Finite Group Databasebeta

← #16958396

Subgroups — #16958396

Order 4352.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587612C211yesmaximal, characteristic, complemented
2C2×#11762709C211yesmaximal, characteristic
3C2×#11762701C211yesmaximal, characteristic, complemented
4C2×#11762698C211yesmaximal, characteristic, complemented
5C2×#11762688C211yesmaximal, characteristic
6#14527048C211yesmaximal, characteristic, complemented
7#14527030C211yesmaximal, characteristic, complemented
8#14527027C211yesmaximal, characteristic, complemented
9#14527023C211yesmaximal, characteristic
10#14527021C211yesmaximal, characteristic, complemented
11#14527020C211yesmaximal, characteristic, complemented
12#14527018C211yesmaximal, characteristic, complemented
13#14527015C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C17×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C2×#10587612—24no—
18C2×#10587612—24no—
19C2×#10587612—24no—
20C22×C4⋊Dic17C2211yescharacteristic
21C22×C4⋊Dic17C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36C22×C4×Dic17C2211yescharacteristic
37#11762709—24no—
38#11762701—24no—
39#11762698—24no—
40#11762688C418yescomplemented
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C24×C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C24×D17C2311yescharacteristic
60C23×C4×C17—22no—
61C23×C4×C17—22no—
62C23×C4×C17—22no—
63C23×C4×C17—22no—
64C23×C4×C17—22no—
65C23×C4×C17—22no—
66C23×C4×C17C2×C414yes—
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C22×C22⋊D17—22no—
74C22×C22⋊D17—22no—
75C22×C22⋊D17—22no—
76C22×C22⋊D17—22no—
77C22×C22⋊D17—41no—
78C22×C22⋊D17—41no—
79C22×C22⋊D17C2×C414yes—
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C2×C22⋊C4×C17—22no—
88C2×C22⋊C4×C17—22no—
89C2×C22⋊C4×C17—22no—
90C2×C22⋊C4×C17—22no—
91C2×C22⋊C4×C17—41no—
92C2×C22⋊C4×C17—41no—
93C2×C22⋊Dic17—22no—
94C2×C22⋊Dic17—22no—
95C2×C22⋊Dic17—22no—
96C2×C22⋊Dic17—22no—
97C2×C22⋊Dic17—22no—
98C2×C22⋊Dic17—41no—
99C2×C22⋊Dic17—41no—
100C2×C22⋊Dic17C2×C414yes—
101C2×C22⋊Dic17D414yes—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—22no—
105C2×#63227—22no—
106C2×#63227—22no—
107C2×#63227—22no—
108C2×#63227—22no—
109C2×#63227—22no—
110C2×#63227—22no—
111C2×#63227—22no—
112C2×#63227—22no—
113C2×#63227—22no—
114C2×#63227—41no—
115C2×#63227—41no—
116C2×#63227—41no—
117C2×#63227—41no—
118C2×#63227C2×C414yes—
119C2×#63227C2×C414yes—
120#10587612—232no—
121C2×C4⋊Dic17—22no—
122C2×C4⋊Dic17—22no—
123C2×C4⋊Dic17—22no—
124C2×C4⋊Dic17—22no—
125C2×C4⋊Dic17—22no—
126C2×C4⋊Dic17D414yescomplemented
127C2×#63225—22no—
128C2×#63225—22no—
129C2×#63225—22no—
130C2×#63225—41no—
131C2×#63225—41no—
132C2×#63225—41no—
133C2×C4×Dic17—22no—
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—22no—
141C2×C4×Dic17—22no—
142C2×C4×Dic17—41no—
143C2×C4×Dic17—41no—
144C2×C4×Dic17D414yescomplemented
145C17×#95—22no—
146C17×#95—22no—
147C17×#95—22no—
148C17×#95—22no—
149#10587502—22no—
150#10587502—22no—
151#10587502—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—41no—
155#10587502—41no—
156#10587502—41no—
157#10587502C2×C414yes—
158#10587502C2×C414yes—
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×C17C22×C412yes—
172C24×C17C2×D412yes—
173C24×C17#4112yes—
174C24×C17C2411yescharacteristic
175C23×D17—21no—
176C23×D17—21no—
177C23×D17—21no—
178C23×D17—21no—
179C23×D17—21no—
180C23×D17—21no—
181C23×D17—21no—
182C23×D17—21no—
183C23×D17—21no—
184C23×D17—21no—
185C23×D17—21no—
186C23×D17—21no—
187C23×D17—21no—
188C23×D17—21no—
189C23×D17C22×C412yes—
190C22×C4×C17—28no—
191C22×C4×C17—28no—
192C22×C4×C17—28no—
193C22×C4×C17—28no—
194C22×C4×C17—28no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—28no—
204C22×C4×C17—28no—
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—21no—
228C22×C4×C17—21no—
229C22×C4×C17—21no—
230C22×C4×C17—21no—
231C22×C4×C17C22×C412yes—
232C22×C4×C17C22×C412yes—
233C22×C4×C17C2×D412yes—
234C22×C4×C17C2×D412yes—
235C22×C4×C17#4112yes—
236C22×C4×C17#4112yes—
237C22×C4×C17#4112yes—
238C22×C4×C17#4112yes—
239C2×C22⋊D17—28no—
240C2×C22⋊D17—28no—
241C2×C22⋊D17—44no—
242C2×C22⋊D17—44no—
243C2×C22⋊D17—44no—
244C2×C22⋊D17—44no—
245C2×C22⋊D17—44no—
246C22×Dic17—21no—
247C22×Dic17—21no—
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—21no—
279C22×Dic17—21no—
280C22×Dic17—21no—
281C22×Dic17—21no—
282C22×Dic17—21no—
283C22×Dic17—21no—
284C22×Dic17C22×C412yes—
285C22×Dic17C22×C412yes—
286C22×Dic17C22×C412yes—
287C22×Dic17C2×D412yes—
288C22×Dic17C2×D412yes—
289C22×Dic17C2×D412yes—
290C22×Dic17C2×D412yes—
291C22×Dic17C2×D412yes—
292C22×Dic17C2×D412yes—
293C22×Dic17#4112yes—
294C22×Dic17#4112yes—
295C22⋊C4×C17—44no—
296C22⋊C4×C17—44no—
297C22⋊Dic17—28no—
298C22⋊Dic17—28no—
299C22⋊Dic17—44no—
300#63227—28no—
301#63227—28no—
302#63227—44no—
303#63227—44no—
304#63227—44no—
305#63227—44no—
306C4⋊Dic17—28no—
307C4⋊Dic17—28no—
308#63225—44no—
309#63225—44no—
310C4×Dic17—28no—
311C4×Dic17—28no—
312C4×Dic17—44no—
313C4×Dic17—44no—
314#14071—171nomaximal, Sylow
315C23×C17—22no—
316C23×C17—22no—
317C23×C17—22no—
318C23×C17—22no—
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—41no—
334C23×C17—41no—
335C23×C17—41no—
336C23×C17—41no—
337C23×C17—41no—
338C23×C17—41no—
339C23×C17—41no—
340C23×C17—41no—
341C23×C17—41no—
342C23×C17—41no—
343C23×C17—41no—
344C23×C17—41no—
345C23×C17—41no—
346C23×C17—41no—
347C23×C17—41no—
348C23×C17—41no—
349C23×C17C4×D414yes—
350C23×C17C23×C411yescharacteristic
351C23×C17C22×D411yescharacteristic
352C23×C17C22×D411yescharacteristic
353C23×C17C22×D411yescharacteristic
354C23×C17C2×#4111yescharacteristic
355C23×C17C2×#4111yescharacteristic
356C23×C17C2×#4111yescharacteristic
357C23×C17C2×#4111yescharacteristic
358C23×C17C2×#4111yescharacteristic
359C23×C17C2×#4111yescharacteristic
360C23×C17C2×#4111yescharacteristic
361C23×C17H(5,𝔽2)11yescharacteristic
362C23×C17H(5,𝔽2)11yescharacteristic
363C23×C17H(5,𝔽2)11yescharacteristic
364C23×C172−1+411yescharacteristic
365C22×D17—22no—
366C22×D17—22no—
367C22×D17—22no—
368C22×D17—22no—
369C22×D17—22no—
370C22×D17—22no—
371C22×D17—22no—
372C22×D17—41no—
373C22×D17—41no—
374C22×D17—41no—
375C22×D17—41no—
376C22×D17—41no—
377C22×D17—41no—
378C22×D17—41no—
379C22×D17—41no—
380C22×D17—41no—
381C22×D17—41no—
382C22×D17—41no—
383C22×D17—41no—
384C22×D17—41no—
385C22×D17—41no—
386C22×D17—41no—
387C22×D17—41no—
388C22×D17—41no—
389C22×D17—41no—
390C22×D17—41no—
391C22×D17—41no—
392C22×D17—41no—
393C22×D17—41no—
394C22×D17—41no—
395C22×D17—41no—
396C22×D17—41no—
397C22×D17—41no—
398C22×D17—41no—
399C22×D17—41no—
400C2×C4×C17—232no—
401C2×C4×C17—22no—
402C2×C4×C17—22no—
403C2×C4×C17—22no—
404C2×C4×C17—22no—
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—41no—
420C2×C4×C17—41no—
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—41no—
441C2×C4×C17C4×D414yes—
442C2×C4×C17C4×D414yes—
443C22⋊D17—416no—
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—22no—
469C2×Dic17—22no—
470C2×Dic17—22no—
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#11714yescomplemented
492C2×Dic17#12014yes—
493C22×#117—171no—
494C2×#390—171no—
495C2×#388—171no—
496C2×#388—171no—
497C2×#386—171no—
498#1444—171no—
499#1439—171no—
500#1439—171no—
501#1438—171no—
502#1437—171no—
503#1437—171no—
504#1436—171no—
505#1436—171no—
506C22⋊#95D1711yescharacteristic, complemented
507C4×#95—171no—
508C22×C17—24no—
509C22×C17—24no—
510C22×C17—24no—
511C22×C17—42no—
512C22×C17—42no—
513C22×C17—42no—
514C22×C17—42no—
515C22×C17—42no—
516C22×C17—42no—
517C22×C17—42no—
518C22×C17—42no—
519C22×C17—42no—
520C22×C17—42no—
521C22×C17—42no—
522C22×C17—42no—
523C22×C17C2×#11711yescharacteristic
524C22×C17C2×C4×D411yescharacteristic
525C22×C17C2×C4×D411yescharacteristic
526C22×C17C2×C4×D411yescharacteristic
527C22×C17C4×#4111yescharacteristic
528C22×C17#51811yescharacteristic
529C22×C17#52011yescharacteristic
530C22×C17C2×#12011yescharacteristic
531C22×C17#52511yescharacteristic
532C22×C17#52511yescharacteristic
533C22×C17#52511yescharacteristic
534C22×C17#52911yescharacteristic
535C22×C17#52911yescharacteristic
536C22×C17#53211yescharacteristic
537C22×C17#53211yescharacteristic
538C22×C17#53511yescharacteristic
539C22×C17#53711yescharacteristic
540C22×C17#54011yescharacteristic
541C22×C17#54211yescharacteristic
542C22×C17#54611yescharacteristic
543C22×C17#54611yescharacteristic
544C22×C17#54611yescharacteristic
545C22×C17#54611yescharacteristic
546C22×C17#54711yescharacteristic
547C22×C17#54711yescharacteristic
548C22×C17#55011yescharacteristic
549C22×C17#55011yescharacteristic
550C22×C17#55111yescharacteristic
551C22×C17#55111yescharacteristic
552C22×C17#55111yescharacteristic
553C22×C17#55211yescharacteristic
554C22×C17#55311yescharacteristic
555C22×C17#55511yescharacteristic
556C22×C17#55511yescharacteristic
557C22×C17#55611yescharacteristic
558C2×D17—42no—
559C2×D17—42no—
560C2×D17—42no—
561C2×D17—42no—
562C2×D17—42no—
563C2×D17—42no—
564C2×D17—42no—
565C2×D17—81no—
566C2×D17—81no—
567C2×D17—81no—
568C2×D17—81no—
569C2×D17—81no—
570C2×D17—81no—
571C2×D17—81no—
572C2×D17—81no—
573C4×C17—24no—
574C4×C17—24no—
575C4×C17—42no—
576C4×C17—42no—
577C4×C17—81no—
578C4×C17—81no—
579Dic17—24no—
580Dic17—24no—
581Dic17—42no—
582Dic17—42no—
583Dic17—42no—
584Dic17—42no—
585Dic17—42no—
586C23×D4—171no—
587C24×C4C2×D1711yescharacteristic
588C2×#117—344no—
589C2×#117—344no—
590C2×#117—344no—
591C22×C4⋊C4—171no—
592C22×C4⋊C4—171no—
593C22×C4⋊C4—171no—
594C22×C4⋊C4—171no—
595C22×C22⋊C4—171no—
596C22×C22⋊C4—171no—
597C22×C22⋊C4—171no—
598C22×C22⋊C4—171no—
599C22×C22⋊C4—171no—
600C22×C22⋊C4—171no—
601C22×C22⋊C4—171no—
602C22×C22⋊C4—171no—
603C22×C22⋊C4—171no—
604C22×C22⋊C4C2×D1711yescharacteristic
605C22×C22⋊C4C2×D1711yescharacteristic
606C22×C42—171no—
607C22×C42—171no—
608C22×C42—171no—
609C22×C42—171no—
610#390—344no—
611#388—344no—
612#388—344no—
613#386—178no—
614C2×#95—171no—
615C2×#95—171no—
616C2×#95—171no—
617C2×#95—171no—
618C2×#95—171no—
619C2×#95—171no—
620C2×#95—171no—
621C2×#95—171no—
622C2×#95—171no—
623C2×#95—171no—
624C2×#95C2×D1711yescharacteristic
625C2×#95C2×D1711yescharacteristic
626C2×#95C2×D1711yescharacteristic
627C2×#95C2×D1711yescharacteristic
628C2×C17—44no—
629C2×C17#229311yescharacteristic
630C2×C17C4×#12011yescharacteristic
631C2×C17#232411yescharacteristic
632C2×C17#234211yescharacteristic
633C2×C17#235411yescharacteristic
634C2×C17#235911yescharacteristic
635C2×C17#236311yescharacteristic
636C2×C17#243011yescharacteristic
637C2×C17#243111yescharacteristic
638C2×C17#247111yescharacteristic
639C2×C17#247411yescharacteristic
640C2×C17#247611yescharacteristic
641C2×C17#247911yescharacteristic
642C2×C17#260111yescharacteristic
643C2×C17#261011yescharacteristic
644D17—82no—
645C25—171no—
646C25C22×D1711yescharacteristic
647C22×D4—174no—
648C22×D4—342no—
649C22×D4—342no—
650C22×D4—342no—
651C22×D4—342no—
652C22×D4—681no—
653C22×D4—681no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—171no—
661C23×C4—171no—
662C23×C4—171no—
663C23×C4—171no—
664C23×C4—171no—
665C23×C4—171no—
666C23×C4—171no—
667C23×C4C4×D1714yes—
668C23×C4C22×D1711yescharacteristic
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C23×C4C22×D1711yescharacteristic
672C23×C4C22×D1711yescharacteristic
673C23×C4C22×D1711yescharacteristic
674#117—3432no—
675C2×C4⋊C4—174no—
676C2×C4⋊C4—342no—
677C2×C4⋊C4—342no—
678C2×C4⋊C4—342no—
679C2×C4⋊C4—342no—
680C2×C4⋊C4—342no—
681C2×C4⋊C4—342no—
682C2×C4⋊C4—342no—
683C2×C4⋊C4—342no—
684C2×C4⋊C4—681no—
685C2×C4⋊C4—681no—
686C2×C4⋊C4—681no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—174no—
694C2×C22⋊C4—174no—
695C2×C22⋊C4—174no—
696C2×C22⋊C4—174no—
697C2×C22⋊C4—342no—
698C2×C22⋊C4—342no—
699C2×C22⋊C4—342no—
700C2×C22⋊C4—342no—
701C2×C22⋊C4—342no—
702C2×C22⋊C4—342no—
703C2×C22⋊C4—342no—
704C2×C22⋊C4—342no—
705C2×C22⋊C4—342no—
706C2×C22⋊C4—342no—
707C2×C22⋊C4—342no—
708C2×C22⋊C4—342no—
709C2×C22⋊C4—342no—
710C2×C22⋊C4—342no—
711C2×C22⋊C4—342no—
712C2×C22⋊C4—342no—
713C2×C22⋊C4—342no—
714C2×C22⋊C4—681no—
715C2×C22⋊C4—681no—
716C2×C22⋊C4—681no—
717C2×C22⋊C4—681no—
718C2×C22⋊C4—681no—
719C2×C22⋊C4—681no—
720C2×C42—174no—
721C2×C42—342no—
722C2×C42—342no—
723C2×C42—342no—
724C2×C42—342no—
725C2×C42—342no—
726C2×C42—342no—
727C2×C42—342no—
728C2×C42—342no—
729C2×C42—342no—
730C2×C42—681no—
731C2×C42—681no—
732#95—22no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—174no—
737#95—174no—
738#95—342no—
739#95—342no—
740#95—342no—
741#95—342no—
742#95—342no—
743#95—681no—
744#95—681no—
745#95—681no—
746C17#1407111yescharacteristic, complemented, Sylow
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—172no—
760C24—341no—
761C24—341no—
762C24—341no—
763C24—341no—
764C24—341no—
765C24—341no—
766C24—341no—
767C24—341no—
768C24—341no—
769C24—341no—
770C24—341no—
771C24—341no—
772C24—341no—
773C24—341no—
774C24C2×C4×D1712yes—
775C24D4×D1712yes—
776C24#6325412yes—
777C24C23×D1711yescharacteristic
778C2×D4—348no—
779C2×D4—348no—
780C2×D4—684no—
781C2×D4—684no—
782C2×D4—684no—
783C2×D4—684no—
784C2×D4—684no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—28no—
798C22×C4—28no—
799C22×C4—28no—
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—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
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—341no—
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×C4C2×C4×D1712yes—
876C22×C4C2×C4×D1712yes—
877C22×C4#6325212yes—
878C22×C4#6325212yes—
879C22×C4D4×D1712yes—
880C22×C4D4×D1712yes—
881C22×C4#6325412yes—
882C22×C4#6325412yes—
883C4⋊C4—348no—
884C4⋊C4—348no—
885C4⋊C4—684no—
886C4⋊C4—684no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—348no—
890C22⋊C4—348no—
891C22⋊C4—348no—
892C22⋊C4—348no—
893C22⋊C4—684no—
894C22⋊C4—684no—
895C22⋊C4—684no—
896C22⋊C4—684no—
897C22⋊C4—684no—
898C42—348no—
899C42—348no—
900C42—684no—
901C42—684no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—342no—
937C23—342no—
938C23—342no—
939C23—342no—
940C23—342no—
941C23—342no—
942C23—342no—
943C23—681no—
944C23—681no—
945C23—681no—
946C23—681no—
947C23—681no—
948C23—681no—
949C23—681no—
950C23—681no—
951C23—681no—
952C23—681no—
953C23—681no—
954C23—681no—
955C23—681no—
956C23—681no—
957C23—681no—
958C23—681no—
959C23—681no—
960C23—681no—
961C23—681no—
962C23—681no—
963C23—681no—
964C23—681no—
965C23—681no—
966C23—681no—
967C23—681no—
968C23—681no—
969C23—681no—
970C23—681no—
971C23#1058756714yes—
972C23C22×C4×D1711yescharacteristic
973C23C2×#6325211yescharacteristic
974C23C2×#6325211yescharacteristic
975C23C2×D4×D1711yescharacteristic
976C23C2×D4×D1711yescharacteristic
977C23C2×D4×D1711yescharacteristic
978C23C2×#6325411yescharacteristic
979C23C2×#6325411yescharacteristic
980C23C2×#6325411yescharacteristic
981C23#1058769111yescharacteristic
982C23#1058769411yescharacteristic
983C23#41×D1711yescharacteristic
984C23#41×D1711yescharacteristic
985C23#1058769611yescharacteristic
986C23#1058769611yescharacteristic
987D4—6816no—
988C2×C4—232no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
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—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
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—174no—
1030C2×C4—174no—
1031C2×C4—342no—
1032C2×C4—342no—
1033C2×C4—342no—
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—681no—
1059C2×C4—681no—
1060C2×C4—681no—
1061C2×C4—681no—
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#1058756714yes—
1079C2×C4#1058756714yes—
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—682no—
1096C22—682no—
1097C22—682no—
1098C22—682no—
1099C22—682no—
1100C22—682no—
1101C22—682no—
1102C22—1361no—
1103C22—1361no—
1104C22—1361no—
1105C22—1361no—
1106C22—1361no—
1107C22—1361no—
1108C22—1361no—
1109C22—1361no—
1110C22#117×D1711yescharacteristic
1111C22C2×#1058756711yescharacteristic
1112C22C2×#1058756711yescharacteristic
1113C22C2×#1058756711yescharacteristic
1114C22C4×#6325211yescharacteristic
1115C22#1176328311yescharacteristic
1116C22#1176329011yescharacteristic
1117C22#120×D1711yescharacteristic
1118C22#1176331511yescharacteristic
1119C22#1176331511yescharacteristic
1120C22#1176331511yescharacteristic
1121C22#1176333911yescharacteristic
1122C22#1176333911yescharacteristic
1123C22#1176335611yescharacteristic
1124C22#1176335611yescharacteristic
1125C22#1176337511yescharacteristic
1126C22#1176338911yescharacteristic
1127C22#1176341211yescharacteristic
1128C22#1176343211yescharacteristic
1129C22#1176344911yescharacteristic
1130C22#1176345111yescharacteristic
1131C22#1176345111yescharacteristic
1132C22#1176345511yescharacteristic
1133C22#1176346011yescharacteristic
1134C22#1176346111yescharacteristic
1135C22#1176347711yescharacteristic
1136C22#1176348011yescharacteristic
1137C22#1176348211yescharacteristic
1138C22#1176348211yescharacteristic
1139C22#1176348511yescharacteristic
1140C22#1176349411yescharacteristic
1141C22#1176350511yescharacteristic
1142C22#1176352311yescharacteristic
1143C22#1176352411yescharacteristic
1144C22#1176353011yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—81no—
1150C4—81no—
1151C4—344no—
1152C4—344no—
1153C4—682no—
1154C4—682no—
1155C4—682no—
1156C4—682no—
1157C4—682no—
1158C2—44no—
1159C2—1362no—
1160C2#1453124711yescharacteristic
1161C2#1453128311yescharacteristic
1162C2#1453147311yescharacteristic
1163C2#1453162611yescharacteristic
1164C2#1453172811yescharacteristic
1165C2#1453177211yescharacteristic
1166C2#1453182011yescharacteristic
1167C2#1453239311yescharacteristic
1168C2#1453240111yescharacteristic
1169C2#1453289211yescharacteristic
1170C2#1453293711yescharacteristic
1171C2#1453296711yescharacteristic
1172C2#1453301211yescharacteristic
1173C2#1453438511yescharacteristic
1174C2#1453446711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C22⋊#95C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC22⋊#95D17
hypocenterC17#14071
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C22×#10587612C2semidirect
3. C2×#11762701C2semidirect
4. C2×#11762698C2semidirect
6. #14527048C2semidirect
7. #14527030C2semidirect
8. #14527027C2semidirect
10. #14527021C2semidirect
11. #14527020C2semidirect
12. #14527018C2semidirect
13. #14527015C2semidirect
14. #95×Dic17C2semidirect
15. C17×C22⋊#95C2semidirect
40. #11762688C4semidirect
126. C2×C4⋊Dic17D4semidirect
144. C2×C4×Dic17D4semidirect
491. C2×Dic17#117semidirect
506. C22⋊#95D17semidirect
746. C17#14071semidirect

Maximal subgroups

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

subgroupindex
C22×#105876122
C2×#117627092
C2×#117627012
C2×#117626982
C2×#117626882
#145270482
#145270302
#145270272
#145270232
#145270212
#145270202
#145270182
#145270152
#95×Dic172
C17×C22⋊#952
#1407117