Finite Group Databasebeta

← #16958592

Subgroups — #16958592

Order 4352.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762709C211yesmaximal, characteristic
2C2×#11762703C211yesmaximal, characteristic, complemented
3C2×#11762693C211yesmaximal, characteristic, complemented
4C2×#11762685C211yesmaximal, characteristic
5C2×#11762683C211yesmaximal, characteristic, complemented
6C2×C4×#63227C211yesmaximal, characteristic, complemented
7#14527050C211yesmaximal, characteristic, complemented
8#14527029C211yesmaximal, characteristic, complemented
9#14527026C211yesmaximal, characteristic, complemented
10#14527023C211yesmaximal, characteristic
11#14527021C211yesmaximal, characteristic, complemented
12#14527020C211yesmaximal, characteristic, complemented
13#14527013C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762709C418yescomplemented
33#11762703—24no—
34#11762693—24no—
35#11762685—24no—
36#11762683—24no—
37C4×#63227—24no—
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C22×C4⋊C4×C17C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C17×#388—24no—
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C24×D17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C22×C22⋊D17—22no—
67C22×C22⋊D17—22no—
68C22×C22⋊D17—22no—
69C22×C22⋊D17—22no—
70C22×C22⋊D17—41no—
71C22×C22⋊D17—41no—
72C22×C22⋊D17C2×C414yes—
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—22no—
83C22×C4×D17—22no—
84C22×C4×D17—22no—
85C22×C4×D17—41no—
86C22×C4×D17—41no—
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—41no—
98C2×C22⋊C4×C17C2×C414yescomplemented
99C2×C42×C17—22no—
100C2×C42×C17—22no—
101C2×C42×C17—22no—
102C2×C22⋊Dic17—22no—
103C2×C22⋊Dic17—22no—
104C2×C22⋊Dic17—22no—
105C2×C22⋊Dic17—22no—
106C2×C22⋊Dic17—22no—
107C2×C22⋊Dic17—41no—
108C2×C22⋊Dic17—41no—
109C2×C22⋊Dic17—41no—
110C2×C22⋊Dic17C2×C414yescomplemented
111C2×#63227—22no—
112C2×#63227—22no—
113C2×#63227—22no—
114C2×#63227—22no—
115C2×#63227—22no—
116C2×#63227—22no—
117C2×#63227—22no—
118C2×#63227—22no—
119C2×#63227—22no—
120C2×#63227—22no—
121C2×#63227—22no—
122C2×#63227—41no—
123C2×#63227—41no—
124C2×#63227C2×C414yes—
125C2×#63227C2×C414yes—
126C2×C4⋊Dic17—22no—
127C2×C4⋊Dic17—22no—
128C2×C4⋊Dic17—41no—
129C2×#63225—22no—
130C2×#63225—22no—
131C2×#63225—22no—
132C2×#63225—22no—
133C2×#63225—22no—
134C2×#63225C2×C414yescomplemented
135C2×C4×Dic17—22no—
136C2×C4×Dic17—41no—
137C2×C4×Dic17—41no—
138C2×C4×Dic17—41no—
139C2×C4×Dic17—41no—
140C2×C4×Dic17—41no—
141C2×C4×Dic17—41no—
142C2×C4×Dic17C2×C414yescomplemented
143C2×C4×Dic17D414yescomplemented
144C17×#95—22no—
145C17×#95D414yescomplemented
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—22no—
156#10587502—22no—
157#10587502D414yes—
158C24×C17—21no—
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×C17C22×C412yes—
173C24×C17C2411yescharacteristic
174C23×D17—21no—
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×D17C22×C412yes—
187C23×D17#4112yes—
188C23×D17#4112yes—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
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—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×C17C22×C412yes—
223C22×C4×C17C22×C412yes—
224C22×C4×C17C2×D412yes—
225C22×C4×C17C2×D412yes—
226C22×C4×C17C2×D412yes—
227C22×C4×C17C2×D412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17#4112yes—
230C22×C4×C17#4112yes—
231C2×C22⋊D17—28no—
232C2×C22⋊D17—28no—
233C2×C22⋊D17—44no—
234C2×C22⋊D17—44no—
235C2×C22⋊D17—44no—
236C2×C22⋊D17—44no—
237C2×C22⋊D17—44no—
238C22×Dic17—21no—
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—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×Dic17C22×C412yes—
278C22×Dic17C22×C412yes—
279C22×Dic17C22×C412yes—
280C22×Dic17C2×D412yes—
281C22×Dic17C2×D412yes—
282C22×Dic17C2×D412yes—
283C22×Dic17C2×D412yes—
284C22×Dic17#4112yes—
285C22×Dic17#4112yes—
286C22×Dic17#4112yes—
287C2×C4×D17—28no—
288C2×C4×D17—44no—
289C2×C4×D17—44no—
290C2×C4×D17—44no—
291C2×C4×D17—44no—
292C2×C4×D17—44no—
293C2×C4×D17—44no—
294C4⋊C4×C17—44no—
295C22⋊C4×C17—28no—
296C22⋊C4×C17—44no—
297C22⋊C4×C17—44no—
298C42×C17—44no—
299C22⋊Dic17—28no—
300C22⋊Dic17—44no—
301C22⋊Dic17—44no—
302#63227—28no—
303#63227—28no—
304#63227—28no—
305#63227—44no—
306#63227—44no—
307C4⋊Dic17—44no—
308#63225—28no—
309#63225—44no—
310C4×Dic17—44no—
311C4×Dic17—44no—
312C4×Dic17—44no—
313#14084—171nomaximal, Sylow
314C23×C17—22no—
315C23×C17—22no—
316C23×C17—22no—
317C23×C17—22no—
318C23×C17—22no—
319C23×C17—22no—
320C23×C17—22no—
321C23×C17—41no—
322C23×C17—41no—
323C23×C17—41no—
324C23×C17—41no—
325C23×C17—41no—
326C23×C17—41no—
327C23×C17—41no—
328C23×C17—41no—
329C23×C17—41no—
330C23×C17—41no—
331C23×C17—41no—
332C23×C17—41no—
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×C17C23×C411yescharacteristic
350C23×C17C22×D411yescharacteristic
351C23×C17C22×D411yescharacteristic
352C23×C17C22×D411yescharacteristic
353C23×C17C2×#4111yescharacteristic
354C23×C17C2×#4111yescharacteristic
355C23×C17C2×#4111yescharacteristic
356C23×C17C2×#4111yescharacteristic
357C23×C17C2×#4111yescharacteristic
358C23×C17C2×#4111yescharacteristic
359C23×C17C2×#4111yescharacteristic
360C23×C17H(5,𝔽2)11yescharacteristic
361C23×C17H(5,𝔽2)11yescharacteristic
362C23×C17H(5,𝔽2)11yescharacteristic
363C23×C172−1+411yescharacteristic
364C22×D17—22no—
365C22×D17—22no—
366C22×D17—22no—
367C22×D17—22no—
368C22×D17—22no—
369C22×D17—22no—
370C22×D17—22no—
371C22×D17—22no—
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—22no—
375C22×D17—22no—
376C22×D17—22no—
377C22×D17—22no—
378C22×D17—22no—
379C22×D17—22no—
380C22×D17—22no—
381C22×D17—22no—
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#11714yes—
399C2×C4×C17—22no—
400C2×C4×C17—22no—
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—22no—
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×C17C4×D414yes—
440C2×C4×C17#12714yes—
441C22⋊D17—416no—
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—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×Dic17C4×D414yes—
490C2×Dic17C4×D414yes—
491C4×D17—416no—
492C2×#390—171no—
493C2×#388—171no—
494C2×#388D1711yescharacteristic, complemented
495C2×#387—171no—
496C2×#386—171no—
497C2×#385—171no—
498C2×C4×C22⋊C4—171no—
499#1445—171no—
500#1439—171no—
501#1439—171no—
502#1438—171no—
503#1437—171no—
504#1437—171no—
505C4⋊#95—171no—
506C4×#95—171no—
507C22×C17—42no—
508C22×C17—42no—
509C22×C17—42no—
510C22×C17—42no—
511C22×C17—42no—
512C22×C17—42no—
513C22×C17—42no—
514C22×C17—81no—
515C22×C17—81no—
516C22×C17—81no—
517C22×C17—81no—
518C22×C17—81no—
519C22×C17—81no—
520C22×C17—81no—
521C22×C17—81no—
522C22×C17C2×#11711yescharacteristic
523C22×C17C2×C4×D411yescharacteristic
524C22×C17C2×C4×D411yescharacteristic
525C22×C17C2×C4×D411yescharacteristic
526C22×C17C4×#4111yescharacteristic
527C22×C17#51811yescharacteristic
528C22×C17#52011yescharacteristic
529C22×C17#52511yescharacteristic
530C22×C17#52511yescharacteristic
531C22×C17#52911yescharacteristic
532C22×C17#52911yescharacteristic
533C22×C17C2×#12711yescharacteristic
534C22×C17#53211yescharacteristic
535C22×C17#53211yescharacteristic
536C22×C17#53211yescharacteristic
537C22×C17#53411yescharacteristic
538C22×C17#53711yescharacteristic
539C22×C17#53811yescharacteristic
540C22×C17#53911yescharacteristic
541C22×C17#54611yescharacteristic
542C22×C17#54611yescharacteristic
543C22×C17#54611yescharacteristic
544C22×C17#54611yescharacteristic
545C22×C17#54611yescharacteristic
546C22×C17#54611yescharacteristic
547C22×C17#54811yescharacteristic
548C22×C17#54811yescharacteristic
549C22×C17#55111yescharacteristic
550C22×C17#55111yescharacteristic
551C22×C17#55211yescharacteristic
552C22×C17#55311yescharacteristic
553C22×C17#55311yescharacteristic
554C22×C17#55311yescharacteristic
555C22×C17#55611yescharacteristic
556C22×C17#55911yescharacteristic
557C2×D17—24no—
558C2×D17—24no—
559C2×D17—24no—
560C2×D17—42no—
561C2×D17—42no—
562C2×D17—42no—
563C2×D17—42no—
564C2×D17—42no—
565C2×D17—42no—
566C2×D17—42no—
567C2×D17—42no—
568C2×D17—42no—
569C2×D17—42no—
570C2×D17—42no—
571C2×D17—42no—
572C4×C17—24no—
573C4×C17—24no—
574C4×C17—42no—
575C4×C17—42no—
576C4×C17—42no—
577C4×C17—81no—
578Dic17—24no—
579Dic17—24no—
580Dic17—42no—
581Dic17—42no—
582Dic17—42no—
583Dic17—42no—
584Dic17—81no—
585C23×D4—171no—
586C24×C4—171no—
587C22×C4⋊C4—171no—
588C22×C4⋊C4—171no—
589C22×C4⋊C4—171no—
590C22×C4⋊C4C2×D1711yescharacteristic
591C22×C22⋊C4—171no—
592C22×C22⋊C4—171no—
593C22×C22⋊C4—171no—
594C22×C22⋊C4—171no—
595C22×C22⋊C4—171no—
596C22×C22⋊C4—171no—
597C22×C22⋊C4—171no—
598C22×C22⋊C4—171no—
599C22×C22⋊C4C2×D1711yescharacteristic
600C22×C22⋊C4C2×D1711yescharacteristic
601C22×C22⋊C4C2×D1711yescharacteristic
602C22×C42—171no—
603C22×C42—171no—
604C22×C42—171no—
605C22×C42C2×D1711yescharacteristic
606#390—178no—
607#388—24no—
608#388—344no—
609#387—344no—
610#386—344no—
611#385—344no—
612C4×C22⋊C4—344no—
613C2×#95—171no—
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×#95C2×D1711yescharacteristic
626C2×#95C2×D1711yescharacteristic
627C2×C17—82no—
628C2×C17#229011yescharacteristic
629C2×C17C4×#12711yescharacteristic
630C2×C17#232511yescharacteristic
631C2×C17#234211yescharacteristic
632C2×C17#235211yescharacteristic
633C2×C17#236411yescharacteristic
634C2×C17#236711yescharacteristic
635C2×C17#253911yescharacteristic
636C2×C17#254011yescharacteristic
637C2×C17#255711yescharacteristic
638C2×C17#255811yescharacteristic
639C2×C17#255911yescharacteristic
640C2×C17#256011yescharacteristic
641C2×C17#260111yescharacteristic
642C2×C17#260211yescharacteristic
643D17—44no—
644C25—171no—
645C25C22×D1711yescharacteristic
646C22×D4—174no—
647C22×D4—342no—
648C22×D4—342no—
649C22×D4—342no—
650C22×D4—342no—
651C22×D4—681no—
652C22×D4—681no—
653C23×C4—171no—
654C23×C4—171no—
655C23×C4—171no—
656C23×C4—171no—
657C23×C4—171no—
658C23×C4—171no—
659C23×C4—171no—
660C23×C4—342no—
661C23×C4—342no—
662C23×C4—342no—
663C23×C4—342no—
664C23×C4—342no—
665C23×C4—681no—
666C23×C4—681no—
667C23×C4C22×D1711yescharacteristic
668C23×C4C22×D1711yescharacteristic
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C23×C4C22×D1711yescharacteristic
672C23×C4C22×D1711yescharacteristic
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—41no—
676C2×C4⋊C4—174no—
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×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—174no—
694C2×C22⋊C4—174no—
695C2×C22⋊C4—174no—
696C2×C22⋊C4—342no—
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—681no—
713C2×C22⋊C4—681no—
714C2×C22⋊C4—681no—
715C2×C22⋊C4—681no—
716C2×C22⋊C4—681no—
717C2×C22⋊C4C4×D1714yescomplemented
718C2×C42—22no—
719C2×C42—22no—
720C2×C42—22no—
721C2×C42—174no—
722C2×C42—174no—
723C2×C42—342no—
724C2×C42—681no—
725C2×C42—681no—
726C2×C42—681no—
727C2×C42—681no—
728C2×C42—681no—
729C2×C42—681no—
730#95—22no—
731#95—174no—
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—342no—
743#95C22⋊D1714yescomplemented
744C17#1408411yescharacteristic, complemented, Sylow
745C24—21no—
746C24—21no—
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—172no—
761C24—172no—
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—
775C24C23×D1711yescharacteristic
776C2×D4—348no—
777C2×D4—348no—
778C2×D4—684no—
779C2×D4—684no—
780C2×D4—684no—
781C2×D4—684no—
782C2×D4—684no—
783C22×C4—21no—
784C22×C4—21no—
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—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—172no—
817C22×C4—172no—
818C22×C4—172no—
819C22×C4—172no—
820C22×C4—172no—
821C22×C4—172no—
822C22×C4—172no—
823C22×C4—172no—
824C22×C4—172no—
825C22×C4—172no—
826C22×C4—348no—
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—341no—
863C22×C4—341no—
864C22×C4—341no—
865C22×C4—341no—
866C22×C4—684no—
867C22×C4—684no—
868C22×C4—684no—
869C22×C4—684no—
870C22×C4—684no—
871C22×C4—684no—
872C22×C4C2×C4×D1712yes—
873C22×C4C2×C4×D1712yes—
874C22×C4#6325212yes—
875C22×C4D4×D1712yes—
876C22×C4D4×D1712yes—
877C22×C4#6325412yes—
878C22×C4C2×C22⋊D1712yes—
879C22×C4C2×C22⋊D1712yes—
880C22×C4C2×C22⋊D1712yes—
881C4⋊C4—44no—
882C4⋊C4—348no—
883C4⋊C4—684no—
884C4⋊C4—684no—
885C22⋊C4—28no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—348no—
889C22⋊C4—348no—
890C22⋊C4—348no—
891C22⋊C4—348no—
892C22⋊C4—684no—
893C22⋊C4—684no—
894C22⋊C4—684no—
895C22⋊C4—684no—
896C42—44no—
897C42—684no—
898C42—684no—
899C42—684no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
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—174no—
936C23—342no—
937C23—342no—
938C23—342no—
939C23—342no—
940C23—342no—
941C23—342no—
942C23—342no—
943C23—342no—
944C23—342no—
945C23—342no—
946C23—342no—
947C23—342no—
948C23—342no—
949C23—342no—
950C23—342no—
951C23—342no—
952C23—342no—
953C23—342no—
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—
970C23C22×C4×D1711yescharacteristic
971C23C2×#6325211yescharacteristic
972C23C2×D4×D1711yescharacteristic
973C23C2×D4×D1711yescharacteristic
974C23C2×#6325411yescharacteristic
975C23#1058769111yescharacteristic
976C23#41×D1711yescharacteristic
977C23#41×D1711yescharacteristic
978C23#41×D1711yescharacteristic
979C23#41×D1711yescharacteristic
980C23#41×D1711yescharacteristic
981C23#1058769611yescharacteristic
982C23#1058769611yescharacteristic
983C23#1058769711yescharacteristic
984C23C22×C22⋊D1711yescharacteristic
985D4—6816no—
986C2×C4—22no—
987C2×C4—22no—
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—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—174no—
1027C2×C4—174no—
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—342no—
1051C2×C4—342no—
1052C2×C4—6816no—
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×C4C4×C22⋊D1714yes—
1077C2×C4#1058762614yes—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—344no—
1094C22—344no—
1095C22—344no—
1096C22—682no—
1097C22—682no—
1098C22—682no—
1099C22—682no—
1100C22—682no—
1101C22—682no—
1102C22—682no—
1103C22—682no—
1104C22—682no—
1105C22—682no—
1106C22—682no—
1107C22—682no—
1108C22#117×D1711yescharacteristic
1109C22C4×D4×D1711yescharacteristic
1110C22C4×D4×D1711yescharacteristic
1111C22C2×C4×C22⋊D1711yescharacteristic
1112C22C4×#6325411yescharacteristic
1113C22#1176328111yescharacteristic
1114C22#1176328911yescharacteristic
1115C22#1176331711yescharacteristic
1116C22#1176331911yescharacteristic
1117C22#1176333811yescharacteristic
1118C22#1176334211yescharacteristic
1119C22C2×#1058762611yescharacteristic
1120C22#1176335511yescharacteristic
1121C22#1176335611yescharacteristic
1122C22#1176335611yescharacteristic
1123C22#1176337011yescharacteristic
1124C22#1176338811yescharacteristic
1125C22#1176339311yescharacteristic
1126C22#1176340011yescharacteristic
1127C22#1176344711yescharacteristic
1128C22#1176344711yescharacteristic
1129C22#1176345111yescharacteristic
1130C22#1176345111yescharacteristic
1131C22#1176345311yescharacteristic
1132C22#1176345611yescharacteristic
1133C22#1176346511yescharacteristic
1134C22#1176346611yescharacteristic
1135C22#1176348411yescharacteristic
1136C22#1176348911yescharacteristic
1137C22#1176349811yescharacteristic
1138C22#1176350311yescharacteristic
1139C22#1176350511yescharacteristic
1140C22#1176350811yescharacteristic
1141C22#1176352611yescharacteristic
1142C22#1176354111yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—81no—
1149C4—344no—
1150C4—344no—
1151C4—682no—
1152C4—682no—
1153C4—682no—
1154C4—682no—
1155C4—1361no—
1156C2—82no—
1157C2—684no—
1158C2#1453122611yescharacteristic
1159C2C4×#1058762611yescharacteristic
1160C2#1453148811yescharacteristic
1161C2#1453162811yescharacteristic
1162C2#1453171411yescharacteristic
1163C2#1453182911yescharacteristic
1164C2#1453185811yescharacteristic
1165C2#1453371411yescharacteristic
1166C2#1453372011yescharacteristic
1167C2#1453388111yescharacteristic
1168C2#1453390411yescharacteristic
1169C2#1453391911yescharacteristic
1170C2#1453392611yescharacteristic
1171C2#1453438711yescharacteristic
1172C2#1453440211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×#388D17
hypocenterC17#14084
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#11762703C2semidirect
3. C2×#11762693C2semidirect
5. C2×#11762683C2semidirect
6. C2×C4×#63227C2semidirect
7. #14527050C2semidirect
8. #14527029C2semidirect
9. #14527026C2semidirect
11. #14527021C2semidirect
12. #14527020C2semidirect
13. #14527013C2semidirect
14. #95×Dic17C2semidirect
15. C2×C17×#388C2semidirect
32. #11762709C4semidirect
98. C2×C22⋊C4×C17C2×C4semidirect
110. C2×C22⋊Dic17C2×C4semidirect
134. C2×#63225C2×C4semidirect
142. C2×C4×Dic17C2×C4semidirect
143. C2×C4×Dic17D4semidirect
145. C17×#95D4semidirect
494. C2×#388D17semidirect
717. C2×C22⋊C4C4×D17semidirect
743. #95C22⋊D17semidirect
744. C17#14084semidirect

Maximal subgroups

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

subgroupindex
C2×#117627092
C2×#117627032
C2×#117626932
C2×#117626852
C2×#117626832
C2×C4×#632272
#145270502
#145270292
#145270262
#145270232
#145270212
#145270202
#145270132
#95×Dic172
C2×C17×#3882
#1408417