Finite Group Databasebeta

← #11903623

Subgroups — #11903623

Order 1152.

2477 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5555C211yesmaximal, characteristic, complemented
3C3×#5543C211yesmaximal, characteristic, complemented
4#10595254C212yesmaximal, complemented
5Dic3×#237C212yesmaximal, complemented
6#10594989C212yesmaximal, complemented
7#10594922C212yesmaximal, complemented
8C2×#63849C212yesmaximal, complemented
9#10594825C212yesmaximal, complemented
10#10594579C212yesmaximal, complemented
11#10594453C212yesmaximal, complemented
12#10594164C214yesmaximal, complemented
13#10594144C214yesmaximal, complemented
14#10593987C211yesmaximal, characteristic, complemented
15C4×#3796C211yesmaximal, characteristic, complemented
16#10593866C211yesmaximal, characteristic, complemented
17#10593865C211yesmaximal, characteristic, complemented
18#86922—31nomaximal
19#86675—31nomaximal
20C2×D4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2212yes—
22C2×C3×#237C2212yes—
23C2×#3796C2211yescharacteristic
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×#930C2212yescomplemented
35C2×C3×C4⋊Dic3C2212yescomplemented
36C2×C3×C4⋊Dic3C2212yescomplemented
37C3×#924C2212yescomplemented
38C3×#897C2212yescomplemented
39C3×#890C2212yescomplemented
40C3×#886C2214yescomplemented
41C3×#878C2214yescomplemented
42C3×C4×D12C2211yescharacteristic, complemented
43C3×#869C2211yescharacteristic, complemented
44C3×#869C2211yescharacteristic, complemented
45C3×C4×Dic6C2211yescharacteristic, complemented
46#63981C2214yes—
47#63978C2214yes—
48#67⋊Dic3C2214yescomplemented
49Dic3×#67C2214yescomplemented
50#63966C2214yes—
51C2×#3722C2214yes—
52#63955C2214yescomplemented
53C2×Dic32C2214yescomplemented
54#63916C2212yescomplemented
55#63909C2212yes—
56#63907C2214yescomplemented
57C4×#626C2212yes—
58#63898C2211yescharacteristic, complemented
59#63890C2214yescomplemented
60#63881C2212yes—
61#63881C2214yescomplemented
62#63878C2212yescomplemented
63C4×D3×Dic3C2212yescomplemented
64#63872C2212yescomplemented
65#63871C2212yes—
66#63871C2212yes—
67#63871C2212yescomplemented
68#63864C2212yes—
69#63858C2214yescomplemented
70#63853C2214yes—
71#63849C2211yescharacteristic
72#63849C2214yes—
73#63849C2212yes—
74#63849C2212yescomplemented
75#63849C2212yescomplemented
76#63849C2214yescomplemented
77#63848C2214yescomplemented
78#63848C2214yescomplemented
79#63846C2214yescomplemented
80#63843C2211yescharacteristic, complemented
81#63843C2212yescomplemented
82#63843C2212yescomplemented
83Dic3×Dic6C2212yescomplemented
84#63841C2212yescomplemented
85C3×#554—31no—
86C3×#547—31no—
87#5829—32no—
88Dic3×#41—32no—
89#5734—31no—
90#5732—31no—
91#5728—31no—
92#5728—31no—
93#5694—32no—
94#5691—32no—
95#5658—34no—
96#5649—34no—
97#5642—32no—
98#5639—32no—
99#5637—34no—
100#5627—32no—
101#5624—32no—
102#5624—34no—
103#5618—32no—
104#5606—32no—
105#5584—31no—
106C4×#239—31no—
107#5563—31no—
108#5555D311yescharacteristic, complemented
109#5554—32no—
110C4×D3×D4—31no—
111C4×D3×D4—31no—
112C4×D3×D4—61no—
113#5543D311yescharacteristic, complemented
114C4×#237—32no—
115C4×#237—31no—
116#5514—32no—
117#5513—32no—
118C2×#892—32no—
119C2×#892—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—28no—
128C2×C4×C3⋊D3C2311yescharacteristic
129C2×C4×C3⋊D3C2312yes—
130C2×C4×C3⋊D3C2312yes—
131C2×C4×C3⋊D3C2312yes—
132C2×C4×C3⋊D3C2311yescharacteristic
133C2×C4×C3⋊D3C2311yescharacteristic
134C2×C3×#67C2314yes—
135C22×C3×Dic3C2314yes—
136C22×C3×Dic3C2314yes—
137C3×#237—28no—
138C2×C3×D12C2311yescharacteristic
139C2×C3×C4×D3C2312yes—
140C2×C3×Dic6C2312yes—
141C2×C3×Dic6C2311yescharacteristic
142C2×C3×Dic6C2312yes—
143C2×#626C2312yes—
144C2×#626C2314yes—
145C2×D3×Dic3C2312yes—
146C2×D3×Dic3C2312yes—
147#3796—24no—
148C32×C4⋊C4C2311yescharacteristic
149C32×C22⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151#3757C2312yes—
152#3752C2312yes—
153#3752C2312yes—
154C4⋊(C3⋊Dic3)C2311yescharacteristic
155#3750C2312yes—
156C4×C3⋊Dic3C2311yescharacteristic
157C4×C3⋊Dic3C2311yescharacteristic
158C4×C3⋊Dic3C2311yescharacteristic
159C3×#217C2314yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×C4⋊Dic3C2314yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2314yes—
165C3×C4⋊Dic3C2312yes—
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2311yescharacteristic
168C3×C4⋊Dic3C2311yescharacteristic
169C3×C4⋊Dic3C2312yes—
170C3×Dic3⋊C4C2312yes—
171C3×Dic3⋊C4C2314yes—
172C3×C4×Dic3C2312yes—
173Dic3⋊Dic3C2314yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2314yes—
177#3722C2314yes—
178#3722C2314yes—
179#3722C2314yes—
180#3722C2312yes—
181#3722C2314yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184Dic32C2314yes—
185Dic32C2314yes—
186Dic32C2314yes—
187Dic32C2312yes—
188Dic32C2312yes—
189#3475—91noSylow
190C2×C3×#41—32no—
191C2×#239—31no—
192C2×#237—31no—
193C2×#237C2×D312yes—
194C2×D3×D4—31no—
195C2×D3×D4—31no—
196C2×D3×D4—61no—
197C22×C4×D3—32no—
198C22×C4×D3—32no—
199C22×C4×D3—62no—
200C3×C4⋊Q8—31no—
201C3×C4⋊Q8—31no—
202C3×#125—32no—
203C3×#123—34no—
204C3×C22⋊Q8—32no—
205C3×C22⋊Q8—32no—
206C3×C22⋊Q8—34no—
207C3×#121—32no—
208C3×C4×Q8—31no—
209C3×C4×D4—21no—
210C3×C4×D4—32no—
211C3×C4×D4—31no—
212C3×C4×D4C2×D311yescharacteristic
213C3×C4×D4C2×D311yescharacteristic
214C2×C3×C4⋊C4—32no—
215C2×C3×C4⋊C4—32no—
216#947—34no—
217#947—32no—
218#946—32no—
219#946—32no—
220#946—32no—
221Q8×Dic3—31no—
222Q8×Dic3—32no—
223Q8×Dic3—32no—
224Q8×Dic3—32no—
225#939—34no—
226#938—32no—
227#937—34no—
228D4×Dic3—31no—
229D4×Dic3—31no—
230D4×Dic3—34no—
231D4×Dic3—34no—
232D4×Dic3—31no—
233D4×Dic3—61no—
234D4×Dic3C2×D312yes—
235#930—34no—
236#930—32no—
237#930C2×D312yescomplemented
238#929—34no—
239C4×#67—32no—
240C4×#67—32no—
241C4×#67—34no—
242C4×#67—32no—
243C4×#67—62no—
244C2×(C2×D3)⋊C4—34no—
245C2×(C2×D3)⋊C4—34no—
246#926—34no—
247#926—32no—
248C2×C4⋊Dic3C2×D312yescomplemented
249C2×C4⋊Dic3C2×D312yescomplemented
250#924C2×D312yescomplemented
251C2×C4×Dic3—34no—
252C2×C4×Dic3—34no—
253C2×C4×Dic3—32no—
254#898—34no—
255#898—34no—
256#898—34no—
257#898—34no—
258#898—34no—
259#897—32no—
260#897—32no—
261#897—32no—
262#897C2×D312yescomplemented
263#895—32no—
264#895—32no—
265#894—34no—
266#894—34no—
267#893—31no—
268#893—31no—
269#893—31no—
270#893—32no—
271#893—34no—
272#893—61no—
273#892—32no—
274#892—32no—
275#892—34no—
276#892—34no—
277#892—32no—
278#892—34no—
279#892—34no—
280#892—32no—
281#892—32no—
282#892—32no—
283#892—31no—
284#892—31no—
285#892—32no—
286#892—32no—
287D3×C4⋊C4—31no—
288D3×C4⋊C4—31no—
289D3×C4⋊C4—61no—
290#890—34no—
291#890—32no—
292#890—32no—
293#890C2×D312yescomplemented
294#889—34no—
295#887—32no—
296#887—32no—
297#887—31no—
298#886—34no—
299#886—34no—
300#886C2×D314yescomplemented
301#885—34no—
302#883—34no—
303#882—34no—
304#67⋊C4—34no—
305#67⋊C4—32no—
306#67⋊C4—32no—
307#67⋊C4—34no—
308#67⋊C4—32no—
309#67⋊C4—62no—
310D3×C22⋊C4—32no—
311D3×C22⋊C4—32no—
312D3×C22⋊C4—62no—
313#879—34no—
314#878C2×D314yescomplemented
315#877—34no—
316#877—32no—
317#875—32no—
318C4×D12—32no—
319C4×D12—31no—
320C4×D12—31no—
321C4×D12—61no—
322C4×D12C2×D311yescharacteristic, complemented
323C42×D3—32no—
324C42×D3—31no—
325C42×D3—31no—
326C42×D3—61no—
327#869C2×D311yescharacteristic, complemented
328#869C2×D311yescharacteristic, complemented
329C4×Dic6—32no—
330C4×Dic6C2×D311yescharacteristic, complemented
331C23×C32C2412yes—
332C22×C3⋊D3—24no—
333C22×C3⋊D3—24no—
334C22×C3⋊D3—42no—
335C22×C3⋊D3C2412yes—
336C22×C3⋊D3C2411yescharacteristic
337C22×C3×D3C2412yes—
338C32×D4#4114yescomplemented
339C2×C32×C4—24no—
340C2×C32×C4C2412yes—
341C2×C32×C4C2411yescharacteristic
342C2×C32×C4C2411yescharacteristic
343C2×C32×C4C2411yescharacteristic
344#638—24no—
345C2×C3⋊Dic3—24no—
346C2×C3⋊Dic3C2412yes—
347C2×C3⋊Dic3C2411yescharacteristic
348C2×C3⋊Dic3C2411yescharacteristic
349C2×C3⋊Dic3C2411yescharacteristic
350C4⋊(C3⋊D3)—22no—
351C4×C3⋊D3—22no—
352C4×C3⋊D3—24no—
353C4×C3⋊D3—24no—
354C4×C3⋊D3—24no—
355C4×C3⋊D3—41no—
356C4×C3⋊D3#4114yescomplemented
357C3×#67—28no—
358C2×C3×Dic3—28no—
359C2×C3×Dic3—44no—
360C2×C3×Dic3C2412yes—
361C2×C3×Dic3C2412yes—
362C2×C3×Dic3C2414yes—
363C2×C3×Dic3C2414yes—
364C2×C3×Dic3C2412yes—
365C3×D12—22no—
366C3×C4×D3—24no—
367C3×Dic6—22no—
368C3×Dic6—24no—
369C3×Dic6—42no—
370#626—24no—
371#626—44no—
372D3×Dic3—24no—
373D3×Dic3—42no—
374#556—91no—
375#555—91no—
376#554—31no—
377#553—92no—
378#552—92no—
379#552—92no—
380#551—94no—
381#547—31no—
382#546—92no—
383#533—91no—
384#529—94no—
385#529—92no—
386#525—92no—
387C4×#41—91no—
388C4×#41—92no—
389C2×C4×D4—91no—
390C2×#117—92no—
391C23×D3—32no—
392C23×D3—32no—
393C23×D3—62no—
394C3×#41—68no—
395C2×C3×Q8—32no—
396C2×C3×Q8—31no—
397C2×C3×Q8—32no—
398C2×C3×D4—21no—
399C2×C3×D4—34no—
400C2×C3×D4—31no—
401C2×C3×D4C22×D311yescharacteristic
402C2×C3×D4C22×D311yescharacteristic
403C22×C3×C4—22no—
404C22×C3×C4—34no—
405C22×C3×C4—34no—
406C22×C3×C4—32no—
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—32no—
418C22×Dic3—32no—
419C22×Dic3—62no—
420C22×Dic3C22×D314yes—
421C22×Dic3C22×D314yes—
422#239—64no—
423#237—28no—
424#237—64no—
425D3×D4—68no—
426D3×D4—64no—
427D3×D4—64no—
428C2×D12—32no—
429C2×D12—31no—
430C2×D12—31no—
431C2×D12—34no—
432C2×D12—61no—
433C2×D12C22×D311yescharacteristic
434C2×C4×D3—31no—
435C2×C4×D3—31no—
436C2×C4×D3—32no—
437C2×C4×D3—31no—
438C2×C4×D3—31no—
439C2×C4×D3—32no—
440C2×C4×D3—32no—
441C2×C4×D3—32no—
442C2×C4×D3—32no—
443C2×C4×D3—32no—
444C2×C4×D3—32no—
445C2×C4×D3—32no—
446C2×C4×D3—31no—
447C2×C4×D3—31no—
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—68no—
455C2×C4×D3—68no—
456C2×C4×D3—128no—
457C2×C4×D3C22×D312yes—
458C2×Dic6C22×D312yes—
459C2×Dic6C22×D311yescharacteristic
460C2×Dic6C22×D312yes—
461C3×C4⋊C4—21no—
462C3×C4⋊C4—31no—
463C3×C4⋊C4—32no—
464C3×C4⋊C4—32no—
465C3×C4⋊C4—34no—
466C3×C4⋊C4—32no—
467C3×C4⋊C4—32no—
468C3×C4⋊C4—34no—
469C3×C4⋊C4—31no—
470C3×C4⋊C4—34no—
471C3×C4⋊C4—32no—
472C3×C4⋊C4C22×D311yescharacteristic
473C3×C4⋊C4C22×D311yescharacteristic
474C3×C22⋊C4—22no—
475C3×C22⋊C4—34no—
476C3×C22⋊C4—32no—
477C3×C22⋊C4—34no—
478C3×C22⋊C4C22×D312yes—
479C3×C22⋊C4C22×D312yes—
480C3×C42—21no—
481C3×C42—32no—
482C3×C42C22×D311yescharacteristic
483C3×C42C22×D311yescharacteristic
484#217—32no—
485#217—32no—
486#217—32no—
487#217—34no—
488#217—62no—
489#217C22×D314yes—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—32no—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—32no—
495(C2×D3)⋊C4—32no—
496(C2×D3)⋊C4—32no—
497(C2×D3)⋊C4—34no—
498(C2×D3)⋊C4—34no—
499(C2×D3)⋊C4—32no—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—34no—
504(C2×D3)⋊C4—34no—
505(C2×D3)⋊C4—34no—
506(C2×D3)⋊C4—62no—
507(C2×D3)⋊C4—62no—
508(C2×D3)⋊C4C22×D312yes—
509(C2×D3)⋊C4C22×D314yes—
510C4⋊Dic3—31no—
511C4⋊Dic3—31no—
512C4⋊Dic3—32no—
513C4⋊Dic3—34no—
514C4⋊Dic3—34no—
515C4⋊Dic3—34no—
516C4⋊Dic3—61no—
517C4⋊Dic3C22×D311yescharacteristic
518C4⋊Dic3C22×D312yes—
519C4⋊Dic3C22×D312yes—
520C4⋊Dic3C22×D312yes—
521C4⋊Dic3C22×D312yes—
522C4⋊Dic3C22×D311yescharacteristic
523C4⋊Dic3C22×D314yes—
524C4⋊Dic3C22×D314yes—
525Dic3⋊C4—32no—
526Dic3⋊C4—32no—
527Dic3⋊C4—34no—
528Dic3⋊C4—32no—
529Dic3⋊C4—34no—
530Dic3⋊C4—34no—
531Dic3⋊C4—62no—
532Dic3⋊C4C22×D312yes—
533Dic3⋊C4C22×D314yes—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—31no—
539C4×Dic3—31no—
540C4×Dic3—34no—
541C4×Dic3—32no—
542C4×Dic3—32no—
543C4×Dic3—34no—
544C4×Dic3—32no—
545C4×Dic3—34no—
546C4×Dic3—34no—
547C4×Dic3—34no—
548C4×Dic3—32no—
549C4×Dic3—34no—
550C4×Dic3—61no—
551C4×Dic3—61no—
552C4×Dic3—61no—
553C4×Dic3C22×D312yes—
554C22×C32—22no—
555C22×C32—22no—
556C22×C32C2×#4114yes—
557C22×C32C2511yescharacteristic
558C2×C3⋊D3—21no—
559C2×C3⋊D3—21no—
560C2×C3⋊D3—22no—
561C2×C3⋊D3—22no—
562C2×C3⋊D3—22no—
563C2×C3⋊D3—48no—
564C2×C3⋊D3C2×#4112yes—
565C2×C3×D3—22no—
566C2×C3×D3—22no—
567C2×C3×D3—22no—
568C32×C4—22no—
569C32×C4—21no—
570C32×C4C2×#4112yes—
571C32×C4C2×#4112yes—
572C3⋊Dic3—21no—
573C3⋊Dic3—22no—
574C3⋊Dic3—21no—
575C3⋊Dic3C2×#4112yes—
576C3×Dic3—22no—
577C3×Dic3—24no—
578C3×Dic3—22no—
579C3×Dic3—22no—
580C3×Dic3—24no—
581C2×#41—32no—
582C2×#41—91no—
583C22×D4—91no—
584C23×C4—92no—
585C4⋊Q8—31no—
586C4⋊Q8—31no—
587#126—94no—
588#126—94no—
589#126—94no—
590#125—32no—
591#125—94no—
592#125—92no—
593#124—92no—
594#124—94no—
595#123—34no—
596#123—94no—
597#123—94no—
598#123—94no—
599C22⋊Q8—32no—
600C22⋊Q8—32no—
601C22⋊Q8—34no—
602C22⋊Q8—92no—
603C22⋊Q8—92no—
604C22⋊Q8—92no—
605#121—32no—
606#121—92no—
607#121—92no—
608#121—94no—
609#120—94no—
610C4×Q8—31no—
611C4×Q8—92no—
612C4×Q8—92no—
613C4×Q8—91no—
614C4×Q8—92no—
615C4×D4—32no—
616C4×D4—31no—
617C4×D4—92no—
618C4×D4—92no—
619C4×D4—94no—
620C4×D4—94no—
621C4×D4—91no—
622C4×D4—94no—
623C4×D4—91no—
624C4×D4—92no—
625C4×D4—91no—
626C4×D4—92no—
627C4×D4—91no—
628C4×D4D3211yescharacteristic
629#117—92no—
630#117—94no—
631#117—91no—
632#117—92no—
633#117—94no—
634#117—94no—
635#117—92no—
636#117—92no—
637#117—92no—
638C2×C4⋊C4—32no—
639C2×C4⋊C4—32no—
640C2×C4⋊C4—91no—
641C2×C22⋊C4—94no—
642C2×C22⋊C4—92no—
643C2×C42—92no—
644C2×C42—94no—
645C2×C42—91no—
646C23×C3—22no—
647C23×C3—32no—
648C23×C3C23×D312yes—
649C23×C3C23×D312yes—
650C22×D3—31no—
651C22×D3—31no—
652C22×D3—32no—
653C22×D3—32no—
654C22×D3—61no—
655C22×D3—62no—
656C22×D3—64no—
657C22×D3—64no—
658C22×D3—68no—
659C22×D3—64no—
660C22×D3—64no—
661C22×D3—124no—
662C22×D3—122no—
663C22×D3—122no—
664C22×D3—124no—
665C22×D3C23×D312yes—
666C3×Q8—64no—
667C3×Q8—62no—
668C3×Q8—122no—
669C3×D4—24no—
670C3×D4—68no—
671C3×D4—62no—
672C3×D4#23714yescomplemented
673C3×D4#23914yescomplemented
674C2×C3×C4—24no—
675C2×C3×C4—24no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—22no—
680C2×C3×C4—32no—
681C2×C3×C4—32no—
682C2×C3×C4—34no—
683C2×C3×C4—34no—
684C2×C3×C4—32no—
685C2×C3×C4—44no—
686C2×C3×C4—68no—
687C2×C3×C4—64no—
688C2×C3×C4—124no—
689C2×C3×C4C23×D311yescharacteristic
690C2×C3×C4C23×D311yescharacteristic
691C2×C3×C4C23×D312yes—
692C2×C3×C4C23×D312yes—
693C2×C3×C4C23×D311yescharacteristic
694C2×C3×C4C23×D311yescharacteristic
695C2×C3×C4C23×D311yescharacteristic
696C2×C3×C4C23×D311yescharacteristic
697#67—28no—
698#67—64no—
699#67—68no—
700#67—64no—
701#67—64no—
702#67—124no—
703C2×Dic3—28no—
704C2×Dic3—31no—
705C2×Dic3—31no—
706C2×Dic3—31no—
707C2×Dic3—32no—
708C2×Dic3—32no—
709C2×Dic3—31no—
710C2×Dic3—31no—
711C2×Dic3—31no—
712C2×Dic3—44no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—62no—
717C2×Dic3—64no—
718C2×Dic3—64no—
719C2×Dic3—64no—
720C2×Dic3—124no—
721C2×Dic3—122no—
722C2×Dic3C23×D312yes—
723C2×Dic3C23×D312yes—
724C2×Dic3C23×D314yes—
725C2×Dic3C23×D314yes—
726C2×Dic3C23×D312yes—
727D12—22no—
728D12—64no—
729D12—64no—
730D12—62no—
731D12—62no—
732D12—124no—
733C4×D3—24no—
734C4×D3—34no—
735C4×D3—34no—
736C4×D3—64no—
737C4×D3—64no—
738C4×D3—64no—
739C4×D3—64no—
740C4×D3—64no—
741C4×D3—64no—
742C4×D3—64no—
743C4×D3—62no—
744C4×D3—62no—
745C4×D3—64no—
746C4×D3—64no—
747C4×D3—124no—
748C4×D3—124no—
749C4×D3—124no—
750C4×D3—121no—
751C4×D3—121no—
752C4×D3—122no—
753C4×D3—122no—
754Dic6—24no—
755Dic6—22no—
756Dic6—42no—
757C2×C32—24no—
758C2×C32C22×#4111yescharacteristic
759C2×C32C22×#4111yescharacteristic
760C2×C32#58511yescharacteristic
761C3⋊D3—22no—
762C3⋊D3—42no—
763C3×D3—42no—
764C24—92no—
765#41—68no—
766#41—184no—
767C2×Q8—31no—
768C2×Q8—32no—
769C2×Q8—32no—
770C2×D4—34no—
771C2×D4—31no—
772C2×D4—92no—
773C2×D4—94no—
774C2×D4—92no—
775C2×D4—91no—
776C2×D4—184no—
777C2×D4C2×D3211yescharacteristic
778C22×C4—34no—
779C22×C4—34no—
780C22×C4—32no—
781C22×C4—92no—
782C22×C4—92no—
783C22×C4—91no—
784C22×C4—92no—
785C22×C4—91no—
786C22×C4—92no—
787C22×C4—92no—
788C22×C4—92no—
789C22×C4—91no—
790C22×C4—188no—
791C22×C4C2×D3212yes—
792C4⋊C4—31no—
793C4⋊C4—31no—
794C4⋊C4—32no—
795C4⋊C4—32no—
796C4⋊C4—34no—
797C4⋊C4—34no—
798C4⋊C4—32no—
799C4⋊C4—32no—
800C4⋊C4—34no—
801C4⋊C4—32no—
802C4⋊C4—94no—
803C4⋊C4—94no—
804C4⋊C4—92no—
805C4⋊C4—94no—
806C4⋊C4—91no—
807C4⋊C4—92no—
808C4⋊C4C2×D3211yescharacteristic
809C22⋊C4—34no—
810C22⋊C4—32no—
811C22⋊C4—34no—
812C22⋊C4—92no—
813C22⋊C4—94no—
814C22⋊C4—94no—
815C22⋊C4—94no—
816C22⋊C4—94no—
817C22⋊C4—92no—
818C22⋊C4—94no—
819C22⋊C4—92no—
820C22⋊C4—92no—
821C22⋊C4—92no—
822C22⋊C4C2×D3212yes—
823C42—32no—
824C42—92no—
825C42—94no—
826C42—94no—
827C42—94no—
828C42—92no—
829C42—91no—
830C42—91no—
831C42—91no—
832C42C2×D3211yescharacteristic
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—24no—
838C22×C3—21no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3C2×#23714yes—
845C22×C3C2×#23914yes—
846C22×C3C24×D311yescharacteristic
847C22×C3C24×D311yescharacteristic
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—32no—
852C2×D3—32no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—62no—
856C2×D3—61no—
857C2×D3—61no—
858C2×D3—61no—
859C2×D3—61no—
860C2×D3—64no—
861C2×D3—62no—
862C2×D3—62no—
863C2×D3—62no—
864C2×D3—62no—
865C2×D3—62no—
866C2×D3—62no—
867C2×D3—122no—
868C2×D3—122no—
869C2×D3—128no—
870C2×D3—128no—
871C2×D3—1216no—
872C3×C4—22no—
873C3×C4—22no—
874C3×C4—21no—
875C3×C4—21no—
876C3×C4—22no—
877C3×C4—22no—
878C3×C4—42no—
879C3×C4—41no—
880C3×C4—62no—
881C3×C4—64no—
882C3×C4—62no—
883C3×C4—62no—
884C3×C4—64no—
885C3×C4C2×#23712yes—
886C3×C4C2×#23912yes—
887C3×C4D3×#4112yes—
888C3×C4D3×#4112yes—
889Dic3—24no—
890Dic3—22no—
891Dic3—22no—
892Dic3—24no—
893Dic3—22no—
894Dic3—32no—
895Dic3—32no—
896Dic3—62no—
897Dic3—62no—
898Dic3—61no—
899Dic3—61no—
900Dic3—62no—
901Dic3—62no—
902Dic3—61no—
903Dic3—61no—
904Dic3—122no—
905Dic3—121no—
906C32#347511yescharacteristic, complemented, Sylow
907C23—32no—
908C23—91no—
909C23—92no—
910C23—184no—
911C23—184no—
912C23—362no—
913C23C22×D3212yes—
914Q8—64no—
915Q8—62no—
916Q8—122no—
917D4—68no—
918D4—62no—
919D4—184no—
920D4—184no—
921D4—182no—
922D4—364no—
923D4#379614yescomplemented
924C2×C4—24no—
925C2×C4—32no—
926C2×C4—32no—
927C2×C4—32no—
928C2×C4—34no—
929C2×C4—34no—
930C2×C4—68no—
931C2×C4—64no—
932C2×C4—91no—
933C2×C4—94no—
934C2×C4—92no—
935C2×C4—91no—
936C2×C4—91no—
937C2×C4—124no—
938C2×C4—184no—
939C2×C4—184no—
940C2×C4—184no—
941C2×C4—184no—
942C2×C4—182no—
943C2×C4—184no—
944C2×C4—361no—
945C2×C4—362no—
946C2×C4C22×D3211yescharacteristic
947C2×C4C22×D3212yes—
948C2×C4C22×D3211yescharacteristic
949C2×C4C22×D3211yescharacteristic
950C2×C3—24no—
951C2×C3—24no—
952C2×C3—21no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—44no—
956C2×C3—122no—
957C2×C3C22×#23711yescharacteristic
958C2×C3C22×#23911yescharacteristic
959C2×C3C2×D3×#4111yescharacteristic
960C2×C3C2×D3×#4111yescharacteristic
961C2×C3#596611yescharacteristic
962C2×C3#596811yescharacteristic
963D3—42no—
964D3—64no—
965D3—62no—
966D3—62no—
967D3—124no—
968D3—122no—
969D3—122no—
970C22—22no—
971C22—22no—
972C22—62no—
973C22—62no—
974C22—62no—
975C22—92no—
976C22—181no—
977C22—181no—
978C22—182no—
979C22—182no—
980C22—182no—
981C22—368no—
982C22C2×#379614yes—
983C22C23×D3211yescharacteristic
984C4—22no—
985C4—21no—
986C4—62no—
987C4—64no—
988C4—62no—
989C4—62no—
990C4—64no—
991C4—92no—
992C4—181no—
993C4—182no—
994C4—181no—
995C4C2×#379612yes—
996C4#6431212yes—
997C3—21no—
998C3#8667511yescharacteristic, complemented
999C3#8692211yescharacteristic, complemented
1000C2—24no—
1001C2—122no—
1002C2—182no—
1003C2—362no—
1004C2C22×#379611yescharacteristic
1005C2C2×#6431211yescharacteristic
1006C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3475
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×#5555C2semidirect
3. C3×#5543C2semidirect
4. #10595254C2semidirect
5. Dic3×#237C2semidirect
6. #10594989C2semidirect
7. #10594922C2semidirect
8. C2×#63849C2semidirect
9. #10594825C2semidirect
10. #10594579C2semidirect
11. #10594453C2semidirect
12. #10594164C2semidirect
13. #10594144C2semidirect
14. #10593987C2semidirect
15. C4×#3796C2semidirect
16. #10593866C2semidirect
17. #10593865C2semidirect
34. C3×#930C22semidirect
35. C2×C3×C4⋊Dic3C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C3×#924C22semidirect
38. C3×#897C22semidirect
39. C3×#890C22semidirect
40. C3×#886C22semidirect
41. C3×#878C22semidirect
42. C3×C4×D12C22semidirect
43. C3×#869C22semidirect
44. C3×#869C22semidirect
45. C3×C4×Dic6C22semidirect
48. #67⋊Dic3C22semidirect
49. Dic3×#67C22semidirect
52. #63955C22semidirect
53. C2×Dic32C22semidirect
54. #63916C22semidirect
56. #63907C22semidirect
58. #63898C22semidirect
59. #63890C22semidirect
61. #63881C22semidirect
62. #63878C22semidirect
63. C4×D3×Dic3C22semidirect
64. #63872C22semidirect
67. #63871C22semidirect
69. #63858C22semidirect
74. #63849C22semidirect
75. #63849C22semidirect
76. #63849C22semidirect
77. #63848C22semidirect
78. #63848C22semidirect
79. #63846C22semidirect
80. #63843C22semidirect
81. #63843C22semidirect
82. #63843C22semidirect
83. Dic3×Dic6C22semidirect
84. #63841C22semidirect
108. #5555D3semidirect
113. #5543D3semidirect
237. #930C2×D3semidirect
248. C2×C4⋊Dic3C2×D3semidirect
249. C2×C4⋊Dic3C2×D3semidirect
250. #924C2×D3semidirect
262. #897C2×D3semidirect
293. #890C2×D3semidirect
300. #886C2×D3semidirect
314. #878C2×D3semidirect
322. C4×D12C2×D3semidirect
327. #869C2×D3semidirect
328. #869C2×D3semidirect
330. C4×Dic6C2×D3semidirect
338. C32×D4#41semidirect
356. C4×C3⋊D3#41semidirect
672. C3×D4#237semidirect
673. C3×D4#239semidirect
906. C32#3475semidirect
923. D4#3796semidirect
998. C3#86675semidirect
999. C3#86922semidirect

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×#55552
C3×#55432
#105952542
Dic3×#2372
#105949892
#105949222
C2×#638492
#105948252
#105945792
#105944532
#105941642
#105941442
#105939872
C4×#37962
#105938662
#105938652
#869223
#866753