Finite Group Databasebeta

← #16963500

Subgroups — #16963500

Order 4352.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587572C211yesmaximal, characteristic
2C2×#11762702C211yesmaximal, characteristic, complemented
3#14527053C211yesmaximal, characteristic, complemented
4#14527051C211yesmaximal, characteristic, complemented
5#14527030C211yesmaximal, characteristic, complemented
6#14527026C211yesmaximal, characteristic, complemented
7#14527023C211yesmaximal, characteristic
8#14527023C211yesmaximal, characteristic
9#14527022C211yesmaximal, characteristic, complemented
10#14527020C211yesmaximal, characteristic, complemented
11#14527014C211yesmaximal, characteristic, complemented
12#14527013C211yesmaximal, characteristic, complemented
13#14527006C211yesmaximal, characteristic, complemented
14#14527006C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C2×#10587572—24no—
19C2×#10587572—24no—
20C2×#10587572C418yescomplemented
21C22×C4⋊Dic17C2211yescharacteristic
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C4⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33#11762702—24no—
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C22×C4⋊C4×C17C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C22×C22⋊C4×C17C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C22×C42×C17C2211yescharacteristic
53C17×#388—24no—
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C25×C17C2311yescharacteristic
57C24×D17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C22×C22⋊D17—22no—
65C22×C22⋊D17—22no—
66C22×C22⋊D17—41no—
67C22×C22⋊D17—41no—
68C22×C22⋊D17—41no—
69C22×C22⋊D17—41no—
70C22×C22⋊D17C2×C414yes—
71C23×Dic17—22no—
72C23×Dic17—22no—
73C23×Dic17—41no—
74C23×Dic17—41no—
75C23×Dic17—41no—
76C23×Dic17—41no—
77C23×Dic17C2×C414yes—
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C2×C4⋊C4×C17—22no—
86C2×C4⋊C4×C17—22no—
87C2×C4⋊C4×C17—41no—
88C2×C22⋊C4×C17—22no—
89C2×C22⋊C4×C17—22no—
90C2×C22⋊C4×C17—22no—
91C2×C22⋊C4×C17—22no—
92C2×C22⋊C4×C17—41no—
93C2×C22⋊C4×C17—41no—
94C2×C22⋊C4×C17C2×C414yes—
95C2×C22⋊C4×C17D414yes—
96C2×C22⋊C4×C17D414yes—
97C2×C42×C17—22no—
98C2×C42×C17—22no—
99C2×C42×C17—41no—
100C2×C22⋊Dic17—22no—
101C2×C22⋊Dic17—22no—
102C2×C22⋊Dic17—22no—
103C2×C22⋊Dic17—22no—
104C2×C22⋊Dic17—41no—
105C2×C22⋊Dic17—41no—
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×#63227—41no—
119C2×#63227—41no—
120C2×#63227—41no—
121C2×#63227—41no—
122C2×#63227C2×C414yes—
123C2×#63227C2×C414yes—
124C2×C4⋊Dic17—22no—
125C2×C4⋊Dic17—22no—
126C2×C4⋊Dic17—22no—
127C2×C4⋊Dic17—22no—
128C2×C4⋊Dic17—22no—
129C2×C4⋊Dic17—22no—
130C2×C4⋊Dic17—41no—
131C2×C4⋊Dic17C2×C414yes—
132C2×C4⋊Dic17C2×C414yes—
133C2×C4×Dic17—22no—
134C2×C4×Dic17—22no—
135C2×C4×Dic17—41no—
136#10587572—232no—
137C17×#95—22no—
138C17×#95—22no—
139#10587502—22no—
140#10587502—22no—
141#10587502—41no—
142#10587502—41no—
143#10587502—41no—
144#10587502—41no—
145#10587502—41no—
146#10587502—41no—
147#10587502—41no—
148#10587502—41no—
149#10587502—41no—
150#10587502—41no—
151#10587502—41no—
152#10587502—41no—
153C24×C17—21no—
154C24×C17—21no—
155C24×C17—21no—
156C24×C17—21no—
157C24×C17—21no—
158C24×C17—21no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17—21no—
165C24×C17C22×C412yes—
166C24×C17C2×D412yes—
167C24×C17C2×D412yes—
168C24×C17C2411yescharacteristic
169C23×D17—21no—
170C23×D17—21no—
171C23×D17—21no—
172C23×D17—21no—
173C23×D17—21no—
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×D17C22×C412yes—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
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×C17C22×C412yes—
219C22×C4×C17C22×C412yes—
220C22×C4×C17C2×D412yes—
221C22×C4×C17C2×D412yes—
222C22×C4×C17C2×D412yes—
223C22×C4×C17C2×D412yes—
224C22×C4×C17#4112yes—
225C22×C4×C17#4112yes—
226C2×C22⋊D17—28no—
227C2×C22⋊D17—44no—
228C2×C22⋊D17—44no—
229C2×C22⋊D17—44no—
230C2×C22⋊D17—44no—
231C2×C22⋊D17—44no—
232C2×C22⋊D17—44no—
233C22×Dic17—28no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
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×Dic17—21no—
278C22×Dic17—44no—
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×Dic17#4112yes—
288C22×Dic17#4112yes—
289C4⋊C4×C17—44no—
290C22⋊C4×C17—44no—
291C22⋊C4×C17—44no—
292C22⋊C4×C17C22⋊C4116yescomplemented
293C42×C17—44no—
294C22⋊Dic17—44no—
295C22⋊Dic17—44no—
296#63227—28no—
297#63227—28no—
298#63227—44no—
299#63227—44no—
300#63227—44no—
301#63227—44no—
302C4⋊Dic17—28no—
303C4⋊Dic17—28no—
304C4⋊Dic17—44no—
305C4×Dic17—44no—
306#14506—171nomaximal, Sylow
307C23×C17—22no—
308C23×C17—22no—
309C23×C17—22no—
310C23×C17—22no—
311C23×C17—22no—
312C23×C17—22no—
313C23×C17—22no—
314C23×C17—22no—
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—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×C17C2×C22⋊C414yes—
342C23×C17C23×C411yescharacteristic
343C23×C17C22×D411yescharacteristic
344C23×C17C22×D411yescharacteristic
345C23×C17C2×#4111yescharacteristic
346C23×C17C2×#4111yescharacteristic
347C23×C17C2×#4111yescharacteristic
348C23×C17C2×#4111yescharacteristic
349C23×C17H(5,𝔽2)11yescharacteristic
350C23×C17H(5,𝔽2)11yescharacteristic
351C23×C17H(5,𝔽2)11yescharacteristic
352C23×C17H(5,𝔽2)11yescharacteristic
353C23×C17H(5,𝔽2)11yescharacteristic
354C23×C17H(5,𝔽2)11yescharacteristic
355C23×C172−1+411yescharacteristic
356C23×C172−1+411yescharacteristic
357C22×D17—22no—
358C22×D17—22no—
359C22×D17—22no—
360C22×D17—22no—
361C22×D17—22no—
362C22×D17—22no—
363C22×D17—22no—
364C22×D17—41no—
365C22×D17—41no—
366C22×D17—41no—
367C22×D17—41no—
368C22×D17—41no—
369C22×D17—41no—
370C22×D17—41no—
371C22×D17—41no—
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—
392C2×C4×C17—22no—
393C2×C4×C17—22no—
394C2×C4×C17—22no—
395C2×C4×C17—22no—
396C2×C4×C17—22no—
397C2×C4×C17—22no—
398C2×C4×C17—22no—
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—41no—
411C2×C4×C17—41no—
412C2×C4×C17—41no—
413C2×C4×C17—41no—
414C2×C4×C17—41no—
415C2×C4×C17—41no—
416C2×C4×C17—41no—
417C2×C4×C17—41no—
418C2×C4×C17—41no—
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×C17C2×C22⋊C414yes—
433C2×C4×C17C2×C22⋊C414yes—
434C22⋊D17—416no—
435C2×Dic17—22no—
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—416no—
451C2×Dic17—41no—
452C2×Dic17—41no—
453C2×Dic17—41no—
454C2×Dic17—41no—
455C2×Dic17—41no—
456C2×Dic17—41no—
457C2×Dic17—41no—
458C2×Dic17—41no—
459C2×Dic17—41no—
460C2×Dic17—41no—
461C2×Dic17—41no—
462C2×Dic17—41no—
463C2×Dic17—41no—
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—
485C22×#123—171no—
486C2×#388—171no—
487C2×#388D1711yescharacteristic, complemented
488#1445—171no—
489#1445—171no—
490#1439—171no—
491#1439—171no—
492#1438—171no—
493#1438—171no—
494#1437—171no—
495#1437—171no—
496C4⋊#95—171no—
497C4⋊#95—171no—
498C22⋊#95—171no—
499C22⋊#95—171no—
500C22×C17—24no—
501C22×C17—24no—
502C22×C17—24no—
503C22×C17—42no—
504C22×C17—42no—
505C22×C17—42no—
506C22×C17—42no—
507C22×C17—42no—
508C22×C17—42no—
509C22×C17—42no—
510C22×C17—42no—
511C22×C17—42no—
512C22×C17—42no—
513C22×C17—42no—
514C22×C17—42no—
515C22×C17C22×C22⋊C411yescharacteristic
516C22×C17C4×#4111yescharacteristic
517C22×C17C4×#4111yescharacteristic
518C22×C17#51811yescharacteristic
519C22×C17#51811yescharacteristic
520C22×C17#52011yescharacteristic
521C22×C17#52011yescharacteristic
522C22×C17#53511yescharacteristic
523C22×C17#53511yescharacteristic
524C22×C17#53511yescharacteristic
525C22×C17#53511yescharacteristic
526C22×C17#53811yescharacteristic
527C22×C17#53811yescharacteristic
528C22×C17#53911yescharacteristic
529C22×C17#53911yescharacteristic
530C22×C17#54011yescharacteristic
531C22×C17#54011yescharacteristic
532C22×C17#54211yescharacteristic
533C22×C17#54211yescharacteristic
534C22×C17#54611yescharacteristic
535C22×C17#54611yescharacteristic
536C22×C17#54611yescharacteristic
537C22×C17#54611yescharacteristic
538C22×C17#54711yescharacteristic
539C22×C17#54711yescharacteristic
540C22×C17#54711yescharacteristic
541C22×C17#54711yescharacteristic
542C22×C17#55111yescharacteristic
543C22×C17#55311yescharacteristic
544C22×C17#55311yescharacteristic
545C22×C17#55911yescharacteristic
546C22×C17#56011yescharacteristic
547C22×C17#56211yescharacteristic
548C22×C17#56211yescharacteristic
549C22×C17#56311yescharacteristic
550C2×D17—42no—
551C2×D17—42no—
552C2×D17—42no—
553C2×D17—42no—
554C2×D17—42no—
555C2×D17—42no—
556C2×D17—42no—
557C2×D17—81no—
558C2×D17—81no—
559C2×D17—81no—
560C2×D17—81no—
561C2×D17—81no—
562C2×D17—81no—
563C2×D17—81no—
564C2×D17—81no—
565C4×C17—24no—
566C4×C17—24no—
567C4×C17—42no—
568C4×C17—42no—
569C4×C17—81no—
570C4×C17—81no—
571Dic17—42no—
572Dic17—42no—
573Dic17—42no—
574Dic17—42no—
575Dic17—42no—
576Dic17—81no—
577Dic17—81no—
578C23×D4—171no—
579C24×C4—171no—
580C2×#123—178no—
581C2×#123—344no—
582C2×#123—344no—
583C22×C4⋊C4—171no—
584C22×C4⋊C4—171no—
585C22×C4⋊C4—171no—
586C22×C4⋊C4C2×D1711yescharacteristic
587C22×C22⋊C4—171no—
588C22×C22⋊C4—171no—
589C22×C22⋊C4—171no—
590C22×C22⋊C4—171no—
591C22×C22⋊C4—171no—
592C22×C22⋊C4—171no—
593C22×C22⋊C4—171no—
594C22×C22⋊C4—171no—
595C22×C22⋊C4C2×D1711yescharacteristic
596C22×C22⋊C4C2×D1711yescharacteristic
597C22×C22⋊C4C2×D1711yescharacteristic
598C22×C42—171no—
599C22×C42C2×D1711yescharacteristic
600#388—24no—
601#388—344no—
602C2×#95—171no—
603C2×#95—171no—
604C2×#95—171no—
605C2×#95—171no—
606C2×#95—171no—
607C2×#95—171no—
608C2×#95—171no—
609C2×#95—171no—
610C2×#95—171no—
611C2×#95—171no—
612C2×#95—171no—
613C2×#95—171no—
614C2×#95—171no—
615C2×#95—171no—
616C2×#95C2×D1711yescharacteristic
617C2×#95C2×D1711yescharacteristic
618C2×C17—44no—
619C2×C17#230911yescharacteristic
620C2×C17#233511yescharacteristic
621C2×C17#233511yescharacteristic
622C2×C17#233911yescharacteristic
623C2×C17#233911yescharacteristic
624C2×C17#237411yescharacteristic
625C2×C17#237611yescharacteristic
626C2×C17#270311yescharacteristic
627C2×C17#270311yescharacteristic
628C2×C17#270611yescharacteristic
629C2×C17#270611yescharacteristic
630C2×C17#271011yescharacteristic
631C2×C17#271011yescharacteristic
632C2×C17#271811yescharacteristic
633C2×C17#271811yescharacteristic
634D17—82no—
635C25—171no—
636C25C22×D1711yescharacteristic
637C22×D4—174no—
638C22×D4—342no—
639C22×D4—342no—
640C22×D4—681no—
641C22×D4—681no—
642C22×D4—681no—
643C22×D4—681no—
644C23×C4—171no—
645C23×C4—171no—
646C23×C4—171no—
647C23×C4—171no—
648C23×C4—171no—
649C23×C4—174no—
650C23×C4—171no—
651C23×C4—171no—
652C23×C4—342no—
653C23×C4—342no—
654C23×C4—681no—
655C23×C4—681no—
656C23×C4—681no—
657C23×C4—681no—
658C23×C4C22×D1711yescharacteristic
659C23×C4C22×D1711yescharacteristic
660C23×C4C22×D1711yescharacteristic
661C23×C4C22×D1711yescharacteristic
662C23×C4C22×D1711yescharacteristic
663C23×C4C22×D1711yescharacteristic
664#123—3432no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—174no—
669C2×C4⋊C4—174no—
670C2×C4⋊C4—342no—
671C2×C4⋊C4—342no—
672C2×C4⋊C4—342no—
673C2×C4⋊C4—342no—
674C2×C4⋊C4—342no—
675C2×C4⋊C4—342no—
676C2×C4⋊C4—681no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—174no—
684C2×C22⋊C4—174no—
685C2×C22⋊C4—342no—
686C2×C22⋊C4—342no—
687C2×C22⋊C4—342no—
688C2×C22⋊C4—342no—
689C2×C22⋊C4—342no—
690C2×C22⋊C4—342no—
691C2×C22⋊C4—342no—
692C2×C22⋊C4—342no—
693C2×C22⋊C4—342no—
694C2×C22⋊C4—342no—
695C2×C22⋊C4—342no—
696C2×C22⋊C4—342no—
697C2×C22⋊C4—681no—
698C2×C22⋊C4—681no—
699C2×C22⋊C4—681no—
700C2×C22⋊C4—681no—
701C2×C22⋊C4—681no—
702C2×C22⋊C4—681no—
703C2×C22⋊C4—681no—
704C2×C22⋊C4—681no—
705C2×C22⋊C4—681no—
706C2×C22⋊C4—681no—
707C2×C22⋊C4C4×D1714yes—
708C2×C22⋊C4D6814yes—
709C2×C22⋊C4C22⋊D1714yes—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—41no—
713C2×C42—342no—
714C2×C42—342no—
715C2×C42—681no—
716#95—22no—
717#95—22no—
718#95—342no—
719#95—342no—
720#95—681no—
721#95—681no—
722#95—681no—
723#95—681no—
724#95—681no—
725#95—681no—
726#95—681no—
727#95—681no—
728#95—681no—
729#95—681no—
730#95—681no—
731#95—681no—
732C17#1450611yescharacteristic, complemented, Sylow
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—172no—
746C24—341no—
747C24—341no—
748C24—341no—
749C24—341no—
750C24—341no—
751C24—341no—
752C24—341no—
753C24—341no—
754C24—341no—
755C24—341no—
756C24—341no—
757C24—341no—
758C24—341no—
759C24—341no—
760C24C2×C4×D1712yes—
761C24C2×D6812yes—
762C24C2×C22⋊D1712yes—
763C24C23×D1711yescharacteristic
764C2×D4—348no—
765C2×D4—684no—
766C2×D4—684no—
767C2×D4—684no—
768C2×D4—684no—
769C2×D4—684no—
770C2×D4—684no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
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—172no—
806C22×C4—172no—
807C22×C4—172no—
808C22×C4—172no—
809C22×C4—172no—
810C22×C4—341no—
811C22×C4—341no—
812C22×C4—341no—
813C22×C4—341no—
814C22×C4—341no—
815C22×C4—341no—
816C22×C4—341no—
817C22×C4—341no—
818C22×C4—341no—
819C22×C4—341no—
820C22×C4—341no—
821C22×C4—341no—
822C22×C4—341no—
823C22×C4—341no—
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—348no—
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—684no—
856C22×C4—684no—
857C22×C4—684no—
858C22×C4—684no—
859C22×C4—684no—
860C22×C4—684no—
861C22×C4C2×C4×D1712yes—
862C22×C4C2×C4×D1712yes—
863C22×C4C2×D6812yes—
864C22×C4C2×D6812yes—
865C22×C4#6325412yes—
866C22×C4#6325412yes—
867C22×C4C2×C22⋊D1712yes—
868C22×C4C2×C22⋊D1712yes—
869C4⋊C4—44no—
870C4⋊C4—348no—
871C4⋊C4—348no—
872C4⋊C4—684no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—348no—
876C22⋊C4—348no—
877C22⋊C4—684no—
878C22⋊C4—684no—
879C22⋊C4—684no—
880C22⋊C4—684no—
881C22⋊C4—684no—
882C22⋊C4—684no—
883C22⋊C4#63227116yescomplemented
884C42—44no—
885C42—684no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—41no—
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—342no—
921C23—342no—
922C23—342no—
923C23—342no—
924C23—342no—
925C23—342no—
926C23—342no—
927C23—681no—
928C23—681no—
929C23—681no—
930C23—681no—
931C23—681no—
932C23—681no—
933C23—681no—
934C23—681no—
935C23—681no—
936C23—681no—
937C23—681no—
938C23—681no—
939C23—681no—
940C23—681no—
941C23—681no—
942C23—681no—
943C23—681no—
944C23—681no—
945C23—681no—
946C23—681no—
947C23—681no—
948C23—681no—
949C23—681no—
950C23—681no—
951C23—681no—
952C23—681no—
953C23—681no—
954C23—681no—
955C23C2×#6322714yes—
956C23C22×C4×D1711yescharacteristic
957C23C22×D6811yescharacteristic
958C23C2×#6325411yescharacteristic
959C23C2×#6325411yescharacteristic
960C23#1058769111yescharacteristic
961C23#1058769111yescharacteristic
962C23#41×D1711yescharacteristic
963C23#41×D1711yescharacteristic
964C23#1058769611yescharacteristic
965C23#1058769611yescharacteristic
966C23#1058769611yescharacteristic
967C23#1058769611yescharacteristic
968C23#1058769711yescharacteristic
969C23#1058769711yescharacteristic
970C23C22×C22⋊D1711yescharacteristic
971D4—6816no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—342no—
1013C2×C4—342no—
1014C2×C4—342no—
1015C2×C4—342no—
1016C2×C4—342no—
1017C2×C4—342no—
1018C2×C4—342no—
1019C2×C4—342no—
1020C2×C4—342no—
1021C2×C4—342no—
1022C2×C4—342no—
1023C2×C4—342no—
1024C2×C4—342no—
1025C2×C4—342no—
1026C2×C4—342no—
1027C2×C4—6816no—
1028C2×C4—681no—
1029C2×C4—681no—
1030C2×C4—681no—
1031C2×C4—681no—
1032C2×C4—681no—
1033C2×C4—681no—
1034C2×C4—681no—
1035C2×C4—681no—
1036C2×C4—681no—
1037C2×C4—681no—
1038C2×C4—681no—
1039C2×C4—681no—
1040C2×C4—681no—
1041C2×C4—681no—
1042C2×C4—681no—
1043C2×C4—681no—
1044C2×C4—681no—
1045C2×C4—681no—
1046C2×C4—681no—
1047C2×C4—681no—
1048C2×C4—681no—
1049C2×C4—681no—
1050C2×C4—681no—
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×C4C2×#6322714yes—
1063C2×C4C2×#6322714yes—
1064C22—24no—
1065C22—24no—
1066C22—24no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—682no—
1080C22—682no—
1081C22—682no—
1082C22—682no—
1083C22—682no—
1084C22—682no—
1085C22—682no—
1086C22—1361no—
1087C22—1361no—
1088C22—1361no—
1089C22—1361no—
1090C22—1361no—
1091C22—1361no—
1092C22—1361no—
1093C22—1361no—
1094C22C22×#6322711yescharacteristic
1095C22C4×#6325411yescharacteristic
1096C22C4×#6325411yescharacteristic
1097C22#1176328311yescharacteristic
1098C22#1176328311yescharacteristic
1099C22#1176328811yescharacteristic
1100C22#1176328811yescharacteristic
1101C22#1176337311yescharacteristic
1102C22#1176337311yescharacteristic
1103C22#1176337811yescharacteristic
1104C22#1176337811yescharacteristic
1105C22#1176339311yescharacteristic
1106C22#1176339611yescharacteristic
1107C22#1176340011yescharacteristic
1108C22#1176340311yescharacteristic
1109C22#1176341111yescharacteristic
1110C22#1176341211yescharacteristic
1111C22#1176342511yescharacteristic
1112C22#1176342811yescharacteristic
1113C22#1176345311yescharacteristic
1114C22#1176345311yescharacteristic
1115C22#1176345411yescharacteristic
1116C22#1176345411yescharacteristic
1117C22#1176345811yescharacteristic
1118C22#1176345811yescharacteristic
1119C22#1176346311yescharacteristic
1120C22#1176346311yescharacteristic
1121C22#1176348211yescharacteristic
1122C22#1176351011yescharacteristic
1123C22#1176351111yescharacteristic
1124C22#1176354111yescharacteristic
1125C22#1176354711yescharacteristic
1126C22#1176355311yescharacteristic
1127C22#1176355611yescharacteristic
1128C22#1176356111yescharacteristic
1129C4—24no—
1130C4—24no—
1131C4—42no—
1132C4—42no—
1133C4—81no—
1134C4—81no—
1135C4—682no—
1136C4—682no—
1137C4—682no—
1138C4—682no—
1139C4—682no—
1140C4—1361no—
1141C4—1361no—
1142C2—44no—
1143C2—1362no—
1144C2#1453136411yescharacteristic
1145C2#1453156711yescharacteristic
1146C2#1453157911yescharacteristic
1147C2#1453160911yescharacteristic
1148C2#1453160911yescharacteristic
1149C2#1453191411yescharacteristic
1150C2#1453193011yescharacteristic
1151C2#1453542311yescharacteristic
1152C2#1453542511yescharacteristic
1153C2#1453546811yescharacteristic
1154C2#1453547011yescharacteristic
1155C2#1453552011yescharacteristic
1156C2#1453552411yescharacteristic
1157C2#1453562811yescharacteristic
1158C2#1453563211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×#388D17
hypocenterC17#14506
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#11762702C2semidirect
3. #14527053C2semidirect
4. #14527051C2semidirect
5. #14527030C2semidirect
6. #14527026C2semidirect
9. #14527022C2semidirect
10. #14527020C2semidirect
11. #14527014C2semidirect
12. #14527013C2semidirect
13. #14527006C2semidirect
14. #14527006C2semidirect
15. C2×C17×#388C2semidirect
20. C2×#10587572C4semidirect
292. C22⋊C4×C17C22⋊C4semidirect
487. C2×#388D17semidirect
732. C17#14506semidirect
883. C22⋊C4#63227semidirect

Maximal subgroups

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

subgroupindex
C22×#105875722
C2×#117627022
#145270532
#145270512
#145270302
#145270262
#145270232
#145270222
#145270202
#145270142
#145270132
#145270062
C2×C17×#3882
#1450617