Finite Group Databasebeta

← #16955740

Subgroups — #16955740

Order 4352.

2574 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D17C211yesmaximal, characteristic
2C2×#11762666C211yesmaximal, characteristic
3C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Dic17C211yesmaximal, characteristic, complemented
5C2×C4×#63227C211yesmaximal, characteristic
6C2×#11762656C212yesmaximal
7#14527015C212yesmaximal, complemented
8#14527015C212yesmaximal, complemented
9#14527013C211yesmaximal, characteristic, complemented
10#14527005C212yesmaximal
11C17×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D17C2212yes—
13C23×C4×D17C2211yescharacteristic
14C22×C4⋊Dic17C2211yescharacteristic
15C22×C4⋊Dic17C2211yescharacteristic
16C22×#63225C2212yes—
17C2×C4⋊C4×D17—24no—
18C2×C4⋊C4×D17—24no—
19C2×C4⋊C4×D17C418yescomplemented
20C22×#63227C2211yescharacteristic
21C22×#63227C2212yes—
22C22×#63227C2211yescharacteristic
23C22×C4×Dic17C2212yes—
24C22×C4×Dic17C2212yes—
25C22×C4×Dic17C2211yescharacteristic
26#11762666C418yescomplemented
27C4⋊C4×Dic17—24no—
28C4×C4⋊Dic17—24no—
29C4×#63227C418yescomplemented
30#11762656—28no—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2212yes—
38C22×C4⋊C4×C17C2211yescharacteristic
39C22×C4⋊C4×C17C2211yescharacteristic
40C22×C42×C17C2211yescharacteristic
41C2×C17×#95C2212yes—
42C2×C17×#95C2212yes—
43C24×D17C2311yescharacteristic
44C23×C4×C17C2311yescharacteristic
45C23×C4×C17C2312yes—
46C23×C4×C17C2312yes—
47C23×C4×C17C2311yescharacteristic
48C23×C4×C17C2311yescharacteristic
49C23×Dic17C2312yes—
50C23×Dic17C2311yescharacteristic
51C23×Dic17C2311yescharacteristic
52C23×Dic17C2312yes—
53C23×Dic17C2311yescharacteristic
54C22×C4×D17—22no—
55C22×C4×D17—22no—
56C22×C4×D17—22no—
57C22×C4×D17—22no—
58C22×C4×D17—24no—
59C22×C4×D17—24no—
60C22×C4×D17—24no—
61C22×C4×D17—24no—
62C22×C4×D17—42no—
63C22×C4×D17—42no—
64C22×C4×D17C2×C418yes—
65C22×C4×D17C2×C414yes—
66C22×C4×D17C2×C414yes—
67C22×C4×D17C2×C414yes—
68C2×C4⋊C4×C17—22no—
69C2×C4⋊C4×C17—22no—
70C2×C4⋊C4×C17—22no—
71C2×C4⋊C4×C17—22no—
72C2×C4⋊C4×C17C2×C414yes—
73C2×C4⋊C4×C17C2×C414yescomplemented
74C2×C42×C17—22no—
75C2×C42×C17—22no—
76C2×C42×C17C2×C414yescomplemented
77C2×#63227—24no—
78C2×#63227—22no—
79C2×#63227—22no—
80C2×#63227—24no—
81C2×#63227C2×C414yes—
82C2×#63227C2×C418yes—
83C2×#63227C2×C414yes—
84C2×#63227D414yes—
85C2×#63227Q814yes—
86C2×C4⋊Dic17—22no—
87C2×C4⋊Dic17—22no—
88C2×C4⋊Dic17C2×C414yes—
89C2×C4⋊Dic17C2×C414yescomplemented
90C2×C4⋊Dic17D414yes—
91C2×C4⋊Dic17D414yes—
92C2×#63225—24no—
93C2×#63225—24no—
94C2×#63225C2×C418yes—
95C2×C4×Dic17—22no—
96C2×C4×Dic17—24no—
97C2×C4×Dic17—22no—
98C2×C4×Dic17—24no—
99C2×C4×Dic17—24no—
100C2×C4×Dic17—24no—
101C2×C4×Dic17—42no—
102C2×C4×Dic17—42no—
103C2×C4×Dic17C2×C414yescomplemented
104C4⋊C4×D17—232no—
105C17×#95—24no—
106C17×#95—42no—
107#10587502—24no—
108#10587502—24no—
109#10587502—24no—
110#10587502—42no—
111#10587502C2×C414yescomplemented
112#10587502C2×C414yescomplemented
113#10587502C2×C418yescomplemented
114C24×C17C2411yescharacteristic
115C23×D17—21no—
116C23×D17—21no—
117C23×D17—21no—
118C23×D17—21no—
119C23×D17—21no—
120C23×D17—21no—
121C23×D17—21no—
122C23×D17—21no—
123C23×D17C22×C412yes—
124C23×D17C22×C412yes—
125C23×D17C22×C412yes—
126C23×D17C2×D412yes—
127C23×D17C2×Q812yes—
128C23×D17#4112yes—
129C23×D17#4112yes—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17—22no—
135C22×C4×C17—22no—
136C22×C4×C17—22no—
137C22×C4×C17—21no—
138C22×C4×C17—22no—
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17—22no—
144C22×C4×C17—21no—
145C22×C4×C17—22no—
146C22×C4×C17—22no—
147C22×C4×C17—22no—
148C22×C4×C17—21no—
149C22×C4×C17—22no—
150C22×C4×C17—21no—
151C22×C4×C17—22no—
152C22×C4×C17C22×C414yes—
153C22×C4×C17C22×C412yes—
154C22×C4×C17C22×C414yes—
155C22×C4×C17C22×C412yes—
156C22×C4×C17C22×C412yes—
157C22×C4×C17C22×C412yes—
158C22×C4×C17C22×C412yes—
159C22×C4×C17C2×D412yes—
160C22×C4×C17C2×D412yes—
161C22×C4×C17C2×D412yes—
162C22×C4×C17C2×Q812yes—
163C22×C4×C17#4112yes—
164C22×C4×C17#4112yes—
165C22×Dic17—22no—
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17—21no—
169C22×Dic17—21no—
170C22×Dic17—21no—
171C22×Dic17—22no—
172C22×Dic17—21no—
173C22×Dic17—22no—
174C22×Dic17—22no—
175C22×Dic17—21no—
176C22×Dic17—21no—
177C22×Dic17—21no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—21no—
181C22×Dic17—22no—
182C22×Dic17—21no—
183C22×Dic17—21no—
184C22×Dic17—22no—
185C22×Dic17—21no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—21no—
189C22×Dic17C22×C412yes—
190C22×Dic17C22×C414yes—
191C22×Dic17C22×C412yes—
192C22×Dic17C22×C412yes—
193C22×Dic17C22×C412yes—
194C22×Dic17C22×C414yes—
195C22×Dic17C22×C412yes—
196C22×Dic17C2×D414yes—
197C22×Dic17C2×D414yes—
198C22×Dic17C2×D412yes—
199C22×Dic17C2×Q812yes—
200C2×C4×D17—28no—
201C2×C4×D17—28no—
202C2×C4×D17—28no—
203C2×C4×D17—28no—
204C2×C4×D17—28no—
205C2×C4×D17—28no—
206C2×C4×D17—216no—
207C2×C4×D17—216no—
208C2×C4×D17—48no—
209C2×C4×D17—48no—
210C2×C4×D17—48no—
211C2×C4×D17—48no—
212C2×C4×D17—48no—
213C2×C4×D17C42116yescomplemented
214C4⋊C4×C17—28no—
215C4⋊C4×C17—28no—
216C42×C17—28no—
217#63227—28no—
218#63227—216no—
219#63227C4⋊C4116yescomplemented
220C4⋊Dic17—28no—
221C4⋊Dic17C22⋊C4116yescomplemented
222#63225—216no—
223C4×Dic17—28no—
224C4×Dic17—48no—
225C4×Dic17—48no—
226C22⋊C4×C4⋊C4—171nomaximal, Sylow
227C23×C17C23×C411yescharacteristic
228C23×C17C23×C411yescharacteristic
229C23×C17C23×C411yescharacteristic
230C23×C17C22×D411yescharacteristic
231C23×C17C22×D411yescharacteristic
232C23×C17C22×D411yescharacteristic
233C23×C17C22×Q811yescharacteristic
234C23×C17C2×#4111yescharacteristic
235C23×C17C2×#4111yescharacteristic
236C23×C17C2×#4111yescharacteristic
237C23×C17C2×#4111yescharacteristic
238C23×C17H(5,𝔽2)11yescharacteristic
239C23×C17H(5,𝔽2)11yescharacteristic
240C23×C172−1+411yescharacteristic
241C23×C172−1+411yescharacteristic
242C22×D17—22no—
243C22×D17—22no—
244C22×D17—22no—
245C22×D17—22no—
246C22×D17—22no—
247C22×D17—22no—
248C22×D17—22no—
249C22×D17—22no—
250C22×D17—22no—
251C22×D17—22no—
252C22×D17—22no—
253C22×D17—22no—
254C22×D17—22no—
255C22×D17—22no—
256C22×D17—22no—
257C22×D17—22no—
258C22×D17—22no—
259C22×D17—22no—
260C22×D17—22no—
261C22×D17—22no—
262C22×D17—22no—
263C22×D17—22no—
264C22×D17—22no—
265C22×D17—22no—
266C22×D17—22no—
267C22×D17—22no—
268C22×D17—22no—
269C22×D17—22no—
270C22×D17C2×C4214yes—
271C22×D17C2×C4⋊C414yes—
272C22×D17#11714yes—
273C22×D17C4×D414yes—
274C22×D17C4×D414yes—
275C22×D17C4×Q814yes—
276C22×D17C4×Q814yes—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—24no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—24no—
287C2×C4×C17—24no—
288C2×C4×C17—24no—
289C2×C4×C17—24no—
290C2×C4×C17—24no—
291C2×C4×C17—22no—
292C2×C4×C17—42no—
293C2×C4×C17—42no—
294C2×C4×C17—42no—
295C2×C4×C17—42no—
296C2×C4×C17—42no—
297C2×C4×C17—41no—
298C2×C4×C17—42no—
299C2×C4×C17—42no—
300C2×C4×C17—41no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17—42no—
304C2×C4×C17C2×C4214yes—
305C2×C4×C17C2×C22⋊C414yes—
306C2×C4×C17C2×C4⋊C414yescomplemented
307C2×C4×C17#11714yes—
308C2×C4×C17C4×D414yes—
309C2×C4×C17C4×D414yes—
310C2×C4×C17C4×D414yes—
311C2×C4×C17C4×D414yes—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—24no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—24no—
321C2×Dic17—22no—
322C2×Dic17—24no—
323C2×Dic17—24no—
324C2×Dic17—22no—
325C2×Dic17—24no—
326C2×Dic17—24no—
327C2×Dic17—22no—
328C2×Dic17—22no—
329C2×Dic17—22no—
330C2×Dic17—22no—
331C2×Dic17—22no—
332C2×Dic17—24no—
333C2×Dic17—24no—
334C2×Dic17—22no—
335C2×Dic17—24no—
336C2×Dic17—42no—
337C2×Dic17—41no—
338C2×Dic17—42no—
339C2×Dic17—41no—
340C2×Dic17—42no—
341C2×Dic17—41no—
342C2×Dic17—41no—
343C2×Dic17—42no—
344C2×Dic17C2×C4214yes—
345C2×Dic17C2×C22⋊C418yes—
346C2×Dic17C2×C4⋊C414yescomplemented
347C4×D17—232no—
348C4×D17—432no—
349C23×C4⋊C4—171no—
350C2×#380—171no—
351C2×C4×C4⋊C4—171no—
352C2×C4×C4⋊C4—171no—
353C2×C4×C22⋊C4—171no—
354C2×C4×C22⋊C4—172no—
355#1436—172no—
356#1436—172no—
357C4⋊#95—171no—
358C4⋊#95D1711yescharacteristic, complemented
359C22⋊#95—172no—
360C22×C17C22×C4211yescharacteristic
361C22×C17C22×C22⋊C411yescharacteristic
362C22×C17C22×C4⋊C411yescharacteristic
363C22×C17C2×#11711yescharacteristic
364C22×C17C2×#11711yescharacteristic
365C22×C17C2×C4×D411yescharacteristic
366C22×C17C2×C4×D411yescharacteristic
367C22×C17C2×C4×D411yescharacteristic
368C22×C17C2×C4×D411yescharacteristic
369C22×C17C2×C4×D411yescharacteristic
370C22×C17C2×C4×D411yescharacteristic
371C22×C17C2×C4×Q811yescharacteristic
372C22×C17C2×C4×Q811yescharacteristic
373C22×C17#51811yescharacteristic
374C22×C17#51911yescharacteristic
375C22×C17#52011yescharacteristic
376C22×C17#52011yescharacteristic
377C22×C17#52011yescharacteristic
378C22×C17#52011yescharacteristic
379C22×C17D4211yescharacteristic
380C22×C17D4211yescharacteristic
381C22×C17#54611yescharacteristic
382C22×C17#54611yescharacteristic
383C22×C17#54711yescharacteristic
384C22×C17#54711yescharacteristic
385C22×C17#54811yescharacteristic
386C22×C17#54811yescharacteristic
387C22×C17D4×Q811yescharacteristic
388C22×C17D4×Q811yescharacteristic
389C22×C17#55211yescharacteristic
390C22×C17#55211yescharacteristic
391C22×C17#55311yescharacteristic
392C22×C17#55311yescharacteristic
393C22×C17#55411yescharacteristic
394C22×C17#55411yescharacteristic
395C2×D17—24no—
396C2×D17—24no—
397C2×D17—24no—
398C2×D17—24no—
399C2×D17—24no—
400C2×D17—24no—
401C2×D17—24no—
402C2×D17—24no—
403C2×D17—24no—
404C2×D17—24no—
405C2×D17—24no—
406C2×D17—24no—
407C2×D17—24no—
408C2×D17—24no—
409C2×D17C4×C4⋊C418yescomplemented
410C4×C17—24no—
411C4×C17—44no—
412C4×C17—42no—
413C4×C17—44no—
414C4×C17C4×C22⋊C418yescomplemented
415Dic17—28no—
416Dic17—24no—
417Dic17—24no—
418Dic17—42no—
419Dic17—44no—
420C24×C4—171no—
421C24×C4—172no—
422C22×C4⋊C4—171no—
423C22×C4⋊C4—172no—
424C22×C4⋊C4—171no—
425C22×C4⋊C4—178no—
426C22×C4⋊C4—344no—
427C22×C4⋊C4—344no—
428C22×C4⋊C4C2×D1711yescharacteristic
429C22×C4⋊C4C2×D1711yescharacteristic
430C22×C22⋊C4—171no—
431C22×C22⋊C4—171no—
432C22×C22⋊C4—172no—
433C22×C42—171no—
434C22×C42—172no—
435C22×C42—172no—
436C22×C42C2×D1711yescharacteristic
437#380—178no—
438C4×C4⋊C4—344no—
439C4×C4⋊C4—344no—
440C4×C22⋊C4—178no—
441C4×C22⋊C4—348no—
442C2×#95—171no—
443C2×#95—171no—
444C2×#95—172no—
445C2×#95—172no—
446C2×#95—172no—
447C2×#95—172no—
448C2×#95—172no—
449C2×#95C2×D1712yes—
450C2×#95C2×D1712yes—
451C2×C17C2×C4×C22⋊C411yescharacteristic
452C2×C17C2×C4×C4⋊C411yescharacteristic
453C2×C17#227411yescharacteristic
454C2×C17D4×C22⋊C411yescharacteristic
455C2×C17Q8×C22⋊C411yescharacteristic
456C2×C17#234411yescharacteristic
457C2×C17#234511yescharacteristic
458C2×C17D4×C4⋊C411yescharacteristic
459C2×C17D4×C4⋊C411yescharacteristic
460C2×C17#235211yescharacteristic
461C2×C17#235211yescharacteristic
462C2×C17#236011yescharacteristic
463C2×C17#236011yescharacteristic
464C2×C17#236111yescharacteristic
465C2×C17#236111yescharacteristic
466D17—28no—
467C25—171no—
468C23×C4—171no—
469C23×C4—171no—
470C23×C4—172no—
471C23×C4—174no—
472C23×C4—174no—
473C23×C4—174no—
474C23×C4—172no—
475C23×C4—171no—
476C23×C4—178no—
477C23×C4—344no—
478C23×C4—344no—
479C23×C4—344no—
480C23×C4—344no—
481C23×C4—342no—
482C23×C4—342no—
483C23×C4—342no—
484C23×C4—342no—
485C23×C4—682no—
486C23×C4—682no—
487C23×C4C22×D1712yes—
488C23×C4C22×D1711yescharacteristic
489C23×C4C22×D1712yes—
490C23×C4C22×D1711yescharacteristic
491C23×C4C22×D1711yescharacteristic
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—174no—
497C2×C4⋊C4—174no—
498C2×C4⋊C4—174no—
499C2×C4⋊C4—178no—
500C2×C4⋊C4—174no—
501C2×C4⋊C4—3432no—
502C2×C4⋊C4—344no—
503C2×C4⋊C4—344no—
504C2×C4⋊C4—342no—
505C2×C4⋊C4—342no—
506C2×C4⋊C4C4×D1714yes—
507C2×C4⋊C4C4×D1714yescomplemented
508C2×C22⋊C4—174no—
509C2×C22⋊C4—174no—
510C2×C22⋊C4—174no—
511C2×C22⋊C4—174no—
512C2×C22⋊C4—178no—
513C2×C22⋊C4—344no—
514C2×C22⋊C4—342no—
515C2×C22⋊C4—344no—
516C2×C22⋊C4—342no—
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—174no—
520C2×C42—342no—
521C2×C42—342no—
522C2×C42—344no—
523C2×C42—344no—
524C2×C42—344no—
525C2×C42—344no—
526C2×C42—682no—
527C2×C42—682no—
528C2×C42C4×D1714yescomplemented
529#95—24no—
530#95—42no—
531#95—174no—
532#95—174no—
533#95—178no—
534#95—344no—
535#95—344no—
536#95—344no—
537#95—682no—
538C17C22⋊C4×C4⋊C411yescharacteristic, complemented, Sylow
539C24—172no—
540C24—172no—
541C24—172no—
542C24—172no—
543C24—172no—
544C24—172no—
545C24—172no—
546C24—341no—
547C24—341no—
548C24—341no—
549C24—341no—
550C24—341no—
551C24—341no—
552C24—341no—
553C24—341no—
554C24C23×D1711yescharacteristic
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—172no—
578C22×C4—172no—
579C22×C4—172no—
580C22×C4—172no—
581C22×C4—174no—
582C22×C4—172no—
583C22×C4—174no—
584C22×C4—174no—
585C22×C4—172no—
586C22×C4—1716no—
587C22×C4—172no—
588C22×C4—174no—
589C22×C4—3416no—
590C22×C4—3416no—
591C22×C4—341no—
592C22×C4—342no—
593C22×C4—341no—
594C22×C4—341no—
595C22×C4—341no—
596C22×C4—341no—
597C22×C4—342no—
598C22×C4—341no—
599C22×C4—341no—
600C22×C4—341no—
601C22×C4—342no—
602C22×C4—342no—
603C22×C4—348no—
604C22×C4—348no—
605C22×C4—348no—
606C22×C4—348no—
607C22×C4—348no—
608C22×C4—348no—
609C22×C4—341no—
610C22×C4—342no—
611C22×C4—342no—
612C22×C4—341no—
613C22×C4—342no—
614C22×C4—342no—
615C22×C4—341no—
616C22×C4—341no—
617C22×C4—342no—
618C22×C4—341no—
619C22×C4—342no—
620C22×C4—341no—
621C22×C4—688no—
622C22×C4—688no—
623C22×C4—688no—
624C22×C4—688no—
625C22×C4—688no—
626C22×C4C2×C4×D1712yes—
627C22×C4C2×C4×D1714yes—
628C22×C4C2×C4×D1714yes—
629C22×C4C2×C4×D1712yes—
630C22×C4C2×C4×D1712yes—
631C22×C4C2×C4×D1712yes—
632C22×C4C2×C4×D1712yes—
633C22×C4D4×D1712yes—
634C22×C4D4×D1712yes—
635C22×C4D4×D1712yes—
636C22×C4#6325412yes—
637C22×C4Q8×D1712yes—
638C22×C4#6325612yes—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—1716no—
642C4⋊C4—3416no—
643C4⋊C4—348no—
644C22⋊C4—1716no—
645C22⋊C4—348no—
646C22⋊C4—3416no—
647C42—28no—
648C42—348no—
649C42—688no—
650C42—688no—
651C23—174no—
652C23—174no—
653C23—174no—
654C23—174no—
655C23—174no—
656C23—174no—
657C23—174no—
658C23—342no—
659C23—342no—
660C23—342no—
661C23—342no—
662C23—342no—
663C23—342no—
664C23—342no—
665C23—342no—
666C23—342no—
667C23—342no—
668C23—342no—
669C23—342no—
670C23—342no—
671C23—342no—
672C23—342no—
673C23—342no—
674C23—342no—
675C23—342no—
676C23—342no—
677C23—342no—
678C23—342no—
679C23—342no—
680C23—342no—
681C23—342no—
682C23—342no—
683C23—342no—
684C23—342no—
685C23—342no—
686C23C22×C4×D1711yescharacteristic
687C23C22×C4×D1711yescharacteristic
688C23C22×C4×D1711yescharacteristic
689C23C2×D4×D1711yescharacteristic
690C23C2×D4×D1711yescharacteristic
691C23C2×D4×D1711yescharacteristic
692C23C2×#6325411yescharacteristic
693C23#1058769111yescharacteristic
694C23C2×Q8×D1711yescharacteristic
695C23C2×#6325611yescharacteristic
696C23#1058769411yescharacteristic
697C23#41×D1711yescharacteristic
698C23#41×D1711yescharacteristic
699C23#1058769611yescharacteristic
700C23#1058769711yescharacteristic
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—174no—
729C2×C4—178no—
730C2×C4—174no—
731C2×C4—344no—
732C2×C4—342no—
733C2×C4—342no—
734C2×C4—342no—
735C2×C4—342no—
736C2×C4—342no—
737C2×C4—344no—
738C2×C4—342no—
739C2×C4—342no—
740C2×C4—342no—
741C2×C4—342no—
742C2×C4—342no—
743C2×C4—344no—
744C2×C4—342no—
745C2×C4—344no—
746C2×C4—342no—
747C2×C4—344no—
748C2×C4—344no—
749C2×C4—3432no—
750C2×C4—342no—
751C2×C4—344no—
752C2×C4—342no—
753C2×C4—344no—
754C2×C4—342no—
755C2×C4—344no—
756C2×C4—6832no—
757C2×C4—682no—
758C2×C4—681no—
759C2×C4—682no—
760C2×C4—681no—
761C2×C4—681no—
762C2×C4—682no—
763C2×C4—682no—
764C2×C4—681no—
765C2×C4C42×D1714yes—
766C2×C4C22⋊C4×D1714yes—
767C2×C4#1058756714yes—
768C2×C4#1058756714yes—
769C2×C4C4⋊C4×D1714yescomplemented
770C2×C4#1058757814yes—
771C2×C4#1058757914yes—
772C2×C4#1058757914yes—
773C22—178no—
774C22—344no—
775C22—344no—
776C22—344no—
777C22—344no—
778C22—344no—
779C22—344no—
780C22—344no—
781C22—344no—
782C22—344no—
783C22—344no—
784C22—344no—
785C22—344no—
786C22—344no—
787C22—344no—
788C22C2×C42×D1711yescharacteristic
789C22C2×C22⋊C4×D1711yescharacteristic
790C22C2×C4⋊C4×D1711yescharacteristic
791C22#117×D1711yescharacteristic
792C22C2×#1058757811yescharacteristic
793C22C4×D4×D1711yescharacteristic
794C22C4×D4×D1711yescharacteristic
795C22C2×#1058756711yescharacteristic
796C22C2×#1058756711yescharacteristic
797C22C2×#1058757911yescharacteristic
798C22C2×#1058757911yescharacteristic
799C22C4×Q8×D1711yescharacteristic
800C22C4×Q8×D1711yescharacteristic
801C22#1176328111yescharacteristic
802C22#1176328511yescharacteristic
803C22#1176328811yescharacteristic
804C22#1176328911yescharacteristic
805C22#1176329011yescharacteristic
806C22#1176329111yescharacteristic
807C22#1176344311yescharacteristic
808C22#1176344411yescharacteristic
809C22#1176345211yescharacteristic
810C22#1176345611yescharacteristic
811C22#1176345911yescharacteristic
812C22#1176346211yescharacteristic
813C22#1176346711yescharacteristic
814C22#1176346911yescharacteristic
815C22#1176347211yescharacteristic
816C22#1176347411yescharacteristic
817C22#1176349311yescharacteristic
818C22#1176349711yescharacteristic
819C22#1176350611yescharacteristic
820C22#1176351211yescharacteristic
821C22#1176351711yescharacteristic
822C22#1176352011yescharacteristic
823C4—24no—
824C4—44no—
825C4—42no—
826C4—44no—
827C4—348no—
828C4—344no—
829C4—344no—
830C4—682no—
831C4—684no—
832C4#1176265618yescomplemented
833C2—348no—
834C2C2×#1176265611yescharacteristic
835C2C4×C4⋊C4×D1711yescharacteristic
836C2#1453113811yescharacteristic
837C2#1453160511yescharacteristic
838C2#1453161811yescharacteristic
839C2#1453165211yescharacteristic
840C2#1453166011yescharacteristic
841C2#1453168011yescharacteristic
842C2#1453168411yescharacteristic
843C2#1453170611yescharacteristic
844C2#1453171011yescharacteristic
845C2#1453178811yescharacteristic
846C2#1453179411yescharacteristic
847C2#1453179911yescharacteristic
848C2#1453180511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC17×C4⋊#95C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenterC4⋊#95D17
hypocenterC17C22⋊C4×C4⋊C4
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic17C2semidirect
4. C2×C4×C4⋊Dic17C2semidirect
7. #14527015C2semidirect
8. #14527015C2semidirect
9. #14527013C2semidirect
11. C17×C4⋊#95C2semidirect
19. C2×C4⋊C4×D17C4semidirect
26. #11762666C4semidirect
29. C4×#63227C4semidirect
73. C2×C4⋊C4×C17C2×C4semidirect
76. C2×C42×C17C2×C4semidirect
89. C2×C4⋊Dic17C2×C4semidirect
103. C2×C4×Dic17C2×C4semidirect
111. #10587502C2×C4semidirect
112. #10587502C2×C4semidirect
113. #10587502C2×C4semidirect
213. C2×C4×D17C42semidirect
219. #63227C4⋊C4semidirect
221. C4⋊Dic17C22⋊C4semidirect
306. C2×C4×C17C2×C4⋊C4semidirect
346. C2×Dic17C2×C4⋊C4semidirect
358. C4⋊#95D17semidirect
409. C2×D17C4×C4⋊C4semidirect
414. C4×C17C4×C22⋊C4semidirect
507. C2×C4⋊C4C4×D17semidirect
528. C2×C42C4×D17semidirect
538. C17C22⋊C4×C4⋊C4semidirect
769. C2×C4C4⋊C4×D17semidirect
832. C4#11762656semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D172
C2×#117626662
C2×C4⋊C4×Dic172
C2×C4×C4⋊Dic172
C2×C4×#632272
C2×#117626562
#145270152
#145270132
#145270052
C17×C4⋊#952
C22⋊C4×C4⋊C417