Finite Group Databasebeta

← #16958757

Subgroups — #16958757

Order 4352.

2158 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×#10587621C211yesmaximal, characteristic
2C2×#11762690C211yesmaximal, characteristic, complemented
3C2×C4×#63225C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
5#14527034C211yesmaximal, characteristic, complemented
6#14527027C211yesmaximal, characteristic, complemented
7#14527027C211yesmaximal, characteristic, complemented
8#14527025C211yesmaximal, characteristic
9#14527021C211yesmaximal, characteristic, complemented
10#14527021C211yesmaximal, characteristic, complemented
11#14527021C211yesmaximal, characteristic, complemented
12#14527021C211yesmaximal, characteristic, complemented
13#14527017C211yesmaximal, characteristic, complemented
14#14527006C211yesmaximal, characteristic, complemented
15C2×C17×#390C211yesmaximal, 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#11762690—24no—
34C4×#63225—24no—
35C22⋊C4×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
51C22×C4⋊C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C22×C22⋊C4×C17C2211yescharacteristic
56C22×C42×C17C2211yescharacteristic
57C17×#390—24no—
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×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×Dic17—22no—
73C23×Dic17—22no—
74C23×Dic17—22no—
75C23×Dic17—22no—
76C23×Dic17—41no—
77C23×Dic17—41no—
78C23×Dic17C2×C414yes—
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C2×C4⋊C4×C17—22no—
88C2×C4⋊C4×C17—22no—
89C2×C4⋊C4×C17—41no—
90C2×C22⋊C4×C17—22no—
91C2×C22⋊C4×C17—22no—
92C2×C22⋊C4×C17—22no—
93C2×C22⋊C4×C17—22no—
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—41no—
100C2×C22⋊C4×C17—41no—
101C2×C22⋊C4×C17D414yes—
102C2×C42×C17—22no—
103C2×C42×C17—22no—
104C2×C42×C17—41no—
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—22no—
118C2×C22⋊Dic17—22no—
119C2×C22⋊Dic17—41no—
120C2×C22⋊Dic17—41no—
121C2×C22⋊Dic17—41no—
122C2×C22⋊Dic17—41no—
123C2×C22⋊Dic17C2×C414yes—
124C2×C22⋊Dic17C2×C414yes—
125C2×C22⋊Dic17C2×C414yes—
126#10587621—232no—
127C2×#63225—22no—
128C2×#63225—22no—
129C2×#63225—22no—
130C2×#63225—22no—
131C2×#63225—22no—
132C2×#63225C2×C414yes—
133C2×#63225C2×C414yes—
134C2×#63225D414yes—
135C2×#63225D414yes—
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—22no—
143C2×C4×Dic17—41no—
144C2×C4×Dic17—41no—
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×C17—21no—
184C24×C17—21no—
185C24×C17C22×C412yes—
186C24×C17C22×C412yes—
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—21no—
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×C17C22×C412yes—
225C22×C4×C17C2×D412yes—
226C22×C4×C17C2×D412yes—
227C22×C4×C17C2×D412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17#4112yes—
230C22×C4×C17#4112yes—
231C22×C4×C17#4112yes—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—28no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
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—28no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17—44no—
280C22×Dic17—44no—
281C22×Dic17—44no—
282C22×Dic17—44no—
283C22×Dic17—44no—
284C22×Dic17C22×C412yes—
285C22×Dic17C22×C412yes—
286C22×Dic17C22×C412yes—
287C22×Dic17C22×C412yes—
288C22×Dic17C2×D412yes—
289C22×Dic17C2×D412yes—
290C22×Dic17C2×D412yes—
291C22×Dic17C2×D412yes—
292C22×Dic17#4112yes—
293C22×Dic17#4112yes—
294C22×Dic17#4112yes—
295C4⋊C4×C17—44no—
296C22⋊C4×C17—28no—
297C22⋊C4×C17—44no—
298C22⋊C4×C17—44no—
299C22⋊C4×C17—44no—
300C42×C17—44no—
301C22⋊Dic17—28no—
302C22⋊Dic17—28no—
303C22⋊Dic17—28no—
304C22⋊Dic17—28no—
305C22⋊Dic17—44no—
306C22⋊Dic17—44no—
307C22⋊Dic17—44no—
308#63225—28no—
309#63225—28no—
310#63225C22⋊C4116yescomplemented
311C4×Dic17—28no—
312C4×Dic17—44no—
313C4×Dic17—44no—
314#14095—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—22no—
334C23×C17—22no—
335C23×C17—22no—
336C23×C17—22no—
337C23×C17—22no—
338C23×C17—22no—
339C23×C17—22no—
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×C17—41no—
350C23×C17—41no—
351C23×C17—41no—
352C23×C17—41no—
353C23×C17—41no—
354C23×C17—41no—
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×C17C4×D414yes—
385C23×C17C23×C411yescharacteristic
386C23×C17C22×D411yescharacteristic
387C23×C17C22×D411yescharacteristic
388C23×C17C22×D411yescharacteristic
389C23×C17C2×#4111yescharacteristic
390C23×C17C2×#4111yescharacteristic
391C23×C17C2×#4111yescharacteristic
392C23×C17C2×#4111yescharacteristic
393C23×C17C2×#4111yescharacteristic
394C23×C17C2×#4111yescharacteristic
395C23×C17C2×#4111yescharacteristic
396C23×C17H(5,𝔽2)11yescharacteristic
397C23×C17H(5,𝔽2)11yescharacteristic
398C23×C17H(5,𝔽2)11yescharacteristic
399C23×C172−1+411yescharacteristic
400D4×C17—416no—
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×C17C2×C22⋊C414yes—
435C2×C4×C17#12314yescomplemented
436C2×Dic17—22no—
437C2×Dic17—22no—
438C2×Dic17—22no—
439C2×Dic17—22no—
440C2×Dic17—22no—
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—416no—
464C2×Dic17—41no—
465C2×Dic17—41no—
466C2×Dic17—41no—
467C2×Dic17—41no—
468C2×Dic17—41no—
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×Dic17C2×C22⋊C414yes—
492C2×Dic17C2×C22⋊C414yes—
493C22×#123—171no—
494C2×#390D1711yescharacteristic
495C2×#387—171no—
496C2×C4×C4⋊C4—171no—
497C2×C4×C22⋊C4—171no—
498#1441—171no—
499#1439—171no—
500#1439—171no—
501#1438—171no—
502#1437—171no—
503#1437—171no—
504#1437—171no—
505#1437—171no—
506#1436—171no—
507C22⋊#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×C17—42no—
524C22×C17—42no—
525C22×C17—42no—
526C22×C17—42no—
527C22×C17—42no—
528C22×C17—42no—
529C22×C17—42no—
530C22×C17—81no—
531C22×C17—81no—
532C22×C17—81no—
533C22×C17—81no—
534C22×C17—81no—
535C22×C17—81no—
536C22×C17—81no—
537C22×C17—81no—
538C22×C17C22×C22⋊C411yescharacteristic
539C22×C17C2×C4×D411yescharacteristic
540C22×C17C4×#4111yescharacteristic
541C22×C17C4×#4111yescharacteristic
542C22×C17C4×#4111yescharacteristic
543C22×C17#51811yescharacteristic
544C22×C17#52011yescharacteristic
545C22×C17C2×#12311yescharacteristic
546C22×C17#52511yescharacteristic
547C22×C17#52511yescharacteristic
548C22×C17#52511yescharacteristic
549C22×C17#52911yescharacteristic
550C22×C17#52911yescharacteristic
551C22×C17#53211yescharacteristic
552C22×C17#53211yescharacteristic
553C22×C17#53811yescharacteristic
554C22×C17#53911yescharacteristic
555C22×C17#54011yescharacteristic
556C22×C17#54211yescharacteristic
557C22×C17D4211yescharacteristic
558C22×C17D4211yescharacteristic
559C22×C17#54611yescharacteristic
560C22×C17#54611yescharacteristic
561C22×C17#54611yescharacteristic
562C22×C17#54711yescharacteristic
563C22×C17#54811yescharacteristic
564C22×C17#54811yescharacteristic
565C22×C17#55011yescharacteristic
566C22×C17#55011yescharacteristic
567C22×C17#55111yescharacteristic
568C22×C17#55111yescharacteristic
569C22×C17#55211yescharacteristic
570C22×C17#55311yescharacteristic
571C22×C17#55311yescharacteristic
572C22×C17#55911yescharacteristic
573C4×C17—24no—
574C4×C17—24no—
575C4×C17—42no—
576C4×C17—42no—
577C4×C17—81no—
578Dic17—24no—
579Dic17—24no—
580Dic17—42no—
581Dic17—42no—
582Dic17—42no—
583Dic17—42no—
584Dic17—42no—
585Dic17—81no—
586C23×D4C2×D1711yescharacteristic
587C24×C4—171no—
588C2×#123—178no—
589C2×#123—344no—
590C2×#123—344no—
591C22×C4⋊C4—171no—
592C22×C4⋊C4—171no—
593C22×C4⋊C4—171no—
594C22×C4⋊C4C2×D1711yescharacteristic
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⋊C4C2×D1711yescharacteristic
603C22×C22⋊C4C2×D1711yescharacteristic
604C22×C22⋊C4C2×D1711yescharacteristic
605C22×C22⋊C4C2×D1711yescharacteristic
606C22×C42—171no—
607C22×C42—171no—
608C22×C42—171no—
609C22×C42C2×D1711yescharacteristic
610#390—24no—
611#387—344no—
612C4×C4⋊C4—344no—
613C4×C22⋊C4—344no—
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×#95—171no—
625C2×#95—171no—
626C2×#95—171no—
627C2×#95—171no—
628C2×C17—44no—
629C2×C17—82no—
630C2×C17#229711yescharacteristic
631C2×C17C4×#12311yescharacteristic
632C2×C17#233511yescharacteristic
633C2×C17D4×C22⋊C411yescharacteristic
634C2×C17#234111yescharacteristic
635C2×C17#235911yescharacteristic
636C2×C17#237411yescharacteristic
637C2×C17#244311yescharacteristic
638C2×C17#244511yescharacteristic
639C2×C17#245611yescharacteristic
640C2×C17#245811yescharacteristic
641C2×C17#246111yescharacteristic
642C2×C17#247111yescharacteristic
643C2×C17#255411yescharacteristic
644C2×C17#255811yescharacteristic
645C25C22×D1711yescharacteristic
646C25C22×D1711yescharacteristic
647C22×D4—22no—
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—41no—
652C22×D4—41no—
653C22×D4C4×D1714yes—
654C23×C4—171no—
655C23×C4—171no—
656C23×C4—171no—
657C23×C4—171no—
658C23×C4—171no—
659C23×C4—171no—
660C23×C4—171no—
661C23×C4—174no—
662C23×C4—171no—
663C23×C4—342no—
664C23×C4—342no—
665C23×C4—342no—
666C23×C4—342no—
667C23×C4—681no—
668C23×C4—681no—
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C23×C4C22×D1711yescharacteristic
672C23×C4C22×D1711yescharacteristic
673C23×C4C22×D1711yescharacteristic
674#123—3432no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4—174no—
679C2×C4⋊C4—174no—
680C2×C4⋊C4—174no—
681C2×C4⋊C4—174no—
682C2×C4⋊C4—342no—
683C2×C4⋊C4—342no—
684C2×C4⋊C4—342no—
685C2×C4⋊C4—342no—
686C2×C4⋊C4—342no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—174no—
699C2×C22⋊C4—174no—
700C2×C22⋊C4—174no—
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—342no—
715C2×C22⋊C4—681no—
716C2×C22⋊C4—681no—
717C2×C22⋊C4—681no—
718C2×C22⋊C4—681no—
719C2×C22⋊C4C22⋊D1714yes—
720C2×C42—22no—
721C2×C42—22no—
722C2×C42—41no—
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—342no—
733#95—342no—
734#95—342no—
735#95—342no—
736#95—342no—
737#95—342no—
738#95—342no—
739#95—342no—
740#95—342no—
741#95—342no—
742#95—681no—
743#95—681no—
744#95—681no—
745#95—681no—
746C17#1409511yescharacteristic, 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—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—
773C24C2×C4×D1712yes—
774C24C2×C4×D1712yes—
775C24#6325212yes—
776C24C2×C22⋊D1712yes—
777C24C23×D1711yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
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—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—172no—
813C22×C4—172no—
814C22×C4—172no—
815C22×C4—172no—
816C22×C4—172no—
817C22×C4—172no—
818C22×C4—172no—
819C22×C4—172no—
820C22×C4—172no—
821C22×C4—172no—
822C22×C4—172no—
823C22×C4—348no—
824C22×C4—341no—
825C22×C4—341no—
826C22×C4—341no—
827C22×C4—341no—
828C22×C4—341no—
829C22×C4—341no—
830C22×C4—341no—
831C22×C4—341no—
832C22×C4—341no—
833C22×C4—341no—
834C22×C4—341no—
835C22×C4—341no—
836C22×C4—341no—
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—348no—
863C22×C4—341no—
864C22×C4—341no—
865C22×C4—341no—
866C22×C4—341no—
867C22×C4—341no—
868C22×C4—341no—
869C22×C4—341no—
870C22×C4—684no—
871C22×C4—684no—
872C22×C4—684no—
873C22×C4—684no—
874C22×C4—684no—
875C22×C4C2×C4×D1712yes—
876C22×C4D4×D1712yes—
877C22×C4D4×D1712yes—
878C22×C4#6325412yes—
879C22×C4#6325412yes—
880C22×C4#6325412yes—
881C22×C4C2×C22⋊D1712yes—
882C22×C4C2×C22⋊D1712yes—
883C4⋊C4—44no—
884C4⋊C4—1716no—
885C4⋊C4—348no—
886C4⋊C4—348no—
887C22⋊C4—28no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—348no—
892C22⋊C4—348no—
893C22⋊C4—348no—
894C22⋊C4—348no—
895C22⋊C4—684no—
896C22⋊C4—684no—
897C22⋊C4—684no—
898C42—44no—
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—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
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—
971C23C4×C22⋊D1714yes—
972C23C22×C4×D1711yescharacteristic
973C23C2×#6325211yescharacteristic
974C23C2×D4×D1711yescharacteristic
975C23C2×D4×D1711yescharacteristic
976C23C2×#6325411yescharacteristic
977C23C2×#6325411yescharacteristic
978C23C2×#6325411yescharacteristic
979C23#1058769111yescharacteristic
980C23#1058769111yescharacteristic
981C23#1058769111yescharacteristic
982C23#41×D1711yescharacteristic
983C23#41×D1711yescharacteristic
984C23#41×D1711yescharacteristic
985C23#1058769711yescharacteristic
986C23C22×C22⋊D1711yescharacteristic
987D4—416no—
988C2×C4—22no—
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—41no—
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—174no—
1022C2×C4—174no—
1023C2×C4—342no—
1024C2×C4—342no—
1025C2×C4—342no—
1026C2×C4—342no—
1027C2×C4—342no—
1028C2×C4—342no—
1029C2×C4—342no—
1030C2×C4—342no—
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—6816no—
1051C2×C4—681no—
1052C2×C4—681no—
1053C2×C4—681no—
1054C2×C4—681no—
1055C2×C4—681no—
1056C2×C4—681no—
1057C2×C4—681no—
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×C4C22⋊C4×D1714yes—
1079C2×C4#1058762114yescomplemented
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—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C2×C22⋊C4×D1711yescharacteristic
1111C22C2×C4×C22⋊D1711yescharacteristic
1112C22C4×#6325411yescharacteristic
1113C22C4×#6325411yescharacteristic
1114C22C4×#6325411yescharacteristic
1115C22#1176328211yescharacteristic
1116C22#1176328811yescharacteristic
1117C22C2×#1058762111yescharacteristic
1118C22#1176331611yescharacteristic
1119C22#1176331911yescharacteristic
1120C22#1176331911yescharacteristic
1121C22#1176333911yescharacteristic
1122C22#1176333911yescharacteristic
1123C22#1176335711yescharacteristic
1124C22#1176335811yescharacteristic
1125C22#1176339111yescharacteristic
1126C22#1176340411yescharacteristic
1127C22#1176341311yescharacteristic
1128C22#1176342311yescharacteristic
1129C22D4×C22⋊D1711yescharacteristic
1130C22D4×C22⋊D1711yescharacteristic
1131C22#1176344911yescharacteristic
1132C22#1176344911yescharacteristic
1133C22#1176345311yescharacteristic
1134C22#1176345811yescharacteristic
1135C22#1176346511yescharacteristic
1136C22#1176346711yescharacteristic
1137C22#1176347711yescharacteristic
1138C22#1176347911yescharacteristic
1139C22#1176348811yescharacteristic
1140C22#1176348911yescharacteristic
1141C22#1176349911yescharacteristic
1142C22#1176350211yescharacteristic
1143C22#1176350211yescharacteristic
1144C22#1176354511yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—81no—
1150C4—344no—
1151C4—344no—
1152C4—682no—
1153C4—682no—
1154C4—682no—
1155C4—682no—
1156C4—682no—
1157C4—1361no—
1158C2—44no—
1159C2—82no—
1160C2#1453127111yescharacteristic
1161C2C4×#1058762111yescharacteristic
1162C2#1453157111yescharacteristic
1163C2C22⋊C4×C22⋊D1711yescharacteristic
1164C2#1453162311yescharacteristic
1165C2#1453177011yescharacteristic
1166C2#1453191911yescharacteristic
1167C2#1453251511yescharacteristic
1168C2#1453254511yescharacteristic
1169C2#1453268111yescharacteristic
1170C2#1453271111yescharacteristic
1171C2#1453274711yescharacteristic
1172C2#1453290011yescharacteristic
1173C2#1453384911yescharacteristic
1174C2#1453390311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#390C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC2×#390D17
hypocenterC17#14095
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#11762690C2semidirect
3. C2×C4×#63225C2semidirect
4. C2×C22⋊C4×Dic17C2semidirect
5. #14527034C2semidirect
6. #14527027C2semidirect
7. #14527027C2semidirect
9. #14527021C2semidirect
10. #14527021C2semidirect
11. #14527021C2semidirect
12. #14527021C2semidirect
13. #14527017C2semidirect
14. #14527006C2semidirect
19. C2×#10587621C4semidirect
310. #63225C22⋊C4semidirect
435. C2×C4×C17#123semidirect
746. C17#14095semidirect
1079. 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×#117626902
C2×C4×#632252
C2×C22⋊C4×Dic172
#145270342
#145270272
#145270252
#145270212
#145270172
#145270062
C2×C17×#3902
#1409517