Finite Group Databasebeta

← #11903646

Subgroups — #11903646

Order 1152.

2419 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3832C211yesmaximal, characteristic, complemented
2C3×#5584C211yesmaximal, characteristic, complemented
3C3×#5579C211yesmaximal, characteristic, complemented
4#10595430C212yesmaximal, complemented
5#10595380C212yesmaximal, complemented
6#10594655C214yesmaximal, complemented
7D3×#892C212yesmaximal, complemented
8#10594559C212yesmaximal, complemented
9#10594442C214yesmaximal, complemented
10#10594005C212yesmaximal, complemented
11C4×#3802C211yesmaximal, characteristic, complemented
12#10593987C211yesmaximal, characteristic, complemented
13#10593947C212yesmaximal, complemented
14#10593943C212yesmaximal, complemented
15#10593896C211yesmaximal, characteristic, complemented
16C4×#3796C212yesmaximal, complemented
17#10593866C211yesmaximal, characteristic, complemented
18#86979—31nomaximal
19#86922—31nomaximal
20C2×#3832C2211yescharacteristic
21C2×#3802C2211yescharacteristic
22C2×C4×D32C2212yes—
23C2×#3796C2212yes—
24C32×C4×Q8C2211yescharacteristic, complemented
25Q8×C3⋊Dic3C2211yescharacteristic, complemented
26#64102C2212yes—
27#64102C2211yescharacteristic, complemented
28#64101C2211yescharacteristic
29#64101C2212yescomplemented
30C4×C4⋊(C3⋊D3)C2212yes—
31C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
32C42×C3⋊D3C2211yescharacteristic
33C42×C3⋊D3C2212yescomplemented
34C3×#946C2212yescomplemented
35C3×#946C2212yescomplemented
36C3×#898C2214yescomplemented
37C3×#896C2214yescomplemented
38C3×#892C2212yescomplemented
39C3×D3×C4⋊C4C2212yescomplemented
40C3×#875C2212yes—
41C3×C4×D12C2212yes—
42C3×C4×D12C2211yescharacteristic
43C3×C4×D12C2211yescharacteristic
44C3×#870C2212yescomplemented
45C3×#869C2211yescharacteristic, complemented
46C3×#869C2211yescharacteristic, complemented
47C3×C4×Dic6C2212yescomplemented
48#63923C2214yes—
49#63921C2212yes—
50D3×(C2×D3)⋊C4C2214yes—
51#63916C2212yes—
52#63909C2212yescomplemented
53#63909C2212yescomplemented
54#63907C2214yescomplemented
55#63906C2214yes—
56C4×#626C2214yescomplemented
57#63902C2212yes—
58C4×#625C2212yes—
59#63900C2211yescharacteristic
60#63898C2211yescharacteristic
61#63898C2211yescharacteristic
62#63897C2214yes—
63#63891C2214yes—
64#63890C2214yescomplemented
65D3×C4⋊Dic3C2212yescomplemented
66#63881C2214yescomplemented
67#63881C2214yescomplemented
68#63878C2214yescomplemented
69#63878C2214yescomplemented
70C4×D3×Dic3C2214yescomplemented
71#63872C2212yescomplemented
72#63871C2212yes—
73#63871C2212yes—
74#63871C2212yescomplemented
75#63868C2214yescomplemented
76#63862C2214yescomplemented
77#63853C2214yescomplemented
78#63849C2212yes—
79#63849C2212yescomplemented
80#63845C2214yescomplemented
81#63843C2212yescomplemented
82#63843C2212yescomplemented
83#63841C2212yescomplemented
84#63836C2214yes—
85C3×#556—31no—
86C3×#554—31no—
87#5734—31no—
88#5728—31no—
89#5728—31no—
90#5726—31no—
91#5706—34no—
92#5705—34no—
93#5694—32no—
94#5691—32no—
95#5680—32no—
96#5676—32no—
97#5642—32no—
98#5639—32no—
99#5637—34no—
100#5627—32no—
101#5627—32no—
102#5624—34no—
103#5584D311yescharacteristic, complemented
104#5581—32no—
105#5579D311yescharacteristic, complemented
106C4×#239—31no—
107C4×#239—31no—
108C4×#239—32no—
109C4×#239—61no—
110#5563—31no—
111#5555—31no—
112#5554—32no—
113C4×D3×D4—31no—
114C4×D3×D4—31no—
115C4×#237—32no—
116#5530—32no—
117D3×#117—32no—
118#5514—32no—
119C2×#892—32no—
120C22×D32C2312yes—
121C2×C32×Q8C2311yescharacteristic
122#3832—24no—
123C2×C4⋊(C3⋊D3)C2312yes—
124C2×C4⋊(C3⋊D3)C2311yescharacteristic
125C2×C4×C3⋊D3C2312yes—
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×C4×C3⋊D3C2312yes—
128C2×C4×C3⋊D3C2311yescharacteristic
129C2×C4×C3⋊D3C2312yes—
130C2×C4×C3⋊D3C2311yescharacteristic
131C2×C3×D12C2311yescharacteristic
132C2×C3×D12C2311yescharacteristic
133C2×C3×C4×D3C2312yes—
134C2×C3×C4×D3C2312yes—
135C2×C3×C4×D3C2314yes—
136C2×C3×Dic6C2312yes—
137C2×C3×Dic6C2312yes—
138C2×#626C2314yes—
139C2×#626C2314yes—
140C2×#625C2312yes—
141C2×#624C2312yes—
142C2×D3×Dic3C2314yes—
143C2×D3×Dic3C2312yes—
144C2×D3×Dic3C2312yes—
145#3802—24no—
146C4×D32—28no—
147#3796—28no—
148C32×C4⋊C4C2311yescharacteristic
149C32×C4⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151C32×C42C2312yes—
152#3752C2312yes—
153#3752C2312yes—
154#3752C2312yes—
155C4⋊(C3⋊Dic3)C2312yes—
156C4⋊(C3⋊Dic3)C2311yescharacteristic
157C4×C3⋊Dic3C2311yescharacteristic
158C4×C3⋊Dic3C2311yescharacteristic
159C4×C3⋊Dic3C2311yescharacteristic
160C4×C3⋊Dic3C2312yes—
161C4×C3⋊Dic3C2312yes—
162C3×(C2×D3)⋊C4C2314yes—
163C3×(C2×D3)⋊C4C2312yes—
164C3×(C2×D3)⋊C4C2314yes—
165C3×(C2×D3)⋊C4C2312yes—
166C3×(C2×D3)⋊C4C2314yes—
167C3×C4⋊Dic3C2312yes—
168C3×C4⋊Dic3C2312yes—
169C3×C4⋊Dic3C2312yes—
170C3×C4⋊Dic3C2312yes—
171C3×C4⋊Dic3C2311yescharacteristic
172C3×C4⋊Dic3C2311yescharacteristic
173C3×Dic3⋊C4C2314yes—
174C3×Dic3⋊C4C2314yes—
175C3×Dic3⋊C4C2314yes—
176C3×C4×Dic3C2314yes—
177#3724C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181#3722C2314yes—
182#3722C2314yes—
183#3722C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2312yes—
186(C2×D3)⋊Dic3C2312yes—
187Dic32C2314yes—
188Dic32C2314yes—
189#3475—91noSylow
190C2×#239—31no—
191C2×#239—31no—
192C2×#239—32no—
193C2×#239—61no—
194C2×#237—32no—
195C2×D3×D4—31no—
196C2×D3×D4—31no—
197C22×C4×D3—32no—
198C22×C4×D3—32no—
199C3×C4⋊Q8—31no—
200C3×C4⋊Q8—31no—
201C3×#126—34no—
202C3×#125—32no—
203C3×#124—32no—
204C3×C22⋊Q8—32no—
205C3×C22⋊Q8—32no—
206C3×C22⋊Q8—34no—
207C3×C4×Q8—21no—
208C3×C4×Q8—32no—
209C3×C4×Q8C2×D311yescharacteristic, complemented
210C3×C4×Q8C2×D311yescharacteristic, complemented
211C3×C4×D4—32no—
212C3×C4×D4—31no—
213C3×C4×D4—31no—
214C3×#117—32no—
215C2×C3×C4⋊C4—32no—
216#947—34no—
217#946—32no—
218#946—32no—
219#946—32no—
220#946C2×D312yescomplemented
221#946C2×D312yescomplemented
222Q8×Dic3—31no—
223Q8×Dic3—31no—
224Q8×Dic3—32no—
225Q8×Dic3—32no—
226Q8×Dic3—61no—
227#938—32no—
228D4×Dic3—31no—
229D4×Dic3—31no—
230#930—34no—
231#930—32no—
232#930—32no—
233C4×#67—32no—
234C4×#67—32no—
235C4×#67—34no—
236C2×(C2×D3)⋊C4—34no—
237#926—32no—
238C2×C4⋊Dic3—32no—
239C2×C4×Dic3—34no—
240#898—34no—
241#898—34no—
242#898C2×D314yescomplemented
243#897—32no—
244#897—32no—
245#897—32no—
246#896C2×D314yescomplemented
247#895—32no—
248#895—32no—
249#895—32no—
250#894—34no—
251#894—34no—
252#894—34no—
253#894—34no—
254#893—31no—
255#893—31no—
256#893—32no—
257#893—32no—
258#893—31no—
259#893—31no—
260#893—34no—
261#893—34no—
262#893—62no—
263#893—61no—
264#892—32no—
265#892—32no—
266#892—31no—
267#892—31no—
268#892—32no—
269#892—34no—
270#892—34no—
271#892—32no—
272#892—32no—
273#892—32no—
274#892—32no—
275#892—34no—
276#892—61no—
277#892—62no—
278#892C2×D312yescomplemented
279D3×C4⋊C4—32no—
280D3×C4⋊C4—31no—
281D3×C4⋊C4—31no—
282D3×C4⋊C4C2×D312yescomplemented
283#890—32no—
284#890—32no—
285#890—34no—
286#889—34no—
287#887—32no—
288#887—32no—
289#886—34no—
290#886—34no—
291#885—34no—
292#884—34no—
293#883—34no—
294#883—34no—
295#882—34no—
296#882—34no—
297#67⋊C4—32no—
298#67⋊C4—32no—
299#67⋊C4—34no—
300#67⋊C4—34no—
301D3×C22⋊C4—34no—
302D3×C22⋊C4—32no—
303D3×C22⋊C4—32no—
304#879—34no—
305#877—34no—
306#877—34no—
307#876—34no—
308#875C2×D312yes—
309C4×D12—34no—
310C4×D12—32no—
311C4×D12—32no—
312C4×D12—31no—
313C4×D12—31no—
314C4×D12—62no—
315C4×D12—61no—
316C4×D12C2×D312yes—
317C4×D12C2×D311yescharacteristic
318C4×D12C2×D311yescharacteristic
319#872—34no—
320C42×D3—34no—
321C42×D3—32no—
322C42×D3—32no—
323C42×D3—31no—
324C42×D3—31no—
325C42×D3—61no—
326C42×D3—62no—
327#870C2×D312yescomplemented
328#869C2×D311yescharacteristic, complemented
329#869C2×D311yescharacteristic, complemented
330C4×Dic6C2×D312yescomplemented
331C22×C3⋊D3C2412yes—
332C22×C3⋊D3C2411yescharacteristic
333C22×C3×D3C2412yes—
334C22×C3×D3C2412yes—
335C2×D32—24no—
336C2×D32—24no—
337C2×D32—42no—
338C32×Q8—22no—
339C2×C32×C4C2412yes—
340C2×C32×C4C2412yes—
341C2×C32×C4C2411yescharacteristic
342C2×C32×C4C2411yescharacteristic
343C2×C32×C4C2411yescharacteristic
344C2×C3⋊Dic3C2412yes—
345C2×C3⋊Dic3C2411yescharacteristic
346C2×C3⋊Dic3C2411yescharacteristic
347C2×C3⋊Dic3C2411yescharacteristic
348C4⋊(C3⋊D3)—24no—
349C4⋊(C3⋊D3)—22no—
350C4×C3⋊D3—24no—
351C4×C3⋊D3—24no—
352C4×C3⋊D3—22no—
353C4×C3⋊D3—41no—
354C4×C3⋊D3—42no—
355C4×C3⋊D3#4114yescomplemented
356C2×C3×Dic3C2414yes—
357C2×C3×Dic3C2412yes—
358C2×C3×Dic3C2414yes—
359C2×C3×Dic3C2412yes—
360C3×D12—22no—
361C3×D12#4114yescomplemented
362C3×C4×D3—24no—
363C3×C4×D3—24no—
364C3×C4×D3—44no—
365C3×Dic6—24no—
366C3×Dic6—42no—
367#626—28no—
368#626—44no—
369#625—24no—
370#624—24no—
371D3×Dic3—28no—
372D3×Dic3—24no—
373D3×Dic3—24no—
374#556—31no—
375#555—91no—
376#554—31no—
377#553—92no—
378#552—92no—
379#552—92no—
380#551—94no—
381#547—91no—
382#546—92no—
383#533—91no—
384#529—94no—
385#529—92no—
386#525—92no—
387C4×#41—92no—
388C4×#41—91no—
389C2×C4×D4—91no—
390C2×#117—92no—
391C23×D3—32no—
392C23×D3—32no—
393C2×C3×Q8—21no—
394C2×C3×Q8—32no—
395C2×C3×Q8—32no—
396C2×C3×Q8C22×D311yescharacteristic
397C2×C3×Q8C22×D311yescharacteristic
398C2×C3×D4—31no—
399C2×C3×D4—31no—
400C22×C3×C4—32no—
401C22×C3×C4—32no—
402C22×C3×C4—34no—
403C2×#67—32no—
404C2×#67—32no—
405C2×#67—34no—
406C2×#67—34no—
407C22×Dic3—32no—
408C22×Dic3—34no—
409C22×Dic3—32no—
410#239—64no—
411#239—64no—
412#239—68no—
413#239—68no—
414#237—68no—
415D3×D4—64no—
416D3×D4—64no—
417C2×D12—34no—
418C2×D12—32no—
419C2×D12—32no—
420C2×D12—31no—
421C2×D12—31no—
422C2×D12—34no—
423C2×D12—62no—
424C2×D12—61no—
425C2×D12C22×D311yescharacteristic
426C2×D12C22×D311yescharacteristic
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—32no—
430C2×C4×D3—34no—
431C2×C4×D3—32no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—32no—
435C2×C4×D3—32no—
436C2×C4×D3—32no—
437C2×C4×D3—32no—
438C2×C4×D3—32no—
439C2×C4×D3—32no—
440C2×C4×D3—32no—
441C2×C4×D3—31no—
442C2×C4×D3—31no—
443C2×C4×D3—32no—
444C2×C4×D3—61no—
445C2×C4×D3—62no—
446C2×C4×D3—61no—
447C2×C4×D3—62no—
448C2×C4×D3—61no—
449C2×C4×D3—62no—
450C2×C4×D3—68no—
451C2×C4×D3—68no—
452C2×C4×D3C22×D312yes—
453C2×C4×D3C22×D312yes—
454C2×C4×D3C22×D314yes—
455C2×Dic6C22×D312yes—
456C2×Dic6C22×D312yes—
457C3×C4⋊C4—21no—
458C3×C4⋊C4—22no—
459C3×C4⋊C4—32no—
460C3×C4⋊C4—32no—
461C3×C4⋊C4—34no—
462C3×C4⋊C4—32no—
463C3×C4⋊C4—32no—
464C3×C4⋊C4—34no—
465C3×C4⋊C4—31no—
466C3×C4⋊C4—31no—
467C3×C4⋊C4—34no—
468C3×C4⋊C4C22×D311yescharacteristic
469C3×C4⋊C4C22×D311yescharacteristic
470C3×C4⋊C4C22×D312yes—
471C3×C4⋊C4C22×D312yes—
472C3×C22⋊C4—34no—
473C3×C22⋊C4—34no—
474C3×C22⋊C4—34no—
475C3×C22⋊C4—32no—
476C3×C22⋊C4—32no—
477C3×C42—21no—
478C3×C42—22no—
479C3×C42—34no—
480C3×C42C22×D312yes—
481C3×C42C22×D311yescharacteristic
482C3×C42C22×D311yescharacteristic
483C3×C42C22×D312yes—
484#217—32no—
485#217—34no—
486#217—32no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—34no—
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—32no—
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—34no—
502(C2×D3)⋊C4—62no—
503(C2×D3)⋊C4—62no—
504(C2×D3)⋊C4—62no—
505(C2×D3)⋊C4C22×D312yes—
506(C2×D3)⋊C4C22×D312yes—
507(C2×D3)⋊C4C22×D314yes—
508(C2×D3)⋊C4C22×D314yes—
509(C2×D3)⋊C4C22×D314yes—
510C4⋊Dic3—32no—
511C4⋊Dic3—32no—
512C4⋊Dic3—31no—
513C4⋊Dic3—31no—
514C4⋊Dic3—34no—
515C4⋊Dic3—34no—
516C4⋊Dic3—34no—
517C4⋊Dic3—61no—
518C4⋊Dic3—62no—
519C4⋊Dic3C22×D311yescharacteristic
520C4⋊Dic3C22×D312yes—
521C4⋊Dic3C22×D312yes—
522C4⋊Dic3C22×D312yes—
523C4⋊Dic3C22×D312yes—
524C4⋊Dic3C22×D311yescharacteristic
525Dic3⋊C4—34no—
526Dic3⋊C4—32no—
527Dic3⋊C4—34no—
528Dic3⋊C4—34no—
529Dic3⋊C4—32no—
530Dic3⋊C4C22×D314yes—
531Dic3⋊C4C22×D314yes—
532Dic3⋊C4C22×D314yes—
533C4×Dic3—32no—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—32no—
537C4×Dic3—32no—
538C4×Dic3—31no—
539C4×Dic3—31no—
540C4×Dic3—31no—
541C4×Dic3—31no—
542C4×Dic3—32no—
543C4×Dic3—34no—
544C4×Dic3—34no—
545C4×Dic3—34no—
546C4×Dic3—34no—
547C4×Dic3—61no—
548C4×Dic3—62no—
549C4×Dic3—61no—
550C4×Dic3—62no—
551C4×Dic3—61no—
552C4×Dic3C22×D314yes—
553C22×C32C2511yescharacteristic
554C2×C3⋊D3—22no—
555C2×C3⋊D3—21no—
556C2×C3⋊D3—21no—
557C2×C3⋊D3—22no—
558C2×C3⋊D3—22no—
559C2×C3⋊D3C2×#4112yes—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—22no—
563C2×C3×D3—22no—
564C2×C3×D3—22no—
565C2×C3×D3C2×#4114yes—
566D32—48no—
567C32×C4—22no—
568C32×C4—21no—
569C32×C4—22no—
570C32×C4C2×#4112yes—
571C32×C4C2×#4112yes—
572C3⋊Dic3—21no—
573C3⋊Dic3—22no—
574C3⋊Dic3—21no—
575C3⋊Dic3C2×#4112yes—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—24no—
579C3×Dic3—24no—
580C2×#41—92no—
581C2×#41—91no—
582C22×D4—91no—
583C23×C4—92no—
584C4⋊Q8—31no—
585C4⋊Q8—31no—
586#126—34no—
587#126—94no—
588#126—94no—
589#125—32no—
590#125—94no—
591#125—92no—
592#124—32no—
593#124—94no—
594#123—94no—
595#123—94no—
596#123—94no—
597#123—94no—
598C22⋊Q8—32no—
599C22⋊Q8—32no—
600C22⋊Q8—34no—
601C22⋊Q8—92no—
602C22⋊Q8—92no—
603C22⋊Q8—92no—
604#121—94no—
605#121—92no—
606#121—92no—
607#121—92no—
608#120—94no—
609C4×Q8—32no—
610C4×Q8—92no—
611C4×Q8—92no—
612C4×Q8—91no—
613C4×Q8D3211yescharacteristic, complemented
614C4×D4—31no—
615C4×D4—31no—
616C4×D4—32no—
617C4×D4—94no—
618C4×D4—92no—
619C4×D4—94no—
620C4×D4—94no—
621C4×D4—91no—
622C4×D4—91no—
623C4×D4—92no—
624C4×D4—92no—
625C4×D4—91no—
626C4×D4—92no—
627C4×D4—91no—
628#117—32no—
629#117—94no—
630#117—94no—
631#117—94no—
632#117—92no—
633#117—92no—
634#117—92no—
635#117—91no—
636#117—92no—
637C2×C4⋊C4—32no—
638C2×C4⋊C4—91no—
639C2×C4⋊C4—92no—
640C2×C22⋊C4—92no—
641C2×C22⋊C4—94no—
642C2×C42—94no—
643C2×C42—91no—
644C2×C42—92no—
645C23×C3—32no—
646C23×C3—32no—
647C22×D3—31no—
648C22×D3—31no—
649C22×D3—32no—
650C22×D3—32no—
651C22×D3—61no—
652C22×D3—62no—
653C22×D3—64no—
654C22×D3—64no—
655C22×D3—64no—
656C22×D3—64no—
657C22×D3—122no—
658C22×D3—122no—
659C22×D3C23×D312yes—
660C22×D3C23×D312yes—
661C3×Q8—24no—
662C3×Q8—22no—
663C3×Q8—22no—
664C3×Q8—64no—
665C3×Q8—122no—
666C3×D4—34no—
667C3×D4—62no—
668C2×C3×C4—22no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—22no—
672C2×C3×C4—21no—
673C2×C3×C4—34no—
674C2×C3×C4—32no—
675C2×C3×C4—34no—
676C2×C3×C4—32no—
677C2×C3×C4—64no—
678C2×C3×C4—64no—
679C2×C3×C4—124no—
680C2×C3×C4C23×D312yes—
681C2×C3×C4C23×D312yes—
682C2×C3×C4C23×D312yes—
683C2×C3×C4C23×D312yes—
684C2×C3×C4C23×D311yescharacteristic
685C2×C3×C4C23×D311yescharacteristic
686C2×C3×C4C23×D311yescharacteristic
687C2×C3×C4C23×D311yescharacteristic
688C2×C3×C4C23×D311yescharacteristic
689C2×C3×C4C23×D311yescharacteristic
690#67—68no—
691#67—64no—
692#67—64no—
693#67—124no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—32no—
698C2×Dic3—32no—
699C2×Dic3—31no—
700C2×Dic3—31no—
701C2×Dic3—31no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—62no—
705C2×Dic3—61no—
706C2×Dic3—64no—
707C2×Dic3—64no—
708C2×Dic3—68no—
709C2×Dic3C23×D312yes—
710C2×Dic3C23×D314yes—
711C2×Dic3C23×D314yes—
712C2×Dic3C23×D312yes—
713D12—22no—
714D12—64no—
715D12—64no—
716D12—68no—
717D12—64no—
718D12—68no—
719D12—62no—
720D12—62no—
721D12—124no—
722D12#23914yescomplemented
723C4×D3—24no—
724C4×D3—24no—
725C4×D3—34no—
726C4×D3—34no—
727C4×D3—44no—
728C4×D3—64no—
729C4×D3—64no—
730C4×D3—64no—
731C4×D3—64no—
732C4×D3—64no—
733C4×D3—64no—
734C4×D3—64no—
735C4×D3—68no—
736C4×D3—68no—
737C4×D3—62no—
738C4×D3—64no—
739C4×D3—62no—
740C4×D3—64no—
741C4×D3—122no—
742C4×D3—124no—
743C4×D3—121no—
744C4×D3—122no—
745C4×D3—122no—
746C4×D3—121no—
747C4×D3—124no—
748C4×D3—122no—
749Dic6—24no—
750Dic6—42no—
751C2×C32C22×#4111yescharacteristic
752C2×C32C22×#4111yescharacteristic
753C2×C32#58511yescharacteristic
754C3⋊D3—22no—
755C3⋊D3—42no—
756C3×D3—24no—
757C3×D3—42no—
758C24—92no—
759#41—184no—
760#41—188no—
761C2×Q8—32no—
762C2×Q8—32no—
763C2×Q8C2×D3211yescharacteristic
764C2×D4—31no—
765C2×D4—31no—
766C2×D4—94no—
767C2×D4—94no—
768C2×D4—92no—
769C2×D4—92no—
770C2×D4—91no—
771C2×D4—184no—
772C22×C4—32no—
773C22×C4—32no—
774C22×C4—34no—
775C22×C4—92no—
776C22×C4—92no—
777C22×C4—94no—
778C22×C4—92no—
779C22×C4—91no—
780C22×C4—91no—
781C22×C4—92no—
782C22×C4—92no—
783C22×C4—91no—
784C22×C4—92no—
785C22×C4—188no—
786C4⋊C4—32no—
787C4⋊C4—34no—
788C4⋊C4—32no—
789C4⋊C4—31no—
790C4⋊C4—31no—
791C4⋊C4—32no—
792C4⋊C4—34no—
793C4⋊C4—34no—
794C4⋊C4—32no—
795C4⋊C4—94no—
796C4⋊C4—92no—
797C4⋊C4—94no—
798C4⋊C4—94no—
799C4⋊C4—91no—
800C4⋊C4—92no—
801C4⋊C4C2×D3211yescharacteristic
802C4⋊C4C2×D3212yes—
803C22⋊C4—34no—
804C22⋊C4—32no—
805C22⋊C4—32no—
806C22⋊C4—34no—
807C22⋊C4—34no—
808C22⋊C4—94no—
809C22⋊C4—94no—
810C22⋊C4—94no—
811C22⋊C4—92no—
812C22⋊C4—94no—
813C22⋊C4—92no—
814C22⋊C4—92no—
815C22⋊C4—92no—
816C22⋊C4—92no—
817C42—34no—
818C42—94no—
819C42—94no—
820C42—92no—
821C42—91no—
822C42—91no—
823C42—92no—
824C42—91no—
825C42C2×D3211yescharacteristic
826C42C2×D3212yes—
827C22×C3—21no—
828C22×C3—34no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3C24×D311yescharacteristic
835C22×C3C24×D311yescharacteristic
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—32no—
842C2×D3—32no—
843C2×D3—62no—
844C2×D3—61no—
845C2×D3—61no—
846C2×D3—61no—
847C2×D3—61no—
848C2×D3—64no—
849C2×D3—62no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—121no—
856C2×D3—121no—
857C2×D3—122no—
858C2×D3—122no—
859C2×D3—128no—
860C2×D3—128no—
861C2×D3C2×#23914yes—
862C3×C4—24no—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—21no—
866C3×C4—22no—
867C3×C4—22no—
868C3×C4—21no—
869C3×C4—22no—
870C3×C4—22no—
871C3×C4—42no—
872C3×C4—41no—
873C3×C4—64no—
874C3×C4—62no—
875C3×C4—62no—
876C3×C4—64no—
877C3×C4C2×#23912yes—
878C3×C4D3×#4112yes—
879C3×C4D3×#4112yes—
880C3×C4D3×#4112yes—
881Dic3—24no—
882Dic3—22no—
883Dic3—22no—
884Dic3—24no—
885Dic3—32no—
886Dic3—32no—
887Dic3—62no—
888Dic3—62no—
889Dic3—62no—
890Dic3—61no—
891Dic3—62no—
892Dic3—61no—
893Dic3—61no—
894Dic3—61no—
895Dic3—122no—
896Dic3—121no—
897C32#347511yescharacteristic, complemented, Sylow
898C23—32no—
899C23—32no—
900C23—91no—
901C23—92no—
902C23—184no—
903C23—184no—
904C23—362no—
905Q8—22no—
906Q8—64no—
907Q8—122no—
908D4—34no—
909D4—62no—
910D4—184no—
911D4—188no—
912D4—184no—
913D4—182no—
914D4—364no—
915C2×C4—32no—
916C2×C4—34no—
917C2×C4—34no—
918C2×C4—32no—
919C2×C4—64no—
920C2×C4—64no—
921C2×C4—91no—
922C2×C4—94no—
923C2×C4—92no—
924C2×C4—91no—
925C2×C4—91no—
926C2×C4—124no—
927C2×C4—184no—
928C2×C4—184no—
929C2×C4—184no—
930C2×C4—184no—
931C2×C4—188no—
932C2×C4—182no—
933C2×C4—184no—
934C2×C4—362no—
935C2×C4—361no—
936C2×C4C22×D3212yes—
937C2×C4C22×D3211yescharacteristic
938C2×C4C22×D3212yes—
939C2×C4C22×D3211yescharacteristic
940C2×C4C22×D3211yescharacteristic
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—21no—
944C2×C3—64no—
945C2×C3—122no—
946C2×C3C22×#23911yescharacteristic
947C2×C3C2×D3×#4111yescharacteristic
948C2×C3C2×D3×#4111yescharacteristic
949C2×C3C2×D3×#4111yescharacteristic
950C2×C3#596611yescharacteristic
951C2×C3#596811yescharacteristic
952D3—24no—
953D3—42no—
954D3—62no—
955D3—62no—
956D3—122no—
957D3—124no—
958D3—122no—
959D3—122no—
960C22—34no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—62no—
966C22—92no—
967C22—181no—
968C22—181no—
969C22—182no—
970C22—182no—
971C22—182no—
972C22—368no—
973C22C23×D3211yescharacteristic
974C4—22no—
975C4—22no—
976C4—21no—
977C4—62no—
978C4—62no—
979C4—64no—
980C4—64no—
981C4—92no—
982C4—182no—
983C4—181no—
984C4—181no—
985C4#6430612yes—
986C4D3×#23912yes—
987C3—21no—
988C3#8692211yescharacteristic, complemented
989C3#8697911yescharacteristic, complemented
990C2—64no—
991C2—122no—
992C2—182no—
993C2—362no—
994C2C2×#6430611yescharacteristic
995C2C2×D3×#23911yescharacteristic
996C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3475
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×#3832C2semidirect
2. C3×#5584C2semidirect
3. C3×#5579C2semidirect
4. #10595430C2semidirect
5. #10595380C2semidirect
6. #10594655C2semidirect
7. D3×#892C2semidirect
8. #10594559C2semidirect
9. #10594442C2semidirect
10. #10594005C2semidirect
11. C4×#3802C2semidirect
12. #10593987C2semidirect
13. #10593947C2semidirect
14. #10593943C2semidirect
15. #10593896C2semidirect
16. C4×#3796C2semidirect
17. #10593866C2semidirect
24. C32×C4×Q8C22semidirect
25. Q8×C3⋊Dic3C22semidirect
27. #64102C22semidirect
29. #64101C22semidirect
31. C4×C4⋊(C3⋊D3)C22semidirect
33. C42×C3⋊D3C22semidirect
34. C3×#946C22semidirect
35. C3×#946C22semidirect
36. C3×#898C22semidirect
37. C3×#896C22semidirect
38. C3×#892C22semidirect
39. C3×D3×C4⋊C4C22semidirect
44. C3×#870C22semidirect
45. C3×#869C22semidirect
46. C3×#869C22semidirect
47. C3×C4×Dic6C22semidirect
52. #63909C22semidirect
53. #63909C22semidirect
54. #63907C22semidirect
56. C4×#626C22semidirect
64. #63890C22semidirect
65. D3×C4⋊Dic3C22semidirect
66. #63881C22semidirect
67. #63881C22semidirect
68. #63878C22semidirect
69. #63878C22semidirect
70. C4×D3×Dic3C22semidirect
71. #63872C22semidirect
74. #63871C22semidirect
75. #63868C22semidirect
76. #63862C22semidirect
77. #63853C22semidirect
79. #63849C22semidirect
80. #63845C22semidirect
81. #63843C22semidirect
82. #63843C22semidirect
83. #63841C22semidirect
103. #5584D3semidirect
105. #5579D3semidirect
209. C3×C4×Q8C2×D3semidirect
210. C3×C4×Q8C2×D3semidirect
220. #946C2×D3semidirect
221. #946C2×D3semidirect
242. #898C2×D3semidirect
246. #896C2×D3semidirect
278. #892C2×D3semidirect
282. D3×C4⋊C4C2×D3semidirect
327. #870C2×D3semidirect
328. #869C2×D3semidirect
329. #869C2×D3semidirect
330. C4×Dic6C2×D3semidirect
355. C4×C3⋊D3#41semidirect
361. C3×D12#41semidirect
613. C4×Q8D32semidirect
722. D12#239semidirect
897. C32#3475semidirect
988. C3#86922semidirect
989. C3#86979semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
C3×#55842
C3×#55792
#105954302
#105953802
#105946552
D3×#8922
#105945592
#105944422
#105940052
C4×#38022
#105939872
#105939472
#105939432
#105938962
C4×#37962
#105938662
#869793
#869223