Finite Group Databasebeta

← #10800529

Subgroups — #10800529

Order 768.

1678 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5627C211yesmaximal, characteristic
2#73862C211yesmaximal, characteristic, complemented
3C4×D3×C22⋊C4C211yesmaximal, characteristic, complemented
4C3×#1996C211yesmaximal, characteristic, complemented
5#71701C211yesmaximal, characteristic, complemented
6#69528C211yesmaximal, characteristic, complemented
7#69456C211yesmaximal, characteristic, complemented
8#68970C214yesmaximal, complemented
9#68952C214yesmaximal, complemented
10#21420—31nomaximal, Sylow
11C22×#239C411yescharacteristic, complemented
12C23×C4×D3C2211yescharacteristic
13C2×C3×C22⋊Q8C2211yescharacteristic
14C2×#946C411yescharacteristic, complemented
15C2×#930C2211yescharacteristic
16#5627—21no—
17#5627—21no—
18#5627—21no—
19#5627—21no—
20#5627—21no—
21#5627—21no—
22#5627—21no—
23#5627—21no—
24C2×#895C411yescharacteristic, complemented
25C2×#894C412yescomplemented
26C2×#893C412yescomplemented
27C2×#892—21no—
28C2×#892C411yescharacteristic, complemented
29C2×#882C2212yes—
30C2×#67⋊C4C2212yes—
31C2×D3×C22⋊C4C2212yes—
32C2×C42×D3—21no—
33C3×#380C2211yescharacteristic
34C3×C4×C22⋊C4C2211yescharacteristic
35#5212C2211yescharacteristic
36C4×#217C2211yescharacteristic
37#4987—21no—
38#4955C2212yes—
39C2×#806C2214yes—
40C2×#806C2214yes—
41Dic3×C22⋊C4C2212yes—
42Dic3×C22⋊C4C2212yes—
43C4×(C2×D3)⋊C4—21no—
44#4666—21no—
45#4666—21no—
46#4664—21no—
47D3×#95—21no—
48C3×#342C2214yes—
49#4526C2214yes—
50C2×#525—31no—
51#2280—31no—
52C2×C4×C22⋊C4—31no—
53#1996—31no—
54#1996D311yescharacteristic, complemented
55#1964—31no—
56#1964—31no—
57#1898—34no—
58C4×#99—34no—
59C24×D3C2311yescharacteristic
60C22×C3×Q8C2×C411yescharacteristic, complemented
61C23×C3×C4C2311yescharacteristic
62C22×#67C2312yes—
63C23×Dic3C2311yescharacteristic
64C2×#239—21no—
65C2×#239—21no—
66C2×#239—21no—
67C2×#239—21no—
68C2×#239—44no—
69C22×D12C2×C412yes—
70C22×D12C2×C412yes—
71C22×D12C2×C411yescharacteristic, complemented
72C22×C4×D3—22no—
73C22×C4×D3—44no—
74C22×C4×D3C2×C411yescharacteristic
75C22×C4×D3C2×C411yescharacteristic
76C22×C4×D3C2×C411yescharacteristic
77C22×C4×D3C2×C411yescharacteristic
78C22×C4×D3C2×C412yescomplemented
79C22×C4×D3D411yescharacteristic
80C22×C4×D3D411yescharacteristic
81C22×C4×D3D411yescharacteristic
82C22×C4×D3D411yescharacteristic
83C22×C4×D3D411yescharacteristic
84C22×C4×D3D411yescharacteristic
85C22×C4×D3D411yescharacteristic
86C22×C4×D3D411yescharacteristic
87C3×C22⋊Q8—21no—
88C3×C22⋊Q8—21no—
89C3×C22⋊Q8—21no—
90C3×C22⋊Q8—21no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4C2×C411yescharacteristic, complemented
93C2×C3×C4⋊C4C2×C412yescomplemented
94C2×C3×C22⋊C4C2312yes—
95C2×C3×C22⋊C4C2312yes—
96C2×C3×C22⋊C4C2312yes—
97C2×C3×C42—21no—
98C2×#217C2312yes—
99C2×#217C2312yes—
100#946—21no—
101#946—21no—
102#946—21no—
103#946—21no—
104#930—21no—
105#930—21no—
106#930—21no—
107#930—21no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—22no—
111C2×(C2×D3)⋊C4C2×C412yes—
112C2×(C2×D3)⋊C4C2×C412yes—
113C2×(C2×D3)⋊C4C2×C412yescomplemented
114C2×(C2×D3)⋊C4C2×C412yescomplemented
115C2×C4⋊Dic3—21no—
116C2×C4⋊Dic3C2×C411yescharacteristic, complemented
117C2×Dic3⋊C4C2×C412yescomplemented
118C2×C4×Dic3—21no—
119C2×C4×Dic3—22no—
120C2×C4×Dic3—22no—
121C2×C4×Dic3C2×C412yescomplemented
122#895—21no—
123#895—21no—
124#895—21no—
125#895—21no—
126#894—22no—
127#894—22no—
128#894—22no—
129#894—22no—
130#893—22no—
131#893—22no—
132#893—22no—
133#893—22no—
134#892—21no—
135#892—21no—
136#892—21no—
137#892—21no—
138#892—44no—
139#882—22no—
140#882—22no—
141#882—22no—
142#882—22no—
143#67⋊C4—22no—
144#67⋊C4—22no—
145#67⋊C4—22no—
146#67⋊C4—22no—
147D3×C22⋊C4—24no—
148D3×C22⋊C4—24no—
149C42×D3—44no—
150C3×#95—21no—
151C3×#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156#806—28no—
157#806—28no—
158C22×#41—31no—
159C24×C4—31no—
160#525—61no—
161#525—61no—
162#525—61no—
163#525—61no—
164#525—61no—
165#525—61no—
166#525—61no—
167#525—61no—
168C2×#123—32no—
169C2×C22⋊Q8—31no—
170C2×C22⋊Q8C2×D311yescharacteristic
171C2×#121—31no—
172C2×#121—31no—
173C2×#120—32no—
174C2×C4×D4—32no—
175C2×C4×D4—32no—
176C2×#117—31no—
177C2×#117—61no—
178C22×C22⋊C4—32no—
179C22×C42—61no—
180C2×#99—34no—
181C2×#99—34no—
182#381—61no—
183#380—31no—
184#380—61no—
185#380C2×D311yescharacteristic
186#379—32no—
187C4×C22⋊C4—31no—
188C4×C22⋊C4—32no—
189C4×C22⋊C4—32no—
190C4×C22⋊C4—61no—
191C4×C22⋊C4—61no—
192C4×C22⋊C4—61no—
193C4×C22⋊C4C2×D311yescharacteristic
194C2×#95—61no—
195#342—34no—
196#342C2×D314yes—
197C24×C3C2411yescharacteristic
198C23×D3—22no—
199C23×D3—22no—
200C23×D3—42no—
201C23×D3—42no—
202C23×D3C22×C411yescharacteristic
203C23×D3C22×C411yescharacteristic
204C23×D3C22×C412yes—
205C23×D3C2×D411yescharacteristic
206C23×D3C2×D411yescharacteristic
207C23×D3C2×D411yescharacteristic
208C23×D3C2×D411yescharacteristic
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—42no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—42no—
215C22×C3×C4C22×C411yescharacteristic
216C22×C3×C4C22×C412yes—
217C22×C3×C4C22×C412yes—
218C22×C3×C4C22×C411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C2×#67—22no—
224C2×#67—22no—
225C2×#67—24no—
226C2×#67—24no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—42no—
230C22×Dic3C22×C412yes—
231C22×Dic3C22×C411yescharacteristic
232C22×Dic3C22×C411yescharacteristic
233C22×Dic3C2×D411yescharacteristic
234C22×Dic3C2×D411yescharacteristic
235C22×Dic3C2×D411yescharacteristic
236C22×Dic3C2×D411yescharacteristic
237#239—44no—
238#239—44no—
239#239—44no—
240#239—44no—
241C2×D12—22no—
242C2×D12—22no—
243C2×D12—22no—
244C2×D12—22no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—42no—
248C2×D12—44no—
249C2×D12—44no—
250C2×C4×D3—24no—
251C2×C4×D3—24no—
252C2×C4×D3—24no—
253C2×C4×D3—28no—
254C2×C4×D3—22no—
255C2×C4×D3—22no—
256C2×C4×D3—42no—
257C2×C4×D3—42no—
258C2×C4×D3—42no—
259C2×C4×D3—42no—
260C2×C4×D3—42no—
261C2×C4×D3—42no—
262C2×C4×D3—42no—
263C2×C4×D3—42no—
264C2×C4×D3—42no—
265C2×C4×D3—44no—
266C2×C4×D3—44no—
267C2×C4×D3—44no—
268C2×C4×D3C22⋊C411yescharacteristic
269C2×C4×D3C22⋊C411yescharacteristic
270C2×C4×D3C22⋊C411yescharacteristic
271C2×C4×D3C22⋊C411yescharacteristic
272C2×C4×D3C22⋊C411yescharacteristic
273C2×C4×D3C22⋊C411yescharacteristic
274C2×C4×D3C22⋊C411yescharacteristic
275C2×C4×D3C22⋊C411yescharacteristic
276C2×C4×D3C22⋊C411yescharacteristic
277C2×C4×D3C22⋊C411yescharacteristic
278C2×C4×D3C22⋊C411yescharacteristic
279C2×C4×D3C22⋊C411yescharacteristic
280C2×C4×D3C22⋊C411yescharacteristic
281C2×C4×D3C22⋊C411yescharacteristic
282C2×C4×D3C22⋊C411yescharacteristic
283C2×C4×D3C22⋊C411yescharacteristic
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—22no—
287C3×C4⋊C4—22no—
288C3×C4⋊C4—42no—
289C3×C22⋊C4—22no—
290C3×C22⋊C4—22no—
291C3×C22⋊C4—22no—
292C3×C22⋊C4—24no—
293C3×C22⋊C4#4114yescomplemented
294C3×C42—42no—
295#217—22no—
296#217—24no—
297#217#4114yescomplemented
298(C2×D3)⋊C4—28no—
299(C2×D3)⋊C4—22no—
300(C2×D3)⋊C4—22no—
301(C2×D3)⋊C4—22no—
302(C2×D3)⋊C4—22no—
303(C2×D3)⋊C4—22no—
304(C2×D3)⋊C4—22no—
305(C2×D3)⋊C4—22no—
306(C2×D3)⋊C4—22no—
307(C2×D3)⋊C4—44no—
308(C2×D3)⋊C4—44no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—42no—
312Dic3⋊C4—22no—
313Dic3⋊C4—22no—
314C4×Dic3—22no—
315C4×Dic3—22no—
316C4×Dic3—44no—
317C4×Dic3—44no—
318C4×Dic3—42no—
319C25—31no—
320C2×#41—61no—
321C2×#41—61no—
322C2×#41—61no—
323C2×#41—61no—
324C2×#41—124no—
325C22×Q8C4×D311yescharacteristic, complemented
326C22×D4—32no—
327C22×D4—32no—
328C22×D4—32no—
329C22×D4—31no—
330C23×C4—31no—
331C23×C4—31no—
332C23×C4—31no—
333C23×C4—31no—
334C23×C4—31no—
335C23×C4—31no—
336C23×C4—31no—
337C23×C4—31no—
338C23×C4—31no—
339C23×C4—31no—
340C23×C4—31no—
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—32no—
344C23×C4—62no—
345C23×C4—124no—
346C23×C4C22×D311yescharacteristic
347#123—62no—
348#123—62no—
349#123—62no—
350#123—62no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355C22⋊Q8—61no—
356C22⋊Q8—61no—
357C22⋊Q8—61no—
358C22⋊Q8—61no—
359#121—61no—
360#121—61no—
361#121—61no—
362#121—61no—
363#121—61no—
364#121—61no—
365#121—61no—
366#121—61no—
367#120—62no—
368#120—62no—
369#120—62no—
370#120—62no—
371C4×D4—62no—
372C4×D4—62no—
373C4×D4—62no—
374C4×D4—62no—
375C4×D4—62no—
376C4×D4—62no—
377C4×D4—62no—
378C4×D4—62no—
379#117—61no—
380#117—61no—
381#117—61no—
382#117—61no—
383#117—124no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—32no—
387C2×C4⋊C4—61no—
388C2×C4⋊C4C4×D311yescharacteristic, complemented
389C2×C4⋊C4C4×D312yescomplemented
390C2×C22⋊C4—32no—
391C2×C22⋊C4—32no—
392C2×C22⋊C4—32no—
393C2×C22⋊C4—32no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—64no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—64no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4C22×D312yes—
402C2×C22⋊C4C22×D312yes—
403C2×C22⋊C4C22×D312yes—
404C2×C42—21no—
405C2×C42—32no—
406C2×C42—62no—
407C2×C42—62no—
408C2×C42—61no—
409C2×C42—124no—
410#99—68no—
411#99—68no—
412#95—21no—
413#95—21no—
414#95—62no—
415#95—62no—
416#95—61no—
417#95—61no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3C23×C411yescharacteristic
421C23×C3C22×D411yescharacteristic
422C23×C3C22×D411yescharacteristic
423C23×C3C2×#4112yes—
424C23×C3C2×#4112yes—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—24no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—48no—
448C22×D3—48no—
449C22×D3—42no—
450C22×D3—42no—
451C22×D3C2×C22⋊C411yescharacteristic
452C22×D3C2×C22⋊C411yescharacteristic
453C22×D3C2×C22⋊C411yescharacteristic
454C22×D3C2×C22⋊C411yescharacteristic
455C3×Q8—42no—
456C3×Q8—42no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—24no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—42no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4—42no—
473C2×C3×C4C2×C22⋊C411yescharacteristic
474C2×C3×C4C2×C22⋊C411yescharacteristic
475C2×C3×C4C2×C22⋊C411yescharacteristic
476C2×C3×C4C2×C22⋊C411yescharacteristic
477#67—44no—
478#67—42no—
479#67—42no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—24no—
485C2×Dic3—24no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—42no—
490C2×Dic3—42no—
491C2×Dic3—42no—
492C2×Dic3—42no—
493C2×Dic3—42no—
494C2×Dic3C2×C22⋊C411yescharacteristic
495C2×Dic3C2×C22⋊C411yescharacteristic
496C2×Dic3C2×C22⋊C411yescharacteristic
497C2×Dic3C2×C22⋊C411yescharacteristic
498D12—42no—
499D12—44no—
500D12—44no—
501D12—44no—
502D12—44no—
503D12—42no—
504C4×D3—22no—
505C4×D3—22no—
506C4×D3—22no—
507C4×D3—22no—
508C4×D3—22no—
509C4×D3—22no—
510C4×D3—22no—
511C4×D3—22no—
512C4×D3—22no—
513C4×D3—41no—
514C4×D3—41no—
515C4×D3—41no—
516C4×D3—41no—
517C4×D3—41no—
518C4×D3—41no—
519C4×D3—44no—
520C4×D3—416no—
521C4×D3—44no—
522C4×D3#9914yescomplemented
523C24—31no—
524C24—31no—
525C24—31no—
526C24—31no—
527C24—31no—
528C24—31no—
529C24—32no—
530C24—62no—
531C24—62no—
532C24—122no—
533C24—122no—
534C24C23×D311yescharacteristic
535#41—124no—
536#41—124no—
537#41—124no—
538#41—124no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—42no—
542C2×D4—62no—
543C2×D4—62no—
544C2×D4—62no—
545C2×D4—62no—
546C2×D4—62no—
547C2×D4—62no—
548C2×D4—64no—
549C2×D4—64no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—122no—
553C2×D4—124no—
554C2×D4—124no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—31no—
579C22×C4—32no—
580C22×C4—42no—
581C22×C4—64no—
582C22×C4—64no—
583C22×C4—64no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—68no—
587C22×C4—62no—
588C22×C4—62no—
589C22×C4—122no—
590C22×C4—122no—
591C22×C4—122no—
592C22×C4—122no—
593C22×C4—122no—
594C22×C4—122no—
595C22×C4—122no—
596C22×C4—122no—
597C22×C4—122no—
598C22×C4—124no—
599C22×C4—124no—
600C22×C4—124no—
601C22×C4—122no—
602C22×C4C2×C4×D311yescharacteristic
603C22×C4C2×C4×D312yes—
604C22×C4C2×C4×D312yes—
605C22×C4C2×C4×D311yescharacteristic
606C22×C4D3×D411yescharacteristic
607C22×C4D3×D411yescharacteristic
608C22×C4D3×D411yescharacteristic
609C22×C4D3×D411yescharacteristic
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—42no—
615C4⋊C4—62no—
616C4⋊C4—62no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—122no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—24no—
624C22⋊C4—34no—
625C22⋊C4—62no—
626C22⋊C4—62no—
627C22⋊C4—62no—
628C22⋊C4—62no—
629C22⋊C4—62no—
630C22⋊C4—62no—
631C22⋊C4—68no—
632C22⋊C4—62no—
633C22⋊C4—62no—
634C22⋊C4—62no—
635C22⋊C4—64no—
636C22⋊C4—124no—
637C22⋊C4—124no—
638C22⋊C4#23914yescomplemented
639C42—42no—
640C42—62no—
641C42—62no—
642C42—122no—
643C42—124no—
644C42—124no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3C22×C22⋊C411yescharacteristic
654C22×C3C4×#4112yes—
655C22×C3#52512yes—
656C22×C3#53211yescharacteristic
657C22×C3#53211yescharacteristic
658C2×D3—28no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—42no—
670C2×D3—42no—
671C2×D3—44no—
672C2×D3—42no—
673C2×D3—42no—
674C2×D3—44no—
675C2×D3—44no—
676C2×D3—42no—
677C2×D3—42no—
678C2×D3—42no—
679C2×D3—84no—
680C2×D3C2×#9912yes—
681C2×D3#41012yes—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—44no—
686C3×C4—42no—
687C3×C4—42no—
688C3×C4—82no—
689C3×C4C2×#9912yes—
690Dic3—21no—
691Dic3—21no—
692Dic3—21no—
693Dic3—44no—
694Dic3—42no—
695Dic3—82no—
696Dic3C2×#9912yes—
697C23—31no—
698C23—31no—
699C23—31no—
700C23—31no—
701C23—41no—
702C23—41no—
703C23—62no—
704C23—62no—
705C23—62no—
706C23—62no—
707C23—62no—
708C23—62no—
709C23—62no—
710C23—61no—
711C23—61no—
712C23—61no—
713C23—61no—
714C23—62no—
715C23—62no—
716C23—62no—
717C23—62no—
718C23—64no—
719C23—121no—
720C23—121no—
721C23—121no—
722C23—121no—
723C23—121no—
724C23—121no—
725C23—122no—
726C23—122no—
727C23—128no—
728C23—128no—
729C23C22×C4×D311yescharacteristic
730C23C2×D3×D411yescharacteristic
731C23C2×D3×D411yescharacteristic
732C23C2×#23912yes—
733C23D3×#4112yes—
734Q8—42no—
735Q8—42no—
736D4—122no—
737D4—124no—
738D4—124no—
739D4—124no—
740D4—124no—
741D4—122no—
742D4—122no—
743D4—124no—
744D4—122no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—31no—
752C2×C4—34no—
753C2×C4—31no—
754C2×C4—31no—
755C2×C4—31no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—64no—
780C2×C4—64no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4—124no—
788C2×C4—124no—
789C2×C4—1216no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—122no—
794C2×C4—122no—
795C2×C4—122no—
796C2×C4—122no—
797C2×C4—122no—
798C2×C4D3×C22⋊C411yescharacteristic
799C2×C4D3×C22⋊C411yescharacteristic
800C2×C4D3×C22⋊C411yescharacteristic
801C2×C4D3×C22⋊C411yescharacteristic
802C2×C3—22no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—22no—
806C2×C3#229711yescharacteristic
807C2×C3C22×#9911yescharacteristic
808C2×C3C2×#41011yescharacteristic
809D3—22no—
810D3—22no—
811D3—41no—
812D3—41no—
813D3—82no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—32no—
821C22—32no—
822C22—42no—
823C22—42no—
824C22—68no—
825C22—61no—
826C22—61no—
827C22—61no—
828C22—61no—
829C22—61no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—61no—
835C22—122no—
836C22—122no—
837C22—122no—
838C22—122no—
839C22—124no—
840C22—124no—
841C22—124no—
842C22—122no—
843C22—122no—
844C22—122no—
845C22—244no—
846C22C2×D3×C22⋊C411yescharacteristic
847C22C4×#23912yes—
848C22#562712yes—
849C22#566811yescharacteristic
850C22#572511yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—32no—
855C4—44no—
856C4—42no—
857C4—42no—
858C4—61no—
859C4—61no—
860C4—61no—
861C4—82no—
862C4—124no—
863C4—122no—
864C4—242no—
865C4D3×#9912yes—
866C3#2142011yescharacteristic, complemented, Sylow
867C2—22no—
868C2—21no—
869C2—21no—
870C2—22no—
871C2—62no—
872C2—62no—
873C2—121no—
874C2—121no—
875C2—242no—
876C2#7647811yescharacteristic
877C2C2×D3×#9911yescharacteristic
878C2D3×#41011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×#1996C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#5627C2
cosocleC24×C3C24
hypercenter#1996D3
hypocenterC3#21420
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. #73862C2semidirect
3. C4×D3×C22⋊C4C2semidirect
4. C3×#1996C2semidirect
5. #71701C2semidirect
6. #69528C2semidirect
7. #69456C2semidirect
8. #68970C2semidirect
9. #68952C2semidirect
11. C22×#239C4semidirect
14. C2×#946C4semidirect
24. C2×#895C4semidirect
25. C2×#894C4semidirect
26. C2×#893C4semidirect
28. C2×#892C4semidirect
54. #1996D3semidirect
60. C22×C3×Q8C2×C4semidirect
71. C22×D12C2×C4semidirect
78. C22×C4×D3C2×C4semidirect
92. C2×C3×C4⋊C4C2×C4semidirect
93. C2×C3×C4⋊C4C2×C4semidirect
113. C2×(C2×D3)⋊C4C2×C4semidirect
114. C2×(C2×D3)⋊C4C2×C4semidirect
116. C2×C4⋊Dic3C2×C4semidirect
117. C2×Dic3⋊C4C2×C4semidirect
121. C2×C4×Dic3C2×C4semidirect
293. C3×C22⋊C4#41semidirect
297. #217#41semidirect
325. C22×Q8C4×D3semidirect
388. C2×C4⋊C4C4×D3semidirect
389. C2×C4⋊C4C4×D3semidirect
522. C4×D3#99semidirect
638. C22⋊C4#239semidirect
866. C3#21420semidirect

Maximal subgroups

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

subgroupindex
C2×#56272
#738622
C4×D3×C22⋊C42
C3×#19962
#717012
#695282
#694562
#689702
#689522
#214203