Finite Group Databasebeta

← #16958780

Subgroups — #16958780

Order 4352.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587621C211yesmaximal, characteristic
2C2×#11762697C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic17C211yesmaximal, characteristic, complemented
5#14527050C211yesmaximal, characteristic, complemented
6#14527031C211yesmaximal, characteristic, complemented
7#14527027C211yesmaximal, characteristic, complemented
8#14527025C211yesmaximal, characteristic
9#14527021C211yesmaximal, characteristic, complemented
10#14527015C211yesmaximal, characteristic, complemented
11#14527015C211yesmaximal, characteristic, complemented
12#14527012C211yesmaximal, characteristic, complemented
13#14527007C211yesmaximal, characteristic, complemented
14#14527006C211yesmaximal, characteristic, complemented
15C2×C17×#386C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C2×#10587621—24no—
18C2×#10587621—24no—
19C2×#10587621C418yescomplemented
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C22⋊Dic17C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33#11762697—24no—
34C22⋊C4×Dic17—24no—
35C4×C22⋊Dic17—24no—
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C23×D4×C17C2211yescharacteristic
51C24×C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C17×#386—24no—
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C25×C17C2311yescharacteristic
60C22×D4×C17—22no—
61C22×D4×C17—22no—
62C22×D4×C17—22no—
63C22×D4×C17—22no—
64C22×D4×C17—41no—
65C22×D4×C17—41no—
66C22×D4×C17C2×C414yes—
67C23×C4×C17—22no—
68C23×C4×C17—22no—
69C23×C4×C17—22no—
70C23×C4×C17—22no—
71C23×C4×C17—22no—
72C23×C4×C17—41no—
73C23×C4×C17—41no—
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×Dic17—22no—
80C23×Dic17—22no—
81C23×Dic17—22no—
82C23×Dic17—22no—
83C23×Dic17—41no—
84C23×Dic17—41no—
85C23×Dic17C2×C414yescomplemented
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C23×Dic17C2311yescharacteristic
90C23×Dic17C2311yescharacteristic
91C23×Dic17C2311yescharacteristic
92C23×Dic17C2311yescharacteristic
93C23×Dic17C2311yescharacteristic
94C2×C22⋊C4×C17—22no—
95C2×C22⋊C4×C17—22no—
96C2×C22⋊C4×C17—22no—
97C2×C22⋊C4×C17—22no—
98C2×C22⋊C4×C17—22no—
99C2×C22⋊C4×C17—22no—
100C2×C22⋊C4×C17—41no—
101C2×C22⋊C4×C17—41no—
102C2×C22⋊C4×C17D414yes—
103C2×C22⋊Dic17—22no—
104C2×C22⋊Dic17—22no—
105C2×C22⋊Dic17—22no—
106C2×C22⋊Dic17—22no—
107C2×C22⋊Dic17—22no—
108C2×C22⋊Dic17—22no—
109C2×C22⋊Dic17—22no—
110C2×C22⋊Dic17—22no—
111C2×C22⋊Dic17—22no—
112C2×C22⋊Dic17—22no—
113C2×C22⋊Dic17—22no—
114C2×C22⋊Dic17—22no—
115C2×C22⋊Dic17—22no—
116C2×C22⋊Dic17—22no—
117C2×C22⋊Dic17—41no—
118C2×C22⋊Dic17—41no—
119C2×C22⋊Dic17C2×C414yes—
120C2×C22⋊Dic17C2×C414yes—
121C2×C22⋊Dic17C2×C414yescomplemented
122C2×C22⋊Dic17D414yes—
123C2×C22⋊Dic17D414yes—
124#10587621—232no—
125C2×#63225—22no—
126C2×#63225—22no—
127C2×#63225—22no—
128C2×#63225—22no—
129C2×#63225—22no—
130C2×#63225—22no—
131C2×#63225—41no—
132C2×#63225C2×C414yescomplemented
133C2×#63225C2×C414yescomplemented
134C2×C4×Dic17—22no—
135C2×C4×Dic17—22no—
136C2×C4×Dic17—22no—
137C2×C4×Dic17—22no—
138C2×C4×Dic17—22no—
139C2×C4×Dic17—22no—
140C2×C4×Dic17—41no—
141C2×C4×Dic17—41no—
142C2×C4×Dic17—41no—
143C17×#95—22no—
144C17×#95—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—22no—
150#10587502—22no—
151#10587502—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—22no—
155#10587502—41no—
156#10587502—41no—
157#10587502—41no—
158#10587502—41no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17—21no—
165C24×C17—21no—
166C24×C17—21no—
167C24×C17—21no—
168C24×C17—21no—
169C24×C17—21no—
170C24×C17—21no—
171C24×C17—21no—
172C24×C17—21no—
173C24×C17—21no—
174C24×C17—21no—
175C24×C17—21no—
176C24×C17—21no—
177C24×C17—21no—
178C24×C17—21no—
179C24×C17—21no—
180C24×C17—21no—
181C24×C17—21no—
182C24×C17—21no—
183C24×C17C22×C412yes—
184C24×C17C22×C412yes—
185C24×C17C2×D412yes—
186C24×C17C2×D412yes—
187C24×C17C2×D412yes—
188C24×C17#4112yes—
189C24×C17C2411yescharacteristic
190C2×D4×C17—28no—
191C2×D4×C17—28no—
192C2×D4×C17—44no—
193C2×D4×C17—44no—
194C2×D4×C17—44no—
195C2×D4×C17—44no—
196C2×D4×C17—44no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—28no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17—21no—
227C22×C4×C17—44no—
228C22×C4×C17—44no—
229C22×C4×C17—44no—
230C22×C4×C17—44no—
231C22×C4×C17—44no—
232C22×C4×C17—44no—
233C22×C4×C17C22×C412yes—
234C22×C4×C17C2×D412yes—
235C22×C4×C17C2×D412yes—
236C22×C4×C17#4112yes—
237C22×C4×C17#4112yes—
238C22×C4×C17#4112yes—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—28no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—28no—
279C22×Dic17—21no—
280C22×Dic17—21no—
281C22×Dic17—21no—
282C22×Dic17—21no—
283C22×Dic17—21no—
284C22×Dic17—21no—
285C22×Dic17—21no—
286C22×Dic17—44no—
287C22×Dic17—44no—
288C22×Dic17—44no—
289C22×Dic17—44no—
290C22×Dic17—44no—
291C22×Dic17C22×C412yes—
292C22×Dic17C22×C412yes—
293C22×Dic17C22×C412yes—
294C22×Dic17C22×C412yes—
295C22×Dic17C2×D412yes—
296C22×Dic17C2×D412yes—
297C22×Dic17C2×D412yes—
298C22×Dic17C2×D412yes—
299C22×Dic17#4112yes—
300C22×Dic17#4112yes—
301C22×Dic17#4112yes—
302C22⋊C4×C17—28no—
303C22⋊C4×C17—44no—
304C22⋊C4×C17—44no—
305C22⋊Dic17—28no—
306C22⋊Dic17—28no—
307C22⋊Dic17—28no—
308C22⋊Dic17—28no—
309C22⋊Dic17—44no—
310C22⋊Dic17—44no—
311C22⋊Dic17C22⋊C4116yescomplemented
312#63225—28no—
313#63225—28no—
314#63225—44no—
315C4×Dic17—44no—
316C4×Dic17—44no—
317C4×Dic17—44no—
318#14096—171nomaximal, Sylow
319C23×C17—22no—
320C23×C17—22no—
321C23×C17—22no—
322C23×C17—22no—
323C23×C17—22no—
324C23×C17—22no—
325C23×C17—22no—
326C23×C17—22no—
327C23×C17—22no—
328C23×C17—22no—
329C23×C17—22no—
330C23×C17—22no—
331C23×C17—22no—
332C23×C17—22no—
333C23×C17—22no—
334C23×C17—22no—
335C23×C17—22no—
336C23×C17—22no—
337C23×C17—22no—
338C23×C17—22no—
339C23×C17—22no—
340C23×C17—22no—
341C23×C17—22no—
342C23×C17—22no—
343C23×C17—22no—
344C23×C17—22no—
345C23×C17—22no—
346C23×C17—22no—
347C23×C17—22no—
348C23×C17—22no—
349C23×C17—22no—
350C23×C17—22no—
351C23×C17—22no—
352C23×C17—22no—
353C23×C17—22no—
354C23×C17—22no—
355C23×C17—41no—
356C23×C17—41no—
357C23×C17—41no—
358C23×C17—41no—
359C23×C17—41no—
360C23×C17—41no—
361C23×C17—41no—
362C23×C17—41no—
363C23×C17—41no—
364C23×C17—41no—
365C23×C17—41no—
366C23×C17—41no—
367C23×C17—41no—
368C23×C17—41no—
369C23×C17—41no—
370C23×C17—41no—
371C23×C17—41no—
372C23×C17—41no—
373C23×C17—41no—
374C23×C17—41no—
375C23×C17—41no—
376C23×C17—41no—
377C23×C17—41no—
378C23×C17—41no—
379C23×C17—41no—
380C23×C17—41no—
381C23×C17—41no—
382C23×C17—41no—
383C23×C17—41no—
384C23×C17—41no—
385C23×C17—41no—
386C23×C17—41no—
387C23×C17C2×C22⋊C414yes—
388C23×C17C4×D414yes—
389C23×C17C23×C411yescharacteristic
390C23×C17C22×D411yescharacteristic
391C23×C17C22×D411yescharacteristic
392C23×C17C22×D411yescharacteristic
393C23×C17C2×#4111yescharacteristic
394C23×C17C2×#4111yescharacteristic
395C23×C17C2×#4111yescharacteristic
396C23×C17C2×#4111yescharacteristic
397C23×C17C2×#4111yescharacteristic
398C23×C17C2×#4111yescharacteristic
399C23×C17C2×#4111yescharacteristic
400C23×C17H(5,𝔽2)11yescharacteristic
401C23×C17H(5,𝔽2)11yescharacteristic
402C23×C17H(5,𝔽2)11yescharacteristic
403C23×C172−1+411yescharacteristic
404D4×C17—416no—
405C2×C4×C17—22no—
406C2×C4×C17—22no—
407C2×C4×C17—22no—
408C2×C4×C17—22no—
409C2×C4×C17—22no—
410C2×C4×C17—22no—
411C2×C4×C17—22no—
412C2×C4×C17—22no—
413C2×C4×C17—22no—
414C2×C4×C17—22no—
415C2×C4×C17—22no—
416C2×C4×C17—22no—
417C2×C4×C17—22no—
418C2×C4×C17—22no—
419C2×C4×C17—22no—
420C2×C4×C17—416no—
421C2×C4×C17—41no—
422C2×C4×C17—41no—
423C2×C4×C17—41no—
424C2×C4×C17—41no—
425C2×C4×C17—41no—
426C2×C4×C17—41no—
427C2×C4×C17—41no—
428C2×C4×C17—41no—
429C2×C4×C17—41no—
430C2×C4×C17—41no—
431C2×C4×C17—41no—
432C2×C4×C17—41no—
433C2×C4×C17—41no—
434C2×C4×C17—41no—
435C2×C4×C17—41no—
436C2×C4×C17—41no—
437C2×C4×C17—41no—
438C2×C4×C17—41no—
439C2×C4×C17—41no—
440C2×C4×C17#12314yescomplemented
441C2×Dic17—22no—
442C2×Dic17—22no—
443C2×Dic17—22no—
444C2×Dic17—22no—
445C2×Dic17—22no—
446C2×Dic17—22no—
447C2×Dic17—22no—
448C2×Dic17—22no—
449C2×Dic17—22no—
450C2×Dic17—22no—
451C2×Dic17—22no—
452C2×Dic17—22no—
453C2×Dic17—22no—
454C2×Dic17—22no—
455C2×Dic17—22no—
456C2×Dic17—22no—
457C2×Dic17—22no—
458C2×Dic17—22no—
459C2×Dic17—22no—
460C2×Dic17—22no—
461C2×Dic17—22no—
462C2×Dic17—22no—
463C2×Dic17—22no—
464C2×Dic17—22no—
465C2×Dic17—22no—
466C2×Dic17—22no—
467C2×Dic17—22no—
468C2×Dic17—416no—
469C2×Dic17—41no—
470C2×Dic17—41no—
471C2×Dic17—41no—
472C2×Dic17—41no—
473C2×Dic17—41no—
474C2×Dic17—41no—
475C2×Dic17—41no—
476C2×Dic17—41no—
477C2×Dic17—41no—
478C2×Dic17—41no—
479C2×Dic17—41no—
480C2×Dic17—41no—
481C2×Dic17—41no—
482C2×Dic17—41no—
483C2×Dic17—41no—
484C2×Dic17—41no—
485C2×Dic17—41no—
486C2×Dic17—41no—
487C2×Dic17—41no—
488C2×Dic17—41no—
489C2×Dic17—41no—
490C2×Dic17—41no—
491C2×Dic17—41no—
492C2×Dic17—41no—
493C2×Dic17—41no—
494C2×Dic17—41no—
495C2×Dic17—41no—
496C2×Dic17C2×C22⋊C414yes—
497C2×Dic17C2×C22⋊C414yes—
498C22×#123—171no—
499C2×#388—171no—
500C2×#386D1711yescharacteristic
501C2×C4×C22⋊C4—171no—
502C2×C4×C22⋊C4—171no—
503#1445—171no—
504#1440—171no—
505#1439—171no—
506#1438—171no—
507#1437—171no—
508#1436—171no—
509#1436—171no—
510C4⋊#95—171no—
511C22⋊#95—171no—
512C22⋊#95—171no—
513C22×C17—24no—
514C22×C17—24no—
515C22×C17—24no—
516C22×C17—24no—
517C22×C17—24no—
518C22×C17—24no—
519C22×C17—42no—
520C22×C17—42no—
521C22×C17—42no—
522C22×C17—42no—
523C22×C17—42no—
524C22×C17—42no—
525C22×C17—42no—
526C22×C17—42no—
527C22×C17—42no—
528C22×C17—42no—
529C22×C17—42no—
530C22×C17—42no—
531C22×C17—42no—
532C22×C17—42no—
533C22×C17—42no—
534C22×C17—42no—
535C22×C17—42no—
536C22×C17—42no—
537C22×C17—42no—
538C22×C17—42no—
539C22×C17—42no—
540C22×C17—42no—
541C22×C17—42no—
542C22×C17—42no—
543C22×C17C22×C22⋊C411yescharacteristic
544C22×C17C2×C4×D411yescharacteristic
545C22×C17C4×#4111yescharacteristic
546C22×C17C4×#4111yescharacteristic
547C22×C17C4×#4111yescharacteristic
548C22×C17#51811yescharacteristic
549C22×C17#52011yescharacteristic
550C22×C17C2×#12311yescharacteristic
551C22×C17#52511yescharacteristic
552C22×C17#52511yescharacteristic
553C22×C17#52511yescharacteristic
554C22×C17#52911yescharacteristic
555C22×C17#52911yescharacteristic
556C22×C17#53211yescharacteristic
557C22×C17#53211yescharacteristic
558C22×C17#53811yescharacteristic
559C22×C17#53911yescharacteristic
560C22×C17#54011yescharacteristic
561C22×C17#54211yescharacteristic
562C22×C17D4211yescharacteristic
563C22×C17D4211yescharacteristic
564C22×C17#54611yescharacteristic
565C22×C17#54611yescharacteristic
566C22×C17#54611yescharacteristic
567C22×C17#54611yescharacteristic
568C22×C17#54611yescharacteristic
569C22×C17#54711yescharacteristic
570C22×C17#54711yescharacteristic
571C22×C17#54711yescharacteristic
572C22×C17#55111yescharacteristic
573C22×C17#55111yescharacteristic
574C22×C17#55211yescharacteristic
575C22×C17#55311yescharacteristic
576C22×C17#55311yescharacteristic
577C22×C17#55911yescharacteristic
578C4×C17—24no—
579C4×C17—42no—
580C4×C17—42no—
581C4×C17—42no—
582C4×C17—81no—
583Dic17—24no—
584Dic17—24no—
585Dic17—42no—
586Dic17—42no—
587Dic17—42no—
588Dic17—42no—
589Dic17—42no—
590Dic17—81no—
591C23×D4C2×D1711yescharacteristic
592C24×C4—171no—
593C24×C4C2×D1711yescharacteristic
594C2×#123—178no—
595C2×#123—344no—
596C2×#123—344no—
597C22×C4⋊C4—171no—
598C22×C4⋊C4—171no—
599C22×C4⋊C4—171no—
600C22×C22⋊C4—171no—
601C22×C22⋊C4—171no—
602C22×C22⋊C4—171no—
603C22×C22⋊C4—171no—
604C22×C22⋊C4—171no—
605C22×C22⋊C4—171no—
606C22×C22⋊C4—171no—
607C22×C22⋊C4C2×D1711yescharacteristic
608C22×C22⋊C4C2×D1711yescharacteristic
609C22×C22⋊C4C2×D1711yescharacteristic
610C22×C42—171no—
611C22×C42—171no—
612C22×C42—171no—
613#388—344no—
614#386—24no—
615C4×C22⋊C4—344no—
616C4×C22⋊C4—344no—
617C2×#95—171no—
618C2×#95—171no—
619C2×#95—171no—
620C2×#95—171no—
621C2×#95—171no—
622C2×#95—171no—
623C2×#95—171no—
624C2×#95—171no—
625C2×#95—171no—
626C2×#95—171no—
627C2×#95—171no—
628C2×#95—171no—
629C2×#95—171no—
630C2×#95—171no—
631C2×#95C2×D1711yescharacteristic
632C2×#95C2×D1711yescharacteristic
633C2×C17—44no—
634C2×C17—44no—
635C2×C17#229711yescharacteristic
636C2×C17C4×#12311yescharacteristic
637C2×C17#233511yescharacteristic
638C2×C17D4×C22⋊C411yescharacteristic
639C2×C17#233911yescharacteristic
640C2×C17#235911yescharacteristic
641C2×C17#237411yescharacteristic
642C2×C17#241811yescharacteristic
643C2×C17#242211yescharacteristic
644C2×C17#245511yescharacteristic
645C2×C17#245711yescharacteristic
646C2×C17#246411yescharacteristic
647C2×C17#247011yescharacteristic
648C2×C17#255311yescharacteristic
649C2×C17#255711yescharacteristic
650C25C22×D1711yescharacteristic
651C25C22×D1711yescharacteristic
652C22×D4—22no—
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—22no—
656C22×D4—41no—
657C22×D4—41no—
658C22×D4C4×D1714yes—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—41no—
665C23×C4—41no—
666C23×C4—171no—
667C23×C4—171no—
668C23×C4—171no—
669C23×C4—171no—
670C23×C4—171no—
671C23×C4—171no—
672C23×C4—171no—
673C23×C4—174no—
674C23×C4—171no—
675C23×C4—342no—
676C23×C4—342no—
677C23×C4—342no—
678C23×C4—342no—
679C23×C4—681no—
680C23×C4—681no—
681C23×C4C22×D1711yescharacteristic
682C23×C4C22×D1711yescharacteristic
683C23×C4C22×D1711yescharacteristic
684C23×C4C22×D1711yescharacteristic
685C23×C4C22×D1711yescharacteristic
686#123—3432no—
687C2×C4⋊C4—174no—
688C2×C4⋊C4—174no—
689C2×C4⋊C4—342no—
690C2×C4⋊C4—342no—
691C2×C4⋊C4—342no—
692C2×C4⋊C4—342no—
693C2×C4⋊C4—342no—
694C2×C4⋊C4—342no—
695C2×C4⋊C4—681no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—174no—
705C2×C22⋊C4—174no—
706C2×C22⋊C4—174no—
707C2×C22⋊C4—174no—
708C2×C22⋊C4—174no—
709C2×C22⋊C4—342no—
710C2×C22⋊C4—342no—
711C2×C22⋊C4—342no—
712C2×C22⋊C4—342no—
713C2×C22⋊C4—342no—
714C2×C22⋊C4—342no—
715C2×C22⋊C4—342no—
716C2×C22⋊C4—342no—
717C2×C22⋊C4—342no—
718C2×C22⋊C4—342no—
719C2×C22⋊C4—342no—
720C2×C22⋊C4—342no—
721C2×C22⋊C4—342no—
722C2×C22⋊C4—342no—
723C2×C22⋊C4—681no—
724C2×C22⋊C4—681no—
725C2×C22⋊C4C22⋊D1714yes—
726C2×C42—342no—
727C2×C42—342no—
728C2×C42—342no—
729C2×C42—342no—
730C2×C42—342no—
731C2×C42—342no—
732C2×C42—681no—
733C2×C42—681no—
734C2×C42—681no—
735#95—22no—
736#95—22no—
737#95—342no—
738#95—342no—
739#95—342no—
740#95—342no—
741#95—342no—
742#95—342no—
743#95—342no—
744#95—342no—
745#95—342no—
746#95—342no—
747#95—681no—
748#95—681no—
749#95—681no—
750#95—681no—
751C17#1409611yescharacteristic, complemented, Sylow
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24C2×C4×D1712yes—
777C24C2×C4×D1712yes—
778C24#6325212yes—
779C24D4×D1712yes—
780C24D4×D1712yes—
781C24C2×C22⋊D1712yes—
782C24C23×D1711yescharacteristic
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—28no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—172no—
827C22×C4—172no—
828C22×C4—172no—
829C22×C4—172no—
830C22×C4—172no—
831C22×C4—172no—
832C22×C4—172no—
833C22×C4—172no—
834C22×C4—172no—
835C22×C4—172no—
836C22×C4—172no—
837C22×C4—348no—
838C22×C4—341no—
839C22×C4—341no—
840C22×C4—341no—
841C22×C4—341no—
842C22×C4—341no—
843C22×C4—341no—
844C22×C4—341no—
845C22×C4—341no—
846C22×C4—341no—
847C22×C4—341no—
848C22×C4—341no—
849C22×C4—341no—
850C22×C4—341no—
851C22×C4—341no—
852C22×C4—341no—
853C22×C4—341no—
854C22×C4—341no—
855C22×C4—341no—
856C22×C4—341no—
857C22×C4—341no—
858C22×C4—341no—
859C22×C4—341no—
860C22×C4—341no—
861C22×C4—341no—
862C22×C4—341no—
863C22×C4—341no—
864C22×C4—341no—
865C22×C4—341no—
866C22×C4—341no—
867C22×C4—341no—
868C22×C4—341no—
869C22×C4—341no—
870C22×C4—341no—
871C22×C4—341no—
872C22×C4—341no—
873C22×C4—341no—
874C22×C4—341no—
875C22×C4—341no—
876C22×C4—348no—
877C22×C4—341no—
878C22×C4—341no—
879C22×C4—341no—
880C22×C4—341no—
881C22×C4—341no—
882C22×C4—341no—
883C22×C4—341no—
884C22×C4—684no—
885C22×C4—684no—
886C22×C4—684no—
887C22×C4—684no—
888C22×C4—684no—
889C22×C4C2×C4×D1712yes—
890C22×C4#6325412yes—
891C22×C4#6325412yes—
892C22×C4#6325412yes—
893C22×C4C2×C22⋊D1712yes—
894C22×C4C2×C22⋊D1712yes—
895C4⋊C4—348no—
896C4⋊C4—348no—
897C4⋊C4—684no—
898C22⋊C4—28no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—1716no—
902C22⋊C4—348no—
903C22⋊C4—348no—
904C22⋊C4—348no—
905C22⋊C4—348no—
906C22⋊C4—684no—
907C22⋊C4—684no—
908C42—684no—
909C42—684no—
910C42—684no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23C22⋊C4×D1714yes—
980C23C4×C22⋊D1714yes—
981C23C22×C4×D1711yescharacteristic
982C23C2×#6325211yescharacteristic
983C23C2×D4×D1711yescharacteristic
984C23C2×D4×D1711yescharacteristic
985C23C2×#6325411yescharacteristic
986C23C2×#6325411yescharacteristic
987C23C2×#6325411yescharacteristic
988C23#1058769111yescharacteristic
989C23#1058769111yescharacteristic
990C23#1058769111yescharacteristic
991C23#41×D1711yescharacteristic
992C23#41×D1711yescharacteristic
993C23#41×D1711yescharacteristic
994C23#1058769711yescharacteristic
995C23C22×C22⋊D1711yescharacteristic
996D4—416no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—416no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—174no—
1033C2×C4—174no—
1034C2×C4—342no—
1035C2×C4—342no—
1036C2×C4—342no—
1037C2×C4—342no—
1038C2×C4—342no—
1039C2×C4—342no—
1040C2×C4—342no—
1041C2×C4—342no—
1042C2×C4—342no—
1043C2×C4—342no—
1044C2×C4—342no—
1045C2×C4—342no—
1046C2×C4—342no—
1047C2×C4—342no—
1048C2×C4—342no—
1049C2×C4—342no—
1050C2×C4—342no—
1051C2×C4—342no—
1052C2×C4—342no—
1053C2×C4—342no—
1054C2×C4—342no—
1055C2×C4—342no—
1056C2×C4—342no—
1057C2×C4—342no—
1058C2×C4—342no—
1059C2×C4—342no—
1060C2×C4—342no—
1061C2×C4—6816no—
1062C2×C4—681no—
1063C2×C4—681no—
1064C2×C4—681no—
1065C2×C4—681no—
1066C2×C4—681no—
1067C2×C4—681no—
1068C2×C4—681no—
1069C2×C4—681no—
1070C2×C4—681no—
1071C2×C4—681no—
1072C2×C4—681no—
1073C2×C4—681no—
1074C2×C4—681no—
1075C2×C4—681no—
1076C2×C4—681no—
1077C2×C4—681no—
1078C2×C4—681no—
1079C2×C4—681no—
1080C2×C4—681no—
1081C2×C4—681no—
1082C2×C4—681no—
1083C2×C4—681no—
1084C2×C4—681no—
1085C2×C4—681no—
1086C2×C4—681no—
1087C2×C4—681no—
1088C2×C4—681no—
1089C2×C4#1058762114yescomplemented
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C2×C22⋊C4×D1711yescharacteristic
1121C22C2×C4×C22⋊D1711yescharacteristic
1122C22C4×#6325411yescharacteristic
1123C22C4×#6325411yescharacteristic
1124C22C4×#6325411yescharacteristic
1125C22#1176328211yescharacteristic
1126C22#1176328811yescharacteristic
1127C22C2×#1058762111yescharacteristic
1128C22#1176331511yescharacteristic
1129C22#1176331611yescharacteristic
1130C22#1176331711yescharacteristic
1131C22#1176333911yescharacteristic
1132C22#1176333911yescharacteristic
1133C22#1176335411yescharacteristic
1134C22#1176335411yescharacteristic
1135C22#1176339411yescharacteristic
1136C22#1176340211yescharacteristic
1137C22#1176340911yescharacteristic
1138C22#1176342611yescharacteristic
1139C22D4×C22⋊D1711yescharacteristic
1140C22D4×C22⋊D1711yescharacteristic
1141C22#1176344611yescharacteristic
1142C22#1176344811yescharacteristic
1143C22#1176344911yescharacteristic
1144C22#1176344911yescharacteristic
1145C22#1176345311yescharacteristic
1146C22#1176345711yescharacteristic
1147C22#1176345811yescharacteristic
1148C22#1176345911yescharacteristic
1149C22#1176348811yescharacteristic
1150C22#1176349011yescharacteristic
1151C22#1176349911yescharacteristic
1152C22#1176350611yescharacteristic
1153C22#1176350611yescharacteristic
1154C22#1176354311yescharacteristic
1155C4—24no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—344no—
1161C4—344no—
1162C4—682no—
1163C4—682no—
1164C4—682no—
1165C4—682no—
1166C4—682no—
1167C4—1361no—
1168C2—44no—
1169C2—44no—
1170C2#1453126911yescharacteristic
1171C2C4×#1058762111yescharacteristic
1172C2#1453157511yescharacteristic
1173C2C22⋊C4×C22⋊D1711yescharacteristic
1174C2#1453161011yescharacteristic
1175C2#1453177011yescharacteristic
1176C2#1453191711yescharacteristic
1177C2#1453224211yescharacteristic
1178C2#1453229411yescharacteristic
1179C2#1453266311yescharacteristic
1180C2#1453268811yescharacteristic
1181C2#1453278611yescharacteristic
1182C2#1453287711yescharacteristic
1183C2#1453382611yescharacteristic
1184C2#1453388011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#386C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC2×#386D17
hypocenterC17#14096
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#11762697C2semidirect
3. C2×C22⋊C4×Dic17C2semidirect
4. C2×C4×C22⋊Dic17C2semidirect
5. #14527050C2semidirect
6. #14527031C2semidirect
7. #14527027C2semidirect
9. #14527021C2semidirect
10. #14527015C2semidirect
11. #14527015C2semidirect
12. #14527012C2semidirect
13. #14527007C2semidirect
14. #14527006C2semidirect
19. C2×#10587621C4semidirect
85. C23×Dic17C2×C4semidirect
121. C2×C22⋊Dic17C2×C4semidirect
132. C2×#63225C2×C4semidirect
133. C2×#63225C2×C4semidirect
311. C22⋊Dic17C22⋊C4semidirect
440. C2×C4×C17#123semidirect
751. C17#14096semidirect
1089. C2×C4#10587621semidirect

Maximal subgroups

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

subgroupindex
C22×#105876212
C2×#117626972
C2×C22⋊C4×Dic172
C2×C4×C22⋊Dic172
#145270502
#145270312
#145270272
#145270252
#145270212
#145270152
#145270122
#145270072
#145270062
C2×C17×#3862
#1409617