Finite Group Databasebeta

← #6379360

Subgroups — #6379360

Order 512.

3313 conjugacy classes of subgroups.

The subgroup lattice has 787 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3501C211yesmaximal, characteristic
2#34212C212yesmaximal, complemented
3#22513C214yesmaximal, complemented
4#22513C218yesmaximal, complemented
5Q8×#99C214yesmaximal, complemented
6#21333C214yesmaximal, complemented
7C2×#1996C212yesmaximal, complemented
8#20633C212yesmaximal
9C2×#1799C211yesmaximal, characteristic
10#20392C212yesmaximal
11C2×C4×#99C211yesmaximal, characteristic
12#3501—24no—
13#3501—24no—
14#3501—24no—
15#3501—24no—
16C2×#554C412yescomplemented
17C2×#554C414yescomplemented
18C2×#554C2212yes—
19C2×#554C2214yes—
20C2×D4×Q8C412yescomplemented
21C2×D4×Q8C2212yes—
22C2×#544C412yescomplemented
23C2×#543C412yescomplemented
24C2×#543C2212yes—
25C2×#533C412yescomplemented
26C22×C22⋊Q8C412yescomplemented
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C2×#518C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×#99C2212yes—
32C22×#99C2211yescharacteristic
33C22×#99C2211yescharacteristic
34#2368—24no—
35#2360—24no—
36#2345C2214yescomplemented
37#2345C2218yescomplemented
38Q8×C22⋊C4C2214yescomplemented
39#2329—24no—
40#2315C2214yes—
41C4×C22⋊Q8—24no—
42C2×#380C2212yes—
43#2273C2214yes—
44C2×C4×C22⋊C4C2212yes—
45#1996C2218yescomplemented
46#1996C2218yescomplemented
47#1996C22116yescomplemented
48#1996C22116yescomplemented
49#1799C2214yes—
50#1799C2214yes—
51#1799C2218yes—
52#1799C2218yes—
53C4×#99C2214yes—
54C4×#99C2214yes—
55C4×#99C2218yes—
56C4×#99C2218yes—
57C2×#342C2214yes—
58C2×#342C2214yes—
59C2×#342C2212yes—
60C2×#342C2212yes—
61C23×Q8C2×C411yescharacteristic
62C23×Q8C2×C412yescomplemented
63C23×Q8C2311yescharacteristic
64C23×D4C2311yescharacteristic
65C24×C4C2×C411yescharacteristic
66C24×C4C2311yescharacteristic
67#554—28no—
68#554—28no—
69#554—216no—
70#554—216no—
71#554—216no—
72#554—28no—
73#554—28no—
74#554—216no—
75D4×Q8—28no—
76D4×Q8—28no—
77D4×Q8—28no—
78D4×Q8—28no—
79#544—28no—
80#544—28no—
81#543—28no—
82#543—28no—
83#543—28no—
84#543—28no—
85#533—24no—
86#533—24no—
87#533—24no—
88#533—24no—
89C2×C4⋊Q8C2×C412yescomplemented
90C2×C4⋊Q8C2×C412yescomplemented
91C2×C4⋊Q8C2×C414yescomplemented
92C2×C4⋊Q8C2×C414yescomplemented
93C2×#125C2×C414yescomplemented
94C2×#125C2×C414yescomplemented
95C2×#125C2×C414yescomplemented
96C2×C22⋊Q8—22no—
97C2×C22⋊Q8—22no—
98C2×C22⋊Q8—22no—
99C2×C22⋊Q8—22no—
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8C2×C412yes—
105C2×C22⋊Q8C2×C414yes—
106C2×C22⋊Q8C2×C412yes—
107C2×C22⋊Q8C2×C414yes—
108C2×C22⋊Q8C2×C414yes—
109C2×C22⋊Q8C2×C414yes—
110C2×C22⋊Q8C2×C412yes—
111C2×C22⋊Q8C2×C412yes—
112C2×C22⋊Q8C2×C412yes—
113C2×C22⋊Q8C2×C412yes—
114C2×C22⋊Q8C2×C412yescomplemented
115C2×C22⋊Q8C2×C412yescomplemented
116C2×C22⋊Q8C2×C414yescomplemented
117C2×C22⋊Q8C2×C414yescomplemented
118C2×C22⋊Q8C2×C414yescomplemented
119C2×C22⋊Q8C2×C414yescomplemented
120C2×C22⋊Q8C2×C414yescomplemented
121C2×C22⋊Q8D414yes—
122C2×C22⋊Q8D414yes—
123C2×C22⋊Q8D414yes—
124C2×C22⋊Q8D414yes—
125C2×C22⋊Q8C2312yes—
126C2×C22⋊Q8C2312yes—
127C2×C22⋊Q8C2314yes—
128C2×C22⋊Q8C2314yes—
129#518—28no—
130#518—28no—
131C2×C4×Q8—24no—
132C2×C4×Q8C2×C412yescomplemented
133C2×C4×Q8C2×C412yescomplemented
134C2×C4×Q8C2×C414yescomplemented
135C2×C4×D4—22no—
136C2×C4×D4—22no—
137C2×C4×D4—22no—
138C2×C4×D4—22no—
139C2×C4×D4C2×C412yes—
140C2×C4×D4C2×C412yes—
141C2×C4×D4C2×C414yes—
142C2×C4×D4C2×C414yes—
143C2×C4×D4C2312yes—
144C2×C4×D4C2312yes—
145C2×C4×D4C2314yes—
146C2×C4×D4C2314yes—
147C2×#117C2×C414yes—
148C22×C4⋊C4—22no—
149C22×C4⋊C4C2×C411yescharacteristic
150C22×C4⋊C4C2×C412yes—
151C22×C4⋊C4C2×C411yescharacteristic
152C22×C4⋊C4C2×C414yescomplemented
153C22×C4⋊C4C2×C412yescomplemented
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2311yescharacteristic
156C22×C22⋊C4C2×C411yescharacteristic
157C22×C22⋊C4C2×C414yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C42—22no—
165C22×C42C2×C411yescharacteristic
166C2×#99—28no—
167C2×#99—24no—
168C2×#99Q818yescomplemented
169C2×#99C2318yes—
170C2×#99C2314yes—
171C2×#99C2314yes—
172#391—28no—
173#391—24no—
174#389—28no—
175#389—24no—
176#387—28no—
177#387—28no—
178#387—28no—
179#385—28no—
180#385—28no—
181#380—22no—
182#380—22no—
183#380C2318yes—
184#380C2318yes—
185#380C2314yes—
186#380C2314yes—
187C4×C4⋊C4—24no—
188C4×C4⋊C4—28no—
189C4×C22⋊C4—22no—
190C4×C22⋊C4—22no—
191C4×C22⋊C4—28no—
192C4×C22⋊C4—28no—
193C4×C22⋊C4C2314yes—
194C4×C22⋊C4C2318yes—
195C4×C22⋊C4C2314yes—
196C4×C22⋊C4C2318yes—
197C2×#95—22no—
198C2×#95—22no—
199#342C2318yes—
200#342C23116yes—
201#342C23116yes—
202#342C2318yes—
203C25C22×C411yescharacteristic
204C25C2411yescharacteristic
205C22×Q8—24no—
206C22×Q8—24no—
207C22×Q8—22no—
208C22×Q8—22no—
209C22×Q8—82no—
210C22×Q8—82no—
211C22×Q8—84no—
212C22×Q8C22×C412yes—
213C22×Q8C22×C414yes—
214C22×Q8C22×C414yes—
215C22×Q8C22×C412yes—
216C22×Q8C22×C412yes—
217C22×Q8C22×C412yes—
218C22×Q8C2×D414yes—
219C22×Q8C2×D414yes—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—24no—
223C22×D4C22×C412yes—
224C22×D4C2×Q814yes—
225C22×D4#4114yes—
226C22×D4C2412yes—
227C23×C4—22no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—24no—
233C23×C4—22no—
234C23×C4—82no—
235C23×C4—82no—
236C23×C4C22×C411yescharacteristic
237C23×C4C22×C412yes—
238C23×C4C22×C411yescharacteristic
239C23×C4C22×C414yes—
240C23×C4C22×C414yes—
241C23×C4C22×C412yes—
242C23×C4C22×C412yes—
243C23×C4C22×C411yescharacteristic
244C23×C4C22×C412yes—
245C23×C4C22×C411yescharacteristic
246C23×C4C22×C411yescharacteristic
247C23×C4C22×C411yescharacteristic
248C23×C4C22×C411yescharacteristic
249C23×C4C2×D412yes—
250C23×C4C2×D412yes—
251C23×C4C2×D412yes—
252C23×C4C2×D412yes—
253C23×C4C2411yescharacteristic
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2411yescharacteristic
257C4⋊Q8—24no—
258C4⋊Q8—24no—
259C4⋊Q8—216no—
260C4⋊Q8—24no—
261C4⋊Q8—24no—
262C4⋊Q8—216no—
263#125—28no—
264#125—28no—
265#125—216no—
266#125—216no—
267C22⋊Q8—24no—
268C22⋊Q8—24no—
269C22⋊Q8—216no—
270C22⋊Q8—22no—
271C22⋊Q8—22no—
272C22⋊Q8—22no—
273C22⋊Q8—22no—
274C22⋊Q8—24no—
275C22⋊Q8—24no—
276C22⋊Q8—24no—
277C22⋊Q8—24no—
278C22⋊Q8—24no—
279C22⋊Q8—24no—
280C22⋊Q8—216no—
281C22⋊Q8—216no—
282C22⋊Q8—24no—
283C22⋊Q8—24no—
284C22⋊Q8—28no—
285C22⋊Q8—28no—
286C22⋊Q8—216no—
287C22⋊Q8—216no—
288C22⋊Q8—216no—
289C22⋊Q8—28no—
290C22⋊Q8—28no—
291C22⋊Q8—28no—
292C22⋊Q8—28no—
293C22⋊Q8—216no—
294C22⋊Q8—216no—
295C22⋊Q8C22⋊C414yes—
296C22⋊Q8C22⋊C414yes—
297C22⋊Q8C22⋊C414yes—
298C22⋊Q8C22⋊C414yes—
299C22⋊Q8C22⋊C418yes—
300C22⋊Q8C22⋊C418yes—
301C22⋊Q8C22⋊C418yes—
302C22⋊Q8C22⋊C418yes—
303C22⋊Q8C22⋊C418yes—
304C22⋊Q8C22⋊C418yes—
305C4×Q8—24no—
306C4×Q8—24no—
307C4×Q8—24no—
308C4×Q8—24no—
309C4×Q8—28no—
310C4×Q8—28no—
311C4×Q8—88no—
312C4×D4—24no—
313C4×D4—24no—
314C4×D4—24no—
315C4×D4—24no—
316C4×D4—24no—
317C4×D4—24no—
318C4×D4—24no—
319C4×D4—24no—
320C4×D4—216no—
321C4×D4—216no—
322C4×D4—216no—
323C4×D4—216no—
324#117—28no—
325#117—28no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—84no—
341C2×C4⋊C4C22×C414yes—
342C2×C4⋊C4C22×C412yes—
343C2×C4⋊C4C22×C412yes—
344C2×C4⋊C4C22×C412yes—
345C2×C4⋊C4C22×C412yes—
346C2×C4⋊C4C22×C414yes—
347C2×C4⋊C4C22×C414yes—
348C2×C4⋊C4C22×C414yes—
349C2×C4⋊C4C22×C414yes—
350C2×C4⋊C4C22×C414yes—
351C2×C4⋊C4C22×C414yes—
352C2×C4⋊C4C22×C414yes—
353C2×C4⋊C4C22×C414yes—
354C2×C4⋊C4C22×C414yes—
355C2×C4⋊C4C22×C414yes—
356C2×C4⋊C4C22×C412yes—
357C2×C4⋊C4C22×C412yes—
358C2×C4⋊C4C22×C414yes—
359C2×C4⋊C4C2×D418yes—
360C2×C4⋊C4C2×D414yes—
361C2×C4⋊C4C2×D414yes—
362C2×C4⋊C4C2×D418yes—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4C22×C414yes—
380C2×C22⋊C4C22×C412yes—
381C2×C22⋊C4C22×C412yes—
382C2×C22⋊C4C22×C414yes—
383C2×C22⋊C4C22×C414yes—
384C2×C22⋊C4C22×C412yes—
385C2×C22⋊C4C22×C414yes—
386C2×C22⋊C4C22×C414yes—
387C2×C22⋊C4C2×D418yes—
388C2×C22⋊C4C2×D418yes—
389C2×C22⋊C4C2×Q818yescomplemented
390C2×C22⋊C4C2414yes—
391C2×C22⋊C4C2418yes—
392C2×C22⋊C4C2412yes—
393C2×C22⋊C4C2414yes—
394C2×C22⋊C4C2414yes—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—24no—
400C2×C42—28no—
401C2×C42—28no—
402C2×C42—24no—
403C2×C42—84no—
404C2×C42C22×C414yes—
405C2×C42C22×C414yes—
406C2×C42C22×C412yes—
407C2×C42C22×C412yes—
408#99—216no—
409#99—28no—
410#99C2×Q8116yescomplemented
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—28no—
416#95—28no—
417#95—28no—
418#95—28no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—81no—
423C24—81no—
424C24—81no—
425C24—81no—
426C24C4×Q814yescomplemented
427C24C23×C412yes—
428C24C23×C411yescharacteristic
429C24C23×C411yescharacteristic
430C24C22×D412yes—
431C24C22×D412yes—
432C24C22×Q812yes—
433C24C2×#4112yes—
434C242−1+414yes—
435C24C2511yescharacteristic
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—28no—
439C2×Q8—24no—
440C2×Q8—28no—
441C2×Q8—48no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—84no—
445C2×Q8—82no—
446C2×Q8—84no—
447C2×Q8—82no—
448C2×Q8—84no—
449C2×Q8—84no—
450C2×Q8—88no—
451C2×Q8—84no—
452C2×Q8—88no—
453C2×Q8C2×C22⋊C414yes—
454C2×Q8C2×C22⋊C414yes—
455C2×Q8C2×C22⋊C418yes—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—28no—
459C2×D4—28no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—24no—
463C2×D4—24no—
464C2×D4C4×Q818yescomplemented
465C2×D4C22×Q814yes—
466C2×D4C2×#4114yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—28no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—28no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—48no—
494C22×C4—82no—
495C22×C4—82no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4—82no—
499C22×C4—82no—
500C22×C4—81no—
501C22×C4—82no—
502C22×C4—82no—
503C22×C4—82no—
504C22×C4—82no—
505C22×C4—82no—
506C22×C4—82no—
507C22×C4—82no—
508C22×C4—82no—
509C22×C4—82no—
510C22×C4—81no—
511C22×C4—84no—
512C22×C4—82no—
513C22×C4—81no—
514C22×C4—84no—
515C22×C4—82no—
516C22×C4—84no—
517C22×C4—84no—
518C22×C4C2×C22⋊C411yescharacteristic
519C22×C4C2×C22⋊C411yescharacteristic
520C22×C4C2×C22⋊C412yes—
521C22×C4C2×C22⋊C411yescharacteristic
522C22×C4C2×C22⋊C411yescharacteristic
523C22×C4C2×C22⋊C412yes—
524C22×C4C2×C22⋊C412yes—
525C22×C4C2×C22⋊C412yes—
526C22×C4C2×C22⋊C412yes—
527C22×C4C2×C22⋊C412yes—
528C22×C4C4×Q814yescomplemented
529C22×C4C23×C411yescharacteristic
530C22×C4C23×C412yes—
531C22×C4C23×C412yes—
532C22×C4C23×C414yes—
533C22×C4C23×C414yes—
534C22×C4C23×C412yes—
535C22×C4C23×C411yescharacteristic
536C22×C4C23×C414yes—
537C22×C4C23×C414yes—
538C22×C4C23×C411yescharacteristic
539C22×C4C23×C411yescharacteristic
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D418yes—
544C22×C4C22×D418yes—
545C22×C4C22×D412yes—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—28no—
554C4⋊C4—28no—
555C4⋊C4—28no—
556C4⋊C4—28no—
557C4⋊C4—28no—
558C4⋊C4—28no—
559C4⋊C4—28no—
560C4⋊C4—28no—
561C4⋊C4—28no—
562C4⋊C4—48no—
563C4⋊C4—88no—
564C4⋊C4—84no—
565C4⋊C4—88no—
566C4⋊C4C2×C22⋊C418yes—
567C4⋊C4C2×C22⋊C418yes—
568C4⋊C4C2×C22⋊C414yes—
569C4⋊C4C2×C22⋊C414yes—
570C4⋊C4C2×C22⋊C418yes—
571C4⋊C4C2×C22⋊C4116yes—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—28no—
576C22⋊C4—24no—
577C22⋊C4—28no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—28no—
582C22⋊C4—28no—
583C22⋊C4—24no—
584C22⋊C4—28no—
585C22⋊C4—24no—
586C22⋊C4—28no—
587C22⋊C4—48no—
588C22⋊C4—44no—
589C22⋊C4C2×C22⋊C418yes—
590C22⋊C4C2×C22⋊C418yes—
591C22⋊C4C2×C22⋊C4116yes—
592C22⋊C4C22×Q818yes—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—28no—
598C42—28no—
599C42—48no—
600C42—88no—
601C42—84no—
602C42—88no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—41no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—42no—
614C23—42no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—81no—
620C23—81no—
621C23—81no—
622C23—81no—
623C23—82no—
624C23—82no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23C22×C22⋊C411yescharacteristic
629C23C22×C22⋊C411yescharacteristic
630C23C22×C22⋊C412yes—
631C23C2×C4×Q814yes—
632C23C2×C4×Q812yes—
633C23C2×C4×Q812yes—
634C23#51912yes—
635C23#51912yes—
636C23#54814yes—
637C23#54814yes—
638C23D4×Q814yes—
639C23D4×Q814yes—
640C23C24×C411yescharacteristic
641C23C23×D412yes—
642C23C23×Q811yescharacteristic
643C23C22×#4111yescharacteristic
644C23C2×2−1+412yes—
645Q8—28no—
646Q8—44no—
647Q8—48no—
648Q8—44no—
649Q8—44no—
650Q8—88no—
651Q8—84no—
652Q8—88no—
653D4—216no—
654D4—28no—
655D4—28no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—28no—
670C2×C4—42no—
671C2×C4—48no—
672C2×C4—48no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—42no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—48no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—48no—
701C2×C4—88no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—88no—
705C2×C4—84no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—84no—
711C2×C4—88no—
712C2×C4—88no—
713C2×C4—168no—
714C2×C4C22×C22⋊C411yescharacteristic
715C2×C4C22×C22⋊C411yescharacteristic
716C2×C4C22×C22⋊C411yescharacteristic
717C2×C4C22×C22⋊C418yes—
718C2×C4C22×C22⋊C418yes—
719C2×C4C22×C22⋊C412yes—
720C2×C4C22×C22⋊C412yes—
721C2×C4C22×C22⋊C411yescharacteristic
722C2×C4C2×C4×Q814yes—
723C22—22no—
724C22—21no—
725C22—22no—
726C22—21no—
727C22—21no—
728C22—22no—
729C22—21no—
730C22—22no—
731C22—21no—
732C22—21no—
733C22—24no—
734C22—44no—
735C22—44no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—44no—
742C22—41no—
743C22—41no—
744C22—42no—
745C22—44no—
746C22—44no—
747C22—42no—
748C22—42no—
749C22—84no—
750C22—84no—
751C22Q8×C22⋊C412yes—
752C22Q8×C22⋊C412yes—
753C22Q8×C22⋊C414yes—
754C22C23×C22⋊C411yescharacteristic
755C22C22×C4×Q811yescharacteristic
756C22C2×#51911yescharacteristic
757C22C2×#54812yes—
758C22C2×D4×Q812yes—
759C4—24no—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—22no—
764C4—22no—
765C4—28no—
766C4—28no—
767C4—48no—
768C4—42no—
769C4—44no—
770C4—44no—
771C4—42no—
772C4—84no—
773C4—88no—
774C4#288312yes—
775C2—22no—
776C2—22no—
777C2—21no—
778C2—21no—
779C2—22no—
780C2—22no—
781C2—24no—
782C2—44no—
783C2C2×Q8×C22⋊C411yescharacteristic
784C2C2×#288311yescharacteristic
785C2#6007011yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C22⋊Q8 ◁ G
LECSG ▷ C24 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34212C2semidirect
3. #22513C2semidirect
4. #22513C2semidirect
5. Q8×#99C2semidirect
6. #21333C2semidirect
7. C2×#1996C2semidirect
16. C2×#554C4semidirect
17. C2×#554C4semidirect
20. C2×D4×Q8C4semidirect
22. C2×#544C4semidirect
23. C2×#543C4semidirect
25. C2×#533C4semidirect
26. C22×C22⋊Q8C4semidirect
36. #2345C22semidirect
37. #2345C22semidirect
38. Q8×C22⋊C4C22semidirect
45. #1996C22semidirect
46. #1996C22semidirect
47. #1996C22semidirect
48. #1996C22semidirect
62. C23×Q8C2×C4semidirect
89. C2×C4⋊Q8C2×C4semidirect
90. C2×C4⋊Q8C2×C4semidirect
91. C2×C4⋊Q8C2×C4semidirect
92. C2×C4⋊Q8C2×C4semidirect
93. C2×#125C2×C4semidirect
94. C2×#125C2×C4semidirect
95. C2×#125C2×C4semidirect
114. C2×C22⋊Q8C2×C4semidirect
115. C2×C22⋊Q8C2×C4semidirect
116. C2×C22⋊Q8C2×C4semidirect
117. C2×C22⋊Q8C2×C4semidirect
118. C2×C22⋊Q8C2×C4semidirect
119. C2×C22⋊Q8C2×C4semidirect
120. C2×C22⋊Q8C2×C4semidirect
132. C2×C4×Q8C2×C4semidirect
133. C2×C4×Q8C2×C4semidirect
134. C2×C4×Q8C2×C4semidirect
152. C22×C4⋊C4C2×C4semidirect
153. C22×C4⋊C4C2×C4semidirect
168. C2×#99Q8semidirect
389. C2×C22⋊C4C2×Q8semidirect
410. #99C2×Q8semidirect
426. C24C4×Q8semidirect
464. C2×D4C4×Q8semidirect
528. C22×C4C4×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#35012
#342122
#225132
Q8×#992
#213332
C2×#19962
#206332
C2×#17992
#203922
C2×C4×#992