Finite Group Databasebeta

← #16955618

Subgroups — #16955618

Order 4352.

2686 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D17C211yesmaximal, characteristic
2C2×#11762685C212yesmaximal
3C2×#11762656C211yesmaximal, characteristic, complemented
4C2×#95×D17C211yesmaximal, characteristic, complemented
5#14527021C212yesmaximal, complemented
6#14527015C212yesmaximal, complemented
7#14527008C211yesmaximal, characteristic, complemented
8#14527008C211yesmaximal, characteristic, complemented
9#14527007C211yesmaximal, characteristic, complemented
10#14527005C212yesmaximal, complemented
11C17×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D17C2211yescharacteristic
13C23×C4×D17C2212yes—
14C23×C4×D17C2211yescharacteristic
15C2×C4×C22⋊D17—24no—
16C2×C4×C22⋊D17—24no—
17C2×C4×C22⋊D17C418yescomplemented
18C22×#63225C2211yescharacteristic
19C22×C22⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2212yes—
21C22×#63227C2211yescharacteristic
22C22×#63227C2212yes—
23C22×C4×Dic17C2211yescharacteristic
24C22×C4×Dic17C2212yes—
25#11762685C4116yescomplemented
26#11762656—24no—
27C2×#10587502C2211yescharacteristic
28C2×#10587502C2211yescharacteristic
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35#95×D17—24no—
36C24×C4×C17C2211yescharacteristic
37C22×C22⋊C4×C17C2212yes—
38C2×C17×#95C2211yescharacteristic
39C2×C17×#95C2211yescharacteristic
40C2×C17×#95C2212yes—
41C25×C17C2311yescharacteristic
42C24×D17C2311yescharacteristic
43C23×C4×C17—22no—
44C23×C4×C17—22no—
45C23×C4×C17—42no—
46C23×C4×C17—42no—
47C23×C4×C17C2×C414yescomplemented
48C23×C4×C17C2312yes—
49C23×C4×C17C2312yes—
50C23×C4×C17C2311yescharacteristic
51C23×C4×C17C2311yescharacteristic
52C22×C22⋊D17—22no—
53C22×C22⋊D17—22no—
54C22×C22⋊D17—24no—
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—42no—
65C22×C4×D17—42no—
66C22×C4×D17—42no—
67C22×C4×D17—42no—
68C22×C4×D17—42no—
69C22×C4×D17—42no—
70C22×C4×D17C2×C414yes—
71C22×C4×D17C2×C418yescomplemented
72C22×C4×D17D414yes—
73C22×C4×D17D414yes—
74C2×C22⋊C4×C17—42no—
75C2×C22⋊C4×C17—42no—
76C2×C22⋊C4×C17C2×C418yescomplemented
77C2×C22⋊Dic17—22no—
78C2×C22⋊Dic17—22no—
79C2×C22⋊Dic17—42no—
80C2×C22⋊Dic17—42no—
81C2×C22⋊Dic17C2×C414yescomplemented
82C2×C22⋊Dic17C2×C418yescomplemented
83C4×C22⋊D17—232no—
84C2×#63227—22no—
85C2×#63227—22no—
86C2×#63227—24no—
87C2×#63227—24no—
88C2×#63227C2×C414yes—
89C2×#63227C2×C418yescomplemented
90C2×#63225—22no—
91C2×#63225—22no—
92C2×#63225C2×C414yescomplemented
93C2×C4×Dic17—22no—
94C2×C4×Dic17—22no—
95C2×C4×Dic17—24no—
96C2×C4×Dic17—42no—
97C2×C4×Dic17—42no—
98C2×C4×Dic17C2×C414yescomplemented
99C17×#95—22no—
100C17×#95—22no—
101C17×#95—42no—
102#10587502—22no—
103#10587502—22no—
104#10587502—24no—
105#10587502—42no—
106#10587502—42no—
107#10587502—42no—
108#10587502C2×C418yescomplemented
109#10587502C2×C418yescomplemented
110C24×C17—21no—
111C24×C17—21no—
112C24×C17—22no—
113C24×C17—22no—
114C24×C17—22no—
115C24×C17—21no—
116C24×C17—21no—
117C24×C17—21no—
118C24×C17—21no—
119C24×C17C22×C412yes—
120C24×C17C22×C414yes—
121C24×C17C2411yescharacteristic
122C23×D17—22no—
123C23×D17—22no—
124C23×D17—21no—
125C23×D17—21no—
126C23×D17—21no—
127C23×D17—21no—
128C23×D17C22×C412yes—
129C23×D17C22×C414yes—
130C23×D17C2×D412yes—
131C23×D17C2×D412yes—
132C23×D17#4114yes—
133C22×C4×C17—22no—
134C22×C4×C17—22no—
135C22×C4×C17—22no—
136C22×C4×C17—21no—
137C22×C4×C17—21no—
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—22no—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—22no—
151C22×C4×C17—28no—
152C22×C4×C17—44no—
153C22×C4×C17—44no—
154C22×C4×C17—48no—
155C22×C4×C17—48no—
156C22×C4×C17C22×C414yes—
157C22×C4×C17C22×C412yes—
158C22×C4×C17C22×C414yes—
159C22×C4×C17C22×C412yes—
160C22×C4×C17C2×D412yes—
161C22×C4×C17C2×D412yes—
162C2×C22⋊D17—28no—
163C2×C22⋊D17—28no—
164C2×C22⋊D17—216no—
165C2×C22⋊D17—216no—
166C2×C22⋊D17C42116yescomplemented
167C22×Dic17—21no—
168C22×Dic17—21no—
169C22×Dic17—22no—
170C22×Dic17—22no—
171C22×Dic17—22no—
172C22×Dic17—22no—
173C22×Dic17—22no—
174C22×Dic17—21no—
175C22×Dic17—21no—
176C22×Dic17—22no—
177C22×Dic17—22no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—21no—
183C22×Dic17—21no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—21no—
188C22×Dic17—22no—
189C22×Dic17—21no—
190C22×Dic17C22×C414yes—
191C22×Dic17C22×C414yes—
192C22×Dic17C22×C412yes—
193C22×Dic17C22×C414yes—
194C22×Dic17C22×C412yes—
195C22×Dic17C22×C412yes—
196C22×Dic17C2×D412yes—
197C22×Dic17C2×D412yes—
198C2×C4×D17—216no—
199C2×C4×D17—44no—
200C2×C4×D17—44no—
201C2×C4×D17—48no—
202C2×C4×D17—48no—
203C2×C4×D17—48no—
204C2×C4×D17—48no—
205C2×C4×D17—48no—
206C2×C4×D17—48no—
207C2×C4×D17—48no—
208C2×C4×D17—48no—
209C2×C4×D17C22⋊C4116yescomplemented
210C22⋊C4×C17—48no—
211C22⋊Dic17—28no—
212C22⋊Dic17—48no—
213#63227—28no—
214#63227—216no—
215#63225—28no—
216C4×Dic17—28no—
217C4×Dic17—48no—
218#13784—171nomaximal, Sylow
219C23×C17—22no—
220C23×C17—22no—
221C23×C17—24no—
222C23×C17—24no—
223C23×C17—24no—
224C23×C17—24no—
225C23×C17—22no—
226C23×C17—22no—
227C23×C17—24no—
228C23×C17—22no—
229C23×C17—22no—
230C23×C17—24no—
231C23×C17—42no—
232C23×C17—42no—
233C23×C17—41no—
234C23×C17—41no—
235C23×C17—41no—
236C23×C17—41no—
237C23×C17—42no—
238C23×C17—42no—
239C23×C17—42no—
240C23×C17—42no—
241C23×C17C2×C4214yes—
242C23×C17C23×C411yescharacteristic
243C23×C17C23×C412yes—
244C23×C17C22×D411yescharacteristic
245C23×C17C22×D411yescharacteristic
246C23×C17C2×#4112yes—
247C23×C17H(5,𝔽2)12yes—
248C23×C17H(5,𝔽2)12yes—
249C23×C17H(5,𝔽2)11yescharacteristic
250C23×C17H(5,𝔽2)11yescharacteristic
251C23×C172−1+411yescharacteristic
252C23×C172−1+411yescharacteristic
253C22×D17—24no—
254C22×D17—22no—
255C22×D17—22no—
256C22×D17—24no—
257C22×D17—24no—
258C22×D17—22no—
259C22×D17—22no—
260C22×D17—24no—
261C22×D17—24no—
262C22×D17—24no—
263C22×D17—22no—
264C22×D17—22no—
265C22×D17—22no—
266C22×D17—22no—
267C22×D17—24no—
268C22×D17—24no—
269C22×D17—24no—
270C22×D17—24no—
271C22×D17C2×C4214yes—
272C22×D17C2×C22⋊C414yes—
273C22×D17#11714yes—
274C22×D17C4×D418yes—
275C22×D17C4×D418yes—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—24no—
279C2×C4×C17—24no—
280C2×C4×C17—22no—
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—24no—
289C2×C4×C17—416no—
290C2×C4×C17—42no—
291C2×C4×C17—42no—
292C2×C4×C17—42no—
293C2×C4×C17—42no—
294C2×C4×C17—42no—
295C2×C4×C17—42no—
296C2×C4×C17—42no—
297C2×C4×C17—42no—
298C2×C4×C17—42no—
299C2×C4×C17—42no—
300C2×C4×C17C2×C22⋊C414yes—
301C22⋊D17—232no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—24no—
305C2×Dic17—24no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—24no—
309C2×Dic17—24no—
310C2×Dic17—22no—
311C2×Dic17—24no—
312C2×Dic17—24no—
313C2×Dic17—24no—
314C2×Dic17—24no—
315C2×Dic17—24no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—24no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321C2×Dic17—42no—
322C2×Dic17—41no—
323C2×Dic17—41no—
324C2×Dic17—41no—
325C2×Dic17—41no—
326C2×Dic17—42no—
327C2×Dic17—42no—
328C2×Dic17—42no—
329C2×Dic17—42no—
330C2×Dic17—42no—
331C2×Dic17C2×C4214yes—
332C2×Dic17C2×C22⋊C414yes—
333C4×D17—416no—
334C4×D17—432no—
335C22×C4×D4—171no—
336C2×#386—172no—
337C2×C4×C22⋊C4—171no—
338C22×#95—171no—
339#1437—172no—
340#1436—172no—
341#1434—171no—
342#1434—171no—
343C22⋊#95—172no—
344C22⋊#95—171no—
345C22⋊#95D1711yescharacteristic, complemented
346C22×C17—24no—
347C22×C17—24no—
348C22×C17—24no—
349C22×C17—42no—
350C22×C17—42no—
351C22×C17—42no—
352C22×C17—42no—
353C22×C17—44no—
354C22×C17—44no—
355C22×C17—44no—
356C22×C17—44no—
357C22×C17C22×C4211yescharacteristic
358C22×C17C22×C22⋊C411yescharacteristic
359C22×C17C2×#11711yescharacteristic
360C22×C17C2×C4×D412yes—
361C22×C17C2×C4×D412yes—
362C22×C17#51812yes—
363C22×C17#51811yescharacteristic
364C22×C17#51811yescharacteristic
365C22×C17#51812yes—
366C22×C17#52012yes—
367C22×C17#52011yescharacteristic
368C22×C17#52011yescharacteristic
369C22×C17#52012yes—
370C22×C17#53412yes—
371C22×C17#53412yes—
372C22×C17#53511yescharacteristic
373C22×C17#53611yescharacteristic
374C22×C17#53711yescharacteristic
375C22×C17#53711yescharacteristic
376C22×C17#53812yes—
377C22×C17#53812yes—
378C22×C17#53912yes—
379C22×C17#53912yes—
380C2×D17—24no—
381C2×D17—24no—
382C2×D17—24no—
383C2×D17—24no—
384C2×D17—28no—
385C2×D17—28no—
386C2×D17—28no—
387C2×D17—28no—
388C2×D17—24no—
389C2×D17—24no—
390C2×D17C4×C22⋊C418yes—
391C4×C17—24no—
392C4×C17—42no—
393C4×C17—44no—
394C4×C17—44no—
395Dic17—24no—
396Dic17—24no—
397Dic17—42no—
398Dic17—44no—
399Dic17—44no—
400C23×D4—171no—
401C24×C4—171no—
402C24×C4—172no—
403C24×C4C2×D1711yescharacteristic
404C2×C4×D4—178no—
405C2×C4×D4—344no—
406C2×C4×D4—344no—
407C22×C4⋊C4—171no—
408C22×C22⋊C4—171no—
409C22×C22⋊C4—171no—
410C22×C22⋊C4—172no—
411C22×C22⋊C4—172no—
412C22×C22⋊C4C2×D1712yes—
413C22×C42—171no—
414C22×C42—172no—
415#386—1716no—
416C4×C22⋊C4—344no—
417C2×#95—172no—
418C2×#95—172no—
419C2×#95—171no—
420C2×#95—171no—
421C2×#95—172no—
422C2×#95—172no—
423C2×#95—172no—
424C2×#95—172no—
425C2×#95—344no—
426C2×#95C2×D1711yescharacteristic
427C2×#95C2×D1711yescharacteristic
428C2×#95C2×D1712yes—
429C2×C17—44no—
430C2×C17C2×C4×C22⋊C411yescharacteristic
431C2×C17#227511yescharacteristic
432C2×C17#227511yescharacteristic
433C2×C17#230811yescharacteristic
434C2×C17#231111yescharacteristic
435C2×C17#231811yescharacteristic
436C2×C17#231811yescharacteristic
437C2×C17#232112yes—
438C2×C17#232212yes—
439C2×C17#232512yes—
440C2×C17#232512yes—
441D17—28no—
442C25—171no—
443C25C22×D1711yescharacteristic
444C22×D4—174no—
445C22×D4—178no—
446C22×D4—342no—
447C22×D4—342no—
448C22×D4—344no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—42no—
452C23×C4—42no—
453C23×C4—171no—
454C23×C4—171no—
455C23×C4—174no—
456C23×C4—174no—
457C23×C4—174no—
458C23×C4—172no—
459C23×C4—171no—
460C23×C4—172no—
461C23×C4—178no—
462C23×C4—344no—
463C23×C4—344no—
464C23×C4—682no—
465C23×C4—682no—
466C23×C4—682no—
467C23×C4—682no—
468C23×C4—682no—
469C23×C4—682no—
470C23×C4C4×D1714yescomplemented
471C23×C4C22×D1712yes—
472C23×C4C22×D1711yescharacteristic
473C23×C4C22×D1712yes—
474C23×C4C22×D1711yescharacteristic
475C4×D4—3432no—
476C2×C4⋊C4—174no—
477C2×C4⋊C4—342no—
478C2×C4⋊C4—342no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—174no—
482C2×C22⋊C4—174no—
483C2×C22⋊C4—178no—
484C2×C22⋊C4—178no—
485C2×C22⋊C4—342no—
486C2×C22⋊C4—342no—
487C2×C22⋊C4—344no—
488C2×C22⋊C4—344no—
489C2×C22⋊C4—342no—
490C2×C22⋊C4—342no—
491C2×C22⋊C4—682no—
492C2×C22⋊C4—682no—
493C2×C22⋊C4C4×D1718yescomplemented
494C2×C42—174no—
495C2×C42—342no—
496C2×C42—342no—
497C2×C42—344no—
498C2×C42—682no—
499C2×C42—682no—
500#95—22no—
501#95—22no—
502#95—42no—
503#95—178no—
504#95—178no—
505#95—344no—
506#95—342no—
507#95—342no—
508#95—682no—
509#95—682no—
510#95—682no—
511C17#1378411yescharacteristic, complemented, Sylow
512C24—21no—
513C24—21no—
514C24—21no—
515C24—22no—
516C24—22no—
517C24—21no—
518C24—22no—
519C24—21no—
520C24—21no—
521C24—172no—
522C24—174no—
523C24—172no—
524C24—172no—
525C24—174no—
526C24—342no—
527C24—342no—
528C24—341no—
529C24—341no—
530C24—341no—
531C24—341no—
532C24C2×C4×D1714yes—
533C24C2×C4×D1712yes—
534C24C23×D1711yescharacteristic
535C2×D4—1716no—
536C2×D4—348no—
537C2×D4—348no—
538C2×D4—3416no—
539C2×D4—3416no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—28no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—174no—
564C22×C4—172no—
565C22×C4—172no—
566C22×C4—172no—
567C22×C4—172no—
568C22×C4—1716no—
569C22×C4—174no—
570C22×C4—174no—
571C22×C4—172no—
572C22×C4—3416no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—342no—
576C22×C4—342no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—341no—
581C22×C4—341no—
582C22×C4—341no—
583C22×C4—342no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—342no—
587C22×C4—342no—
588C22×C4—341no—
589C22×C4—342no—
590C22×C4—342no—
591C22×C4—342no—
592C22×C4—341no—
593C22×C4—342no—
594C22×C4—342no—
595C22×C4—341no—
596C22×C4—684no—
597C22×C4—684no—
598C22×C4—688no—
599C22×C4—688no—
600C22×C4—688no—
601C22×C4—688no—
602C22×C4—688no—
603C22×C4—688no—
604C22×C4—688no—
605C22×C4—688no—
606C22×C4C2×C4×D1714yes—
607C22×C4C2×C4×D1714yes—
608C22×C4C2×C4×D1712yes—
609C22×C4C2×C4×D1712yes—
610C22×C4D4×D1712yes—
611C22×C4D4×D1712yes—
612C4⋊C4—348no—
613C22⋊C4—48no—
614C22⋊C4—348no—
615C22⋊C4—3416no—
616C22⋊C4—348no—
617C22⋊C4—688no—
618C42—348no—
619C42—688no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—42no—
633C23—42no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—174no—
643C23—174no—
644C23—174no—
645C23—178no—
646C23—178no—
647C23—344no—
648C23—342no—
649C23—342no—
650C23—344no—
651C23—344no—
652C23—342no—
653C23—342no—
654C23—344no—
655C23—344no—
656C23—344no—
657C23—342no—
658C23—342no—
659C23—342no—
660C23—342no—
661C23—344no—
662C23—344no—
663C23—344no—
664C23—344no—
665C23C42×D1714yes—
666C23C22×C4×D1711yescharacteristic
667C23C22×C4×D1712yes—
668C23C2×D4×D1711yescharacteristic
669C23C2×D4×D1711yescharacteristic
670C23#1058769112yes—
671C23#1058769112yes—
672C23#1058769111yescharacteristic
673C23#1058769411yescharacteristic
674C23#41×D1712yes—
675C23#1058769611yescharacteristic
676C23#1058769711yescharacteristic
677D4—3432no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—416no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—174no—
703C2×C4—174no—
704C2×C4—342no—
705C2×C4—342no—
706C2×C4—344no—
707C2×C4—344no—
708C2×C4—342no—
709C2×C4—342no—
710C2×C4—344no—
711C2×C4—344no—
712C2×C4—342no—
713C2×C4—344no—
714C2×C4—344no—
715C2×C4—344no—
716C2×C4—344no—
717C2×C4—344no—
718C2×C4—342no—
719C2×C4—342no—
720C2×C4—344no—
721C2×C4—6816no—
722C2×C4—6832no—
723C2×C4—682no—
724C2×C4—682no—
725C2×C4—682no—
726C2×C4—681no—
727C2×C4—681no—
728C2×C4—681no—
729C2×C4—681no—
730C2×C4—682no—
731C2×C4—682no—
732C2×C4—682no—
733C2×C4—682no—
734C2×C4—682no—
735C2×C4C22⋊C4×D1714yes—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—178no—
748C22—344no—
749C22—344no—
750C22—344no—
751C22—344no—
752C22—344no—
753C22—344no—
754C22—348no—
755C22—348no—
756C22—348no—
757C22—348no—
758C22C2×C42×D1711yescharacteristic
759C22C2×C22⋊C4×D1711yescharacteristic
760C22#117×D1711yescharacteristic
761C22C4×D4×D1712yes—
762C22C4×D4×D1712yes—
763C22#1176328112yes—
764C22#1176328211yescharacteristic
765C22#1176328211yescharacteristic
766C22#1176328212yes—
767C22#1176328812yes—
768C22#1176328911yescharacteristic
769C22#1176329011yescharacteristic
770C22#1176329012yes—
771C22#1176336912yes—
772C22#1176336912yes—
773C22#1176337511yescharacteristic
774C22#1176338211yescharacteristic
775C22#1176338811yescharacteristic
776C22#1176338911yescharacteristic
777C22#1176339112yes—
778C22#1176339512yes—
779C22#1176340212yes—
780C22#1176340512yes—
781C4—24no—
782C4—42no—
783C4—44no—
784C4—44no—
785C4—344no—
786C4—344no—
787C4—682no—
788C4—684no—
789C4—684no—
790C2—44no—
791C2—348no—
792C2C4×C22⋊C4×D1711yescharacteristic
793C2#1453114211yescharacteristic
794C2#1453114311yescharacteristic
795C2#1453136011yescharacteristic
796C2#1453137311yescharacteristic
797C2#1453141311yescharacteristic
798C2#1453141911yescharacteristic
799C2#1453144012yes—
800C2#1453145112yes—
801C2#1453148112yes—
802C2#1453148612yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC17×C22⋊#95C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC22⋊#95D17
hypocenterC17#13784
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#11762656C2semidirect
4. C2×#95×D17C2semidirect
5. #14527021C2semidirect
6. #14527015C2semidirect
7. #14527008C2semidirect
8. #14527008C2semidirect
9. #14527007C2semidirect
10. #14527005C2semidirect
11. C17×C22⋊#95C2semidirect
17. C2×C4×C22⋊D17C4semidirect
25. #11762685C4semidirect
47. C23×C4×C17C2×C4semidirect
71. C22×C4×D17C2×C4semidirect
76. C2×C22⋊C4×C17C2×C4semidirect
81. C2×C22⋊Dic17C2×C4semidirect
82. C2×C22⋊Dic17C2×C4semidirect
89. C2×#63227C2×C4semidirect
92. C2×#63225C2×C4semidirect
98. C2×C4×Dic17C2×C4semidirect
108. #10587502C2×C4semidirect
109. #10587502C2×C4semidirect
166. C2×C22⋊D17C42semidirect
209. C2×C4×D17C22⋊C4semidirect
345. C22⋊#95D17semidirect
470. C23×C4C4×D17semidirect
493. C2×C22⋊C4C4×D17semidirect
511. C17#13784semidirect

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×#117626562
C2×#95×D172
#145270212
#145270152
#145270082
#145270072
#145270052
C17×C22⋊#952
#1378417