Finite Group Databasebeta

← #16955824

Subgroups — #16955824

Order 4352.

2882 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic17C211yesmaximal, characteristic
2C2×#11762689C211yesmaximal, characteristic
3C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic17C211yesmaximal, characteristic, complemented
6C22×#10587502C211yesmaximal, characteristic, complemented
7#14527021C211yesmaximal, characteristic, complemented
8#14527021C211yesmaximal, characteristic, complemented
9#14527018C211yesmaximal, characteristic, complemented
10#14527018C211yesmaximal, characteristic, complemented
11#14527009C211yesmaximal, characteristic, complemented
12#14527006C211yesmaximal, characteristic, complemented
13#14527006C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C2×C17×#386C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C24×Dic17C2211yescharacteristic
19C2×D4×Dic17—24no—
20C2×D4×Dic17—24no—
21C2×D4×Dic17C418yescomplemented
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33#11762689C418yescomplemented
34C22⋊C4×Dic17—24no—
35C22⋊C4×Dic17—24no—
36C4×C22⋊Dic17—24no—
37C2×#10587502—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
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C23×D4×C17C2211yescharacteristic
53C24×C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C22×C22⋊C4×C17C2211yescharacteristic
56C22×C22⋊C4×C17C2211yescharacteristic
57C17×#386C418yescomplemented
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C25×C17C2311yescharacteristic
61C25×C17C2311yescharacteristic
62C22×D4×C17—22no—
63C22×D4×C17—22no—
64C22×D4×C17—22no—
65C22×D4×C17—22no—
66C22×D4×C17C2×C414yes—
67C22×D4×C17C2×C414yes—
68C22×D4×C17C2×C414yes—
69C23×C4×C17—22no—
70C23×C4×C17—22no—
71C23×C4×C17—22no—
72C23×C4×C17—22no—
73C23×C4×C17—41no—
74C23×C4×C17—41no—
75C23×C4×C17C2×C414yescomplemented
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C23×Dic17—22no—
82C23×Dic17—22no—
83C23×Dic17—22no—
84C23×Dic17—22no—
85C23×Dic17—22no—
86C23×Dic17—22no—
87C23×Dic17—22no—
88C23×Dic17—22no—
89C23×Dic17—22no—
90C23×Dic17—22no—
91C23×Dic17—22no—
92C23×Dic17—22no—
93C23×Dic17—41no—
94C23×Dic17—41no—
95C23×Dic17—41no—
96C23×Dic17—41no—
97C23×Dic17—41no—
98C23×Dic17—41no—
99C23×Dic17C2×C414yes—
100C23×Dic17C2×C414yescomplemented
101C23×Dic17C2×C414yescomplemented
102C23×Dic17C2311yescharacteristic
103C23×Dic17C2311yescharacteristic
104C23×Dic17C2311yescharacteristic
105C23×Dic17C2311yescharacteristic
106C23×Dic17C2311yescharacteristic
107C23×Dic17C2311yescharacteristic
108C23×Dic17C2311yescharacteristic
109C23×Dic17C2311yescharacteristic
110C2×C22⋊C4×C17—22no—
111C2×C22⋊C4×C17—22no—
112C2×C22⋊C4×C17—22no—
113C2×C22⋊C4×C17—22no—
114C2×C22⋊C4×C17—41no—
115C2×C22⋊C4×C17—41no—
116C2×C22⋊C4×C17C2×C414yescomplemented
117C2×C22⋊C4×C17C2×C414yescomplemented
118C2×C22⋊C4×C17C2×C414yescomplemented
119C2×C22⋊Dic17—22no—
120C2×C22⋊Dic17—22no—
121C2×C22⋊Dic17—22no—
122C2×C22⋊Dic17—22no—
123C2×C22⋊Dic17—22no—
124C2×C22⋊Dic17—22no—
125C2×C22⋊Dic17—41no—
126C2×C22⋊Dic17—41no—
127C2×C22⋊Dic17C2×C414yes—
128C2×C22⋊Dic17C2×C414yescomplemented
129C2×C22⋊Dic17C2×C414yescomplemented
130C2×C22⋊Dic17C2×C414yescomplemented
131C2×C22⋊Dic17C2×C414yescomplemented
132C2×C22⋊Dic17D414yes—
133C2×C22⋊Dic17D414yes—
134D4×Dic17—232no—
135C2×C4⋊Dic17—22no—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17C2×C414yescomplemented
138C2×C4×Dic17—22no—
139C2×C4×Dic17—22no—
140C2×C4×Dic17—22no—
141C2×C4×Dic17—22no—
142C2×C4×Dic17—22no—
143C2×C4×Dic17—22no—
144C2×C4×Dic17—22no—
145C2×C4×Dic17—22no—
146C2×C4×Dic17—22no—
147C2×C4×Dic17—22no—
148C2×C4×Dic17—41no—
149C2×C4×Dic17—41no—
150C2×C4×Dic17—41no—
151C2×C4×Dic17—41no—
152C2×C4×Dic17C2×C414yescomplemented
153C17×#95C2×C414yescomplemented
154C17×#95C2×C414yescomplemented
155#10587502—22no—
156#10587502—22no—
157#10587502—22no—
158#10587502—22no—
159#10587502—22no—
160#10587502—22no—
161#10587502—22no—
162#10587502—22no—
163#10587502—22no—
164#10587502—41no—
165#10587502—41no—
166#10587502C2×C414yescomplemented
167#10587502C2×C414yescomplemented
168#10587502D414yescomplemented
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×C17—21no—
186C24×C17—21no—
187C24×C17—21no—
188C24×C17—21no—
189C24×C17C22×C412yes—
190C24×C17C22×C412yes—
191C24×C17C22×C412yes—
192C24×C17C22×C412yes—
193C24×C17C22×C412yes—
194C24×C17C22×C412yes—
195C24×C17C2×D412yes—
196C24×C17C2×D412yes—
197C24×C17#4112yes—
198C24×C17#4112yes—
199C24×C17C2411yescharacteristic
200C2×D4×C17—28no—
201C2×D4×C17—28no—
202C2×D4×C17—28no—
203C2×D4×C17—28no—
204C2×D4×C17—28no—
205C2×D4×C17—28no—
206C2×D4×C17C42116yescomplemented
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—28no—
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×C17—21no—
232C22×C4×C17—21no—
233C22×C4×C17—21no—
234C22×C4×C17—28no—
235C22×C4×C17—44no—
236C22×C4×C17—44no—
237C22×C4×C17—44no—
238C22×C4×C17—44no—
239C22×C4×C17—44no—
240C22×C4×C17C22×C412yes—
241C22×C4×C17C22×C412yes—
242C22×C4×C17C22×C412yes—
243C22×C4×C17C22×C412yes—
244C22×C4×C17C22×C412yes—
245C22×C4×C17C22×C412yes—
246C22×C4×C17C22×C412yes—
247C22×C4×C17C2×D412yes—
248C22×C4×C17#4112yes—
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—28no—
266C22×Dic17—28no—
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×Dic17—21no—
285C22×Dic17—21no—
286C22×Dic17—21no—
287C22×Dic17—21no—
288C22×Dic17—21no—
289C22×Dic17—21no—
290C22×Dic17—21no—
291C22×Dic17—28no—
292C22×Dic17—28no—
293C22×Dic17—28no—
294C22×Dic17—28no—
295C22×Dic17—44no—
296C22×Dic17—44no—
297C22×Dic17—44no—
298C22×Dic17—44no—
299C22×Dic17—44no—
300C22×Dic17—44no—
301C22×Dic17—44no—
302C22×Dic17—44no—
303C22×Dic17—44no—
304C22×Dic17—44no—
305C22×Dic17—44no—
306C22×Dic17—44no—
307C22×Dic17—44no—
308C22×Dic17—44no—
309C22×Dic17—44no—
310C22×Dic17C22×C412yes—
311C22×Dic17C22×C412yes—
312C22×Dic17C22×C412yes—
313C22×Dic17C22×C412yes—
314C22×Dic17C22×C412yes—
315C22×Dic17C22×C412yes—
316C22×Dic17C22×C412yes—
317C22×Dic17C22×C412yes—
318C22×Dic17C2×D412yes—
319C22×Dic17C2×D412yes—
320C22×Dic17C2×D412yes—
321C22×Dic17C2×D412yes—
322C22×Dic17C2×D412yes—
323C22×Dic17C2×D412yes—
324C22×Dic17#4112yes—
325C22×Dic17#4112yes—
326C22⋊C4×C17—28no—
327C22⋊C4×C17—28no—
328C22⋊C4×C17—44no—
329C22⋊Dic17—28no—
330C22⋊Dic17—28no—
331C22⋊Dic17—28no—
332C22⋊Dic17—44no—
333C22⋊Dic17C22⋊C4116yescomplemented
334C4⋊Dic17—28no—
335C4×Dic17—28no—
336C4×Dic17—44no—
337C4×Dic17—44no—
338C4×Dic17—44no—
339C4×Dic17—44no—
340#13813—171nomaximal, Sylow
341C23×C17—22no—
342C23×C17—22no—
343C23×C17—22no—
344C23×C17—22no—
345C23×C17—22no—
346C23×C17—22no—
347C23×C17—22no—
348C23×C17—22no—
349C23×C17—22no—
350C23×C17—22no—
351C23×C17—22no—
352C23×C17—22no—
353C23×C17—22no—
354C23×C17—22no—
355C23×C17—22no—
356C23×C17—22no—
357C23×C17—22no—
358C23×C17—22no—
359C23×C17—22no—
360C23×C17—22no—
361C23×C17—22no—
362C23×C17—22no—
363C23×C17—22no—
364C23×C17—22no—
365C23×C17—22no—
366C23×C17—22no—
367C23×C17—22no—
368C23×C17—22no—
369C23×C17—22no—
370C23×C17—22no—
371C23×C17—22no—
372C23×C17—22no—
373C23×C17—22no—
374C23×C17—22no—
375C23×C17—22no—
376C23×C17—22no—
377C23×C17—22no—
378C23×C17—22no—
379C23×C17—22no—
380C23×C17—22no—
381C23×C17—22no—
382C23×C17—22no—
383C23×C17—22no—
384C23×C17—22no—
385C23×C17—22no—
386C23×C17—22no—
387C23×C17—41no—
388C23×C17—41no—
389C23×C17—41no—
390C23×C17—41no—
391C23×C17—41no—
392C23×C17—41no—
393C23×C17—41no—
394C23×C17—41no—
395C23×C17—41no—
396C23×C17—41no—
397C23×C17—41no—
398C23×C17—41no—
399C23×C17—41no—
400C23×C17—41no—
401C23×C17—41no—
402C23×C17—41no—
403C23×C17C2×C4214yes—
404C23×C17C2×C4214yes—
405C23×C17C2×C22⋊C414yes—
406C23×C17#11714yes—
407C23×C17C4×D414yes—
408C23×C17C4×D414yes—
409C23×C17C4×D414yes—
410C23×C17C4×D414yes—
411C23×C17C23×C411yescharacteristic
412C23×C17C23×C411yescharacteristic
413C23×C17C23×C411yescharacteristic
414C23×C17C22×D411yescharacteristic
415C23×C17C22×D411yescharacteristic
416C23×C17C22×D411yescharacteristic
417C23×C17C2×#4111yescharacteristic
418C23×C17C2×#4111yescharacteristic
419C23×C17C2×#4111yescharacteristic
420C23×C17C2×#4111yescharacteristic
421C23×C17C2×#4111yescharacteristic
422C23×C17H(5,𝔽2)11yescharacteristic
423C23×C17H(5,𝔽2)11yescharacteristic
424C23×C17H(5,𝔽2)11yescharacteristic
425C23×C172−1+411yescharacteristic
426D4×C17—232no—
427C2×C4×C17—22no—
428C2×C4×C17—22no—
429C2×C4×C17—22no—
430C2×C4×C17—22no—
431C2×C4×C17—22no—
432C2×C4×C17—22no—
433C2×C4×C17—22no—
434C2×C4×C17—22no—
435C2×C4×C17—22no—
436C2×C4×C17—22no—
437C2×C4×C17—22no—
438C2×C4×C17—22no—
439C2×C4×C17—22no—
440C2×C4×C17—22no—
441C2×C4×C17—22no—
442C2×C4×C17—22no—
443C2×C4×C17—22no—
444C2×C4×C17—22no—
445C2×C4×C17—22no—
446C2×C4×C17—22no—
447C2×C4×C17—22no—
448C2×C4×C17—416no—
449C2×C4×C17—41no—
450C2×C4×C17—41no—
451C2×C4×C17—41no—
452C2×C4×C17—41no—
453C2×C4×C17—41no—
454C2×C4×C17—41no—
455C2×C4×C17—41no—
456C2×C4×C17—41no—
457C2×C4×C17—41no—
458C2×C4×C17—41no—
459C2×C4×C17—41no—
460C2×C4×C17—41no—
461C2×C4×C17C2×C4214yes—
462C2×C4×C17C4×D414yescomplemented
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—22no—
472C2×Dic17—22no—
473C2×Dic17—22no—
474C2×Dic17—22no—
475C2×Dic17—22no—
476C2×Dic17—22no—
477C2×Dic17—22no—
478C2×Dic17—22no—
479C2×Dic17—22no—
480C2×Dic17—22no—
481C2×Dic17—22no—
482C2×Dic17—22no—
483C2×Dic17—22no—
484C2×Dic17—22no—
485C2×Dic17—22no—
486C2×Dic17—22no—
487C2×Dic17—22no—
488C2×Dic17—22no—
489C2×Dic17—22no—
490C2×Dic17—22no—
491C2×Dic17—22no—
492C2×Dic17—22no—
493C2×Dic17—22no—
494C2×Dic17—22no—
495C2×Dic17—22no—
496C2×Dic17—22no—
497C2×Dic17—22no—
498C2×Dic17—22no—
499C2×Dic17—416no—
500C2×Dic17—416no—
501C2×Dic17—416no—
502C2×Dic17—41no—
503C2×Dic17—41no—
504C2×Dic17—41no—
505C2×Dic17—41no—
506C2×Dic17—41no—
507C2×Dic17—41no—
508C2×Dic17—41no—
509C2×Dic17—41no—
510C2×Dic17—41no—
511C2×Dic17—41no—
512C2×Dic17—41no—
513C2×Dic17—41no—
514C2×Dic17—41no—
515C2×Dic17—41no—
516C2×Dic17—41no—
517C2×Dic17—41no—
518C2×Dic17C2×C22⋊C414yes—
519C2×Dic17C2×C22⋊C414yes—
520C2×Dic17C4×D414yes—
521C2×Dic17C4×D414yescomplemented
522C22×C4×D4—171no—
523C2×#386—171no—
524C2×#386D1711yescharacteristic
525C2×C4×C22⋊C4—171no—
526C2×C4×C22⋊C4—171no—
527C2×C4×C22⋊C4—171no—
528C22×#95—171no—
529#1437—171no—
530#1437—171no—
531#1436—171no—
532#1436—171no—
533#1434—171no—
534C22⋊#95—171no—
535C22⋊#95—171no—
536C4×#95—171no—
537C22×C17—24no—
538C22×C17—24no—
539C22×C17—24no—
540C22×C17—24no—
541C22×C17—24no—
542C22×C17—24no—
543C22×C17—24no—
544C22×C17—24no—
545C22×C17—24no—
546C22×C17—24no—
547C22×C17—24no—
548C22×C17—24no—
549C22×C17—24no—
550C22×C17—24no—
551C22×C17—24no—
552C22×C17—24no—
553C22×C17—24no—
554C22×C17—42no—
555C22×C17—42no—
556C22×C17—42no—
557C22×C17—42no—
558C22×C17—42no—
559C22×C17—42no—
560C22×C17—42no—
561C22×C17—42no—
562C22×C17—42no—
563C22×C17—42no—
564C22×C17—42no—
565C22×C17—42no—
566C22×C17C4×C22⋊C418yescomplemented
567C22×C17C22×C4211yescharacteristic
568C22×C17C22×C22⋊C411yescharacteristic
569C22×C17C2×#11711yescharacteristic
570C22×C17C2×C4×D411yescharacteristic
571C22×C17C2×C4×D411yescharacteristic
572C22×C17C2×C4×D411yescharacteristic
573C22×C17C2×C4×D411yescharacteristic
574C22×C17C2×C4×D411yescharacteristic
575C22×C17C2×C4×D411yescharacteristic
576C22×C17C2×C4×D411yescharacteristic
577C22×C17C4×#4111yescharacteristic
578C22×C17C4×#4111yescharacteristic
579C22×C17C4×#4111yescharacteristic
580C22×C17#51811yescharacteristic
581C22×C17#51811yescharacteristic
582C22×C17#51811yescharacteristic
583C22×C17#52011yescharacteristic
584C22×C17#52011yescharacteristic
585C22×C17#52011yescharacteristic
586C22×C17D4211yescharacteristic
587C22×C17D4211yescharacteristic
588C22×C17#54611yescharacteristic
589C22×C17#54611yescharacteristic
590C22×C17#54611yescharacteristic
591C22×C17#54611yescharacteristic
592C22×C17#54611yescharacteristic
593C22×C17#54711yescharacteristic
594C22×C17#54711yescharacteristic
595C22×C17#54811yescharacteristic
596C22×C17#55111yescharacteristic
597C22×C17#55111yescharacteristic
598C22×C17#55211yescharacteristic
599C22×C17#55311yescharacteristic
600C22×C17#55311yescharacteristic
601C22×C17#55311yescharacteristic
602C4×C17—24no—
603C4×C17—24no—
604C4×C17—42no—
605C4×C17—42no—
606C4×C17—42no—
607Dic17—24no—
608Dic17—24no—
609Dic17—24no—
610Dic17—24no—
611Dic17—42no—
612Dic17—42no—
613Dic17—42no—
614Dic17—42no—
615C23×D4C2×D1711yescharacteristic
616C24×C4—171no—
617C24×C4—171no—
618C24×C4—171no—
619C24×C4C2×D1711yescharacteristic
620C2×C4×D4—178no—
621C2×C4×D4—344no—
622C2×C4×D4—344no—
623C22×C4⋊C4—171no—
624C22×C22⋊C4—171no—
625C22×C22⋊C4—171no—
626C22×C22⋊C4—171no—
627C22×C22⋊C4—171no—
628C22×C22⋊C4—171no—
629C22×C22⋊C4C2×D1711yescharacteristic
630C22×C22⋊C4C2×D1711yescharacteristic
631C22×C22⋊C4C2×D1711yescharacteristic
632C22×C42—171no—
633C22×C42—171no—
634C22×C42—171no—
635C22×C42—171no—
636C22×C42—171no—
637#386—178no—
638#386Dic1718yescomplemented
639C4×C22⋊C4—344no—
640C4×C22⋊C4—344no—
641C4×C22⋊C4—344no—
642C2×#95—171no—
643C2×#95—171no—
644C2×#95—171no—
645C2×#95—171no—
646C2×#95—171no—
647C2×#95—171no—
648C2×#95—171no—
649C2×#95—171no—
650C2×#95—171no—
651C2×#95—171no—
652C2×#95—171no—
653C2×#95—171no—
654C2×#95—171no—
655C2×#95—171no—
656C2×#95—344no—
657C2×#95C2×D1711yescharacteristic
658C2×#95C2×D1711yescharacteristic
659C2×C17—28no—
660C2×C17—44no—
661C2×C17C2×C4×C22⋊C411yescharacteristic
662C2×C17C42×D411yescharacteristic
663C2×C17#227511yescharacteristic
664C2×C17D4×C22⋊C411yescharacteristic
665C2×C17#233911yescharacteristic
666C2×C17#235211yescharacteristic
667C2×C17#235311yescharacteristic
668C2×C17#235811yescharacteristic
669C2×C17#235811yescharacteristic
670C2×C17#235911yescharacteristic
671C2×C17#235911yescharacteristic
672C2×C17#236111yescharacteristic
673C2×C17#236111yescharacteristic
674C2×C17#236411yescharacteristic
675C2×C17#236411yescharacteristic
676C25C22×D1711yescharacteristic
677C25C22×D1711yescharacteristic
678C22×D4—22no—
679C22×D4—22no—
680C22×D4—22no—
681C22×D4—22no—
682C22×D4C4×D1714yes—
683C22×D4C4×D1714yes—
684C22×D4C2×Dic1714yes—
685C23×C4—22no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—41no—
690C23×C4—41no—
691C23×C4—171no—
692C23×C4—171no—
693C23×C4—171no—
694C23×C4—171no—
695C23×C4—171no—
696C23×C4—171no—
697C23×C4—171no—
698C23×C4—171no—
699C23×C4—174no—
700C23×C4—174no—
701C23×C4—174no—
702C23×C4—342no—
703C23×C4—342no—
704C23×C4—342no—
705C23×C4—342no—
706C23×C4—342no—
707C23×C4—342no—
708C23×C4—342no—
709C23×C4—342no—
710C23×C4—342no—
711C23×C4—342no—
712C23×C4—342no—
713C23×C4—342no—
714C23×C4—681no—
715C23×C4—681no—
716C23×C4—681no—
717C23×C4—681no—
718C23×C4—681no—
719C23×C4—681no—
720C23×C4C2×Dic1714yescomplemented
721C23×C4C22×D1711yescharacteristic
722C23×C4C22×D1711yescharacteristic
723C23×C4C22×D1711yescharacteristic
724C23×C4C22×D1711yescharacteristic
725C23×C4C22×D1711yescharacteristic
726C4×D4—3432no—
727C2×C4⋊C4—174no—
728C2×C4⋊C4—342no—
729C2×C4⋊C4—342no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—41no—
735C2×C22⋊C4—41no—
736C2×C22⋊C4—174no—
737C2×C22⋊C4—174no—
738C2×C22⋊C4—174no—
739C2×C22⋊C4—174no—
740C2×C22⋊C4—174no—
741C2×C22⋊C4—174no—
742C2×C22⋊C4—174no—
743C2×C22⋊C4—342no—
744C2×C22⋊C4—342no—
745C2×C22⋊C4—342no—
746C2×C22⋊C4—342no—
747C2×C22⋊C4—342no—
748C2×C22⋊C4—342no—
749C2×C22⋊C4—681no—
750C2×C22⋊C4—681no—
751C2×C22⋊C4C2×Dic1714yescomplemented
752C2×C22⋊C4C2×Dic1714yescomplemented
753C2×C22⋊C4C2×Dic1714yescomplemented
754C2×C42—174no—
755C2×C42—342no—
756C2×C42—342no—
757C2×C42—342no—
758C2×C42—342no—
759C2×C42—342no—
760C2×C42—342no—
761C2×C42—342no—
762C2×C42—342no—
763C2×C42—342no—
764C2×C42—342no—
765C2×C42—681no—
766C2×C42—681no—
767C2×C42—681no—
768C2×C42—681no—
769#95—174no—
770#95—174no—
771#95—174no—
772#95—342no—
773#95—342no—
774#95—342no—
775#95—342no—
776#95—342no—
777#95—342no—
778#95—342no—
779#95—342no—
780#95—342no—
781#95—681no—
782#95—681no—
783#95C2×Dic1714yescomplemented
784#95C2×Dic1714yescomplemented
785C17#1381311yescharacteristic, complemented, Sylow
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24C2×C4×D1712yes—
807C24C2×C4×D1712yes—
808C24C2×C4×D1712yes—
809C24C2×C4×D1712yes—
810C24D4×D1712yes—
811C24D4×D1712yes—
812C24#6325412yes—
813C24#6325412yes—
814C24C22×Dic1712yes—
815C24C22×Dic1712yes—
816C24C23×D1711yescharacteristic
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—28no—
823C2×D4C4×Dic17116yescomplemented
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—28no—
851C22×C4—28no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—172no—
858C22×C4—172no—
859C22×C4—172no—
860C22×C4—172no—
861C22×C4—172no—
862C22×C4—172no—
863C22×C4—172no—
864C22×C4—172no—
865C22×C4—172no—
866C22×C4—172no—
867C22×C4—172no—
868C22×C4—172no—
869C22×C4—172no—
870C22×C4—172no—
871C22×C4—172no—
872C22×C4—172no—
873C22×C4—348no—
874C22×C4—348no—
875C22×C4—348no—
876C22×C4—348no—
877C22×C4—341no—
878C22×C4—341no—
879C22×C4—341no—
880C22×C4—341no—
881C22×C4—341no—
882C22×C4—341no—
883C22×C4—341no—
884C22×C4—341no—
885C22×C4—341no—
886C22×C4—341no—
887C22×C4—341no—
888C22×C4—341no—
889C22×C4—341no—
890C22×C4—341no—
891C22×C4—341no—
892C22×C4—341no—
893C22×C4—341no—
894C22×C4—341no—
895C22×C4—341no—
896C22×C4—341no—
897C22×C4—341no—
898C22×C4—341no—
899C22×C4—341no—
900C22×C4—341no—
901C22×C4—341no—
902C22×C4—341no—
903C22×C4—341no—
904C22×C4—341no—
905C22×C4—341no—
906C22×C4—341no—
907C22×C4—341no—
908C22×C4—341no—
909C22×C4—341no—
910C22×C4—341no—
911C22×C4—341no—
912C22×C4—341no—
913C22×C4—341no—
914C22×C4—341no—
915C22×C4—341no—
916C22×C4—341no—
917C22×C4—348no—
918C22×C4—348no—
919C22×C4—684no—
920C22×C4—684no—
921C22×C4—684no—
922C22×C4—684no—
923C22×C4—684no—
924C22×C4—684no—
925C22×C4—684no—
926C22×C4—684no—
927C22×C4—684no—
928C22×C4—684no—
929C22×C4—684no—
930C22×C4—684no—
931C22×C4—684no—
932C22×C4—684no—
933C22×C4—684no—
934C22×C4C2×C4×D1712yes—
935C22×C4C2×C4×D1712yes—
936C22×C4D4×D1712yes—
937C22×C4#6325412yes—
938C22×C4C22×Dic1712yes—
939C22×C4C22×Dic1712yes—
940C22×C4C22×Dic1712yes—
941C22×C4C22×Dic1712yes—
942C22×C4C22×Dic1712yes—
943C4⋊C4—348no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—44no—
947C22⋊C4—1716no—
948C22⋊C4—348no—
949C22⋊C4—348no—
950C22⋊C4—348no—
951C22⋊C4—684no—
952C42—348no—
953C42—684no—
954C42—684no—
955C42—684no—
956C42—684no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23#1058756314yes—
1020C23C22⋊C4×D1714yes—
1021C23#1058756714yes—
1022C23#1058756714yes—
1023C23C2×C4×Dic1714yes—
1024C23C2×C4×Dic1714yes—
1025C23D4×Dic1714yes—
1026C23D4×Dic1714yes—
1027C23C22×C4×D1711yescharacteristic
1028C23C22×C4×D1711yescharacteristic
1029C23C2×D4×D1711yescharacteristic
1030C23C2×D4×D1711yescharacteristic
1031C23C2×D4×D1711yescharacteristic
1032C23C2×#6325411yescharacteristic
1033C23C2×#6325411yescharacteristic
1034C23C2×#6325411yescharacteristic
1035C23#1058769111yescharacteristic
1036C23#1058769111yescharacteristic
1037C23#41×D1711yescharacteristic
1038C23#41×D1711yescharacteristic
1039C23#1058769611yescharacteristic
1040C23#1058769711yescharacteristic
1041C23C23×Dic1711yescharacteristic
1042D4—232no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—416no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—174no—
1078C2×C4—174no—
1079C2×C4—174no—
1080C2×C4—174no—
1081C2×C4—342no—
1082C2×C4—342no—
1083C2×C4—342no—
1084C2×C4—342no—
1085C2×C4—342no—
1086C2×C4—342no—
1087C2×C4—342no—
1088C2×C4—342no—
1089C2×C4—342no—
1090C2×C4—342no—
1091C2×C4—342no—
1092C2×C4—342no—
1093C2×C4—342no—
1094C2×C4—342no—
1095C2×C4—342no—
1096C2×C4—342no—
1097C2×C4—342no—
1098C2×C4—342no—
1099C2×C4—342no—
1100C2×C4—342no—
1101C2×C4—342no—
1102C2×C4—342no—
1103C2×C4—342no—
1104C2×C4—342no—
1105C2×C4—342no—
1106C2×C4—342no—
1107C2×C4—342no—
1108C2×C4—342no—
1109C2×C4—342no—
1110C2×C4—342no—
1111C2×C4—342no—
1112C2×C4—342no—
1113C2×C4—342no—
1114C2×C4—342no—
1115C2×C4—342no—
1116C2×C4—342no—
1117C2×C4—6816no—
1118C2×C4—6816no—
1119C2×C4—6816no—
1120C2×C4—681no—
1121C2×C4—681no—
1122C2×C4—681no—
1123C2×C4—681no—
1124C2×C4—681no—
1125C2×C4—681no—
1126C2×C4—681no—
1127C2×C4—681no—
1128C2×C4—681no—
1129C2×C4—681no—
1130C2×C4—681no—
1131C2×C4—681no—
1132C2×C4—681no—
1133C2×C4—681no—
1134C2×C4—681no—
1135C2×C4—681no—
1136C2×C4C2×C4×Dic1714yes—
1137C2×C4D4×Dic1714yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—24no—
1153C22—24no—
1154C22—24no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22C22⋊C4×Dic1718yescomplemented
1168C22C22×C4×Dic1711yescharacteristic
1169C22C2×C22⋊C4×D1711yescharacteristic
1170C22C2×#1058756311yescharacteristic
1171C22C4×D4×D1711yescharacteristic
1172C22C4×D4×D1711yescharacteristic
1173C22C2×#1058756711yescharacteristic
1174C22C2×#1058756711yescharacteristic
1175C22C2×D4×Dic1711yescharacteristic
1176C22C2×D4×Dic1711yescharacteristic
1177C22C2×D4×Dic1711yescharacteristic
1178C22C4×#6325411yescharacteristic
1179C22C4×#6325411yescharacteristic
1180C22#41×Dic1711yescharacteristic
1181C22#1176328111yescharacteristic
1182C22#1176328111yescharacteristic
1183C22#1176328411yescharacteristic
1184C22#1176328811yescharacteristic
1185C22#1176328811yescharacteristic
1186C22#1176329211yescharacteristic
1187C22#1176344111yescharacteristic
1188C22#1176344311yescharacteristic
1189C22#1176344611yescharacteristic
1190C22#1176344611yescharacteristic
1191C22#1176344811yescharacteristic
1192C22#1176344811yescharacteristic
1193C22#1176345111yescharacteristic
1194C22#1176345711yescharacteristic
1195C22#1176345911yescharacteristic
1196C22#1176346511yescharacteristic
1197C22#1176348211yescharacteristic
1198C22#1176349011yescharacteristic
1199C22#1176349611yescharacteristic
1200C22#1176350211yescharacteristic
1201C22#1176350211yescharacteristic
1202C22#1176351111yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—344no—
1209C4—344no—
1210C4—344no—
1211C4—344no—
1212C4—682no—
1213C4—682no—
1214C4—682no—
1215C4—682no—
1216C2—28no—
1217C2—44no—
1218C2C2×C22⋊C4×Dic1711yescharacteristic
1219C2C4×D4×Dic1711yescharacteristic
1220C2#1453114511yescharacteristic
1221C2#1453160211yescharacteristic
1222C2#1453161011yescharacteristic
1223C2#1453171111yescharacteristic
1224C2#1453172211yescharacteristic
1225C2#1453176411yescharacteristic
1226C2#1453176811yescharacteristic
1227C2#1453178011yescharacteristic
1228C2#1453178211yescharacteristic
1229C2#1453179511yescharacteristic
1230C2#1453180411yescharacteristic
1231C2#1453183211yescharacteristic
1232C2#1453183611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC2×C17×#386C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC2×#386D17
hypocenterC17#13813
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic17C2semidirect
4. C2×C22⋊C4×Dic17C2semidirect
5. C2×C4×C22⋊Dic17C2semidirect
6. C22×#10587502C2semidirect
7. #14527021C2semidirect
8. #14527021C2semidirect
9. #14527018C2semidirect
10. #14527018C2semidirect
11. #14527009C2semidirect
12. #14527006C2semidirect
13. #14527006C2semidirect
14. #95×Dic17C2semidirect
21. C2×D4×Dic17C4semidirect
33. #11762689C4semidirect
57. C17×#386C4semidirect
75. C23×C4×C17C2×C4semidirect
100. C23×Dic17C2×C4semidirect
101. C23×Dic17C2×C4semidirect
116. C2×C22⋊C4×C17C2×C4semidirect
117. C2×C22⋊C4×C17C2×C4semidirect
118. C2×C22⋊C4×C17C2×C4semidirect
128. C2×C22⋊Dic17C2×C4semidirect
129. C2×C22⋊Dic17C2×C4semidirect
130. C2×C22⋊Dic17C2×C4semidirect
131. C2×C22⋊Dic17C2×C4semidirect
137. C2×C4⋊Dic17C2×C4semidirect
152. C2×C4×Dic17C2×C4semidirect
153. C17×#95C2×C4semidirect
154. C17×#95C2×C4semidirect
166. #10587502C2×C4semidirect
167. #10587502C2×C4semidirect
168. #10587502D4semidirect
206. C2×D4×C17C42semidirect
333. C22⋊Dic17C22⋊C4semidirect
462. C2×C4×C17C4×D4semidirect
521. C2×Dic17C4×D4semidirect
566. C22×C17C4×C22⋊C4semidirect
638. #386Dic17semidirect
720. C23×C4C2×Dic17semidirect
751. C2×C22⋊C4C2×Dic17semidirect
752. C2×C22⋊C4C2×Dic17semidirect
753. C2×C22⋊C4C2×Dic17semidirect
783. #95C2×Dic17semidirect
784. #95C2×Dic17semidirect
785. C17#13813semidirect
823. C2×D4C4×Dic17semidirect
1137. C2×C4D4×Dic17semidirect
1167. C22C22⋊C4×Dic17semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic172
C2×#117626892
C2×C22⋊C4×Dic172
C2×C4×C22⋊Dic172
C22×#105875022
#145270212
#145270182
#145270092
#145270062
#95×Dic172
C2×C17×#3862
#1381317