Finite Group Databasebeta

← #16957461

Subgroups — #16957461

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
1C22×#10587583C211yesmaximal, characteristic
2C2×#11762715C211yesmaximal, characteristic, complemented
3C2×#11762714C211yesmaximal, characteristic, complemented
4C2×#11762666C211yesmaximal, characteristic
5C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
6C2×C4×#63227C211yesmaximal, characteristic
7#14527053C212yesmaximal, complemented
8#14527026C212yesmaximal
9#14527020C212yesmaximal
10#14527013C212yesmaximal, complemented
11C2×C17×#389C211yesmaximal, characteristic, complemented
12C23×Dic34C2211yescharacteristic
13C23×C4×D17C2211yescharacteristic
14C2×#10587583—24no—
15C2×#10587583—24no—
16C2×#10587583C418yescomplemented
17C22×C4⋊Dic17C2212yes—
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63227C2211yescharacteristic
20C22×#63227C2212yes—
21C22×#63227C2212yes—
22C22×#63227C2211yescharacteristic
23C22×C4×Dic17C2212yes—
24C22×C4×Dic17C2211yescharacteristic
25#11762715—24no—
26#11762714—24no—
27#11762666—24no—
28C4⋊C4×Dic17—24no—
29C4×#63227—24no—
30C2×#10587502C2211yescharacteristic
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2212yes—
36C2×#10587502C2212yes—
37C2×#10587502C2212yes—
38C22×C4⋊C4×C17C2211yescharacteristic
39C22×C4⋊C4×C17C2212yes—
40C22×C4⋊C4×C17C2211yescharacteristic
41C22×C42×C17C2211yescharacteristic
42C17×#389—24no—
43C2×C17×#95C2212yes—
44C24×D17C2311yescharacteristic
45C23×C4×C17C2312yes—
46C23×C4×C17C2311yescharacteristic
47C23×C4×C17C2311yescharacteristic
48C23×C4×C17C2312yes—
49C23×C4×C17C2311yescharacteristic
50C23×Dic17C2312yes—
51C23×Dic17C2311yescharacteristic
52C23×Dic17C2312yes—
53C23×Dic17C2311yescharacteristic
54C23×Dic17C2311yescharacteristic
55C22×C4×D17—22no—
56C22×C4×D17—22no—
57C22×C4×D17—22no—
58C22×C4×D17—22no—
59C22×C4×D17—22no—
60C22×C4×D17—22no—
61C22×C4×D17C2×C414yes—
62C22×Dic34—22no—
63C22×Dic34—22no—
64C22×Dic34—22no—
65C22×Dic34—22no—
66C22×Dic34—22no—
67C22×Dic34—22no—
68C22×Dic34C2×C414yes—
69C2×C4⋊C4×C17—22no—
70C2×C4⋊C4×C17—24no—
71C2×C4⋊C4×C17—22no—
72C2×C4⋊C4×C17—22no—
73C2×C4⋊C4×C17—24no—
74C2×C4⋊C4×C17—42no—
75C2×C4⋊C4×C17C2×C414yes—
76C2×C4⋊C4×C17D414yes—
77C2×C4⋊C4×C17D414yes—
78C2×C42×C17—22no—
79C2×C42×C17—22no—
80C2×C42×C17—22no—
81C2×#63227—22no—
82C2×#63227—24no—
83C2×#63227—24no—
84C2×#63227—24no—
85C2×#63227—22no—
86C2×#63227—22no—
87C2×#63227—22no—
88C2×#63227—24no—
89C2×#63227—22no—
90C2×#63227—42no—
91C2×#63227C2×C418yes—
92C2×#63227Q814yescomplemented
93C2×C4⋊Dic17—24no—
94C2×C4⋊Dic17—24no—
95C2×C4⋊Dic17—22no—
96C2×C4⋊Dic17—22no—
97C2×C4⋊Dic17C2×C418yes—
98C2×C4⋊Dic17D414yes—
99C2×C4×Dic17—22no—
100C2×C4×Dic17—24no—
101C2×C4×Dic17—22no—
102C2×C4×Dic17—24no—
103C2×C4×Dic17—42no—
104C2×C4×Dic17D414yes—
105#10587583—232no—
106C17×#95—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×C17C2411yescharacteristic
116C23×D17—21no—
117C23×D17—21no—
118C23×D17—21no—
119C23×D17—21no—
120C23×D17—21no—
121C23×D17—21no—
122C23×D17—21no—
123C23×D17—21no—
124C23×D17—21no—
125C23×D17—21no—
126C23×D17—21no—
127C23×D17—21no—
128C23×D17C22×C412yes—
129C23×D17C2×Q812yes—
130C23×D17#4112yes—
131C22×C4×C17—22no—
132C22×C4×C17—22no—
133C22×C4×C17—22no—
134C22×C4×C17—22no—
135C22×C4×C17—21no—
136C22×C4×C17—21no—
137C22×C4×C17—21no—
138C22×C4×C17—21no—
139C22×C4×C17—21no—
140C22×C4×C17—21no—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—22no—
151C22×C4×C17—22no—
152C22×C4×C17—22no—
153C22×C4×C17—22no—
154C22×C4×C17C22×C414yes—
155C22×C4×C17C22×C412yes—
156C22×C4×C17C2×D414yes—
157C22×C4×C17C2×D412yes—
158C22×C4×C17C2×D412yes—
159C22×C4×C17C2×D412yes—
160C22×C4×C17C2×D414yes—
161C22×C4×C17C2×D412yes—
162C22×C4×C17C2×Q812yes—
163C22×C4×C17#4112yes—
164C22×C4×C17#4112yes—
165C22×C4×C17#4112yes—
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17—21no—
169C22×Dic17—21no—
170C22×Dic17—22no—
171C22×Dic17—22no—
172C22×Dic17—22no—
173C22×Dic17—22no—
174C22×Dic17—21no—
175C22×Dic17—21no—
176C22×Dic17—21no—
177C22×Dic17—21no—
178C22×Dic17—21no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—21no—
183C22×Dic17—21no—
184C22×Dic17—21no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—21no—
188C22×Dic17—21no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17—21no—
192C22×Dic17—22no—
193C22×Dic17—21no—
194C22×Dic17C22×C414yes—
195C22×Dic17C22×C412yes—
196C22×Dic17C2×D412yes—
197C22×Dic17C2×D414yes—
198C22×Dic17C2×D412yes—
199C22×Dic17C2×Q812yes—
200C22×Dic17#4112yes—
201C2×C4×D17—28no—
202C2×C4×D17—28no—
203C2×C4×D17—28no—
204C2×C4×D17—44no—
205C2×C4×D17—44no—
206C2×C4×D17—44no—
207C2×C4×D17—44no—
208C2×Dic34—28no—
209C2×Dic34—28no—
210C2×Dic34—28no—
211C2×Dic34—44no—
212C2×Dic34—44no—
213C2×Dic34—44no—
214C2×Dic34—44no—
215C4⋊C4×C17—48no—
216C4⋊C4×C17—44no—
217C4⋊C4×C17C22⋊C4116yescomplemented
218C42×C17—44no—
219#63227—28no—
220#63227—216no—
221#63227—28no—
222#63227—48no—
223C4⋊Dic17—216no—
224C4⋊Dic17—28no—
225C4×Dic17—28no—
226C4×Dic17—48no—
227#13997—171nomaximal, Sylow
228C23×C17C23×C411yescharacteristic
229C23×C17C22×D411yescharacteristic
230C23×C17C22×D411yescharacteristic
231C23×C17C22×D411yescharacteristic
232C23×C17C22×D411yescharacteristic
233C23×C17C22×Q811yescharacteristic
234C23×C17C2×#4111yescharacteristic
235C23×C17C2×#4111yescharacteristic
236C23×C17C2×#4111yescharacteristic
237C23×C17C2×#4111yescharacteristic
238C23×C17C2×#4111yescharacteristic
239C23×C17H(5,𝔽2)11yescharacteristic
240C23×C172−1+411yescharacteristic
241C23×C172−1+411yescharacteristic
242C23×C172−1+411yescharacteristic
243C22×D17—22no—
244C22×D17—22no—
245C22×D17—22no—
246C22×D17—22no—
247C22×D17—22no—
248C22×D17—22no—
249C22×D17—22no—
250C22×D17—22no—
251C22×D17—22no—
252C22×D17—22no—
253C22×D17—22no—
254C22×D17—22no—
255C22×D17—22no—
256C22×D17—22no—
257C22×D17—22no—
258C22×D17—22no—
259C22×D17—22no—
260C22×D17—22no—
261C22×D17—41no—
262C22×D17—41no—
263C22×D17—41no—
264C22×D17—41no—
265C22×D17—41no—
266C22×D17—41no—
267C22×D17—41no—
268C22×D17—41no—
269C22×D17—41no—
270C22×D17—41no—
271C22×D17—41no—
272C22×D17—41no—
273C22×D17—41no—
274C22×D17—41no—
275C22×D17—41no—
276C22×D17—41no—
277C22×D17C4×Q814yes—
278C2×C4×C17—24no—
279C2×C4×C17—24no—
280C2×C4×C17—24no—
281C2×C4×C17—24no—
282C2×C4×C17—24no—
283C2×C4×C17—24no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—41no—
291C2×C4×C17—41no—
292C2×C4×C17—41no—
293C2×C4×C17—41no—
294C2×C4×C17—41no—
295C2×C4×C17—41no—
296C2×C4×C17—41no—
297C2×C4×C17—41no—
298C2×C4×C17—42no—
299C2×C4×C17—42no—
300C2×C4×C17—42no—
301C2×C4×C17—42no—
302C2×C4×C17—42no—
303C2×C4×C17—42no—
304C2×C4×C17—42no—
305C2×C4×C17C2×C22⋊C418yes—
306C2×C4×C17C2×C22⋊C414yes—
307C2×C4×C17C4×D414yes—
308C2×C4×C17C4×D414yes—
309C2×C4×C17#12114yes—
310C2×C4×C17#12114yes—
311C2×C4×C17#12414yes—
312C2×C4×C17#12714yes—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—24no—
320C2×Dic17—22no—
321C2×Dic17—24no—
322C2×Dic17—24no—
323C2×Dic17—22no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—24no—
327C2×Dic17—22no—
328C2×Dic17—22no—
329C2×Dic17—24no—
330C2×Dic17—24no—
331C2×Dic17—42no—
332C2×Dic17—42no—
333C2×Dic17—41no—
334C2×Dic17—41no—
335C2×Dic17—42no—
336C2×Dic17—41no—
337C2×Dic17—42no—
338C2×Dic17—42no—
339C2×Dic17—41no—
340C2×Dic17—42no—
341C2×Dic17—42no—
342C2×Dic17—41no—
343C2×Dic17—41no—
344C2×Dic17—42no—
345C2×Dic17—41no—
346C2×Dic17—41no—
347C2×Dic17C22⋊Q814yescomplemented
348C4×D17—416no—
349Dic34—416no—
350C22×C22⋊Q8—171no—
351C2×#391—171no—
352C2×#391—171no—
353C2×#389D1711yescharacteristic, complemented
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×C17C22×C22⋊C411yescharacteristic
362C22×C17C2×C4×D411yescharacteristic
363C22×C17C2×C4×D411yescharacteristic
364C22×C17C2×C4×Q811yescharacteristic
365C22×C17C4×#4111yescharacteristic
366C22×C17#51911yescharacteristic
367C22×C17#52011yescharacteristic
368C22×C17C2×#12111yescharacteristic
369C22×C17C2×#12111yescharacteristic
370C22×C17C2×C22⋊Q811yescharacteristic
371C22×C17#52511yescharacteristic
372C22×C17C2×#12411yescharacteristic
373C22×C17#52911yescharacteristic
374C22×C17C2×#12711yescharacteristic
375C22×C17#53311yescharacteristic
376C22×C17#53611yescharacteristic
377C22×C17#53711yescharacteristic
378C22×C17#54111yescharacteristic
379C22×C17#54211yescharacteristic
380C22×C17#54611yescharacteristic
381C22×C17#54611yescharacteristic
382C22×C17#54611yescharacteristic
383C22×C17#54711yescharacteristic
384C22×C17#54711yescharacteristic
385C22×C17#54711yescharacteristic
386C22×C17#54811yescharacteristic
387C22×C17#54811yescharacteristic
388C22×C17#54811yescharacteristic
389C22×C17D4×Q811yescharacteristic
390C22×C17D4×Q811yescharacteristic
391C22×C17D4×Q811yescharacteristic
392C22×C17#55211yescharacteristic
393C22×C17#55211yescharacteristic
394C22×C17#55411yescharacteristic
395C22×C17#55611yescharacteristic
396C2×D17—24no—
397C2×D17—24no—
398C2×D17—24no—
399C2×D17—42no—
400C2×D17—42no—
401C2×D17—42no—
402C2×D17—42no—
403C2×D17—42no—
404C2×D17—42no—
405C2×D17—42no—
406C2×D17—42no—
407C2×D17—42no—
408C2×D17—42no—
409C2×D17—42no—
410C2×D17—42no—
411C4×C17—28no—
412C4×C17—42no—
413C4×C17—42no—
414C4×C17—82no—
415C4×C17#39018yes—
416Dic17—24no—
417Dic17—42no—
418Dic17—44no—
419Dic17—44no—
420Dic17—42no—
421C23×Q8—171no—
422C24×C4—171no—
423C2×C22⋊Q8—178no—
424C2×C22⋊Q8—344no—
425C2×C22⋊Q8—344no—
426C22×C4⋊C4—172no—
427C22×C4⋊C4—171no—
428C22×C4⋊C4C2×D1711yescharacteristic
429C22×C4⋊C4C2×D1712yes—
430C22×C4⋊C4C2×D1711yescharacteristic
431C22×C22⋊C4—172no—
432C22×C22⋊C4—171no—
433C22×C22⋊C4—171no—
434C22×C22⋊C4—172no—
435C22×C42—171no—
436C22×C42—172no—
437C22×C42C2×D1711yescharacteristic
438#391—344no—
439#391—344no—
440#389—24no—
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—171no—
452C2×#95C2×D1712yes—
453C2×C17C2×#39011yescharacteristic
454C2×C17C4×C22⋊Q811yescharacteristic
455C2×C17#232311yescharacteristic
456C2×C17#233911yescharacteristic
457C2×C17Q8×C22⋊C411yescharacteristic
458C2×C17#236011yescharacteristic
459C2×C17#236211yescharacteristic
460C2×C17#241511yescharacteristic
461C2×C17#241711yescharacteristic
462C2×C17#242711yescharacteristic
463C2×C17#242911yescharacteristic
464C2×C17#248911yescharacteristic
465C2×C17#249211yescharacteristic
466C2×C17#254011yescharacteristic
467C2×C17#254211yescharacteristic
468D17—44no—
469C25—171no—
470C22×Q8—174no—
471C22×Q8—342no—
472C22×Q8—342no—
473C22×Q8—342no—
474C22×Q8—342no—
475C22×Q8—342no—
476C22×Q8—342no—
477C23×C4—171no—
478C23×C4—172no—
479C23×C4—172no—
480C23×C4—171no—
481C23×C4—171no—
482C23×C4—174no—
483C23×C4—342no—
484C23×C4—342no—
485C23×C4—342no—
486C23×C4—342no—
487C23×C4—342no—
488C23×C4—342no—
489C23×C4C22×D1712yes—
490C23×C4C22×D1711yescharacteristic
491C23×C4C22×D1711yescharacteristic
492C23×C4C22×D1712yes—
493C23×C4C22×D1711yescharacteristic
494C22⋊Q8—3432no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4—178no—
502C2×C4⋊C4—174no—
503C2×C4⋊C4—344no—
504C2×C4⋊C4—342no—
505C2×C4⋊C4—342no—
506C2×C4⋊C4—344no—
507C2×C4⋊C4C4×D1714yes—
508C2×C4⋊C4D6814yes—
509C2×C4⋊C4C22⋊D1714yes—
510C2×C22⋊C4—178no—
511C2×C22⋊C4—174no—
512C2×C22⋊C4—342no—
513C2×C22⋊C4—342no—
514C2×C22⋊C4—342no—
515C2×C22⋊C4—342no—
516C2×C22⋊C4—344no—
517C2×C22⋊C4—342no—
518C2×C22⋊C4—344no—
519C2×C22⋊C4—344no—
520C2×C22⋊C4—344no—
521C2×C22⋊C4—682no—
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—174no—
526C2×C42—342no—
527C2×C42—342no—
528C2×C42—344no—
529C2×C42—344no—
530C2×C42—682no—
531#95—24no—
532#95—342no—
533#95—342no—
534#95—344no—
535#95—344no—
536#95—344no—
537#95—344no—
538#95—344no—
539#95—344no—
540C17#1399711yescharacteristic, complemented, Sylow
541C24—172no—
542C24—172no—
543C24—172no—
544C24—341no—
545C24—341no—
546C24—341no—
547C24—341no—
548C24—341no—
549C24—341no—
550C24—341no—
551C24—341no—
552C24—341no—
553C24—341no—
554C24—341no—
555C24—341no—
556C24C23×D1711yescharacteristic
557C2×Q8—348no—
558C2×Q8—348no—
559C2×Q8—348no—
560C2×Q8—684no—
561C2×Q8—684no—
562C2×Q8—684no—
563C2×Q8—684no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—172no—
588C22×C4—172no—
589C22×C4—172no—
590C22×C4—174no—
591C22×C4—172no—
592C22×C4—172no—
593C22×C4—174no—
594C22×C4—341no—
595C22×C4—341no—
596C22×C4—341no—
597C22×C4—341no—
598C22×C4—341no—
599C22×C4—342no—
600C22×C4—342no—
601C22×C4—341no—
602C22×C4—341no—
603C22×C4—341no—
604C22×C4—342no—
605C22×C4—342no—
606C22×C4—341no—
607C22×C4—342no—
608C22×C4—341no—
609C22×C4—342no—
610C22×C4—341no—
611C22×C4—341no—
612C22×C4—342no—
613C22×C4—342no—
614C22×C4—342no—
615C22×C4—341no—
616C22×C4—342no—
617C22×C4—342no—
618C22×C4—341no—
619C22×C4—341no—
620C22×C4—342no—
621C22×C4—341no—
622C22×C4—348no—
623C22×C4—348no—
624C22×C4—348no—
625C22×C4—684no—
626C22×C4—684no—
627C22×C4—684no—
628C22×C4—684no—
629C22×C4C2×C4×D1714yes—
630C22×C4C2×C4×D1712yes—
631C22×C4C2×D6814yes—
632C22×C4C2×D6812yes—
633C22×C4D4×D1712yes—
634C22×C4D4×D1712yes—
635C22×C4#6325412yes—
636C22×C4Q8×D1712yes—
637C22×C4#6325612yes—
638C22×C4#6325612yes—
639C22×C4C2×C22⋊D1714yes—
640C22×C4C2×C22⋊D1712yes—
641C4⋊C4—48no—
642C4⋊C4—44no—
643C4⋊C4—348no—
644C4⋊C4—3416no—
645C4⋊C4#63227116yescomplemented
646C22⋊C4—348no—
647C22⋊C4—348no—
648C22⋊C4—3416no—
649C22⋊C4—688no—
650C42—44no—
651C42—348no—
652C42—688no—
653C23—174no—
654C23—342no—
655C23—342no—
656C23—342no—
657C23—342no—
658C23—342no—
659C23—342no—
660C23—342no—
661C23—342no—
662C23—342no—
663C23—342no—
664C23—342no—
665C23—342no—
666C23—342no—
667C23—342no—
668C23—342no—
669C23—342no—
670C23—342no—
671C23—342no—
672C23—681no—
673C23—681no—
674C23—681no—
675C23—681no—
676C23—681no—
677C23—681no—
678C23—681no—
679C23—681no—
680C23—681no—
681C23—681no—
682C23—681no—
683C23—681no—
684C23—681no—
685C23—681no—
686C23—681no—
687C23—681no—
688C23C22×C4×D1711yescharacteristic
689C23C22×D6811yescharacteristic
690C23C2×D4×D1711yescharacteristic
691C23C2×D4×D1711yescharacteristic
692C23C2×#6325411yescharacteristic
693C23#1058769111yescharacteristic
694C23C2×Q8×D1711yescharacteristic
695C23C2×#6325611yescharacteristic
696C23C2×#6325611yescharacteristic
697C23#1058769411yescharacteristic
698C23#41×D1711yescharacteristic
699C23#41×D1711yescharacteristic
700C23#1058769711yescharacteristic
701C23#1058769711yescharacteristic
702C23C22×C22⋊D1711yescharacteristic
703Q8—6816no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—174no—
732C2×C4—342no—
733C2×C4—342no—
734C2×C4—342no—
735C2×C4—342no—
736C2×C4—342no—
737C2×C4—342no—
738C2×C4—344no—
739C2×C4—344no—
740C2×C4—344no—
741C2×C4—342no—
742C2×C4—342no—
743C2×C4—342no—
744C2×C4—344no—
745C2×C4—344no—
746C2×C4—342no—
747C2×C4—344no—
748C2×C4—342no—
749C2×C4—342no—
750C2×C4—681no—
751C2×C4—682no—
752C2×C4—681no—
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—681no—
763C2×C4—682no—
764C2×C4—682no—
765C2×C4—682no—
766C2×C4—6816no—
767C2×C4#1058757914yes—
768C2×C4#1058757914yes—
769C2×C4#1058758114yes—
770C2×C4#1058758114yes—
771C2×C4C2×#6322718yes—
772C2×C4C2×#6322714yes—
773C2×C4#1058762614yes—
774C2×C4#1058763314yes—
775C22—344no—
776C22—344no—
777C22—344no—
778C22—682no—
779C22—682no—
780C22—682no—
781C22—682no—
782C22—682no—
783C22—682no—
784C22—682no—
785C22—682no—
786C22—682no—
787C22—682no—
788C22—682no—
789C22—682no—
790C22C22×#6322711yescharacteristic
791C22C2×#1058757911yescharacteristic
792C22C2×#1058757911yescharacteristic
793C22C4×Q8×D1711yescharacteristic
794C22C4×#6325411yescharacteristic
795C22#1176328511yescharacteristic
796C22#1176328811yescharacteristic
797C22C2×#1058758111yescharacteristic
798C22C2×#1058758111yescharacteristic
799C22C22⋊Q8×D1711yescharacteristic
800C22#1176331911yescharacteristic
801C22C2×#1058763311yescharacteristic
802C22#1176334411yescharacteristic
803C22C2×#1058762611yescharacteristic
804C22#1176336411yescharacteristic
805C22#1176338211yescharacteristic
806C22#1176338811yescharacteristic
807C22#1176342211yescharacteristic
808C22#1176343311yescharacteristic
809C22#1176345311yescharacteristic
810C22#1176345411yescharacteristic
811C22#1176345611yescharacteristic
812C22#1176345811yescharacteristic
813C22#1176346111yescharacteristic
814C22#1176346311yescharacteristic
815C22#1176346511yescharacteristic
816C22#1176346611yescharacteristic
817C22#1176347111yescharacteristic
818C22#1176347211yescharacteristic
819C22Q8×C22⋊D1711yescharacteristic
820C22Q8×D6811yescharacteristic
821C22#1176349711yescharacteristic
822C22#1176349711yescharacteristic
823C22#1176352011yescharacteristic
824C22#1176353311yescharacteristic
825C4—28no—
826C4—42no—
827C4—42no—
828C4—82no—
829C4—344no—
830C4—684no—
831C4—682no—
832C4—682no—
833C4—684no—
834C4#1176271018yes—
835C2—684no—
836C2C2×#1176271011yescharacteristic
837C2#1453131411yescharacteristic
838C2#1453146411yescharacteristic
839C2#1453160911yescharacteristic
840C2Q8×#6322711yescharacteristic
841C2#1453178811yescharacteristic
842C2#1453181011yescharacteristic
843C2#1453221111yescharacteristic
844C2#1453223311yescharacteristic
845C2#1453235911yescharacteristic
846C2#1453238111yescharacteristic
847C2#1453312811yescharacteristic
848C2#1453316111yescharacteristic
849C2#1453372011yescharacteristic
850C2#1453373411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#389C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenterC2×#389D17
hypocenterC17#13997
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#11762715C2semidirect
3. C2×#11762714C2semidirect
5. C2×C4⋊C4×Dic17C2semidirect
7. #14527053C2semidirect
10. #14527013C2semidirect
11. C2×C17×#389C2semidirect
16. C2×#10587583C4semidirect
92. C2×#63227Q8semidirect
217. C4⋊C4×C17C22⋊C4semidirect
347. C2×Dic17C22⋊Q8semidirect
353. C2×#389D17semidirect
540. C17#13997semidirect
645. C4⋊C4#63227semidirect

Maximal subgroups

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

subgroupindex
C22×#105875832
C2×#117627152
C2×#117627142
C2×#117626662
C2×C4⋊C4×Dic172
C2×C4×#632272
#145270532
#145270262
#145270202
#145270132
C2×C17×#3892
#1399717