Finite Group Databasebeta

← C4⋊C4×C22⋊#595 #17963021

Subgroups — C4⋊C4×C22⋊#595 #17963021

Order 4352.

2574 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763751C211yesmaximal, characteristic
2C2×C4⋊C4×#595C212yesmaximal, complemented
3C2×C4×C22⋊#595C212yesmaximal
4C2×C4×C22⋊#595C211yesmaximal, characteristic
5#14543963C214yesmaximal, complemented
6#14543961C212yesmaximal, complemented
7#14543958C212yesmaximal
8C22×C4⋊C4×D17C211yesmaximal, characteristic
9C22×C4⋊#595C2212yes—
10C22×C22⋊#595C2212yes—
11C22×C22⋊#595C2211yescharacteristic
12C22×C22⋊#595C2211yescharacteristic
13C22×C4×#595C2214yes—
14C22×C4×#595C2212yes—
15#11763751C418yescomplemented
16C4⋊C4×#595—28no—
17C4×C22⋊#595—28no—
18C4×C22⋊#595C418yescomplemented
19C2×(C2×#595)⋊C4C2214yes—
20C2×(C2×#595)⋊C4C2214yes—
21C2×(C2×#595)⋊C4C2214yes—
22C2×(C2×#595)⋊C4C2212yes—
23C2×(C2×#595)⋊C4C2212yes—
24C23×C4×D17C2212yes—
25C23×C4×D17C2211yescharacteristic
26C22×C4⋊Dic17C411yescharacteristic, complemented
27C22×#63225C412yescomplemented
28C2×C4⋊C4×D17—28no—
29C2×C4⋊C4×D17C411yescharacteristic, complemented
30C2×C4⋊C4×D17C412yescomplemented
31C2×C4⋊C4×D17C411yescharacteristic, complemented
32C2×C4⋊C4×D17C2211yescharacteristic
33C2×C4⋊C4×D17C2212yes—
34C2×C4⋊C4×D17C2211yescharacteristic
35C22×C4⋊C4×C17C411yescharacteristic, complemented
36C24×D17C2311yescharacteristic
37C23×#595C2312yes—
38C23×#595C2314yes—
39C23×#595C2312yes—
40C23×C4×C17C2×C412yes—
41C23×C4×C17C2×C411yescharacteristic
42C23×Dic17C2×C412yes—
43C23×Dic17C2×C411yescharacteristic
44C22×C4×D17—24no—
45C22×C4×D17—24no—
46C22×C4×D17—24no—
47C22×C4×D17—24no—
48C22×C4×D17—28no—
49C22×C4×D17—44no—
50C22×C4×D17C2×C412yes—
51C22×C4×D17C2×C412yes—
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17C2×C411yescharacteristic
54C22×C4×D17C2×C414yes—
55C22×C4×D17C2×C414yes—
56C22×C4×D17C2312yes—
57C22×C4×D17C2311yescharacteristic
58C22×C4×D17C2312yes—
59C22×C4×D17C2311yescharacteristic
60C2×C22⋊#595—24no—
61C2×C22⋊#595—22no—
62C2×C22⋊#595—22no—
63C2×C22⋊#595—24no—
64C2×C22⋊#595C2×C414yes—
65C2×C22⋊#595C2×C418yes—
66C2×C22⋊#595C2×C414yes—
67C2×C22⋊#595D414yes—
68C2×C22⋊#595Q814yes—
69C2×C4⋊#595—24no—
70C2×C4⋊#595—24no—
71C2×C4⋊#595C2×C418yescomplemented
72C2×C4×#595—24no—
73C2×C4×#595—24no—
74C2×C4×#595—28no—
75C2×C4×#595—28no—
76C2×C4×#595—44no—
77C2×C4×#595C2×C418yescomplemented
78C2×C4⋊C4×C17—24no—
79C2×C4⋊C4×C17C2×C411yescharacteristic
80C2×C4⋊C4×C17C2×C412yes—
81C2×C4⋊C4×C17C2×C411yescharacteristic
82C2×C4⋊Dic17—24no—
83C2×C4⋊Dic17C2×C411yescharacteristic
84C2×C4⋊Dic17C2×C412yes—
85C2×C4⋊Dic17C2×C411yescharacteristic
86C2×#63225—28no—
87C2×#63225C2×C412yes—
88C2×#63225C2×C412yes—
89C2×#63225C2×C412yes—
90C2×#63225C2×C412yes—
91C4⋊C4×D17—24no—
92C4⋊C4×D17—28no—
93C4⋊C4×D17—28no—
94C4⋊C4×D17—24no—
95C4⋊C4×D17—24no—
96C4⋊C4×D17D418yes—
97(C2×#595)⋊C4—28no—
98(C2×#595)⋊C4—28no—
99(C2×#595)⋊C4—44no—
100(C2×#595)⋊C4C2×C418yescomplemented
101(C2×#595)⋊C4C2×C418yescomplemented
102C24×C17C22×C411yescharacteristic
103C23×D17—22no—
104C23×D17—22no—
105C23×D17—22no—
106C23×D17—22no—
107C23×D17C22×C411yescharacteristic
108C23×D17C22×C412yes—
109C23×D17C22×C412yes—
110C23×D17C2×D412yes—
111C23×D17C2×Q812yes—
112C23×D17#4112yes—
113C23×D17#4112yes—
114C23×D17C2411yescharacteristic
115C22×#595—22no—
116C22×#595—22no—
117C22×#595—22no—
118C22×#595—22no—
119C22×#595—24no—
120C22×#595—24no—
121C22×#595—22no—
122C22×#595—22no—
123C22×#595—24no—
124C22×#595—22no—
125C22×#595—22no—
126C22×#595—24no—
127C22×#595—24no—
128C22×#595—22no—
129C22×#595—24no—
130C22×#595—22no—
131C22×#595C22×C414yes—
132C22×#595C22×C418yes—
133C22×#595C22×C414yes—
134C22×#595C2×D414yes—
135C22×#595C2×Q814yes—
136C22×C4×C17—22no—
137C22×C4×C17—22no—
138C22×C4×C17—24no—
139C22×C4×C17—24no—
140C22×C4×C17—42no—
141C22×C4×C17C4214yescomplemented
142C22×C4×C17C22×C412yes—
143C22×C4×C17C22×C411yescharacteristic
144C22×C4×C17C22×C412yes—
145C22×C4×C17C22×C411yescharacteristic
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—24no—
149C22×Dic17—24no—
150C22×Dic17—42no—
151C22×Dic17C4214yescomplemented
152C22×Dic17C22×C412yes—
153C22×Dic17C22×C411yescharacteristic
154C22×Dic17C22×C412yes—
155C22×Dic17C22×C411yescharacteristic
156C2×C4×D17—22no—
157C2×C4×D17—22no—
158C2×C4×D17—22no—
159C2×C4×D17—22no—
160C2×C4×D17—24no—
161C2×C4×D17—22no—
162C2×C4×D17—22no—
163C2×C4×D17—22no—
164C2×C4×D17—22no—
165C2×C4×D17—216no—
166C2×C4×D17—216no—
167C2×C4×D17—24no—
168C2×C4×D17—24no—
169C2×C4×D17—22no—
170C2×C4×D17—24no—
171C2×C4×D17—22no—
172C2×C4×D17—24no—
173C2×C4×D17—24no—
174C2×C4×D17—24no—
175C2×C4×D17—416no—
176C2×C4×D17—416no—
177C2×C4×D17—42no—
178C2×C4×D17—42no—
179C2×C4×D17C4214yescomplemented
180C2×C4×D17C4214yescomplemented
181C2×C4×D17C22×C412yes—
182C2×C4×D17C22×C412yes—
183C2×C4×D17C22×C412yes—
184C2×C4×D17C22×C412yes—
185C2×C4×D17C2×D418yes—
186C2×C4×D17C2×D414yes—
187C2×C4×D17#4114yes—
188C22⋊#595—28no—
189C22⋊#595—216no—
190C22⋊#595C4⋊C4116yesdirect product factor
191C4⋊#595—216no—
192C4×#595—216no—
193C4×#595—416no—
194C4⋊C4×C17—24no—
195C4⋊C4×C17—22no—
196C4⋊C4×C17C22⋊C414yescomplemented
197C4⋊Dic17—22no—
198C4⋊Dic17—24no—
199C4⋊Dic17C22⋊C414yescomplemented
200#63225—24no—
201#63225—24no—
202#63225—24no—
203#63225C22⋊C418yescomplemented
204C22⋊C4×C4⋊C4—171nomaximal, Sylow
205C23×C17—21no—
206C23×C17—21no—
207C23×C17—21no—
208C23×C17—21no—
209C23×C17C2×C4212yes—
210C23×C17C4×D412yes—
211C23×C17C4×Q812yes—
212C23×C17C23×C411yescharacteristic
213C22×D17—21no—
214C22×D17—21no—
215C22×D17—21no—
216C22×D17—21no—
217C22×D17—24no—
218C22×D17—24no—
219C22×D17—24no—
220C22×D17—24no—
221C22×D17—24no—
222C22×D17—24no—
223C22×D17—24no—
224C22×D17—24no—
225C22×D17—24no—
226C22×D17—24no—
227C22×D17—24no—
228C22×D17—24no—
229C22×D17C2×C4212yes—
230C22×D17C2×C4⋊C414yes—
231C22×D17#11714yes—
232C22×D17C4×D414yes—
233C22×D17C4×D412yes—
234C22×D17C4×Q814yes—
235C22×D17C4×Q812yes—
236C22×D17C23×C411yescharacteristic
237C22×D17C23×C411yescharacteristic
238C22×D17C22×D411yescharacteristic
239C22×D17C22×D412yes—
240C22×D17C22×Q811yescharacteristic
241C22×D17C2×#4111yescharacteristic
242C22×D17C2×#4111yescharacteristic
243C22×D17C2×#4112yes—
244C22×D17H(5,𝔽2)12yes—
245C22×D172−1+412yes—
246C2×#595—24no—
247C2×#595—24no—
248C2×#595—24no—
249C2×#595—24no—
250C2×#595—24no—
251C2×#595—24no—
252C2×#595—24no—
253C2×#595—24no—
254C2×#595—28no—
255C2×#595—28no—
256C2×#595—24no—
257C2×#595—28no—
258C2×#595—44no—
259C2×#595—42no—
260C2×#595—44no—
261C2×#595—42no—
262C2×#595—44no—
263C2×#595—42no—
264C2×#595—42no—
265C2×#595—44no—
266C2×#595C2×C4⋊C418yescomplemented
267C2×C4×C17—21no—
268C2×C4×C17—21no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—28no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—48no—
276C2×C4×C17C2×C4212yes—
277C2×C4×C17C2×C4212yes—
278C2×C4×C17C2×C22⋊C414yes—
279C2×C4×C17C2×C22⋊C412yes—
280C2×C4×C17#11712yes—
281C2×Dic17—21no—
282C2×Dic17—21no—
283C2×Dic17—22no—
284C2×Dic17—22no—
285C2×Dic17—28no—
286C2×Dic17—22no—
287C2×Dic17—22no—
288C2×Dic17—22no—
289C2×Dic17—48no—
290C2×Dic17C2×C4212yes—
291C2×Dic17C2×C4212yes—
292C2×Dic17C2×C22⋊C414yes—
293C2×Dic17C2×C22⋊C412yes—
294C2×Dic17#11712yes—
295C4×D17—24no—
296C4×D17—24no—
297C4×D17—28no—
298C4×D17—28no—
299C4×D17—28no—
300C4×D17—28no—
301C4×D17—48no—
302C4×D17—48no—
303C4×D17—44no—
304C4×D17—44no—
305C4×D17C4×D418yes—
306C4×D17C4×D418yes—
307C23×C4⋊C4—171no—
308C2×#380—171no—
309C2×C4×C4⋊C4—172no—
310C2×C4×C22⋊C4—171no—
311C2×C4×C22⋊C4—172no—
312#1436—174no—
313C4⋊#95—172no—
314C22⋊#95—172no—
315C22×C17—22no—
316C22×C17—22no—
317C22×C17—22no—
318C22×C17—22no—
319C22×C17—22no—
320C22×C17—22no—
321C22×C17C4×C4⋊C414yescomplemented
322C22×C17C22×C4211yescharacteristic
323C22×C17C22×C22⋊C411yescharacteristic
324C22×C17C2×#11711yescharacteristic
325C22×C17C2×C4×D411yescharacteristic
326C22×C17C2×C4×Q811yescharacteristic
327C22×C17#51811yescharacteristic
328C22×C17#51911yescharacteristic
329C2×D17—22no—
330C2×D17—22no—
331C2×D17—22no—
332C2×D17—22no—
333C2×D17—22no—
334C2×D17—22no—
335C2×D17—28no—
336C2×D17—28no—
337C2×D17—28no—
338C2×D17—28no—
339C2×D17C4×C4⋊C414yescomplemented
340C2×D17C22×C4⋊C411yescharacteristic
341C2×D17C2×#11711yescharacteristic
342C2×D17C2×C4×D412yes—
343C2×D17C2×C4×D412yes—
344C2×D17C2×C4×D411yescharacteristic
345C2×D17C2×C4×Q811yescharacteristic
346C2×D17#52012yes—
347C2×D17#52012yes—
348C2×D17D4212yes—
349C2×D17#54612yes—
350C2×D17#54712yes—
351C2×D17#54812yes—
352C2×D17D4×Q812yes—
353C2×D17#55212yes—
354C2×D17#55312yes—
355C2×D17#55412yes—
356#595—28no—
357#595—44no—
358#595—48no—
359C4×C17—24no—
360C4×C17—22no—
361C4×C17—42no—
362C4×C17C4×C22⋊C414yescomplemented
363Dic17—24no—
364Dic17—22no—
365Dic17—42no—
366Dic17C4×C22⋊C414yescomplemented
367C24×C4—171no—
368C24×C4—172no—
369C22×C4⋊C4—171no—
370C22×C4⋊C4—172no—
371C22×C4⋊C4—172no—
372C22×C4⋊C4—171no—
373C22×C4⋊C4—172no—
374C22×C4⋊C4—171no—
375C22×C4⋊C4—171no—
376C22×C4⋊C4—171no—
377C22×C4⋊C4—172no—
378C22×C4⋊C4—348no—
379C22×C4⋊C4#59511yescharacteristic, complemented
380C22×C22⋊C4—171no—
381C22×C22⋊C4—171no—
382C22×C22⋊C4—172no—
383C22×C42—172no—
384C22×C42—174no—
385#380—178no—
386C4×C4⋊C4—348no—
387C4×C22⋊C4—178no—
388C4×C22⋊C4—348no—
389C2×#95—172no—
390C2×#95—172no—
391C2×#95—174no—
392C2×#95—174no—
393C2×#95—174no—
394C2×C17—24no—
395C2×C17C2×C4×C22⋊C411yescharacteristic
396C2×C17C2×C4×C4⋊C411yescharacteristic
397C2×C17#227411yescharacteristic
398C2×C17D4×C22⋊C411yescharacteristic
399C2×C17Q8×C22⋊C411yescharacteristic
400C2×C17#234411yescharacteristic
401C2×C17#234511yescharacteristic
402D17—24no—
403D17D4×C4⋊C412yes—
404D17#235212yes—
405D17#236012yes—
406D17#236112yes—
407C25—171no—
408C23×C4—171no—
409C23×C4—172no—
410C23×C4—171no—
411C23×C4—174no—
412C23×C4—174no—
413C23×C4—171no—
414C23×C4—171no—
415C23×C4—171no—
416C23×C4—172no—
417C23×C4—174no—
418C23×C4—172no—
419C23×C4—172no—
420C23×C4—172no—
421C23×C4—172no—
422C23×C4—172no—
423C23×C4—344no—
424C23×C4—344no—
425C23×C4—348no—
426C23×C4—344no—
427C23×C4—344no—
428C23×C4—684no—
429C23×C4C2×#59512yes—
430C23×C4C2×#59511yescharacteristic
431C2×C4⋊C4—24no—
432C2×C4⋊C4—172no—
433C2×C4⋊C4—171no—
434C2×C4⋊C4—178no—
435C2×C4⋊C4—178no—
436C2×C4⋊C4—172no—
437C2×C4⋊C4—172no—
438C2×C4⋊C4—172no—
439C2×C4⋊C4—172no—
440C2×C4⋊C4—171no—
441C2×C4⋊C4—348no—
442C2×C4⋊C4—344no—
443C2×C4⋊C4—344no—
444C2×C4⋊C4—348no—
445C2×C4⋊C4—348no—
446C2×C4⋊C4—344no—
447C2×C4⋊C4—344no—
448C2×C4⋊C4—344no—
449C2×C4⋊C4—344no—
450C2×C4⋊C4C2×#59511yescharacteristic
451C2×C4⋊C4C2×#59512yes—
452C2×C4⋊C4C2×#59511yescharacteristic
453C2×C22⋊C4—174no—
454C2×C22⋊C4—174no—
455C2×C22⋊C4—174no—
456C2×C22⋊C4—174no—
457C2×C22⋊C4—178no—
458C2×C22⋊C4—342no—
459C2×C22⋊C4—342no—
460C2×C22⋊C4—344no—
461C2×C22⋊C4—344no—
462C2×C42—178no—
463C2×C42—344no—
464C2×C42—344no—
465C2×C42—348no—
466C2×C42—348no—
467C2×C42—684no—
468#95—178no—
469#95—178no—
470#95—348no—
471#95—348no—
472#95—684no—
473C17C22⋊C4×C4⋊C411yescharacteristic, complemented, Sylow
474C24—171no—
475C24—172no—
476C24—172no—
477C24—172no—
478C24—172no—
479C24—172no—
480C24—172no—
481C24—171no—
482C24—342no—
483C24—342no—
484C24—342no—
485C24—342no—
486C24C22×#59511yescharacteristic
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—42no—
492C22×C4—171no—
493C22×C4—172no—
494C22×C4—172no—
495C22×C4—174no—
496C22×C4—174no—
497C22×C4—174no—
498C22×C4—174no—
499C22×C4—174no—
500C22×C4—174no—
501C22×C4—171no—
502C22×C4—172no—
503C22×C4—174no—
504C22×C4—174no—
505C22×C4—172no—
506C22×C4—172no—
507C22×C4—178no—
508C22×C4—174no—
509C22×C4—178no—
510C22×C4—172no—
511C22×C4—342no—
512C22×C4—342no—
513C22×C4—3416no—
514C22×C4—3416no—
515C22×C4—344no—
516C22×C4—342no—
517C22×C4—344no—
518C22×C4—342no—
519C22×C4—342no—
520C22×C4—342no—
521C22×C4—342no—
522C22×C4—344no—
523C22×C4—344no—
524C22×C4—344no—
525C22×C4—344no—
526C22×C4—342no—
527C22×C4—342no—
528C22×C4—342no—
529C22×C4—344no—
530C22×C4—342no—
531C22×C4—342no—
532C22×C4—342no—
533C22×C4—342no—
534C22×C4—342no—
535C22×C4—342no—
536C22×C4—342no—
537C22×C4—344no—
538C22×C4—344no—
539C22×C4—342no—
540C22×C4—344no—
541C22×C4—342no—
542C22×C4—342no—
543C22×C4—344no—
544C22×C4—342no—
545C22×C4—344no—
546C22×C4—344no—
547C22×C4—342no—
548C22×C4—344no—
549C22×C4—344no—
550C22×C4—682no—
551C22×C4—682no—
552C22×C4—6816no—
553C22×C4—6816no—
554C22×C4—682no—
555C22×C4C4×#59514yescomplemented
556C22×C4C22×#59512yes—
557C22×C4C22×#59511yescharacteristic
558C22×C4C22×#59512yes—
559C22×C4C22×#59511yescharacteristic
560C4⋊C4—24no—
561C4⋊C4—22no—
562C4⋊C4—178no—
563C4⋊C4—174no—
564C4⋊C4—344no—
565C4⋊C4—344no—
566C4⋊C4—344no—
567C4⋊C4—3416no—
568C4⋊C4—344no—
569C4⋊C4—342no—
570C4⋊C4C22⋊#59514yesdirect product factor
571C22⋊C4—1716no—
572C22⋊C4—3416no—
573C22⋊C4—348no—
574C42—3416no—
575C42—6816no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—171no—
581C23—171no—
582C23—172no—
583C23—172no—
584C23—171no—
585C23—171no—
586C23—171no—
587C23—171no—
588C23—172no—
589C23—172no—
590C23—174no—
591C23—174no—
592C23—174no—
593C23—174no—
594C23—172no—
595C23—172no—
596C23—172no—
597C23—344no—
598C23—344no—
599C23—344no—
600C23—344no—
601C23—344no—
602C23—344no—
603C23—344no—
604C23—344no—
605C23—344no—
606C23—344no—
607C23—344no—
608C23—344no—
609C23—341no—
610C23—341no—
611C23—341no—
612C23—341no—
613C23C2×C4×#59512yes—
614C23D4×#59512yes—
615C23Q8×#59512yes—
616C23C23×#59511yescharacteristic
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—28no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—48no—
626C2×C4—172no—
627C2×C4—172no—
628C2×C4—172no—
629C2×C4—178no—
630C2×C4—178no—
631C2×C4—178no—
632C2×C4—172no—
633C2×C4—174no—
634C2×C4—348no—
635C2×C4—348no—
636C2×C4—344no—
637C2×C4—344no—
638C2×C4—348no—
639C2×C4—348no—
640C2×C4—344no—
641C2×C4—344no—
642C2×C4—344no—
643C2×C4—344no—
644C2×C4—344no—
645C2×C4—344no—
646C2×C4—341no—
647C2×C4—341no—
648C2×C4—342no—
649C2×C4—342no—
650C2×C4—348no—
651C2×C4—344no—
652C2×C4—348no—
653C2×C4—344no—
654C2×C4—348no—
655C2×C4—344no—
656C2×C4—348no—
657C2×C4—342no—
658C2×C4—342no—
659C2×C4—342no—
660C2×C4—688no—
661C2×C4—688no—
662C2×C4—684no—
663C2×C4—684no—
664C2×C4—688no—
665C2×C4—684no—
666C2×C4—682no—
667C2×C4—682no—
668C2×C4—684no—
669C2×C4—684no—
670C2×C4—682no—
671C2×C4—682no—
672C2×C4—684no—
673C2×C4C2×C4×#59512yes—
674C2×C4C2×C4×#59512yes—
675C2×C4#1058767712yes—
676C2×C4C2×C22⋊#59514yes—
677C2×C4C2×C22⋊#59512yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—172no—
685C22—172no—
686C22—171no—
687C22—171no—
688C22—171no—
689C22—171no—
690C22—172no—
691C22—172no—
692C22—172no—
693C22—172no—
694C22—172no—
695C22—172no—
696C22—172no—
697C22—172no—
698C22—172no—
699C22—172no—
700C22—174no—
701C22—348no—
702C22—348no—
703C22—348no—
704C22—348no—
705C22—342no—
706C22—342no—
707C22—342no—
708C22—342no—
709C22—342no—
710C22—342no—
711C22C4⋊C4×#59514yescomplemented
712C22C22×C4×#59511yescharacteristic
713C22C22×C22⋊#59511yescharacteristic
714C22C2×#1058767711yescharacteristic
715C22C2×D4×#59511yescharacteristic
716C22C2×Q8×#59511yescharacteristic
717C22#1176387611yescharacteristic
718C22#1176387711yescharacteristic
719C4—22no—
720C4—24no—
721C4—42no—
722C4—174no—
723C4—348no—
724C4—342no—
725C4—344no—
726C4—688no—
727C4—684no—
728C4—682no—
729C4C4×C22⋊#59514yescomplemented
730C2—24no—
731C2—172no—
732C2—172no—
733C2—172no—
734C2—172no—
735C2—344no—
736C2C2×C4×C22⋊#59511yescharacteristic
737C2C2×C4⋊C4×#59511yescharacteristic
738C2#1454522211yescharacteristic
739C2D4×C22⋊#59511yescharacteristic
740C2Q8×C22⋊#59511yescharacteristic
741C2#1454529211yescharacteristic
742C2#1454529311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C22×C42
FittingC22×C4⋊C4×C17C4
socleC23×C17C23×C4
prime radicalC24×D17C23
cosocleC23×D17C24
hypercenterC22×C4⋊C4#595
hypocenterC17C22⋊C4×C4⋊C4
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×#595C2semidirect
5. #14543963C2semidirect
6. #14543961C2semidirect
15. #11763751C4semidirect
18. C4×C22⋊#595C4semidirect
26. C22×C4⋊Dic17C4semidirect
27. C22×#63225C4semidirect
29. C2×C4⋊C4×D17C4semidirect
30. C2×C4⋊C4×D17C4semidirect
31. C2×C4⋊C4×D17C4semidirect
35. C22×C4⋊C4×C17C4semidirect
71. C2×C4⋊#595C2×C4semidirect
77. C2×C4×#595C2×C4semidirect
100. (C2×#595)⋊C4C2×C4semidirect
101. (C2×#595)⋊C4C2×C4semidirect
141. C22×C4×C17C42semidirect
151. C22×Dic17C42semidirect
179. C2×C4×D17C42semidirect
180. C2×C4×D17C42semidirect
190. C22⋊#595C4⋊C4direct (N × H)
196. C4⋊C4×C17C22⋊C4semidirect
199. C4⋊Dic17C22⋊C4semidirect
203. #63225C22⋊C4semidirect
266. C2×#595C2×C4⋊C4semidirect
321. C22×C17C4×C4⋊C4semidirect
339. C2×D17C4×C4⋊C4semidirect
362. C4×C17C4×C22⋊C4semidirect
366. Dic17C4×C22⋊C4semidirect
379. C22×C4⋊C4#595semidirect
473. C17C22⋊C4×C4⋊C4semidirect
555. C22×C4C4×#595semidirect
570. C4⋊C4C22⋊#595direct (N × H)
711. C22C4⋊C4×#595semidirect
729. C4C4×C22⋊#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637512
C2×C4⋊C4×#5952
C2×C4×C22⋊#5952
#145439632
#145439612
#145439582
C22×C4⋊C4×D172
C22⋊C4×C4⋊C417