Finite Group Databasebeta

← #16955671

Subgroups — #16955671

Order 4352.

1826 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×#11762684C211yesmaximal, characteristic
3C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic17C211yesmaximal, characteristic
5#14527021C211yesmaximal, characteristic
6#14527021C211yesmaximal, characteristic
7#14527018C211yesmaximal, characteristic, complemented
8#14527018C211yesmaximal, characteristic, complemented
9#14527018C211yesmaximal, characteristic, complemented
10#14527016C211yesmaximal, characteristic, complemented
11#14527014C211yesmaximal, characteristic, complemented
12#14527009C211yesmaximal, characteristic, complemented
13#14527006C211yesmaximal, characteristic
14C4×#10587502C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C4×Dic17C2211yescharacteristic
24C22×C4×Dic17C2211yescharacteristic
25C22×C4×Dic17C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28#11762702C418yescomplemented
29#11762684C418yescomplemented
30C4⋊C4×Dic17—24no—
31C22⋊C4×Dic17—24no—
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×#388C418yescomplemented
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—41no—
66C23×Dic17—41no—
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×C17C2×C414yescomplemented
81C2×C22⋊C4×C17—22no—
82C2×C22⋊C4×C17—22no—
83C2×C22⋊C4×C17—41no—
84C2×C22⋊C4×C17—41no—
85C2×C22⋊C4×C17C2×C414yes—
86C2×C22⋊C4×C17C2×C414yes—
87C2×C22⋊C4×C17C2×C414yes—
88C2×C22⋊C4×C17C2×C414yes—
89C2×C22⋊C4×C17C2×C414yes—
90C2×C42×C17—41no—
91C2×C42×C17—41no—
92C2×C42×C17C2×C414yescomplemented
93C2×C22⋊Dic17—22no—
94C2×C22⋊Dic17—22no—
95C2×C22⋊Dic17—41no—
96C2×C22⋊Dic17—41no—
97C2×C22⋊Dic17—41no—
98C2×C22⋊Dic17—41no—
99C2×C22⋊Dic17C2×C414yes—
100C2×C22⋊Dic17C2×C414yes—
101C2×C22⋊Dic17C2×C414yes—
102C2×C4⋊Dic17—22no—
103C2×C4⋊Dic17—22no—
104C2×C4⋊Dic17—41no—
105C2×C4⋊Dic17—41no—
106C2×C4⋊Dic17—41no—
107C2×C4⋊Dic17—41no—
108C2×C4⋊Dic17C2×C414yes—
109C2×C4⋊Dic17C2×C414yes—
110C2×C4⋊Dic17C2×C414yescomplemented
111C2×C4×Dic17—22no—
112C2×C4×Dic17—22no—
113C2×C4×Dic17—22no—
114C2×C4×Dic17—22no—
115C2×C4×Dic17—22no—
116C2×C4×Dic17—41no—
117C2×C4×Dic17—41no—
118C2×C4×Dic17—41no—
119C2×C4×Dic17—41no—
120C2×C4×Dic17—41no—
121C2×C4×Dic17—41no—
122C2×C4×Dic17—41no—
123C2×C4×Dic17—41no—
124C2×C4×Dic17C2×C414yescomplemented
125C2×C4×Dic17D414yes—
126C17×#95C2×C414yescomplemented
127C17×#95C2×C414yescomplemented
128#10587502—22no—
129#10587502—22no—
130#10587502—22no—
131#10587502—22no—
132#10587502—22no—
133#10587502—22no—
134#10587502—41no—
135#10587502—41no—
136#10587502—41no—
137#10587502—41no—
138#10587502—41no—
139#10587502—41no—
140#10587502C2×C414yes—
141#10587502C2×C414yes—
142#10587502C2×C414yescomplemented
143#10587502C2×C414yescomplemented
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×C17C22×C412yes—
158C24×C17C22×C412yes—
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×C17C22×C412yes—
191C22×C4×C17C22×C412yes—
192C22×C4×C17C22×C412yes—
193C22×C4×C17C22×C412yes—
194C22×C4×C17C22×C412yes—
195C22×C4×C17C22×C412yes—
196C22×C4×C17C22×C412yes—
197C22×C4×C17C22×C412yes—
198C22×C4×C17C22×C412yes—
199C22×C4×C17C22×C412yes—
200C22×C4×C17C2×D412yes—
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—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—28no—
247C22×Dic17—44no—
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×Dic17C22×C412yes—
258C22×Dic17C22×C412yes—
259C22×Dic17C22×C412yes—
260C22×Dic17C22×C412yes—
261C22×Dic17C2×D412yes—
262C22×Dic17C2×D412yes—
263C22×Dic17#4112yes—
264C22×Dic17#4112yes—
265C4⋊C4×C17—28no—
266C22⋊C4×C17—28no—
267C22⋊C4×C17—44no—
268C22⋊C4×C17C42116yescomplemented
269C42×C17—44no—
270C22⋊Dic17—28no—
271C22⋊Dic17—44no—
272C22⋊Dic17—44no—
273C4⋊Dic17—28no—
274C4⋊Dic17—44no—
275C4⋊Dic17—44no—
276C4×Dic17—28no—
277C4×Dic17—44no—
278C4×Dic17—44no—
279C4×Dic17—44no—
280C4×Dic17—44no—
281#13789—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×C4214yes—
317C23×C17C23×C411yescharacteristic
318C23×C17C23×C411yescharacteristic
319C23×C17C23×C411yescharacteristic
320C23×C17C22×D411yescharacteristic
321C23×C17C2×#4111yescharacteristic
322C23×C17C2×#4111yescharacteristic
323C23×C17C2×#4111yescharacteristic
324C23×C17H(5,𝔽2)11yescharacteristic
325C23×C17H(5,𝔽2)11yescharacteristic
326C23×C17H(5,𝔽2)11yescharacteristic
327C23×C17H(5,𝔽2)11yescharacteristic
328C23×C17H(5,𝔽2)11yescharacteristic
329C23×C172−1+411yescharacteristic
330C23×C172−1+411yescharacteristic
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—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—22no—
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×C17C2×C4214yes—
372C2×C4×C17C2×C4214yes—
373C2×C4×C17C4×D414yes—
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×Dic17—41no—
428C2×Dic17—41no—
429C2×Dic17C4×D414yes—
430C2×Dic17C4×D414yes—
431C2×#388—171no—
432C2×#388D1711yescharacteristic
433C2×#385—171no—
434C2×C4×C4⋊C4—171no—
435C2×C4×C22⋊C4—171no—
436#1437—171no—
437#1437—171no—
438#1436—171no—
439#1436—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×C4211yescharacteristic
462C22×C17C2×C4×D411yescharacteristic
463C22×C17C2×C4×D411yescharacteristic
464C22×C17C2×C4×D411yescharacteristic
465C22×C17C4×#4111yescharacteristic
466C22×C17C4×#4111yescharacteristic
467C22×C17C4×#4111yescharacteristic
468C22×C17#51811yescharacteristic
469C22×C17#51811yescharacteristic
470C22×C17#51811yescharacteristic
471C22×C17#51811yescharacteristic
472C22×C17#51911yescharacteristic
473C22×C17#52011yescharacteristic
474C22×C17#52011yescharacteristic
475C22×C17#52011yescharacteristic
476C22×C17#52011yescharacteristic
477C22×C17#52011yescharacteristic
478C22×C17#52011yescharacteristic
479C22×C17#52011yescharacteristic
480C22×C17#53411yescharacteristic
481C22×C17#53511yescharacteristic
482C22×C17#53611yescharacteristic
483C22×C17#53711yescharacteristic
484C22×C17#53811yescharacteristic
485C22×C17#53811yescharacteristic
486C22×C17#53811yescharacteristic
487C22×C17#53911yescharacteristic
488C22×C17#53911yescharacteristic
489C22×C17#53911yescharacteristic
490C22×C17#54011yescharacteristic
491C22×C17#54111yescharacteristic
492C22×C17#54211yescharacteristic
493C22×C17#54211yescharacteristic
494C22×C17#54211yescharacteristic
495C22×C17#54211yescharacteristic
496C4×C17—24no—
497C4×C17—24no—
498C4×C17—24no—
499C4×C17—42no—
500C4×C17—42no—
501C4×C17—42no—
502Dic17—24no—
503Dic17—24no—
504Dic17—42no—
505Dic17—42no—
506Dic17—42no—
507Dic17—42no—
508Dic17—42no—
509Dic17—42no—
510C24×C4—171no—
511C22×C4⋊C4—171no—
512C22×C4⋊C4—171no—
513C22×C4⋊C4—171no—
514C22×C4⋊C4C2×D1711yescharacteristic
515C22×C22⋊C4—171no—
516C22×C22⋊C4—171no—
517C22×C22⋊C4—171no—
518C22×C22⋊C4C2×D1711yescharacteristic
519C22×C22⋊C4C2×D1711yescharacteristic
520C22×C22⋊C4C2×D1711yescharacteristic
521C22×C42—171no—
522C22×C42—171no—
523C22×C42—171no—
524C22×C42—171no—
525C22×C42—171no—
526C22×C42C2×D1711yescharacteristic
527#388—178no—
528#388Dic1718yescomplemented
529#385—178no—
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×#95—171no—
547C2×#95—171no—
548C2×#95C2×D1711yescharacteristic
549C2×#95C2×D1711yescharacteristic
550C2×C17—44no—
551C2×C17C42×D411yescharacteristic
552C2×C17#227411yescharacteristic
553C2×C17#227511yescharacteristic
554C2×C17#232111yescharacteristic
555C2×C17#232211yescharacteristic
556C2×C17#232311yescharacteristic
557C2×C17#232411yescharacteristic
558C2×C17#232511yescharacteristic
559C2×C17#232611yescharacteristic
560C2×C17#233211yescharacteristic
561C2×C17#233411yescharacteristic
562C2×C17#233411yescharacteristic
563C2×C17#233511yescharacteristic
564C2×C17#233511yescharacteristic
565C2×C17#233711yescharacteristic
566C25C22×D1711yescharacteristic
567C23×C4—171no—
568C23×C4—171no—
569C23×C4—171no—
570C23×C4—171no—
571C23×C4—171no—
572C23×C4—171no—
573C23×C4—171no—
574C23×C4—171no—
575C23×C4—174no—
576C23×C4—342no—
577C23×C4—342no—
578C23×C4—681no—
579C23×C4—681no—
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—174no—
591C2×C4⋊C4—174no—
592C2×C4⋊C4—174no—
593C2×C4⋊C4—342no—
594C2×C4⋊C4—342no—
595C2×C4⋊C4—681no—
596C2×C4⋊C4—681no—
597C2×C4⋊C4—681no—
598C2×C4⋊C4—681no—
599C2×C4⋊C4C2×Dic1714yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—174no—
605C2×C22⋊C4—174no—
606C2×C22⋊C4—174no—
607C2×C22⋊C4—342no—
608C2×C22⋊C4—342no—
609C2×C22⋊C4—681no—
610C2×C22⋊C4—681no—
611C2×C22⋊C4—681no—
612C2×C22⋊C4—681no—
613C2×C22⋊C4C4×D1714yes—
614C2×C22⋊C4C4×D1714yes—
615C2×C22⋊C4C2×Dic1714yes—
616C2×C22⋊C4C2×Dic1714yes—
617C2×C22⋊C4C2×Dic1714yes—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42—174no—
621C2×C42—174no—
622C2×C42—342no—
623C2×C42—342no—
624C2×C42—342no—
625C2×C42—342no—
626C2×C42—342no—
627C2×C42—681no—
628C2×C42—681no—
629C2×C42—681no—
630C2×C42—681no—
631C2×C42—681no—
632C2×C42—681no—
633C2×C42—681no—
634C2×C42—681no—
635C2×C42C2×Dic1714yescomplemented
636#95—174no—
637#95—174no—
638#95—174no—
639#95—174no—
640#95—342no—
641#95—342no—
642#95—342no—
643#95—342no—
644#95—342no—
645#95—342no—
646#95—681no—
647#95—681no—
648#95—681no—
649#95—681no—
650#95—681no—
651#95—681no—
652#95C2×Dic1714yescomplemented
653#95C2×Dic1714yescomplemented
654C17#1378911yescharacteristic, 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—
668C24C2×C4×D1712yes—
669C24C22×Dic1712yes—
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—172no—
702C22×C4—172no—
703C22×C4—172no—
704C22×C4—172no—
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—348no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
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—684no—
759C22×C4—684no—
760C22×C4—684no—
761C22×C4—684no—
762C22×C4—684no—
763C22×C4—684no—
764C22×C4C2×C4×D1712yes—
765C22×C4C2×C4×D1712yes—
766C22×C4C2×C4×D1712yes—
767C22×C4C2×C4×D1712yes—
768C22×C4D4×D1712yes—
769C22×C4#6325412yes—
770C22×C4C22×Dic1712yes—
771C22×C4C22×Dic1712yes—
772C22×C4C22×Dic1712yes—
773C22×C4C22×Dic1712yes—
774C22×C4C22×Dic1712yes—
775C22×C4C22×Dic1712yes—
776C4⋊C4—28no—
777C4⋊C4—348no—
778C4⋊C4—684no—
779C4⋊C4—684no—
780C22⋊C4—28no—
781C22⋊C4—44no—
782C22⋊C4—348no—
783C22⋊C4—684no—
784C22⋊C4—684no—
785C22⋊C4C4×Dic17116yescomplemented
786C42—44no—
787C42—348no—
788C42—684no—
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—
826C23C2×C4×Dic1714yes—
827C23C22×C4×D1711yescharacteristic
828C23C22×C4×D1711yescharacteristic
829C23C2×D4×D1711yescharacteristic
830C23C2×#6325411yescharacteristic
831C23#1058769111yescharacteristic
832C23#1058769111yescharacteristic
833C23#41×D1711yescharacteristic
834C23#41×D1711yescharacteristic
835C23#1058769611yescharacteristic
836C23#1058769611yescharacteristic
837C23#1058769611yescharacteristic
838C23#1058769711yescharacteristic
839C23#1058769711yescharacteristic
840C23#1058769711yescharacteristic
841C23C23×Dic1711yescharacteristic
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—22no—
867C2×C4—22no—
868C2×C4—22no—
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—174no—
882C2×C4—174no—
883C2×C4—342no—
884C2×C4—342no—
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—342no—
913C2×C4—6816no—
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×C4C2×C4×Dic1714yes—
939C2×C4C2×C4×Dic1714yes—
940C2×C4D4×Dic1714yes—
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×C4×Dic1711yescharacteristic
957C22C4×D4×D1711yescharacteristic
958C22C4×D4×D1711yescharacteristic
959C22C2×D4×Dic1711yescharacteristic
960C22C4×#6325411yescharacteristic
961C22C4×#6325411yescharacteristic
962C22#41×Dic1711yescharacteristic
963C22#1176328111yescharacteristic
964C22#1176328111yescharacteristic
965C22#1176328311yescharacteristic
966C22#1176328411yescharacteristic
967C22#1176328611yescharacteristic
968C22#1176328811yescharacteristic
969C22#1176328811yescharacteristic
970C22#1176328911yescharacteristic
971C22#1176328911yescharacteristic
972C22#1176329211yescharacteristic
973C22#1176329211yescharacteristic
974C22#1176329211yescharacteristic
975C22#1176336711yescharacteristic
976C22#1176337711yescharacteristic
977C22#1176337911yescharacteristic
978C22#1176338611yescharacteristic
979C22#1176339511yescharacteristic
980C22#1176339611yescharacteristic
981C22#1176339811yescharacteristic
982C22#1176340011yescharacteristic
983C22#1176340211yescharacteristic
984C22#1176340411yescharacteristic
985C22#1176341111yescharacteristic
986C22#1176341611yescharacteristic
987C22#1176342511yescharacteristic
988C22#1176342711yescharacteristic
989C22#1176342811yescharacteristic
990C22#1176342811yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—344no—
998C4—344no—
999C4—682no—
1000C4—682no—
1001C4—682no—
1002C4—682no—
1003C4—682no—
1004C4—682no—
1005C2—44no—
1006C2C4×D4×Dic1711yescharacteristic
1007C2#1453114011yescharacteristic
1008C2#1453114511yescharacteristic
1009C2#1453143711yescharacteristic
1010C2#1453145411yescharacteristic
1011C2#1453145911yescharacteristic
1012C2#1453147211yescharacteristic
1013C2#1453148911yescharacteristic
1014C2#1453149711yescharacteristic
1015C2#1453153411yescharacteristic
1016C2#1453155611yescharacteristic
1017C2#1453156311yescharacteristic
1018C2#1453156711yescharacteristic
1019C2#1453157811yescharacteristic
1020C2#1453159111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#388D17
hypocenterC17#13789
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic17C2semidirect
7. #14527018C2semidirect
8. #14527018C2semidirect
9. #14527018C2semidirect
10. #14527016C2semidirect
11. #14527014C2semidirect
12. #14527009C2semidirect
14. C4×#10587502C2semidirect
28. #11762702C4semidirect
29. #11762684C4semidirect
53. C17×#388C4semidirect
80. C2×C4⋊C4×C17C2×C4semidirect
92. C2×C42×C17C2×C4semidirect
110. C2×C4⋊Dic17C2×C4semidirect
124. C2×C4×Dic17C2×C4semidirect
126. C17×#95C2×C4semidirect
127. C17×#95C2×C4semidirect
142. #10587502C2×C4semidirect
143. #10587502C2×C4semidirect
268. C22⋊C4×C17C42semidirect
528. #388Dic17semidirect
599. C2×C4⋊C4C2×Dic17semidirect
635. C2×C42C2×Dic17semidirect
652. #95C2×Dic17semidirect
653. #95C2×Dic17semidirect
654. C17#13789semidirect
785. C22⋊C4C4×Dic17semidirect

Maximal subgroups

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

subgroupindex
C2×#117627022
C2×#117626842
C2×C4⋊C4×Dic172
C2×C22⋊C4×Dic172
#145270212
#145270182
#145270162
#145270142
#145270092
#145270062
C4×#105875022
C2×C17×#3882
#1378917