Finite Group Databasebeta

← #16939604

Subgroups — #16939604

Order 4352.

1518 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587578C211yesmaximal, characteristic
2C22×#10587491C211yesmaximal, characteristic
3C2×#11762666C211yesmaximal, characteristic
4C2×#11762572C211yesmaximal, characteristic, complemented
5C2×#11762571C211yesmaximal, characteristic, complemented
6C2×#11762571C211yesmaximal, characteristic, complemented
7C2×C17×#340C211yesmaximal, characteristic, complemented
8C23×C4×D17C2211yescharacteristic
9C23×#3622C2211yescharacteristic
10C2×#10587578—22no—
11C2×#10587578—22no—
12C2×#10587578—22no—
13C2×#10587578—22no—
14C2×#10587578—22no—
15C2×#10587578C414yescomplemented
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63227—21no—
19C22×#63227—21no—
20C22×C4×Dic17—21no—
21C2×#10587491—22no—
22C2×#10587491—22no—
23C2×#10587491C414yescomplemented
24#11762666—22no—
25#11762666C414yescomplemented
26C2×#10587502—21no—
27#11762572—22no—
28#11762571—22no—
29#11762571—22no—
30C23×C8×C17C2211yescharacteristic
31C22×C4⋊C4×C17C2211yescharacteristic
32C22×C4⋊C4×C17C2211yescharacteristic
33C17×#340—22no—
34C24×D17D411yescharacteristic
35C23×C4×C17—21no—
36C23×C4×C17—21no—
37C23×C4×C17C2311yescharacteristic
38C23×Dic17—21no—
39C23×Dic17—21no—
40C23×Dic17D411yescharacteristic
41C22×C4×D17—21no—
42C22×C4×D17—21no—
43C22×C4×D17—21no—
44C22×C4×D17—21no—
45C22×C4×D17—21no—
46C22×C4×D17—21no—
47C22×C4×D17—21no—
48C22×C4×D17—21no—
49C22×C4×D17C2×C412yes—
50C22×C4×D17C2×C412yes—
51C22×C4×D17C2×C412yes—
52C22×C4×D17D412yes—
53C22×C4×D17D412yes—
54C22×C4×D17Q812yes—
55C22×C8×C17—21no—
56C22×C8×C17—21no—
57C22×C8×C17—21no—
58C22×C8×C17—21no—
59C22×C8×C17—21no—
60C22×C8×C17—21no—
61C22×C8×C17C2×C412yes—
62C2×C4⋊C4×C17—21no—
63C2×C4⋊C4×C17—21no—
64C2×C4⋊C4×C17—21no—
65C2×C4⋊C4×C17—21no—
66C2×C4⋊C4×C17—21no—
67C2×C4⋊C4×C17—21no—
68C2×C4⋊C4×C17—21no—
69C2×C4⋊C4×C17—21no—
70C2×C4⋊C4×C17C2×C412yes—
71C2×C4⋊C4×C17C2×C412yes—
72C2×C4⋊C4×C17D412yes—
73C2×C4⋊C4×C17D412yes—
74C2×#63227—24no—
75C2×#63227—24no—
76C2×#63227—24no—
77C2×#63227—24no—
78C2×#63227—42no—
79C2×#63227—42no—
80C2×C4⋊Dic17—21no—
81C2×C4⋊Dic17—21no—
82C2×C4⋊Dic17—21no—
83C2×C4⋊Dic17—21no—
84C2×C4⋊Dic17—21no—
85C2×C4⋊Dic17—21no—
86C2×C4⋊Dic17—21no—
87C2×C4⋊Dic17—21no—
88C2×C4⋊Dic17C2×C412yes—
89C2×C4⋊Dic17C2×C412yes—
90C2×C4⋊Dic17D412yes—
91C2×C4⋊Dic17D412yes—
92C2×C4×Dic17—24no—
93C2×C4×Dic17—24no—
94C2×C4×Dic17—24no—
95C22×#3622—21no—
96C22×#3622—21no—
97C22×#3622—21no—
98C22×#3622—21no—
99C22×#3622—21no—
100C22×#3622—21no—
101C22×#3622C2×C412yes—
102#10587578—28no—
103#10587578—28no—
104#10587578—28no—
105#10587578—28no—
106#10587502—24no—
107#10587491—28no—
108C24×C17C2×D411yescharacteristic
109C23×D17—21no—
110C23×D17—21no—
111C23×D17—21no—
112C23×D17—21no—
113C23×D17—21no—
114C23×D17—21no—
115C23×D17—21no—
116C23×D17—21no—
117C23×D17—21no—
118C23×D17—21no—
119C23×D17—21no—
120C23×D17—21no—
121C23×D17C22⋊C412yes—
122C23×D17C22⋊C412yes—
123C23×D17C4⋊C412yes—
124C22×C4×C17—22no—
125C22×C4×C17—22no—
126C22×C4×C17—22no—
127C22×C4×C17—22no—
128C22×C4×C17—41no—
129C22×C4×C17—41no—
130C22×C4×C17—41no—
131C22×C4×C17—41no—
132C22×C4×C17—41no—
133C22×C4×C17—41no—
134C22×C4×C17—41no—
135C22×C4×C17—41no—
136C22×C4×C17—41no—
137C22×C4×C17—41no—
138C22×C4×C17C22×C411yescharacteristic
139C22×C4×C17C22×C411yescharacteristic
140C22×C4×C17C22×C411yescharacteristic
141C22×C4×C17C2×D411yescharacteristic
142C22×C4×C17C2×D411yescharacteristic
143C22×C4×C17C2×D411yescharacteristic
144C22×C4×C17C2×D411yescharacteristic
145C22×C4×C17C2×D411yescharacteristic
146C22×C4×C17C2×D411yescharacteristic
147C22×C4×C17C2×Q811yescharacteristic
148C22×C4×C17#4111yescharacteristic
149C22×C4×C17#4111yescharacteristic
150C22×C4×C17#4111yescharacteristic
151C22×C4×C17#4111yescharacteristic
152C22×Dic17—21no—
153C22×Dic17—21no—
154C22×Dic17—21no—
155C22×Dic17—21no—
156C22×Dic17—22no—
157C22×Dic17—22no—
158C22×Dic17—22no—
159C22×Dic17—22no—
160C22×Dic17—41no—
161C22×Dic17—41no—
162C22×Dic17—41no—
163C22×Dic17—41no—
164C22×Dic17—41no—
165C22×Dic17—41no—
166C22×Dic17—41no—
167C22×Dic17—41no—
168C22×Dic17—41no—
169C22×Dic17—41no—
170C22×Dic17C22⋊C412yes—
171C22×Dic17C22⋊C412yes—
172C22×Dic17C4⋊C412yes—
173C2×C4×D17—22no—
174C2×C4×D17—22no—
175C2×C4×D17—22no—
176C2×C4×D17—22no—
177C2×C4×D17—22no—
178C2×C4×D17—22no—
179C2×C4×D17—22no—
180C2×C4×D17—22no—
181C2×C4×D17—22no—
182C2×C4×D17—22no—
183C2×C4×D17—22no—
184C2×C4×D17—22no—
185C2×C4×D17—22no—
186C2×C4×D17—22no—
187C2×C4×D17—22no—
188C2×C4×D17—22no—
189C2×C4×D17—22no—
190C2×C4×D17—22no—
191C2×C4×D17—22no—
192C2×C4×D17—22no—
193C2×C4×D17—22no—
194C2×C4×D17—22no—
195C2×C4×D17—22no—
196C2×C4×D17—22no—
197C2×C4×D17C4214yes—
198C2×C4×D17C22⋊C414yes—
199C2×C4×D17C4⋊C414yes—
200C2×C4×D17C4⋊C414yes—
201C2×C8×C17—22no—
202C2×C8×C17—22no—
203C2×C8×C17—22no—
204C2×C8×C17—41no—
205C2×C8×C17—41no—
206C2×C8×C17—41no—
207C2×C8×C17—41no—
208C4⋊C4×C17—22no—
209C4⋊C4×C17—22no—
210C4⋊C4×C17—22no—
211C4⋊C4×C17—22no—
212C4⋊C4×C17—22no—
213C4⋊C4×C17—41no—
214C4⋊C4×C17—41no—
215C4⋊C4×C17C22⋊C414yescomplemented
216#63227—216no—
217#63227—48no—
218C4⋊Dic17—22no—
219C4⋊Dic17—22no—
220C4⋊Dic17—22no—
221C4⋊Dic17—22no—
222C4⋊Dic17—22no—
223C4⋊Dic17—41no—
224C4⋊Dic17—41no—
225C4⋊Dic17C22⋊C414yescomplemented
226C4×Dic17—216no—
227C2×#3622—22no—
228C2×#3622—22no—
229C2×#3622—22no—
230C2×#3622—41no—
231C2×#3622—41no—
232C2×#3622—41no—
233C2×#3622—41no—
234#10731—171nomaximal, Sylow
235C23×C17C2×C22⋊C411yescharacteristic
236C23×C17C2×C22⋊C411yescharacteristic
237C23×C17C2×C4⋊C411yescharacteristic
238C23×C17#12011yescharacteristic
239C23×C17#12011yescharacteristic
240C23×C17#12311yescharacteristic
241C23×C17#12311yescharacteristic
242C23×C17#13511yescharacteristic
243C23×C17#13511yescharacteristic
244C23×C17#13511yescharacteristic
245C23×C17#13511yescharacteristic
246C23×C17AGL(1,ℤ/8)11yescharacteristic
247C23×C17AGL(1,ℤ/8)11yescharacteristic
248C23×C17#13711yescharacteristic
249C23×C17#13711yescharacteristic
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—41no—
269C22×D17—41no—
270C22×D17—41no—
271C22×D17—41no—
272C22×D17—41no—
273C22×D17—41no—
274C22×D17—41no—
275C22×D17—41no—
276C22×D17—41no—
277C22×D17—41no—
278C22×D17—41no—
279C22×D17—41no—
280C22×D17—41no—
281C22×D17—41no—
282C22×D17—41no—
283C22×D17—41no—
284C22×D17#9514yes—
285C2×C4×C17—24no—
286C2×C4×C17—42no—
287C2×C4×C17—42no—
288C2×C4×C17—42no—
289C2×C4×C17—42no—
290C2×C4×C17—42no—
291C2×C4×C17—42no—
292C2×C4×C17—42no—
293C2×C4×C17—42no—
294C2×C4×C17—42no—
295C2×C4×C17—81no—
296C2×C4×C17—81no—
297C2×C4×C17—81no—
298C2×C4×C17—81no—
299C2×C4×C17C2×C4211yescharacteristic
300C2×C4×C17C2×C22⋊C411yescharacteristic
301C2×C4×C17C2×C22⋊C411yescharacteristic
302C2×C4×C17C2×C22⋊C411yescharacteristic
303C2×C4×C17C2×C4⋊C411yescharacteristic
304C2×C4×C17C2×C4⋊C411yescharacteristic
305C2×C4×C17#11711yescharacteristic
306C2×C4×C17#11711yescharacteristic
307C2×C4×C17C4×D411yescharacteristic
308C2×C4×C17C4×D411yescharacteristic
309C2×C4×C17C4×D411yescharacteristic
310C2×C4×C17C4×D411yescharacteristic
311C2×C4×C17C4×D411yescharacteristic
312C2×C4×C17C4×D411yescharacteristic
313C2×C4×C17C4×D411yescharacteristic
314C2×C4×C17C4×D411yescharacteristic
315C2×C4×C17#12011yescharacteristic
316C2×C4×C17#12011yescharacteristic
317C2×C4×C17#12111yescharacteristic
318C2×C4×C17#12111yescharacteristic
319C2×C4×C17#12111yescharacteristic
320C2×C4×C17#12111yescharacteristic
321C2×C4×C17C22⋊Q811yescharacteristic
322C2×C4×C17C22⋊Q811yescharacteristic
323C2×C4×C17C22⋊Q811yescharacteristic
324C2×C4×C17C22⋊Q811yescharacteristic
325C2×C4×C17#12311yescharacteristic
326C2×C4×C17#12311yescharacteristic
327C2×Dic17—22no—
328C2×Dic17—22no—
329C2×Dic17—22no—
330C2×Dic17—22no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—24no—
334C2×Dic17—42no—
335C2×Dic17—42no—
336C2×Dic17—42no—
337C2×Dic17—42no—
338C2×Dic17—42no—
339C2×Dic17—42no—
340C2×Dic17—42no—
341C2×Dic17—42no—
342C2×Dic17—42no—
343C2×Dic17—81no—
344C2×Dic17—81no—
345C2×Dic17—81no—
346C2×Dic17—81no—
347C2×Dic17#9514yes—
348C4×D17—24no—
349C4×D17—24no—
350C4×D17—24no—
351C4×D17—24no—
352C4×D17—24no—
353C4×D17—24no—
354C4×D17—24no—
355C4×D17—24no—
356C8×C17—42no—
357#3622—42no—
358C22×#117—171no—
359C22×C22⋊C8—171no—
360C2×#380—171no—
361C2×#340—171no—
362C2×#340—171no—
363C2×#340—171no—
364C2×#340D1711yescharacteristic, complemented
365C22×C17C2×#9511yescharacteristic
366C22×C17#37911yescharacteristic
367C22×C17#38111yescharacteristic
368C22×C17#38511yescharacteristic
369C22×C17#38511yescharacteristic
370C22×C17#38611yescharacteristic
371C22×C17#38611yescharacteristic
372C22×C17#41611yescharacteristic
373C22×C17#41611yescharacteristic
374C22×C17#41611yescharacteristic
375C22×C17#41611yescharacteristic
376C22×C17#41711yescharacteristic
377C22×C17#41711yescharacteristic
378C22×C17#41811yescharacteristic
379C22×C17#41911yescharacteristic
380C22×C17#42711yescharacteristic
381C22×C17#42711yescharacteristic
382C22×C17#42811yescharacteristic
383C22×C17#42811yescharacteristic
384C22×C17#44911yescharacteristic
385C22×C17#44911yescharacteristic
386C22×C17#44911yescharacteristic
387C22×C17#44911yescharacteristic
388C22×C17#45211yescharacteristic
389C22×C17#45211yescharacteristic
390C22×C17#45211yescharacteristic
391C22×C17#45211yescharacteristic
392C22×C17#48211yescharacteristic
393C22×C17#48211yescharacteristic
394C22×C17#48211yescharacteristic
395C22×C17#48211yescharacteristic
396C22×C17#48511yescharacteristic
397C22×C17#48511yescharacteristic
398C22×C17#48511yescharacteristic
399C22×C17#48511yescharacteristic
400C2×D17—24no—
401C2×D17—24no—
402C2×D17—24no—
403C2×D17—42no—
404C2×D17—42no—
405C2×D17—42no—
406C2×D17—42no—
407C2×D17—42no—
408C2×D17—42no—
409C2×D17—42no—
410C2×D17—42no—
411C2×D17—42no—
412C2×D17—42no—
413C2×D17—42no—
414C2×D17—42no—
415C4×C17—44no—
416C4×C17—82no—
417C4×C17C4×C22⋊C411yescharacteristic
418C4×C17C4×C22⋊C411yescharacteristic
419C4×C17#38011yescharacteristic
420C4×C17#38011yescharacteristic
421C4×C17#38511yescharacteristic
422C4×C17#38511yescharacteristic
423C4×C17#38611yescharacteristic
424C4×C17#38611yescharacteristic
425Dic17—24no—
426Dic17—44no—
427Dic17—82no—
428C24×C4—171no—
429C23×C8—171no—
430C23×C8C2×D1711yescharacteristic
431C2×#117—174no—
432C2×#117—342no—
433C2×#117—342no—
434C2×#117—342no—
435C2×#117—342no—
436C2×#117—342no—
437C22×C4⋊C4—171no—
438C22×C4⋊C4—171no—
439C22×C4⋊C4C2×D1711yescharacteristic
440C22×C4⋊C4C2×D1711yescharacteristic
441C22×C22⋊C4—341no—
442C22×C22⋊C4—341no—
443C22×C42—341no—
444C2×C22⋊C8—174no—
445C2×C22⋊C8—342no—
446C2×C22⋊C8—342no—
447#380—174no—
448#380—342no—
449C2×#95—341no—
450#340—22no—
451#340—342no—
452#340—342no—
453#340—342no—
454C2×C17C22⋊#9511yescharacteristic
455C2×C17#173511yescharacteristic
456C2×C17#173611yescharacteristic
457C2×C17#178811yescharacteristic
458C2×C17#178811yescharacteristic
459C2×C17#182511yescharacteristic
460C2×C17#182511yescharacteristic
461C2×C17#185411yescharacteristic
462C2×C17#185411yescharacteristic
463C2×C17#185411yescharacteristic
464C2×C17#185411yescharacteristic
465C2×C17#187311yescharacteristic
466C2×C17#187311yescharacteristic
467C2×C17#187511yescharacteristic
468C2×C17#187511yescharacteristic
469D17—44no—
470C25—171no—
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—171no—
474C23×C4—172no—
475C23×C4—172no—
476C23×C4—172no—
477C23×C4—172no—
478C23×C4—172no—
479C23×C4—172no—
480C23×C4—341no—
481C23×C4—341no—
482C23×C4—341no—
483C23×C4—341no—
484C23×C4—341no—
485C23×C4—341no—
486C23×C4—341no—
487C23×C4—341no—
488C23×C4—341no—
489C23×C4—341no—
490C23×C4C22×D1711yescharacteristic
491C22×C8—21no—
492C22×C8—21no—
493C22×C8—21no—
494C22×C8—21no—
495C22×C8—21no—
496C22×C8—21no—
497C22×C8—172no—
498C22×C8—341no—
499C22×C8—341no—
500C22×C8—341no—
501C22×C8—341no—
502C22×C8—341no—
503C22×C8—341no—
504C22×C8C4×D1712yes—
505#117—348no—
506#117—348no—
507#117—348no—
508#117—348no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—172no—
518C2×C4⋊C4—172no—
519C2×C4⋊C4—172no—
520C2×C4⋊C4—172no—
521C2×C4⋊C4—341no—
522C2×C4⋊C4—341no—
523C2×C4⋊C4—341no—
524C2×C4⋊C4—341no—
525C2×C4⋊C4—341no—
526C2×C4⋊C4—341no—
527C2×C4⋊C4—341no—
528C2×C4⋊C4—341no—
529C2×C4⋊C4C4×D1712yes—
530C2×C4⋊C4C4×D1712yes—
531C2×C4⋊C4D6812yes—
532C2×C4⋊C4C22⋊D1712yes—
533C2×C22⋊C4—344no—
534C2×C22⋊C4—344no—
535C2×C22⋊C4—344no—
536C2×C22⋊C4—344no—
537C2×C22⋊C4—682no—
538C2×C22⋊C4—682no—
539C2×C42—344no—
540C2×C42—344no—
541C2×C42—344no—
542C22⋊C8—348no—
543#95—344no—
544C17#1073111yescharacteristic, complemented, Sylow
545C24—172no—
546C24—172no—
547C24—172no—
548C24—341no—
549C24—341no—
550C24—341no—
551C24—341no—
552C24—341no—
553C24—341no—
554C24—341no—
555C24—341no—
556C24—341no—
557C24—341no—
558C24—341no—
559C24—341no—
560C24D4×D1711yescharacteristic
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—172no—
576C22×C4—172no—
577C22×C4—172no—
578C22×C4—174no—
579C22×C4—174no—
580C22×C4—174no—
581C22×C4—174no—
582C22×C4—341no—
583C22×C4—341no—
584C22×C4—341no—
585C22×C4—341no—
586C22×C4—342no—
587C22×C4—342no—
588C22×C4—342no—
589C22×C4—342no—
590C22×C4—342no—
591C22×C4—342no—
592C22×C4—342no—
593C22×C4—342no—
594C22×C4—342no—
595C22×C4—342no—
596C22×C4—342no—
597C22×C4—342no—
598C22×C4—342no—
599C22×C4—342no—
600C22×C4—342no—
601C22×C4—342no—
602C22×C4—342no—
603C22×C4—342no—
604C22×C4—342no—
605C22×C4—342no—
606C22×C4—342no—
607C22×C4—342no—
608C22×C4—342no—
609C22×C4—342no—
610C22×C4—342no—
611C22×C4—342no—
612C22×C4—342no—
613C22×C4—342no—
614C22×C4—681no—
615C22×C4—681no—
616C22×C4—681no—
617C22×C4—681no—
618C22×C4—681no—
619C22×C4—681no—
620C22×C4—681no—
621C22×C4—681no—
622C22×C4—681no—
623C22×C4—681no—
624C22×C4C2×C4×D1711yescharacteristic
625C22×C4C2×C4×D1711yescharacteristic
626C22×C4C2×C4×D1711yescharacteristic
627C22×C4C2×D6811yescharacteristic
628C22×C4#6325211yescharacteristic
629C22×C4#6325211yescharacteristic
630C22×C4D4×D1711yescharacteristic
631C22×C4D4×D1711yescharacteristic
632C22×C4D4×D1711yescharacteristic
633C22×C4D4×D1711yescharacteristic
634C22×C4#6325411yescharacteristic
635C22×C4Q8×D1711yescharacteristic
636C22×C4#6325611yescharacteristic
637C22×C4C2×C22⋊D1711yescharacteristic
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—342no—
646C2×C8—342no—
647C2×C8—342no—
648C2×C8—681no—
649C2×C8—681no—
650C2×C8—681no—
651C2×C8—681no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—174no—
660C4⋊C4—342no—
661C4⋊C4—342no—
662C4⋊C4—342no—
663C4⋊C4—342no—
664C4⋊C4—342no—
665C4⋊C4—681no—
666C4⋊C4—681no—
667C4⋊C4#6322714yescomplemented
668C22⋊C4—3416no—
669C22⋊C4—688no—
670C42—3416no—
671C23—174no—
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—
686C23—342no—
687C23—342no—
688C23—342no—
689C23—342no—
690C23—681no—
691C23—681no—
692C23—681no—
693C23—681no—
694C23—681no—
695C23—681no—
696C23—681no—
697C23—681no—
698C23—681no—
699C23—681no—
700C23—681no—
701C23—681no—
702C23—681no—
703C23—681no—
704C23—681no—
705C23—681no—
706C23C22⋊C4×D1711yescharacteristic
707C23C22⋊C4×D1711yescharacteristic
708C23#1058756811yescharacteristic
709C23#1058756911yescharacteristic
710C23C4⋊C4×D1711yescharacteristic
711C23#1058758011yescharacteristic
712C23#1058759711yescharacteristic
713C23#1058759811yescharacteristic
714C23#1058760011yescharacteristic
715C23#1058760111yescharacteristic
716C23#1058760211yescharacteristic
717C23#1058760211yescharacteristic
718C23#1058760411yescharacteristic
719C23#1058760511yescharacteristic
720C23#1058762311yescharacteristic
721C2×C4—24no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—174no—
736C2×C4—342no—
737C2×C4—342no—
738C2×C4—342no—
739C2×C4—342no—
740C2×C4—342no—
741C2×C4—342no—
742C2×C4—344no—
743C2×C4—344no—
744C2×C4—344no—
745C2×C4—344no—
746C2×C4—344no—
747C2×C4—344no—
748C2×C4—344no—
749C2×C4—344no—
750C2×C4—344no—
751C2×C4—682no—
752C2×C4—682no—
753C2×C4—682no—
754C2×C4—682no—
755C2×C4—682no—
756C2×C4—682no—
757C2×C4—682no—
758C2×C4—682no—
759C2×C4—682no—
760C2×C4—1361no—
761C2×C4—1361no—
762C2×C4—1361no—
763C2×C4—1361no—
764C2×C4C42×D1711yescharacteristic
765C2×C4#1058755811yescharacteristic
766C2×C4C4×D6811yescharacteristic
767C2×C4C4×D6811yescharacteristic
768C2×C4C22⋊C4×D1711yescharacteristic
769C2×C4C22⋊C4×D1711yescharacteristic
770C2×C4#1058756711yescharacteristic
771C2×C4#1058756711yescharacteristic
772C2×C4#1058756811yescharacteristic
773C2×C4#1058756911yescharacteristic
774C2×C4#1058757011yescharacteristic
775C2×C4#1058757011yescharacteristic
776C2×C4C4⋊C4×D1711yescharacteristic
777C2×C4C4⋊C4×D1711yescharacteristic
778C2×C4#1058757811yescharacteristic
779C2×C4#1058757911yescharacteristic
780C2×C4#1058757911yescharacteristic
781C2×C4#1058758011yescharacteristic
782C2×C4#1058758111yescharacteristic
783C2×C4#1058758211yescharacteristic
784C2×C4#1058758211yescharacteristic
785C2×C4#1058758311yescharacteristic
786C2×C4C2×#6322711yescharacteristic
787C2×C4C4×C22⋊D1711yescharacteristic
788C2×C4C4×C22⋊D1711yescharacteristic
789C2×C4#1058762311yescharacteristic
790C2×C4#1058762411yescharacteristic
791C2×C4#1058763211yescharacteristic
792C8—42no—
793C8—682no—
794C22—344no—
795C22—344no—
796C22—344no—
797C22—682no—
798C22—682no—
799C22—682no—
800C22—682no—
801C22—682no—
802C22—682no—
803C22—682no—
804C22—682no—
805C22—682no—
806C22—682no—
807C22—682no—
808C22—682no—
809C22#95×D1711yescharacteristic
810C22#1176266411yescharacteristic
811C22#1176267111yescharacteristic
812C22#1176268011yescharacteristic
813C22#1176268311yescharacteristic
814C22#1176268511yescharacteristic
815C22#1176268711yescharacteristic
816C22#1176280211yescharacteristic
817C22#1176280211yescharacteristic
818C22#1176280411yescharacteristic
819C22#1176280411yescharacteristic
820C22#1176280711yescharacteristic
821C22#1176280911yescharacteristic
822C22#1176281211yescharacteristic
823C22#1176281611yescharacteristic
824C22#1176284411yescharacteristic
825C22#1176284611yescharacteristic
826C22#1176284811yescharacteristic
827C22#1176285011yescharacteristic
828C22#1176295111yescharacteristic
829C22#1176295311yescharacteristic
830C22#1176295511yescharacteristic
831C22#1176295711yescharacteristic
832C22#1176296811yescharacteristic
833C22#1176297011yescharacteristic
834C22#1176297211yescharacteristic
835C22#1176297411yescharacteristic
836C22#1176313111yescharacteristic
837C22#1176313211yescharacteristic
838C22#1176313511yescharacteristic
839C22#1176313611yescharacteristic
840C22#1176314811yescharacteristic
841C22#1176314911yescharacteristic
842C22#1176315211yescharacteristic
843C22#1176315311yescharacteristic
844C4—44no—
845C4—82no—
846C4—344no—
847C4—684no—
848C4—1362no—
849C4#1176265611yescharacteristic
850C4C4×#6322711yescharacteristic
851C4#1176266611yescharacteristic
852C4#1176266811yescharacteristic
853C4#1176268011yescharacteristic
854C4#1176268311yescharacteristic
855C4#1176268511yescharacteristic
856C4#1176268711yescharacteristic
857C2—684no—
858C2#1452700511yescharacteristic
859C2#1452849911yescharacteristic
860C2#1452850211yescharacteristic
861C2#1452872111yescharacteristic
862C2#1452872311yescharacteristic
863C2#1452887711yescharacteristic
864C2#1452887811yescharacteristic
865C2#1452898011yescharacteristic
866C2#1452898211yescharacteristic
867C2#1452898411yescharacteristic
868C2#1452898611yescharacteristic
869C2#1452909311yescharacteristic
870C2#1452909511yescharacteristic
871C2#1452910311yescharacteristic
872C2#1452910511yescharacteristic
subgroupG/H
centerC24D4×D17
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC2×C17×#340C2
socleC24×C17C2×D4
prime radicalC24×D17D4
cosocleC23×C4×C17C23
hypercenterC2×#340D17
hypocenterC17#10731
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×#11762572C2semidirect
5. C2×#11762571C2semidirect
6. C2×#11762571C2semidirect
7. C2×C17×#340C2semidirect
15. C2×#10587578C4semidirect
23. C2×#10587491C4semidirect
25. #11762666C4semidirect
215. C4⋊C4×C17C22⋊C4semidirect
225. C4⋊Dic17C22⋊C4semidirect
364. C2×#340D17semidirect
544. C17#10731semidirect
667. C4⋊C4#63227semidirect

Maximal subgroups

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

subgroupindex
C22×#105875782
C22×#105874912
C2×#117626662
C2×#117625722
C2×#117625712
C2×C17×#3402
#1073117