—
438C2×C4×D3—32no—
439C2×C4×D3—32no—
440C2×C4×D3—34no—
441C2×C4×D3—34no—
442C2×C4×D3—32no—
443C2×C4×D3—32no—
444C2×C4×D3—32no—
445C2×C4×D3—32no—
446C2×C4×D3—34no—
447C2×C4×D3—34no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3—62no—
452C2×C4×D3—62no—
453C2×C4×D3—62no—
454C2×C4×D3—124no—
455C2×C4×D3—124no—
456C2×C4×D3—128no—
457C2×C4×D3C22×D312yes—
458C2×C4×D3C22×D314yes—
459C2×Dic6—34no—
460C2×Dic6—34no—
461C2×Dic6C22×D311yescharacteristic
462C2×Dic6C22×D312yes—
463C2×Dic6C22×D312yes—
464C3×C4⋊C4—21no—
465C3×C4⋊C4—32no—
466C3×C4⋊C4—32no—
467C3×C4⋊C4—34no—
468C3×C4⋊C4—31no—
469C3×C4⋊C4—32no—
470C3×C4⋊C4—32no—
471C3×C4⋊C4—31no—
472C3×C4⋊C4—34no—
473C3×C4⋊C4—32no—
474C3×C4⋊C4C22×D311yescharacteristic
475C3×C4⋊C4C22×D311yescharacteristic
476C3×C22⋊C4—22no—
477C3×C22⋊C4—34no—
478C3×C22⋊C4—34no—
479C3×C22⋊C4—34no—
480C3×C22⋊C4—32no—
481C3×C22⋊C4C22×D312yes—
482C3×C22⋊C4C22×D312yes—
483C3×C42—21no—
484C3×C42—32no—
485C3×C42—34no—
486C3×C42C22×D311yescharacteristic
487C3×C42C22×D311yescharacteristic
488#217—32no—
489#217—32no—
490#217—32no—
491#217—32no—
492#217—34no—
493#217—32no—
494#217—62no—
495#217C22×D314yes—
496#217C22×D314yes—
497#217C22×D314yes—
498(C2×D3)⋊C4—32no—
499(C2×D3)⋊C4—32no—
500(C2×D3)⋊C4—32no—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—32no—
503(C2×D3)⋊C4—32no—
504(C2×D3)⋊C4—32no—
505(C2×D3)⋊C4—32no—
506(C2×D3)⋊C4—34no—
507(C2×D3)⋊C4—32no—
508(C2×D3)⋊C4—34no—
509(C2×D3)⋊C4—32no—
510(C2×D3)⋊C4—34no—
511(C2×D3)⋊C4—34no—
512(C2×D3)⋊C4—62no—
513(C2×D3)⋊C4—62no—
514(C2×D3)⋊C4C22×D312yes—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—34no—
518C4⋊Dic3—32no—
519C4⋊Dic3—34no—
520C4⋊Dic3—32no—
521C4⋊Dic3—32no—
522C4⋊Dic3—34no—
523C4⋊Dic3—61no—
524C4⋊Dic3C22×D311yescharacteristic
525C4⋊Dic3C22×D312yes—
526C4⋊Dic3C22×D312yes—
527C4⋊Dic3C22×D312yes—
528C4⋊Dic3C22×D312yes—
529C4⋊Dic3C22×D311yescharacteristic
530Dic3⋊C4—32no—
531Dic3⋊C4—32no—
532Dic3⋊C4—34no—
533Dic3⋊C4—34no—
534Dic3⋊C4—32no—
535Dic3⋊C4—32no—
536Dic3⋊C4—34no—
537Dic3⋊C4—34no—
538Dic3⋊C4—32no—
539Dic3⋊C4—34no—
540Dic3⋊C4—62no—
541Dic3⋊C4C22×D312yes—
542Dic3⋊C4C22×D314yes—
543Dic3⋊C4C22×D314yes—
544C4×Dic3—31no—
545C4×Dic3—31no—
546C4×Dic3—31no—
547C4×Dic3—31no—
548C4×Dic3—31no—
549C4×Dic3—31no—
550C4×Dic3—34no—
551C4×Dic3—34no—
552C4×Dic3—61no—
553C4×Dic3—61no—
554C4×Dic3—61no—
555C4×Dic3C22×D312yes—
556C4×Dic3C22×D314yes—
557C22×C32—22no—
558C22×C32—22no—
559C22×C32—22no—
560C22×C32C2511yescharacteristic
561C2×C3⋊D3—21no—
562C2×C3⋊D3—21no—
563C2×C3⋊D3—22no—
564C2×C3⋊D3—22no—
565C2×C3⋊D3—48no—
566C2×C3⋊D3C2×#4114yes—
567C2×C3⋊D32−1+412yes—
568C2×C3×D3—22no—
569C2×C3×D3—22no—
570C2×C3×D3—22no—
571C32×C4—22no—
572C32×C4—21no—
573C32×C4C2×#4112yes—
574C32×C4H(5,𝔽2)12yes—
575C3⋊Dic3—21no—
576C3⋊Dic3—21no—
577C3⋊Dic3—22no—
578C3⋊Dic3—21no—
579C3×Dic3—22no—
580C3×Dic3—24no—
581C3×Dic3—22no—
582C3×Dic3—24no—
583C3×Dic3—22no—
584C2×#41—32no—
585C2×#41—92no—
586C22×Q8—92no—
587C22×D4—91no—
588C23×C4—92no—
589C4⋊Q8—31no—
590C4⋊Q8—31no—
591C4⋊Q8—92no—
592#126—34no—
593#126—94no—
594#126—92no—
595#125—94no—
596#125—91no—
597#125—92no—
598#124—32no—
599#124—94no—
600#124—91no—
601#123—34no—
602#123—94no—
603#123—92no—
604#123—94no—
605#123—94no—
606C22⋊Q8—32no—
607C22⋊Q8—32no—
608C22⋊Q8—94no—
609C22⋊Q8—94no—
610C22⋊Q8—94no—
611C22⋊Q8—94no—
612C22⋊Q8—91no—
613C22⋊Q8—92no—
614C22⋊Q8—92no—
615C22⋊Q8—92no—
616C22⋊Q8—92no—
617#121—32no—
618#121—94no—
619#121—91no—
620#121—92no—
621#120—94no—
622C4×Q8—32no—
623C4×Q8—31no—
624C4×Q8—92no—
625C4×Q8—92no—
626C4×D4—31no—
627C4×D4—92no—
628C4×D4—94no—
629C4×D4—94no—
630C4×D4—92no—
631C4×D4—94no—
632C4×D4—91no—
633C4×D4—92no—
634C4×D4—91no—
635C4×D4—92no—
636C4×D4—91no—
637C4×D4D3211yescharacteristic
638#117—32no—
639#117—94no—
640#117—92no—
641#117—92no—
642C2×C4⋊C4—32no—
643C2×C4⋊C4—94no—
644C2×C4⋊C4—92no—
645C2×C4⋊C4—91no—
646C2×C22⋊C4—94no—
647C2×C22⋊C4—92no—
648C2×C42—91no—
649C23×C3—22no—
650C23×C3—32no—
651C23×C3C23×D312yes—
652C23×C3C23×D312yes—
653C22×D3—31no—
654C22×D3—31no—
655C22×D3—32no—
656C22×D3—32no—
657C22×D3—61no—
658C22×D3—62no—
659C22×D3—64no—
660C22×D3—64no—
661C22×D3—64no—
662C22×D3—64no—
663C22×D3—68no—
664C22×D3—124no—
665C22×D3—122no—
666C22×D3—122no—
667C22×D3—124no—
668C22×D3C23×D312yes—
669C3×Q8—62no—
670C3×Q8—64no—
671C3×Q8—64no—
672C3×D4—24no—
673C3×D4—22no—
674C3×D4—22no—
675C3×D4—62no—
676C3×D4—124no—
677C2×C3×C4—24no—
678C2×C3×C4—24no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—22no—
683C2×C3×C4—34no—
684C2×C3×C4—34no—
685C2×C3×C4—32no—
686C2×C3×C4—32no—
687C2×C3×C4—32no—
688C2×C3×C4—44no—
689C2×C3×C4—64no—
690C2×C3×C4—124no—
691C2×C3×C4C23×D311yescharacteristic
692C2×C3×C4C23×D311yescharacteristic
693C2×C3×C4C23×D312yes—
694C2×C3×C4C23×D312yes—
695C2×C3×C4C23×D311yescharacteristic
696C2×C3×C4C23×D311yescharacteristic
697C2×C3×C4C23×D311yescharacteristic
698C2×C3×C4C23×D311yescharacteristic
699#67—44no—
700#67—68no—
701#67—64no—
702#67—64no—
703#67—64no—
704#67—68no—
705C2×Dic3—31no—
706C2×Dic3—31no—
707C2×Dic3—31no—
708C2×Dic3—31no—
709C2×Dic3—31no—
710C2×Dic3—31no—
711C2×Dic3—32no—
712C2×Dic3—32no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—62no—
717C2×Dic3—122no—
718C2×Dic3—122no—
719C2×Dic3—124no—
720C2×Dic3C23×D314yes—
721C2×Dic3C23×D314yes—
722C2×Dic3C23×D312yes—
723C2×Dic3C23×D312yes—
724C2×Dic3C23×D312yes—
725D12—22no—
726D12—34no—
727D12—34no—
728D12—64no—
729D12—64no—
730D12—68no—
731C4×D3—24no—
732C4×D3—44no—
733C4×D3—68no—
734C4×D3—68no—
735C4×D3—62no—
736C4×D3—62no—
737C4×D3—64no—
738C4×D3—64no—
739C4×D3—62no—
740C4×D3—64no—
741C4×D3—62no—
742C4×D3—62no—
743C4×D3—62no—
744C4×D3—64no—
745C4×D3—124no—
746C4×D3—122no—
747C4×D3—124no—
748C4×D3—124no—
749C4×D3—122no—
750C4×D3—122no—
751C4×D3—122no—
752C4×D3—122no—
753C4×D3—124no—
754C4×D3—124no—
755Dic6—24no—
756Dic6—24no—
757Dic6—22no—
758Dic6—124no—
759Dic6—124no—
760C2×C32—42no—
761C2×C32C22×#4111yescharacteristic
762C2×C32C2×H(5,𝔽2)11yescharacteristic
763C2×C32C2×2−1+411yescharacteristic
764C3⋊D3—22no—
765C3⋊D3—24no—
766C3×D3—42no—
767C24—92no—
768#41—124no—
769#41—188no—
770C2×Q8—32no—
771C2×Q8—31no—
772C2×Q8—32no—
773C2×Q8—94no—
774C2×Q8—364no—
775C2×D4—34no—
776C2×D4—31no—
777C2×D4—92no—
778C2×D4—94no—
779C2×D4—92no—
780C2×D4—91no—
781C2×D4—184no—
782C2×D4C2×D3211yescharacteristic
783C22×C4—32no—
784C22×C4—34no—
785C22×C4—94no—
786C22×C4—94no—
787C22×C4—92no—
788C22×C4—91no—
789C22×C4—91no—
790C22×C4—91no—
791C22×C4—92no—
792C22×C4—92no—
793C22×C4—92no—
794C22×C4—364no—
795C22×C4C2×D3212yes—
796C4⋊C4—34no—
797C4⋊C4—32no—
798C4⋊C4—31no—
799C4⋊C4—32no—
800C4⋊C4—34no—
801C4⋊C4—31no—
802C4⋊C4—32no—
803C4⋊C4—32no—
804C4⋊C4—32no—
805C4⋊C4—92no—
806C4⋊C4—94no—
807C4⋊C4—94no—
808C4⋊C4—92no—
809C4⋊C4—94no—
810C4⋊C4—92no—
811C4⋊C4—94no—
812C4⋊C4—92no—
813C4⋊C4—91no—
814C4⋊C4C2×D3211yescharacteristic
815C22⋊C4—34no—
816C22⋊C4—34no—
817C22⋊C4—34no—
818C22⋊C4—32no—
819C22⋊C4—92no—
820C22⋊C4—94no—
821C22⋊C4—94no—
822C22⋊C4—92no—
823C22⋊C4—92no—
824C22⋊C4—92no—
825C22⋊C4—94no—
826C22⋊C4—92no—
827C22⋊C4—92no—
828C22⋊C4—92no—
829C22⋊C4C2×D3212yes—
830C42—34no—
831C42—32no—
832C42—94no—
833C42—91no—
834C42—91no—
835C42—91no—
836C42C2×D3211yescharacteristic
837C22×C3—24no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—22no—
844C22×C3—21no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—62no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3C24×D311yescharacteristic
851C22×C3C24×D311yescharacteristic
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—34no—
856C2×D3—34no—
857C2×D3—32no—
858C2×D3—32no—
859C2×D3—62no—
860C2×D3—64no—
861C2×D3—62no—
862C2×D3—62no—
863C2×D3—62no—
864C2×D3—61no—
865C2×D3—61no—
866C2×D3—61no—
867C2×D3—62no—
868C2×D3—61no—
869C2×D3—62no—
870C2×D3—62no—
871C2×D3—122no—
872C2×D3—122no—
873C2×D3—128no—
874C2×D3—128no—
875C2×D3—1216no—
876C3×C4—22no—
877C3×C4—22no—
878C3×C4—21no—
879C3×C4—21no—
880C3×C4—22no—
881C3×C4—22no—
882C3×C4—42no—
883C3×C4—41no—
884C3×C4—62no—
885C3×C4—62no—
886C3×C4—64no—
887C3×C4—64no—
888C3×C4—62no—
889C3×C4#100412yes—
890C3×C4D3×#4112yes—
891C3×C4D3×#4112yes—
892C3×C4#100912yes—
893Dic3—24no—
894Dic3—24no—
895Dic3—22no—
896Dic3—22no—
897Dic3—22no—
898Dic3—62no—
899Dic3—62no—
900Dic3—62no—
901Dic3—61no—
902Dic3—61no—
903Dic3—61no—
904Dic3—62no—
905Dic3—61no—
906Dic3—61no—
907Dic3—61no—
908Dic3—122no—
909Dic3—121no—
910C32#352011yescharacteristic, complemented, Sylow
911C23—32no—
912C23—91no—
913C23—92no—
914C23—184no—
915C23—184no—
916C23—362no—
917C23C22×D3212yes—
918Q8—64no—
919Q8—62no—
920Q8—64no—
921Q8—364no—
922D4—22no—
923D4—62no—
924D4—94no—
925D4—124no—
926D4—188no—
927D4—184no—
928D4—184no—
929C2×C4—24no—
930C2×C4—32no—
931C2×C4—34no—
932C2×C4—32no—
933C2×C4—34no—
934C2×C4—32no—
935C2×C4—64no—
936C2×C4—91no—
937C2×C4—91no—
938C2×C4—91no—
939C2×C4—92no—
940C2×C4—124no—
941C2×C4—182no—
942C2×C4—188no—
943C2×C4—182no—
944C2×C4—182no—
945C2×C4—184no—
946C2×C4—362no—
947C2×C4—362no—
948C2×C4—364no—
949C2×C4—362no—
950C2×C4C22×D3212yes—
951C2×C4C22×D3211yescharacteristic
952C2×C4C22×D3211yescharacteristic
953C2×C4C22×D3211yescharacteristic
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—44no—
958C2×C3—42no—
959C2×C3—42no—
960C2×C3—122no—
961C2×C3C2×#100411yescharacteristic
962C2×C3C2×D3×#4111yescharacteristic
963C2×C3C2×D3×#4111yescharacteristic
964C2×C3C2×#100911yescharacteristic
965C2×C3D3×2−1+411yescharacteristic
966C2×C3D3×2−1+411yescharacteristic
967D3—42no—
968D3—64no—
969D3—62no—
970D3—64no—
971D3—62no—
972D3—64no—
973D3—124no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—62no—
978C22—62no—
979C22—62no—
980C22—94no—
981C22—92no—
982C22—181no—
983C22—182no—
984C22—181no—
985C22—182no—
986C22—368no—
987C22C23×D3211yescharacteristic
988C4—22no—
989C4—21no—
990C4—62no—
991C4—64no—
992C4—64no—
993C4—62no—
994C4—62no—
995C4—181no—
996C4—181no—
997C4—182no—
998C4—181no—
999C4#6430612yes—
1000C4#6431412yes—
1001C3—21no—
1002C3#8668611yescharacteristic, complemented
1003C3#8699011yescharacteristic, complemented
1004C2—42no—
1005C2—122no—
1006C2—182no—
1007C2—184no—
1008C2C2×#6430611yescharacteristic
1009C2C2×#6431411yescharacteristic
1010C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3520
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×D4×C3⋊D3C2semidirect
2. C3×#5551C2semidirect
3. C3×#5542C2semidirect
4. #10595243C2semidirect
5. #10595126C2semidirect
6. #10595034C2semidirect
7. #10594970C2semidirect
8. #10594925C2semidirect
9. #10594830C2semidirect
10. #10594536C2semidirect
11. #10594327C2semidirect
12. #10594228C2semidirect
13. #10594227C2semidirect
14. #10593903C2semidirect
15. #10593875C2semidirect
16. #10593869C2semidirect
17. #10593866C2semidirect
22. C2×C3×#235C22semidirect
24. C2×#3797C22semidirect
36. C3×#926C22semidirect
37. C3×#924C22semidirect
38. C3×#924C22semidirect
39. C3×D3×C4⋊C4C22semidirect
40. C3×#887C22semidirect
41. C3×#883C22semidirect
42. C3×#879C22semidirect
43. C3×C4×D12C22semidirect
44. C3×#869C22semidirect
45. C3×#869C22semidirect
46. C3×C4×Dic6C22semidirect
47. #63982C22semidirect
51. #63962C22semidirect
52. #63959C22semidirect
54. #63956C22semidirect
55. #63918C22semidirect
57. #63916C22semidirect
58. #63904C22semidirect
61. C4×#626C22semidirect
62. #63900C22semidirect
63. #63895C22semidirect
65. #63883C22semidirect
66. #63872C22semidirect
67. #63872C22semidirect
71. #63871C22semidirect
72. #63867C22semidirect
74. #63863C22semidirect
75. #63862C22semidirect
76. #63856C22semidirect
77. #63855C22semidirect
78. #63854C22semidirect
80. #63851C22semidirect
82. #63843C22semidirect
83. #63843C22semidirect
84. #63836C22semidirect
111. #5551D3semidirect
115. #5542D3semidirect
199. C2×#235C2×D3semidirect
247. #926C2×D3semidirect
250. #924C2×D3semidirect
251. #924C2×D3semidirect
281. D3×C4⋊C4C2×D3semidirect
290. #887C2×D3semidirect
298. #883C2×D3semidirect
311. #879C2×D3semidirect
321. C4×D12C2×D3semidirect
329. #869C2×D3semidirect
330. #869C2×D3semidirect
331. C4×Dic6C2×D3semidirect
351. C4⋊(C3⋊D3)#41semidirect
910. C32#3520semidirect
1002. C3#86686semidirect
1003. C3#86990semidirect

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×#55512
C3×#55422
#105952432
#105951262
#105950342
#105949702
#105949252
#105948302
#105945362
#105943272
#105942282
#105942272
#105939032
#105938752
#105938692
#105938662
#869903
#866863