Finite Group Databasebeta

← #16956231

Subgroups — #16956231

Order 4352.

2950 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D68C211yesmaximal, characteristic
2C22×C4⋊C4×D17C211yesmaximal, characteristic, complemented
3C2×#11762687C212yesmaximal
4C2×#11762666C211yesmaximal, characteristic, complemented
5C2×#11762666C211yesmaximal, characteristic, complemented
6C2×#11762666C211yesmaximal, characteristic, complemented
7#14527036C212yesmaximal, complemented
8#14527028C212yesmaximal, complemented
9#14527014C211yesmaximal, characteristic, complemented
10#14527005C212yesmaximal, complemented
11C17×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D68C2211yescharacteristic
13C23×C4×D17C2211yescharacteristic
14C23×C4×D17C2212yes—
15C23×C4×D17C2211yescharacteristic
16C2×C4×D68—24no—
17C2×C4×D68—24no—
18C2×C4×D68C418yescomplemented
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21C22×C4⋊Dic17C2211yescharacteristic
22C22×#63225C2212yes—
23C2×C4⋊C4×D17—24no—
24C2×C4⋊C4×D17—24no—
25C2×C4⋊C4×D17—24no—
26C22×#63227C2212yes—
27C22×#63227C2212yes—
28C22×#63227C2212yes—
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31#11762687—28no—
32#11762666—24no—
33#11762666—24no—
34#11762666—24no—
35C2×#10587502C2212yes—
36C2×#10587502C2212yes—
37C2×#10587502C2212yes—
38C2×#10587502C2212yes—
39C2×#10587502C2212yes—
40C22×C4⋊C4×C17C2211yescharacteristic
41C22×C4⋊C4×C17C2211yescharacteristic
42C22×C42×C17C2211yescharacteristic
43C2×C17×#95C2212yes—
44C2×C17×#95C2212yes—
45C24×D17C2311yescharacteristic
46C24×D17C2311yescharacteristic
47C23×C4×C17C2312yes—
48C23×C4×C17C2311yescharacteristic
49C23×C4×C17C2312yes—
50C23×C4×C17C2311yescharacteristic
51C23×C4×C17C2311yescharacteristic
52C23×Dic17C2312yes—
53C23×Dic17C2311yescharacteristic
54C23×Dic17C2312yes—
55C23×Dic17C2311yescharacteristic
56C22×D68—22no—
57C22×D68—22no—
58C22×D68—22no—
59C22×D68—22no—
60C22×D68C2×C414yes—
61C22×D68D414yes—
62C22×D68Q814yes—
63C22×C4×D17—22no—
64C22×C4×D17—22no—
65C22×C4×D17—22no—
66C22×C4×D17—22no—
67C22×C4×D17—24no—
68C22×C4×D17—24no—
69C22×C4×D17—22no—
70C22×C4×D17—22no—
71C22×C4×D17—22no—
72C22×C4×D17—22no—
73C22×C4×D17—22no—
74C22×C4×D17—22no—
75C22×C4×D17—24no—
76C22×C4×D17—24no—
77C22×C4×D17—24no—
78C22×C4×D17—42no—
79C22×C4×D17—42no—
80C22×C4×D17C2×C414yes—
81C22×C4×D17C2×C414yescomplemented
82C22×C4×D17D414yes—
83C22×C4×D17D414yes—
84C2×C4⋊C4×C17—22no—
85C2×C4⋊C4×C17—22no—
86C2×C4⋊C4×C17—22no—
87C2×C4⋊C4×C17—22no—
88C2×C4⋊C4×C17—22no—
89C2×C4⋊C4×C17D414yescomplemented
90C2×C42×C17—22no—
91C2×C42×C17—22no—
92C2×C42×C17C2×C414yescomplemented
93C2×#63227—22no—
94C2×#63227—22no—
95C2×#63227—24no—
96C2×#63227—24no—
97C2×#63227—24no—
98C2×#63227—24no—
99C2×#63227—24no—
100C2×#63227—24no—
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—24no—
104C2×#63227—42no—
105C2×#63227—42no—
106C2×#63227C2×C414yes—
107C2×#63227C2×C414yescomplemented
108C2×C4⋊Dic17—22no—
109C2×C4⋊Dic17—22no—
110C2×C4⋊Dic17—22no—
111C2×C4⋊Dic17—22no—
112C2×C4⋊Dic17—22no—
113C2×C4⋊Dic17—22no—
114C2×C4⋊Dic17—22no—
115C2×C4⋊Dic17C2×C414yescomplemented
116C2×C4⋊Dic17D414yescomplemented
117C2×#63225—24no—
118C2×#63225—24no—
119C2×#63225—24no—
120C4⋊C4×D17—232no—
121C4×D68—232no—
122C17×#95—24no—
123C17×#95—42no—
124#10587502—24no—
125#10587502—24no—
126#10587502—24no—
127#10587502—24no—
128#10587502—42no—
129C24×C17C2411yescharacteristic
130C23×D17—21no—
131C23×D17—21no—
132C23×D17—21no—
133C23×D17—21no—
134C23×D17—21no—
135C23×D17—21no—
136C23×D17—21no—
137C23×D17—21no—
138C23×D17—21no—
139C23×D17—21no—
140C23×D17—21no—
141C23×D17—21no—
142C23×D17—21no—
143C23×D17—21no—
144C23×D17—21no—
145C23×D17—21no—
146C23×D17—21no—
147C23×D17—21no—
148C23×D17—21no—
149C23×D17—21no—
150C23×D17C22×C412yes—
151C23×D17C22×C412yes—
152C23×D17C2×D412yes—
153C23×D17C2×D412yes—
154C23×D17C2×D412yes—
155C23×D17C2×D412yes—
156C23×D17C2×Q812yes—
157C23×D17C2×Q812yes—
158C23×D17#4112yes—
159C23×D17#4112yes—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—22no—
165C22×C4×C17—22no—
166C22×C4×C17—22no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—22no—
170C22×C4×C17—22no—
171C22×C4×C17—22no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—22no—
177C22×C4×C17—22no—
178C22×C4×C17—22no—
179C22×C4×C17—22no—
180C22×C4×C17—22no—
181C22×C4×C17—22no—
182C22×C4×C17—22no—
183C22×C4×C17C22×C412yes—
184C22×C4×C17C22×C412yes—
185C22×C4×C17C22×C412yes—
186C22×C4×C17C2×D414yes—
187C22×C4×C17C2×D412yes—
188C22×C4×C17C2×D412yes—
189C22×C4×C17C2×D412yes—
190C22×C4×C17C2×D412yes—
191C22×C4×C17C2×D412yes—
192C22×C4×C17C2×Q812yes—
193C22×C4×C17#4112yes—
194C22×C4×C17#4112yes—
195C22×Dic17—21no—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—22no—
202C22×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—22no—
209C22×Dic17—22no—
210C22×Dic17—22no—
211C22×Dic17—22no—
212C22×Dic17—22no—
213C22×Dic17—22no—
214C22×Dic17—22no—
215C22×Dic17—22no—
216C22×Dic17—22no—
217C22×Dic17—22no—
218C22×Dic17C22×C412yes—
219C22×Dic17C22×C412yes—
220C22×Dic17C2×D414yes—
221C22×Dic17C2×D412yes—
222C22×Dic17C2×D412yes—
223C2×D68—28no—
224C2×D68—28no—
225C2×D68—28no—
226C2×D68—28no—
227C2×D68—28no—
228C2×D68—28no—
229C2×D68C4⋊C4116yescomplemented
230C2×C4×D17—28no—
231C2×C4×D17—28no—
232C2×C4×D17—28no—
233C2×C4×D17—28no—
234C2×C4×D17—28no—
235C2×C4×D17—28no—
236C2×C4×D17—216no—
237C2×C4×D17—28no—
238C2×C4×D17—28no—
239C2×C4×D17—28no—
240C2×C4×D17—48no—
241C2×C4×D17—48no—
242C2×C4×D17—48no—
243C2×C4×D17—48no—
244C2×C4×D17—48no—
245C2×C4×D17—48no—
246C2×C4×D17—44no—
247C2×C4×D17—44no—
248C2×C4×D17—44no—
249C2×C4×D17—44no—
250C2×C4×D17C22⋊C4116yescomplemented
251C4⋊C4×C17—28no—
252C4⋊C4×C17—44no—
253C42×C17—28no—
254#63227—28no—
255#63227—28no—
256#63227—48no—
257#63227—48no—
258#63227—48no—
259C4⋊Dic17—28no—
260C4⋊Dic17—28no—
261C4⋊Dic17—44no—
262#63225—216no—
263#13872—171nomaximal, Sylow
264C23×C17C23×C411yescharacteristic
265C23×C17C22×D411yescharacteristic
266C23×C17C22×D411yescharacteristic
267C23×C17C22×D411yescharacteristic
268C23×C17C22×D411yescharacteristic
269C23×C17C22×D411yescharacteristic
270C23×C17C22×Q811yescharacteristic
271C23×C17C2×#4111yescharacteristic
272C23×C17C2×#4111yescharacteristic
273C23×C17C2×#4111yescharacteristic
274C23×C17C2×#4111yescharacteristic
275C23×C17H(5,𝔽2)11yescharacteristic
276C23×C17H(5,𝔽2)11yescharacteristic
277C23×C172−1+411yescharacteristic
278C23×C172−1+411yescharacteristic
279C22×D17—22no—
280C22×D17—22no—
281C22×D17—22no—
282C22×D17—22no—
283C22×D17—22no—
284C22×D17—22no—
285C22×D17—22no—
286C22×D17—22no—
287C22×D17—22no—
288C22×D17—22no—
289C22×D17—22no—
290C22×D17—22no—
291C22×D17—22no—
292C22×D17—22no—
293C22×D17—22no—
294C22×D17—22no—
295C22×D17—22no—
296C22×D17—22no—
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—22no—
316C22×D17—22no—
317C22×D17—22no—
318C22×D17—22no—
319C22×D17—22no—
320C22×D17—22no—
321C22×D17—22no—
322C22×D17—22no—
323C22×D17—22no—
324C22×D17—22no—
325C22×D17—41no—
326C22×D17—41no—
327C22×D17—41no—
328C22×D17—41no—
329C22×D17—41no—
330C22×D17—41no—
331C22×D17—41no—
332C22×D17—41no—
333C22×D17—41no—
334C22×D17—41no—
335C22×D17—41no—
336C22×D17—41no—
337C22×D17—41no—
338C22×D17—41no—
339C22×D17—41no—
340C22×D17—41no—
341C22×D17C2×C22⋊C414yes—
342C22×D17C2×C4⋊C414yes—
343C22×D17C2×C4⋊C414yescomplemented
344C22×D17#11714yes—
345C22×D17#12114yes—
346C22×D17#12114yes—
347C22×D17C22⋊Q814yes—
348C22×D17C22⋊Q814yes—
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—22no—
357C2×C4×C17—22no—
358C2×C4×C17—24no—
359C2×C4×C17—24no—
360C2×C4×C17—24no—
361C2×C4×C17—42no—
362C2×C4×C17—42no—
363C2×C4×C17—41no—
364C2×C4×C17—41no—
365C2×C4×C17—41no—
366C2×C4×C17—41no—
367C2×C4×C17—42no—
368C2×C4×C17—42no—
369C2×C4×C17—42no—
370C2×C4×C17—42no—
371C2×C4×C17—42no—
372C2×C4×C17—42no—
373C2×C4×C17—42no—
374C2×C4×C17—42no—
375C2×C4×C17—42no—
376C2×C4×C17C2×C22⋊C414yes—
377C2×C4×C17C2×C4⋊C414yescomplemented
378C2×C4×C17C4×D414yes—
379C2×C4×C17C4×D414yes—
380C2×C4×C17#12014yes—
381C2×C4×C17#12114yes—
382C2×C4×C17#12114yes—
383C2×C4×C17#12314yes—
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—24no—
394C2×Dic17—24no—
395C2×Dic17—24no—
396C2×Dic17—41no—
397C2×Dic17—42no—
398C2×Dic17—41no—
399C2×Dic17—41no—
400C2×Dic17—41no—
401C2×Dic17—42no—
402C2×Dic17—42no—
403C2×Dic17—42no—
404C2×Dic17—42no—
405C2×Dic17—42no—
406C2×Dic17—42no—
407C2×Dic17—42no—
408C2×Dic17—42no—
409C2×Dic17—42no—
410C2×Dic17—42no—
411C2×Dic17C2×C22⋊C414yes—
412D68—232no—
413C4×D17—232no—
414C4×D17—432no—
415C4×D17—416no—
416C22×C4×D4—171no—
417C23×C4⋊C4—171no—
418C2×#386—172no—
419C2×#380—171no—
420C2×#380—171no—
421C2×#380—171no—
422#1441—172no—
423#1439—172no—
424C4⋊#95—171no—
425C4⋊#95D1711yescharacteristic, complemented
426C22⋊#95—172no—
427C22×C17C22×C22⋊C411yescharacteristic
428C22×C17C22×C4⋊C411yescharacteristic
429C22×C17C2×#11711yescharacteristic
430C22×C17C2×C4×D411yescharacteristic
431C22×C17C2×C4×D411yescharacteristic
432C22×C17#52011yescharacteristic
433C22×C17#52011yescharacteristic
434C22×C17C2×#12011yescharacteristic
435C22×C17C2×#12111yescharacteristic
436C22×C17C2×#12111yescharacteristic
437C22×C17C2×#12111yescharacteristic
438C22×C17C2×#12111yescharacteristic
439C22×C17C2×C22⋊Q811yescharacteristic
440C22×C17C2×C22⋊Q811yescharacteristic
441C22×C17C2×#12311yescharacteristic
442C22×C17#53511yescharacteristic
443C22×C17#53611yescharacteristic
444C22×C17#53711yescharacteristic
445C22×C17#53711yescharacteristic
446C22×C17D4211yescharacteristic
447C22×C17D4211yescharacteristic
448C22×C17#54611yescharacteristic
449C22×C17#54611yescharacteristic
450C22×C17#54711yescharacteristic
451C22×C17#54711yescharacteristic
452C22×C17#54811yescharacteristic
453C22×C17#54811yescharacteristic
454C22×C17D4×Q811yescharacteristic
455C22×C17D4×Q811yescharacteristic
456C22×C17#55211yescharacteristic
457C22×C17#55211yescharacteristic
458C22×C17#55311yescharacteristic
459C22×C17#55311yescharacteristic
460C22×C17#55411yescharacteristic
461C22×C17#55411yescharacteristic
462C2×D17—24no—
463C2×D17—24no—
464C2×D17—24no—
465C2×D17—24no—
466C2×D17—24no—
467C2×D17—24no—
468C2×D17—24no—
469C2×D17—24no—
470C2×D17—24no—
471C2×D17—24no—
472C2×D17—24no—
473C2×D17—24no—
474C2×D17—24no—
475C2×D17—24no—
476C2×D17—24no—
477C2×D17—24no—
478C2×D17—24no—
479C2×D17—42no—
480C2×D17—42no—
481C2×D17—42no—
482C2×D17—42no—
483C2×D17—42no—
484C2×D17—42no—
485C2×D17—42no—
486C2×D17—42no—
487C2×D17—42no—
488C2×D17—42no—
489C2×D17—42no—
490C2×D17—42no—
491C2×D17#38018yescomplemented
492C4×C17—24no—
493C4×C17—42no—
494C4×C17—44no—
495C4×C17—82no—
496C4×C17#38618yescomplemented
497Dic17—24no—
498Dic17—44no—
499Dic17—42no—
500Dic17—82no—
501C23×D4—171no—
502C24×C4—171no—
503C24×C4—171no—
504C24×C4—172no—
505C2×C4×D4—178no—
506C2×C4×D4—344no—
507C2×C4×D4—344no—
508C22×C4⋊C4—171no—
509C22×C4⋊C4—171no—
510C22×C4⋊C4—172no—
511C22×C4⋊C4—171no—
512C22×C4⋊C4—344no—
513C22×C4⋊C4—344no—
514C22×C4⋊C4—344no—
515C22×C4⋊C4C2×D1711yescharacteristic
516C22×C4⋊C4C2×D1711yescharacteristic
517C22×C22⋊C4—171no—
518C22×C22⋊C4—171no—
519C22×C22⋊C4—172no—
520C22×C22⋊C4—172no—
521C22×C22⋊C4—172no—
522C22×C42C2×D1711yescharacteristic
523#386—348no—
524#380—344no—
525#380—344no—
526#380—344no—
527C2×#95—172no—
528C2×#95—172no—
529C2×#95—172no—
530C2×#95—172no—
531C2×#95—172no—
532C2×#95C2×D1712yes—
533C2×#95C2×D1712yes—
534C2×C17C2×#38011yescharacteristic
535C2×C17C2×#38611yescharacteristic
536C2×C17#231111yescharacteristic
537C2×C17D4×C4⋊C411yescharacteristic
538C2×C17D4×C4⋊C411yescharacteristic
539C2×C17#235211yescharacteristic
540C2×C17#235211yescharacteristic
541C2×C17#240811yescharacteristic
542C2×C17#240911yescharacteristic
543C2×C17#241611yescharacteristic
544C2×C17#241611yescharacteristic
545C2×C17#241711yescharacteristic
546C2×C17#241711yescharacteristic
547C2×C17#248611yescharacteristic
548C2×C17#248711yescharacteristic
549D17—28no—
550D17—44no—
551C25—171no—
552C25—171no—
553C22×D4—174no—
554C22×D4—174no—
555C22×D4—174no—
556C22×D4—342no—
557C22×D4—342no—
558C22×D4—342no—
559C22×D4—342no—
560C23×C4—171no—
561C23×C4—174no—
562C23×C4—174no—
563C23×C4—174no—
564C23×C4—172no—
565C23×C4—171no—
566C23×C4—174no—
567C23×C4—172no—
568C23×C4—344no—
569C23×C4—344no—
570C23×C4—344no—
571C23×C4—344no—
572C23×C4—342no—
573C23×C4—342no—
574C23×C4—342no—
575C23×C4—342no—
576C23×C4—344no—
577C23×C4—342no—
578C23×C4—342no—
579C23×C4—342no—
580C23×C4—342no—
581C23×C4—342no—
582C23×C4—342no—
583C23×C4—682no—
584C23×C4—682no—
585C23×C4C22×D1712yes—
586C23×C4C22×D1711yescharacteristic
587C23×C4C22×D1712yes—
588C23×C4C22×D1711yescharacteristic
589C23×C4C22×D1711yescharacteristic
590C4×D4—3432no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—174no—
597C2×C4⋊C4—174no—
598C2×C4⋊C4—3432no—
599C2×C4⋊C4—344no—
600C2×C4⋊C4—344no—
601C2×C4⋊C4—342no—
602C2×C4⋊C4—342no—
603C2×C4⋊C4—344no—
604C2×C4⋊C4—342no—
605C2×C4⋊C4—342no—
606C2×C4⋊C4—342no—
607C2×C4⋊C4—342no—
608C2×C4⋊C4—342no—
609C2×C4⋊C4D6814yescomplemented
610C2×C22⋊C4—174no—
611C2×C22⋊C4—174no—
612C2×C22⋊C4—342no—
613C2×C22⋊C4—342no—
614C2×C22⋊C4—342no—
615C2×C22⋊C4—342no—
616C2×C22⋊C4—344no—
617C2×C22⋊C4—344no—
618C2×C22⋊C4—344no—
619C2×C22⋊C4—344no—
620C2×C22⋊C4—344no—
621C2×C22⋊C4—344no—
622C2×C22⋊C4—344no—
623C2×C22⋊C4—682no—
624C2×C22⋊C4—682no—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42C4×D1714yescomplemented
628#95—24no—
629#95—42no—
630#95—344no—
631#95—344no—
632#95—344no—
633#95—344no—
634#95—682no—
635C17#1387211yescharacteristic, complemented, Sylow
636C24—172no—
637C24—172no—
638C24—172no—
639C24—172no—
640C24—172no—
641C24—172no—
642C24—172no—
643C24—172no—
644C24—172no—
645C24—172no—
646C24—341no—
647C24—341no—
648C24—341no—
649C24—341no—
650C24—341no—
651C24—341no—
652C24—341no—
653C24—341no—
654C24—341no—
655C24—341no—
656C24—341no—
657C24—341no—
658C24—341no—
659C24—341no—
660C24—341no—
661C24—341no—
662C24—341no—
663C24—341no—
664C24—341no—
665C24—341no—
666C24C23×D1711yescharacteristic
667C2×D4—1716no—
668C2×D4—348no—
669C2×D4—348no—
670C2×D4—348no—
671C2×D4—348no—
672C2×D4—348no—
673C2×D4—348no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—172no—
698C22×C4—172no—
699C22×C4—172no—
700C22×C4—1716no—
701C22×C4—172no—
702C22×C4—174no—
703C22×C4—3416no—
704C22×C4—341no—
705C22×C4—341no—
706C22×C4—341no—
707C22×C4—341no—
708C22×C4—348no—
709C22×C4—348no—
710C22×C4—348no—
711C22×C4—348no—
712C22×C4—348no—
713C22×C4—348no—
714C22×C4—341no—
715C22×C4—342no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—342no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—342no—
722C22×C4—342no—
723C22×C4—341no—
724C22×C4—342no—
725C22×C4—342no—
726C22×C4—348no—
727C22×C4—348no—
728C22×C4—348no—
729C22×C4—342no—
730C22×C4—342no—
731C22×C4—342no—
732C22×C4—342no—
733C22×C4—342no—
734C22×C4—342no—
735C22×C4—342no—
736C22×C4—688no—
737C22×C4—688no—
738C22×C4—688no—
739C22×C4—688no—
740C22×C4—688no—
741C22×C4—688no—
742C22×C4—684no—
743C22×C4—684no—
744C22×C4—684no—
745C22×C4—684no—
746C22×C4C2×C4×D1712yes—
747C22×C4C2×C4×D1712yes—
748C22×C4C2×C4×D1712yes—
749C22×C4C2×D6814yes—
750C22×C4C2×D6812yes—
751C22×C4#6325212yes—
752C22×C4D4×D1712yes—
753C22×C4D4×D1712yes—
754C22×C4D4×D1712yes—
755C22×C4D4×D1712yes—
756C22×C4Q8×D1712yes—
757C22×C4#6325612yes—
758C4⋊C4—28no—
759C4⋊C4—44no—
760C4⋊C4—348no—
761C4⋊C4—3416no—
762C4⋊C4—348no—
763C4⋊C4—684no—
764C22⋊C4—348no—
765C22⋊C4—348no—
766C22⋊C4—688no—
767C22⋊C4—688no—
768C22⋊C4—688no—
769C42—28no—
770C23—174no—
771C23—174no—
772C23—174no—
773C23—174no—
774C23—174no—
775C23—174no—
776C23—174no—
777C23—174no—
778C23—342no—
779C23—342no—
780C23—342no—
781C23—342no—
782C23—342no—
783C23—342no—
784C23—342no—
785C23—342no—
786C23—342no—
787C23—342no—
788C23—342no—
789C23—342no—
790C23—342no—
791C23—342no—
792C23—342no—
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—342no—
812C23—342no—
813C23—342no—
814C23—342no—
815C23—342no—
816C23—342no—
817C23—342no—
818C23—342no—
819C23—342no—
820C23—342no—
821C23—342no—
822C23—342no—
823C23—342no—
824C23—681no—
825C23—681no—
826C23—681no—
827C23—681no—
828C23—681no—
829C23—681no—
830C23—681no—
831C23—681no—
832C23—681no—
833C23—681no—
834C23—681no—
835C23—681no—
836C23—681no—
837C23—681no—
838C23—681no—
839C23—681no—
840C23C22×C4×D1711yescharacteristic
841C23C22×D6811yescharacteristic
842C23C2×#6325211yescharacteristic
843C23C2×D4×D1711yescharacteristic
844C23C2×D4×D1711yescharacteristic
845C23C2×D4×D1711yescharacteristic
846C23C2×D4×D1711yescharacteristic
847C23#1058769111yescharacteristic
848C23C2×Q8×D1711yescharacteristic
849C23C2×#6325611yescharacteristic
850C23#1058769411yescharacteristic
851C23#41×D1711yescharacteristic
852C23#41×D1711yescharacteristic
853C23#1058769611yescharacteristic
854C23#1058769711yescharacteristic
855D4—3432no—
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—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—174no—
884C2×C4—342no—
885C2×C4—342no—
886C2×C4—342no—
887C2×C4—342no—
888C2×C4—342no—
889C2×C4—342no—
890C2×C4—3432no—
891C2×C4—342no—
892C2×C4—342no—
893C2×C4—342no—
894C2×C4—344no—
895C2×C4—344no—
896C2×C4—344no—
897C2×C4—6832no—
898C2×C4—681no—
899C2×C4—682no—
900C2×C4—681no—
901C2×C4—681no—
902C2×C4—681no—
903C2×C4—682no—
904C2×C4—682no—
905C2×C4—682no—
906C2×C4—6816no—
907C2×C4—682no—
908C2×C4—682no—
909C2×C4—682no—
910C2×C4—682no—
911C2×C4—682no—
912C2×C4—682no—
913C2×C4—682no—
914C2×C4C4×D6814yes—
915C2×C4C22⋊C4×D1714yes—
916C2×C4#1058756814yes—
917C2×C4#1058757014yes—
918C2×C4C4⋊C4×D1714yescomplemented
919C2×C4#1058757914yes—
920C2×C4#1058758014yes—
921C2×C4#1058758114yes—
922C22—178no—
923C22—344no—
924C22—344no—
925C22—344no—
926C22—344no—
927C22—344no—
928C22—344no—
929C22—344no—
930C22—344no—
931C22—344no—
932C22—344no—
933C22—344no—
934C22—344no—
935C22—344no—
936C22—344no—
937C22—344no—
938C22—344no—
939C22—344no—
940C22—682no—
941C22—682no—
942C22—682no—
943C22—682no—
944C22—682no—
945C22—682no—
946C22—682no—
947C22—682no—
948C22—682no—
949C22—682no—
950C22—682no—
951C22—682no—
952C22C2×C22⋊C4×D1711yescharacteristic
953C22C2×C4⋊C4×D1711yescharacteristic
954C22#117×D1711yescharacteristic
955C22C2×#1058757911yescharacteristic
956C22C2×C4×D6811yescharacteristic
957C22#1176328911yescharacteristic
958C22#1176329011yescharacteristic
959C22C2×#1058756811yescharacteristic
960C22#121×D1711yescharacteristic
961C22#121×D1711yescharacteristic
962C22C2×#1058757011yescharacteristic
963C22C2×#1058758111yescharacteristic
964C22C22⋊Q8×D1711yescharacteristic
965C22C22⋊Q8×D1711yescharacteristic
966C22C2×#1058758011yescharacteristic
967C22#1176337511yescharacteristic
968C22#1176338211yescharacteristic
969C22#1176338811yescharacteristic
970C22#1176338911yescharacteristic
971C22#1176344411yescharacteristic
972C22D4×D6811yescharacteristic
973C22#1176345211yescharacteristic
974C22#1176345411yescharacteristic
975C22#1176346211yescharacteristic
976C22#1176346411yescharacteristic
977C22#1176346711yescharacteristic
978C22#1176347111yescharacteristic
979C22#1176347411yescharacteristic
980C22Q8×D6811yescharacteristic
981C22#1176349711yescharacteristic
982C22#1176350011yescharacteristic
983C22#1176350911yescharacteristic
984C22#1176351211yescharacteristic
985C22#1176351911yescharacteristic
986C22#1176352011yescharacteristic
987C4—24no—
988C4—44no—
989C4—42no—
990C4—82no—
991C4—344no—
992C4—684no—
993C4—682no—
994C4—1362no—
995C4#1176268718yescomplemented
996C2—348no—
997C2—684no—
998C2D17×#38011yescharacteristic
999C2C2×#1176268711yescharacteristic
1000C2#1453137311yescharacteristic
1001C2#1453168411yescharacteristic
1002C2C4⋊C4×D6811yescharacteristic
1003C2#1453171011yescharacteristic
1004C2#1453171611yescharacteristic
1005C2#1453213811yescharacteristic
1006C2#1453214711yescharacteristic
1007C2#1453222211yescharacteristic
1008C2#1453222711yescharacteristic
1009C2#1453223311yescharacteristic
1010C2#1453223811yescharacteristic
1011C2#1453309011yescharacteristic
1012C2#1453309911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C4⋊#95C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenterC4⋊#95D17
hypocenterC17#13872
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D17C2semidirect
4. C2×#11762666C2semidirect
5. C2×#11762666C2semidirect
6. C2×#11762666C2semidirect
7. #14527036C2semidirect
8. #14527028C2semidirect
9. #14527014C2semidirect
10. #14527005C2semidirect
11. C17×C4⋊#95C2semidirect
18. C2×C4×D68C4semidirect
81. C22×C4×D17C2×C4semidirect
89. C2×C4⋊C4×C17D4semidirect
92. C2×C42×C17C2×C4semidirect
107. C2×#63227C2×C4semidirect
115. C2×C4⋊Dic17C2×C4semidirect
116. C2×C4⋊Dic17D4semidirect
229. C2×D68C4⋊C4semidirect
250. C2×C4×D17C22⋊C4semidirect
343. C22×D17C2×C4⋊C4semidirect
377. C2×C4×C17C2×C4⋊C4semidirect
425. C4⋊#95D17semidirect
491. C2×D17#380semidirect
496. C4×C17#386semidirect
609. C2×C4⋊C4D68semidirect
627. C2×C42C4×D17semidirect
635. C17#13872semidirect
918. C2×C4C4⋊C4×D17semidirect
995. C4#11762687semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D682
C22×C4⋊C4×D172
C2×#117626872
C2×#117626662
#145270362
#145270282
#145270142
#145270052
C17×C4⋊#952
#1387217