Finite Group Databasebeta

← #11903561

Subgroups — #11903561

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
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×C4×#235C211yesmaximal, characteristic, complemented
3C3×#5470C211yesmaximal, characteristic, complemented
4#10595035C214yesmaximal, complemented
5#10595034C212yesmaximal, complemented
6#10595018C212yesmaximal, complemented
7#10594969C212yesmaximal, complemented
8#10594853C212yesmaximal, complemented
9#10593987C211yesmaximal, characteristic, complemented
10#10593982C212yesmaximal, complemented
11C4×#3799C212yesmaximal, complemented
12#10593958C211yesmaximal, characteristic, complemented
13#10593947C212yesmaximal, complemented
14#10593934C214yesmaximal, complemented
15#10593870C212yesmaximal, complemented
16#10593869C211yesmaximal, characteristic, complemented
17#10593865C211yesmaximal, characteristic, complemented
18#86276—31nomaximal
19#85840—31nomaximal
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2212yes—
22C2×C3×#235C2211yescharacteristic
23C2×#3799C2212yes—
24C2×C32×C42C2211yescharacteristic
25C2×#3752C2212yes—
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30C4×C4⋊(C3⋊D3)C2212yes—
31C4×C4⋊(C3⋊D3)C2212yes—
32C4×C4⋊(C3⋊D3)C2211yescharacteristic
33C3×C4×#67C2212yes—
34C3×C4×#67C2212yes—
35C3×#926C2211yescharacteristic
36C3×#926C2212yes—
37C3×#924C2212yes—
38C3×#924C2212yes—
39C3×C4×D12C2211yescharacteristic, complemented
40C3×C4×D12C2211yescharacteristic, complemented
41C3×#872C2212yescomplemented
42C3×C42×D3C2212yescomplemented
43C3×#870C2212yescomplemented
44C3×#869C2211yescharacteristic, complemented
45C3×#869C2211yescharacteristic, complemented
46C3×C4×Dic6C2211yescharacteristic, complemented
47C3×C4×Dic6C2212yescomplemented
48C3×C4×Dic6C2212yescomplemented
49C3×C4×Dic6C2211yescharacteristic, complemented
50#63981C2214yes—
51#63974C2214yes—
52#63962C2214yes—
53#63957C2214yes—
54#63916C2212yescomplemented
55#63916C2212yescomplemented
56#63910C2214yes—
57#63909C2212yes—
58#63907C2214yescomplemented
59#63904C2214yescomplemented
60C4×#626C2214yescomplemented
61C4×#626C2214yescomplemented
62#63900C2212yescomplemented
63#63900C2212yescomplemented
64#63897C2214yes—
65#63894C2212yes—
66#63888C2214yescomplemented
67C4×#624C2214yescomplemented
68#63874C2214yescomplemented
69#63871C2212yescomplemented
70#63871C2212yescomplemented
71#63869C2212yescomplemented
72#63868C2214yescomplemented
73#63864C2212yes—
74#63861C2214yescomplemented
75#63856C2212yescomplemented
76#63854C2214yescomplemented
77#63850C2214yescomplemented
78#63849C2212yescomplemented
79#63849C2212yescomplemented
80#63848C2214yescomplemented
81#63845C2214yescomplemented
82Dic3×Dic6C2212yescomplemented
83#63841C2212yescomplemented
84#63836C2214yescomplemented
85C3×#533—31no—
86C3×C4×#41—31no—
87#5828—32no—
88#5734—31no—
89#5732—31no—
90#5730—31no—
91#5726—31no—
92#5695—32no—
93#5694—32no—
94#5642—32no—
95#5637—34no—
96#5630—32no—
97#5584—31no—
98#5581—32no—
99#5580—34no—
100#5580—32no—
101#5579—31no—
102C4×#239—32no—
103#5563—31no—
104#5558—32no—
105#5556—34no—
106#5551—31no—
107#5550—32no—
108#5541—32no—
109#5528—34no—
110#5524—32no—
111D3×#117—32no—
112D3×#117—32no—
113#5479—32no—
114C4×#235—32no—
115C4×#235D311yescharacteristic, complemented
116C2×C4×D12—31no—
117C2×C4×D12—31no—
118C2×C4×D12—61no—
119#5470D311yescharacteristic, complemented
120C23×C3⋊D3C2312yes—
121C22×C32×C4C2311yescharacteristic
122C22×C32×C4C2311yescharacteristic
123C22×C32×C4C2311yescharacteristic
124C22×C3⋊Dic3C2312yes—
125C2×C4⋊(C3⋊D3)—24no—
126C2×C4⋊(C3⋊D3)C2311yescharacteristic
127C2×C4⋊(C3⋊D3)C2312yes—
128C2×C4⋊(C3⋊D3)C2311yescharacteristic
129C2×C4×C3⋊D3—28no—
130C2×C4×C3⋊D3C2312yes—
131C2×C4×C3⋊D3C2312yes—
132C2×C4×C3⋊D3C2312yes—
133C2×C4×C3⋊D3C2312yes—
134C2×C3×#67C2312yes—
135C3×#235—24no—
136C2×C3×D12C2311yescharacteristic
137C2×C3×C4×D3C2312yes—
138C2×C3×C4×D3C2312yes—
139C2×C3×C4×D3C2312yes—
140C2×C3×Dic6C2312yes—
141C2×C3×Dic6C2311yescharacteristic
142C2×C3×Dic6C2312yes—
143C2×#626C2314yes—
144C2×#626C2314yes—
145C2×#624C2314yes—
146C2×#624C2314yes—
147#3799—28no—
148C32×C42C2311yescharacteristic
149C32×C42C2311yescharacteristic
150C32×C42C2311yescharacteristic
151C32×C42C2311yescharacteristic
152#3752C2312yes—
153#3752C2312yes—
154#3752C2312yes—
155#3752C2312yes—
156C4⋊(C3⋊Dic3)C2311yescharacteristic
157C4⋊(C3⋊Dic3)C2312yes—
158C4⋊(C3⋊Dic3)C2311yescharacteristic
159C3×#217C2314yes—
160C3×#217C2312yes—
161C3×(C2×D3)⋊C4C2312yes—
162C3×(C2×D3)⋊C4C2312yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×C4⋊Dic3C2311yescharacteristic
167C3×C4⋊Dic3C2312yes—
168C3×C4⋊Dic3C2312yes—
169C3×Dic3⋊C4C2314yes—
170C3×Dic3⋊C4C2314yes—
171C3×Dic3⋊C4C2312yes—
172C3×Dic3⋊C4C2312yes—
173C3×C4×Dic3C2312yes—
174C3×C4×Dic3C2314yes—
175C3×C4×Dic3C2312yes—
176C3×C4×Dic3C2312yes—
177#3724C2314yes—
178#3724C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181#3722C2314yes—
182#3722C2314yes—
183#3722C2314yes—
184#3722C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187Dic32C2314yes—
188Dic32C2314yes—
189#3475—91noSylow
190C2×C3×#41—31no—
191C2×#239—32no—
192C2×#235—32no—
193C2×#235C2×D311yescharacteristic
194C22×D12—31no—
195C22×D12—31no—
196C22×D12—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×C22⋊Q8—32no—
204C3×C22⋊Q8—32no—
205C3×C4×Q8—32no—
206C3×C4×Q8—31no—
207C3×C4×Q8—32no—
208C3×C4×Q8—31no—
209C3×C4×D4—32no—
210C3×C4×D4—32no—
211C3×C4×D4—31no—
212C3×C4×D4—31no—
213C3×#117—31no—
214C3×#117—32no—
215C3×#117—32no—
216C2×C3×C42—21no—
217C2×C3×C42—32no—
218C2×C3×C42C2×D311yescharacteristic
219C2×C3×C42C2×D311yescharacteristic
220#947—34no—
221#947—32no—
222#946—32no—
223#946—32no—
224#946—32no—
225#946—34no—
226Q8×Dic3—32no—
227#938—32no—
228#938—32no—
229#937—34no—
230#935—34no—
231#930—32no—
232#929—34no—
233C4×#67—34no—
234C4×#67—34no—
235C4×#67—34no—
236C4×#67C2×D312yes—
237C4×#67C2×D312yes—
238C2×(C2×D3)⋊C4—32no—
239C2×(C2×D3)⋊C4—32no—
240C2×(C2×D3)⋊C4—62no—
241#926—32no—
242#926C2×D312yes—
243#926C2×D311yescharacteristic
244C2×C4⋊Dic3—31no—
245C2×C4⋊Dic3—31no—
246C2×C4⋊Dic3—61no—
247#924—32no—
248#924C2×D312yes—
249#924C2×D312yes—
250#898—34no—
251#898—34no—
252#898—34no—
253#898—34no—
254#897—32no—
255#897—32no—
256#896—34no—
257#895—32no—
258#895—32no—
259#895—32no—
260#895—34no—
261#894—34no—
262#894—34no—
263#894—34no—
264#894—34no—
265#893—34no—
266#893—32no—
267#892—32no—
268#892—32no—
269#892—32no—
270#892—32no—
271#892—32no—
272#892—34no—
273D3×C4⋊C4—32no—
274D3×C4⋊C4—32no—
275D3×C4⋊C4—32no—
276D3×C4⋊C4—32no—
277#890—34no—
278#890—32no—
279#889—34no—
280#886—34no—
281#885—34no—
282#884—34no—
283#883—34no—
284#882—34no—
285D3×C22⋊C4—34no—
286D3×C22⋊C4—34no—
287#879—34no—
288#877—34no—
289#877—34no—
290#876—34no—
291#875—32no—
292C4×D12—34no—
293C4×D12—34no—
294C4×D12—32no—
295C4×D12—31no—
296C4×D12—31no—
297C4×D12—31no—
298C4×D12—31no—
299C4×D12—32no—
300C4×D12—31no—
301C4×D12—32no—
302C4×D12—31no—
303C4×D12—31no—
304C4×D12—32no—
305C4×D12—31no—
306C4×D12—32no—
307C4×D12—61no—
308C4×D12—61no—
309C4×D12—62no—
310C4×D12—61no—
311C4×D12—62no—
312C4×D12—61no—
313C4×D12C2×D311yescharacteristic, complemented
314C4×D12C2×D311yescharacteristic, complemented
315#872—34no—
316#872—34no—
317#872—34no—
318#872C2×D312yescomplemented
319C42×D3—34no—
320C42×D3—34no—
321C42×D3C2×D312yescomplemented
322#870—32no—
323#870C2×D312yescomplemented
324#869C2×D311yescharacteristic, complemented
325#869C2×D311yescharacteristic, complemented
326C4×Dic6—32no—
327C4×Dic6C2×D311yescharacteristic, complemented
328C4×Dic6C2×D312yescomplemented
329C4×Dic6C2×D312yescomplemented
330C4×Dic6C2×D311yescharacteristic, complemented
331C23×C32C2411yescharacteristic
332C22×C3⋊D3—24no—
333C22×C3⋊D3—24no—
334C22×C3⋊D3—42no—
335C22×C3⋊D3C2412yes—
336C22×C3⋊D3C2412yes—
337C22×C3×D3C2412yes—
338C2×C32×C4—22no—
339C2×C32×C4—41no—
340C2×C32×C4#4114yescomplemented
341C2×C32×C4C2411yescharacteristic
342C2×C32×C4C2411yescharacteristic
343C2×C32×C4C2411yescharacteristic
344C2×C32×C4C2411yescharacteristic
345C2×C32×C4C2411yescharacteristic
346C2×C32×C4C2411yescharacteristic
347C2×C3⋊Dic3—24no—
348C2×C3⋊Dic3C2412yes—
349C2×C3⋊Dic3C2412yes—
350C4⋊(C3⋊D3)—24no—
351C4⋊(C3⋊D3)—22no—
352C4⋊(C3⋊D3)#4114yescomplemented
353C4×C3⋊D3—24no—
354C4×C3⋊D3—24no—
355C4×C3⋊D3—24no—
356C4×C3⋊D3—24no—
357C3×#67—24no—
358C2×C3×Dic3C2412yes—
359C2×C3×Dic3C2412yes—
360C2×C3×Dic3C2414yes—
361C2×C3×Dic3C2414yes—
362C2×C3×Dic3C2412yes—
363C3×D12—22no—
364C3×C4×D3—24no—
365C3×C4×D3—24no—
366C3×C4×D3—42no—
367C3×Dic6—24no—
368C3×Dic6—22no—
369C3×Dic6—42no—
370#626—28no—
371#626—44no—
372#624—28no—
373#624—44no—
374#556—91no—
375#555—91no—
376#554—91no—
377#553—92no—
378#552—92no—
379#552—92no—
380#551—94no—
381#547—91no—
382#546—92no—
383#533—31no—
384#529—92no—
385#529—94no—
386#525—92no—
387C4×#41—31no—
388C4×#41—92no—
389C2×C4×D4—91no—
390C2×#117—92no—
391C23×D3—32no—
392C23×D3—32no—
393C23×D3—62no—
394C3×#41—64no—
395C2×C3×Q8—32no—
396C2×C3×Q8—31no—
397C2×C3×Q8—32no—
398C2×C3×D4—32no—
399C2×C3×D4—31no—
400C22×C3×C4—21no—
401C22×C3×C4—21no—
402C22×C3×C4—21no—
403C22×C3×C4—32no—
404C22×C3×C4—32no—
405C22×C3×C4—32no—
406C22×C3×C4C22×D311yescharacteristic
407C22×C3×C4C22×D311yescharacteristic
408C22×C3×C4C22×D311yescharacteristic
409C22×C3×C4C22×D311yescharacteristic
410C22×C3×C4C22×D311yescharacteristic
411C22×C3×C4C22×D311yescharacteristic
412C2×#67—34no—
413C2×#67—34no—
414C2×#67C22×D312yes—
415C22×Dic3—32no—
416C22×Dic3—32no—
417C22×Dic3—62no—
418#239—68no—
419#235—24no—
420#235—68no—
421C2×D12—31no—
422C2×D12—31no—
423C2×D12—34no—
424C2×D12—31no—
425C2×D12—32no—
426C2×D12—32no—
427C2×D12—31no—
428C2×D12—34no—
429C2×D12—61no—
430C2×D12—62no—
431C2×D12—61no—
432C2×D12—64no—
433C2×D12—64no—
434C2×D12—68no—
435C2×D12C22×D311yescharacteristic
436C2×C4×D3—32no—
437C2×C4×D3—32no—
438C2×C4×D3—32no—
439C2×C4×D3—32no—
440C2×C4×D3—32no—
441C2×C4×D3—32no—
442C2×C4×D3—32no—
443C2×C4×D3—32no—
444C2×C4×D3—34no—
445C2×C4×D3—34no—
446C2×C4×D3—34no—
447C2×C4×D3—34no—
448C2×C4×D3—62no—
449C2×C4×D3—62no—
450C2×C4×D3—62no—
451C2×C4×D3—62no—
452C2×C4×D3—68no—
453C2×C4×D3—68no—
454C2×C4×D3—128no—
455C2×C4×D3C22×D312yes—
456C2×C4×D3C22×D312yes—
457C2×C4×D3C22×D312yes—
458C2×Dic6C22×D312yes—
459C2×Dic6C22×D311yescharacteristic
460C2×Dic6C22×D312yes—
461C3×C4⋊C4—32no—
462C3×C4⋊C4—32no—
463C3×C4⋊C4—34no—
464C3×C4⋊C4—31no—
465C3×C4⋊C4—31no—
466C3×C4⋊C4—32no—
467C3×C4⋊C4—32no—
468C3×C4⋊C4—34no—
469C3×C4⋊C4—32no—
470C3×C4⋊C4—32no—
471C3×C22⋊C4—32no—
472C3×C22⋊C4—34no—
473C3×C22⋊C4—32no—
474C3×C22⋊C4—32no—
475C3×C42—21no—
476C3×C42—21no—
477C3×C42—21no—
478C3×C42—21no—
479C3×C42—32no—
480C3×C42—32no—
481C3×C42—34no—
482C3×C42—32no—
483C3×C42C22×D311yescharacteristic
484C3×C42C22×D311yescharacteristic
485C3×C42C22×D311yescharacteristic
486C3×C42C22×D311yescharacteristic
487C3×C42C22×D311yescharacteristic
488C3×C42C22×D311yescharacteristic
489C3×C42C22×D311yescharacteristic
490C3×C42C22×D311yescharacteristic
491#217—34no—
492#217—34no—
493#217C22×D312yes—
494#217C22×D314yes—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—32no—
498(C2×D3)⋊C4—32no—
499(C2×D3)⋊C4—32no—
500(C2×D3)⋊C4—32no—
501(C2×D3)⋊C4—32no—
502(C2×D3)⋊C4—32no—
503(C2×D3)⋊C4—32no—
504(C2×D3)⋊C4—32no—
505(C2×D3)⋊C4—34no—
506(C2×D3)⋊C4—34no—
507(C2×D3)⋊C4—34no—
508(C2×D3)⋊C4—34no—
509(C2×D3)⋊C4—34no—
510(C2×D3)⋊C4—34no—
511(C2×D3)⋊C4—34no—
512(C2×D3)⋊C4—34no—
513(C2×D3)⋊C4—62no—
514(C2×D3)⋊C4—62no—
515(C2×D3)⋊C4—62no—
516(C2×D3)⋊C4—62no—
517(C2×D3)⋊C4C22×D312yes—
518(C2×D3)⋊C4C22×D312yes—
519C4⋊Dic3—31no—
520C4⋊Dic3—31no—
521C4⋊Dic3—32no—
522C4⋊Dic3—32no—
523C4⋊Dic3—31no—
524C4⋊Dic3—31no—
525C4⋊Dic3—34no—
526C4⋊Dic3—34no—
527C4⋊Dic3—61no—
528C4⋊Dic3—61no—
529C4⋊Dic3—62no—
530C4⋊Dic3C22×D312yes—
531C4⋊Dic3C22×D312yes—
532C4⋊Dic3C22×D311yescharacteristic
533C4⋊Dic3C22×D311yescharacteristic
534C4⋊Dic3C22×D312yes—
535C4⋊Dic3C22×D312yes—
536Dic3⋊C4—34no—
537Dic3⋊C4—34no—
538Dic3⋊C4—34no—
539Dic3⋊C4—34no—
540Dic3⋊C4—34no—
541Dic3⋊C4—34no—
542Dic3⋊C4C22×D314yes—
543Dic3⋊C4C22×D314yes—
544Dic3⋊C4C22×D312yes—
545Dic3⋊C4C22×D312yes—
546C4×Dic3—34no—
547C4×Dic3—34no—
548C4×Dic3—34no—
549C4×Dic3—34no—
550C4×Dic3C22×D314yes—
551C4×Dic3C22×D312yes—
552C4×Dic3C22×D312yes—
553C4×Dic3C22×D312yes—
554C22×C32—21no—
555C22×C32—21no—
556C22×C32C2×#4112yes—
557C22×C32C2511yescharacteristic
558C2×C3⋊D3—22no—
559C2×C3⋊D3—22no—
560C2×C3⋊D3—22no—
561C2×C3⋊D3—22no—
562C2×C3⋊D3—22no—
563C2×C3⋊D3—48no—
564C2×C3⋊D3C2×#4114yes—
565C2×C3×D3—22no—
566C2×C3×D3—22no—
567C2×C3×D3—22no—
568C32×C4—21no—
569C32×C4—21no—
570C32×C4—21no—
571C32×C4C2×#4112yes—
572C32×C4C2×#4112yes—
573C32×C4C2×#4112yes—
574C3⋊Dic3—22no—
575C3⋊Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—24no—
578C3×Dic3—22no—
579C3×Dic3—22no—
580C3×Dic3—24no—
581C2×#41—31no—
582C2×#41—92no—
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—92no—
592#125—94no—
593#124—92no—
594#124—94no—
595#123—94no—
596#123—94no—
597#123—94no—
598#123—94no—
599C22⋊Q8—32no—
600C22⋊Q8—32no—
601C22⋊Q8—92no—
602C22⋊Q8—92no—
603C22⋊Q8—94no—
604C22⋊Q8—92no—
605#121—94no—
606#121—92no—
607#121—92no—
608#121—92no—
609#120—94no—
610C4×Q8—31no—
611C4×Q8—31no—
612C4×Q8—32no—
613C4×Q8—32no—
614C4×Q8—92no—
615C4×D4—32no—
616C4×D4—32no—
617C4×D4—31no—
618C4×D4—31no—
619C4×D4—92no—
620C4×D4—94no—
621C4×D4—94no—
622C4×D4—94no—
623C4×D4—91no—
624C4×D4—91no—
625C4×D4—92no—
626C4×D4—91no—
627C4×D4—92no—
628C4×D4—91no—
629#117—31no—
630#117—32no—
631#117—32no—
632#117—94no—
633#117—94no—
634#117—94no—
635#117—92no—
636#117—92no—
637#117—92no—
638C2×C4⋊C4—92no—
639C2×C4⋊C4—92no—
640C2×C4⋊C4—91no—
641C2×C22⋊C4—94no—
642C2×C22⋊C4—92no—
643C2×C42—32no—
644C2×C42—94no—
645C2×C42D3211yescharacteristic
646C23×C3—21no—
647C23×C3—32no—
648C23×C3C23×D311yescharacteristic
649C23×C3C23×D311yescharacteristic
650C22×D3—32no—
651C22×D3—32no—
652C22×D3—32no—
653C22×D3—32no—
654C22×D3—62no—
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—62no—
667C3×Q8—64no—
668C3×Q8—122no—
669C3×D4—64no—
670C3×D4—62no—
671C2×C3×C4—24no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—24no—
681C2×C3×C4—32no—
682C2×C3×C4—32no—
683C2×C3×C4—34no—
684C2×C3×C4—34no—
685C2×C3×C4—32no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—42no—
689C2×C3×C4—64no—
690C2×C3×C4—64no—
691C2×C3×C4—122no—
692C2×C3×C4#23514yescomplemented
693C2×C3×C4#23914yescomplemented
694C2×C3×C4C23×D311yescharacteristic
695C2×C3×C4C23×D311yescharacteristic
696C2×C3×C4C23×D311yescharacteristic
697C2×C3×C4C23×D311yescharacteristic
698C2×C3×C4C23×D311yescharacteristic
699C2×C3×C4C23×D311yescharacteristic
700C2×C3×C4C23×D311yescharacteristic
701C2×C3×C4C23×D311yescharacteristic
702C2×C3×C4C23×D311yescharacteristic
703C2×C3×C4C23×D311yescharacteristic
704C2×C3×C4C23×D311yescharacteristic
705C2×C3×C4C23×D311yescharacteristic
706#67—24no—
707#67—68no—
708#67—124no—
709C2×Dic3—32no—
710C2×Dic3—32no—
711C2×Dic3—32no—
712C2×Dic3—32no—
713C2×Dic3—62no—
714C2×Dic3—62no—
715C2×Dic3—64no—
716C2×Dic3—64no—
717C2×Dic3—124no—
718C2×Dic3C23×D312yes—
719C2×Dic3C23×D312yes—
720C2×Dic3C23×D314yes—
721C2×Dic3C23×D314yes—
722C2×Dic3C23×D312yes—
723D12—22no—
724D12—34no—
725D12—34no—
726D12—64no—
727D12—64no—
728D12—64no—
729D12—68no—
730D12—64no—
731D12—68no—
732D12—62no—
733D12—62no—
734D12—124no—
735C4×D3—24no—
736C4×D3—24no—
737C4×D3—42no—
738C4×D3—68no—
739C4×D3—68no—
740C4×D3—64no—
741C4×D3—64no—
742C4×D3—64no—
743C4×D3—64no—
744C4×D3—64no—
745C4×D3—64no—
746C4×D3—64no—
747C4×D3—64no—
748C4×D3—124no—
749C4×D3—124no—
750C4×D3—124no—
751C4×D3—124no—
752C4×D3—124no—
753C4×D3—124no—
754Dic6—22no—
755Dic6—24no—
756Dic6—42no—
757C2×C32—22no—
758C2×C32C22×#4111yescharacteristic
759C2×C32C22×#4111yescharacteristic
760C2×C32#58511yescharacteristic
761C3⋊D3—24no—
762C3⋊D3—42no—
763C3×D3—42no—
764C24—92no—
765#41—64no—
766#41—188no—
767C2×Q8—31no—
768C2×Q8—32no—
769C2×Q8—32no—
770C2×D4—32no—
771C2×D4—31no—
772C2×D4—94no—
773C2×D4—94no—
774C2×D4—91no—
775C2×D4—92no—
776C2×D4—91no—
777C2×D4—184no—
778C22×C4—32no—
779C22×C4—32no—
780C22×C4—32no—
781C22×C4—94no—
782C22×C4—94no—
783C22×C4—92no—
784C22×C4—92no—
785C22×C4—92no—
786C22×C4—92no—
787C22×C4—92no—
788C22×C4—188no—
789C22×C4C2×D3211yescharacteristic
790C22×C4C2×D3211yescharacteristic
791C22×C4C2×D3211yescharacteristic
792C4⋊C4—31no—
793C4⋊C4—31no—
794C4⋊C4—32no—
795C4⋊C4—32no—
796C4⋊C4—32no—
797C4⋊C4—32no—
798C4⋊C4—32no—
799C4⋊C4—34no—
800C4⋊C4—34no—
801C4⋊C4—32no—
802C4⋊C4—94no—
803C4⋊C4—94no—
804C4⋊C4—94no—
805C4⋊C4—94no—
806C4⋊C4—91no—
807C4⋊C4—91no—
808C4⋊C4—92no—
809C22⋊C4—32no—
810C22⋊C4—34no—
811C22⋊C4—32no—
812C22⋊C4—32no—
813C22⋊C4—94no—
814C22⋊C4—94no—
815C22⋊C4—94no—
816C22⋊C4—94no—
817C22⋊C4—94no—
818C22⋊C4—94no—
819C22⋊C4—92no—
820C22⋊C4—92no—
821C22⋊C4—92no—
822C22⋊C4—92no—
823C42—32no—
824C42—32no—
825C42—32no—
826C42—34no—
827C42—94no—
828C42—94no—
829C42C2×D3211yescharacteristic
830C42C2×D3211yescharacteristic
831C42C2×D3211yescharacteristic
832C42C2×D3211yescharacteristic
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—22no—
840C22×C3—21no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3C2×#23512yes—
845C22×C3C2×#23912yes—
846C22×C3C24×D311yescharacteristic
847C22×C3C24×D311yescharacteristic
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—34no—
852C2×D3—34no—
853C2×D3—64no—
854C2×D3—62no—
855C2×D3—62no—
856C2×D3—62no—
857C2×D3—62no—
858C2×D3—64no—
859C2×D3—62no—
860C2×D3—62no—
861C2×D3—62no—
862C2×D3—62no—
863C2×D3—62no—
864C2×D3—62no—
865C2×D3—122no—
866C2×D3—122no—
867C2×D3—122no—
868C2×D3—122no—
869C2×D3—128no—
870C2×D3—128no—
871C2×D3—1216no—
872C3×C4—22no—
873C3×C4—21no—
874C3×C4—21no—
875C3×C4—21no—
876C3×C4—21no—
877C3×C4—21no—
878C3×C4—21no—
879C3×C4—22no—
880C3×C4—22no—
881C3×C4—22no—
882C3×C4—41no—
883C3×C4—41no—
884C3×C4—62no—
885C3×C4—62no—
886C3×C4—64no—
887C3×C4—62no—
888C3×C4—64no—
889C3×C4C2×#23512yes—
890C3×C4C2×#23512yes—
891C3×C4C2×#23912yes—
892C3×C4C2×#23912yes—
893C3×C4D3×#4112yes—
894C3×C4D3×#4112yes—
895Dic3—22no—
896Dic3—24no—
897Dic3—22no—
898Dic3—24no—
899Dic3—22no—
900Dic3—62no—
901Dic3—62no—
902Dic3—62no—
903Dic3—62no—
904Dic3—122no—
905Dic3—122no—
906C32#347511yescharacteristic, complemented, Sylow
907C23—32no—
908C23—92no—
909C23—92no—
910C23—184no—
911C23—184no—
912C23—362no—
913C23C22×D3211yescharacteristic
914Q8—62no—
915Q8—64no—
916Q8—122no—
917D4—64no—
918D4—62no—
919D4—94no—
920D4—184no—
921D4—188no—
922D4—182no—
923D4—364no—
924C2×C4—22no—
925C2×C4—32no—
926C2×C4—32no—
927C2×C4—32no—
928C2×C4—34no—
929C2×C4—34no—
930C2×C4—41no—
931C2×C4—64no—
932C2×C4—64no—
933C2×C4—92no—
934C2×C4—92no—
935C2×C4—122no—
936C2×C4—188no—
937C2×C4—184no—
938C2×C4—184no—
939C2×C4—184no—
940C2×C4—184no—
941C2×C4—184no—
942C2×C4—364no—
943C2×C4#379914yescomplemented
944C2×C4C22×D3211yescharacteristic
945C2×C4C22×D3211yescharacteristic
946C2×C4C22×D3211yescharacteristic
947C2×C4C22×D3211yescharacteristic
948C2×C4C22×D3211yescharacteristic
949C2×C4C22×D3211yescharacteristic
950C2×C3—24no—
951C2×C3—22no—
952C2×C3—22no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—122no—
957C2×C3C22×#23511yescharacteristic
958C2×C3C22×#23911yescharacteristic
959C2×C3C2×D3×#4111yescharacteristic
960C2×C3C2×D3×#4111yescharacteristic
961C2×C3#596411yescharacteristic
962C2×C3#596411yescharacteristic
963D3—42no—
964D3—64no—
965D3—64no—
966D3—124no—
967D3—124no—
968D3—122no—
969D3—122no—
970C22—21no—
971C22—21no—
972C22—62no—
973C22—62no—
974C22—62no—
975C22—94no—
976C22—182no—
977C22—182no—
978C22—182no—
979C22—182no—
980C22—182no—
981C22—368no—
982C22C2×#379912yes—
983C22C23×D3211yescharacteristic
984C4—21no—
985C4—21no—
986C4—21no—
987C4—62no—
988C4—62no—
989C4—64no—
990C4—62no—
991C4—64no—
992C4—182no—
993C4—182no—
994C4C2×#379912yes—
995C4C2×#379912yes—
996C4#6430612yes—
997C3—21no—
998C3#8584011yescharacteristic, complemented
999C3#8627611yescharacteristic, complemented
1000C2—22no—
1001C2—122no—
1002C2—184no—
1003C2—362no—
1004C2C22×#379911yescharacteristic
1005C2C2×#6430611yescharacteristic
1006C2#1059666911yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3475
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C4⋊(C3⋊D3)C2semidirect
2. C3×C4×#235C2semidirect
3. C3×#5470C2semidirect
4. #10595035C2semidirect
5. #10595034C2semidirect
6. #10595018C2semidirect
7. #10594969C2semidirect
8. #10594853C2semidirect
9. #10593987C2semidirect
10. #10593982C2semidirect
11. C4×#3799C2semidirect
12. #10593958C2semidirect
13. #10593947C2semidirect
14. #10593934C2semidirect
15. #10593870C2semidirect
16. #10593869C2semidirect
17. #10593865C2semidirect
39. C3×C4×D12C22semidirect
40. C3×C4×D12C22semidirect
41. C3×#872C22semidirect
42. C3×C42×D3C22semidirect
43. C3×#870C22semidirect
44. C3×#869C22semidirect
45. C3×#869C22semidirect
46. C3×C4×Dic6C22semidirect
47. C3×C4×Dic6C22semidirect
48. C3×C4×Dic6C22semidirect
49. C3×C4×Dic6C22semidirect
54. #63916C22semidirect
55. #63916C22semidirect
58. #63907C22semidirect
59. #63904C22semidirect
60. C4×#626C22semidirect
61. C4×#626C22semidirect
62. #63900C22semidirect
63. #63900C22semidirect
66. #63888C22semidirect
67. C4×#624C22semidirect
68. #63874C22semidirect
69. #63871C22semidirect
70. #63871C22semidirect
71. #63869C22semidirect
72. #63868C22semidirect
74. #63861C22semidirect
75. #63856C22semidirect
76. #63854C22semidirect
77. #63850C22semidirect
78. #63849C22semidirect
79. #63849C22semidirect
80. #63848C22semidirect
81. #63845C22semidirect
82. Dic3×Dic6C22semidirect
83. #63841C22semidirect
84. #63836C22semidirect
115. C4×#235D3semidirect
119. #5470D3semidirect
313. C4×D12C2×D3semidirect
314. C4×D12C2×D3semidirect
318. #872C2×D3semidirect
321. C42×D3C2×D3semidirect
323. #870C2×D3semidirect
324. #869C2×D3semidirect
325. #869C2×D3semidirect
327. C4×Dic6C2×D3semidirect
328. C4×Dic6C2×D3semidirect
329. C4×Dic6C2×D3semidirect
330. C4×Dic6C2×D3semidirect
340. C2×C32×C4#41semidirect
352. C4⋊(C3⋊D3)#41semidirect
692. C2×C3×C4#235semidirect
693. C2×C3×C4#239semidirect
906. C32#3475semidirect
943. C2×C4#3799semidirect
998. C3#85840semidirect
999. C3#86276semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C3×C4×#2352
C3×#54702
#105950352
#105950342
#105950182
#105949692
#105948532
#105939872
#105939822
C4×#37992
#105939582
#105939472
#105939342
#105938702
#105938692
#105938652
#862763
#858403