Finite Group Databasebeta

← #16957331

Subgroups — #16957331

Order 4352.

1746 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×#11762680C211yesmaximal, characteristic
2C2×#11762666C211yesmaximal, characteristic
3C2×C4×#63225C211yesmaximal, characteristic, complemented
4C2×#11762656C211yesmaximal, characteristic
5#14527047C211yesmaximal, characteristic, complemented
6#14527037C211yesmaximal, characteristic, complemented
7#14527028C211yesmaximal, characteristic
8#14527028C211yesmaximal, characteristic
9#14527022C211yesmaximal, characteristic
10#14527020C211yesmaximal, characteristic
11#14527018C211yesmaximal, characteristic, complemented
12#14527015C211yesmaximal, characteristic, complemented
13#14527015C211yesmaximal, characteristic, complemented
14#14527008C211yesmaximal, characteristic, complemented
15C2×C17×#387C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30#11762680C418yescomplemented
31#11762666—24no—
32C4×#63225—24no—
33#11762656—24no—
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C22×C4⋊C4×C17C2211yescharacteristic
49C22×C4⋊C4×C17C2211yescharacteristic
50C22×C42×C17C2211yescharacteristic
51C17×#387—24no—
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C24×D17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C22×C4×D17—22no—
72C22×C4×D17—22no—
73C22×C4×D17—22no—
74C22×C4×D17—22no—
75C22×C4×D17—41no—
76C22×C4×D17—41no—
77C22×C4×D17C2×C414yes—
78C2×C4⋊C4×C17—22no—
79C2×C4⋊C4×C17—22no—
80C2×C4⋊C4×C17—22no—
81C2×C4⋊C4×C17—22no—
82C2×C4⋊C4×C17—41no—
83C2×C4⋊C4×C17C2×C414yes—
84C2×C42×C17—22no—
85C2×C42×C17—22no—
86C2×C42×C17—41no—
87C2×#63227—22no—
88C2×#63227—22no—
89C2×#63227—22no—
90C2×#63227—22no—
91C2×#63227—22no—
92C2×#63227—22no—
93C2×#63227—22no—
94C2×#63227—22no—
95C2×#63227—22no—
96C2×#63227—22no—
97C2×#63227—22no—
98C2×#63227—41no—
99C2×#63227—41no—
100C2×#63227—41no—
101C2×#63227—41no—
102C2×#63227C2×C414yes—
103C2×#63227C2×C414yes—
104C2×#63227Q814yes—
105C2×C4⋊Dic17—22no—
106C2×C4⋊Dic17—22no—
107C2×C4⋊Dic17—41no—
108C2×#63225—22no—
109C2×#63225—22no—
110C2×#63225—22no—
111C2×#63225—22no—
112C2×#63225—22no—
113C2×#63225—22no—
114C2×#63225—41no—
115C2×#63225—41no—
116C2×#63225C2×C414yes—
117C2×C4×Dic17—22no—
118C2×C4×Dic17—22no—
119C2×C4×Dic17—22no—
120C2×C4×Dic17—22no—
121C2×C4×Dic17—22no—
122C2×C4×Dic17—22no—
123C2×C4×Dic17—22no—
124C2×C4×Dic17—41no—
125C2×C4×Dic17—41no—
126C17×#95—22no—
127C17×#95—22no—
128C17×#95—22no—
129C17×#95D414yes—
130#10587502—22no—
131#10587502—22no—
132#10587502—22no—
133#10587502—22no—
134#10587502—22no—
135#10587502—22no—
136#10587502—41no—
137#10587502—41no—
138#10587502—41no—
139#10587502—41no—
140#10587502—41no—
141#10587502C2×C414yes—
142#10587502C2×C414yes—
143#10587502D414yes—
144C24×C17C2411yescharacteristic
145C23×D17—21no—
146C23×D17—21no—
147C23×D17—21no—
148C23×D17—21no—
149C23×D17—21no—
150C23×D17—21no—
151C23×D17—21no—
152C23×D17—21no—
153C23×D17—21no—
154C23×D17—21no—
155C23×D17—21no—
156C23×D17—21no—
157C23×D17C22×C412yes—
158C23×D17C2×Q812yes—
159C23×D17#4112yes—
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×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17C22×C412yes—
200C22×C4×C17C22×C412yes—
201C22×C4×C17C22×C412yes—
202C22×C4×C17C2×D412yes—
203C22×C4×C17C2×D412yes—
204C22×C4×C17C2×D412yes—
205C22×C4×C17C2×D412yes—
206C22×C4×C17C2×Q812yes—
207C22×C4×C17#4112yes—
208C22×C4×C17#4112yes—
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—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—21no—
247C22×Dic17—21no—
248C22×Dic17C22×C412yes—
249C22×Dic17C22×C412yes—
250C22×Dic17C22×C412yes—
251C22×Dic17C2×D412yes—
252C22×Dic17C2×D412yes—
253C22×Dic17C2×Q812yes—
254C22×Dic17#4112yes—
255C22×Dic17#4112yes—
256C22×Dic17#4112yes—
257C22×Dic17#4112yes—
258C2×C4×D17—28no—
259C2×C4×D17—28no—
260C2×C4×D17—44no—
261C2×C4×D17—44no—
262C2×C4×D17—44no—
263C2×C4×D17—44no—
264C2×C4×D17—44no—
265C4⋊C4×C17—28no—
266C4⋊C4×C17—44no—
267C42×C17—44no—
268#63227—28no—
269#63227—28no—
270#63227—28no—
271#63227—44no—
272#63227—44no—
273#63227—44no—
274C4⋊Dic17—44no—
275#63225—28no—
276#63225—28no—
277#63225—44no—
278C4×Dic17—28no—
279C4×Dic17—44no—
280C4×Dic17—44no—
281#13987—171nomaximal, Sylow
282C23×C17C23×C411yescharacteristic
283C23×C17C22×D411yescharacteristic
284C23×C17C22×D411yescharacteristic
285C23×C17C22×Q811yescharacteristic
286C23×C17C2×#4111yescharacteristic
287C23×C17C2×#4111yescharacteristic
288C23×C17C2×#4111yescharacteristic
289C23×C17C2×#4111yescharacteristic
290C23×C17C2×#4111yescharacteristic
291C23×C17C2×#4111yescharacteristic
292C23×C17C2×#4111yescharacteristic
293C23×C17H(5,𝔽2)11yescharacteristic
294C23×C17H(5,𝔽2)11yescharacteristic
295C23×C17H(5,𝔽2)11yescharacteristic
296C23×C172−1+411yescharacteristic
297C22×D17—22no—
298C22×D17—22no—
299C22×D17—22no—
300C22×D17—22no—
301C22×D17—22no—
302C22×D17—22no—
303C22×D17—22no—
304C22×D17—22no—
305C22×D17—22no—
306C22×D17—22no—
307C22×D17—22no—
308C22×D17—22no—
309C22×D17—22no—
310C22×D17—22no—
311C22×D17—22no—
312C22×D17—22no—
313C22×D17—22no—
314C22×D17—22no—
315C22×D17—41no—
316C22×D17—41no—
317C22×D17—41no—
318C22×D17—41no—
319C22×D17—41no—
320C22×D17—41no—
321C22×D17—41no—
322C22×D17—41no—
323C22×D17—41no—
324C22×D17—41no—
325C22×D17—41no—
326C22×D17—41no—
327C22×D17—41no—
328C22×D17—41no—
329C22×D17—41no—
330C22×D17—41no—
331C22×D17C4×Q814yes—
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—22no—
351C2×C4×C17—22no—
352C2×C4×C17—22no—
353C2×C4×C17—22no—
354C2×C4×C17—22no—
355C2×C4×C17—22no—
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—41no—
374C2×C4×C17—41no—
375C2×C4×C17—41no—
376C2×C4×C17—41no—
377C2×C4×C17—41no—
378C2×C4×C17—41no—
379C2×C4×C17C4×D414yes—
380C2×C4×C17C22⋊Q814yes—
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—22no—
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×Dic17C4×D414yes—
430C4×D17—416no—
431C2×#387D1711yescharacteristic, complemented
432C2×#385—171no—
433C2×#380—171no—
434C2×C4×C4⋊C4—171no—
435C2×C4×C22⋊C4—171no—
436#1444—171no—
437#1441—171no—
438#1439—171no—
439#1439—171no—
440#1437—171no—
441#1437—171no—
442#1436—171no—
443#1436—171no—
444#1436—171no—
445#1434—171no—
446C22×C17C2×#11711yescharacteristic
447C22×C17C2×C4×D411yescharacteristic
448C22×C17C2×C4×D411yescharacteristic
449C22×C17C2×C4×Q811yescharacteristic
450C22×C17C4×#4111yescharacteristic
451C22×C17#51811yescharacteristic
452C22×C17#52011yescharacteristic
453C22×C17C2×C22⋊Q811yescharacteristic
454C22×C17#52511yescharacteristic
455C22×C17#52511yescharacteristic
456C22×C17#52511yescharacteristic
457C22×C17#52911yescharacteristic
458C22×C17#52911yescharacteristic
459C22×C17#52911yescharacteristic
460C22×C17#53311yescharacteristic
461C22×C17#53811yescharacteristic
462C22×C17#53911yescharacteristic
463C22×C17#54011yescharacteristic
464C22×C17#54211yescharacteristic
465C22×C17D4211yescharacteristic
466C22×C17#54611yescharacteristic
467C22×C17#54611yescharacteristic
468C22×C17#54611yescharacteristic
469C22×C17#54711yescharacteristic
470C22×C17D4×Q811yescharacteristic
471C22×C17#55011yescharacteristic
472C22×C17#55111yescharacteristic
473C22×C17#55211yescharacteristic
474C22×C17#55311yescharacteristic
475C22×C17#55311yescharacteristic
476C22×C17#55411yescharacteristic
477C22×C17#55411yescharacteristic
478C22×C17#55411yescharacteristic
479C22×C17#55511yescharacteristic
480C22×C17#55611yescharacteristic
481C2×D17—24no—
482C2×D17—24no—
483C2×D17—24no—
484C2×D17—42no—
485C2×D17—42no—
486C2×D17—42no—
487C2×D17—42no—
488C2×D17—42no—
489C2×D17—42no—
490C2×D17—42no—
491C2×D17—42no—
492C2×D17—42no—
493C2×D17—42no—
494C2×D17—42no—
495C2×D17—42no—
496C4×C17—24no—
497C4×C17—24no—
498C4×C17—42no—
499C4×C17—42no—
500C4×C17—42no—
501C4×C17—42no—
502C4×C17—81no—
503Dic17—24no—
504Dic17—24no—
505Dic17—42no—
506Dic17—42no—
507Dic17—42no—
508Dic17—42no—
509Dic17—81no—
510C24×C4—171no—
511C22×C4⋊C4—171no—
512C22×C4⋊C4—171no—
513C22×C4⋊C4—171no—
514C22×C4⋊C4—171no—
515C22×C4⋊C4C2×D1711yescharacteristic
516C22×C4⋊C4C2×D1711yescharacteristic
517C22×C22⋊C4—171no—
518C22×C22⋊C4—171no—
519C22×C22⋊C4—171no—
520C22×C22⋊C4—171no—
521C22×C22⋊C4—171no—
522C22×C22⋊C4—171no—
523C22×C42—171no—
524C22×C42—171no—
525C22×C42—171no—
526C22×C42C2×D1711yescharacteristic
527#387—24no—
528#385—178no—
529#380—344no—
530C4×C4⋊C4—344no—
531C4×C22⋊C4—344no—
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×#95C2×D1711yescharacteristic
547C2×#95C2×D1711yescharacteristic
548C2×#95C2×D1711yescharacteristic
549C2×#95C2×D1711yescharacteristic
550C2×C17#229011yescharacteristic
551C2×C17C4×C22⋊Q811yescharacteristic
552C2×C17#233511yescharacteristic
553C2×C17#234511yescharacteristic
554C2×C17#235411yescharacteristic
555C2×C17#235811yescharacteristic
556C2×C17#236011yescharacteristic
557C2×C17#244911yescharacteristic
558C2×C17#245411yescharacteristic
559C2×C17#245611yescharacteristic
560C2×C17#246511yescharacteristic
561C2×C17#246811yescharacteristic
562C2×C17#247611yescharacteristic
563C2×C17#257411yescharacteristic
564C2×C17#257711yescharacteristic
565D17—44no—
566C25—171no—
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—342no—
576C23×C4—342no—
577C23×C4—342no—
578C23×C4—342no—
579C23×C4—681no—
580C23×C4—681no—
581C23×C4C22×D1711yescharacteristic
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—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—174no—
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—342no—
601C2×C4⋊C4—342no—
602C2×C4⋊C4—681no—
603C2×C4⋊C4—681no—
604C2×C4⋊C4—681no—
605C2×C4⋊C4C4×D1714yes—
606C2×C22⋊C4—174no—
607C2×C22⋊C4—174no—
608C2×C22⋊C4—174no—
609C2×C22⋊C4—342no—
610C2×C22⋊C4—342no—
611C2×C22⋊C4—342no—
612C2×C22⋊C4—342no—
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—342no—
620C2×C22⋊C4—681no—
621C2×C22⋊C4—681no—
622C2×C22⋊C4—681no—
623C2×C22⋊C4—681no—
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—41no—
627C2×C42—342no—
628C2×C42—342no—
629C2×C42—342no—
630C2×C42—342no—
631C2×C42—342no—
632C2×C42—342no—
633C2×C42—342no—
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—681no—
649#95—681no—
650#95—681no—
651#95—681no—
652#95—681no—
653#95C22⋊D1714yes—
654C17#1398711yescharacteristic, complemented, Sylow
655C24—172no—
656C24—172no—
657C24—172no—
658C24—341no—
659C24—341no—
660C24—341no—
661C24—341no—
662C24—341no—
663C24—341no—
664C24—341no—
665C24—341no—
666C24—341no—
667C24—341no—
668C24—341no—
669C24—341no—
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—21no—
708C22×C4—21no—
709C22×C4—21no—
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—348no—
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—348no—
754C22×C4—341no—
755C22×C4—341no—
756C22×C4—341no—
757C22×C4—341no—
758C22×C4—341no—
759C22×C4—341no—
760C22×C4—341no—
761C22×C4—684no—
762C22×C4—684no—
763C22×C4—684no—
764C22×C4—684no—
765C22×C4—684no—
766C22×C4C2×C4×D1712yes—
767C22×C4C2×C4×D1712yes—
768C22×C4C2×C4×D1712yes—
769C22×C4#6325212yes—
770C22×C4D4×D1712yes—
771C22×C4Q8×D1712yes—
772C22×C4#6325612yes—
773C22×C4C2×C22⋊D1712yes—
774C22×C4C2×C22⋊D1712yes—
775C22×C4C2×C22⋊D1712yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—348no—
779C4⋊C4—348no—
780C4⋊C4—684no—
781C4⋊C4—684no—
782C22⋊C4—348no—
783C22⋊C4—348no—
784C22⋊C4—348no—
785C22⋊C4—684no—
786C22⋊C4—684no—
787C22⋊C4—684no—
788C42—44no—
789C42—348no—
790C42—684no—
791C42—684no—
792C23—174no—
793C23—342no—
794C23—342no—
795C23—342no—
796C23—342no—
797C23—342no—
798C23—342no—
799C23—342no—
800C23—342no—
801C23—342no—
802C23—342no—
803C23—342no—
804C23—342no—
805C23—342no—
806C23—342no—
807C23—342no—
808C23—342no—
809C23—342no—
810C23—342no—
811C23—681no—
812C23—681no—
813C23—681no—
814C23—681no—
815C23—681no—
816C23—681no—
817C23—681no—
818C23—681no—
819C23—681no—
820C23—681no—
821C23—681no—
822C23—681no—
823C23—681no—
824C23—681no—
825C23—681no—
826C23—681no—
827C23C22×C4×D1711yescharacteristic
828C23C2×#6325211yescharacteristic
829C23C2×D4×D1711yescharacteristic
830C23#1058769111yescharacteristic
831C23C2×Q8×D1711yescharacteristic
832C23C2×#6325611yescharacteristic
833C23#41×D1711yescharacteristic
834C23#41×D1711yescharacteristic
835C23#41×D1711yescharacteristic
836C23#41×D1711yescharacteristic
837C23#41×D1711yescharacteristic
838C23#1058769611yescharacteristic
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—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
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—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—174no—
890C2×C4—174no—
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—6816no—
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×C4C4×C22⋊D1714yes—
940C2×C4#1058763214yes—
941C22—344no—
942C22—344no—
943C22—344no—
944C22—682no—
945C22—682no—
946C22—682no—
947C22—682no—
948C22—682no—
949C22—682no—
950C22—682no—
951C22—682no—
952C22—682no—
953C22—682no—
954C22—682no—
955C22—682no—
956C22#117×D1711yescharacteristic
957C22C4×D4×D1711yescharacteristic
958C22C2×C4×C22⋊D1711yescharacteristic
959C22C4×Q8×D1711yescharacteristic
960C22C4×#6325611yescharacteristic
961C22#1176328111yescharacteristic
962C22#1176328911yescharacteristic
963C22C2×#1058763211yescharacteristic
964C22#1176331611yescharacteristic
965C22#1176331711yescharacteristic
966C22#1176332211yescharacteristic
967C22#1176334211yescharacteristic
968C22#1176334411yescharacteristic
969C22#1176334611yescharacteristic
970C22#1176336311yescharacteristic
971C22#1176339511yescharacteristic
972C22#1176340811yescharacteristic
973C22#1176341511yescharacteristic
974C22#1176342511yescharacteristic
975C22D4×C22⋊D1711yescharacteristic
976C22#1176344711yescharacteristic
977C22#1176345111yescharacteristic
978C22#1176345511yescharacteristic
979C22#1176345811yescharacteristic
980C22#1176347211yescharacteristic
981C22#1176347811yescharacteristic
982C22#1176348811yescharacteristic
983C22#1176349511yescharacteristic
984C22#1176350411yescharacteristic
985C22#1176351011yescharacteristic
986C22#1176351311yescharacteristic
987C22#1176351511yescharacteristic
988C22#1176351511yescharacteristic
989C22#1176352211yescharacteristic
990C22#1176352711yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—81no—
998C4—344no—
999C4—344no—
1000C4—682no—
1001C4—682no—
1002C4—682no—
1003C4—682no—
1004C4—1361no—
1005C2—684no—
1006C2#1453122211yescharacteristic
1007C2C4×#1058763211yescharacteristic
1008C2#1453157311yescharacteristic
1009C2#1453165811yescharacteristic
1010C2#1453173411yescharacteristic
1011C2#1453176111yescharacteristic
1012C2#1453179211yescharacteristic
1013C2#1453258911yescharacteristic
1014C2#1453265211yescharacteristic
1015C2#1453267211yescharacteristic
1016C2#1453280411yescharacteristic
1017C2#1453284611yescharacteristic
1018C2#1453297711yescharacteristic
1019C2#1453405511yescharacteristic
1020C2#1453411011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#387C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenterC2×#387D17
hypocenterC17#13987
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. C2×C4×#63225C2semidirect
5. #14527047C2semidirect
6. #14527037C2semidirect
11. #14527018C2semidirect
12. #14527015C2semidirect
13. #14527015C2semidirect
14. #14527008C2semidirect
15. C2×C17×#387C2semidirect
30. #11762680C4semidirect
431. C2×#387D17semidirect
654. C17#13987semidirect

Maximal subgroups

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

subgroupindex
C2×#117626802
C2×#117626662
C2×C4×#632252
C2×#117626562
#145270472
#145270372
#145270282
#145270222
#145270202
#145270182
#145270152
#145270082
C2×C17×#3872
#1398717