Finite Group Databasebeta

← C22⋊C4×#63225 #16955742

Subgroups — C22⋊C4×#63225 #16955742

Order 4352.

2574 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#63225C211yesmaximal, characteristic
2C2×#11762667C211yesmaximal, characteristic
3C2×C4×#63225C212yesmaximal, complemented
4C2×C22⋊C4×Dic17C211yesmaximal, characteristic
5C2×C22⋊C4×Dic17C211yesmaximal, characteristic
6#14527017C212yesmaximal, complemented
7#14527015C212yesmaximal, complemented
8#14527012C212yesmaximal, complemented
9#14527007C211yesmaximal, characteristic
10#14527006C211yesmaximal, characteristic
11C2×C4×C22⋊C4×C17C211yesmaximal, characteristic
12C24×Dic17C2211yescharacteristic
13C24×Dic17C2211yescharacteristic
14C22×#63225—28no—
15C22×#63225C418yescomplemented
16C22×#63225C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2212yes—
20C22×#63225C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C4×Dic17C2212yes—
24C22×C4×Dic17C2212yes—
25#11762667C418yescomplemented
26C4×#63225—28no—
27C22⋊C4×Dic17—24no—
28C22⋊C4×Dic17C418yescomplemented
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C24×C4×C17C2211yescharacteristic
37C22×C22⋊C4×C17C2211yescharacteristic
38C22×C22⋊C4×C17C2211yescharacteristic
39C22×C42×C17C2212yes—
40C4×C22⋊C4×C17—24no—
41C2×C17×#95C2212yes—
42C25×C17C2311yescharacteristic
43C23×C4×C17—22no—
44C23×C4×C17—22no—
45C23×C4×C17—24no—
46C23×C4×C17—42no—
47C23×C4×C17C2×C414yes—
48C23×C4×C17C2312yes—
49C23×C4×C17C2311yescharacteristic
50C23×C4×C17C2311yescharacteristic
51C23×C4×C17C2312yes—
52C23×Dic17—24no—
53C23×Dic17—24no—
54C23×Dic17—22no—
55C23×Dic17—22no—
56C23×Dic17—24no—
57C23×Dic17—42no—
58C23×Dic17C2×C414yes—
59C23×Dic17C2×C414yes—
60C23×Dic17C2×C414yes—
61C23×Dic17C2×C414yes—
62C23×Dic17C2312yes—
63C23×Dic17C2312yes—
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C2×C22⋊C4×C17—22no—
69C2×C22⋊C4×C17—22no—
70C2×C22⋊C4×C17C2×C414yes—
71C2×C22⋊C4×C17C2×C414yes—
72C2×C22⋊C4×C17D414yes—
73C2×C22⋊C4×C17Q814yes—
74C2×C42×C17—24no—
75C2×C42×C17—24no—
76C2×C42×C17—42no—
77C2×C22⋊Dic17—22no—
78C2×C22⋊Dic17—22no—
79C2×C22⋊Dic17—22no—
80C2×C22⋊Dic17—22no—
81C2×C22⋊Dic17C2×C414yes—
82C2×C22⋊Dic17C2×C414yes—
83C2×#63225—232no—
84C2×#63225—24no—
85C2×#63225—24no—
86C2×#63225—24no—
87C2×#63225—24no—
88C2×#63225—24no—
89C2×#63225C2×C414yes—
90C2×#63225C2×C414yes—
91C2×#63225C2×C414yes—
92C2×#63225C2×C414yes—
93C2×#63225C2×C418yescomplemented
94C2×#63225D418yes—
95C2×C4×Dic17—24no—
96C2×C4×Dic17—24no—
97C2×C4×Dic17—24no—
98C2×C4×Dic17—24no—
99C2×C4×Dic17—42no—
100C2×C4×Dic17C2×C418yescomplemented
101C17×#95—24no—
102#10587502—24no—
103#10587502—24no—
104#10587502—24no—
105#10587502—42no—
106#10587502—42no—
107#10587502C2×C418yescomplemented
108#10587502C2×C418yescomplemented
109C24×C17—22no—
110C24×C17—22no—
111C24×C17—22no—
112C24×C17—22no—
113C24×C17C22×C412yes—
114C24×C17C22×C412yes—
115C24×C17C22×C412yes—
116C24×C17C2×D412yes—
117C24×C17C2×Q812yes—
118C24×C17#4112yes—
119C24×C17#4112yes—
120C24×C17C2411yescharacteristic
121C22×C4×C17—21no—
122C22×C4×C17—22no—
123C22×C4×C17—21no—
124C22×C4×C17—22no—
125C22×C4×C17—22no—
126C22×C4×C17—22no—
127C22×C4×C17—22no—
128C22×C4×C17—28no—
129C22×C4×C17—21no—
130C22×C4×C17—22no—
131C22×C4×C17—22no—
132C22×C4×C17—22no—
133C22×C4×C17—21no—
134C22×C4×C17—22no—
135C22×C4×C17—22no—
136C22×C4×C17—22no—
137C22×C4×C17—22no—
138C22×C4×C17—22no—
139C22×C4×C17—28no—
140C22×C4×C17—44no—
141C22×C4×C17—48no—
142C22×C4×C17—48no—
143C22×C4×C17C22×C412yes—
144C22×C4×C17C22×C414yes—
145C22×C4×C17C22×C412yes—
146C22×C4×C17C22×C414yes—
147C22×C4×C17C2×D414yes—
148C22×C4×C17C2×D414yes—
149C22×C4×C17C2×Q814yes—
150C22×Dic17—21no—
151C22×Dic17—22no—
152C22×Dic17—21no—
153C22×Dic17—22no—
154C22×Dic17—22no—
155C22×Dic17—28no—
156C22×Dic17—28no—
157C22×Dic17—216no—
158C22×Dic17—216no—
159C22×Dic17—28no—
160C22×Dic17—21no—
161C22×Dic17—22no—
162C22×Dic17—22no—
163C22×Dic17—22no—
164C22×Dic17—22no—
165C22×Dic17—21no—
166C22×Dic17—22no—
167C22×Dic17—22no—
168C22×Dic17—22no—
169C22×Dic17—22no—
170C22×Dic17—22no—
171C22×Dic17—22no—
172C22×Dic17—22no—
173C22×Dic17—22no—
174C22×Dic17—22no—
175C22×Dic17—22no—
176C22×Dic17—28no—
177C22×Dic17—44no—
178C22×Dic17—48no—
179C22×Dic17—48no—
180C22×Dic17C42116yescomplemented
181C22×Dic17C22×C412yes—
182C22×Dic17C22×C414yes—
183C22×Dic17C22×C414yes—
184C22×Dic17C22×C412yes—
185C22×Dic17C22×C412yes—
186C22×Dic17C22×C412yes—
187C22×Dic17C22×C412yes—
188C22×Dic17C22×C412yes—
189C22×Dic17C22×C412yes—
190C22×Dic17C22×C412yes—
191C22×Dic17C2×D414yes—
192C22×Dic17C2×D414yes—
193C22×Dic17#4114yes—
194C22⋊C4×C17—28no—
195C22⋊C4×C17C4⋊C4116yescomplemented
196C42×C17—48no—
197C22⋊Dic17—28no—
198C22⋊Dic17—28no—
199#63225—28no—
200#63225—28no—
201#63225—28no—
202#63225—216no—
203#63225C22⋊C4116yesdirect product factor
204C4×Dic17—216no—
205C4×Dic17—48no—
206C22⋊C4×C4⋊C4—171nomaximal, Sylow
207C23×C17—22no—
208C23×C17—22no—
209C23×C17—24no—
210C23×C17—24no—
211C23×C17—22no—
212C23×C17—22no—
213C23×C17—24no—
214C23×C17—24no—
215C23×C17—24no—
216C23×C17—24no—
217C23×C17—24no—
218C23×C17—24no—
219C23×C17—24no—
220C23×C17—24no—
221C23×C17—24no—
222C23×C17—24no—
223C23×C17C2×C4214yes—
224C23×C17C2×C4⋊C414yes—
225C23×C17#11714yes—
226C23×C17C4×D414yes—
227C23×C17C4×D414yes—
228C23×C17C4×Q814yes—
229C23×C17C4×Q814yes—
230C23×C17C23×C411yescharacteristic
231C23×C17C23×C411yescharacteristic
232C23×C17C23×C411yescharacteristic
233C23×C17C22×D412yes—
234C23×C17C22×D411yescharacteristic
235C23×C17C22×Q811yescharacteristic
236C23×C17C2×#4111yescharacteristic
237C23×C17C2×#4111yescharacteristic
238C23×C17C2×#4112yes—
239C23×C17H(5,𝔽2)12yes—
240C23×C172−1+412yes—
241C2×C4×C17—22no—
242C2×C4×C17—24no—
243C2×C4×C17—22no—
244C2×C4×C17—24no—
245C2×C4×C17—24no—
246C2×C4×C17—24no—
247C2×C4×C17—24no—
248C2×C4×C17—24no—
249C2×C4×C17—24no—
250C2×C4×C17—24no—
251C2×C4×C17—22no—
252C2×C4×C17—24no—
253C2×C4×C17—22no—
254C2×C4×C17—24no—
255C2×C4×C17—22no—
256C2×C4×C17—24no—
257C2×C4×C17—416no—
258C2×C4×C17—42no—
259C2×C4×C17—42no—
260C2×C4×C17—42no—
261C2×C4×C17—42no—
262C2×C4×C17—42no—
263C2×C4×C17—42no—
264C2×C4×C17C2×C22⋊C414yes—
265C2×C4×C17C2×C4⋊C418yescomplemented
266C2×Dic17—22no—
267C2×Dic17—22no—
268C2×Dic17—24no—
269C2×Dic17—24no—
270C2×Dic17—22no—
271C2×Dic17—22no—
272C2×Dic17—24no—
273C2×Dic17—24no—
274C2×Dic17—232no—
275C2×Dic17—22no—
276C2×Dic17—24no—
277C2×Dic17—24no—
278C2×Dic17—22no—
279C2×Dic17—24no—
280C2×Dic17—24no—
281C2×Dic17—22no—
282C2×Dic17—24no—
283C2×Dic17—24no—
284C2×Dic17—416no—
285C2×Dic17—42no—
286C2×Dic17—42no—
287C2×Dic17—42no—
288C2×Dic17—42no—
289C2×Dic17—42no—
290C2×Dic17—42no—
291C2×Dic17—42no—
292C2×Dic17—42no—
293C2×Dic17—42no—
294C2×Dic17—42no—
295C2×Dic17C2×C4214yes—
296C2×Dic17C2×C4214yes—
297C2×Dic17C2×C22⋊C414yes—
298C2×Dic17C2×C22⋊C414yes—
299C2×Dic17#11714yes—
300C2×Dic17C4×D418yes—
301C2×Dic17C4×D418yes—
302C23×C4⋊C4—171no—
303C2×#380—171no—
304C2×C4×C4⋊C4—172no—
305C2×C4×C22⋊C4—171no—
306C2×C4×C22⋊C4—171no—
307C2×C4×C22⋊C4D1711yescharacteristic
308#1436—172no—
309#1436—172no—
310C4⋊#95—172no—
311C22⋊#95—171no—
312C22⋊#95—171no—
313C22×C17—24no—
314C22×C17—24no—
315C22×C17—24no—
316C22×C17—24no—
317C22×C17—28no—
318C22×C17—28no—
319C22×C17—28no—
320C22×C17—28no—
321C22×C17—24no—
322C22×C17—24no—
323C22×C17C4×C4⋊C418yescomplemented
324C22×C17C22×C4211yescharacteristic
325C22×C17C22×C22⋊C411yescharacteristic
326C22×C17C22×C4⋊C411yescharacteristic
327C22×C17C2×#11711yescharacteristic
328C22×C17C2×#11711yescharacteristic
329C22×C17C2×C4×D412yes—
330C22×C17C2×C4×D412yes—
331C22×C17C2×C4×D411yescharacteristic
332C22×C17C2×C4×D411yescharacteristic
333C22×C17C2×C4×Q811yescharacteristic
334C22×C17C2×C4×Q811yescharacteristic
335C22×C17#51811yescharacteristic
336C22×C17#51911yescharacteristic
337C22×C17#52012yes—
338C22×C17#52012yes—
339C22×C17D4212yes—
340C22×C17#54612yes—
341C22×C17#54712yes—
342C22×C17#54812yes—
343C22×C17D4×Q812yes—
344C22×C17#55212yes—
345C22×C17#55312yes—
346C22×C17#55412yes—
347C4×C17—24no—
348C4×C17—28no—
349C4×C17—42no—
350C4×C17—44no—
351Dic17—24no—
352Dic17—24no—
353Dic17—42no—
354Dic17—44no—
355Dic17—44no—
356Dic17C4×C22⋊C418yescomplemented
357C24×C4—171no—
358C24×C4—171no—
359C24×C4C2×D1711yescharacteristic
360C22×C4⋊C4—171no—
361C22×C4⋊C4—178no—
362C22×C4⋊C4—171no—
363C22×C4⋊C4—171no—
364C22×C4⋊C4—171no—
365C22×C4⋊C4—172no—
366C22×C4⋊C4—348no—
367C22×C22⋊C4—171no—
368C22×C22⋊C4—171no—
369C22×C22⋊C4C2×D1711yescharacteristic
370C22×C22⋊C4C2×D1711yescharacteristic
371C22×C42—172no—
372C22×C42—172no—
373C22×C42C2×D1712yes—
374#380—178no—
375C4×C4⋊C4—348no—
376C4×C22⋊C4—24no—
377C4×C22⋊C4—178no—
378C4×C22⋊C4—344no—
379C2×#95—172no—
380C2×#95—172no—
381C2×#95—172no—
382C2×#95—172no—
383C2×#95—172no—
384C2×#95—172no—
385C2×#95—172no—
386C2×#95C2×D1712yes—
387C2×C17—28no—
388C2×C17C2×C4×C22⋊C411yescharacteristic
389C2×C17C2×C4×C4⋊C411yescharacteristic
390C2×C17#227411yescharacteristic
391C2×C17D4×C22⋊C411yescharacteristic
392C2×C17Q8×C22⋊C411yescharacteristic
393C2×C17#234411yescharacteristic
394C2×C17#234511yescharacteristic
395C2×C17D4×C4⋊C412yes—
396C2×C17#235212yes—
397C2×C17#236012yes—
398C2×C17#236112yes—
399C25C22×D1711yescharacteristic
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—42no—
404C23×C4—171no—
405C23×C4—174no—
406C23×C4—174no—
407C23×C4—174no—
408C23×C4—171no—
409C23×C4—171no—
410C23×C4—172no—
411C23×C4—172no—
412C23×C4—171no—
413C23×C4—174no—
414C23×C4—344no—
415C23×C4—344no—
416C23×C4—344no—
417C23×C4—342no—
418C23×C4—342no—
419C23×C4—682no—
420C23×C4C4×D1714yes—
421C23×C4C22×D1712yes—
422C23×C4C22×D1711yescharacteristic
423C23×C4C22×D1712yes—
424C23×C4C22×D1711yescharacteristic
425C2×C4⋊C4—174no—
426C2×C4⋊C4—178no—
427C2×C4⋊C4—174no—
428C2×C4⋊C4—174no—
429C2×C4⋊C4—174no—
430C2×C4⋊C4—178no—
431C2×C4⋊C4—3432no—
432C2×C4⋊C4—344no—
433C2×C4⋊C4—344no—
434C2×C4⋊C4—344no—
435C2×C4⋊C4—344no—
436C2×C4⋊C4—344no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—174no—
440C2×C22⋊C4—174no—
441C2×C22⋊C4—342no—
442C2×C22⋊C4—342no—
443C2×C22⋊C4—342no—
444C2×C22⋊C4—342no—
445C2×C22⋊C4Dic3414yes—
446C2×C22⋊C4C4×D1714yes—
447C2×C22⋊C4C4×D1714yes—
448C2×C22⋊C4C22⋊D1714yes—
449C2×C42—24no—
450C2×C42—24no—
451C2×C42—42no—
452C2×C42—178no—
453C2×C42—344no—
454C2×C42—344no—
455C2×C42—344no—
456C2×C42—344no—
457C2×C42—682no—
458#95—24no—
459#95—178no—
460#95—178no—
461#95—344no—
462#95—344no—
463#95—344no—
464#95—682no—
465#95—682no—
466C17C22⋊C4×C4⋊C411yescharacteristic, complemented, Sylow
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24C2×Dic3412yes—
472C24C2×C4×D1712yes—
473C24C2×C4×D1712yes—
474C24C2×C4×D1712yes—
475C24#6325212yes—
476C24#6325212yes—
477C24C2×C22⋊D1712yes—
478C24C23×D1711yescharacteristic
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—44no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4—172no—
502C22×C4—172no—
503C22×C4—172no—
504C22×C4—174no—
505C22×C4—174no—
506C22×C4—172no—
507C22×C4—172no—
508C22×C4—172no—
509C22×C4—172no—
510C22×C4—174no—
511C22×C4—1716no—
512C22×C4—174no—
513C22×C4—174no—
514C22×C4—172no—
515C22×C4—348no—
516C22×C4—348no—
517C22×C4—3416no—
518C22×C4—3416no—
519C22×C4—348no—
520C22×C4—341no—
521C22×C4—342no—
522C22×C4—342no—
523C22×C4—342no—
524C22×C4—341no—
525C22×C4—342no—
526C22×C4—342no—
527C22×C4—342no—
528C22×C4—341no—
529C22×C4—342no—
530C22×C4—342no—
531C22×C4—342no—
532C22×C4—342no—
533C22×C4—342no—
534C22×C4—342no—
535C22×C4—342no—
536C22×C4—342no—
537C22×C4—342no—
538C22×C4—342no—
539C22×C4—341no—
540C22×C4—342no—
541C22×C4—348no—
542C22×C4—684no—
543C22×C4—688no—
544C22×C4—688no—
545C22×C4C2×Dic3414yes—
546C22×C4C2×C4×D1714yes—
547C22×C4C2×C4×D1712yes—
548C22×C4C2×C4×D1712yes—
549C22×C4C2×C4×D1714yes—
550C22×C4D4×D1714yes—
551C22×C4C2×C22⋊D1714yes—
552C4⋊C4—1716no—
553C4⋊C4—348no—
554C4⋊C4—348no—
555C4⋊C4—3416no—
556C4⋊C4—348no—
557C22⋊C4—28no—
558C22⋊C4—348no—
559C22⋊C4—348no—
560C22⋊C4#63225116yesdirect product factor
561C42—48no—
562C42—3416no—
563C42—688no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—22no—
570C23—22no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—22no—
575C23—22no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23C4×Dic3414yes—
581C23C4×Dic3414yes—
582C23C42×D1714yes—
583C23#1058755814yes—
584C23C2×#6322514yes—
585C23C4×C22⋊D1714yes—
586C23C4×C22⋊D1714yes—
587C23C22×Dic3411yescharacteristic
588C23C22×C4×D1711yescharacteristic
589C23C22×C4×D1711yescharacteristic
590C23C22×C4×D1711yescharacteristic
591C23C2×#6325211yescharacteristic
592C23C2×#6325211yescharacteristic
593C23C2×D4×D1712yes—
594C23#1058769112yes—
595C23#41×D1712yes—
596C23#1058769712yes—
597C23C22×C22⋊D1711yescharacteristic
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—416no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—174no—
622C2×C4—174no—
623C2×C4—174no—
624C2×C4—178no—
625C2×C4—178no—
626C2×C4—174no—
627C2×C4—174no—
628C2×C4—3432no—
629C2×C4—342no—
630C2×C4—342no—
631C2×C4—344no—
632C2×C4—344no—
633C2×C4—342no—
634C2×C4—342no—
635C2×C4—344no—
636C2×C4—344no—
637C2×C4—342no—
638C2×C4—344no—
639C2×C4—344no—
640C2×C4—344no—
641C2×C4—344no—
642C2×C4—342no—
643C2×C4—342no—
644C2×C4—344no—
645C2×C4—344no—
646C2×C4—6816no—
647C2×C4—682no—
648C2×C4—682no—
649C2×C4—682no—
650C2×C4—682no—
651C2×C4—682no—
652C2×C4—682no—
653C2×C4—682no—
654C2×C4—682no—
655C2×C4—682no—
656C2×C4—682no—
657C2×C4C22⋊C4×D1714yes—
658C2×C4C2×#6322518yescomplemented
659C22—24no—
660C22—24no—
661C22—24no—
662C22—24no—
663C22—24no—
664C22—24no—
665C22—28no—
666C22—28no—
667C22—28no—
668C22—28no—
669C22C4×#6322518yescomplemented
670C22C2×C42×D1711yescharacteristic
671C22C2×C22⋊C4×D1711yescharacteristic
672C22C22×#6322511yescharacteristic
673C22#117×D1711yescharacteristic
674C22C2×#1058755811yescharacteristic
675C22C4×D4×D1712yes—
676C22C4×D4×D1712yes—
677C22C2×C4×C22⋊D1711yescharacteristic
678C22C2×C4×C22⋊D1711yescharacteristic
679C22C2×C4×Dic3411yescharacteristic
680C22C2×C4×Dic3411yescharacteristic
681C22#1176328211yescharacteristic
682C22#1176328611yescharacteristic
683C22#1176328812yes—
684C22#1176328812yes—
685C22D4×C22⋊D1712yes—
686C22#1176344912yes—
687C22#1176345812yes—
688C22#1176346812yes—
689C22D4×Dic3412yes—
690C22#1176349212yes—
691C22#1176350812yes—
692C22#1176351812yes—
693C4—24no—
694C4—28no—
695C4—42no—
696C4—44no—
697C4—178no—
698C4—344no—
699C4—344no—
700C4—682no—
701C4—684no—
702C4—684no—
703C2—28no—
704C2C4×C22⋊C4×D1711yescharacteristic
705C2C2×C4×#6322511yescharacteristic
706C2#1453113911yescharacteristic
707C2C22⋊C4×C22⋊D1711yescharacteristic
708C2C22⋊C4×Dic3411yescharacteristic
709C2#1453165411yescharacteristic
710C2#1453166211yescharacteristic
711C2D4×#6322512yes—
712C2#1453170712yes—
713C2#1453179012yes—
714C2#1453180112yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC2×C4×C22⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×C4×C22⋊C4D17
hypocenterC17C22⋊C4×C4⋊C4
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#63225C2semidirect
6. #14527017C2semidirect
7. #14527015C2semidirect
8. #14527012C2semidirect
15. C22×#63225C4semidirect
25. #11762667C4semidirect
28. C22⋊C4×Dic17C4semidirect
93. C2×#63225C2×C4semidirect
100. C2×C4×Dic17C2×C4semidirect
107. #10587502C2×C4semidirect
108. #10587502C2×C4semidirect
180. C22×Dic17C42semidirect
195. C22⋊C4×C17C4⋊C4semidirect
203. #63225C22⋊C4direct (N × H)
265. C2×C4×C17C2×C4⋊C4semidirect
323. C22×C17C4×C4⋊C4semidirect
356. Dic17C4×C22⋊C4semidirect
466. C17C22⋊C4×C4⋊C4semidirect
560. C22⋊C4#63225direct (N × H)
658. C2×C4C2×#63225semidirect
669. C22C4×#63225semidirect

Maximal subgroups

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

subgroupindex
C23×#632252
C2×#117626672
C2×C4×#632252
C2×C22⋊C4×Dic172
#145270172
#145270152
#145270122
#145270072
#145270062
C2×C4×C22⋊C4×C172
C22⋊C4×C4⋊C417