Finite Group Databasebeta

← C2×#82828 #11429906

Subgroups — C2×#82828 #11429906

Order 768.

3286 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×#946C211yesmaximal, characteristic, complemented
3C22×#929C211yesmaximal, characteristic
4C22×#883C211yesmaximal, characteristic
5C2×#5230C211yesmaximal, characteristic, complemented
6C2×#5210C211yesmaximal, characteristic, complemented
7#82828C2116yesmaximal, direct product factor
8C2×#4992C211yesmaximal, characteristic, complemented
9C2×#4989C211yesmaximal, characteristic, complemented
10C2×#4981C211yesmaximal, characteristic, complemented
11C2×#4982C211yesmaximal, characteristic, complemented
12C2×#4990C211yesmaximal, characteristic, complemented
13C2×#4975C211yesmaximal, characteristic, complemented
14C2×#4959C211yesmaximal, characteristic
15C2×#4952C211yesmaximal, characteristic, complemented
16C2×#4951C211yesmaximal, characteristic, complemented
17C2×#2680—31nomaximal, Sylow
18C23×C3×Q8C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C2×C3×C22⋊Q8—28no—
23C2×C3×C22⋊Q8C2218yescomplemented
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C2×#946—28no—
33C2×#946C2218yescomplemented
34C2×#929—28no—
35C2×#929C2218yes—
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41C22×C4⋊Dic3C2211yescharacteristic
42C22×C4⋊Dic3C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C22×Dic3⋊C4C2211yescharacteristic
48C22×Dic3⋊C4C2211yescharacteristic
49C22×Dic3⋊C4C2211yescharacteristic
50C22×C4×Dic3C2211yescharacteristic
51C2×#883—28no—
52C2×#883C2218yes—
53#5230C2218yescomplemented
54#5210C2218yescomplemented
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2211yescharacteristic
63#4992C2218yescomplemented
64#4990C2218yescomplemented
65#4989C2218yescomplemented
66#4982C2218yescomplemented
67#4981C2218yescomplemented
68#4975C2218yescomplemented
69#4959C2218yes—
70#4952C2218yescomplemented
71#4951C2218yescomplemented
72C22×#123—31no—
73C22×#123—31no—
74C22×C22⋊Q8—31no—
75C22×C22⋊Q8D311yescharacteristic, complemented
76#2680—316no—
77C2×#398—31no—
78C2×#398—31no—
79C2×#397—31no—
80C2×#397—31no—
81C2×#395—31no—
82C2×#394—31no—
83C2×#388—31no—
84C2×#388—31no—
85C2×#385—31no—
86C2×#385—31no—
87C2×#384—31no—
88C25×C3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C22×C3×Q8—24no—
91C22×C3×Q8—24no—
92C22×C3×Q8—42no—
93C22×C3×Q8C2314yes—
94C23×C3×C4—24no—
95C23×C3×C4—24no—
96C23×C3×C4—42no—
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2314yes—
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C22×#67—24no—
105C22×#67—24no—
106C22×#67—42no—
107C22×#67C2314yes—
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C22×C4×D3—24no—
116C22×C4×D3—24no—
117C22×C4×D3—42no—
118C22×C4×D3C2314yes—
119C3×C22⋊Q8—232no—
120C2×C3×C4⋊C4—24no—
121C2×C3×C4⋊C4—24no—
122C2×C3×C4⋊C4—24no—
123C2×C3×C4⋊C4C2314yes—
124C2×C3×C4⋊C4C2314yes—
125C2×C3×C4⋊C4C2314yes—
126C2×C3×C22⋊C4—24no—
127C2×C3×C22⋊C4D418yes—
128C2×C3×C22⋊C4C2314yes—
129C2×C3×C22⋊C4C2314yes—
130C2×#217—24no—
131C2×#217—24no—
132C2×#217—24no—
133C2×#217C2314yes—
134C2×#217C2314yes—
135C2×#217C2314yes—
136#946—232no—
137#929—232no—
138C2×(C2×D3)⋊C4—24no—
139C2×(C2×D3)⋊C4—24no—
140C2×(C2×D3)⋊C4—24no—
141C2×(C2×D3)⋊C4—24no—
142C2×(C2×D3)⋊C4D418yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×C4⋊Dic3—24no—
149C2×C4⋊Dic3—24no—
150C2×C4⋊Dic3C2314yes—
151C2×C4⋊Dic3C2314yes—
152C2×Dic3⋊C4—24no—
153C2×Dic3⋊C4—24no—
154C2×Dic3⋊C4—24no—
155C2×Dic3⋊C4—24no—
156C2×Dic3⋊C4—24no—
157C2×Dic3⋊C4—42no—
158C2×Dic3⋊C4—42no—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2314yes—
163C2×Dic3⋊C4C2314yes—
164C2×Dic3⋊C4C2314yes—
165C2×Dic3⋊C4C2314yes—
166C2×C4×Dic3—24no—
167C2×C4×Dic3C2314yes—
168#883—232no—
169C3⋊#95C2314yes—
170C3⋊#95C2314yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
175C3⋊#95C2314yes—
176C3⋊#95C2314yes—
177C23×Q8C2×D311yescharacteristic
178C23×D4—31no—
179C24×C4—31no—
180C24×C4C2×D311yescharacteristic
181C2×#123—38no—
182C2×#123—38no—
183C2×#123—68no—
184C2×#123—68no—
185C2×C22⋊Q8—28no—
186C2×C22⋊Q8—38no—
187C2×C22⋊Q8—68no—
188C2×C22⋊Q8C2×D318yescomplemented
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4C2×D311yescharacteristic
199C22×C4⋊C4C2×D311yescharacteristic
200C22×C4⋊C4C2×D311yescharacteristic
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C42—31no—
212#398—38no—
213#398—38no—
214#397—38no—
215#397—38no—
216#395—38no—
217#394—38no—
218#388—38no—
219#388—38no—
220#385—38no—
221#385—38no—
222#384—38no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C24×C3—22no—
232C24×C3—22no—
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3C2×D414yes—
238C24×C3C2412yes—
239C24×C3C2411yescharacteristic
240C23×D3—22no—
241C23×D3—22no—
242C23×D3—22no—
243C23×D3—22no—
244C23×D3—22no—
245C23×D3—22no—
246C23×D3C2×D414yes—
247C23×D3C2412yes—
248C2×C3×Q8—28no—
249C2×C3×Q8—28no—
250C2×C3×Q8—44no—
251C2×C3×Q8—416no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—28no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—28no—
269C22×C3×C4—44no—
270C22×C3×C4—416no—
271C22×C3×C4C2×D414yes—
272C22×C3×C4C2×D414yes—
273C22×C3×C4C2×D414yes—
274C22×C3×C4C2412yes—
275C22×C3×C4C2412yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C2×#67—28no—
281C2×#67—28no—
282C2×#67—44no—
283C2×#67—416no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—22no—
295C22×Dic3—22no—
296C22×Dic3—22no—
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—22no—
303C22×Dic3C2×D414yes—
304C22×Dic3#4114yes—
305C22×Dic3C2412yes—
306C22×Dic3C2412yes—
307C22×Dic3C2412yes—
308C22×Dic3C2412yes—
309C22×Dic3C2412yes—
310C22×Dic3C2412yes—
311C22×Dic3C2412yes—
312C2×C4×D3—28no—
313C2×C4×D3—28no—
314C2×C4×D3—44no—
315C2×C4×D3—416no—
316C3×C4⋊C4—28no—
317C3×C4⋊C4—28no—
318C3×C4⋊C4—28no—
319C3×C22⋊C4—28no—
320C3×C22⋊C4C2×D4116yes—
321#217—28no—
322#217—28no—
323#217—28no—
324(C2×D3)⋊C4—28no—
325(C2×D3)⋊C4—28no—
326(C2×D3)⋊C4—28no—
327(C2×D3)⋊C4—28no—
328(C2×D3)⋊C4C2×D4116yes—
329C4⋊Dic3—28no—
330C4⋊Dic3—28no—
331Dic3⋊C4—28no—
332Dic3⋊C4—28no—
333Dic3⋊C4—28no—
334Dic3⋊C4—28no—
335Dic3⋊C4—28no—
336Dic3⋊C4—44no—
337Dic3⋊C4—44no—
338C4×Dic3—28no—
339C25—31no—
340C25C22×D311yescharacteristic
341C22×Q8—24no—
342C22×Q8—24no—
343C22×Q8—42no—
344C22×Q8C22×D314yes—
345C22×D4—34no—
346C22×D4—64no—
347C22×D4—64no—
348C22×D4—122no—
349C23×C4—24no—
350C23×C4—24no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—34no—
359C23×C4—42no—
360C23×C4—64no—
361C23×C4—64no—
362C23×C4—122no—
363C23×C4C22×D311yescharacteristic
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D314yes—
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370#123—632no—
371#123—632no—
372C22⋊Q8—232no—
373C22⋊Q8—632no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—34no—
378C2×C4⋊C4—34no—
379C2×C4⋊C4—34no—
380C2×C4⋊C4—34no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—34no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—64no—
387C2×C4⋊C4—64no—
388C2×C4⋊C4—64no—
389C2×C4⋊C4—64no—
390C2×C4⋊C4—64no—
391C2×C4⋊C4—64no—
392C2×C4⋊C4—64no—
393C2×C4⋊C4—122no—
394C2×C4⋊C4—122no—
395C2×C4⋊C4C22×D314yes—
396C2×C4⋊C4C22×D314yes—
397C2×C4⋊C4C22×D314yes—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—38no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4—64no—
409C2×C22⋊C4—64no—
410C2×C22⋊C4—64no—
411C2×C22⋊C4—64no—
412C2×C22⋊C4—64no—
413C2×C22⋊C4—64no—
414C2×C22⋊C4—64no—
415C2×C22⋊C4#6718yes—
416C2×C22⋊C4C22×D314yes—
417C2×C22⋊C4C22×D314yes—
418C2×C42—34no—
419C2×C42—64no—
420#95—34no—
421#95—34no—
422#95—34no—
423#95—34no—
424#95—34no—
425#95—34no—
426#95—34no—
427#95—34no—
428C23×C3—28no—
429C23×C3—28no—
430C23×C3—28no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—44no—
438C23×C3—44no—
439C23×C3—44no—
440C23×C3—44no—
441C23×C3C22×D412yes—
442C23×C3C22×D414yes—
443C23×C3C22×D412yes—
444C23×C3C2×#4112yes—
445C23×C3H(5,𝔽2)12yes—
446C23×C32−1+412yes—
447C23×C32−1+412yes—
448C23×C32−1+412yes—
449C23×C3C2511yescharacteristic
450C22×D3—28no—
451C22×D3—28no—
452C22×D3—28no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—44no—
460C22×D3—44no—
461C22×D3—44no—
462C22×D3—44no—
463C22×D3C22×D414yes—
464C3×Q8—416no—
465C2×C3×C4—28no—
466C2×C3×C4—28no—
467C2×C3×C4—28no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—416no—
484C2×C3×C4—44no—
485C2×C3×C4—44no—
486C2×C3×C4—44no—
487C2×C3×C4C22×D414yes—
488C2×C3×C4C22×D414yes—
489C2×C3×C4C22×D414yes—
490#67—416no—
491C2×Dic3—28no—
492C2×Dic3—28no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—44no—
513C2×Dic3—44no—
514C2×Dic3—44no—
515C2×Dic3—44no—
516C2×Dic3—44no—
517C2×Dic3C22×D414yes—
518C2×Dic3C2×#4114yes—
519C4×D3—416no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—34no—
527C24—32no—
528C24—62no—
529C24—62no—
530C24—62no—
531C24—62no—
532C24—62no—
533C24—62no—
534C24C2×#6714yes—
535C24C23×D312yes—
536C24C23×D311yescharacteristic
537C2×Q8—28no—
538C2×Q8—28no—
539C2×Q8—44no—
540C2×Q8—416no—
541C2×D4—68no—
542C2×D4—68no—
543C2×D4—124no—
544C2×D4—1216no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—28no—
561C22×C4—28no—
562C22×C4—34no—
563C22×C4—34no—
564C22×C4—32no—
565C22×C4—32no—
566C22×C4—32no—
567C22×C4—32no—
568C22×C4—32no—
569C22×C4—32no—
570C22×C4—32no—
571C22×C4—44no—
572C22×C4—416no—
573C22×C4—68no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4—62no—
578C22×C4—62no—
579C22×C4—62no—
580C22×C4—62no—
581C22×C4—62no—
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—62no—
593C22×C4—68no—
594C22×C4—124no—
595C22×C4—1216no—
596C22×C4D3×D414yes—
597C22×C4C2×#6714yes—
598C22×C4C2×#6714yes—
599C22×C4C23×D312yes—
600C22×C4C23×D312yes—
601C22×C4C23×D312yes—
602C22×C4C23×D312yes—
603C22×C4C23×D312yes—
604C22×C4C23×D312yes—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—68no—
609C4⋊C4—68no—
610C4⋊C4—68no—
611C4⋊C4—68no—
612C4⋊C4—68no—
613C4⋊C4—68no—
614C4⋊C4—68no—
615C4⋊C4—124no—
616C4⋊C4—124no—
617C22⋊C4—28no—
618C22⋊C4—316no—
619C22⋊C4—68no—
620C22⋊C4—68no—
621C22⋊C4—68no—
622C22⋊C4—68no—
623C22⋊C4—68no—
624C22⋊C4—68no—
625C22⋊C4—68no—
626C22⋊C4C2×#67116yes—
627C42—68no—
628C22×C3—24no—
629C22×C3—24no—
630C22×C3—24no—
631C22×C3—42no—
632C22×C3—416no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3#53614yes—
637C22×C3#53614yes—
638C22×C3#53914yes—
639C22×C3D4214yes—
640C22×C3#54714yes—
641C22×C3#54714yes—
642C22×C3#56314yes—
643C22×C3C23×D411yescharacteristic
644C22×C3C23×D411yescharacteristic
645C22×C3C22×#4111yescharacteristic
646C22×C3C2×H(5,𝔽2)11yescharacteristic
647C22×C3C2×2−1+411yescharacteristic
648C22×C3C2×2−1+411yescharacteristic
649C22×C3C2×2−1+411yescharacteristic
650C2×D3—24no—
651C2×D3—24no—
652C2×D3—24no—
653C2×D3—42no—
654C2×D3—416no—
655C2×D3—42no—
656C2×D3—42no—
657C2×D3—42no—
658C3×C4—24no—
659C3×C4—24no—
660C3×C4—24no—
661C3×C4—42no—
662C3×C4—42no—
663C3×C4—42no—
664Dic3—24no—
665Dic3—24no—
666Dic3—42no—
667Dic3—42no—
668Dic3—42no—
669Dic3—42no—
670Dic3—42no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—28no—
678C23—28no—
679C23—28no—
680C23—34no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—62no—
686C23—62no—
687C23—62no—
688C23—62no—
689C23—62no—
690C23—62no—
691C23—68no—
692C23—68no—
693C23—68no—
694C23—124no—
695C23—124no—
696C23—124no—
697C23—124no—
698C23C2×D3×D412yes—
699C23#100412yes—
700C23#100712yes—
701C23#100712yes—
702C23D3×#4112yes—
703C23#101012yes—
704C23C22×#6714yes—
705C23C22×#6712yes—
706C23C24×D311yescharacteristic
707Q8—416no—
708D4—1216no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—34no—
728C2×C4—34no—
729C2×C4—416no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—68no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—68no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—1216no—
755C2×C4—124no—
756C2×C4—124no—
757C2×C4—124no—
758C2×C4—124no—
759C2×C4—124no—
760C2×C4C2×D3×D414yes—
761C2×C4C22×#6714yes—
762C2×C4C22×#6714yes—
763C2×C3—44no—
764C2×C3#268018yescomplemented
765C2×C3C2×#53611yescharacteristic
766C2×C3C2×#53611yescharacteristic
767C2×C3C2×#53911yescharacteristic
768C2×C3C2×D4211yescharacteristic
769C2×C3C2×#54711yescharacteristic
770C2×C3C2×#54711yescharacteristic
771C2×C3C2×#56311yescharacteristic
772D3—44no—
773C22—24no—
774C22—24no—
775C22—24no—
776C22—416no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—64no—
782C22—64no—
783C22—64no—
784C22—1216no—
785C22—122no—
786C22—122no—
787C22—122no—
788C22—122no—
789C22#562814yes—
790C22#563114yes—
791C22#563814yes—
792C22#564614yes—
793C22D4×#6714yes—
794C22#581614yes—
795C22#582414yes—
796C22C22×D3×D411yescharacteristic
797C22C2×#100411yescharacteristic
798C22C2×#100711yescharacteristic
799C22C2×#100711yescharacteristic
800C22C2×D3×#4111yescharacteristic
801C22C2×#101011yescharacteristic
802C22C23×#6711yescharacteristic
803C4—24no—
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—64no—
810C4—64no—
811C4—122no—
812C4—122no—
813C4—122no—
814C4—122no—
815C4—122no—
816C3C2×#268011yescharacteristic, complemented, Sylow
817C2—44no—
818C2—124no—
819C2#8282818yesdirect product factor
820C2C2×#564611yescharacteristic
821C2C2×#562811yescharacteristic
822C2C2×#563811yescharacteristic
823C2C2×#563111yescharacteristic
824C2C2×D4×#6711yescharacteristic
825C2C2×#581611yescharacteristic
826C2C2×#582411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC22×C3×C22⋊Q8C2
socleC24×C3C24
prime radicalC23×#67C22
hypercenterC22×C22⋊Q8D3
hypocenterC3C2×#2680
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
2. C22×#946C2semidirect
5. C2×#5230C2semidirect
6. C2×#5210C2semidirect
7. #82828C2direct (N × H)
8. C2×#4992C2semidirect
9. C2×#4989C2semidirect
10. C2×#4981C2semidirect
11. C2×#4982C2semidirect
12. C2×#4990C2semidirect
13. C2×#4975C2semidirect
15. C2×#4952C2semidirect
16. C2×#4951C2semidirect
23. C2×C3×C22⋊Q8C22semidirect
33. C2×#946C22semidirect
53. #5230C22semidirect
54. #5210C22semidirect
63. #4992C22semidirect
64. #4990C22semidirect
65. #4989C22semidirect
66. #4982C22semidirect
67. #4981C22semidirect
68. #4975C22semidirect
70. #4952C22semidirect
71. #4951C22semidirect
75. C22×C22⋊Q8D3semidirect
188. C2×C22⋊Q8C2×D3semidirect
764. C2×C3#2680semidirect
816. C3C2×#2680semidirect
819. C2#82828direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C22×#9462
C22×#9292
C22×#8832
C2×#52302
C2×#52102
#828282
C2×#49922
C2×#49892
C2×#49812
C2×#49822
C2×#49902
C2×#49752
C2×#49592
C2×#49522
C2×#49512
C2×#26803