Finite Group Databasebeta

← C2×#14543394 #17941702

Subgroups — C2×#14543394 #17941702

Order 4352.

6458 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14543394C2132yesmaximal, direct product factor
2C2×C17⋊#564C212yesmaximal, complemented
3C2×#11763563C212yesmaximal, complemented
4C2×#11763535C212yesmaximal, complemented
5C2×#11763517C212yesmaximal, complemented
6C2×#11763501C212yesmaximal, complemented
7C2×#11763500C212yesmaximal, complemented
8C2×#11763492C214yesmaximal, complemented
9C2×#11763438C212yesmaximal, complemented
10C2×#11763436C212yesmaximal, complemented
11C2×#11763420C212yesmaximal, complemented
12C2×#11763417C214yesmaximal, complemented
13C2×#11763408C212yesmaximal
14C2×#11763343C211yesmaximal, characteristic
15C22×#10587556C211yesmaximal, characteristic, complemented
16C2×C17×#533C211yesmaximal, characteristic, complemented
17C17⋊#564C22132yescomplemented
18#11763563C22132yescomplemented
19#11763535C22132yescomplemented
20#11763517C22132yescomplemented
21#11763501C22132yescomplemented
22#11763500C22132yescomplemented
23#11763492C22164yescomplemented
24#11763438C22132yescomplemented
25#11763436C22132yescomplemented
26#11763420C22132yescomplemented
27#11763417C22164yescomplemented
28#11763408C22132yes—
29C2×#10587574C2214yes—
30C2×#10587574C2212yes—
31C2×#10587630C2214yes—
32#11763343C22116yes—
33C2×#10587584C2214yes—
34C2×#10587584C2214yes—
35C2×#10587584C2214yes—
36C2×#10587562C2212yes—
37C2×#10587562C2214yes—
38C2×#10587556C2214yes—
39C2×#10587556C2212yes—
40C2×#10587556C2212yes—
41C2×#10587556C2212yes—
42C2×#10587556C2212yes—
43C2×#10587556C2211yescharacteristic
44C2×#10587556C22116yescomplemented
45C2×#10587576C2214yes—
46C2×#10587576C2212yes—
47C2×#10587576C2214yes—
48C2×#10587575C2214yes—
49C2×#10587575C2214yes—
50C2×#10587575C2214yes—
51C2×#10587575C2214yes—
52C2×#10587575C2214yes—
53C2×#10587561C2211yescharacteristic
54C2×#10587580C2214yes—
55C2×#10587572C2214yes—
56C2×#10587615C2212yes—
57C2×#10587583C2214yes—
58C2×#10587610C2211yescharacteristic
59C2×#10587582C2214yes—
60C2×#10587564C2214yes—
61C2×#10587632C2214yes—
62C2×#10587632C2212yes—
63C2×#10587632C2212yes—
64C2×#10587616C2211yescharacteristic
65C2×Q8×Dic17C2212yes—
66C2×Q8×Dic17C2212yes—
67C2×C4×Dic34C2211yescharacteristic
68C2×C4×Dic34C2214yes—
69C2×C4×D68C2211yescharacteristic
70C2×C4×C22⋊D17C2212yes—
71C2×#10587567C2214yes—
72C2×#10587578C2212yes—
73C2×#10587558C2214yes—
74C2×#10587558C2212yes—
75C2×#10587563C2214yes—
76C22×C4⋊Dic17C2211yescharacteristic
77C22×C4⋊Dic17C2211yescharacteristic
78C22×#63225C2212yes—
79C22×#63225C2212yes—
80C2×C4⋊C4×D17C2212yes—
81C17×#533C22116yescomplemented
82C2×C17×C4⋊Q8C2211yescharacteristic
83C2×C17×C4⋊Q8C2211yescharacteristic
84C2×C17×#125C2212yes—
85C2×C17×C22⋊Q8C2212yes—
86C2×C17×C22⋊Q8C2212yes—
87C2×C4×Q8×C17C2212yes—
88C2×C4×Q8×C17C2212yes—
89C2×C17×#117C2212yes—
90C22×C42×C17C2211yescharacteristic
91C22×Q8×C17C2312yes—
92C22×Q8×C17C2312yes—
93C23×C4×C17C2311yescharacteristic
94C23×C4×C17C2311yescharacteristic
95C23×C4×C17C2311yescharacteristic
96C22×C22⋊D17C2312yes—
97C23×Dic17C2312yes—
98C23×Dic17C2312yes—
99C22×D68C2311yescharacteristic
100C22×C4×D17C2312yes—
101C22×C4×D17C2314yes—
102C22×Dic34C2314yes—
103C22×Dic34C2311yescharacteristic
104C17×C4⋊Q8C2318yes—
105C17×C4⋊Q8C2318yes—
106C17×#125C23116yes—
107C17×C22⋊Q8C23116yes—
108C17×C22⋊Q8C23116yes—
109C4×Q8×C17C23116yes—
110C4×Q8×C17C23116yes—
111C17×#117C23116yes—
112C2×C4⋊C4×C17C2312yes—
113C2×C4⋊C4×C17C2312yes—
114C2×C4⋊C4×C17C2314yes—
115C2×C4⋊C4×C17C2314yes—
116C2×C4⋊C4×C17C2312yes—
117C2×C4⋊C4×C17C2312yes—
118C2×C22⋊C4×C17C2314yes—
119C2×C42×C17C2311yescharacteristic
120C2×C42×C17C2311yescharacteristic
121C2×C42×C17C2311yescharacteristic
122C2×C42×C17C2311yescharacteristic
123C2×C42×C17C2318yes—
124C2×C42×C17C2314yes—
125C2×C22⋊Dic17C2312yes—
126#10587632C23116yes—
127#10587632C23116yes—
128#10587632C23132yes—
129Q8×Dic17C23116yes—
130Q8×Dic17C23116yes—
131#10587630C23132yes—
132#10587616C2318yes—
133#10587615C23116yes—
134C4×C22⋊D17C23116yes—
135C2×#63227C2312yes—
136C2×#63227C2312yes—
137C2×#63227C2314yes—
138C2×#63227C2312yes—
139C2×#63227C2314yes—
140C2×#63227C2314yes—
141C2×#63227C2312yes—
142C2×C4⋊Dic17C2318yes—
143C2×C4⋊Dic17C2312yes—
144C2×C4⋊Dic17C2318yes—
145C2×C4⋊Dic17C2312yes—
146C2×C4⋊Dic17C2312yes—
147C2×C4⋊Dic17C2312yes—
148C2×C4⋊Dic17C2311yescharacteristic
149C2×C4⋊Dic17C2311yescharacteristic
150C2×C4⋊Dic17C2314yes—
151C2×C4⋊Dic17C2314yes—
152C2×C4⋊Dic17C2314yes—
153#10587610C2318yes—
154C2×#63225C23116yes—
155C2×#63225C2314yes—
156C2×#63225C2314yes—
157C2×#63225C2314yes—
158C2×#63225C2314yes—
159C2×#63225C2314yes—
160C2×#63225C23116yes—
161C2×#63225C2314yes—
162C2×#63225C2314yes—
163C2×#63225C2314yes—
164C2×#63225C2312yes—
165C2×#63225C2312yes—
166C2×#63225C2314yes—
167C2×#63225C2312yes—
168C2×#63225C2312yes—
169C2×C4×Dic17C2314yes—
170C2×C4×Dic17C2314yes—
171C2×C4×Dic17C2312yes—
172C2×C4×Dic17C2314yes—
173#10587584C23132yes—
174#10587584C23132yes—
175#10587584C23132yes—
176#10587583C23132yes—
177#10587582C23132yes—
178#10587580C23132yes—
179#10587578C23116yes—
180C4⋊C4×D17C23116yes—
181#10587576C23116yes—
182#10587576C23132yes—
183#10587576C23132yes—
184#10587575C23132yes—
185#10587575C23132yes—
186#10587575C23132yes—
187#10587575C23132yes—
188#10587575C23132yes—
189#10587574C23116yes—
190#10587574C23132yes—
191#10587572C23132yes—
192#10587567C23132yes—
193#10587564C23132yes—
194#10587563C23132yes—
195#10587562C23132yes—
196#10587562C23116yes—
197#10587561C2318yes—
198C4×D68C2318yes—
199#10587558C23132yes—
200#10587558C23116yes—
201#10587556C23132yes—
202#10587556C23116yes—
203#10587556C23116yes—
204#10587556C2318yes—
205#10587556C23116yes—
206#10587556C23116yes—
207C4×Dic34C23132yes—
208C4×Dic34C2318yes—
209C24×C17C2411yescharacteristic
210C23×D17C2412yes—
211C2×Q8×C17—28no—
212C2×Q8×C17—44no—
213C2×Q8×C17C2418yes—
214C2×Q8×C17C2418yes—
215C22×C4×C17—24no—
216C22×C4×C17—24no—
217C22×C4×C17—42no—
218C22×C4×C17C2414yes—
219C22×C4×C17C2414yes—
220C22×C4×C17C2411yescharacteristic
221C22×C4×C17C2411yescharacteristic
222C22×C4×C17C2411yescharacteristic
223C22×C4×C17C2411yescharacteristic
224C22×C4×C17C2414yes—
225C22×C4×C17C2411yescharacteristic
226C22×C4×C17C2414yes—
227C22×C4×C17C2414yes—
228C22×C4×C17C2411yescharacteristic
229C2×C22⋊D17—28no—
230C2×C22⋊D17C2418yes—
231C22×Dic17—28no—
232C22×Dic17—44no—
233C22×Dic17C2412yes—
234C22×Dic17C2414yes—
235C22×Dic17C2412yes—
236C22×Dic17C2418yes—
237C22×Dic17C2414yes—
238C22×Dic17C2412yes—
239C22×Dic17C2418yes—
240C2×D68—42no—
241C2×D68C2414yes—
242C2×C4×D17—28no—
243C2×C4×D17—48no—
244C2×C4×D17C2418yes—
245C2×C4×D17C24116yes—
246C2×Dic34—42no—
247C2×Dic34—48no—
248C2×Dic34C2414yes—
249C2×Dic34C24116yes—
250C4⋊C4×C17C24116yes—
251C4⋊C4×C17C24116yes—
252C4⋊C4×C17C2418yes—
253C4⋊C4×C17C2418yes—
254C4⋊C4×C17C2418yes—
255C4⋊C4×C17C2418yes—
256C22⋊C4×C17C24116yes—
257C42×C17C2414yes—
258C42×C17C2414yes—
259C42×C17C2414yes—
260C42×C17C24116yes—
261C42×C17C2414yes—
262C22⋊Dic17C2418yes—
263#63227C2418yes—
264#63227C2418yes—
265#63227C2418yes—
266#63227C24116yes—
267#63227C2418yes—
268#63227C24116yes—
269#63227C24116yes—
270C4⋊Dic17C2414yes—
271C4⋊Dic17C24116yes—
272C4⋊Dic17C2418yes—
273C4⋊Dic17C2418yes—
274C4⋊Dic17C2418yes—
275C4⋊Dic17C2418yes—
276C4⋊Dic17C2414yes—
277C4⋊Dic17C24116yes—
278C4⋊Dic17C24116yes—
279#63225C2418yes—
280#63225C24116yes—
281#63225C24116yes—
282#63225C24116yes—
283#63225C24116yes—
284#63225C2418yes—
285#63225C2418yes—
286#63225C24116yes—
287#63225C24116yes—
288#63225C2418yes—
289#63225C24116yes—
290#63225C24116yes—
291#63225C24116yes—
292C4×Dic17C2418yes—
293C4×Dic17C24116yes—
294C4×Dic17C24116yes—
295C4×Dic17C24116yes—
296C2×#3563—171nomaximal, Sylow
297C23×C17—22no—
298C23×C17—22no—
299C23×C172−1+414yes—
300C23×C17C2512yes—
301C23×C17C2511yescharacteristic
302C22×D17—24no—
303C22×D17—24no—
304C22×D17—24no—
305C22×D17C2514yes—
306Q8×C17—216no—
307Q8×C17—48no—
308C2×C4×C17—22no—
309C2×C4×C17—28no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—28no—
313C2×C4×C17—28no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—28no—
317C2×C4×C17—44no—
318C2×C4×C172−1+414yes—
319C2×C4×C17C2512yes—
320C2×C4×C17C2512yes—
321C2×C4×C17C2512yes—
322C2×C4×C17C2512yes—
323C2×C4×C17C2512yes—
324C2×C4×C17C2518yes—
325C2×C4×C17C2518yes—
326C2×C4×C17C2512yes—
327C22⋊D17—216no—
328C2×Dic17—24no—
329C2×Dic17—216no—
330C2×Dic17—28no—
331C2×Dic17—24no—
332C2×Dic17—24no—
333C2×Dic17—28no—
334C2×Dic17—48no—
335C2×Dic17C2514yes—
336C2×Dic17C2514yes—
337C2×Dic17C2518yes—
338C2×Dic17C2518yes—
339C2×Dic17C2514yes—
340D68—44no—
341C4×D17—216no—
342C4×D17—416no—
343Dic34—44no—
344Dic34—416no—
345#3563—1732no—
346C2×#564—172no—
347C2×#563—172no—
348C2×#557—172no—
349C2×#554—172no—
350C2×#552—172no—
351C2×#552—172no—
352C2×#552—174no—
353C2×#544—172no—
354C2×#544—172no—
355C2×#541—172no—
356C2×#541—174no—
357C2×#539—172no—
358C2×#533D1711yescharacteristic, complemented
359C2×#529—171no—
360C22×#125—171no—
361C22×C17—22no—
362C22×C17—22no—
363C22×C17—28no—
364C22×C17C2×2−1+412yes—
365C22×C17C2×2−1+414yes—
366C22×C17C2×2−1+412yes—
367C22×C17#58512yes—
368C22×C17C2611yescharacteristic
369C2×D17—24no—
370C2×D17—24no—
371C2×D17—24no—
372C2×D17—48no—
373C4×C17—22no—
374C4×C17—22no—
375C4×C17—22no—
376C4×C17—28no—
377C4×C17—28no—
378C4×C17—22no—
379C4×C17—22no—
380C4×C17C2×2−1+414yes—
381Dic17—24no—
382Dic17—28no—
383Dic17—24no—
384Dic17—24no—
385Dic17—28no—
386#564—1732no—
387#563—1732no—
388#557—1732no—
389#554—1732no—
390#552—1732no—
391#552—1732no—
392#552—1764no—
393#544—1732no—
394#544—1732no—
395#541—1732no—
396#541—1764no—
397#539—1732no—
398#533C2×D17116yescomplemented
399C2×C4⋊Q8—174no—
400C2×C4⋊Q8—172no—
401C2×C4⋊Q8—174no—
402C2×C4⋊Q8C2×D1711yescharacteristic
403C2×C4⋊Q8C2×D1711yescharacteristic
404#529—1716no—
405C2×#126—174no—
406C2×#126—174no—
407C2×#126—174no—
408C2×#126—172no—
409C2×#126—174no—
410C2×#125—174no—
411C2×#125—174no—
412C2×#125—174no—
413C2×#125—174no—
414C2×#125—174no—
415C2×#125—174no—
416C2×#125—174no—
417C2×#125—172no—
418C2×#125—172no—
419C2×#125—172no—
420C2×#125—172no—
421C2×#125—172no—
422C2×#125—1716no—
423C2×#125—171no—
424C2×#125—174no—
425C2×#125C2×D1712yes—
426C2×#124—171no—
427C2×#123—172no—
428C2×#123—174no—
429C2×#123—174no—
430C2×C22⋊Q8—174no—
431C2×C22⋊Q8—172no—
432C2×C22⋊Q8—172no—
433C2×C22⋊Q8—171no—
434C2×C22⋊Q8—174no—
435C2×C22⋊Q8—174no—
436C2×C22⋊Q8—174no—
437C2×C22⋊Q8C2×D1712yes—
438C2×C22⋊Q8C2×D1712yes—
439C2×#121—171no—
440C2×C4×Q8—172no—
441C2×C4×Q8—172no—
442C2×C4×Q8—171no—
443C2×C4×Q8—174no—
444C2×C4×Q8C2×D1712yes—
445C2×C4×Q8C2×D1712yes—
446C2×C4×D4—172no—
447C2×C4×D4—174no—
448C2×C4×D4—171no—
449C2×#117—172no—
450C2×#117—174no—
451C2×#117—172no—
452C2×#117—174no—
453C2×#117C2×D1712yes—
454C22×C4⋊C4—172no—
455C22×C4⋊C4—172no—
456C22×C4⋊C4—171no—
457C22×C4⋊C4—171no—
458C22×C4⋊C4—172no—
459C22×C42C2×D1711yescharacteristic
460C2×C17—24no—
461C2×C17#356314yescomplemented
462C2×C17C22×2−1+411yescharacteristic
463C2×C17C22×2−1+411yescharacteristic
464C2×C17C2×#58511yescharacteristic
465D17—44no—
466C22×Q8—174no—
467C22×Q8—171no—
468C22×Q8C22×D1712yes—
469C22×Q8C22×D1712yes—
470C22×D4—172no—
471C22×D4—171no—
472C23×C4—172no—
473C23×C4—172no—
474C23×C4—172no—
475C23×C4—174no—
476C23×C4C22×D1711yescharacteristic
477C23×C4C22×D1711yescharacteristic
478C23×C4C22×D1711yescharacteristic
479C4⋊Q8—1732no—
480C4⋊Q8—1716no—
481C4⋊Q8—1732no—
482C4⋊Q8C22×D1718yes—
483C4⋊Q8C22×D1718yes—
484#126—1732no—
485#126—1732no—
486#126—1732no—
487#126—1716no—
488#126—1732no—
489#125—1732no—
490#125—1732no—
491#125—1732no—
492#125—1732no—
493#125—1732no—
494#125—1716no—
495#125—1732no—
496#125—1732no—
497#125—1716no—
498#125—1716no—
499#125—1716no—
500#125—1716no—
501#125—178no—
502#125—1732no—
503#125C22×D17116yes—
504#124—178no—
505#123—1716no—
506#123—1732no—
507#123—1732no—
508C22⋊Q8—1732no—
509C22⋊Q8—1716no—
510C22⋊Q8—1716no—
511C22⋊Q8—178no—
512C22⋊Q8—1732no—
513C22⋊Q8—1732no—
514C22⋊Q8—1732no—
515C22⋊Q8C22×D17116yes—
516C22⋊Q8C22×D17116yes—
517#121—178no—
518C4×Q8—1716no—
519C4×Q8—1716no—
520C4×Q8—178no—
521C4×Q8—1732no—
522C4×Q8C22×D17116yes—
523C4×Q8C22×D17116yes—
524C4×D4—1716no—
525C4×D4—1732no—
526C4×D4—178no—
527#117—1716no—
528#117—1732no—
529#117—1716no—
530#117—1732no—
531#117C22×D17116yes—
532C2×C4⋊C4—172no—
533C2×C4⋊C4—172no—
534C2×C4⋊C4—174no—
535C2×C4⋊C4—172no—
536C2×C4⋊C4—174no—
537C2×C4⋊C4—174no—
538C2×C4⋊C4—174no—
539C2×C4⋊C4—174no—
540C2×C4⋊C4—172no—
541C2×C4⋊C4—1716no—
542C2×C4⋊C4—1716no—
543C2×C4⋊C4—178no—
544C2×C4⋊C4—178no—
545C2×C4⋊C4—174no—
546C2×C4⋊C4—174no—
547C2×C4⋊C4—174no—
548C2×C4⋊C4—172no—
549C2×C4⋊C4—172no—
550C2×C4⋊C4—171no—
551C2×C4⋊C4—174no—
552C2×C4⋊C4—172no—
553C2×C4⋊C4—172no—
554C2×C4⋊C4—171no—
555C2×C4⋊C4—174no—
556C2×C4⋊C4—174no—
557C2×C4⋊C4—174no—
558C2×C4⋊C4—1716no—
559C2×C4⋊C4C22×D1712yes—
560C2×C4⋊C4C22×D1712yes—
561C2×C4⋊C4C22×D1712yes—
562C2×C4⋊C4C22×D1714yes—
563C2×C4⋊C4C22×D1714yes—
564C2×C4⋊C4C22×D1712yes—
565C2×C22⋊C4—172no—
566C2×C22⋊C4—172no—
567C2×C22⋊C4—172no—
568C2×C22⋊C4—174no—
569C2×C22⋊C4—172no—
570C2×C22⋊C4—174no—
571C2×C22⋊C4—174no—
572C2×C22⋊C4—172no—
573C2×C22⋊C4C22×D1714yes—
574C2×C42—174no—
575C2×C42—172no—
576C2×C42—174no—
577C2×C42—174no—
578C2×C42C22×D1711yescharacteristic
579C2×C42C22×D1714yes—
580C2×C42C22×D1711yescharacteristic
581C2×C42C22×D1711yescharacteristic
582C2×C42C22×D1711yescharacteristic
583C2×C42C22×D1718yes—
584C17C2×#356311yescharacteristic, complemented, Sylow
585C24—172no—
586C24C23×D1711yescharacteristic
587C2×Q8—28no—
588C2×Q8—44no—
589C2×Q8—1716no—
590C2×Q8—174no—
591C2×Q8—682no—
592C2×Q8—688no—
593C2×Q8C23×D1718yes—
594C2×Q8C23×D1718yes—
595C2×D4—178no—
596C2×D4—174no—
597C2×D4—348no—
598C2×D4—682no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—42no—
602C22×C4—178no—
603C22×C4—172no—
604C22×C4—172no—
605C22×C4—172no—
606C22×C4—174no—
607C22×C4—174no—
608C22×C4—178no—
609C22×C4—178no—
610C22×C4—1716no—
611C22×C4—348no—
612C22×C4—348no—
613C22×C4—688no—
614C22×C4—684no—
615C22×C4C23×D1714yes—
616C22×C4C23×D1714yes—
617C22×C4C23×D1714yes—
618C22×C4C23×D1714yes—
619C22×C4C23×D1711yescharacteristic
620C22×C4C23×D1711yescharacteristic
621C22×C4C23×D1711yescharacteristic
622C22×C4C23×D1711yescharacteristic
623C22×C4C23×D1711yescharacteristic
624C22×C4C23×D1714yes—
625C22×C4C23×D1711yescharacteristic
626C4⋊C4—178no—
627C4⋊C4—178no—
628C4⋊C4—1716no—
629C4⋊C4—178no—
630C4⋊C4—1716no—
631C4⋊C4—1716no—
632C4⋊C4—1716no—
633C4⋊C4—1716no—
634C4⋊C4—178no—
635C4⋊C4—1716no—
636C4⋊C4—1716no—
637C4⋊C4—1716no—
638C4⋊C4—178no—
639C4⋊C4—178no—
640C4⋊C4—174no—
641C4⋊C4—1716no—
642C4⋊C4—178no—
643C4⋊C4—178no—
644C4⋊C4—174no—
645C4⋊C4—1716no—
646C4⋊C4—1716no—
647C4⋊C4—1716no—
648C4⋊C4C23×D1718yes—
649C4⋊C4C23×D1718yes—
650C4⋊C4C23×D1718yes—
651C4⋊C4C23×D17116yes—
652C4⋊C4C23×D17116yes—
653C4⋊C4C23×D1718yes—
654C22⋊C4—178no—
655C22⋊C4—178no—
656C22⋊C4—178no—
657C22⋊C4—1716no—
658C22⋊C4—178no—
659C22⋊C4—1716no—
660C22⋊C4—1716no—
661C22⋊C4—178no—
662C22⋊C4C23×D17116yes—
663C42—1716no—
664C42—178no—
665C42—1716no—
666C42—1716no—
667C42C23×D1714yes—
668C42C23×D1714yes—
669C42C23×D1714yes—
670C42C23×D1714yes—
671C42C23×D17116yes—
672C23—22no—
673C23—22no—
674C23—174no—
675C23—344no—
676C23—344no—
677C23—344no—
678C23#1058769414yes—
679C23C24×D1712yes—
680C23C24×D1711yescharacteristic
681Q8—216no—
682Q8—48no—
683Q8—684no—
684Q8—6816no—
685D4—3416no—
686D4—684no—
687C2×C4—22no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—44no—
697C2×C4—174no—
698C2×C4—174no—
699C2×C4—174no—
700C2×C4—178no—
701C2×C4—178no—
702C2×C4—344no—
703C2×C4—3416no—
704C2×C4—348no—
705C2×C4—344no—
706C2×C4—348no—
707C2×C4—344no—
708C2×C4—3416no—
709C2×C4—6816no—
710C2×C4—688no—
711C2×C4#1058769714yes—
712C2×C4C24×D1718yes—
713C2×C4C24×D1718yes—
714C2×C4C24×D1712yes—
715C2×C4C24×D1712yes—
716C2×C4C24×D1712yes—
717C2×C4C24×D1712yes—
718C2×C4C24×D1712yes—
719C2×C4C24×D1712yes—
720C22—28no—
721C22—22no—
722C22—22no—
723C22—344no—
724C22—344no—
725C22—344no—
726C22—688no—
727C22C2×#1058769712yes—
728C22C2×#1058769414yes—
729C22C2×#1058769412yes—
730C22#1176364512yes—
731C22C25×D1711yescharacteristic
732C4—22no—
733C4—28no—
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—28no—
739C4—344no—
740C4—348no—
741C4—344no—
742C4—348no—
743C4—344no—
744C4C2×#1058769714yes—
745C2—24no—
746C2—684no—
747C2#1454339414yesdirect product factor
748C2C22×#1058769711yescharacteristic
749C2C22×#1058769411yescharacteristic
750C2C2×#1176364511yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#533C2
socleC23×C17C25
prime radicalC2×#10587616C22
hypercenterC2×#533D17
hypocenterC17C2×#3563
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #14543394C2direct (N × H)
2. C2×C17⋊#564C2semidirect
3. C2×#11763563C2semidirect
4. C2×#11763535C2semidirect
5. C2×#11763517C2semidirect
6. C2×#11763501C2semidirect
7. C2×#11763500C2semidirect
8. C2×#11763492C2semidirect
9. C2×#11763438C2semidirect
10. C2×#11763436C2semidirect
11. C2×#11763420C2semidirect
12. C2×#11763417C2semidirect
15. C22×#10587556C2semidirect
16. C2×C17×#533C2semidirect
17. C17⋊#564C22semidirect
18. #11763563C22semidirect
19. #11763535C22semidirect
20. #11763517C22semidirect
21. #11763501C22semidirect
22. #11763500C22semidirect
23. #11763492C22semidirect
24. #11763438C22semidirect
25. #11763436C22semidirect
26. #11763420C22semidirect
27. #11763417C22semidirect
44. C2×#10587556C22semidirect
81. C17×#533C22semidirect
358. C2×#533D17semidirect
398. #533C2×D17semidirect
461. C2×C17#3563semidirect
584. C17C2×#3563semidirect
747. C2#14543394direct (N × H)

Maximal subgroups

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

subgroupindex
#145433942
C2×C17⋊#5642
C2×#117635632
C2×#117635352
C2×#117635172
C2×#117635012
C2×#117635002
C2×#117634922
C2×#117634382
C2×#117634362
C2×#117634202
C2×#117634172
C2×#117634082
C2×#117633432
C22×#105875562
C2×C17×#5332
C2×#356317