Finite Group Databasebeta

← #16956649

Subgroups — #16956649

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×#11762702C211yesmaximal, characteristic
2C2×#11762674C211yesmaximal, characteristic, complemented
3C2×#11762667C211yesmaximal, characteristic
4C2×C22⋊C4×Dic17C211yesmaximal, characteristic
5#14527048C211yesmaximal, characteristic, complemented
6#14527047C211yesmaximal, characteristic, complemented
7#14527027C211yesmaximal, characteristic
8#14527027C211yesmaximal, characteristic
9#14527017C211yesmaximal, characteristic, complemented
10#14527015C211yesmaximal, characteristic, complemented
11#14527012C211yesmaximal, characteristic, complemented
12#14527010C211yesmaximal, characteristic, complemented
13#14527006C211yesmaximal, characteristic
14C4×#10587502C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, 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
28#11762702—24no—
29#11762674—24no—
30#11762667—24no—
31C22⋊C4×Dic17C418yescomplemented
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2211yescharacteristic
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
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—22no—
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—41no—
86C2×C22⋊C4×C17—41no—
87C2×C22⋊C4×C17C2×C414yes—
88C2×C22⋊C4×C17D414yes—
89C2×C22⋊C4×C17Q814yes—
90C2×C42×C17—22no—
91C2×C42×C17—22no—
92C2×C42×C17—41no—
93C2×C22⋊Dic17—22no—
94C2×C22⋊Dic17—22no—
95C2×C22⋊Dic17—22no—
96C2×C22⋊Dic17—22no—
97C2×C22⋊Dic17—22no—
98C2×C22⋊Dic17—22no—
99C2×C22⋊Dic17—41no—
100C2×C22⋊Dic17—41no—
101C2×C22⋊Dic17C2×C414yes—
102C2×C4⋊Dic17—22no—
103C2×C4⋊Dic17—22no—
104C2×C4⋊Dic17—41no—
105C2×#63225—22no—
106C2×#63225—22no—
107C2×#63225—22no—
108C2×#63225—22no—
109C2×#63225—22no—
110C2×#63225—22no—
111C2×#63225—41no—
112C2×#63225—41no—
113C2×#63225—41no—
114C2×#63225—41no—
115C2×#63225—41no—
116C2×#63225—41no—
117C2×C4×Dic17—22no—
118C2×C4×Dic17—22no—
119C2×C4×Dic17—22no—
120C2×C4×Dic17—22no—
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—
128#10587502—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×C17C22×C412yes—
195C22×C4×C17C22×C412yes—
196C22×C4×C17C2×D412yes—
197C22×C4×C17C2×D412yes—
198C22×C4×C17C2×D412yes—
199C22×C4×C17C2×Q812yes—
200C22×C4×C17C2×Q812yes—
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—21no—
231C22×Dic17—21no—
232C22×Dic17—28no—
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—44no—
249C22×Dic17—44no—
250C22×Dic17—44no—
251C22×Dic17—44no—
252C22×Dic17—44no—
253C22×Dic17C22×C412yes—
254C22×Dic17C22×C412yes—
255C22×Dic17C22×C412yes—
256C22×Dic17C22×C412yes—
257C22×Dic17C2×D412yes—
258C22×Dic17C2×D412yes—
259C22×Dic17#4112yes—
260C22×Dic17#4112yes—
261C22×Dic17#4112yes—
262C22×Dic17#4112yes—
263C22×Dic17#4112yes—
264C22×Dic17#4112yes—
265C4⋊C4×C17—44no—
266C22⋊C4×C17—44no—
267C22⋊C4×C17—44no—
268C22⋊C4×C17C4⋊C4116yescomplemented
269C42×C17—44no—
270C22⋊Dic17—28no—
271C22⋊Dic17—44no—
272C22⋊Dic17—44no—
273C4⋊Dic17—44no—
274#63225—44no—
275#63225—44no—
276#63225—44no—
277#63225—44no—
278C4×Dic17—28no—
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—22no—
348C2×C4×C17—22no—
349C2×C4×C17—22no—
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×C17C2×C4⋊C414yes—
373C2×C4×C17C2×C4⋊C414yes—
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—416no—
402C2×Dic17—41no—
403C2×Dic17—41no—
404C2×Dic17—41no—
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×Dic17—41no—
428C2×Dic17#11714yes—
429C2×Dic17#11714yes—
430C2×Dic17C4×D414yes—
431C2×#388—171no—
432C2×#388D1711yescharacteristic
433C2×#382—171no—
434C2×#380—171no—
435C2×C4×C22⋊C4—171no—
436#1444—171no—
437#1444—171no—
438#1439—171no—
439#1439—171no—
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—24no—
498C4×C17—42no—
499C4×C17—42no—
500C4×C17—81no—
501C4×C17—81no—
502Dic17—24no—
503Dic17—24no—
504Dic17—24no—
505Dic17—42no—
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×C42C2×D1711yescharacteristic
527#388—24no—
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×#95—171no—
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—22no—
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—681no—
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—41no—
611C2×C22⋊C4—41no—
612C2×C22⋊C4—174no—
613C2×C22⋊C4—342no—
614C2×C22⋊C4—342no—
615C2×C22⋊C4—342no—
616C2×C22⋊C4—342no—
617C2×C22⋊C4—342no—
618C2×C22⋊C4—342no—
619C2×C22⋊C4—681no—
620C2×C22⋊C4—681no—
621C2×C22⋊C4Dic3414yes—
622C2×C22⋊C4C4×D1714yes—
623C2×C22⋊C4C22⋊D1714yes—
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—41no—
627C2×C42—174no—
628C2×C42—174no—
629C2×C42—342no—
630C2×C42—342no—
631C2×C42—342no—
632C2×C42—342no—
633C2×C42—681no—
634C2×C42—681no—
635C2×C42—681no—
636#95—22no—
637#95—22no—
638#95—174no—
639#95—174no—
640#95—174no—
641#95—342no—
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×Dic3412yes—
668C24C2×C4×D1712yes—
669C24C2×C22⋊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—172no—
706C22×C4—172no—
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—348no—
718C22×C4—348no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
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—684no—
764C22×C4—684no—
765C22×C4—684no—
766C22×C4—684no—
767C22×C4—684no—
768C22×C4C2×Dic3412yes—
769C22×C4C2×Dic3412yes—
770C22×C4C2×C4×D1712yes—
771C22×C4C2×C4×D1712yes—
772C22×C4D4×D1712yes—
773C22×C4#6325412yes—
774C22×C4C2×C22⋊D1712yes—
775C22×C4C2×C22⋊D1712yes—
776C4⋊C4—44no—
777C4⋊C4—684no—
778C4⋊C4—684no—
779C4⋊C4—684no—
780C4⋊C4—684no—
781C4⋊C4—684no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—348no—
785C22⋊C4—684no—
786C22⋊C4—684no—
787C22⋊C4#63225116yescomplemented
788C42—44no—
789C42—348no—
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—
826C23C2×#6322514yes—
827C23C22×Dic3411yescharacteristic
828C23C22×C4×D1711yescharacteristic
829C23C2×D4×D1711yescharacteristic
830C23C2×#6325411yescharacteristic
831C23#1058769111yescharacteristic
832C23#1058769111yescharacteristic
833C23#41×D1711yescharacteristic
834C23#41×D1711yescharacteristic
835C23#41×D1711yescharacteristic
836C23#41×D1711yescharacteristic
837C23#41×D1711yescharacteristic
838C23#41×D1711yescharacteristic
839C23#1058769611yescharacteristic
840C23#1058769711yescharacteristic
841C23C22×C22⋊D1711yescharacteristic
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—22no—
858C2×C4—22no—
859C2×C4—22no—
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—174no—
883C2×C4—174no—
884C2×C4—174no—
885C2×C4—342no—
886C2×C4—342no—
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—6816no—
913C2×C4—681no—
914C2×C4—681no—
915C2×C4—681no—
916C2×C4—681no—
917C2×C4—681no—
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×C4C2×#6322514yes—
940C2×C4C2×#6322514yes—
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—
956C22C22×#6322511yescharacteristic
957C22#117×D1711yescharacteristic
958C22#117×D1711yescharacteristic
959C22C4×D4×D1711yescharacteristic
960C22C4×#6325411yescharacteristic
961C22#1176328111yescharacteristic
962C22#1176328811yescharacteristic
963C22#1176333611yescharacteristic
964C22#1176334211yescharacteristic
965C22#1176335411yescharacteristic
966C22#1176335511yescharacteristic
967C22#1176335511yescharacteristic
968C22#1176335811yescharacteristic
969C22#1176336211yescharacteristic
970C22#1176336211yescharacteristic
971C22#1176339111yescharacteristic
972C22#1176339311yescharacteristic
973C22#1176340011yescharacteristic
974C22#1176340211yescharacteristic
975C22D4×C22⋊D1711yescharacteristic
976C22#1176344711yescharacteristic
977C22#1176344811yescharacteristic
978C22#1176345211yescharacteristic
979C22#1176345311yescharacteristic
980C22#1176345811yescharacteristic
981C22D4×Dic3411yescharacteristic
982C22#1176348411yescharacteristic
983C22#1176348711yescharacteristic
984C22#1176349511yescharacteristic
985C22#1176349611yescharacteristic
986C22#1176351611yescharacteristic
987C22#1176351811yescharacteristic
988C22#1176351811yescharacteristic
989C22#1176352111yescharacteristic
990C22#1176352311yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—81no—
996C4—81no—
997C4—344no—
998C4—344no—
999C4—344no—
1000C4—682no—
1001C4—682no—
1002C4—682no—
1003C4—1361no—
1004C4—1361no—
1005C2—44no—
1006C2#1453118711yescharacteristic
1007C2#1453124411yescharacteristic
1008C2#1453141411yescharacteristic
1009C2#1453163211yescharacteristic
1010C2#1453166611yescharacteristic
1011C2D4×#6322511yescharacteristic
1012C2#1453168911yescharacteristic
1013C2#1453382511yescharacteristic
1014C2#1453382711yescharacteristic
1015C2#1453385511yescharacteristic
1016C2#1453385711yescharacteristic
1017C2#1453386711yescharacteristic
1018C2#1453387511yescharacteristic
1019C2#1453405711yescharacteristic
1020C2#1453406511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#388D17
hypocenterC17#13915
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#11762674C2semidirect
5. #14527048C2semidirect
6. #14527047C2semidirect
9. #14527017C2semidirect
10. #14527015C2semidirect
11. #14527012C2semidirect
12. #14527010C2semidirect
14. C4×#10587502C2semidirect
31. C22⋊C4×Dic17C4semidirect
268. C22⋊C4×C17C4⋊C4semidirect
654. C17#13915semidirect
787. C22⋊C4#63225semidirect

Maximal subgroups

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

subgroupindex
C2×#117627022
C2×#117626742
C2×#117626672
C2×C22⋊C4×Dic172
#145270482
#145270472
#145270272
#145270172
#145270152
#145270122
#145270102
#145270062
C4×#105875022
C2×C17×#3882
#1391517