Finite Group Databasebeta

← #16961660

Subgroups — #16961660

Order 4352.

2594 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762712C211yesmaximal, characteristic, complemented
2C2×#11762702C211yesmaximal, characteristic, complemented
3C2×#11762689C211yesmaximal, characteristic, complemented
4C2×#11762689C211yesmaximal, characteristic, complemented
5C2×#11762684C211yesmaximal, characteristic, complemented
6C2×#11762669C211yesmaximal, characteristic, complemented
7#14527037C211yesmaximal, characteristic, complemented
8#14527029C211yesmaximal, characteristic, complemented
9#14527029C211yesmaximal, characteristic, complemented
10#14527025C211yesmaximal, characteristic, complemented
11#14527025C211yesmaximal, characteristic, complemented
12#14527025C211yesmaximal, characteristic, complemented
13#14527016C211yesmaximal, characteristic, complemented
14#14527007C211yesmaximal, characteristic, complemented
15C22×C17×#121C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C22⋊Dic17C2211yescharacteristic
30C22×C22⋊Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762712—24no—
33#11762702—24no—
34#11762689—24no—
35#11762689—24no—
36#11762684—24no—
37#11762669—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
50C23×D4×C17C2211yescharacteristic
51C23×D4×C17C2211yescharacteristic
52C23×D4×C17C2211yescharacteristic
53C24×C4×C17C2211yescharacteristic
54C2×C17×#121—24no—
55C2×C17×#121—24no—
56C2×C17×#121C418yescomplemented
57C22×C4⋊C4×C17C2211yescharacteristic
58C22×C22⋊C4×C17C2211yescharacteristic
59C22×C22⋊C4×C17C2211yescharacteristic
60C25×C17C2311yescharacteristic
61C25×C17C2311yescharacteristic
62C25×C17C2311yescharacteristic
63C22×D4×C17—22no—
64C22×D4×C17—22no—
65C22×D4×C17—22no—
66C22×D4×C17—22no—
67C22×D4×C17—22no—
68C22×D4×C17—22no—
69C22×D4×C17—22no—
70C22×D4×C17—22no—
71C22×D4×C17—22no—
72C22×D4×C17—22no—
73C22×D4×C17—22no—
74C22×D4×C17—22no—
75C22×D4×C17—41no—
76C22×D4×C17—41no—
77C22×D4×C17—41no—
78C22×D4×C17—41no—
79C22×D4×C17—41no—
80C22×D4×C17—41no—
81C22×D4×C17C2×C414yes—
82C22×D4×C17C2×C414yes—
83C22×D4×C17C2×C414yescomplemented
84C23×C4×C17—22no—
85C23×C4×C17—22no—
86C23×C4×C17—22no—
87C23×C4×C17—22no—
88C23×C4×C17—41no—
89C23×C4×C17—41no—
90C23×C4×C17C2×C414yescomplemented
91C23×C4×C17C2311yescharacteristic
92C23×C4×C17C2311yescharacteristic
93C23×C4×C17C2311yescharacteristic
94C23×C4×C17C2311yescharacteristic
95C23×Dic17—22no—
96C23×Dic17—22no—
97C23×Dic17—22no—
98C23×Dic17—41no—
99C23×Dic17—41no—
100C23×Dic17—41no—
101C23×Dic17—41no—
102C23×Dic17C2311yescharacteristic
103C23×Dic17C2311yescharacteristic
104C23×Dic17C2311yescharacteristic
105C23×Dic17C2311yescharacteristic
106C23×Dic17C2311yescharacteristic
107C23×Dic17C2311yescharacteristic
108C23×Dic17C2311yescharacteristic
109C23×Dic17C2311yescharacteristic
110C17×#121—232no—
111C2×C4⋊C4×C17—22no—
112C2×C4⋊C4×C17—22no—
113C2×C4⋊C4×C17C2×C414yescomplemented
114C2×C22⋊C4×C17—22no—
115C2×C22⋊C4×C17—22no—
116C2×C22⋊C4×C17C2×C414yes—
117C2×C22⋊C4×C17C2×C414yescomplemented
118C2×C22⋊C4×C17D414yes—
119C2×C22⋊C4×C17D414yes—
120C2×C22⋊Dic17—22no—
121C2×C22⋊Dic17—22no—
122C2×C22⋊Dic17—22no—
123C2×C22⋊Dic17—22no—
124C2×C22⋊Dic17—22no—
125C2×C22⋊Dic17—22no—
126C2×C22⋊Dic17—22no—
127C2×C22⋊Dic17—22no—
128C2×C22⋊Dic17—22no—
129C2×C22⋊Dic17—22no—
130C2×C22⋊Dic17—22no—
131C2×C22⋊Dic17—22no—
132C2×C22⋊Dic17—22no—
133C2×C22⋊Dic17—22no—
134C2×C22⋊Dic17—41no—
135C2×C22⋊Dic17—41no—
136C2×C22⋊Dic17—41no—
137C2×C22⋊Dic17—41no—
138C2×C22⋊Dic17—41no—
139C2×C22⋊Dic17—41no—
140C2×C22⋊Dic17—41no—
141C2×C22⋊Dic17—41no—
142C2×C22⋊Dic17—41no—
143C2×C22⋊Dic17—41no—
144C2×C22⋊Dic17—41no—
145C2×C22⋊Dic17—41no—
146C2×C22⋊Dic17—41no—
147C2×C22⋊Dic17—41no—
148C2×C22⋊Dic17—41no—
149C2×C22⋊Dic17—41no—
150C2×C22⋊Dic17—41no—
151C2×C22⋊Dic17—41no—
152C2×C22⋊Dic17D414yescomplemented
153C2×C4⋊Dic17—22no—
154C2×C4⋊Dic17—22no—
155C2×C4⋊Dic17—22no—
156C2×C4⋊Dic17—22no—
157C2×C4⋊Dic17—22no—
158C2×C4⋊Dic17—22no—
159C2×C4⋊Dic17—41no—
160C2×C4⋊Dic17—41no—
161C2×C4⋊Dic17—41no—
162C2×C4×Dic17—22no—
163C2×C4×Dic17—22no—
164C2×C4×Dic17—41no—
165#10587502—22no—
166#10587502—22no—
167#10587502—22no—
168#10587502—22no—
169#10587502—22no—
170#10587502—22no—
171#10587502—22no—
172#10587502—22no—
173#10587502—22no—
174#10587502—41no—
175#10587502—41no—
176#10587502D414yescomplemented
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×C17—21no—
190C24×C17—21no—
191C24×C17—21no—
192C24×C17—21no—
193C24×C17—21no—
194C24×C17—21no—
195C24×C17—21no—
196C24×C17—21no—
197C24×C17—21no—
198C24×C17—21no—
199C24×C17—21no—
200C24×C17—21no—
201C24×C17—21no—
202C24×C17—21no—
203C24×C17—21no—
204C24×C17—21no—
205C24×C17—21no—
206C24×C17—21no—
207C24×C17—21no—
208C24×C17—21no—
209C24×C17—21no—
210C24×C17—21no—
211C24×C17—21no—
212C24×C17—21no—
213C24×C17—21no—
214C24×C17—21no—
215C24×C17C22×C412yes—
216C24×C17C22×C412yes—
217C24×C17C22×C412yes—
218C24×C17C2×D412yes—
219C24×C17C2×D412yes—
220C24×C17C2×D412yes—
221C24×C17#4112yes—
222C24×C17C2411yescharacteristic
223C2×D4×C17—28no—
224C2×D4×C17—28no—
225C2×D4×C17—28no—
226C2×D4×C17—28no—
227C2×D4×C17—28no—
228C2×D4×C17—28no—
229C2×D4×C17—44no—
230C2×D4×C17—44no—
231C2×D4×C17—44no—
232C2×D4×C17—44no—
233C2×D4×C17—44no—
234C2×D4×C17—44no—
235C2×D4×C17—44no—
236C2×D4×C17—44no—
237C2×D4×C17—44no—
238C2×D4×C17—44no—
239C2×D4×C17—44no—
240C2×D4×C17—44no—
241C2×D4×C17—44no—
242C2×D4×C17—44no—
243C2×D4×C17—44no—
244C22×C4×C17—21no—
245C22×C4×C17—21no—
246C22×C4×C17—21no—
247C22×C4×C17—21no—
248C22×C4×C17—21no—
249C22×C4×C17—21no—
250C22×C4×C17—21no—
251C22×C4×C17—21no—
252C22×C4×C17—21no—
253C22×C4×C17—21no—
254C22×C4×C17—21no—
255C22×C4×C17—21no—
256C22×C4×C17—21no—
257C22×C4×C17—21no—
258C22×C4×C17—21no—
259C22×C4×C17—21no—
260C22×C4×C17—21no—
261C22×C4×C17—21no—
262C22×C4×C17—28no—
263C22×C4×C17—28no—
264C22×C4×C17—44no—
265C22×C4×C17—44no—
266C22×C4×C17—44no—
267C22×C4×C17—44no—
268C22×C4×C17—44no—
269C22×C4×C17C22×C412yes—
270C22×C4×C17C22×C412yes—
271C22×C4×C17C22×C412yes—
272C22×C4×C17C22×C412yes—
273C22×C4×C17C2×D412yes—
274C22×C4×C17C2×D412yes—
275C22×C4×C17C2×D412yes—
276C22×C4×C17C2×D412yes—
277C22×C4×C17C2×D412yes—
278C22×C4×C17#4112yes—
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—21no—
292C22×Dic17—21no—
293C22×Dic17—21no—
294C22×Dic17—21no—
295C22×Dic17—21no—
296C22×Dic17—21no—
297C22×Dic17—21no—
298C22×Dic17—21no—
299C22×Dic17—21no—
300C22×Dic17—21no—
301C22×Dic17—21no—
302C22×Dic17—21no—
303C22×Dic17—21no—
304C22×Dic17—21no—
305C22×Dic17—21no—
306C22×Dic17—21no—
307C22×Dic17—21no—
308C22×Dic17—21no—
309C22×Dic17—21no—
310C22×Dic17—21no—
311C22×Dic17—21no—
312C22×Dic17—21no—
313C22×Dic17—21no—
314C22×Dic17—21no—
315C22×Dic17—21no—
316C22×Dic17—21no—
317C22×Dic17—21no—
318C22×Dic17—21no—
319C22×Dic17—21no—
320C22×Dic17—21no—
321C22×Dic17—21no—
322C22×Dic17—21no—
323C22×Dic17—21no—
324C22×Dic17—21no—
325C22×Dic17—21no—
326C22×Dic17—21no—
327C22×Dic17—21no—
328C22×Dic17—21no—
329C22×Dic17—21no—
330C22×Dic17—21no—
331C22×Dic17—44no—
332C22×Dic17—44no—
333C22×Dic17—44no—
334C22×Dic17—44no—
335C22×Dic17—44no—
336C22×Dic17—44no—
337C22×Dic17—44no—
338C22×Dic17C2×D412yes—
339C22×Dic17C2×D412yes—
340C22×Dic17C2×D412yes—
341C22×Dic17C2×D412yes—
342C4⋊C4×C17—28no—
343C22⋊C4×C17—28no—
344C22⋊C4×C17C22⋊C4116yescomplemented
345C22⋊Dic17—44no—
346C22⋊Dic17—44no—
347C22⋊Dic17—44no—
348C22⋊Dic17—44no—
349C22⋊Dic17—44no—
350C22⋊Dic17—44no—
351C22⋊Dic17—44no—
352C22⋊Dic17—44no—
353C22⋊Dic17—44no—
354C22⋊Dic17—44no—
355C22⋊Dic17—44no—
356C4⋊Dic17—44no—
357C4⋊Dic17—44no—
358C4⋊Dic17—44no—
359C4×Dic17—44no—
360#14361—171nomaximal, Sylow
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—22no—
388C23×C17—22no—
389C23×C17—22no—
390C23×C17—22no—
391C23×C17—22no—
392C23×C17—22no—
393C23×C17—22no—
394C23×C17—22no—
395C23×C17—22no—
396C23×C17—22no—
397C23×C17—22no—
398C23×C17—22no—
399C23×C17—22no—
400C23×C17—22no—
401C23×C17—22no—
402C23×C17—22no—
403C23×C17—22no—
404C23×C17—41no—
405C23×C17—41no—
406C23×C17—41no—
407C23×C17—41no—
408C23×C17—41no—
409C23×C17—41no—
410C23×C17—41no—
411C23×C17—41no—
412C23×C17—41no—
413C23×C17—41no—
414C23×C17—41no—
415C23×C17—41no—
416C23×C17—41no—
417C23×C17—41no—
418C23×C17—41no—
419C23×C17—41no—
420C23×C17—41no—
421C23×C17—41no—
422C23×C17—41no—
423C23×C17—41no—
424C23×C17—41no—
425C23×C17—41no—
426C23×C17—41no—
427C23×C17—41no—
428C23×C17—41no—
429C23×C17—41no—
430C23×C17—41no—
431C23×C17—41no—
432C23×C17—41no—
433C23×C17—41no—
434C23×C17—41no—
435C23×C17—41no—
436C23×C17—41no—
437C23×C17—41no—
438C23×C17—41no—
439C23×C17—41no—
440C23×C17—41no—
441C23×C17—41no—
442C23×C17—41no—
443C23×C17—41no—
444C23×C17—41no—
445C23×C17—41no—
446C23×C17—41no—
447C23×C17—41no—
448C23×C17—41no—
449C23×C17—41no—
450C23×C17—41no—
451C23×C17—41no—
452C23×C17—41no—
453C23×C17—41no—
454C23×C17—41no—
455C23×C17—41no—
456C23×C17—41no—
457C23×C17—41no—
458C23×C17—41no—
459C23×C17—41no—
460C23×C17—41no—
461C23×C17—41no—
462C23×C17—41no—
463C23×C17—41no—
464C23×C17C2×C22⋊C414yes—
465C23×C17C4×D414yes—
466C23×C17C23×C411yescharacteristic
467C23×C17C22×D411yescharacteristic
468C23×C17C22×D411yescharacteristic
469C23×C17C22×D411yescharacteristic
470C23×C17C22×D411yescharacteristic
471C23×C17C2×#4111yescharacteristic
472C23×C17C2×#4111yescharacteristic
473C23×C17H(5,𝔽2)11yescharacteristic
474C23×C17H(5,𝔽2)11yescharacteristic
475C23×C17H(5,𝔽2)11yescharacteristic
476C23×C17H(5,𝔽2)11yescharacteristic
477C23×C17H(5,𝔽2)11yescharacteristic
478C23×C17H(5,𝔽2)11yescharacteristic
479C23×C172−1+411yescharacteristic
480C23×C172−1+411yescharacteristic
481D4×C17—416no—
482D4×C17—416no—
483D4×C17—416no—
484C2×C4×C17—22no—
485C2×C4×C17—22no—
486C2×C4×C17—22no—
487C2×C4×C17—22no—
488C2×C4×C17—22no—
489C2×C4×C17—22no—
490C2×C4×C17—22no—
491C2×C4×C17—22no—
492C2×C4×C17—22no—
493C2×C4×C17—22no—
494C2×C4×C17—22no—
495C2×C4×C17—22no—
496C2×C4×C17—22no—
497C2×C4×C17—22no—
498C2×C4×C17—22no—
499C2×C4×C17—22no—
500C2×C4×C17—22no—
501C2×C4×C17—22no—
502C2×C4×C17—22no—
503C2×C4×C17—22no—
504C2×C4×C17—22no—
505C2×C4×C17—416no—
506C2×C4×C17—41no—
507C2×C4×C17—41no—
508C2×C4×C17—41no—
509C2×C4×C17—41no—
510C2×C4×C17C2×C22⋊C414yes—
511C2×C4×C17C2×C22⋊C414yes—
512C2×C4×C17C4×D414yes—
513C2×Dic17—22no—
514C2×Dic17—22no—
515C2×Dic17—22no—
516C2×Dic17—22no—
517C2×Dic17—22no—
518C2×Dic17—22no—
519C2×Dic17—22no—
520C2×Dic17—22no—
521C2×Dic17—22no—
522C2×Dic17—22no—
523C2×Dic17—22no—
524C2×Dic17—22no—
525C2×Dic17—416no—
526C2×Dic17—41no—
527C2×Dic17—41no—
528C2×Dic17—41no—
529C2×Dic17—41no—
530C2×Dic17—41no—
531C2×Dic17—41no—
532C2×Dic17—41no—
533C2×Dic17—41no—
534C2×Dic17—41no—
535C2×Dic17—41no—
536C2×Dic17—41no—
537C2×Dic17—41no—
538C2×Dic17—41no—
539C2×Dic17—41no—
540C2×Dic17—41no—
541C2×Dic17—41no—
542C2×Dic17—41no—
543C2×Dic17—41no—
544C2×Dic17—41no—
545C2×Dic17—41no—
546C2×Dic17—41no—
547C2×Dic17—41no—
548C2×Dic17—41no—
549C2×Dic17—41no—
550C2×Dic17—41no—
551C2×Dic17—41no—
552C2×Dic17—41no—
553C2×Dic17—41no—
554C2×Dic17—41no—
555C2×Dic17—41no—
556C2×Dic17—41no—
557C2×Dic17—41no—
558C2×Dic17—41no—
559C2×Dic17—41no—
560C2×Dic17—41no—
561C2×Dic17—41no—
562C2×Dic17—41no—
563C2×Dic17—41no—
564C2×Dic17—41no—
565C2×Dic17—41no—
566C2×Dic17—41no—
567C2×Dic17—41no—
568C2×Dic17—41no—
569C2×Dic17—41no—
570C22×#121D1711yescharacteristic
571C2×#390—171no—
572C2×#388—171no—
573C2×#386—171no—
574C2×#386—171no—
575C2×#385—171no—
576C2×#380—171no—
577#1441—171no—
578#1439—171no—
579#1439—171no—
580#1438—171no—
581#1438—171no—
582#1438—171no—
583#1436—171no—
584C22⋊#95—171no—
585C22×C17—24no—
586C22×C17—24no—
587C22×C17—24no—
588C22×C17—24no—
589C22×C17—24no—
590C22×C17—24no—
591C22×C17—42no—
592C22×C17—42no—
593C22×C17—42no—
594C22×C17—42no—
595C22×C17—42no—
596C22×C17—42no—
597C22×C17—42no—
598C22×C17—42no—
599C22×C17—42no—
600C22×C17—42no—
601C22×C17—42no—
602C22×C17—42no—
603C22×C17—42no—
604C22×C17—42no—
605C22×C17—42no—
606C22×C17—42no—
607C22×C17—42no—
608C22×C17—42no—
609C22×C17—42no—
610C22×C17—42no—
611C22×C17—42no—
612C22×C17—42no—
613C22×C17—42no—
614C22×C17—42no—
615C22×C17—42no—
616C22×C17—42no—
617C22×C17—42no—
618C22×C17—42no—
619C22×C17—42no—
620C22×C17—42no—
621C22×C17—42no—
622C22×C17—81no—
623C22×C17—81no—
624C22×C17—81no—
625C22×C17—81no—
626C22×C17—81no—
627C22×C17—81no—
628C22×C17—81no—
629C22×C17—81no—
630C22×C17C22×C22⋊C411yescharacteristic
631C22×C17C2×C4×D411yescharacteristic
632C22×C17C2×C4×D411yescharacteristic
633C22×C17#51811yescharacteristic
634C22×C17#51811yescharacteristic
635C22×C17#52011yescharacteristic
636C22×C17#52011yescharacteristic
637C22×C17#53411yescharacteristic
638C22×C17#53511yescharacteristic
639C22×C17#53511yescharacteristic
640C22×C17#53611yescharacteristic
641C22×C17#53711yescharacteristic
642C22×C17#53711yescharacteristic
643C22×C17#53711yescharacteristic
644C22×C17#53711yescharacteristic
645C22×C17#53811yescharacteristic
646C22×C17#53911yescharacteristic
647C22×C17#54011yescharacteristic
648C22×C17#54211yescharacteristic
649C22×C17D4211yescharacteristic
650C22×C17D4211yescharacteristic
651C22×C17D4211yescharacteristic
652C22×C17D4211yescharacteristic
653C22×C17D4211yescharacteristic
654C22×C17#54611yescharacteristic
655C22×C17#54611yescharacteristic
656C22×C17#54611yescharacteristic
657C22×C17#54611yescharacteristic
658C22×C17#54711yescharacteristic
659C22×C17#54811yescharacteristic
660C22×C17#55311yescharacteristic
661C22×C17#56011yescharacteristic
662C22×C17#56011yescharacteristic
663C22×C17#56211yescharacteristic
664C22×C17#56211yescharacteristic
665C4×C17—24no—
666C4×C17—24no—
667C4×C17—24no—
668C4×C17—42no—
669Dic17—42no—
670Dic17—42no—
671Dic17—42no—
672Dic17—42no—
673Dic17—81no—
674Dic17—81no—
675Dic17—81no—
676Dic17—81no—
677C23×D4C2×D1711yescharacteristic
678C23×D4C2×D1711yescharacteristic
679C23×D4C2×D1711yescharacteristic
680C24×C4—171no—
681C24×C4C2×D1711yescharacteristic
682C2×#121—24no—
683C2×#121—24no—
684C2×#121Dic1718yescomplemented
685C22×C4⋊C4—171no—
686C22×C4⋊C4—171no—
687C22×C4⋊C4—171no—
688C22×C4⋊C4C2×D1711yescharacteristic
689C22×C22⋊C4—171no—
690C22×C22⋊C4—171no—
691C22×C22⋊C4—171no—
692C22×C22⋊C4—171no—
693C22×C22⋊C4—171no—
694C22×C22⋊C4—171no—
695C22×C22⋊C4—171no—
696C22×C22⋊C4—171no—
697C22×C22⋊C4—171no—
698C22×C22⋊C4—171no—
699C22×C22⋊C4—171no—
700C22×C22⋊C4C2×D1711yescharacteristic
701C22×C22⋊C4C2×D1711yescharacteristic
702C22×C42—171no—
703#390—344no—
704#388—344no—
705#386—344no—
706#386—344no—
707#385—344no—
708#380—344no—
709C2×#95—171no—
710C2×#95—171no—
711C2×#95—171no—
712C2×#95—171no—
713C2×#95—171no—
714C2×#95—171no—
715C2×#95—171no—
716C2×#95—171no—
717C2×#95—171no—
718C2×#95—171no—
719C2×#95—171no—
720C2×#95—171no—
721C2×C17—44no—
722C2×C17—44no—
723C2×C17—82no—
724C2×C17#231111yescharacteristic
725C2×C17#232411yescharacteristic
726C2×C17#232511yescharacteristic
727C2×C17D4×C22⋊C411yescharacteristic
728C2×C17D4×C22⋊C411yescharacteristic
729C2×C17#236111yescharacteristic
730C2×C17#237711yescharacteristic
731C2×C17#266911yescharacteristic
732C2×C17#267111yescharacteristic
733C2×C17#267211yescharacteristic
734C2×C17#267511yescharacteristic
735C2×C17#267611yescharacteristic
736C2×C17#268111yescharacteristic
737C2×C17#269111yescharacteristic
738C2×C17#270311yescharacteristic
739C25C22×D1711yescharacteristic
740C25C22×D1711yescharacteristic
741C25C22×D1711yescharacteristic
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—41no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4C2×Dic1714yes—
761C22×D4C2×Dic1714yes—
762C22×D4C2×Dic1714yescomplemented
763C23×C4—22no—
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—22no—
767C23×C4—41no—
768C23×C4—41no—
769C23×C4—171no—
770C23×C4—171no—
771C23×C4—171no—
772C23×C4—171no—
773C23×C4—171no—
774C23×C4—171no—
775C23×C4—171no—
776C23×C4—171no—
777C23×C4—342no—
778C23×C4—342no—
779C23×C4—342no—
780C23×C4—681no—
781C23×C4—681no—
782C23×C4—681no—
783C23×C4—681no—
784C23×C4C2×Dic1714yescomplemented
785C23×C4C22×D1711yescharacteristic
786C23×C4C22×D1711yescharacteristic
787C23×C4C22×D1711yescharacteristic
788C23×C4C22×D1711yescharacteristic
789#121—232no—
790C2×C4⋊C4—22no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—342no—
793C2×C4⋊C4—342no—
794C2×C4⋊C4—342no—
795C2×C4⋊C4—342no—
796C2×C4⋊C4—342no—
797C2×C4⋊C4—342no—
798C2×C4⋊C4—681no—
799C2×C4⋊C4—681no—
800C2×C4⋊C4—681no—
801C2×C4⋊C4C2×Dic1714yescomplemented
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—174no—
805C2×C22⋊C4—342no—
806C2×C22⋊C4—342no—
807C2×C22⋊C4—342no—
808C2×C22⋊C4—342no—
809C2×C22⋊C4—342no—
810C2×C22⋊C4—342no—
811C2×C22⋊C4—342no—
812C2×C22⋊C4—342no—
813C2×C22⋊C4—342no—
814C2×C22⋊C4—342no—
815C2×C22⋊C4—342no—
816C2×C22⋊C4—342no—
817C2×C22⋊C4—342no—
818C2×C22⋊C4—342no—
819C2×C22⋊C4—681no—
820C2×C22⋊C4—681no—
821C2×C22⋊C4—681no—
822C2×C22⋊C4—681no—
823C2×C22⋊C4—681no—
824C2×C22⋊C4—681no—
825C2×C22⋊C4—681no—
826C2×C22⋊C4—681no—
827C2×C22⋊C4—681no—
828C2×C22⋊C4—681no—
829C2×C22⋊C4—681no—
830C2×C22⋊C4—681no—
831C2×C22⋊C4—681no—
832C2×C22⋊C4—681no—
833C2×C22⋊C4—681no—
834C2×C22⋊C4—681no—
835C2×C22⋊C4—681no—
836C2×C22⋊C4—681no—
837C2×C22⋊C4C2×Dic1714yes—
838C2×C22⋊C4C2×Dic1714yescomplemented
839C2×C22⋊C4C22⋊D1714yes—
840C2×C22⋊C4C22⋊D1714yes—
841C2×C42—342no—
842C2×C42—342no—
843C2×C42—681no—
844#95—174no—
845#95—342no—
846#95—342no—
847#95—342no—
848#95—342no—
849#95—342no—
850#95—342no—
851#95—342no—
852#95—342no—
853#95—342no—
854#95—681no—
855#95—681no—
856C17#1436111yescharacteristic, complemented, Sylow
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24D4×D1712yes—
896C24#6325412yes—
897C24C22×Dic1712yes—
898C24C22×Dic1712yes—
899C24C22×Dic1712yes—
900C24C2×C22⋊D1712yes—
901C24C2×C22⋊D1712yes—
902C24C23×D1711yescharacteristic
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—28no—
943C22×C4—28no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—172no—
950C22×C4—172no—
951C22×C4—172no—
952C22×C4—172no—
953C22×C4—341no—
954C22×C4—341no—
955C22×C4—341no—
956C22×C4—341no—
957C22×C4—341no—
958C22×C4—341no—
959C22×C4—341no—
960C22×C4—341no—
961C22×C4—341no—
962C22×C4—341no—
963C22×C4—341no—
964C22×C4—341no—
965C22×C4—341no—
966C22×C4—341no—
967C22×C4—341no—
968C22×C4—341no—
969C22×C4—341no—
970C22×C4—341no—
971C22×C4—341no—
972C22×C4—341no—
973C22×C4—341no—
974C22×C4—341no—
975C22×C4—341no—
976C22×C4—341no—
977C22×C4—341no—
978C22×C4—341no—
979C22×C4—341no—
980C22×C4—341no—
981C22×C4—341no—
982C22×C4—341no—
983C22×C4—341no—
984C22×C4—341no—
985C22×C4—341no—
986C22×C4—341no—
987C22×C4—341no—
988C22×C4—341no—
989C22×C4—341no—
990C22×C4—341no—
991C22×C4—341no—
992C22×C4—341no—
993C22×C4—341no—
994C22×C4—341no—
995C22×C4—341no—
996C22×C4—341no—
997C22×C4—341no—
998C22×C4—341no—
999C22×C4—341no—
1000C22×C4—341no—
1001C22×C4—341no—
1002C22×C4—341no—
1003C22×C4—341no—
1004C22×C4—341no—
1005C22×C4—684no—
1006C22×C4—684no—
1007C22×C4—684no—
1008C22×C4—684no—
1009C22×C4—684no—
1010C22×C4—684no—
1011C22×C4—684no—
1012C22×C4D4×D1712yes—
1013C22×C4#6325412yes—
1014C22×C4C22×Dic1712yes—
1015C22×C4C22×Dic1712yes—
1016C22×C4C22×Dic1712yes—
1017C22×C4C22×Dic1712yes—
1018C22×C4C2×C22⋊D1712yes—
1019C22×C4C2×C22⋊D1712yes—
1020C22×C4C2×C22⋊D1712yes—
1021C22×C4C2×C22⋊D1712yes—
1022C4⋊C4—28no—
1023C4⋊C4—684no—
1024C4⋊C4—684no—
1025C4⋊C4—684no—
1026C22⋊C4—28no—
1027C22⋊C4—684no—
1028C22⋊C4—684no—
1029C22⋊C4—684no—
1030C22⋊C4—684no—
1031C22⋊C4—684no—
1032C22⋊C4—684no—
1033C22⋊C4—684no—
1034C22⋊C4—684no—
1035C22⋊C4—684no—
1036C22⋊C4—684no—
1037C22⋊C4—684no—
1038C22⋊C4C22⋊Dic17116yescomplemented
1039C42—684no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23D4×Dic1714yes—
1144C23C2×C22⋊Dic1714yes—
1145C23C2×D4×D1711yescharacteristic
1146C23C2×D4×D1711yescharacteristic
1147C23C2×#6325411yescharacteristic
1148C23C2×#6325411yescharacteristic
1149C23#1058769111yescharacteristic
1150C23#1058769111yescharacteristic
1151C23#1058769111yescharacteristic
1152C23#1058769111yescharacteristic
1153C23#1058769611yescharacteristic
1154C23#1058769611yescharacteristic
1155C23#1058769711yescharacteristic
1156C23#1058769711yescharacteristic
1157C23C23×Dic1711yescharacteristic
1158C23C22×C22⋊D1711yescharacteristic
1159C23C22×C22⋊D1711yescharacteristic
1160D4—416no—
1161D4—416no—
1162D4—416no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—416no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—342no—
1190C2×C4—342no—
1191C2×C4—342no—
1192C2×C4—342no—
1193C2×C4—342no—
1194C2×C4—342no—
1195C2×C4—342no—
1196C2×C4—342no—
1197C2×C4—342no—
1198C2×C4—342no—
1199C2×C4—342no—
1200C2×C4—342no—
1201C2×C4—6816no—
1202C2×C4—681no—
1203C2×C4—681no—
1204C2×C4—681no—
1205C2×C4—681no—
1206C2×C4—681no—
1207C2×C4—681no—
1208C2×C4—681no—
1209C2×C4—681no—
1210C2×C4—681no—
1211C2×C4—681no—
1212C2×C4—681no—
1213C2×C4—681no—
1214C2×C4—681no—
1215C2×C4—681no—
1216C2×C4—681no—
1217C2×C4—681no—
1218C2×C4—681no—
1219C2×C4—681no—
1220C2×C4—681no—
1221C2×C4—681no—
1222C2×C4—681no—
1223C2×C4—681no—
1224C2×C4—681no—
1225C2×C4—681no—
1226C2×C4—681no—
1227C2×C4—681no—
1228C2×C4—681no—
1229C2×C4—681no—
1230C2×C4—681no—
1231C2×C4—681no—
1232C2×C4—681no—
1233C2×C4—681no—
1234C2×C4—681no—
1235C2×C4—681no—
1236C2×C4—681no—
1237C2×C4—681no—
1238C2×C4—681no—
1239C2×C4—681no—
1240C2×C4—681no—
1241C2×C4—681no—
1242C2×C4—681no—
1243C2×C4—681no—
1244C2×C4—681no—
1245C2×C4—681no—
1246C2×C4D4×Dic1714yes—
1247C2×C4C2×C22⋊Dic1714yes—
1248C2×C4C2×C22⋊Dic1714yes—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22C22×C22⋊Dic1711yescharacteristic
1295C22C2×D4×Dic1711yescharacteristic
1296C22C2×D4×Dic1711yescharacteristic
1297C22#1176328411yescharacteristic
1298C22#1176328411yescharacteristic
1299C22#1176329211yescharacteristic
1300C22#1176329211yescharacteristic
1301C22#1176336711yescharacteristic
1302C22#1176337311yescharacteristic
1303C22#1176337511yescharacteristic
1304C22#1176338011yescharacteristic
1305C22#1176338611yescharacteristic
1306C22#1176338711yescharacteristic
1307C22#1176338711yescharacteristic
1308C22#1176338811yescharacteristic
1309C22#1176339611yescharacteristic
1310C22#1176340411yescharacteristic
1311C22#1176341211yescharacteristic
1312C22#1176342611yescharacteristic
1313C22D4×C22⋊D1711yescharacteristic
1314C22D4×C22⋊D1711yescharacteristic
1315C22D4×C22⋊D1711yescharacteristic
1316C22D4×C22⋊D1711yescharacteristic
1317C22#1176344311yescharacteristic
1318C22#1176345311yescharacteristic
1319C22#1176345311yescharacteristic
1320C22#1176345311yescharacteristic
1321C22#1176345311yescharacteristic
1322C22#1176345911yescharacteristic
1323C22#1176346511yescharacteristic
1324C22#1176351111yescharacteristic
1325C22#1176354711yescharacteristic
1326C22#1176354711yescharacteristic
1327C22#1176355411yescharacteristic
1328C22#1176355411yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—42no—
1333C4—682no—
1334C4—682no—
1335C4—682no—
1336C4—682no—
1337C4—1361no—
1338C4—1361no—
1339C4—1361no—
1340C4—1361no—
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2#1453137611yescharacteristic
1345C2#1453147911yescharacteristic
1346C2#1453148911yescharacteristic
1347C2D4×C22⋊Dic1711yescharacteristic
1348C2D4×C22⋊Dic1711yescharacteristic
1349C2#1453180411yescharacteristic
1350C2#1453194111yescharacteristic
1351C2#1453499611yescharacteristic
1352C2#1453501511yescharacteristic
1353C2#1453502911yescharacteristic
1354C2#1453507411yescharacteristic
1355C2#1453508511yescharacteristic
1356C2#1453513011yescharacteristic
1357C2#1453526111yescharacteristic
1358C2#1453542311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
Fitting, prime radicalC22×C17×#121C2
socle, cosocleC24×C17C24
hypercenterC22×#121D17
hypocenterC17#14361
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#11762712C2semidirect
2. C2×#11762702C2semidirect
3. C2×#11762689C2semidirect
4. C2×#11762689C2semidirect
5. C2×#11762684C2semidirect
6. C2×#11762669C2semidirect
7. #14527037C2semidirect
8. #14527029C2semidirect
9. #14527029C2semidirect
10. #14527025C2semidirect
11. #14527025C2semidirect
12. #14527025C2semidirect
13. #14527016C2semidirect
14. #14527007C2semidirect
56. C2×C17×#121C4semidirect
83. C22×D4×C17C2×C4semidirect
90. C23×C4×C17C2×C4semidirect
113. C2×C4⋊C4×C17C2×C4semidirect
117. C2×C22⋊C4×C17C2×C4semidirect
152. C2×C22⋊Dic17D4semidirect
176. #10587502D4semidirect
344. C22⋊C4×C17C22⋊C4semidirect
684. C2×#121Dic17semidirect
762. C22×D4C2×Dic17semidirect
784. C23×C4C2×Dic17semidirect
801. C2×C4⋊C4C2×Dic17semidirect
838. C2×C22⋊C4C2×Dic17semidirect
856. C17#14361semidirect
1038. C22⋊C4C22⋊Dic17semidirect

Maximal subgroups

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

subgroupindex
C2×#117627122
C2×#117627022
C2×#117626892
C2×#117626842
C2×#117626692
#145270372
#145270292
#145270252
#145270162
#145270072
C22×C17×#1212
#1436117