Finite Group Databasebeta

← C2×#14529961 #17061762

Subgroups — C2×#14529961 #17061762

Order 4352.

1434 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763435C211yesmaximal, characteristic, complemented
2C22×#10587505C211yesmaximal, characteristic
3C22×#10587505C211yesmaximal, characteristic
4#14529961C218yesmaximal, direct product factor
5C2×#11762576C211yesmaximal, characteristic, complemented
6C2×#11762575C211yesmaximal, characteristic, complemented
7C2×#11762575C211yesmaximal, characteristic, complemented
8C22×C17×#99C211yesmaximal, characteristic
9#11763435—22no—
10#11763435—22no—
11#11763435—22no—
12#11763435C2214yescomplemented
13C2×#10587610—22no—
14C2×#10587564—22no—
15C2×#10587564—22no—
16C22×C22⋊Dic17C2211yescharacteristic
17C22×C22⋊Dic17C2211yescharacteristic
18C22×C22⋊Dic17C2211yescharacteristic
19C22×C22⋊Dic17C2211yescharacteristic
20C2×#10587505—22no—
21C2×#10587505—22no—
22C2×#10587505—22no—
23C2×#10587505—22no—
24C2×#10587505C2214yes—
25C2×#10587505C2214yes—
26#11762576C2214yescomplemented
27#11762575C2214yescomplemented
28#11762575C2214yescomplemented
29C23×D4×C17C2211yescharacteristic
30C22×C22⋊C4×C17C2211yescharacteristic
31C22×C22⋊C4×C17C2211yescharacteristic
32C2×C17×#99—22no—
33C2×C17×#99—22no—
34C2×C17×#99C2214yes—
35C25×C17Q811yescharacteristic, complemented
36C25×C17C2311yescharacteristic
37C22×D4×C17—21no—
38C22×D4×C17—21no—
39C22×D4×C17—21no—
40C22×D4×C17—21no—
41C22×D4×C17—21no—
42C22×D4×C17—21no—
43C22×D4×C17—21no—
44C22×D4×C17—21no—
45C22×D4×C17—21no—
46C22×D4×C17—21no—
47C22×D4×C17—21no—
48C22×D4×C17—21no—
49C22×D4×C17Q812yescomplemented
50C22×D4×C17C2312yes—
51C23×C4×C17—21no—
52C23×C4×C17—21no—
53C23×C4×C17Q811yescharacteristic, complemented
54C23×Dic17—21no—
55C23×Dic17—21no—
56C23×Dic17—21no—
57C23×Dic17—21no—
58C22×Dic34—22no—
59C2×C22⋊C4×C17—21no—
60C2×C22⋊C4×C17—21no—
61C2×C22⋊C4×C17—21no—
62C2×C22⋊C4×C17—21no—
63C2×C22⋊C4×C17—21no—
64C2×C22⋊C4×C17—21no—
65C2×C22⋊C4×C17—21no—
66C2×C22⋊C4×C17—21no—
67C2×C22⋊C4×C17D412yes—
68C2×C22⋊C4×C17D412yes—
69C2×C22⋊C4×C17C2312yes—
70C2×C22⋊C4×C17C2312yes—
71C2×C22⋊Dic17—21no—
72C2×C22⋊Dic17—21no—
73C2×C22⋊Dic17—21no—
74C2×C22⋊Dic17—21no—
75C2×C22⋊Dic17—21no—
76C2×C22⋊Dic17—21no—
77C2×C22⋊Dic17—21no—
78C2×C22⋊Dic17—21no—
79C2×C22⋊Dic17—21no—
80C2×C22⋊Dic17—21no—
81C2×C22⋊Dic17—21no—
82C2×C22⋊Dic17—21no—
83C2×C22⋊Dic17—21no—
84C2×C22⋊Dic17—21no—
85C2×C22⋊Dic17—21no—
86C2×C22⋊Dic17—21no—
87C2×C22⋊Dic17D412yes—
88C2×C22⋊Dic17D412yes—
89C2×C22⋊Dic17D412yes—
90C2×C22⋊Dic17D412yes—
91C2×C22⋊Dic17C2312yes—
92C2×C22⋊Dic17C2312yes—
93C2×C22⋊Dic17C2312yes—
94C2×C22⋊Dic17C2312yes—
95C2×C4⋊Dic17—22no—
96#10587610—28no—
97#10587610—28no—
98C2×#63225—24no—
99#10587564—28no—
100#10587564—28no—
101#10587564—28no—
102#10587564—28no—
103C17×#99—28no—
104#10587505—28no—
105#10587505—28no—
106C24×C17—21no—
107C24×C17—21no—
108C24×C17—21no—
109C24×C17—21no—
110C24×C17—21no—
111C24×C17—21no—
112C24×C17—82no—
113C24×C17—82no—
114C24×C17C2×D411yescharacteristic
115C24×C17C2×D411yescharacteristic
116C24×C17C2×D411yescharacteristic
117C24×C17C2×D411yescharacteristic
118C24×C17C2×D411yescharacteristic
119C24×C17C2×D411yescharacteristic
120C24×C17C2×Q811yescharacteristic
121C24×C17C2×Q811yescharacteristic
122C24×C17C2×Q812yescomplemented
123C24×C17#4111yescharacteristic
124C24×C17#4111yescharacteristic
125C24×C17#4111yescharacteristic
126C24×C17#4111yescharacteristic
127C24×C17#4111yescharacteristic
128C24×C17#4111yescharacteristic
129C24×C17C2411yescharacteristic
130C2×D4×C17—22no—
131C2×D4×C17—22no—
132C2×D4×C17—22no—
133C2×D4×C17—22no—
134C2×D4×C17—22no—
135C2×D4×C17—22no—
136C2×D4×C17—22no—
137C2×D4×C17—22no—
138C2×D4×C17—22no—
139C2×D4×C17—22no—
140C2×D4×C17—22no—
141C2×D4×C17—22no—
142C2×D4×C17—41no—
143C2×D4×C17—41no—
144C2×D4×C17—41no—
145C2×D4×C17—41no—
146C2×D4×C17—41no—
147C2×D4×C17—41no—
148C2×D4×C17—41no—
149C2×D4×C17—41no—
150C2×D4×C17—41no—
151C2×D4×C17—41no—
152C2×D4×C17—41no—
153C2×D4×C17—41no—
154C2×D4×C17—41no—
155C2×D4×C17—41no—
156C2×D4×C17—41no—
157C2×D4×C17—41no—
158C22×C4×C17—22no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—22no—
166C22×C4×C17—22no—
167C22×C4×C17—22no—
168C22×C4×C17—41no—
169C22×C4×C17—41no—
170C22×C4×C17—82no—
171C22×C4×C17—82no—
172C22×C4×C17C2×Q812yescomplemented
173C22×Dic17—22no—
174C22×Dic17—22no—
175C22×Dic17—22no—
176C22×Dic17—22no—
177C22×Dic17—22no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—41no—
182C22×Dic17—41no—
183C22×Dic17—41no—
184C22×Dic17—41no—
185C22×Dic17—82no—
186C22×Dic17—82no—
187C22×Dic17—82no—
188C22×Dic17—82no—
189C2×Dic34—28no—
190C2×Dic34—84no—
191C22⋊C4×C17—22no—
192C22⋊C4×C17—22no—
193C22⋊C4×C17—22no—
194C22⋊C4×C17—22no—
195C22⋊C4×C17—22no—
196C22⋊C4×C17—41no—
197C22⋊C4×C17—41no—
198C22⋊C4×C17C2×D414yes—
199C22⋊Dic17—22no—
200C22⋊Dic17—22no—
201C22⋊Dic17—22no—
202C22⋊Dic17—22no—
203C22⋊Dic17—22no—
204C22⋊Dic17—22no—
205C22⋊Dic17—22no—
206C22⋊Dic17—22no—
207C22⋊Dic17—22no—
208C22⋊Dic17—22no—
209C22⋊Dic17—41no—
210C22⋊Dic17—41no—
211C22⋊Dic17—41no—
212C22⋊Dic17—41no—
213C22⋊Dic17C2×D414yes—
214C22⋊Dic17C2×D414yes—
215C4⋊Dic17—28no—
216#63225—216no—
217C2×#2032—171nomaximal, Sylow
218C23×C17—22no—
219C23×C17—22no—
220C23×C17—22no—
221C23×C17—42no—
222C23×C17—42no—
223C23×C17—42no—
224C23×C17—42no—
225C23×C17—42no—
226C23×C17—42no—
227C23×C17—42no—
228C23×C17—41no—
229C23×C17—41no—
230C23×C17—41no—
231C23×C17—41no—
232C23×C17—82no—
233C23×C17—82no—
234C23×C17—82no—
235C23×C17—81no—
236C23×C17—81no—
237C23×C17—81no—
238C23×C17—81no—
239C23×C17—81no—
240C23×C17—81no—
241C23×C17—81no—
242C23×C17—81no—
243C23×C17—82no—
244C23×C17—82no—
245C23×C17—82no—
246C23×C17—82no—
247C23×C17#12011yescharacteristic
248C23×C17#12011yescharacteristic
249C23×C17#12011yescharacteristic
250C23×C17#12011yescharacteristic
251C23×C17C22⋊Q811yescharacteristic
252C23×C17C22⋊Q811yescharacteristic
253C23×C17C22⋊Q811yescharacteristic
254C23×C17C22⋊Q811yescharacteristic
255C23×C17C22⋊Q811yescharacteristic
256C23×C17C22⋊Q811yescharacteristic
257C23×C17C22⋊Q811yescharacteristic
258C23×C17C22⋊Q811yescharacteristic
259C23×C17C22⋊Q811yescharacteristic
260C23×C17C22⋊Q811yescharacteristic
261C23×C17C22⋊Q811yescharacteristic
262C23×C17C22⋊Q811yescharacteristic
263C23×C17#12411yescharacteristic
264C23×C17#12411yescharacteristic
265C23×C17#12411yescharacteristic
266C23×C17#12411yescharacteristic
267C23×C17#12411yescharacteristic
268C23×C17#12411yescharacteristic
269C23×C17#12411yescharacteristic
270C23×C17#12411yescharacteristic
271C23×C17#12411yescharacteristic
272C23×C17#12411yescharacteristic
273C23×C17#12411yescharacteristic
274C23×C17#12411yescharacteristic
275C23×C17C22×D411yescharacteristic
276C23×C17C22×D411yescharacteristic
277C23×C17C22×D411yescharacteristic
278C23×C17C22×Q811yescharacteristic
279C23×C17C2×#4111yescharacteristic
280C23×C17C2×#4111yescharacteristic
281C23×C17C2×#4111yescharacteristic
282D4×C17—42no—
283D4×C17—42no—
284D4×C17—42no—
285D4×C17—42no—
286D4×C17—42no—
287D4×C17—42no—
288D4×C17—42no—
289D4×C17—42no—
290C2×C4×C17—24no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—44no—
295C2×C4×C17—41no—
296C2×C4×C17—41no—
297C2×C4×C17—41no—
298C2×C4×C17—41no—
299C2×C4×C17—42no—
300C2×C4×C17—82no—
301C2×C4×C17—82no—
302C2×C4×C17—82no—
303C2×C4×C17—82no—
304C2×C4×C17—82no—
305C2×Dic17—24no—
306C2×Dic17—24no—
307C2×Dic17—44no—
308C2×Dic17—44no—
309C2×Dic17—42no—
310C2×Dic17—42no—
311C2×Dic17—82no—
312C2×Dic17—82no—
313C2×Dic17—82no—
314C2×Dic17—82no—
315C2×Dic17—82no—
316C2×Dic17—82no—
317C2×Dic17—82no—
318C2×Dic17—82no—
319C2×Dic17—82no—
320C2×Dic17—82no—
321Dic34—88no—
322C2×#543—171no—
323C22×#99—171no—
324C22×#99—171no—
325C22×#99D1711yescharacteristic
326#2032—178no—
327C2×#342—171no—
328C2×#342—171no—
329C2×#342—171no—
330C22×C17—22no—
331C22×C17—22no—
332C22×C17—22no—
333C22×C17—22no—
334C22×C17—22no—
335C22×C17—22no—
336C22×C17—22no—
337C22×C17—41no—
338C22×C17—41no—
339C22×C17—41no—
340C22×C17—41no—
341C22×C17—41no—
342C22×C17—41no—
343C22×C17—41no—
344C22×C17—41no—
345C22×C17—41no—
346C22×C17—41no—
347C22×C17—41no—
348C22×C17—41no—
349C22×C17—41no—
350C22×C17—41no—
351C22×C17—41no—
352C22×C17—41no—
353C22×C17—41no—
354C22×C17—41no—
355C22×C17—41no—
356C22×C17—41no—
357C22×C17—41no—
358C22×C17—41no—
359C22×C17—41no—
360C22×C17—41no—
361C22×C17—41no—
362C22×C17—41no—
363C22×C17—41no—
364C22×C17—41no—
365C22×C17—42no—
366C22×C17—82no—
367C22×C17—82no—
368C22×C17—82no—
369C22×C17—82no—
370C22×C17—82no—
371C22×C17—82no—
372C22×C17—82no—
373C22×C17#39311yescharacteristic
374C22×C17#39311yescharacteristic
375C22×C17#39311yescharacteristic
376C22×C17#39311yescharacteristic
377C22×C17#39311yescharacteristic
378C22×C17#39311yescharacteristic
379C22×C17#39311yescharacteristic
380C22×C17#39311yescharacteristic
381C22×C17C2×#12011yescharacteristic
382C22×C17C2×C22⋊Q811yescharacteristic
383C22×C17C2×C22⋊Q811yescharacteristic
384C22×C17C2×C22⋊Q811yescharacteristic
385C22×C17C2×#12411yescharacteristic
386C22×C17C2×#12411yescharacteristic
387C22×C17C2×#12411yescharacteristic
388C4×C17—44no—
389C4×C17—42no—
390C4×C17—82no—
391Dic17—44no—
392Dic17—44no—
393Dic17—82no—
394Dic17—82no—
395C23×D4C2×D1711yescharacteristic
396#543—174no—
397#543—342no—
398#543—342no—
399#543—342no—
400C2×C22⋊Q8—342no—
401C2×C22⋊Q8—342no—
402C2×C22⋊Q8—342no—
403C22×C22⋊C4—171no—
404C22×C22⋊C4—171no—
405C22×C22⋊C4—171no—
406C22×C22⋊C4—171no—
407C22×C22⋊C4C2×D1711yescharacteristic
408C22×C22⋊C4C2×D1711yescharacteristic
409C2×#99—22no—
410C2×#99—22no—
411C2×#99—174no—
412C2×#99—174no—
413C2×#99—342no—
414C2×#99—342no—
415C2×#99—342no—
416C2×#99—342no—
417C2×#99C2×D1714yes—
418#342—174no—
419#342—174no—
420#342—174no—
421C2×C17—21no—
422C2×C17—21no—
423C2×C17—21no—
424C2×C17—21no—
425C2×C17—21no—
426C2×C17—21no—
427C2×C17—21no—
428C2×C17—21no—
429C2×C17—21no—
430C2×C17—21no—
431C2×C17—21no—
432C2×C17—21no—
433C2×C17—21no—
434C2×C17—21no—
435C2×C17—82no—
436C2×C17#203212yescomplemented
437C2×C17C2×#39311yescharacteristic
438C25Dic3411yescharacteristic, complemented
439C25C22×D1711yescharacteristic
440C22×Q8—342no—
441C22×D4—21no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4Dic3412yescomplemented
454C22×D4C22×D1712yes—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—341no—
458C23×C4—341no—
459C23×C4—341no—
460C23×C4—341no—
461C23×C4Dic3411yescharacteristic, complemented
462C22⋊Q8—348no—
463C22⋊Q8—348no—
464C22⋊Q8—348no—
465C22⋊Q8—348no—
466C22⋊Q8—348no—
467C22⋊Q8—348no—
468C2×C4⋊C4—344no—
469C2×C4⋊C4—342no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—172no—
479C2×C22⋊C4—172no—
480C2×C22⋊C4—172no—
481C2×C22⋊C4—172no—
482C2×C22⋊C4—172no—
483C2×C22⋊C4—172no—
484C2×C22⋊C4—172no—
485C2×C22⋊C4—172no—
486C2×C22⋊C4—341no—
487C2×C22⋊C4—341no—
488C2×C22⋊C4—341no—
489C2×C22⋊C4—341no—
490C2×C22⋊C4—341no—
491C2×C22⋊C4—341no—
492C2×C22⋊C4—341no—
493C2×C22⋊C4—341no—
494C2×C22⋊C4—341no—
495C2×C22⋊C4—341no—
496C2×C22⋊C4—341no—
497C2×C22⋊C4—341no—
498C2×C22⋊C4—341no—
499C2×C22⋊C4—341no—
500C2×C22⋊C4—341no—
501C2×C22⋊C4—341no—
502C2×C22⋊C4C22⋊D1712yes—
503C2×C22⋊C4C22⋊D1712yes—
504C2×C22⋊C4C22×D1712yes—
505C2×C22⋊C4C22×D1712yes—
506#99—28no—
507#99—348no—
508#99—348no—
509C17C2×#203211yescharacteristic, complemented, Sylow
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—82no—
517C24—82no—
518C24C2×Dic3411yescharacteristic
519C24C2×Dic3411yescharacteristic
520C24C2×Dic3412yescomplemented
521C24#6325211yescharacteristic
522C24#6325211yescharacteristic
523C24D4×D1711yescharacteristic
524C24D4×D1711yescharacteristic
525C24D4×D1711yescharacteristic
526C24D4×D1711yescharacteristic
527C24#6325411yescharacteristic
528C24#6325411yescharacteristic
529C24#6325411yescharacteristic
530C24#6325411yescharacteristic
531C24C2×C22⋊D1711yescharacteristic
532C24C2×C22⋊D1711yescharacteristic
533C24C23×D1711yescharacteristic
534C2×Q8—348no—
535C2×Q8—1364no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—82no—
577C22×C4—82no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—342no—
581C22×C4—342no—
582C22×C4—342no—
583C22×C4—342no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—681no—
587C22×C4—681no—
588C22×C4—681no—
589C22×C4—681no—
590C22×C4—1362no—
591C22×C4—1362no—
592C22×C4—1362no—
593C22×C4—1362no—
594C22×C4C2×Dic3412yescomplemented
595C4⋊C4—3416no—
596C4⋊C4—348no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—174no—
605C22⋊C4—174no—
606C22⋊C4—342no—
607C22⋊C4—342no—
608C22⋊C4—342no—
609C22⋊C4—342no—
610C22⋊C4—342no—
611C22⋊C4—342no—
612C22⋊C4—342no—
613C22⋊C4—342no—
614C22⋊C4—342no—
615C22⋊C4—342no—
616C22⋊C4—681no—
617C22⋊C4—681no—
618C22⋊C4—681no—
619C22⋊C4—681no—
620C22⋊C4C2×C22⋊D1714yes—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—82no—
636C23—82no—
637C23—82no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—81no—
643C23—81no—
644C23—81no—
645C23—81no—
646C23—82no—
647C23—82no—
648C23—82no—
649C23—82no—
650C23#1058756411yescharacteristic
651C23#1058756411yescharacteristic
652C23#1058756411yescharacteristic
653C23#1058756411yescharacteristic
654C23#1058756411yescharacteristic
655C23#1058756411yescharacteristic
656C23#1058756411yescharacteristic
657C23#1058756411yescharacteristic
658C23#1058757111yescharacteristic
659C23#1058757111yescharacteristic
660C23#1058757111yescharacteristic
661C23#1058757111yescharacteristic
662C23#1058757111yescharacteristic
663C23#1058757111yescharacteristic
664C23#1058757111yescharacteristic
665C23#1058757111yescharacteristic
666C23#1058761011yescharacteristic
667C23#1058761011yescharacteristic
668C23#1058761011yescharacteristic
669C23#1058761011yescharacteristic
670C23#1058762211yescharacteristic
671C23#1058762211yescharacteristic
672C23#1058762211yescharacteristic
673C23#1058762211yescharacteristic
674C23#1058762311yescharacteristic
675C23#1058762311yescharacteristic
676C23#1058762311yescharacteristic
677C23#1058762311yescharacteristic
678C23C22×Dic3411yescharacteristic
679C23C2×#6325211yescharacteristic
680C23C2×D4×D1711yescharacteristic
681C23C2×D4×D1711yescharacteristic
682C23C2×#6325411yescharacteristic
683C23C2×#6325411yescharacteristic
684C23C22×C22⋊D1711yescharacteristic
685Q8—1368no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—344no—
710C2×C4—344no—
711C2×C4—684no—
712C2×C4—684no—
713C2×C4—682no—
714C2×C4—682no—
715C2×C4—1362no—
716C2×C4—1362no—
717C2×C4—1362no—
718C2×C4—1362no—
719C2×C4—1362no—
720C2×C4—1362no—
721C2×C4—1362no—
722C2×C4—1362no—
723C2×C4—1362no—
724C2×C4—1362no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—42no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22#1176272111yescharacteristic
769C22#1176272111yescharacteristic
770C22#1176272111yescharacteristic
771C22#1176272111yescharacteristic
772C22#1176272111yescharacteristic
773C22#1176272111yescharacteristic
774C22#1176272111yescharacteristic
775C22#1176272111yescharacteristic
776C22C2×#1058762311yescharacteristic
777C22C2×#1058756411yescharacteristic
778C22C2×#1058756411yescharacteristic
779C22C2×#1058761011yescharacteristic
780C22C2×#1058757111yescharacteristic
781C22C2×#1058757111yescharacteristic
782C22C2×#1058762211yescharacteristic
783C4—44no—
784C4—42no—
785C4—82no—
786C4—684no—
787C4—684no—
788C4—1362no—
789C4—1362no—
790C2—21no—
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—82no—
805C2#1452996112yesdirect product factor
806C2C2×#1176272111yescharacteristic
subgroupG/H
centerC22#11762721
commutator, cosocleC24×C17C24
FrattiniC24C23×D17
FittingC22×C17×#99C2
socleC22×C17#393
prime radicalC23×D4×C17C22
hypercenterC22×#99D17
hypocenterC17C2×#2032
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
1. C2×#11763435C2semidirect
4. #14529961C2direct (N × H)
5. C2×#11762576C2semidirect
6. C2×#11762575C2semidirect
7. C2×#11762575C2semidirect
12. #11763435C22semidirect
26. #11762576C22semidirect
27. #11762575C22semidirect
28. #11762575C22semidirect
35. C25×C17Q8semidirect
49. C22×D4×C17Q8semidirect
53. C23×C4×C17Q8semidirect
122. C24×C17C2×Q8semidirect
172. C22×C4×C17C2×Q8semidirect
436. C2×C17#2032semidirect
438. C25Dic34semidirect
453. C22×D4Dic34semidirect
461. C23×C4Dic34semidirect
509. C17C2×#2032semidirect
520. C24C2×Dic34semidirect
594. C22×C4C2×Dic34semidirect
805. C2#14529961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634352
C22×#105875052
#145299612
C2×#117625762
C2×#117625752
C22×C17×#992
C2×#203217