Finite Group Databasebeta

← C2×#14538006 #17900665

Subgroups — C2×#14538006 #17900665

Order 4352.

5130 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#63252C211yesmaximal, characteristic, complemented
2C22×#10587590C212yesmaximal, complemented
3C2×#11763320C211yesmaximal, characteristic, complemented
4#14538006C2116yesmaximal, direct product factor
5C2×#11762973C212yesmaximal, complemented
6C2×#11762956C212yesmaximal, complemented
7C2×#11762967C211yesmaximal, characteristic, complemented
8C2×#11762950C211yesmaximal, characteristic, complemented
9C2×#11762962C211yesmaximal, characteristic, complemented
10C2×#11762945C211yesmaximal, characteristic, complemented
11C2×#11762806C212yesmaximal, complemented
12C22×C17×C22⋊C8C211yesmaximal, characteristic, complemented
13C22×#63252—21no—
14C22×#63252—21no—
15C22×#63252—24no—
16C22×#63252—216no—
17C22×#63252C2212yes—
18C22×#63252C2212yes—
19C22×#63252C2218yescomplemented
20C22×#63252C2211yescharacteristic, complemented
21C23×Dic34C2211yescharacteristic
22C23×D68C2211yescharacteristic
23C23×C22⋊D17—21no—
24C23×C4×D17—21no—
25C2×#10587590—216no—
26C2×#10587590C22116yescomplemented
27C22×Dic68C2212yescomplemented
28C22×#63219C2212yescomplemented
29C22×#63219C2212yescomplemented
30C22×D136C2212yescomplemented
31#11763320—24no—
32#11763320C2218yescomplemented
33C2×#10587615—21no—
34C2×#10587610C2211yescharacteristic
35C2×#10587610C2211yescharacteristic, complemented
36C2×#10587616C2211yescharacteristic
37C2×#10587616C2211yescharacteristic, complemented
38C2×#10587639—21no—
39C2×C4×C22⋊D17—21no—
40C2×C4×C22⋊D17—21no—
41C2×#10587612C2211yescharacteristic, complemented
42#11762973C22116yescomplemented
43#11762967C2218yescomplemented
44#11762962C2218yescomplemented
45#11762956C22116yescomplemented
46#11762950C2218yescomplemented
47#11762945C2218yescomplemented
48#11762806C22116yescomplemented
49C2×#10587487C2212yescomplemented
50C2×#10587487C2212yescomplemented
51C2×#10587492C2212yescomplemented
52C2×#10587492C2212yescomplemented
53C24×C4×C17C2211yescharacteristic
54C23×C8×C17C2212yescomplemented
55C2×C17×C22⋊C8C2211yescharacteristic
56C2×C17×C22⋊C8C2211yescharacteristic
57C2×C17×C22⋊C8C2212yescomplemented
58C2×C17×C22⋊C8C2218yescomplemented
59C25×C17D411yescharacteristic
60C24×D17—21no—
61C23×C4×C17—28no—
62C23×C4×C17D411yescharacteristic
63C23×C4×C17D411yescharacteristic
64C23×C4×C17D411yescharacteristic
65C23×C4×C17D414yes—
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2314yes—
69C23×C4×C17C2311yescharacteristic
70C22×C22⋊D17—216no—
71C22×C22⋊D17—22no—
72C22×C22⋊D17—22no—
73C22×C22⋊D17—28no—
74C22×C22⋊D17—21no—
75C22×C22⋊D17—21no—
76C22×C22⋊D17—21no—
77C23×Dic17—21no—
78C2×#63252—216no—
79C2×#63252—264no—
80C2×#63252—216no—
81C2×#63252—28no—
82C2×#63252—24no—
83C2×#63252—24no—
84C2×#63252—28no—
85C2×#63252—28no—
86C2×#63252—264no—
87C2×#63252—22no—
88C2×#63252—28no—
89C2×#63252—28no—
90C2×#63252—28no—
91C2×#63252D4116yescomplemented
92C2×#63252C2318yes—
93C2×#63252C2318yes—
94C2×#63252C2314yescomplemented
95C22×D68—21no—
96C22×D68—22no—
97C22×D68—28no—
98C22×D68C2314yes—
99C22×D68C2311yescharacteristic
100C22×D68C2312yes—
101C22×C4×D17—216no—
102C22×C4×D17—22no—
103C22×C4×D17—22no—
104C22×C4×D17—28no—
105C22×C4×D17—21no—
106C22×Dic34—21no—
107C22×Dic34—22no—
108C22×Dic34—28no—
109C22×Dic34C2314yes—
110C22×Dic34C2311yescharacteristic
111C22×Dic34C2312yes—
112C22×C8×C17—28no—
113C22×C8×C17C2312yes—
114C22×C8×C17C2312yes—
115C22×C8×C17C2318yescomplemented
116#10587639—28no—
117C2×C22⋊Dic17—21no—
118C2×C22⋊Dic17—21no—
119C2×C22⋊Dic17—21no—
120#10587616—22no—
121#10587616—22no—
122#10587616C2314yes—
123#10587616C2314yescomplemented
124#10587615—28no—
125C4×C22⋊D17—28no—
126C4×C22⋊D17—28no—
127C2×#63227—21no—
128C2×#63227—21no—
129#10587612—22no—
130#10587612C2314yescomplemented
131C2×C4⋊Dic17C2311yescharacteristic
132C2×C4⋊Dic17C2311yescharacteristic
133#10587610—22no—
134#10587610—22no—
135#10587610C2314yes—
136#10587610C2314yescomplemented
137C2×#63225—21no—
138C2×#63225—21no—
139C2×C4×Dic17—21no—
140C2×Dic68—28no—
141C2×Dic68C2318yescomplemented
142#10587590—264no—
143C2×D136—28no—
144C2×D136C2318yescomplemented
145C2×#63219—28no—
146C2×#63219—28no—
147C2×#63219C2318yescomplemented
148C2×#63219C2318yescomplemented
149C17×C22⋊C8C2314yes—
150C17×C22⋊C8C2314yes—
151C17×C22⋊C8C2318yescomplemented
152#10587492C2318yescomplemented
153#10587492C2318yescomplemented
154#10587487C2318yescomplemented
155#10587487C2318yescomplemented
156C24×C17—24no—
157C24×C17—24no—
158C24×C17—42no—
159C24×C17C2×D411yescharacteristic
160C24×C17C2×D414yes—
161C24×C17C2×D411yescharacteristic
162C24×C17C2×D411yescharacteristic
163C23×D17—28no—
164C23×D17—24no—
165C23×D17—22no—
166C23×D17—21no—
167C23×D17—44no—
168C23×D17—44no—
169C22×C4×C17—24no—
170C22×C4×C17—24no—
171C22×C4×C17—24no—
172C22×C4×C17—216no—
173C22×C4×C17—24no—
174C22×C4×C17—24no—
175C22×C4×C17—216no—
176C22×C4×C17C2×D411yescharacteristic
177C22×C4×C17C2×D412yes—
178C22×C4×C17C2×D411yescharacteristic
179C22×C4×C17C2×D414yes—
180C22×C4×C17C2×D412yes—
181C22×C4×C17C2×D414yes—
182C22×C4×C17C2×D414yes—
183C22×C4×C17C2×D412yes—
184C22×C4×C17C2×D411yescharacteristic
185C22×C4×C17C2×D418yes—
186C22×C4×C17C2412yes—
187C22×C4×C17C2412yes—
188C22×C4×C17C2411yescharacteristic
189C22×C4×C17C2412yes—
190C2×C22⋊D17—264no—
191C2×C22⋊D17—216no—
192C2×C22⋊D17—216no—
193C2×C22⋊D17—28no—
194C2×C22⋊D17—28no—
195C2×C22⋊D17—24no—
196C2×C22⋊D17—24no—
197C2×C22⋊D17—24no—
198C2×C22⋊D17—44no—
199C2×C22⋊D17—44no—
200C2×C22⋊D17—44no—
201C22×Dic17—28no—
202C22×Dic17—24no—
203C22×Dic17—22no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207#63252—264no—
208#63252—264no—
209#63252—232no—
210#63252—232no—
211#63252—216no—
212#63252—216no—
213#63252—216no—
214#63252—216no—
215#63252—48no—
216#63252C2×D4132yescomplemented
217C2×D68—28no—
218C2×D68—216no—
219C2×D68—24no—
220C2×D68—22no—
221C2×D68—24no—
222C2×D68—216no—
223C2×D68—24no—
224C2×D68—21no—
225C2×D68C2×D418yes—
226C2×D68C2412yes—
227C2×D68C2414yes—
228C2×C4×D17—216no—
229C2×C4×D17—264no—
230C2×C4×D17—216no—
231C2×C4×D17—28no—
232C2×C4×D17—28no—
233C2×C4×D17—24no—
234C2×C4×D17—44no—
235C2×Dic34—28no—
236C2×Dic34—216no—
237C2×Dic34—24no—
238C2×Dic34—22no—
239C2×Dic34—24no—
240C2×Dic34—216no—
241C2×Dic34—24no—
242C2×Dic34—21no—
243C2×Dic34C2×D418yes—
244C2×Dic34C2412yes—
245C2×Dic34C2414yes—
246C2×C8×C17—24no—
247C2×C8×C17—24no—
248C2×C8×C17—216no—
249C2×C8×C17C2414yes—
250C2×C8×C17C2414yes—
251C22⋊Dic17—24no—
252C22⋊Dic17—24no—
253C22⋊Dic17—24no—
254#63227—24no—
255#63227—24no—
256C4⋊Dic17—21no—
257C4⋊Dic17—21no—
258C4⋊Dic17C2412yes—
259C4⋊Dic17C2412yes—
260#63225—24no—
261#63225—24no—
262C4×Dic17—24no—
263Dic68—216no—
264D136—216no—
265#63219—216no—
266#63219—216no—
267C2×#3002—171nomaximal, Sylow
268C23×C17—22no—
269C23×C17—22no—
270C23×C17—22no—
271C23×C17—22no—
272C23×C17—28no—
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—28no—
276C23×C17—22no—
277C23×C17—44no—
278C23×C17—416no—
279C23×C17#12014yes—
280C23×C17#13514yescomplemented
281C23×C17C22×D412yes—
282C23×C17C22×D412yes—
283C23×C17C22×D412yes—
284C23×C17C22×D411yescharacteristic
285C22×D17—216no—
286C22×D17—28no—
287C22×D17—24no—
288C22×D17—22no—
289C22×D17—432no—
290C22×D17—48no—
291C22×D17—44no—
292C22×D17—48no—
293C22×D17—44no—
294C22×D17—42no—
295C22×D17—42no—
296C22×D17—42no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—28no—
300C2×C4×C17—24no—
301C2×C4×C17—28no—
302C2×C4×C17—28no—
303C2×C4×C17—24no—
304C2×C4×C17—24no—
305C2×C4×C17—24no—
306C2×C4×C17#12014yes—
307C2×C4×C17#12018yes—
308C2×C4×C17C22×D412yes—
309C2×C4×C17C22×D412yes—
310C2×C4×C17C22×D411yescharacteristic
311C2×C4×C17C22×D412yes—
312C2×C4×C17C22×D414yes—
313C2×C4×C17C22×D418yes—
314C2×C4×C17C2511yescharacteristic
315C22⋊D17—232no—
316C22⋊D17—232no—
317C22⋊D17—48no—
318C22⋊D17—48no—
319C22⋊D17—48no—
320C2×Dic17—216no—
321C2×Dic17—28no—
322C2×Dic17—24no—
323C2×Dic17—22no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—42no—
327C2×Dic17—42no—
328C2×Dic17—42no—
329D68—216no—
330D68—28no—
331D68—24no—
332D68—24no—
333D68—42no—
334D68C22×D418yes—
335C4×D17—232no—
336C4×D17—232no—
337C4×D17—48no—
338Dic34—216no—
339Dic34—28no—
340Dic34—24no—
341Dic34—24no—
342Dic34—42no—
343Dic34C22×D418yes—
344C8×C17—24no—
345C8×C17—24no—
346C23×#41—171no—
347C22×#135—172no—
348C2×#525—171no—
349#3002—1716no—
350C2×#452—172no—
351C2×#449—172no—
352C2×#451—171no—
353C2×#448—171no—
354C2×#450—171no—
355C2×#447—171no—
356C2×#416—172no—
357C22×C22⋊C8D1711yescharacteristic, complemented
358C22×C17—22no—
359C22×C17—28no—
360C22×C17—28no—
361C22×C17—22no—
362C22×C17—22no—
363C22×C17—22no—
364C22×C17—22no—
365C22×C17—22no—
366C22×C17—22no—
367C22×C17—416no—
368C22×C17—44no—
369C22×C17C2×#12014yes—
370C22×C17C2×#12012yes—
371C22×C17C2×#13512yes—
372C22×C17C2×#13514yescomplemented
373C22×C17#57512yes—
374C22×C17C23×D411yescharacteristic
375C2×D17—28no—
376C2×D17—432no—
377C2×D17—416no—
378C2×D17—44no—
379C2×D17—44no—
380C2×D17—42no—
381C2×D17—42no—
382C2×D17—42no—
383C2×D17—84no—
384C4×C17—22no—
385C4×C17—22no—
386C4×C17C2×#12012yes—
387C4×C17C2×#12014yes—
388C4×C17C23×D412yes—
389Dic17—28no—
390Dic17—42no—
391Dic17—42no—
392Dic17—42no—
393C22×#41—172no—
394C22×#41—172no—
395C22×#41—178no—
396C22×#41—171no—
397C22×#41—3416no—
398C22×#41—341no—
399C22×#41—344no—
400C22×#41—341no—
401C23×Q8—171no—
402C23×D4—171no—
403C23×D4—341no—
404C24×C4—341no—
405C24×C4C2×D1711yescharacteristic
406C2×#135—1716no—
407C2×#135—3416no—
408C22×Q16—172no—
409C22×SD16—172no—
410C22×SD16—172no—
411C22×D8—172no—
412C23×C8C2×D1712yescomplemented
413#525—178no—
414#525—344no—
415C2×#123—341no—
416C2×C22⋊Q8—171no—
417C2×C22⋊Q8—171no—
418C2×#121—171no—
419C2×#121—171no—
420C2×#120—341no—
421C2×C4×D4—341no—
422C2×C4×D4—341no—
423C2×#117—171no—
424#452—1716no—
425#451—178no—
426#450—178no—
427#449—1716no—
428#448—178no—
429#447—178no—
430#416—1716no—
431C2×#103—172no—
432C2×#103—172no—
433C2×#102—172no—
434C2×#102—172no—
435C2×C22⋊C8C2×D1711yescharacteristic
436C2×C22⋊C8C2×D1711yescharacteristic
437C2×C22⋊C8C2×D1718yescomplemented
438C2×C22⋊C8C2×D1712yescomplemented
439C2×C17—24no—
440C2×C17—24no—
441C2×C17—42no—
442C2×C17#300214yescomplemented
443C2×C17C22×#12011yescharacteristic
444C2×C17C22×#13511yescharacteristic
445C2×C17C2×#57511yescharacteristic
446D17—48no—
447D17—82no—
448C25—341no—
449C25D6811yescharacteristic
450C2×#41—1716no—
451C2×#41—178no—
452C2×#41—174no—
453C2×#41—178no—
454C2×#41—348no—
455C2×#41—348no—
456C2×#41—3464no—
457C2×#41—3416no—
458C2×#41—3464no—
459C2×#41—3416no—
460C2×#41—348no—
461C2×#41—344no—
462C2×#41—348no—
463C2×#41—344no—
464C2×#41—342no—
465C2×#41—348no—
466C2×#41—348no—
467C22×Q8—172no—
468C22×Q8—171no—
469C22×Q8—174no—
470C22×Q8—348no—
471C22×Q8—341no—
472C22×Q8—342no—
473C22×D4—172no—
474C22×D4—171no—
475C22×D4—174no—
476C22×D4—348no—
477C22×D4—3416no—
478C22×D4—342no—
479C22×D4—348no—
480C22×D4—342no—
481C22×D4—341no—
482C22×D4—341no—
483C22×D4—341no—
484C22×D4—341no—
485C22×D4—342no—
486C23×C4—28no—
487C23×C4—3416no—
488C23×C4—341no—
489C23×C4—342no—
490C23×C4—348no—
491C23×C4—342no—
492C23×C4—341no—
493C23×C4D6811yescharacteristic
494C23×C4D6814yes—
495C23×C4D6811yescharacteristic
496C23×C4D6811yescharacteristic
497C23×C4C22×D1711yescharacteristic
498C23×C4C22×D1711yescharacteristic
499C23×C4C22×D1714yes—
500C23×C4C22×D1711yescharacteristic
501#135—3464no—
502C2×Q16—178no—
503C2×Q16—348no—
504C2×SD16—178no—
505C2×SD16—178no—
506C2×SD16—348no—
507C2×SD16—348no—
508C2×D8—178no—
509C2×D8—348no—
510C22×C8—28no—
511C22×C8C22×D1712yes—
512C22×C8C22×D1712yes—
513C22×C8C22×D1718yescomplemented
514#123—348no—
515C22⋊Q8—174no—
516C22⋊Q8—174no—
517C22⋊Q8—342no—
518C22⋊Q8—342no—
519#121—174no—
520#121—174no—
521#121—342no—
522#121—342no—
523#120—348no—
524C4×D4—348no—
525C4×D4—348no—
526#117—174no—
527#117—342no—
528C2×C4⋊C4—171no—
529C2×C4⋊C4—171no—
530C2×C4⋊C4—341no—
531C2×C4⋊C4—341no—
532C2×C22⋊C4—341no—
533C2×C22⋊C4—341no—
534C2×C22⋊C4—341no—
535C2×C22⋊C4—341no—
536C2×C22⋊C4—341no—
537C2×C42—341no—
538#103—178no—
539#103—178no—
540#102—178no—
541#102—178no—
542C22⋊C8C22×D1714yes—
543C22⋊C8C22×D1714yes—
544C22⋊C8C22×D1718yescomplemented
545C17C2×#300211yescharacteristic, complemented, Sylow
546C24—24no—
547C24—24no—
548C24—42no—
549C24—348no—
550C24—344no—
551C24—342no—
552C24—341no—
553C24—684no—
554C24—684no—
555C24C2×D6811yescharacteristic
556C24C2×D6814yes—
557C24C2×D6811yescharacteristic
558C24C2×D6811yescharacteristic
559#41—1732no—
560#41—3416no—
561#41—3416no—
562#41—3464no—
563#41—3432no—
564#41—3464no—
565#41—3416no—
566#41—3432no—
567#41—3416no—
568#41—688no—
569C2×Q8—178no—
570C2×Q8—174no—
571C2×Q8—172no—
572C2×Q8—3416no—
573C2×Q8—348no—
574C2×Q8—3416no—
575C2×Q8—344no—
576C2×Q8—342no—
577C2×Q8—341no—
578C2×Q8—344no—
579C2×Q8—344no—
580C2×D4—178no—
581C2×D4—174no—
582C2×D4—172no—
583C2×D4—3416no—
584C2×D4—348no—
585C2×D4—3416no—
586C2×D4—3464no—
587C2×D4—3416no—
588C2×D4—348no—
589C2×D4—348no—
590C2×D4—3416no—
591C2×D4—344no—
592C2×D4—344no—
593C2×D4—344no—
594C2×D4—344no—
595C2×D4—342no—
596C2×D4—341no—
597C2×D4—344no—
598C2×D4—344no—
599C2×D4—684no—
600C2×D4—684no—
601C2×D4—684no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—216no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—216no—
609C22×C4—3416no—
610C22×C4—3464no—
611C22×C4—348no—
612C22×C4—344no—
613C22×C4—342no—
614C22×C4—348no—
615C22×C4—348no—
616C22×C4—3416no—
617C22×C4—341no—
618C22×C4—341no—
619C22×C4—341no—
620C22×C4—344no—
621C22×C4—684no—
622C22×C4C2×D6811yescharacteristic
623C22×C4C2×D6811yescharacteristic
624C22×C4C2×D6814yes—
625C22×C4C2×D6814yes—
626C22×C4C2×D6812yes—
627C22×C4C2×D6812yes—
628C22×C4C2×D6814yes—
629C22×C4C2×D6812yes—
630C22×C4C2×D6811yescharacteristic
631C22×C4D4×D1718yes—
632C22×C4C23×D1712yes—
633C22×C4C23×D1712yes—
634C22×C4C23×D1711yescharacteristic
635C22×C4C23×D1712yes—
636Q16—3416no—
637SD16—3416no—
638SD16—3416no—
639D8—3416no—
640C2×C8—24no—
641C2×C8—24no—
642C2×C8—216no—
643C2×C8C23×D1714yes—
644C2×C8C23×D1714yes—
645C4⋊C4—172no—
646C4⋊C4—172no—
647C4⋊C4—341no—
648C4⋊C4—341no—
649C4⋊C4—344no—
650C4⋊C4—344no—
651C22⋊C4—344no—
652C22⋊C4—344no—
653C22⋊C4—344no—
654C22⋊C4—344no—
655C22⋊C4—344no—
656C42—344no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—28no—
662C23—22no—
663C23—22no—
664C23—28no—
665C23—22no—
666C23—44no—
667C23—416no—
668C23—3416no—
669C23—348no—
670C23—344no—
671C23—342no—
672C23—6832no—
673C23—688no—
674C23—684no—
675C23—688no—
676C23—684no—
677C23—682no—
678C23—682no—
679C23—682no—
680C23#1058756814yes—
681C23#1058759014yescomplemented
682C23C22×D6812yes—
683C23C22×D6812yes—
684C23C22×D6812yes—
685C23C22×D6811yescharacteristic
686Q8—178no—
687Q8—3416no—
688Q8—348no—
689Q8—344no—
690Q8—344no—
691Q8—682no—
692D4—178no—
693D4—3416no—
694D4—3432no—
695D4—3432no—
696D4—348no—
697D4—344no—
698D4—344no—
699D4—688no—
700D4—688no—
701D4—688no—
702D4—682no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—28no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—3432no—
713C2×C4—3416no—
714C2×C4—348no—
715C2×C4—344no—
716C2×C4—3432no—
717C2×C4—342no—
718C2×C4—342no—
719C2×C4—342no—
720C2×C4—682no—
721C2×C4—682no—
722C2×C4—682no—
723C2×C4—688no—
724C2×C4#1058756814yes—
725C2×C4#1058756818yes—
726C2×C4C22×D6812yes—
727C2×C4C22×D6812yes—
728C2×C4C22×D6812yes—
729C2×C4C22×D6811yescharacteristic
730C2×C4C2×D4×D1714yes—
731C2×C4C2×D4×D1718yes—
732C2×C4C24×D1711yescharacteristic
733C8—24no—
734C8—24no—
735C22—28no—
736C22—28no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—416no—
745C22—44no—
746C22—348no—
747C22—6832no—
748C22—6816no—
749C22—684no—
750C22—684no—
751C22—682no—
752C22—682no—
753C22—682no—
754C22—1364no—
755C22C2×#1058756814yes—
756C22C2×#1058756812yes—
757C22C2×#1058759012yes—
758C22C2×#1058759014yescomplemented
759C22#1176360912yes—
760C22C23×D6811yescharacteristic
761C4—22no—
762C4—22no—
763C4—348no—
764C4—682no—
765C4—682no—
766C4—682no—
767C4C2×#1058756814yes—
768C4C2×#1058756812yes—
769C4C22×D4×D1712yes—
770C2—24no—
771C2—24no—
772C2—42no—
773C2—688no—
774C2—1362no—
775C2#1453800614yesdirect product factor
776C2C22×#1058756811yescharacteristic
777C2C22×#1058759011yescharacteristic
778C2C2×#1176360911yescharacteristic
subgroupG/H
centerC22×C4C2×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC22×C17×C22⋊C8C2
socleC23×C17C22×D4
hypercenterC22×C22⋊C8D17
hypocenterC17C2×#3002
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C23×#63252C2semidirect
2. C22×#10587590C2semidirect
3. C2×#11763320C2semidirect
4. #14538006C2direct (N × H)
5. C2×#11762973C2semidirect
6. C2×#11762956C2semidirect
7. C2×#11762967C2semidirect
8. C2×#11762950C2semidirect
9. C2×#11762962C2semidirect
10. C2×#11762945C2semidirect
11. C2×#11762806C2semidirect
12. C22×C17×C22⋊C8C2semidirect
19. C22×#63252C22semidirect
20. C22×#63252C22semidirect
26. C2×#10587590C22semidirect
27. C22×Dic68C22semidirect
28. C22×#63219C22semidirect
29. C22×#63219C22semidirect
30. C22×D136C22semidirect
32. #11763320C22semidirect
35. C2×#10587610C22semidirect
37. C2×#10587616C22semidirect
41. C2×#10587612C22semidirect
42. #11762973C22semidirect
43. #11762967C22semidirect
44. #11762962C22semidirect
45. #11762956C22semidirect
46. #11762950C22semidirect
47. #11762945C22semidirect
48. #11762806C22semidirect
49. C2×#10587487C22semidirect
50. C2×#10587487C22semidirect
51. C2×#10587492C22semidirect
52. C2×#10587492C22semidirect
54. C23×C8×C17C22semidirect
57. C2×C17×C22⋊C8C22semidirect
58. C2×C17×C22⋊C8C22semidirect
91. C2×#63252D4semidirect
94. C2×#63252C23semidirect
115. C22×C8×C17C23semidirect
123. #10587616C23semidirect
130. #10587612C23semidirect
136. #10587610C23semidirect
141. C2×Dic68C23semidirect
144. C2×D136C23semidirect
147. C2×#63219C23semidirect
148. C2×#63219C23semidirect
151. C17×C22⋊C8C23semidirect
152. #10587492C23semidirect
153. #10587492C23semidirect
154. #10587487C23semidirect
155. #10587487C23semidirect
216. #63252C2×D4semidirect
280. C23×C17#135semidirect
357. C22×C22⋊C8D17semidirect
372. C22×C17C2×#135semidirect
412. C23×C8C2×D17semidirect
437. C2×C22⋊C8C2×D17semidirect
438. C2×C22⋊C8C2×D17semidirect
442. C2×C17#3002semidirect
513. C22×C8C22×D17semidirect
544. C22⋊C8C22×D17semidirect
545. C17C2×#3002semidirect
681. C23#10587590semidirect
758. C22C2×#10587590semidirect
775. C2#14538006direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#632522
C22×#105875902
C2×#117633202
#145380062
C2×#117629732
C2×#117629562
C2×#117629672
C2×#117629502
C2×#117629622
C2×#117629452
C2×#117628062
C22×C17×C22⋊C82
C2×#300217