Finite Group Databasebeta

← #16955821

Subgroups — #16955821

Order 4352.

2882 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D17C211yesmaximal, characteristic
2C2×#11762685C212yesmaximal
3C2×C4×#63227C212yesmaximal, complemented
4C2×#95×D17C211yesmaximal, characteristic, complemented
5#14527021C212yesmaximal, complemented
6#14527017C212yesmaximal, complemented
7#14527010C211yesmaximal, characteristic, complemented
8#14527007C211yesmaximal, characteristic, complemented
9#14527005C211yesmaximal, characteristic, complemented
10#95×Dic17C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C17C211yesmaximal, characteristic, complemented
12C23×C22⋊D17C2211yescharacteristic
13C23×C4×D17C2211yescharacteristic
14C23×C4×D17C2212yes—
15C2×C4×C22⋊D17—28no—
16C2×C4×C22⋊D17C418yescomplemented
17C22×#63225C2211yescharacteristic
18C22×C22⋊Dic17C2211yescharacteristic
19C22×C22⋊Dic17C2212yes—
20C22×#63227C2212yes—
21C22×#63227C2211yescharacteristic
22C22×C4×Dic17C2212yes—
23C22×C4×Dic17C2211yescharacteristic
24#11762685C4116yescomplemented
25C4×#63227—28no—
26C2×#10587502C2211yescharacteristic
27C2×#10587502C2211yescharacteristic
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34#95×D17—24no—
35C24×C4×C17C2211yescharacteristic
36C22×C22⋊C4×C17C2212yes—
37C22×C42×C17C2212yes—
38C4×C22⋊C4×C17—24no—
39C2×C17×#95C2211yescharacteristic
40C2×C17×#95C2211yescharacteristic
41C25×C17C2311yescharacteristic
42C24×D17C2311yescharacteristic
43C23×C4×C17—24no—
44C23×C4×C17—22no—
45C23×C4×C17—22no—
46C23×C4×C17—42no—
47C23×C4×C17C2×C414yescomplemented
48C23×C4×C17C2312yes—
49C23×C4×C17C2311yescharacteristic
50C23×C4×C17C2312yes—
51C23×C4×C17C2311yescharacteristic
52C22×C22⋊D17—24no—
53C22×C22⋊D17—22no—
54C22×C22⋊D17—22no—
55C22×C22⋊D17C2×C414yes—
56C22×C22⋊D17C2×C418yes—
57C23×Dic17C2312yes—
58C23×Dic17C2311yescharacteristic
59C23×Dic17C2312yes—
60C23×Dic17C2311yescharacteristic
61C23×Dic17C2311yescharacteristic
62C22×C4×D17—24no—
63C22×C4×D17—24no—
64C22×C4×D17—24no—
65C22×C4×D17—22no—
66C22×C4×D17—24no—
67C22×C4×D17—22no—
68C22×C4×D17—24no—
69C22×C4×D17—42no—
70C22×C4×D17—42no—
71C22×C4×D17—42no—
72C22×C4×D17C2×C414yes—
73C22×C4×D17C2×C418yescomplemented
74C2×C22⋊C4×C17—24no—
75C2×C22⋊C4×C17—24no—
76C2×C22⋊C4×C17C2×C418yescomplemented
77C2×C42×C17—24no—
78C2×C42×C17—24no—
79C2×C42×C17—42no—
80C2×C22⋊Dic17—24no—
81C2×C22⋊Dic17—42no—
82C2×C22⋊Dic17—42no—
83C2×C22⋊Dic17C2×C414yescomplemented
84C2×C22⋊Dic17C2×C418yescomplemented
85C4×C22⋊D17—232no—
86C2×#63227—24no—
87C2×#63227—24no—
88C2×#63227C2×C414yes—
89C2×#63227C2×C418yescomplemented
90C2×#63227D418yes—
91C2×#63225—24no—
92C2×#63225C2×C414yescomplemented
93C2×C4×Dic17—24no—
94C2×C4×Dic17—24no—
95C2×C4×Dic17—24no—
96C2×C4×Dic17—42no—
97C2×C4×Dic17C2×C414yescomplemented
98C17×#95—22no—
99C17×#95D414yescomplemented
100#10587502—22no—
101#10587502—24no—
102#10587502—24no—
103#10587502—22no—
104#10587502—24no—
105#10587502—42no—
106#10587502C2×C418yescomplemented
107#10587502C2×C418yescomplemented
108C24×C17—22no—
109C24×C17—21no—
110C24×C17—21no—
111C24×C17—21no—
112C24×C17—21no—
113C24×C17—22no—
114C24×C17—22no—
115C24×C17—21no—
116C24×C17—21no—
117C24×C17C22×C412yes—
118C24×C17C22×C414yes—
119C24×C17C2411yescharacteristic
120C23×D17—21no—
121C23×D17—21no—
122C23×D17—22no—
123C23×D17—22no—
124C23×D17—21no—
125C23×D17—21no—
126C23×D17C22×C412yes—
127C23×D17C22×C414yes—
128C23×D17C2×D414yes—
129C23×D17#4112yes—
130C23×D17#4112yes—
131C22×C4×C17—22no—
132C22×C4×C17—22no—
133C22×C4×C17—21no—
134C22×C4×C17—22no—
135C22×C4×C17—21no—
136C22×C4×C17—22no—
137C22×C4×C17—22no—
138C22×C4×C17—22no—
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—22no—
142C22×C4×C17—22no—
143C22×C4×C17—22no—
144C22×C4×C17—22no—
145C22×C4×C17—22no—
146C22×C4×C17—28no—
147C22×C4×C17—28no—
148C22×C4×C17—44no—
149C22×C4×C17—48no—
150C22×C4×C17—48no—
151C22×C4×C17C22×C414yes—
152C22×C4×C17C22×C412yes—
153C22×C4×C17C22×C412yes—
154C22×C4×C17C22×C414yes—
155C22×C4×C17C2×D414yes—
156C22×C4×C17C2×D412yes—
157C22×C4×C17C2×D414yes—
158C22×C4×C17#4112yes—
159C22×C4×C17#4114yes—
160C2×C22⋊D17—28no—
161C2×C22⋊D17—28no—
162C2×C22⋊D17—216no—
163C2×C22⋊D17—216no—
164C2×C22⋊D17C42116yescomplemented
165C22×Dic17—22no—
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17—22no—
169C22×Dic17—21no—
170C22×Dic17—21no—
171C22×Dic17—22no—
172C22×Dic17—21no—
173C22×Dic17—22no—
174C22×Dic17—22no—
175C22×Dic17—22no—
176C22×Dic17—21no—
177C22×Dic17—22no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17C22×C412yes—
188C22×Dic17C22×C414yes—
189C22×Dic17C22×C414yes—
190C22×Dic17C22×C414yes—
191C22×Dic17C22×C412yes—
192C22×Dic17C22×C412yes—
193C22×Dic17C2×D414yes—
194C2×C4×D17—28no—
195C2×C4×D17—216no—
196C2×C4×D17—28no—
197C2×C4×D17—216no—
198C2×C4×D17—44no—
199C2×C4×D17—48no—
200C2×C4×D17—48no—
201C2×C4×D17—48no—
202C2×C4×D17—48no—
203C2×C4×D17—48no—
204C2×C4×D17—48no—
205C2×C4×D17—48no—
206C22⋊C4×C17—216no—
207C42×C17—48no—
208C22⋊Dic17—28no—
209C22⋊Dic17—48no—
210#63227—216no—
211#63227C22⋊C4116yescomplemented
212#63225—28no—
213C4×Dic17—28no—
214C4×Dic17—48no—
215#13813—171nomaximal, Sylow
216C23×C17—22no—
217C23×C17—22no—
218C23×C17—24no—
219C23×C17—24no—
220C23×C17—24no—
221C23×C17—22no—
222C23×C17—22no—
223C23×C17—24no—
224C23×C17—24no—
225C23×C17—22no—
226C23×C17—24no—
227C23×C17—22no—
228C23×C17—42no—
229C23×C17—42no—
230C23×C17—41no—
231C23×C17—42no—
232C23×C17—42no—
233C23×C17—41no—
234C23×C17—42no—
235C23×C17—41no—
236C23×C17—41no—
237C23×C17—42no—
238C23×C17C2×C4214yes—
239C23×C17C23×C411yescharacteristic
240C23×C17C23×C412yes—
241C23×C17C22×D412yes—
242C23×C17C22×D411yescharacteristic
243C23×C17C2×#4111yescharacteristic
244C23×C17C2×#4112yes—
245C23×C17C2×#4111yescharacteristic
246C23×C17C2×#4111yescharacteristic
247C23×C17H(5,𝔽2)12yes—
248C23×C17H(5,𝔽2)11yescharacteristic
249C23×C172−1+411yescharacteristic
250C22×D17—22no—
251C22×D17—24no—
252C22×D17—22no—
253C22×D17—24no—
254C22×D17—24no—
255C22×D17—22no—
256C22×D17—24no—
257C22×D17—22no—
258C22×D17—24no—
259C22×D17—22no—
260C22×D17—24no—
261C22×D17—24no—
262C22×D17—24no—
263C22×D17—22no—
264C22×D17—24no—
265C22×D17—22no—
266C22×D17—22no—
267C22×D17—24no—
268C22×D17C2×C4214yes—
269C22×D17C2×C22⋊C414yes—
270C22×D17#11714yes—
271C22×D17C4×D418yes—
272C22×D17C4×D418yes—
273C2×C4×C17—22no—
274C2×C4×C17—24no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—24no—
278C2×C4×C17—22no—
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—24no—
287C2×C4×C17—24no—
288C2×C4×C17—24no—
289C2×C4×C17—24no—
290C2×C4×C17—416no—
291C2×C4×C17—42no—
292C2×C4×C17—42no—
293C2×C4×C17—42no—
294C2×C4×C17—42no—
295C2×C4×C17C2×C22⋊C414yes—
296C2×C4×C17C4×D414yes—
297C2×C4×C17C4×D418yescomplemented
298C22⋊D17—232no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—24no—
302C2×Dic17—24no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—24no—
306C2×Dic17—24no—
307C2×Dic17—22no—
308C2×Dic17—24no—
309C2×Dic17—22no—
310C2×Dic17—24no—
311C2×Dic17—24no—
312C2×Dic17—24no—
313C2×Dic17—24no—
314C2×Dic17—24no—
315C2×Dic17—22no—
316C2×Dic17—42no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321C2×Dic17—42no—
322C2×Dic17—42no—
323C2×Dic17—42no—
324C2×Dic17—42no—
325C2×Dic17—42no—
326C2×Dic17C2×C4214yes—
327C2×Dic17C2×C22⋊C414yes—
328C4×D17—416no—
329C4×D17—432no—
330C22×C4×D4—171no—
331C2×#386—172no—
332C2×C4×C22⋊C4—172no—
333C2×C4×C22⋊C4D1711yescharacteristic, complemented
334C22×#95—171no—
335#1437—172no—
336#1436—172no—
337#1434—171no—
338C22⋊#95—171no—
339C22⋊#95—171no—
340C4×#95—171no—
341C22×C17—24no—
342C22×C17—24no—
343C22×C17—24no—
344C22×C17—42no—
345C22×C17—42no—
346C22×C17—42no—
347C22×C17—42no—
348C22×C17—44no—
349C22×C17—44no—
350C22×C17—44no—
351C22×C17—44no—
352C22×C17C22×C4211yescharacteristic
353C22×C17C22×C22⋊C411yescharacteristic
354C22×C17C2×#11711yescharacteristic
355C22×C17C2×C4×D412yes—
356C22×C17C2×C4×D412yes—
357C22×C17C2×C4×D411yescharacteristic
358C22×C17C2×C4×D412yes—
359C22×C17C4×#4111yescharacteristic
360C22×C17C4×#4112yes—
361C22×C17#51812yes—
362C22×C17#51811yescharacteristic
363C22×C17#52012yes—
364C22×C17#52011yescharacteristic
365C22×C17D4212yes—
366C22×C17#54611yescharacteristic
367C22×C17#54612yes—
368C22×C17#54612yes—
369C22×C17#54712yes—
370C22×C17#54811yescharacteristic
371C22×C17#55112yes—
372C22×C17#55211yescharacteristic
373C22×C17#55311yescharacteristic
374C22×C17#55312yes—
375C2×D17—24no—
376C2×D17—24no—
377C2×D17—24no—
378C2×D17—24no—
379C2×D17—28no—
380C2×D17—28no—
381C2×D17—28no—
382C2×D17—28no—
383C2×D17—24no—
384C2×D17—24no—
385C2×D17C4×C22⋊C418yescomplemented
386C4×C17—24no—
387C4×C17—24no—
388C4×C17—28no—
389C4×C17—44no—
390Dic17—24no—
391Dic17—24no—
392Dic17—42no—
393Dic17—44no—
394Dic17—44no—
395C23×D4—171no—
396C24×C4—171no—
397C24×C4—172no—
398C24×C4C2×D1711yescharacteristic
399C2×C4×D4—178no—
400C2×C4×D4—348no—
401C22×C4⋊C4—171no—
402C22×C22⋊C4—171no—
403C22×C22⋊C4—171no—
404C22×C22⋊C4—172no—
405C22×C22⋊C4—172no—
406C22×C22⋊C4C2×D1712yes—
407C22×C42—171no—
408C22×C42—172no—
409C22×C42C2×D1712yes—
410#386—1716no—
411C4×C22⋊C4—24no—
412C4×C22⋊C4—348no—
413C2×#95—172no—
414C2×#95—172no—
415C2×#95—171no—
416C2×#95—171no—
417C2×#95—172no—
418C2×#95—172no—
419C2×#95—172no—
420C2×#95—172no—
421C2×#95—344no—
422C2×#95C2×D1711yescharacteristic
423C2×#95C2×D1711yescharacteristic
424C2×C17—44no—
425C2×C17C2×C4×C22⋊C411yescharacteristic
426C2×C17C42×D411yescharacteristic
427C2×C17#227511yescharacteristic
428C2×C17D4×C22⋊C411yescharacteristic
429C2×C17#233911yescharacteristic
430C2×C17#235211yescharacteristic
431C2×C17#235311yescharacteristic
432C2×C17#235812yes—
433C2×C17#235912yes—
434C2×C17#236112yes—
435C2×C17#236412yes—
436D17—28no—
437C25—171no—
438C25C22×D1711yescharacteristic
439C22×D4—174no—
440C22×D4—178no—
441C22×D4—344no—
442C22×D4—342no—
443C22×D4—342no—
444C23×C4—22no—
445C23×C4—24no—
446C23×C4—22no—
447C23×C4—42no—
448C23×C4—171no—
449C23×C4—171no—
450C23×C4—172no—
451C23×C4—171no—
452C23×C4—172no—
453C23×C4—174no—
454C23×C4—178no—
455C23×C4—344no—
456C23×C4—344no—
457C23×C4—344no—
458C23×C4—342no—
459C23×C4—344no—
460C23×C4—342no—
461C23×C4—344no—
462C23×C4—682no—
463C23×C4—682no—
464C23×C4—682no—
465C23×C4C4×D1714yescomplemented
466C23×C4C22×D1712yes—
467C23×C4C22×D1712yes—
468C23×C4C22×D1711yescharacteristic
469C23×C4C22×D1711yescharacteristic
470C4×D4—3432no—
471C2×C4⋊C4—174no—
472C2×C4⋊C4—344no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—174no—
476C2×C22⋊C4—178no—
477C2×C22⋊C4—174no—
478C2×C22⋊C4—178no—
479C2×C22⋊C4—178no—
480C2×C22⋊C4—344no—
481C2×C22⋊C4—344no—
482C2×C22⋊C4—344no—
483C2×C22⋊C4—682no—
484C2×C22⋊C4—682no—
485C2×C22⋊C4C4×D1718yescomplemented
486C2×C42—24no—
487C2×C42—24no—
488C2×C42—42no—
489C2×C42—174no—
490C2×C42—344no—
491C2×C42—344no—
492C2×C42—344no—
493C2×C42—682no—
494#95—22no—
495#95—178no—
496#95—178no—
497#95—344no—
498#95—342no—
499#95—344no—
500#95—342no—
501#95—344no—
502#95—682no—
503#95C22⋊D1714yescomplemented
504C17#1381311yescharacteristic, complemented, Sylow
505C24—22no—
506C24—21no—
507C24—22no—
508C24—22no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—172no—
515C24—174no—
516C24—174no—
517C24—172no—
518C24—172no—
519C24—342no—
520C24—341no—
521C24—342no—
522C24—341no—
523C24—341no—
524C24—341no—
525C24C2×C4×D1714yes—
526C24C2×C4×D1712yes—
527C24C23×D1711yescharacteristic
528C2×D4—1716no—
529C2×D4—348no—
530C2×D4—348no—
531C2×D4—3416no—
532C2×D4—3416no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—44no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4—174no—
554C22×C4—172no—
555C22×C4—172no—
556C22×C4—174no—
557C22×C4—174no—
558C22×C4—174no—
559C22×C4—172no—
560C22×C4—348no—
561C22×C4—3416no—
562C22×C4—342no—
563C22×C4—342no—
564C22×C4—341no—
565C22×C4—341no—
566C22×C4—341no—
567C22×C4—341no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—341no—
572C22×C4—342no—
573C22×C4—342no—
574C22×C4—342no—
575C22×C4—342no—
576C22×C4—342no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—342no—
581C22×C4—342no—
582C22×C4—341no—
583C22×C4—342no—
584C22×C4—348no—
585C22×C4—3416no—
586C22×C4—688no—
587C22×C4—684no—
588C22×C4—688no—
589C22×C4—688no—
590C22×C4—688no—
591C22×C4—688no—
592C22×C4—688no—
593C22×C4—688no—
594C22×C4C2×C4×D1714yes—
595C22×C4C2×C4×D1712yes—
596C22×C4C2×C4×D1712yes—
597C22×C4C2×C4×D1714yes—
598C22×C4#6325212yes—
599C22×C4#6325214yes—
600C22×C4D4×D1714yes—
601C22×C4C2×C22⋊D1712yes—
602C22×C4C2×C22⋊D1714yes—
603C4⋊C4—348no—
604C22⋊C4—216no—
605C22⋊C4—1716no—
606C22⋊C4—3416no—
607C22⋊C4—348no—
608C22⋊C4—688no—
609C42—48no—
610C42—348no—
611C42—688no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—22no—
622C23—24no—
623C23—22no—
624C23—42no—
625C23—41no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—42no—
631C23—41no—
632C23—42no—
633C23—42no—
634C23—174no—
635C23—174no—
636C23—174no—
637C23—178no—
638C23—178no—
639C23—344no—
640C23—342no—
641C23—344no—
642C23—342no—
643C23—342no—
644C23—344no—
645C23—342no—
646C23—344no—
647C23—342no—
648C23—344no—
649C23—344no—
650C23—342no—
651C23—344no—
652C23—342no—
653C23—344no—
654C23—342no—
655C23—344no—
656C23—344no—
657C23C42×D1714yes—
658C23C22×C4×D1711yescharacteristic
659C23C22×C4×D1712yes—
660C23C2×#6325212yes—
661C23C2×#6325211yescharacteristic
662C23C2×D4×D1712yes—
663C23#1058769112yes—
664C23#41×D1711yescharacteristic
665C23#41×D1711yescharacteristic
666C23#1058769611yescharacteristic
667C23#1058769711yescharacteristic
668C23C22×C22⋊D1711yescharacteristic
669D4—3432no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—416no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—174no—
693C2×C4—174no—
694C2×C4—344no—
695C2×C4—342no—
696C2×C4—342no—
697C2×C4—344no—
698C2×C4—344no—
699C2×C4—342no—
700C2×C4—342no—
701C2×C4—344no—
702C2×C4—342no—
703C2×C4—344no—
704C2×C4—344no—
705C2×C4—342no—
706C2×C4—344no—
707C2×C4—344no—
708C2×C4—344no—
709C2×C4—344no—
710C2×C4—342no—
711C2×C4—6816no—
712C2×C4—6832no—
713C2×C4—682no—
714C2×C4—682no—
715C2×C4—682no—
716C2×C4—682no—
717C2×C4—682no—
718C2×C4—682no—
719C2×C4—682no—
720C2×C4—682no—
721C2×C4—682no—
722C2×C4—682no—
723C2×C4C22⋊C4×D1714yes—
724C2×C4C4×C22⋊D1714yes—
725C2×C4C4×C22⋊D1718yescomplemented
726C22—24no—
727C22—24no—
728C22—24no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—44no—
734C22—44no—
735C22—44no—
736C22—44no—
737C22—178no—
738C22—344no—
739C22—344no—
740C22—344no—
741C22—344no—
742C22—344no—
743C22—344no—
744C22—348no—
745C22—348no—
746C22—348no—
747C22—348no—
748C22C2×C42×D1711yescharacteristic
749C22C2×C22⋊C4×D1711yescharacteristic
750C22#117×D1711yescharacteristic
751C22C4×D4×D1712yes—
752C22C4×D4×D1712yes—
753C22C2×C4×C22⋊D1711yescharacteristic
754C22C2×C4×C22⋊D1712yes—
755C22C4×#6325211yescharacteristic
756C22C4×#6325212yes—
757C22#1176328112yes—
758C22#1176328211yescharacteristic
759C22#1176328812yes—
760C22#1176328911yescharacteristic
761C22D4×C22⋊D1712yes—
762C22#1176344711yescharacteristic
763C22#1176344912yes—
764C22#1176345512yes—
765C22#1176346412yes—
766C22#1176346611yescharacteristic
767C22#1176348812yes—
768C22#1176349811yescharacteristic
769C22#1176350311yescharacteristic
770C22#1176350912yes—
771C4—24no—
772C4—24no—
773C4—28no—
774C4—44no—
775C4—344no—
776C4—344no—
777C4—682no—
778C4—684no—
779C4—684no—
780C2—44no—
781C2—348no—
782C2C4×C22⋊C4×D1711yescharacteristic
783C2C42×C22⋊D1711yescharacteristic
784C2#1453114311yescharacteristic
785C2C22⋊C4×C22⋊D1711yescharacteristic
786C2#1453161511yescharacteristic
787C2#1453171411yescharacteristic
788C2#1453172711yescharacteristic
789C2#1453176112yes—
790C2#1453177712yes—
791C2#1453179612yes—
792C2#1453183512yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC2×C4×C22⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×C4×C22⋊C4D17
hypocenterC17#13813
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#63227C2semidirect
4. C2×#95×D17C2semidirect
5. #14527021C2semidirect
6. #14527017C2semidirect
7. #14527010C2semidirect
8. #14527007C2semidirect
9. #14527005C2semidirect
10. #95×Dic17C2semidirect
11. C2×C4×C22⋊C4×C17C2semidirect
16. C2×C4×C22⋊D17C4semidirect
24. #11762685C4semidirect
47. C23×C4×C17C2×C4semidirect
73. C22×C4×D17C2×C4semidirect
76. C2×C22⋊C4×C17C2×C4semidirect
83. C2×C22⋊Dic17C2×C4semidirect
84. C2×C22⋊Dic17C2×C4semidirect
89. C2×#63227C2×C4semidirect
92. C2×#63225C2×C4semidirect
97. C2×C4×Dic17C2×C4semidirect
99. C17×#95D4semidirect
106. #10587502C2×C4semidirect
107. #10587502C2×C4semidirect
164. C2×C22⋊D17C42semidirect
211. #63227C22⋊C4semidirect
297. C2×C4×C17C4×D4semidirect
333. C2×C4×C22⋊C4D17semidirect
385. C2×D17C4×C22⋊C4semidirect
465. C23×C4C4×D17semidirect
485. C2×C22⋊C4C4×D17semidirect
503. #95C22⋊D17semidirect
504. C17#13813semidirect
725. C2×C4C4×C22⋊D17semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D172
C2×#117626852
C2×C4×#632272
C2×#95×D172
#145270212
#145270172
#145270102
#145270072
#145270052
#95×Dic172
C2×C4×C22⋊C4×C172
#1381317