Finite Group Databasebeta

← #10804989

Subgroups — #10804989

Order 768.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5791C211yesmaximal, characteristic
2C3×#2280C211yesmaximal, characteristic, complemented
3C2×#5212C211yesmaximal, characteristic, complemented
4#69530C214yesmaximal, complemented
5#69496C214yesmaximal, complemented
6#69457C212yesmaximal, complemented
7#69456C212yesmaximal, complemented
8#21874—31nomaximal, Sylow
9C24×C3×C4C2211yescharacteristic
10C22×#235C411yescharacteristic, complemented
11C2×C3×#117—21no—
12C2×#953C2212yes—
13C22×#217C2212yes—
14#5791—21no—
15#5791—21no—
16#5791—21no—
17#5791—21no—
18#5791—21no—
19#5791—21no—
20#5791—21no—
21#5791—21no—
22C2×#930C411yescharacteristic, complemented
23C2×#930C2211yescharacteristic
24C2×#929C412yescomplemented
25C2×C4×#67C412yescomplemented
26C2×C4×#67C2212yes—
27C2×#926C411yescharacteristic, complemented
28C22×C4⋊Dic3—21no—
29C2×#924C411yescharacteristic, complemented
30C2×#924C2211yescharacteristic
31C3×#381—21no—
32C3×#380—21no—
33C3×#380C2212yes—
34C3×#379C2212yes—
35C3×C4×C22⋊C4—21no—
36C3×C4×C22⋊C4C2212yes—
37#5212—21no—
38#5212—21no—
39#5212C2212yes—
40#5212C2212yes—
41C2×C3⋊#95—21no—
42C2×#806C2218yes—
43#4527C2218yes—
44C2×#525—31no—
45#2280D311yescharacteristic, complemented
46C2×#380—31no—
47#1996—32no—
48#1964—32no—
49#1898—34no—
50#1799—34no—
51C25×C3C2311yescharacteristic
52C23×C3×C4—44no—
53C23×C3×C4C2×C411yescharacteristic
54C23×C3×C4C2×C411yescharacteristic
55C23×C3×C4C2×C411yescharacteristic
56C23×C3×C4C2×C411yescharacteristic
57C23×C3×C4D411yescharacteristic
58C23×C3×C4D411yescharacteristic
59C23×C3×C4D411yescharacteristic
60C23×C3×C4D411yescharacteristic
61C23×C3×C4D411yescharacteristic
62C23×C3×C4D411yescharacteristic
63C23×C3×C4D411yescharacteristic
64C23×C3×C4D411yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2311yescharacteristic
67C22×#67C2×C412yes—
68C22×#67C2×C412yes—
69C22×#67C2312yes—
70C23×Dic3—22no—
71C2×#235—21no—
72C2×#235—21no—
73C2×#235—21no—
74C2×#235—21no—
75C2×#235—44no—
76C22×D12C2×C411yescharacteristic, complemented
77C22×C4×D3C2×C412yescomplemented
78C22×Dic6C2×C411yescharacteristic, complemented
79C3×#117—44no—
80C2×C3×C4⋊C4—22no—
81C2×C3×C22⋊C4—22no—
82C2×C3×C22⋊C4—22no—
83C2×C3×C22⋊C4C2314yes—
84C2×C3×C42—22no—
85#953—22no—
86#953—22no—
87#953—22no—
88#953—22no—
89C2×#217—22no—
90C2×#217—44no—
91C2×#217C2×C412yes—
92C2×#217C2×C412yes—
93C2×#217C2314yes—
94C2×#217C2312yes—
95#930—21no—
96#930—21no—
97#930—21no—
98#930—21no—
99#930—21no—
100#930—21no—
101#930—21no—
102#930—21no—
103#929—22no—
104#929—22no—
105#929—22no—
106#929—22no—
107C4×#67—22no—
108C4×#67—22no—
109C4×#67—22no—
110C4×#67—22no—
111C4×#67—22no—
112C4×#67—22no—
113C4×#67—22no—
114C4×#67—22no—
115C2×(C2×D3)⋊C4C2×C412yescomplemented
116C2×(C2×D3)⋊C4C2×C412yescomplemented
117#926—21no—
118#926—21no—
119#926—21no—
120#926—21no—
121C2×C4⋊Dic3—22no—
122C2×C4⋊Dic3—22no—
123C2×C4⋊Dic3—44no—
124C2×C4⋊Dic3C2×C411yescharacteristic, complemented
125C2×C4⋊Dic3C2×C411yescharacteristic, complemented
126#924—21no—
127#924—21no—
128#924—21no—
129#924—21no—
130#924—21no—
131#924—21no—
132#924—21no—
133#924—21no—
134C2×Dic3⋊C4C2×C412yescomplemented
135C2×Dic3⋊C4C2×C412yescomplemented
136C2×C4×Dic3C2×C412yescomplemented
137C3×#95—22no—
138C3×#95—22no—
139C3⋊#95—22no—
140C3⋊#95—22no—
141#806—48no—
142C22×#41—31no—
143C24×C4C2×D311yescharacteristic
144#525—61no—
145#525—61no—
146#525—61no—
147#525—61no—
148#525—61no—
149#525—61no—
150#525—61no—
151#525—61no—
152C2×#123—32no—
153C2×C22⋊Q8—31no—
154C2×C22⋊Q8—31no—
155C2×#121—31no—
156C2×#121—31no—
157C2×#120—32no—
158C2×C4×D4—32no—
159C2×C4×D4—32no—
160C2×#117—21no—
161C2×#117—31no—
162C22×C4⋊C4—61no—
163C22×C22⋊C4—32no—
164C2×#99—38no—
165#381—21no—
166#380—21no—
167#380—32no—
168#380—32no—
169#380—61no—
170#380—61no—
171#380C2×D312yes—
172#379C2×D312yes—
173C4×C22⋊C4—21no—
174C4×C22⋊C4C2×D312yes—
175C2×#95—61no—
176#342—38no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—42no—
180C24×C3—42no—
181C24×C3C22×C411yescharacteristic
182C24×C3C22×C411yescharacteristic
183C24×C3C2×D411yescharacteristic
184C24×C3C2×D411yescharacteristic
185C24×C3C2×D411yescharacteristic
186C24×C3C2×D411yescharacteristic
187C24×C3C2411yescharacteristic
188C23×D3C22×C412yes—
189C22×C3×C4—24no—
190C22×C3×C4—24no—
191C22×C3×C4—24no—
192C22×C3×C4—24no—
193C22×C3×C4—42no—
194C22×C3×C4—42no—
195C22×C3×C4—42no—
196C22×C3×C4—42no—
197C22×C3×C4—42no—
198C22×C3×C4—42no—
199C22×C3×C4—42no—
200C22×C3×C4—42no—
201C22×C3×C4—42no—
202C22×C3×C4—42no—
203C22×C3×C4—42no—
204C22×C3×C4C22⋊C411yescharacteristic
205C22×C3×C4C22⋊C411yescharacteristic
206C22×C3×C4C22⋊C411yescharacteristic
207C22×C3×C4C22⋊C411yescharacteristic
208C22×C3×C4C22⋊C411yescharacteristic
209C22×C3×C4C22⋊C411yescharacteristic
210C22×C3×C4C22⋊C411yescharacteristic
211C22×C3×C4C22⋊C411yescharacteristic
212C22×C3×C4C22⋊C411yescharacteristic
213C22×C3×C4C22⋊C411yescharacteristic
214C22×C3×C4C22⋊C411yescharacteristic
215C22×C3×C4C22⋊C411yescharacteristic
216C22×C3×C4C22⋊C411yescharacteristic
217C22×C3×C4C22⋊C411yescharacteristic
218C22×C3×C4C22⋊C411yescharacteristic
219C22×C3×C4C22⋊C411yescharacteristic
220C22×C3×C4C22×C411yescharacteristic
221C22×C3×C4C22×C411yescharacteristic
222C22×C3×C4C22×C411yescharacteristic
223C22×C3×C4C22×C411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C2×#67—22no—
233C2×#67—22no—
234C2×#67—22no—
235C2×#67—22no—
236C2×#67—22no—
237C2×#67—22no—
238C2×#67—24no—
239C2×#67—24no—
240C2×#67—44no—
241C2×#67—44no—
242C22×Dic3—24no—
243C22×Dic3—44no—
244C22×Dic3—44no—
245C22×Dic3—44no—
246C22×Dic3C22×C412yes—
247C22×Dic3C22×C412yes—
248C22×Dic3C22×C412yes—
249#235—44no—
250#235—44no—
251#235—44no—
252#235—44no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—42no—
256C2×C4×D3—22no—
257C2×C4×D3—22no—
258C2×C4×D3—44no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—42no—
262C3×C4⋊C4—44no—
263C3×C22⋊C4—24no—
264C3×C22⋊C4—24no—
265C3×C22⋊C4—44no—
266C3×C22⋊C4—44no—
267C3×C42—44no—
268#217—22no—
269#217—22no—
270#217—22no—
271#217—22no—
272#217—22no—
273#217—22no—
274#217—28no—
275#217—44no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—22no—
278(C2×D3)⋊C4—22no—
279(C2×D3)⋊C4—22no—
280C4⋊Dic3—21no—
281C4⋊Dic3—21no—
282C4⋊Dic3—21no—
283C4⋊Dic3—21no—
284C4⋊Dic3—44no—
285C4⋊Dic3—44no—
286Dic3⋊C4—22no—
287Dic3⋊C4—22no—
288Dic3⋊C4—22no—
289Dic3⋊C4—22no—
290C4×Dic3—22no—
291C4×Dic3—22no—
292C25C22×D311yescharacteristic
293C2×#41—61no—
294C2×#41—61no—
295C2×#41—61no—
296C2×#41—61no—
297C2×#41—124no—
298C22×Q8—31no—
299C22×D4—32no—
300C22×D4—32no—
301C22×D4—32no—
302C22×D4—31no—
303C23×C4—32no—
304C23×C4—44no—
305C23×C4—62no—
306C23×C4C4×D311yescharacteristic
307C23×C4C4×D311yescharacteristic
308C23×C4C4×D311yescharacteristic
309C23×C4C4×D311yescharacteristic
310C23×C4D1211yescharacteristic
311C23×C4D1211yescharacteristic
312C23×C4D1211yescharacteristic
313C23×C4D1211yescharacteristic
314C23×C4#6711yescharacteristic
315C23×C4#6711yescharacteristic
316C23×C4#6711yescharacteristic
317C23×C4#6711yescharacteristic
318C23×C4C22×D311yescharacteristic
319C23×C4C22×D311yescharacteristic
320#123—62no—
321#123—62no—
322#123—62no—
323#123—62no—
324C22⋊Q8—61no—
325C22⋊Q8—61no—
326C22⋊Q8—61no—
327C22⋊Q8—61no—
328C22⋊Q8—61no—
329C22⋊Q8—61no—
330C22⋊Q8—61no—
331C22⋊Q8—61no—
332#121—61no—
333#121—61no—
334#121—61no—
335#121—61no—
336#121—61no—
337#121—61no—
338#121—61no—
339#121—61no—
340#120—62no—
341#120—62no—
342#120—62no—
343#120—62no—
344C4×D4—62no—
345C4×D4—62no—
346C4×D4—62no—
347C4×D4—62no—
348C4×D4—62no—
349C4×D4—62no—
350C4×D4—62no—
351C4×D4—62no—
352#117—44no—
353#117—61no—
354#117—61no—
355#117—61no—
356#117—61no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—32no—
362C2×C4⋊C4—62no—
363C2×C4⋊C4—62no—
364C2×C4⋊C4—124no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—32no—
368C2×C22⋊C4—32no—
369C2×C22⋊C4—32no—
370C2×C22⋊C4—32no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4—34no—
373C2×C22⋊C4—62no—
374C2×C22⋊C4—124no—
375C2×C22⋊C4C22×D314yes—
376C2×C42—22no—
377C2×C42—32no—
378#99—128no—
379#95—22no—
380#95—22no—
381#95—62no—
382#95—62no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—48no—
406C23×C3—48no—
407C23×C3C2×C22⋊C411yescharacteristic
408C23×C3C2×C22⋊C411yescharacteristic
409C23×C3C2×C22⋊C411yescharacteristic
410C23×C3C2×C22⋊C411yescharacteristic
411C23×C3C23×C411yescharacteristic
412C23×C3C22×D411yescharacteristic
413C23×C3C22×D411yescharacteristic
414C23×C3H(5,𝔽2)12yes—
415C23×C32−1+412yes—
416C22×D3—22no—
417C22×D3—24no—
418C22×D3—42no—
419C22×D3—42no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—44no—
448C2×C3×C4—44no—
449C2×C3×C4—44no—
450C2×C3×C4#9914yescomplemented
451C2×C3×C4C2×C22⋊C411yescharacteristic
452C2×C3×C4C2×C22⋊C411yescharacteristic
453C2×C3×C4C2×C22⋊C411yescharacteristic
454C2×C3×C4C2×C22⋊C411yescharacteristic
455C2×C3×C4C2×C22⋊C411yescharacteristic
456C2×C3×C4C2×C22⋊C411yescharacteristic
457C2×C3×C4C2×C22⋊C411yescharacteristic
458C2×C3×C4C2×C22⋊C411yescharacteristic
459#67—44no—
460#67—44no—
461#67—42no—
462#67—42no—
463#67—44no—
464#67—44no—
465#67—44no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—24no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C2×Dic3—44no—
473C2×Dic3—44no—
474C2×Dic3—44no—
475C2×Dic3—88no—
476D12—42no—
477D12—42no—
478C4×D3—44no—
479C4×D3—44no—
480Dic6—42no—
481Dic6—42no—
482C24—22no—
483C24—22no—
484C24—32no—
485C24—42no—
486C24—42no—
487C24C2×C4×D311yescharacteristic
488C24C2×C4×D311yescharacteristic
489C24C2×D1211yescharacteristic
490C24C2×D1211yescharacteristic
491C24C2×#6711yescharacteristic
492C24C2×#6711yescharacteristic
493C24C23×D311yescharacteristic
494#41—124no—
495#41—124no—
496#41—124no—
497#41—124no—
498C2×Q8—61no—
499C2×Q8—61no—
500C2×Q8—122no—
501C2×D4—62no—
502C2×D4—62no—
503C2×D4—62no—
504C2×D4—62no—
505C2×D4—62no—
506C2×D4—64no—
507C2×D4—64no—
508C2×D4—62no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—122no—
512C2×D4—124no—
513C2×D4—124no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—32no—
519C22×C4—32no—
520C22×C4—32no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—64no—
535C22×C4—124no—
536C22×C4—124no—
537C22×C4—124no—
538C22×C4—124no—
539C22×C4(C2×D3)⋊C411yescharacteristic
540C22×C4(C2×D3)⋊C411yescharacteristic
541C22×C4(C2×D3)⋊C411yescharacteristic
542C22×C4(C2×D3)⋊C411yescharacteristic
543C22×C4(C2×D3)⋊C411yescharacteristic
544C22×C4(C2×D3)⋊C411yescharacteristic
545C22×C4(C2×D3)⋊C411yescharacteristic
546C22×C4(C2×D3)⋊C411yescharacteristic
547C22×C4(C2×D3)⋊C411yescharacteristic
548C22×C4(C2×D3)⋊C411yescharacteristic
549C22×C4(C2×D3)⋊C411yescharacteristic
550C22×C4(C2×D3)⋊C411yescharacteristic
551C22×C4(C2×D3)⋊C411yescharacteristic
552C22×C4(C2×D3)⋊C411yescharacteristic
553C22×C4(C2×D3)⋊C411yescharacteristic
554C22×C4(C2×D3)⋊C411yescharacteristic
555C22×C4C2×C4×D311yescharacteristic
556C22×C4C2×C4×D311yescharacteristic
557C22×C4C2×C4×D311yescharacteristic
558C22×C4C2×C4×D311yescharacteristic
559C22×C4C2×D1211yescharacteristic
560C22×C4C2×D1211yescharacteristic
561C22×C4C2×D1211yescharacteristic
562C22×C4C2×D1211yescharacteristic
563C22×C4C2×#6711yescharacteristic
564C22×C4C2×#6711yescharacteristic
565C22×C4C2×#6711yescharacteristic
566C22×C4C2×#6711yescharacteristic
567C4⋊C4—44no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—62no—
573C4⋊C4—62no—
574C4⋊C4—62no—
575C4⋊C4—62no—
576C4⋊C4—124no—
577C4⋊C4—124no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—44no—
581C22⋊C4—44no—
582C22⋊C4—62no—
583C22⋊C4—62no—
584C22⋊C4—62no—
585C22⋊C4—62no—
586C22⋊C4—62no—
587C22⋊C4—62no—
588C22⋊C4—62no—
589C22⋊C4—62no—
590C22⋊C4—62no—
591C22⋊C4—62no—
592C22⋊C4—68no—
593C22⋊C4—124no—
594C42—44no—
595C42—62no—
596C42—62no—
597C22×C3—24no—
598C22×C3—24no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—44no—
618C22×C3—44no—
619C22×C3—44no—
620C22×C3—44no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3C2×#9912yes—
624C22×C3#41012yes—
625C22×C3C22×C22⋊C411yescharacteristic
626C22×C3#52012yes—
627C22×C3#53511yescharacteristic
628C22×C3#53611yescharacteristic
629C22×C3#53712yes—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—84no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—84no—
641C3×C4C2×#9912yes—
642C3×C4C2×#9912yes—
643Dic3—42no—
644Dic3—42no—
645Dic3—42no—
646Dic3—84no—
647C23—22no—
648C23—22no—
649C23—21no—
650C23—21no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—21no—
658C23—21no—
659C23—22no—
660C23—22no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—48no—
670C23—48no—
671C23—62no—
672C23—64no—
673C23—122no—
674C23—122no—
675C23C2×(C2×D3)⋊C411yescharacteristic
676C23C2×(C2×D3)⋊C411yescharacteristic
677C23C2×(C2×D3)⋊C411yescharacteristic
678C23C2×(C2×D3)⋊C411yescharacteristic
679C23C22×C4×D311yescharacteristic
680C23C22×D1211yescharacteristic
681C23#100912yes—
682C23#101012yes—
683C23C22×#6711yescharacteristic
684Q8—122no—
685Q8—122no—
686D4—122no—
687D4—124no—
688D4—124no—
689D4—124no—
690D4—124no—
691D4—122no—
692D4—122no—
693D4—124no—
694D4—122no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—64no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—124no—
730C2×C4—124no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—124no—
734C2×C4—124no—
735C2×C4—124no—
736C2×C4—248no—
737C2×C4#80614yescomplemented
738C2×C4C2×(C2×D3)⋊C411yescharacteristic
739C2×C4C2×(C2×D3)⋊C411yescharacteristic
740C2×C4C2×(C2×D3)⋊C411yescharacteristic
741C2×C4C2×(C2×D3)⋊C411yescharacteristic
742C2×C4C2×(C2×D3)⋊C411yescharacteristic
743C2×C4C2×(C2×D3)⋊C411yescharacteristic
744C2×C4C2×(C2×D3)⋊C411yescharacteristic
745C2×C4C2×(C2×D3)⋊C411yescharacteristic
746C2×C3—21no—
747C2×C3—22no—
748C2×C3—22no—
749C2×C3—21no—
750C2×C3—22no—
751C2×C3—22no—
752C2×C3—41no—
753C2×C3—41no—
754C2×C3#231111yescharacteristic
755C2×C3C22×#9911yescharacteristic
756C2×C3C2×#41011yescharacteristic
757D3—82no—
758C22—24no—
759C22—24no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—42no—
777C22—42no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—122no—
785C22—122no—
786C22—122no—
787C22—244no—
788C22C2×#80612yes—
789C22#500612yes—
790C22#552312yes—
791C22#552511yescharacteristic
792C22#552611yescharacteristic
793C22C22×(C2×D3)⋊C411yescharacteristic
794C22#583312yes—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—84no—
802C4—122no—
803C4—122no—
804C4—122no—
805C4—244no—
806C4C2×#80612yes—
807C4C2×#80612yes—
808C3#2187411yescharacteristic, complemented, Sylow
809C2—22no—
810C2—21no—
811C2—22no—
812C2—22no—
813C2—21no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—242no—
818C2C22×#80611yescharacteristic
819C2C2×#500611yescharacteristic
820C2#8227011yescharacteristic
subgroupG/H
centerC22C22×(C2×D3)⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×#2280C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#5791C2
cosocleC24×C3C24
hypercenter#2280D3
hypocenterC3#21874
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C3×#2280C2semidirect
3. C2×#5212C2semidirect
4. #69530C2semidirect
5. #69496C2semidirect
6. #69457C2semidirect
7. #69456C2semidirect
10. C22×#235C4semidirect
22. C2×#930C4semidirect
24. C2×#929C4semidirect
25. C2×C4×#67C4semidirect
27. C2×#926C4semidirect
29. C2×#924C4semidirect
45. #2280D3semidirect
76. C22×D12C2×C4semidirect
77. C22×C4×D3C2×C4semidirect
78. C22×Dic6C2×C4semidirect
115. C2×(C2×D3)⋊C4C2×C4semidirect
116. C2×(C2×D3)⋊C4C2×C4semidirect
124. C2×C4⋊Dic3C2×C4semidirect
125. C2×C4⋊Dic3C2×C4semidirect
134. C2×Dic3⋊C4C2×C4semidirect
135. C2×Dic3⋊C4C2×C4semidirect
136. C2×C4×Dic3C2×C4semidirect
450. C2×C3×C4#99semidirect
737. C2×C4#806semidirect
808. C3#21874semidirect

Maximal subgroups

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

subgroupindex
C2×#57912
C3×#22802
C2×#52122
#695302
#694962
#694572
#694562
#218743