Finite Group Databasebeta

← #11903645

Subgroups — #11903645

Order 1152.

2378 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596050C211yesmaximal, characteristic, complemented
2C3×#5584C211yesmaximal, characteristic, complemented
3C3×C4×#239C211yesmaximal, characteristic, complemented
4#10595424C212yesmaximal, complemented
5#10595344C212yesmaximal, complemented
6#10594645C214yesmaximal, complemented
7#10594602C212yesmaximal, complemented
8#10594583C212yesmaximal, complemented
9#10594417C214yesmaximal, complemented
10#10594007C212yesmaximal, complemented
11C4×D3×D12C211yesmaximal, characteristic, complemented
12#10593988C211yesmaximal, characteristic, complemented
13C4×#3799C212yesmaximal, complemented
14#10593921C212yesmaximal, complemented
15#10593917C212yesmaximal, complemented
16#10593869C211yesmaximal, characteristic, complemented
17#10593859C211yesmaximal, characteristic, complemented
18#86979—31nomaximal
19#85840—31nomaximal
20C2×C3×#239C2211yescharacteristic
21C2×D3×D12C2211yescharacteristic
22C2×C4×D32C2212yes—
23C2×#3799C2212yes—
24C32×C4×Q8C2211yescharacteristic, complemented
25#64155C2212yescomplemented
26#64105C2214yescomplemented
27C4⋊C4×C3⋊D3C2212yescomplemented
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×C4⋊(C3⋊D3)C2212yes—
30#64079C2212yescomplemented
31#64078C2211yescharacteristic, complemented
32C3×#946C2212yescomplemented
33C3×Q8×Dic3C2211yescharacteristic, complemented
34C3×#898C2214yescomplemented
35C3×#893C2212yes—
36C3×#893C2211yescharacteristic, complemented
37C3×#892C2211yescharacteristic
38C3×#892C2212yescomplemented
39C3×#892C2212yescomplemented
40C3×#875C2212yes—
41C3×C4×D12C2212yes—
42C3×C4×D12C2211yescharacteristic
43C3×C4×D12C2211yescharacteristic, complemented
44C3×C42×D3C2211yescharacteristic
45C3×C42×D3C2212yescomplemented
46C3×#869C2211yescharacteristic, complemented
47C3×C4×Dic6C2212yescomplemented
48#63922C2214yes—
49#63921C2214yes—
50D3×(C2×D3)⋊C4C2212yes—
51#63916C2212yescomplemented
52#63913C2214yescomplemented
53#63912C2214yes—
54#63908C2212yes—
55#63908C2212yescomplemented
56#63905C2214yescomplemented
57#63904C2214yescomplemented
58C4×#626C2212yes—
59C4×#626C2214yescomplemented
60#63900C2212yescomplemented
61#63894C2211yescharacteristic
62Dic3×D12C2211yescharacteristic
63D3×C4⋊Dic3C2211yescharacteristic
64#63884C2214yes—
65C4×#624C2214yescomplemented
66#63880C2212yes—
67#63879C2214yescomplemented
68#63877C2214yes—
69#63877C2214yescomplemented
70#63869C2212yescomplemented
71#63859C2214yescomplemented
72#63859C2214yescomplemented
73#63857C2212yes—
74#63856C2212yes—
75#63856C2212yescomplemented
76#63854C2214yes—
77#63854C2214yescomplemented
78#63847C2214yescomplemented
79#63844C2212yescomplemented
80Dic3×Dic6C2212yescomplemented
81#63841C2212yes—
82#63841C2212yescomplemented
83#63841C2212yescomplemented
84#63836C2214yescomplemented
85C3×#556—31no—
86C3×C4×#41—31no—
87#5828—32no—
88#5728—31no—
89#5726—31no—
90#5706—34no—
91#5705—34no—
92#5680—32no—
93#5676—32no—
94#5639—32no—
95#5627—32no—
96#5584D311yescharacteristic, complemented
97#5581—32no—
98#5581—32no—
99#5579—31no—
100#5579—31no—
101#5579—61no—
102C4×#239—32no—
103C4×#239D311yescharacteristic, complemented
104#5563—31no—
105#5563—31no—
106#5558—32no—
107#5556—34no—
108#5551—31no—
109#5550—32no—
110C4×D3×D4—31no—
111#5541—32no—
112#5530—32no—
113#5528—34no—
114D3×#117—32no—
115D3×#117—32no—
116#5479—32no—
117C4×#235—32no—
118C2×C4×D12—31no—
119#5470—31no—
120C22×D32C2312yes—
121C2×C32×Q8C2311yescharacteristic
122C2×C4⋊(C3⋊D3)C2311yescharacteristic
123C2×C4×C3⋊D3C2312yes—
124C2×C4×C3⋊D3C2314yes—
125C2×#634C2312yes—
126C3×#239—24no—
127C2×C3×D12C2312yes—
128C2×C3×D12C2311yescharacteristic
129C2×C3×D12C2311yescharacteristic
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2312yes—
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×Dic6C2312yes—
138C2×#626C2314yes—
139C2×#626C2312yes—
140C2×#625C2314yes—
141C2×#624C2314yes—
142C2×#624C2312yes—
143C2×D3×Dic3C2312yes—
144C2×D3×Dic3C2312yes—
145D3×D12—24no—
146C4×D32—28no—
147#3799—28no—
148C32×C4⋊C4C2311yescharacteristic
149C32×C4⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151C32×C42C2312yes—
152#3752C2314yes—
153#3752C2312yes—
154C4⋊(C3⋊Dic3)C2312yes—
155C4⋊(C3⋊Dic3)C2312yes—
156C4⋊(C3⋊Dic3)C2311yescharacteristic
157#3750C2314yes—
158#3750C2314yes—
159C3×(C2×D3)⋊C4C2312yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×(C2×D3)⋊C4C2312yes—
162C3×(C2×D3)⋊C4C2314yes—
163C3×(C2×D3)⋊C4C2312yes—
164C3×(C2×D3)⋊C4C2314yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2312yes—
168C3×C4⋊Dic3C2312yes—
169C3×C4⋊Dic3C2311yescharacteristic
170C3×Dic3⋊C4C2314yes—
171C3×C4×Dic3C2312yes—
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2314yes—
174C3×C4×Dic3C2312yes—
175C3×C4×Dic3C2311yescharacteristic
176C3×C4×Dic3C2311yescharacteristic
177#3724C2314yes—
178#3724C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2312yes—
181#3722C2312yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2312yes—
187Dic32C2314yes—
188Dic32C2314yes—
189#3475—91noSylow
190C2×C3×#41—31no—
191C2×#239—32no—
192C2×#239C2×D311yescharacteristic
193C2×D3×D4—31no—
194C2×#235—32no—
195C22×D12—31no—
196C22×C4×D3—32no—
197C22×C4×D3—32no—
198C3×C4⋊Q8—31no—
199C3×#126—34no—
200C3×#124—32no—
201C3×C22⋊Q8—32no—
202C3×C4×Q8—21no—
203C3×C4×Q8—31no—
204C3×C4×Q8—32no—
205C3×C4×Q8C2×D311yescharacteristic, complemented
206C3×C4×Q8C2×D311yescharacteristic, complemented
207C3×C4×D4—32no—
208C3×C4×D4—31no—
209C3×C4×D4—32no—
210C3×C4×D4—31no—
211C3×C4×D4—31no—
212C3×#117—31no—
213C3×#117—32no—
214C3×#117—32no—
215C2×C3×C42—31no—
216C2×C3×C42—32no—
217#946—32no—
218#946—32no—
219#946—32no—
220#946—32no—
221#946—62no—
222#946C2×D312yescomplemented
223Q8×Dic3—32no—
224Q8×Dic3C2×D311yescharacteristic, complemented
225#938—32no—
226#938—32no—
227#938—32no—
228#937—34no—
229#935—34no—
230D4×Dic3—31no—
231#930—32no—
232#930—32no—
233#929—34no—
234C4×#67—34no—
235C4×#67—34no—
236C4×#67—32no—
237C4×#67—34no—
238C2×(C2×D3)⋊C4—32no—
239#926—32no—
240#926—32no—
241#926—32no—
242C2×C4⋊Dic3—31no—
243#924—32no—
244#924—32no—
245#924—32no—
246#898C2×D314yescomplemented
247#897—32no—
248#896—34no—
249#896—34no—
250#896—64no—
251#895—32no—
252#894—34no—
253#894—34no—
254#894—34no—
255#893—34no—
256#893—31no—
257#893C2×D312yes—
258#893C2×D311yescharacteristic, complemented
259#892—32no—
260#892—32no—
261#892—32no—
262#892—34no—
263#892C2×D311yescharacteristic
264#892C2×D312yescomplemented
265#892C2×D312yescomplemented
266D3×C4⋊C4—31no—
267D3×C4⋊C4—32no—
268D3×C4⋊C4—32no—
269D3×C4⋊C4—32no—
270D3×C4⋊C4—32no—
271D3×C4⋊C4—62no—
272#890—32no—
273#889—34no—
274#889—34no—
275#887—32no—
276#885—34no—
277#885—34no—
278#884—34no—
279#884—34no—
280#883—34no—
281#883—34no—
282#883—34no—
283#882—34no—
284#67⋊C4—34no—
285#67⋊C4—32no—
286D3×C22⋊C4—32no—
287D3×C22⋊C4—34no—
288D3×C22⋊C4—34no—
289#879—34no—
290#879—34no—
291#877—34no—
292#877—34no—
293#876—34no—
294#876—34no—
295#875C2×D312yes—
296C4×D12—31no—
297C4×D12—34no—
298C4×D12—32no—
299C4×D12—32no—
300C4×D12—31no—
301C4×D12—31no—
302C4×D12—32no—
303C4×D12—32no—
304C4×D12—31no—
305C4×D12—61no—
306C4×D12—62no—
307C4×D12C2×D312yes—
308C4×D12C2×D311yescharacteristic
309C4×D12C2×D311yescharacteristic, complemented
310#872—34no—
311#872—34no—
312#872—34no—
313C42×D3—34no—
314C42×D3—34no—
315C42×D3C2×D311yescharacteristic
316C42×D3C2×D312yescomplemented
317#870—32no—
318#870—32no—
319#870—32no—
320#870—62no—
321#869—31no—
322#869—31no—
323#869—61no—
324#869C2×D311yescharacteristic, complemented
325C4×Dic6—32no—
326C4×Dic6—32no—
327C4×Dic6C2×D312yescomplemented
328C22×C3⋊D3C2412yes—
329C22×C3×D3C2412yes—
330C22×C3×D3C2412yes—
331C22×C3×D3C2411yescharacteristic
332C2×D32—24no—
333C2×D32—24no—
334C2×D32—42no—
335C32×Q8—22no—
336C2×C32×C4C2412yes—
337C2×C32×C4C2412yes—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2411yescharacteristic
341C2×C3⋊Dic3C2414yes—
342C2×C3⋊Dic3C2412yes—
343C4⋊(C3⋊D3)#4114yescomplemented
344C4×C3⋊D3—24no—
345C4×C3⋊D3—44no—
346#634—42no—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2414yes—
350C2×C3×Dic3C2411yescharacteristic
351C2×C3×Dic3C2411yescharacteristic
352C2×C3×Dic3C2411yescharacteristic
353C3×D12—24no—
354C3×D12—22no—
355C3×D12—22no—
356C3×C4×D3—24no—
357C3×C4×D3—24no—
358C3×C4×D3—22no—
359C3×C4×D3—24no—
360C3×C4×D3—41no—
361C3×C4×D3—42no—
362C3×C4×D3#4114yescomplemented
363C3×Dic6—24no—
364#626—28no—
365#626—24no—
366#625—44no—
367#624—28no—
368#624—24no—
369D3×Dic3—24no—
370D3×Dic3—24no—
371#556—31no—
372#555—91no—
373#554—91no—
374#553—92no—
375#552—92no—
376#552—92no—
377#551—94no—
378#547—91no—
379#546—92no—
380#533—91no—
381#529—92no—
382#529—94no—
383#525—92no—
384C4×#41—31no—
385C4×#41—92no—
386C2×C4×D4—91no—
387C2×#117—92no—
388C23×D3—32no—
389C23×D3—32no—
390C3×#41—64no—
391C2×C3×Q8—21no—
392C2×C3×Q8—32no—
393C2×C3×Q8C22×D311yescharacteristic
394C2×C3×Q8C22×D311yescharacteristic
395C2×C3×D4—31no—
396C2×C3×D4—32no—
397C2×C3×D4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—31no—
400C22×C3×C4—32no—
401C22×C3×C4—32no—
402C22×C3×C4—32no—
403C22×C3×C4—31no—
404C22×C3×C4—32no—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67—32no—
408C2×#67—34no—
409C22×Dic3—32no—
410C22×Dic3—32no—
411#239—24no—
412#239—68no—
413D3×D4—64no—
414#235—68no—
415C2×D12—31no—
416C2×D12—31no—
417C2×D12—32no—
418C2×D12—34no—
419C2×D12—61no—
420C2×D12—64no—
421C2×D12C22×D311yescharacteristic
422C2×D12C22×D312yes—
423C2×D12C22×D311yescharacteristic
424C2×C4×D3—32no—
425C2×C4×D3—32no—
426C2×C4×D3—32no—
427C2×C4×D3—32no—
428C2×C4×D3—32no—
429C2×C4×D3—32no—
430C2×C4×D3—34no—
431C2×C4×D3—34no—
432C2×C4×D3—34no—
433C2×C4×D3—34no—
434C2×C4×D3—62no—
435C2×C4×D3—64no—
436C2×C4×D3—68no—
437C2×C4×D3—68no—
438C2×C4×D3C22×D311yescharacteristic
439C2×C4×D3C22×D312yes—
440C2×C4×D3C22×D312yes—
441C2×C4×D3C22×D312yes—
442C2×C4×D3C22×D311yescharacteristic
443C2×C4×D3C22×D312yes—
444C2×C4×D3C22×D311yescharacteristic
445C2×Dic6—32no—
446C2×Dic6—32no—
447C2×Dic6—62no—
448C2×Dic6C22×D312yes—
449C3×C4⋊C4—21no—
450C3×C4⋊C4—22no—
451C3×C4⋊C4—32no—
452C3×C4⋊C4—32no—
453C3×C4⋊C4—34no—
454C3×C4⋊C4—32no—
455C3×C4⋊C4—31no—
456C3×C4⋊C4—31no—
457C3×C4⋊C4C22×D311yescharacteristic
458C3×C4⋊C4C22×D311yescharacteristic
459C3×C4⋊C4C22×D312yes—
460C3×C4⋊C4C22×D312yes—
461C3×C22⋊C4—32no—
462C3×C22⋊C4—34no—
463C3×C22⋊C4—32no—
464C3×C22⋊C4—34no—
465C3×C22⋊C4—32no—
466C3×C22⋊C4—32no—
467C3×C42—21no—
468C3×C42—22no—
469C3×C42—31no—
470C3×C42—31no—
471C3×C42—31no—
472C3×C42—32no—
473C3×C42—34no—
474C3×C42—32no—
475C3×C42C22×D312yes—
476C3×C42C22×D311yescharacteristic
477C3×C42C22×D311yescharacteristic
478C3×C42C22×D312yes—
479#217—34no—
480#217—34no—
481#217—32no—
482#217—34no—
483#217—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4—32no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—32no—
495(C2×D3)⋊C4—62no—
496(C2×D3)⋊C4—64no—
497(C2×D3)⋊C4C22×D312yes—
498(C2×D3)⋊C4C22×D314yes—
499(C2×D3)⋊C4C22×D312yes—
500(C2×D3)⋊C4C22×D312yes—
501(C2×D3)⋊C4C22×D312yes—
502(C2×D3)⋊C4C22×D314yes—
503C4⋊Dic3—32no—
504C4⋊Dic3—32no—
505C4⋊Dic3—32no—
506C4⋊Dic3—32no—
507C4⋊Dic3—31no—
508C4⋊Dic3—31no—
509C4⋊Dic3—32no—
510C4⋊Dic3—34no—
511C4⋊Dic3—62no—
512C4⋊Dic3—62no—
513C4⋊Dic3—61no—
514C4⋊Dic3C22×D312yes—
515C4⋊Dic3C22×D311yescharacteristic
516C4⋊Dic3C22×D312yes—
517C4⋊Dic3C22×D312yes—
518C4⋊Dic3C22×D311yescharacteristic
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—34no—
526Dic3⋊C4—34no—
527Dic3⋊C4—32no—
528Dic3⋊C4—34no—
529Dic3⋊C4—64no—
530Dic3⋊C4—64no—
531Dic3⋊C4C22×D314yes—
532C4×Dic3—34no—
533C4×Dic3—34no—
534C4×Dic3—34no—
535C4×Dic3—34no—
536C4×Dic3C22×D314yes—
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D311yescharacteristic
539C4×Dic3C22×D311yescharacteristic
540C4×Dic3C22×D311yescharacteristic
541C4×Dic3C22×D312yes—
542C22×C32C2511yescharacteristic
543C2×C3⋊D3—22no—
544C2×C3⋊D3—22no—
545C2×C3⋊D3C2×#4114yes—
546C2×C3×D3—21no—
547C2×C3×D3—21no—
548C2×C3×D3—22no—
549C2×C3×D3—22no—
550C2×C3×D3—22no—
551C2×C3×D3—22no—
552C2×C3×D3—22no—
553C2×C3×D3—22no—
554C2×C3×D3C2×#4112yes—
555D32—48no—
556C32×C4—22no—
557C32×C4—21no—
558C32×C4—22no—
559C32×C4C2×#4112yes—
560C32×C4C2×#4112yes—
561C3⋊Dic3—22no—
562C3⋊Dic3—24no—
563C3×Dic3—22no—
564C3×Dic3—22no—
565C3×Dic3—24no—
566C3×Dic3—21no—
567C3×Dic3—21no—
568C3×Dic3C2×#4112yes—
569C2×#41—31no—
570C2×#41—92no—
571C22×D4—91no—
572C23×C4—92no—
573C4⋊Q8—31no—
574C4⋊Q8—91no—
575#126—34no—
576#126—94no—
577#126—94no—
578#125—92no—
579#125—94no—
580#125—92no—
581#124—32no—
582#124—94no—
583#123—94no—
584#123—94no—
585#123—94no—
586#123—94no—
587C22⋊Q8—32no—
588C22⋊Q8—92no—
589C22⋊Q8—92no—
590C22⋊Q8—92no—
591C22⋊Q8—92no—
592C22⋊Q8—94no—
593#121—94no—
594#121—92no—
595#121—92no—
596#121—92no—
597#120—94no—
598C4×Q8—31no—
599C4×Q8—32no—
600C4×Q8—92no—
601C4×Q8—92no—
602C4×Q8D3211yescharacteristic, complemented
603C4×D4—32no—
604C4×D4—31no—
605C4×D4—31no—
606C4×D4—32no—
607C4×D4—31no—
608C4×D4—92no—
609C4×D4—91no—
610C4×D4—92no—
611C4×D4—94no—
612C4×D4—91no—
613C4×D4—94no—
614C4×D4—94no—
615C4×D4—91no—
616C4×D4—92no—
617#117—31no—
618#117—32no—
619#117—32no—
620#117—94no—
621#117—94no—
622#117—94no—
623#117—92no—
624#117—92no—
625#117—92no—
626C2×C4⋊C4—92no—
627C2×C4⋊C4—91no—
628C2×C4⋊C4—92no—
629C2×C22⋊C4—94no—
630C2×C22⋊C4—92no—
631C2×C42—31no—
632C2×C42—32no—
633C2×C42—94no—
634C23×C3—31no—
635C23×C3—32no—
636C23×C3—32no—
637C22×D3—32no—
638C22×D3—32no—
639C22×D3—62no—
640C22×D3—64no—
641C22×D3—64no—
642C22×D3—64no—
643C22×D3—64no—
644C22×D3—122no—
645C22×D3—122no—
646C22×D3C23×D312yes—
647C22×D3C23×D312yes—
648C22×D3C23×D311yescharacteristic
649C3×Q8—22no—
650C3×Q8—22no—
651C3×Q8—42no—
652C3×Q8—64no—
653C3×D4—64no—
654C3×D4—62no—
655C3×D4—62no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—21no—
661C2×C3×C4—31no—
662C2×C3×C4—34no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—34no—
666C2×C3×C4—31no—
667C2×C3×C4—31no—
668C2×C3×C4—64no—
669C2×C3×C4—64no—
670C2×C3×C4—62no—
671C2×C3×C4—64no—
672C2×C3×C4—121no—
673C2×C3×C4—122no—
674C2×C3×C4C23×D312yes—
675C2×C3×C4C23×D312yes—
676C2×C3×C4C23×D312yes—
677C2×C3×C4C23×D311yescharacteristic
678C2×C3×C4C23×D312yes—
679C2×C3×C4C23×D311yescharacteristic
680C2×C3×C4C23×D311yescharacteristic
681C2×C3×C4C23×D311yescharacteristic
682C2×C3×C4C23×D311yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684#67—68no—
685#67—64no—
686#67—124no—
687#67—124no—
688C2×Dic3—34no—
689C2×Dic3—34no—
690C2×Dic3—32no—
691C2×Dic3—32no—
692C2×Dic3—62no—
693C2×Dic3—64no—
694C2×Dic3—64no—
695C2×Dic3—64no—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D312yes—
698C2×Dic3C23×D314yes—
699C2×Dic3C23×D311yescharacteristic
700C2×Dic3C23×D311yescharacteristic
701C2×Dic3C23×D311yescharacteristic
702D12—24no—
703D12—22no—
704D12—22no—
705D12—34no—
706D12—34no—
707D12—64no—
708D12—64no—
709D12—68no—
710C4×D3—24no—
711C4×D3—22no—
712C4×D3—24no—
713C4×D3—24no—
714C4×D3—41no—
715C4×D3—42no—
716C4×D3—64no—
717C4×D3—68no—
718C4×D3—68no—
719C4×D3—64no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—64no—
723C4×D3—64no—
724C4×D3—124no—
725C4×D3—124no—
726C4×D3—124no—
727C4×D3—244no—
728C4×D3#23514yescomplemented
729Dic6—24no—
730Dic6—122no—
731Dic6—122no—
732Dic6—242no—
733C2×C32C22×#4111yescharacteristic
734C2×C32C22×#4111yescharacteristic
735C2×C32#58511yescharacteristic
736C3⋊D3—24no—
737C3×D3—22no—
738C3×D3—42no—
739C3×D3—42no—
740C24—92no—
741#41—64no—
742#41—188no—
743C2×Q8—32no—
744C2×Q8—92no—
745C2×Q8C2×D3211yescharacteristic
746C2×D4—32no—
747C2×D4—31no—
748C2×D4—31no—
749C2×D4—94no—
750C2×D4—92no—
751C2×D4—94no—
752C2×D4—91no—
753C2×D4—184no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—32no—
757C22×C4—32no—
758C22×C4—32no—
759C22×C4—31no—
760C22×C4—32no—
761C22×C4—92no—
762C22×C4—94no—
763C22×C4—92no—
764C22×C4—92no—
765C22×C4—92no—
766C22×C4—94no—
767C22×C4—188no—
768C4⋊C4—31no—
769C4⋊C4—32no—
770C4⋊C4—31no—
771C4⋊C4—32no—
772C4⋊C4—34no—
773C4⋊C4—32no—
774C4⋊C4—94no—
775C4⋊C4—92no—
776C4⋊C4—94no—
777C4⋊C4—94no—
778C4⋊C4—92no—
779C4⋊C4—94no—
780C4⋊C4—91no—
781C4⋊C4—92no—
782C4⋊C4—94no—
783C4⋊C4C2×D3211yescharacteristic
784C4⋊C4C2×D3212yes—
785C22⋊C4—32no—
786C22⋊C4—34no—
787C22⋊C4—32no—
788C22⋊C4—32no—
789C22⋊C4—32no—
790C22⋊C4—34no—
791C22⋊C4—92no—
792C22⋊C4—94no—
793C22⋊C4—94no—
794C22⋊C4—92no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C22⋊C4—92no—
798C22⋊C4—94no—
799C42—31no—
800C42—32no—
801C42—31no—
802C42—32no—
803C42—31no—
804C42—34no—
805C42—94no—
806C42—94no—
807C42C2×D3211yescharacteristic
808C42C2×D3212yes—
809C22×C3—21no—
810C22×C3—32no—
811C22×C3—61no—
812C22×C3—61no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3C24×D311yescharacteristic
820C22×C3C24×D311yescharacteristic
821C2×D3—21no—
822C2×D3—21no—
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—34no—
830C2×D3—34no—
831C2×D3—64no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—122no—
837C2×D3—122no—
838C2×D3—128no—
839C2×D3—128no—
840C2×D3C2×#23512yes—
841C3×C4—22no—
842C3×C4—22no—
843C3×C4—21no—
844C3×C4—22no—
845C3×C4—21no—
846C3×C4—22no—
847C3×C4—22no—
848C3×C4—22no—
849C3×C4—32no—
850C3×C4—41no—
851C3×C4—42no—
852C3×C4—42no—
853C3×C4—62no—
854C3×C4—62no—
855C3×C4—64no—
856C3×C4—61no—
857C3×C4—61no—
858C3×C4C2×#23512yes—
859C3×C4D3×#4112yes—
860C3×C4D3×#4112yes—
861C3×C4D3×#4112yes—
862Dic3—24no—
863Dic3—22no—
864Dic3—22no—
865Dic3—21no—
866Dic3—21no—
867Dic3—62no—
868Dic3—62no—
869Dic3—64no—
870Dic3—64no—
871Dic3—124no—
872Dic3—122no—
873Dic3C2×#23512yes—
874C32#347511yescharacteristic, complemented, Sylow
875C23—31no—
876C23—32no—
877C23—32no—
878C23—92no—
879C23—184no—
880C23—184no—
881C23—362no—
882Q8—22no—
883Q8—64no—
884Q8—362no—
885D4—64no—
886D4—62no—
887D4—62no—
888D4—94no—
889D4—184no—
890D4—188no—
891D4—364no—
892C2×C4—31no—
893C2×C4—34no—
894C2×C4—31no—
895C2×C4—32no—
896C2×C4—32no—
897C2×C4—31no—
898C2×C4—34no—
899C2×C4—64no—
900C2×C4—64no—
901C2×C4—62no—
902C2×C4—64no—
903C2×C4—94no—
904C2×C4—92no—
905C2×C4—122no—
906C2×C4—121no—
907C2×C4—184no—
908C2×C4—184no—
909C2×C4—188no—
910C2×C4—184no—
911C2×C4—184no—
912C2×C4—364no—
913C2×C4C22×D3212yes—
914C2×C4C22×D3211yescharacteristic
915C2×C4C22×D3212yes—
916C2×C4C22×D3211yescharacteristic
917C2×C4C22×D3211yescharacteristic
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—62no—
922C2×C3—122no—
923C2×C3—122no—
924C2×C3C22×#23511yescharacteristic
925C2×C3C2×D3×#4111yescharacteristic
926C2×C3C2×D3×#4111yescharacteristic
927C2×C3C2×D3×#4111yescharacteristic
928C2×C3#596411yescharacteristic
929C2×C3#596811yescharacteristic
930D3—22no—
931D3—42no—
932D3—42no—
933D3—64no—
934D3—64no—
935D3—124no—
936C22—32no—
937C22—61no—
938C22—61no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—62no—
943C22—62no—
944C22—62no—
945C22—94no—
946C22—182no—
947C22—182no—
948C22—368no—
949C22C23×D3211yescharacteristic
950C4—22no—
951C4—22no—
952C4—21no—
953C4—32no—
954C4—62no—
955C4—62no—
956C4—61no—
957C4—64no—
958C4—61no—
959C4—182no—
960C4—184no—
961C4D3×#23512yes—
962C4#6431912yes—
963C3—21no—
964C3#8584011yescharacteristic, complemented
965C3#8697911yescharacteristic, complemented
966C2—62no—
967C2—122no—
968C2—122no—
969C2—184no—
970C2C2×D3×#23511yescharacteristic
971C2C2×#6431911yescharacteristic
972C2#1059669711yescharacteristic
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. #10596050C2semidirect
2. C3×#5584C2semidirect
3. C3×C4×#239C2semidirect
4. #10595424C2semidirect
5. #10595344C2semidirect
6. #10594645C2semidirect
7. #10594602C2semidirect
8. #10594583C2semidirect
9. #10594417C2semidirect
10. #10594007C2semidirect
11. C4×D3×D12C2semidirect
12. #10593988C2semidirect
13. C4×#3799C2semidirect
14. #10593921C2semidirect
15. #10593917C2semidirect
16. #10593869C2semidirect
17. #10593859C2semidirect
24. C32×C4×Q8C22semidirect
25. #64155C22semidirect
26. #64105C22semidirect
27. C4⋊C4×C3⋊D3C22semidirect
30. #64079C22semidirect
31. #64078C22semidirect
32. C3×#946C22semidirect
33. C3×Q8×Dic3C22semidirect
34. C3×#898C22semidirect
36. C3×#893C22semidirect
38. C3×#892C22semidirect
39. C3×#892C22semidirect
43. C3×C4×D12C22semidirect
45. C3×C42×D3C22semidirect
46. C3×#869C22semidirect
47. C3×C4×Dic6C22semidirect
51. #63916C22semidirect
52. #63913C22semidirect
55. #63908C22semidirect
56. #63905C22semidirect
57. #63904C22semidirect
59. C4×#626C22semidirect
60. #63900C22semidirect
65. C4×#624C22semidirect
67. #63879C22semidirect
69. #63877C22semidirect
70. #63869C22semidirect
71. #63859C22semidirect
72. #63859C22semidirect
75. #63856C22semidirect
77. #63854C22semidirect
78. #63847C22semidirect
79. #63844C22semidirect
80. Dic3×Dic6C22semidirect
82. #63841C22semidirect
83. #63841C22semidirect
84. #63836C22semidirect
96. #5584D3semidirect
103. C4×#239D3semidirect
205. C3×C4×Q8C2×D3semidirect
206. C3×C4×Q8C2×D3semidirect
222. #946C2×D3semidirect
224. Q8×Dic3C2×D3semidirect
246. #898C2×D3semidirect
258. #893C2×D3semidirect
264. #892C2×D3semidirect
265. #892C2×D3semidirect
309. C4×D12C2×D3semidirect
316. C42×D3C2×D3semidirect
324. #869C2×D3semidirect
327. C4×Dic6C2×D3semidirect
343. C4⋊(C3⋊D3)#41semidirect
362. C3×C4×D3#41semidirect
602. C4×Q8D32semidirect
728. C4×D3#235semidirect
874. C32#3475semidirect
964. C3#85840semidirect
965. C3#86979semidirect

Maximal subgroups

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

subgroupindex
#105960502
C3×#55842
C3×C4×#2392
#105954242
#105953442
#105946452
#105946022
#105945832
#105944172
#105940072
C4×D3×D122
#105939882
C4×#37992
#105939212
#105939172
#105938692
#105938592
#869793
#858403