Finite Group Databasebeta

← #16956643

Subgroups — #16956643

Order 4352.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762703C211yesmaximal, characteristic
2C2×#11762697C211yesmaximal, characteristic
3C2×#11762673C211yesmaximal, characteristic, complemented
4C2×#11762667C211yesmaximal, characteristic
5C2×C22⋊C4×Dic17C211yesmaximal, characteristic
6#14527048C211yesmaximal, characteristic, complemented
7#14527047C211yesmaximal, characteristic, complemented
8#14527029C211yesmaximal, characteristic
9#14527019C211yesmaximal, characteristic, complemented
10#14527015C211yesmaximal, characteristic, complemented
11#14527013C211yesmaximal, characteristic, complemented
12#14527009C211yesmaximal, characteristic, complemented
13#14527006C211yesmaximal, characteristic
14#95×Dic17C211yesmaximal, characteristic, complemented
15C17×#1439C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C4×Dic17C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29#11762703—24no—
30#11762697—24no—
31#11762673—24no—
32#11762667—24no—
33C22⋊C4×Dic17C418yescomplemented
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
48C2×#10587502C2211yescharacteristic
49C22×C4⋊C4×C17C2211yescharacteristic
50C22×C22⋊C4×C17C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C25×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×Dic17—22no—
64C23×Dic17—22no—
65C23×Dic17—22no—
66C23×Dic17—22no—
67C23×Dic17—41no—
68C23×Dic17—41no—
69C23×Dic17C2×C414yes—
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C2×C4⋊C4×C17—22no—
79C2×C4⋊C4×C17—41no—
80C2×C4⋊C4×C17—41no—
81C2×C22⋊C4×C17—22no—
82C2×C22⋊C4×C17—22no—
83C2×C22⋊C4×C17—22no—
84C2×C22⋊C4×C17—22no—
85C2×C22⋊C4×C17—22no—
86C2×C22⋊C4×C17—22no—
87C2×C22⋊C4×C17—41no—
88C2×C22⋊C4×C17—41no—
89C2×C22⋊C4×C17C2×C414yes—
90C2×C22⋊Dic17—22no—
91C2×C22⋊Dic17—22no—
92C2×C22⋊Dic17—22no—
93C2×C22⋊Dic17—22no—
94C2×C22⋊Dic17—41no—
95C2×C22⋊Dic17—41no—
96C2×C22⋊Dic17C2×C414yes—
97C2×C22⋊Dic17D414yes—
98C2×C22⋊Dic17Q814yes—
99C2×C4⋊Dic17—22no—
100C2×C4⋊Dic17—41no—
101C2×C4⋊Dic17—41no—
102C2×#63225—22no—
103C2×#63225—22no—
104C2×#63225—22no—
105C2×#63225—22no—
106C2×#63225—22no—
107C2×#63225—22no—
108C2×#63225—22no—
109C2×#63225—22no—
110C2×#63225—41no—
111C2×#63225—41no—
112C2×#63225—41no—
113C2×#63225—41no—
114C2×C4×Dic17—22no—
115C2×C4×Dic17—22no—
116C2×C4×Dic17—22no—
117C2×C4×Dic17—22no—
118C2×C4×Dic17—22no—
119C2×C4×Dic17—22no—
120C2×C4×Dic17—41no—
121C2×C4×Dic17—41no—
122C2×C4×Dic17—41no—
123C2×C4×Dic17—41no—
124C2×C4×Dic17C2×C414yes—
125C2×C4×Dic17C2×C414yes—
126C17×#95—22no—
127C17×#95—22no—
128C17×#95—22no—
129#10587502—22no—
130#10587502—22no—
131#10587502—22no—
132#10587502—22no—
133#10587502—22no—
134#10587502—22no—
135#10587502—22no—
136#10587502—22no—
137#10587502—22no—
138#10587502—22no—
139#10587502—22no—
140#10587502—22no—
141#10587502C2×C414yes—
142#10587502C2×C414yes—
143#10587502D414yes—
144C24×C17—21no—
145C24×C17—21no—
146C24×C17—21no—
147C24×C17—21no—
148C24×C17—21no—
149C24×C17—21no—
150C24×C17—21no—
151C24×C17—21no—
152C24×C17—21no—
153C24×C17—21no—
154C24×C17—21no—
155C24×C17—21no—
156C24×C17C22×C412yes—
157C24×C17C2×D412yes—
158C24×C17C2×Q812yes—
159C24×C17C2411yescharacteristic
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
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×C17C22×C412yes—
197C22×C4×C17C22×C412yes—
198C22×C4×C17C2×D412yes—
199C22×C4×C17#4112yes—
200C22×C4×C17#4112yes—
201C22×C4×C17#4112yes—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—28no—
231C22×Dic17—28no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—44no—
247C22×Dic17—44no—
248C22×Dic17—44no—
249C22×Dic17—44no—
250C22×Dic17—44no—
251C22×Dic17C22×C412yes—
252C22×Dic17C22×C412yes—
253C22×Dic17C22×C412yes—
254C22×Dic17C22×C412yes—
255C22×Dic17C2×D412yes—
256C22×Dic17C2×D412yes—
257C22×Dic17C2×D412yes—
258C22×Dic17C2×D412yes—
259C22×Dic17C2×Q812yes—
260C22×Dic17C2×Q812yes—
261C22×Dic17#4112yes—
262C22×Dic17#4112yes—
263C22×Dic17#4112yes—
264C22×Dic17#4112yes—
265C4⋊C4×C17—44no—
266C22⋊C4×C17—28no—
267C22⋊C4×C17—44no—
268C22⋊C4×C17—44no—
269C22⋊Dic17—44no—
270C22⋊Dic17—44no—
271C22⋊Dic17C4⋊C4116yescomplemented
272C4⋊Dic17—44no—
273#63225—44no—
274#63225—44no—
275#63225—44no—
276#63225—44no—
277C4×Dic17—28no—
278C4×Dic17—44no—
279C4×Dic17—44no—
280C4×Dic17—44no—
281#13915—171nomaximal, Sylow
282C23×C17—22no—
283C23×C17—22no—
284C23×C17—22no—
285C23×C17—22no—
286C23×C17—22no—
287C23×C17—22no—
288C23×C17—22no—
289C23×C17—22no—
290C23×C17—22no—
291C23×C17—22no—
292C23×C17—22no—
293C23×C17—22no—
294C23×C17—22no—
295C23×C17—22no—
296C23×C17—22no—
297C23×C17—22no—
298C23×C17—22no—
299C23×C17—22no—
300C23×C17—41no—
301C23×C17—41no—
302C23×C17—41no—
303C23×C17—41no—
304C23×C17—41no—
305C23×C17—41no—
306C23×C17—41no—
307C23×C17—41no—
308C23×C17—41no—
309C23×C17—41no—
310C23×C17—41no—
311C23×C17—41no—
312C23×C17—41no—
313C23×C17—41no—
314C23×C17—41no—
315C23×C17—41no—
316C23×C17C2×C4⋊C414yes—
317C23×C17C23×C411yescharacteristic
318C23×C17C22×D411yescharacteristic
319C23×C17C22×D411yescharacteristic
320C23×C17C22×Q811yescharacteristic
321C23×C17C2×#4111yescharacteristic
322C23×C17C2×#4111yescharacteristic
323C23×C17C2×#4111yescharacteristic
324C23×C17C2×#4111yescharacteristic
325C23×C17C2×#4111yescharacteristic
326C23×C17C2×#4111yescharacteristic
327C23×C17C2×#4111yescharacteristic
328C23×C17H(5,𝔽2)11yescharacteristic
329C23×C17H(5,𝔽2)11yescharacteristic
330C23×C17H(5,𝔽2)11yescharacteristic
331C23×C172−1+411yescharacteristic
332C2×C4×C17—22no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—22no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—22no—
339C2×C4×C17—22no—
340C2×C4×C17—22no—
341C2×C4×C17—22no—
342C2×C4×C17—22no—
343C2×C4×C17—22no—
344C2×C4×C17—22no—
345C2×C4×C17—22no—
346C2×C4×C17—22no—
347C2×C4×C17—41no—
348C2×C4×C17—41no—
349C2×C4×C17—41no—
350C2×C4×C17—41no—
351C2×C4×C17—41no—
352C2×C4×C17—41no—
353C2×C4×C17—41no—
354C2×C4×C17—41no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—41no—
358C2×C4×C17—41no—
359C2×C4×C17—41no—
360C2×C4×C17—41no—
361C2×C4×C17—41no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
364C2×C4×C17—41no—
365C2×C4×C17—41no—
366C2×C4×C17—41no—
367C2×C4×C17—41no—
368C2×C4×C17—41no—
369C2×C4×C17—41no—
370C2×C4×C17—41no—
371C2×C4×C17—41no—
372C2×C4×C17—41no—
373C2×C4×C17#11714yes—
374C2×Dic17—22no—
375C2×Dic17—22no—
376C2×Dic17—22no—
377C2×Dic17—22no—
378C2×Dic17—22no—
379C2×Dic17—22no—
380C2×Dic17—22no—
381C2×Dic17—22no—
382C2×Dic17—22no—
383C2×Dic17—22no—
384C2×Dic17—22no—
385C2×Dic17—22no—
386C2×Dic17—22no—
387C2×Dic17—22no—
388C2×Dic17—22no—
389C2×Dic17—22no—
390C2×Dic17—22no—
391C2×Dic17—22no—
392C2×Dic17—22no—
393C2×Dic17—22no—
394C2×Dic17—22no—
395C2×Dic17—22no—
396C2×Dic17—22no—
397C2×Dic17—22no—
398C2×Dic17—22no—
399C2×Dic17—22no—
400C2×Dic17—22no—
401C2×Dic17—22no—
402C2×Dic17—22no—
403C2×Dic17—22no—
404C2×Dic17—416no—
405C2×Dic17—41no—
406C2×Dic17—41no—
407C2×Dic17—41no—
408C2×Dic17—41no—
409C2×Dic17—41no—
410C2×Dic17—41no—
411C2×Dic17—41no—
412C2×Dic17—41no—
413C2×Dic17—41no—
414C2×Dic17—41no—
415C2×Dic17—41no—
416C2×Dic17—41no—
417C2×Dic17—41no—
418C2×Dic17—41no—
419C2×Dic17—41no—
420C2×Dic17—41no—
421C2×Dic17—41no—
422C2×Dic17—41no—
423C2×Dic17—41no—
424C2×Dic17—41no—
425C2×Dic17—41no—
426C2×Dic17—41no—
427C2×Dic17C2×C4⋊C414yes—
428C2×Dic17C2×C4⋊C414yes—
429C2×Dic17#11714yes—
430C2×Dic17C4×D414yes—
431C2×#388—171no—
432C2×#388—171no—
433C2×#382—171no—
434C2×#380—171no—
435C2×C4×C22⋊C4—171no—
436#1444—171no—
437#1444—171no—
438#1439—171no—
439#1439D1711yescharacteristic
440#1436—171no—
441#1436—171no—
442C4⋊#95—171no—
443#1434—171no—
444C22⋊#95—171no—
445C4×#95—171no—
446C22×C17—24no—
447C22×C17—24no—
448C22×C17—24no—
449C22×C17—42no—
450C22×C17—42no—
451C22×C17—42no—
452C22×C17—42no—
453C22×C17—42no—
454C22×C17—42no—
455C22×C17—42no—
456C22×C17—42no—
457C22×C17—42no—
458C22×C17—42no—
459C22×C17—42no—
460C22×C17—42no—
461C22×C17C22×C4⋊C411yescharacteristic
462C22×C17C2×#11711yescharacteristic
463C22×C17C2×#11711yescharacteristic
464C22×C17C2×C4×D411yescharacteristic
465C22×C17C4×#4111yescharacteristic
466C22×C17#51811yescharacteristic
467C22×C17#52011yescharacteristic
468C22×C17#52911yescharacteristic
469C22×C17#52911yescharacteristic
470C22×C17#53211yescharacteristic
471C22×C17#53211yescharacteristic
472C22×C17#53211yescharacteristic
473C22×C17#53211yescharacteristic
474C22×C17#53311yescharacteristic
475C22×C17#53311yescharacteristic
476C22×C17#53811yescharacteristic
477C22×C17#53811yescharacteristic
478C22×C17#53911yescharacteristic
479C22×C17#53911yescharacteristic
480C22×C17D4211yescharacteristic
481C22×C17#54611yescharacteristic
482C22×C17#54611yescharacteristic
483C22×C17#54611yescharacteristic
484C22×C17#54611yescharacteristic
485C22×C17#54711yescharacteristic
486C22×C17D4×Q811yescharacteristic
487C22×C17#55111yescharacteristic
488C22×C17#55111yescharacteristic
489C22×C17#55211yescharacteristic
490C22×C17#55211yescharacteristic
491C22×C17#55411yescharacteristic
492C22×C17#55411yescharacteristic
493C22×C17#55411yescharacteristic
494C22×C17#55511yescharacteristic
495C22×C17#55511yescharacteristic
496C4×C17—24no—
497C4×C17—42no—
498C4×C17—42no—
499C4×C17—42no—
500C4×C17—81no—
501C4×C17—81no—
502Dic17—24no—
503Dic17—24no—
504Dic17—24no—
505Dic17—24no—
506Dic17—42no—
507Dic17—42no—
508Dic17—81no—
509Dic17—81no—
510C24×C4—171no—
511C22×C4⋊C4—171no—
512C22×C4⋊C4—171no—
513C22×C4⋊C4—171no—
514C22×C4⋊C4—171no—
515C22×C4⋊C4—171no—
516C22×C4⋊C4C2×D1711yescharacteristic
517C22×C22⋊C4—171no—
518C22×C22⋊C4—171no—
519C22×C22⋊C4—171no—
520C22×C22⋊C4C2×D1711yescharacteristic
521C22×C22⋊C4C2×D1711yescharacteristic
522C22×C22⋊C4C2×D1711yescharacteristic
523C22×C42—171no—
524C22×C42—171no—
525C22×C42—171no—
526C22×C42—171no—
527#388—344no—
528#388—344no—
529#382—344no—
530#380—344no—
531C4×C22⋊C4—178no—
532C2×#95—171no—
533C2×#95—171no—
534C2×#95—171no—
535C2×#95—171no—
536C2×#95—171no—
537C2×#95—171no—
538C2×#95—171no—
539C2×#95—171no—
540C2×#95—171no—
541C2×#95—171no—
542C2×#95—171no—
543C2×#95—171no—
544C2×#95—171no—
545C2×#95—171no—
546C2×#95—171no—
547C2×#95C2×D1711yescharacteristic
548C2×#95C2×D1711yescharacteristic
549C2×#95C2×D1711yescharacteristic
550C2×C17—44no—
551C2×C17#228511yescharacteristic
552C2×C17#229311yescharacteristic
553C2×C17#231811yescharacteristic
554C2×C17#234211yescharacteristic
555C2×C17#234611yescharacteristic
556C2×C17D4×C4⋊C411yescharacteristic
557C2×C17#234911yescharacteristic
558C2×C17#255311yescharacteristic
559C2×C17#255311yescharacteristic
560C2×C17#255511yescharacteristic
561C2×C17#255511yescharacteristic
562C2×C17#255611yescharacteristic
563C2×C17#255611yescharacteristic
564C2×C17#257411yescharacteristic
565C2×C17#257411yescharacteristic
566C25C22×D1711yescharacteristic
567C23×C4—171no—
568C23×C4—171no—
569C23×C4—171no—
570C23×C4—171no—
571C23×C4—171no—
572C23×C4—171no—
573C23×C4—174no—
574C23×C4—171no—
575C23×C4—171no—
576C23×C4—342no—
577C23×C4—342no—
578C23×C4—342no—
579C23×C4—342no—
580C23×C4—681no—
581C23×C4—681no—
582C23×C4C22×D1711yescharacteristic
583C23×C4C22×D1711yescharacteristic
584C23×C4C22×D1711yescharacteristic
585C23×C4C22×D1711yescharacteristic
586C23×C4C22×D1711yescharacteristic
587C23×C4C22×D1711yescharacteristic
588C2×C4⋊C4—22no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—342no—
592C2×C4⋊C4—342no—
593C2×C4⋊C4—342no—
594C2×C4⋊C4—342no—
595C2×C4⋊C4—342no—
596C2×C4⋊C4—342no—
597C2×C4⋊C4—342no—
598C2×C4⋊C4—342no—
599C2×C4⋊C4—342no—
600C2×C4⋊C4—681no—
601C2×C4⋊C4—681no—
602C2×C4⋊C4—681no—
603C2×C4⋊C4—681no—
604C2×C4⋊C4—681no—
605C2×C4⋊C4—681no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—41no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—174no—
615C2×C22⋊C4—174no—
616C2×C22⋊C4—174no—
617C2×C22⋊C4—342no—
618C2×C22⋊C4—342no—
619C2×C22⋊C4—342no—
620C2×C22⋊C4—342no—
621C2×C22⋊C4—681no—
622C2×C22⋊C4—681no—
623C2×C22⋊C4C4×D1714yes—
624C2×C42—174no—
625C2×C42—174no—
626C2×C42—342no—
627C2×C42—342no—
628C2×C42—342no—
629C2×C42—342no—
630C2×C42—342no—
631C2×C42—342no—
632C2×C42—681no—
633C2×C42—681no—
634C2×C42—681no—
635C2×C42—681no—
636#95—22no—
637#95—22no—
638#95—22no—
639#95—174no—
640#95—174no—
641#95—174no—
642#95—342no—
643#95—342no—
644#95—342no—
645#95—342no—
646#95—342no—
647#95—342no—
648#95—342no—
649#95—342no—
650#95—342no—
651#95—342no—
652#95—342no—
653#95—342no—
654C17#1391511yescharacteristic, complemented, Sylow
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×C4×D1712yes—
668C24D4×D1712yes—
669C24Q8×D1712yes—
670C24C23×D1711yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—172no—
708C22×C4—172no—
709C22×C4—172no—
710C22×C4—172no—
711C22×C4—172no—
712C22×C4—172no—
713C22×C4—172no—
714C22×C4—172no—
715C22×C4—172no—
716C22×C4—172no—
717C22×C4—172no—
718C22×C4—172no—
719C22×C4—172no—
720C22×C4—172no—
721C22×C4—348no—
722C22×C4—348no—
723C22×C4—341no—
724C22×C4—341no—
725C22×C4—341no—
726C22×C4—341no—
727C22×C4—341no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4—341no—
734C22×C4—341no—
735C22×C4—341no—
736C22×C4—341no—
737C22×C4—341no—
738C22×C4—341no—
739C22×C4—341no—
740C22×C4—341no—
741C22×C4—341no—
742C22×C4—341no—
743C22×C4—341no—
744C22×C4—341no—
745C22×C4—341no—
746C22×C4—341no—
747C22×C4—341no—
748C22×C4—341no—
749C22×C4—341no—
750C22×C4—341no—
751C22×C4—341no—
752C22×C4—341no—
753C22×C4—341no—
754C22×C4—341no—
755C22×C4—341no—
756C22×C4—341no—
757C22×C4—341no—
758C22×C4—341no—
759C22×C4—341no—
760C22×C4—341no—
761C22×C4—341no—
762C22×C4—341no—
763C22×C4—341no—
764C22×C4—341no—
765C22×C4—684no—
766C22×C4—684no—
767C22×C4—684no—
768C22×C4—684no—
769C22×C4—684no—
770C22×C4C2×C4×D1712yes—
771C22×C4C2×C4×D1712yes—
772C22×C4D4×D1712yes—
773C22×C4#6325412yes—
774C22×C4#6325412yes—
775C22×C4#6325412yes—
776C4⋊C4—44no—
777C4⋊C4—684no—
778C4⋊C4—684no—
779C4⋊C4—684no—
780C4⋊C4—684no—
781C4⋊C4—684no—
782C22⋊C4—28no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—1716no—
786C22⋊C4—684no—
787C22⋊C4—684no—
788C42—348no—
789C42—684no—
790C42—684no—
791C42—684no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C4⋊C4×D1714yes—
827C23C22×C4×D1711yescharacteristic
828C23C2×D4×D1711yescharacteristic
829C23C2×D4×D1711yescharacteristic
830C23C2×#6325411yescharacteristic
831C23C2×#6325411yescharacteristic
832C23C2×#6325411yescharacteristic
833C23#1058769111yescharacteristic
834C23#1058769111yescharacteristic
835C23C2×Q8×D1711yescharacteristic
836C23#41×D1711yescharacteristic
837C23#41×D1711yescharacteristic
838C23#41×D1711yescharacteristic
839C23#41×D1711yescharacteristic
840C23#1058769611yescharacteristic
841C23#1058769711yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—174no—
884C2×C4—174no—
885C2×C4—174no—
886C2×C4—174no—
887C2×C4—342no—
888C2×C4—342no—
889C2×C4—342no—
890C2×C4—342no—
891C2×C4—342no—
892C2×C4—342no—
893C2×C4—342no—
894C2×C4—342no—
895C2×C4—342no—
896C2×C4—342no—
897C2×C4—342no—
898C2×C4—342no—
899C2×C4—342no—
900C2×C4—342no—
901C2×C4—342no—
902C2×C4—342no—
903C2×C4—342no—
904C2×C4—342no—
905C2×C4—342no—
906C2×C4—342no—
907C2×C4—342no—
908C2×C4—342no—
909C2×C4—342no—
910C2×C4—342no—
911C2×C4—342no—
912C2×C4—342no—
913C2×C4—342no—
914C2×C4—342no—
915C2×C4—342no—
916C2×C4—342no—
917C2×C4—6816no—
918C2×C4—681no—
919C2×C4—681no—
920C2×C4—681no—
921C2×C4—681no—
922C2×C4—681no—
923C2×C4—681no—
924C2×C4—681no—
925C2×C4—681no—
926C2×C4—681no—
927C2×C4—681no—
928C2×C4—681no—
929C2×C4—681no—
930C2×C4—681no—
931C2×C4—681no—
932C2×C4—681no—
933C2×C4—681no—
934C2×C4—681no—
935C2×C4—681no—
936C2×C4—681no—
937C2×C4—681no—
938C2×C4—681no—
939C2×C4—681no—
940C2×C4#1058756314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C2×C4⋊C4×D1711yescharacteristic
957C22#117×D1711yescharacteristic
958C22C2×#1058756311yescharacteristic
959C22C4×D4×D1711yescharacteristic
960C22C4×#6325411yescharacteristic
961C22#1176328111yescharacteristic
962C22#1176328811yescharacteristic
963C22#1176333811yescharacteristic
964C22#1176334011yescharacteristic
965C22#1176335411yescharacteristic
966C22#1176335411yescharacteristic
967C22#1176335411yescharacteristic
968C22#1176335711yescharacteristic
969C22#1176336111yescharacteristic
970C22#1176336111yescharacteristic
971C22#1176339411yescharacteristic
972C22#1176339611yescharacteristic
973C22#1176340311yescharacteristic
974C22#1176340411yescharacteristic
975C22#1176344111yescharacteristic
976C22#1176344611yescharacteristic
977C22#1176345111yescharacteristic
978C22#1176345111yescharacteristic
979C22#1176345611yescharacteristic
980C22#1176345711yescharacteristic
981C22#1176347211yescharacteristic
982C22#1176348411yescharacteristic
983C22#1176348911yescharacteristic
984C22#1176349511yescharacteristic
985C22#1176349611yescharacteristic
986C22#1176351311yescharacteristic
987C22#1176351311yescharacteristic
988C22#1176351711yescharacteristic
989C22#1176352111yescharacteristic
990C22#1176352311yescharacteristic
991C4—24no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—81no—
996C4—81no—
997C4—344no—
998C4—344no—
999C4—344no—
1000C4—344no—
1001C4—682no—
1002C4—682no—
1003C4—1361no—
1004C4—1361no—
1005C2—44no—
1006C2#1453118611yescharacteristic
1007C2#1453124611yescharacteristic
1008C2#1453141011yescharacteristic
1009C2#1453162811yescharacteristic
1010C2#1453166611yescharacteristic
1011C2#1453168211yescharacteristic
1012C2#1453169011yescharacteristic
1013C2#1453382211yescharacteristic
1014C2#1453382411yescharacteristic
1015C2#1453385211yescharacteristic
1016C2#1453385411yescharacteristic
1017C2#1453386111yescharacteristic
1018C2#1453386911yescharacteristic
1019C2#1453405111yescharacteristic
1020C2#1453405911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1439C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenter#1439D17
hypocenterC17#13915
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×#11762673C2semidirect
6. #14527048C2semidirect
7. #14527047C2semidirect
9. #14527019C2semidirect
10. #14527015C2semidirect
11. #14527013C2semidirect
12. #14527009C2semidirect
14. #95×Dic17C2semidirect
33. C22⋊C4×Dic17C4semidirect
271. C22⋊Dic17C4⋊C4semidirect
654. C17#13915semidirect

Maximal subgroups

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

subgroupindex
C2×#117627032
C2×#117626972
C2×#117626732
C2×#117626672
C2×C22⋊C4×Dic172
#145270482
#145270472
#145270292
#145270192
#145270152
#145270132
#145270092
#145270062
#95×Dic172
C17×#14392
#1391517