Finite Group Databasebeta

← #16957460

Subgroups — #16957460

Order 4352.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762716C211yesmaximal, characteristic, complemented
2C2×#11762716C211yesmaximal, characteristic, complemented
3C2×#11762708C211yesmaximal, characteristic, complemented
4C2×#11762669C211yesmaximal, characteristic
5C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic17C211yesmaximal, characteristic
7#14527052C212yesmaximal, complemented
8#14527029C212yesmaximal
9#14527021C212yesmaximal
10#14527013C212yesmaximal, complemented
11C22×C17×C22⋊Q8C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2212yes—
14C22×C4⋊Dic17C2211yescharacteristic
15C22×C22⋊Dic17C2211yescharacteristic
16C22×C22⋊Dic17C2212yes—
17C22×C22⋊Dic17C2211yescharacteristic
18C22×C4×Dic17C2211yescharacteristic
19C22×C4×Dic17C2212yes—
20C22×C4×Dic17C2211yescharacteristic
21#11762716—24no—
22#11762716—24no—
23#11762708—24no—
24#11762669—24no—
25C4⋊C4×Dic17—24no—
26C4×C22⋊Dic17—24no—
27C2×#10587502C2211yescharacteristic
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C23×Q8×C17C2211yescharacteristic
37C24×C4×C17C2211yescharacteristic
38C2×C17×C22⋊Q8—24no—
39C2×C17×C22⋊Q8—24no—
40C2×C17×C22⋊Q8C418yescomplemented
41C22×C4⋊C4×C17C2212yes—
42C22×C4⋊C4×C17C2211yescharacteristic
43C22×C22⋊C4×C17C2212yes—
44C25×C17C2311yescharacteristic
45C22×Q8×C17—22no—
46C22×Q8×C17—22no—
47C22×Q8×C17—22no—
48C22×Q8×C17—22no—
49C22×Q8×C17—22no—
50C22×Q8×C17—22no—
51C22×Q8×C17C2×C414yes—
52C23×C4×C17—22no—
53C23×C4×C17—22no—
54C23×C4×C17—22no—
55C23×C4×C17—22no—
56C23×C4×C17—22no—
57C23×C4×C17—22no—
58C23×C4×C17C2×C414yes—
59C23×C4×C17C2312yes—
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2312yes—
62C23×C4×C17C2311yescharacteristic
63C23×Dic17C2312yes—
64C23×Dic17C2312yes—
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C17×C22⋊Q8—232no—
70C2×C4⋊C4×C17—24no—
71C2×C4⋊C4×C17—24no—
72C2×C4⋊C4×C17C2×C418yes—
73C2×C4⋊C4×C17C2×C414yes—
74C2×C4⋊C4×C17D414yes—
75C2×C4⋊C4×C17D414yes—
76C2×C22⋊C4×C17—24no—
77C2×C22⋊C4×C17—24no—
78C2×C22⋊C4×C17C2×C418yes—
79C2×C22⋊Dic17—22no—
80C2×C22⋊Dic17—22no—
81C2×C22⋊Dic17—22no—
82C2×C22⋊Dic17—22no—
83C2×C22⋊Dic17—22no—
84C2×C22⋊Dic17—24no—
85C2×C22⋊Dic17—24no—
86C2×C22⋊Dic17—42no—
87C2×C22⋊Dic17Q814yescomplemented
88C2×C4⋊Dic17—22no—
89C2×C4⋊Dic17—24no—
90C2×C4⋊Dic17—22no—
91C2×C4⋊Dic17—22no—
92C2×C4⋊Dic17—22no—
93C2×C4⋊Dic17—22no—
94C2×C4⋊Dic17—24no—
95C2×C4⋊Dic17—42no—
96C2×C4⋊Dic17D414yes—
97C2×C4×Dic17—22no—
98C2×C4×Dic17—22no—
99C2×C4×Dic17—22no—
100C2×C4×Dic17—22no—
101C2×C4×Dic17—24no—
102C2×C4×Dic17—22no—
103C2×C4×Dic17—24no—
104C2×C4×Dic17—42no—
105C2×C4×Dic17D414yes—
106#10587502—24no—
107#10587502—24no—
108#10587502—24no—
109#10587502—24no—
110#10587502—24no—
111#10587502—24no—
112#10587502—22no—
113#10587502—22no—
114#10587502—24no—
115C24×C17—21no—
116C24×C17—21no—
117C24×C17—21no—
118C24×C17—21no—
119C24×C17—21no—
120C24×C17—21no—
121C24×C17—21no—
122C24×C17—21no—
123C24×C17—21no—
124C24×C17—21no—
125C24×C17—21no—
126C24×C17—21no—
127C24×C17C22×C412yes—
128C24×C17C2×Q812yes—
129C24×C17#4112yes—
130C24×C17C2411yescharacteristic
131C2×Q8×C17—28no—
132C2×Q8×C17—28no—
133C2×Q8×C17—28no—
134C2×Q8×C17—44no—
135C2×Q8×C17—44no—
136C2×Q8×C17—44no—
137C2×Q8×C17—44no—
138C22×C4×C17—22no—
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—22no—
142C22×C4×C17—21no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—22no—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—22no—
153C22×C4×C17—22no—
154C22×C4×C17—28no—
155C22×C4×C17—28no—
156C22×C4×C17—28no—
157C22×C4×C17—44no—
158C22×C4×C17—44no—
159C22×C4×C17—44no—
160C22×C4×C17—44no—
161C22×C4×C17C22×C412yes—
162C22×C4×C17C22×C414yes—
163C22×C4×C17C22×C414yes—
164C22×C4×C17C22×C412yes—
165C22×C4×C17C2×D412yes—
166C22×C4×C17C2×D412yes—
167C22×C4×C17C2×D414yes—
168C22×C4×C17C2×D414yes—
169C22×C4×C17C2×D412yes—
170C22×C4×C17C2×D412yes—
171C22×C4×C17#4112yes—
172C22×C4×C17#4112yes—
173C22×Dic17—21no—
174C22×Dic17—21no—
175C22×Dic17—21no—
176C22×Dic17—21no—
177C22×Dic17—21no—
178C22×Dic17—21no—
179C22×Dic17—21no—
180C22×Dic17—21no—
181C22×Dic17—22no—
182C22×Dic17—21no—
183C22×Dic17—21no—
184C22×Dic17—21no—
185C22×Dic17—21no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—21no—
189C22×Dic17—21no—
190C22×Dic17—22no—
191C22×Dic17—21no—
192C22×Dic17—21no—
193C22×Dic17—22no—
194C22×Dic17—21no—
195C22×Dic17—21no—
196C22×Dic17—22no—
197C22×Dic17—21no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—22no—
202C22×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17—22no—
205C22×Dic17—22no—
206C22×Dic17—22no—
207C22×Dic17—22no—
208C22×Dic17C2×D412yes—
209C22×Dic17C2×D414yes—
210C22×Dic17C2×D412yes—
211C22×Dic17C2×Q812yes—
212C22×Dic17C2×Q812yes—
213C22×Dic17#4112yes—
214C22×Dic17#4112yes—
215C4⋊C4×C17—216no—
216C4⋊C4×C17C22⋊C4116yescomplemented
217C22⋊C4×C17—216no—
218C22⋊Dic17—28no—
219C22⋊Dic17—28no—
220C22⋊Dic17—48no—
221C4⋊Dic17—28no—
222C4⋊Dic17—48no—
223C4⋊Dic17—44no—
224C4×Dic17—28no—
225C4×Dic17—48no—
226C4×Dic17—44no—
227#13997—171nomaximal, Sylow
228C23×C17—22no—
229C23×C17—22no—
230C23×C17—22no—
231C23×C17—22no—
232C23×C17—22no—
233C23×C17—22no—
234C23×C17—22no—
235C23×C17—22no—
236C23×C17—22no—
237C23×C17—22no—
238C23×C17—22no—
239C23×C17—22no—
240C23×C17—22no—
241C23×C17—22no—
242C23×C17—22no—
243C23×C17—22no—
244C23×C17—22no—
245C23×C17—22no—
246C23×C17—41no—
247C23×C17—41no—
248C23×C17—41no—
249C23×C17—41no—
250C23×C17—41no—
251C23×C17—41no—
252C23×C17—41no—
253C23×C17—41no—
254C23×C17—41no—
255C23×C17—41no—
256C23×C17—41no—
257C23×C17—41no—
258C23×C17—41no—
259C23×C17—41no—
260C23×C17—41no—
261C23×C17—41no—
262C23×C17C4×Q814yes—
263C23×C17C23×C411yescharacteristic
264C23×C17C22×D411yescharacteristic
265C23×C17C22×D411yescharacteristic
266C23×C17C22×D411yescharacteristic
267C23×C17C22×D411yescharacteristic
268C23×C17C22×Q811yescharacteristic
269C23×C17C2×#4111yescharacteristic
270C23×C17C2×#4111yescharacteristic
271C23×C17C2×#4111yescharacteristic
272C23×C17C2×#4111yescharacteristic
273C23×C17C2×#4111yescharacteristic
274C23×C17H(5,𝔽2)11yescharacteristic
275C23×C172−1+411yescharacteristic
276C23×C172−1+411yescharacteristic
277C23×C172−1+411yescharacteristic
278Q8×C17—416no—
279C2×C4×C17—24no—
280C2×C4×C17—24no—
281C2×C4×C17—24no—
282C2×C4×C17—24no—
283C2×C4×C17—24no—
284C2×C4×C17—24no—
285C2×C4×C17—24no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—24no—
290C2×C4×C17—24no—
291C2×C4×C17—41no—
292C2×C4×C17—41no—
293C2×C4×C17—42no—
294C2×C4×C17—42no—
295C2×C4×C17—41no—
296C2×C4×C17—42no—
297C2×C4×C17—41no—
298C2×C4×C17—42no—
299C2×C4×C17—416no—
300C2×C4×C17C2×C22⋊C418yes—
301C2×C4×C17C2×C22⋊C414yes—
302C2×C4×C17C4×D414yes—
303C2×C4×C17C4×D414yes—
304C2×C4×C17#12114yes—
305C2×C4×C17#12114yes—
306C2×C4×C17#12414yes—
307C2×C4×C17#12714yes—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—24no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—24no—
321C2×Dic17—22no—
322C2×Dic17—24no—
323C2×Dic17—22no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—42no—
327C2×Dic17—41no—
328C2×Dic17—41no—
329C2×Dic17—41no—
330C2×Dic17—41no—
331C2×Dic17—42no—
332C2×Dic17—41no—
333C2×Dic17—42no—
334C2×Dic17—41no—
335C2×Dic17—41no—
336C2×Dic17—41no—
337C2×Dic17—41no—
338C2×Dic17—42no—
339C2×Dic17—41no—
340C2×Dic17—41no—
341C2×Dic17—41no—
342C2×Dic17—42no—
343C2×Dic17—42no—
344C2×Dic17—42no—
345C2×Dic17—42no—
346C2×Dic17—42no—
347C2×Dic17—42no—
348C2×Dic17—42no—
349C2×Dic17C22⋊Q814yescomplemented
350C22×C22⋊Q8D1711yescharacteristic
351C2×#391—171no—
352C2×#391—171no—
353C2×#389—171no—
354C2×#380—171no—
355C2×C4×C4⋊C4—171no—
356C2×C4×C22⋊C4—171no—
357#1445—172no—
358#1439—172no—
359#1437—172no—
360C4⋊#95—172no—
361C22×C17—24no—
362C22×C17—24no—
363C22×C17—24no—
364C22×C17—42no—
365C22×C17—42no—
366C22×C17—42no—
367C22×C17—42no—
368C22×C17—42no—
369C22×C17—42no—
370C22×C17—42no—
371C22×C17—42no—
372C22×C17—42no—
373C22×C17—42no—
374C22×C17—42no—
375C22×C17—42no—
376C22×C17C22×C22⋊C411yescharacteristic
377C22×C17C2×C4×D411yescharacteristic
378C22×C17C2×C4×D411yescharacteristic
379C22×C17C2×C4×Q811yescharacteristic
380C22×C17C4×#4111yescharacteristic
381C22×C17#51911yescharacteristic
382C22×C17#52011yescharacteristic
383C22×C17C2×#12111yescharacteristic
384C22×C17C2×#12111yescharacteristic
385C22×C17C2×C22⋊Q811yescharacteristic
386C22×C17#52511yescharacteristic
387C22×C17C2×#12411yescharacteristic
388C22×C17#52911yescharacteristic
389C22×C17C2×#12711yescharacteristic
390C22×C17#53311yescharacteristic
391C22×C17#53611yescharacteristic
392C22×C17#53711yescharacteristic
393C22×C17#54111yescharacteristic
394C22×C17#54211yescharacteristic
395C22×C17#54611yescharacteristic
396C22×C17#54611yescharacteristic
397C22×C17#54611yescharacteristic
398C22×C17#54711yescharacteristic
399C22×C17#54711yescharacteristic
400C22×C17#54711yescharacteristic
401C22×C17#54811yescharacteristic
402C22×C17#54811yescharacteristic
403C22×C17#54811yescharacteristic
404C22×C17D4×Q811yescharacteristic
405C22×C17D4×Q811yescharacteristic
406C22×C17D4×Q811yescharacteristic
407C22×C17#55211yescharacteristic
408C22×C17#55211yescharacteristic
409C22×C17#55411yescharacteristic
410C22×C17#55611yescharacteristic
411C4×C17—28no—
412C4×C17—42no—
413C4×C17—44no—
414C4×C17#39018yes—
415Dic17—24no—
416Dic17—42no—
417Dic17—44no—
418Dic17—42no—
419Dic17—42no—
420Dic17—82no—
421C23×Q8C2×D1711yescharacteristic
422C24×C4C2×D1711yescharacteristic
423C2×C22⋊Q8—24no—
424C2×C22⋊Q8—24no—
425C2×C22⋊Q8Dic1718yescomplemented
426C22×C4⋊C4—171no—
427C22×C4⋊C4—171no—
428C22×C4⋊C4—172no—
429C22×C4⋊C4C2×D1712yes—
430C22×C4⋊C4C2×D1711yescharacteristic
431C22×C22⋊C4—171no—
432C22×C22⋊C4—171no—
433C22×C22⋊C4—172no—
434C22×C22⋊C4C2×D1712yes—
435C22×C42—171no—
436C22×C42—171no—
437C22×C42—172no—
438#391—344no—
439#391—344no—
440#389—344no—
441#380—344no—
442C4×C4⋊C4—344no—
443C4×C22⋊C4—344no—
444C2×#95—171no—
445C2×#95—172no—
446C2×#95—172no—
447C2×#95—172no—
448C2×#95—172no—
449C2×#95—172no—
450C2×#95—172no—
451C2×#95—172no—
452C2×#95—171no—
453C2×C17—44no—
454C2×C17C2×#39011yescharacteristic
455C2×C17C4×C22⋊Q811yescharacteristic
456C2×C17#232311yescharacteristic
457C2×C17#233911yescharacteristic
458C2×C17Q8×C22⋊C411yescharacteristic
459C2×C17#236011yescharacteristic
460C2×C17#236211yescharacteristic
461C2×C17#241511yescharacteristic
462C2×C17#241711yescharacteristic
463C2×C17#242711yescharacteristic
464C2×C17#242911yescharacteristic
465C2×C17#248911yescharacteristic
466C2×C17#249211yescharacteristic
467C2×C17#254011yescharacteristic
468C2×C17#254211yescharacteristic
469C25C22×D1711yescharacteristic
470C22×Q8—22no—
471C22×Q8—22no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—22no—
475C22×Q8—22no—
476C22×Q8C2×Dic1714yes—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—171no—
484C23×C4—171no—
485C23×C4—172no—
486C23×C4—171no—
487C23×C4—171no—
488C23×C4—172no—
489C23×C4C2×Dic1714yes—
490C23×C4C22×D1712yes—
491C23×C4C22×D1711yescharacteristic
492C23×C4C22×D1712yes—
493C23×C4C22×D1711yescharacteristic
494C22⋊Q8—232no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—174no—
498C2×C4⋊C4—342no—
499C2×C4⋊C4—342no—
500C2×C4⋊C4—344no—
501C2×C4⋊C4—342no—
502C2×C4⋊C4—342no—
503C2×C4⋊C4—344no—
504C2×C4⋊C4—342no—
505C2×C4⋊C4—682no—
506C2×C4⋊C4C2×Dic1718yes—
507C2×C4⋊C4C2×Dic1714yes—
508C2×C4⋊C4C22⋊D1714yes—
509C2×C4⋊C4C22⋊D1714yes—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—174no—
513C2×C22⋊C4—342no—
514C2×C22⋊C4—342no—
515C2×C22⋊C4—342no—
516C2×C22⋊C4—342no—
517C2×C22⋊C4—342no—
518C2×C22⋊C4—344no—
519C2×C22⋊C4—344no—
520C2×C22⋊C4—682no—
521C2×C22⋊C4C2×Dic1718yes—
522C2×C42—174no—
523C2×C42—342no—
524C2×C42—342no—
525C2×C42—344no—
526C2×C42—342no—
527C2×C42—342no—
528C2×C42—344no—
529C2×C42—342no—
530C2×C42—682no—
531#95—342no—
532#95—342no—
533#95—344no—
534#95—344no—
535#95—344no—
536#95—344no—
537#95—344no—
538#95—344no—
539#95—344no—
540C17#1399711yescharacteristic, complemented, Sylow
541C24—21no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24Q8×D1712yes—
554C24#6325612yes—
555C24C22×Dic1712yes—
556C24C23×D1711yescharacteristic
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—44no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—172no—
588C22×C4—172no—
589C22×C4—172no—
590C22×C4—172no—
591C22×C4—174no—
592C22×C4—172no—
593C22×C4—172no—
594C22×C4—341no—
595C22×C4—341no—
596C22×C4—341no—
597C22×C4—341no—
598C22×C4—341no—
599C22×C4—341no—
600C22×C4—341no—
601C22×C4—341no—
602C22×C4—341no—
603C22×C4—342no—
604C22×C4—341no—
605C22×C4—341no—
606C22×C4—342no—
607C22×C4—342no—
608C22×C4—341no—
609C22×C4—341no—
610C22×C4—341no—
611C22×C4—342no—
612C22×C4—341no—
613C22×C4—341no—
614C22×C4—342no—
615C22×C4—341no—
616C22×C4—341no—
617C22×C4—341no—
618C22×C4—341no—
619C22×C4—341no—
620C22×C4—342no—
621C22×C4—341no—
622C22×C4—342no—
623C22×C4—342no—
624C22×C4—342no—
625C22×C4—342no—
626C22×C4—342no—
627C22×C4—342no—
628C22×C4—342no—
629C22×C4D4×D1712yes—
630C22×C4D4×D1712yes—
631C22×C4#6325412yes—
632C22×C4#6325412yes—
633C22×C4C22×Dic1714yes—
634C22×C4C22×Dic1712yes—
635C22×C4C22×Dic1714yes—
636C22×C4C22×Dic1712yes—
637C22×C4C2×C22⋊D1714yes—
638C22×C4C2×C22⋊D1714yes—
639C22×C4C2×C22⋊D1712yes—
640C22×C4C2×C22⋊D1712yes—
641C4⋊C4—216no—
642C4⋊C4—348no—
643C4⋊C4—688no—
644C4⋊C4—684no—
645C4⋊C4C22⋊Dic17116yescomplemented
646C22⋊C4—216no—
647C22⋊C4—348no—
648C22⋊C4—348no—
649C22⋊C4—688no—
650C42—348no—
651C42—688no—
652C42—684no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23Q8×Dic1714yes—
688C23C2×D4×D1711yescharacteristic
689C23C2×D4×D1711yescharacteristic
690C23C2×#6325411yescharacteristic
691C23C2×#6325411yescharacteristic
692C23C2×Q8×D1711yescharacteristic
693C23C2×#6325611yescharacteristic
694C23#1058769411yescharacteristic
695C23#1058769411yescharacteristic
696C23#41×D1711yescharacteristic
697C23#41×D1711yescharacteristic
698C23#1058769611yescharacteristic
699C23#1058769711yescharacteristic
700C23C23×Dic1711yescharacteristic
701C23C22×C22⋊D1711yescharacteristic
702C23C22×C22⋊D1711yescharacteristic
703Q8—416no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—416no—
725C2×C4—174no—
726C2×C4—342no—
727C2×C4—342no—
728C2×C4—342no—
729C2×C4—342no—
730C2×C4—342no—
731C2×C4—342no—
732C2×C4—344no—
733C2×C4—342no—
734C2×C4—342no—
735C2×C4—342no—
736C2×C4—342no—
737C2×C4—344no—
738C2×C4—342no—
739C2×C4—342no—
740C2×C4—342no—
741C2×C4—342no—
742C2×C4—342no—
743C2×C4—344no—
744C2×C4—681no—
745C2×C4—681no—
746C2×C4—681no—
747C2×C4—682no—
748C2×C4—681no—
749C2×C4—681no—
750C2×C4—681no—
751C2×C4—681no—
752C2×C4—682no—
753C2×C4—681no—
754C2×C4—681no—
755C2×C4—681no—
756C2×C4—681no—
757C2×C4—682no—
758C2×C4—682no—
759C2×C4—681no—
760C2×C4—682no—
761C2×C4—682no—
762C2×C4—682no—
763C2×C4—682no—
764C2×C4—682no—
765C2×C4—682no—
766C2×C4—682no—
767C2×C4D4×Dic1714yes—
768C2×C4D4×Dic1714yes—
769C2×C4#1058762214yes—
770C2×C4#1058762414yes—
771C2×C4#1058762414yes—
772C2×C4#1058762614yes—
773C2×C4C2×C22⋊Dic1718yes—
774C2×C4C2×C22⋊Dic1714yes—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22C22×C22⋊Dic1711yescharacteristic
791C22C2×D4×Dic1711yescharacteristic
792C22C2×D4×Dic1711yescharacteristic
793C22C2×Q8×Dic1711yescharacteristic
794C22#41×Dic1711yescharacteristic
795C22#1176328711yescharacteristic
796C22#1176329211yescharacteristic
797C22C2×#1058762411yescharacteristic
798C22C2×#1058762411yescharacteristic
799C22C22⋊Q8×D1711yescharacteristic
800C22#1176332211yescharacteristic
801C22C2×#1058762211yescharacteristic
802C22#1176334511yescharacteristic
803C22C2×#1058762611yescharacteristic
804C22#1176336111yescharacteristic
805C22#1176338211yescharacteristic
806C22#1176338911yescharacteristic
807C22#1176341911yescharacteristic
808C22#1176343211yescharacteristic
809C22#1176344711yescharacteristic
810C22#1176344711yescharacteristic
811C22#1176345011yescharacteristic
812C22#1176345811yescharacteristic
813C22#1176345811yescharacteristic
814C22#1176346111yescharacteristic
815C22#1176346911yescharacteristic
816C22#1176347011yescharacteristic
817C22#1176347011yescharacteristic
818C22#1176347211yescharacteristic
819C22Q8×C22⋊D1711yescharacteristic
820C22Q8×C22⋊D1711yescharacteristic
821C22#1176349311yescharacteristic
822C22#1176350111yescharacteristic
823C22#1176351711yescharacteristic
824C22#1176353011yescharacteristic
825C4—28no—
826C4—42no—
827C4—44no—
828C4—344no—
829C4—684no—
830C4—682no—
831C4—682no—
832C4—682no—
833C4—1362no—
834C4#1176271218yes—
835C2—44no—
836C2C2×#1176271211yescharacteristic
837C2C22⋊Q8×Dic1711yescharacteristic
838C2#1453146811yescharacteristic
839C2#1453161411yescharacteristic
840C2Q8×C22⋊Dic1711yescharacteristic
841C2#1453179311yescharacteristic
842C2#1453181511yescharacteristic
843C2#1453220911yescharacteristic
844C2#1453223111yescharacteristic
845C2#1453235711yescharacteristic
846C2#1453237911yescharacteristic
847C2#1453312711yescharacteristic
848C2#1453316011yescharacteristic
849C2#1453372211yescharacteristic
850C2#1453373411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC22×C17×C22⋊Q8C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC22×C22⋊Q8D17
hypocenterC17#13997
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11762716C2semidirect
2. C2×#11762716C2semidirect
3. C2×#11762708C2semidirect
5. C2×C4⋊C4×Dic17C2semidirect
7. #14527052C2semidirect
10. #14527013C2semidirect
40. C2×C17×C22⋊Q8C4semidirect
87. C2×C22⋊Dic17Q8semidirect
216. C4⋊C4×C17C22⋊C4semidirect
349. C2×Dic17C22⋊Q8semidirect
425. C2×C22⋊Q8Dic17semidirect
540. C17#13997semidirect
645. C4⋊C4C22⋊Dic17semidirect

Maximal subgroups

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

subgroupindex
C2×#117627162
C2×#117627082
C2×#117626692
C2×C4⋊C4×Dic172
C2×C4×C22⋊Dic172
#145270522
#145270292
#145270212
#145270132
C22×C17×C22⋊Q82
#1399717