Finite Group Databasebeta

← C2×#14542663 #17942760

Subgroups — C2×#14542663 #17942760

Order 4352.

7022 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542663C2132yesmaximal, direct product factor
2C2×#11763536C212yesmaximal, complemented
3C2×#11763535C212yesmaximal, complemented
4C2×#11763530C212yesmaximal, complemented
5C2×#11763527C212yesmaximal, complemented
6C2×#11763500C212yesmaximal, complemented
7C2×#11763498C212yesmaximal, complemented
8C2×#11763497C212yesmaximal, complemented
9C2×#11763493C212yesmaximal, complemented
10C2×#11763419C212yesmaximal, complemented
11C2×#11763417C212yesmaximal, complemented
12C2×#11763382C212yesmaximal
13C2×#11763366C211yesmaximal, characteristic, complemented
14C2×#11763364C211yesmaximal, characteristic, complemented
15C2×#11763364C211yesmaximal, characteristic, complemented
16C2×#11763364C211yesmaximal, characteristic, complemented
17C2×C4⋊Q8×D17C211yesmaximal, characteristic, complemented
18C2×#11763285C212yesmaximal, complemented
19C2×C4×#63252C211yesmaximal, characteristic
20C2×C17×#533C211yesmaximal, characteristic, complemented
21C22×#63252C2211yescharacteristic
22C22×Q8×D17C2212yes—
23#11763536C22132yescomplemented
24#11763535C22132yescomplemented
25#11763530C22132yescomplemented
26#11763527C22132yescomplemented
27#11763500C22132yescomplemented
28#11763498C22132yescomplemented
29#11763497C22132yescomplemented
30#11763493C22132yescomplemented
31#11763419C22132yescomplemented
32#11763417C22132yescomplemented
33#11763382C22132yes—
34#11763366C22116yescomplemented
35#11763364C22116yescomplemented
36#11763364C22116yescomplemented
37#11763364C22116yescomplemented
38C2×#10587555C2211yescharacteristic
39C2×#10587555C2211yescharacteristic
40C2×#10587574C2214yes—
41C2×#10587574C2212yes—
42C2×#10587574C2212yes—
43C2×#10587630C2212yes—
44C4⋊Q8×D17C22116yescomplemented
45C2×#10587584C2214yes—
46C2×#10587562C2214yes—
47C2×#10587565C2214yes—
48C2×#10587565C2214yes—
49C2×#10587556C2214yes—
50C2×#10587556C2212yes—
51C2×#10587576C2214yes—
52C2×#10587576C2212yes—
53C2×#10587576C2212yes—
54C2×#10587576C2212yes—
55C2×#10587575C2214yes—
56C2×#10587575C2214yes—
57C2×#10587571C2214yes—
58C2×#10587580C2214yes—
59C2×#10587569C2214yes—
60C2×#10587583C2212yes—
61C2×#10587583C2212yes—
62C2×#10587583C2212yes—
63C2×#10587610C2212yes—
64C2×#10587610C2212yes—
65C2×#10587632C2212yes—
66C2×#10587632C2212yes—
67C2×#10587632C2212yes—
68#11763285C22132yescomplemented
69C4×#63252C22116yes—
70C2×Q8×Dic17C2212yes—
71C2×Q8×Dic17C2212yes—
72C2×Q8×Dic17C2212yes—
73C2×C4×Dic34C2211yescharacteristic
74C2×C4×Dic34C2214yes—
75C2×C4×Dic34C2211yescharacteristic
76C2×C4×Dic34C2212yes—
77C2×C4×Dic34C2212yes—
78C2×#10587573C2214yes—
79C2×#10587573C2212yes—
80C2×#10587573C2212yes—
81C2×#10587573C2212yes—
82C2×C4×D68C2211yescharacteristic
83C2×C4×D68C2211yescharacteristic
84C2×C4×C22⋊D17C2211yescharacteristic
85C2×C4×C22⋊D17C2211yescharacteristic
86C2×C4×C22⋊D17C2211yescharacteristic
87C2×C4×C22⋊D17C2211yescharacteristic
88C2×#10587612C2211yescharacteristic
89C2×#10587612C2212yes—
90C2×#10587578C2212yes—
91C2×#10587578C2214yes—
92C2×#10587578C2212yes—
93C2×#10587578C2212yes—
94C2×#10587558C2211yescharacteristic
95C2×#10587558C2211yescharacteristic
96C2×#10587558C2214yes—
97C2×C4⋊C4×D17C2212yes—
98C2×C4⋊C4×D17C2212yes—
99C2×C42×D17C2211yescharacteristic
100C2×C42×D17C2211yescharacteristic
101C17×#533C22116yescomplemented
102C2×C17×C4⋊Q8C2211yescharacteristic
103C2×C17×C4⋊Q8C2211yescharacteristic
104C2×C17×#125C2212yes—
105C2×C17×C22⋊Q8C2212yes—
106C2×C17×C22⋊Q8C2212yes—
107C2×C4×Q8×C17C2212yes—
108C2×C4×Q8×C17C2212yes—
109C2×C17×#117C2212yes—
110C22×C42×C17C2211yescharacteristic
111C22×Q8×C17C2312yes—
112C22×Q8×C17C2312yes—
113C23×C4×C17C2311yescharacteristic
114C23×C4×C17C2311yescharacteristic
115C23×C4×C17C2311yescharacteristic
116C22×C22⋊D17C2311yescharacteristic
117C22×C22⋊D17C2311yescharacteristic
118C2×Q8×D17—216no—
119C2×Q8×D17C23116yes—
120C2×#63252—28no—
121C2×#63252C2318yes—
122C22×D68C2311yescharacteristic
123C22×C4×D17C2311yescharacteristic
124C22×C4×D17C2311yescharacteristic
125C22×C4×D17C2311yescharacteristic
126C22×C4×D17C2311yescharacteristic
127C22×C4×D17C2311yescharacteristic
128C22×C4×D17C2314yes—
129C22×C4×D17C2311yescharacteristic
130C22×Dic34C2312yes—
131C22×Dic34C2312yes—
132C22×Dic34C2314yes—
133C22×Dic34C2311yescharacteristic
134C17×C4⋊Q8C2318yes—
135C17×C4⋊Q8C2318yes—
136C17×#125C23116yes—
137C17×C22⋊Q8C23116yes—
138C17×C22⋊Q8C23116yes—
139C4×Q8×C17C23116yes—
140C4×Q8×C17C23116yes—
141C17×#117C23116yes—
142C2×C4⋊C4×C17C2312yes—
143C2×C4⋊C4×C17C2312yes—
144C2×C4⋊C4×C17C2314yes—
145C2×C4⋊C4×C17C2314yes—
146C2×C4⋊C4×C17C2312yes—
147C2×C4⋊C4×C17C2312yes—
148C2×C22⋊C4×C17C2314yes—
149C2×C42×C17C2311yescharacteristic
150C2×C42×C17C2311yescharacteristic
151C2×C42×C17C2311yescharacteristic
152C2×C42×C17C2311yescharacteristic
153C2×C42×C17C2318yes—
154C2×C42×C17C2314yes—
155C2×C22⋊Dic17C2311yescharacteristic
156C2×C22⋊Dic17C2311yescharacteristic
157C2×C22⋊Dic17C2314yes—
158#10587632C23116yes—
159#10587632C23116yes—
160#10587632C23116yes—
161Q8×Dic17C23116yes—
162Q8×Dic17C23116yes—
163Q8×Dic17C23116yes—
164#10587630C23116yes—
165C4×C22⋊D17C2318yes—
166C4×C22⋊D17C2318yes—
167C4×C22⋊D17C2318yes—
168C4×C22⋊D17C2318yes—
169C2×#63227C2311yescharacteristic
170C2×#63227C2311yescharacteristic
171C2×#63227C2314yes—
172C2×#63227C2311yescharacteristic
173C2×#63227C2311yescharacteristic
174C2×#63227C2314yes—
175C2×#63227C2314yes—
176#10587612C23116yes—
177#10587612C2318yes—
178C2×C4⋊Dic17C2312yes—
179C2×C4⋊Dic17C2312yes—
180C2×C4⋊Dic17C2312yes—
181C2×C4⋊Dic17C2312yes—
182C2×C4⋊Dic17C2314yes—
183C2×C4⋊Dic17C2311yescharacteristic
184C2×C4⋊Dic17C2311yescharacteristic
185C2×C4⋊Dic17C2314yes—
186C2×C4⋊Dic17C2314yes—
187#10587610C23116yes—
188#10587610C23116yes—
189C2×#63225C2314yes—
190C2×#63225C2314yes—
191C2×#63225C2311yescharacteristic
192C2×#63225C2311yescharacteristic
193C2×#63225C2311yescharacteristic
194C2×#63225C2311yescharacteristic
195C2×#63225C2314yes—
196C2×#63225C2314yes—
197C2×#63225C2314yes—
198C2×#63225C2314yes—
199C2×#63225C2314yes—
200C2×C4×Dic17C2311yescharacteristic
201C2×C4×Dic17C2311yescharacteristic
202C2×C4×Dic17C2311yescharacteristic
203C2×C4×Dic17C2311yescharacteristic
204C2×C4×Dic17C2311yescharacteristic
205C2×C4×Dic17C2311yescharacteristic
206C2×C4×Dic17C2314yes—
207C2×C4×Dic17C2314yes—
208C2×C4×Dic17C2314yes—
209C2×C4×Dic17C2314yes—
210#10587584C23132yes—
211#10587583C23116yes—
212#10587583C23116yes—
213#10587583C23116yes—
214#10587580C23132yes—
215#10587578C23132yes—
216#10587578C23116yes—
217#10587578C23116yes—
218#10587578C23116yes—
219C4⋊C4×D17C23116yes—
220C4⋊C4×D17C23116yes—
221#10587576C23116yes—
222#10587576C23132yes—
223#10587576C23116yes—
224#10587576C23116yes—
225#10587575C23132yes—
226#10587575C23132yes—
227#10587574C23116yes—
228#10587574C23116yes—
229#10587574C23132yes—
230#10587573C23116yes—
231#10587573C23116yes—
232#10587573C23132yes—
233#10587573C23116yes—
234#10587571C23132yes—
235#10587569C23132yes—
236#10587565C23132yes—
237#10587565C23132yes—
238#10587562C23132yes—
239C4×D68C2318yes—
240C4×D68C2318yes—
241#10587558C23132yes—
242#10587558C2318yes—
243#10587558C2318yes—
244C42×D17C2318yes—
245C42×D17C2318yes—
246#10587556C23132yes—
247#10587556C23116yes—
248#10587555C2318yes—
249#10587555C2318yes—
250C4×Dic34C23116yes—
251C4×Dic34C23132yes—
252C4×Dic34C2318yes—
253C4×Dic34C2318yes—
254C4×Dic34C23116yes—
255C24×C17C2411yescharacteristic
256C23×D17C2411yescharacteristic
257C23×D17C2411yescharacteristic
258C2×Q8×C17—28no—
259C2×Q8×C17—28no—
260C2×Q8×C17C2418yes—
261C2×Q8×C17C2418yes—
262C22×C4×C17—24no—
263C22×C4×C17—24no—
264C22×C4×C17—24no—
265C22×C4×C17C2414yes—
266C22×C4×C17C2414yes—
267C22×C4×C17C2414yes—
268C22×C4×C17C2411yescharacteristic
269C22×C4×C17C2411yescharacteristic
270C22×C4×C17C2411yescharacteristic
271C22×C4×C17C2414yes—
272C22×C4×C17C2414yes—
273C22×C4×C17C2411yescharacteristic
274C22×C4×C17C2411yescharacteristic
275C22×C4×C17C2411yescharacteristic
276C2×C22⋊D17—24no—
277C2×C22⋊D17—24no—
278C2×C22⋊D17C2414yes—
279C2×C22⋊D17C2414yes—
280C22×Dic17C2414yes—
281C22×Dic17C2411yescharacteristic
282C22×Dic17C2414yes—
283C22×Dic17C2411yescharacteristic
284C22×Dic17C2411yescharacteristic
285C22×Dic17C2411yescharacteristic
286C22×Dic17C2411yescharacteristic
287C22×Dic17C2411yescharacteristic
288Q8×D17—264no—
289#63252—232no—
290C2×D68—24no—
291C2×D68C2414yes—
292C2×C4×D17—216no—
293C2×C4×D17—24no—
294C2×C4×D17—24no—
295C2×C4×D17—24no—
296C2×C4×D17—24no—
297C2×C4×D17—24no—
298C2×C4×D17#4118yes—
299C2×C4×D17C2414yes—
300C2×C4×D17C24116yes—
301C2×C4×D17C2414yes—
302C2×C4×D17C2414yes—
303C2×C4×D17C2414yes—
304C2×C4×D17C2414yes—
305C2×C4×D17C2414yes—
306C2×Dic34—28no—
307C2×Dic34—28no—
308C2×Dic34—24no—
309C2×Dic34—216no—
310C2×Dic34C2414yes—
311C2×Dic34C2418yes—
312C2×Dic34C24116yes—
313C2×Dic34C2418yes—
314C4⋊C4×C17C24116yes—
315C4⋊C4×C17C24116yes—
316C4⋊C4×C17C2418yes—
317C4⋊C4×C17C2418yes—
318C4⋊C4×C17C2418yes—
319C4⋊C4×C17C2418yes—
320C22⋊C4×C17C24116yes—
321C42×C17C2414yes—
322C42×C17C2414yes—
323C42×C17C2414yes—
324C42×C17C2414yes—
325C42×C17C24116yes—
326C22⋊Dic17C2414yes—
327C22⋊Dic17C2414yes—
328C22⋊Dic17C24116yes—
329#63227C2414yes—
330#63227C2414yes—
331#63227C2414yes—
332#63227C2414yes—
333#63227C24116yes—
334#63227C24116yes—
335#63227C24116yes—
336C4⋊Dic17C2418yes—
337C4⋊Dic17C2418yes—
338C4⋊Dic17C2414yes—
339C4⋊Dic17C2414yes—
340C4⋊Dic17C24116yes—
341C4⋊Dic17C2418yes—
342C4⋊Dic17C2418yes—
343C4⋊Dic17C24116yes—
344C4⋊Dic17C24116yes—
345#63225C2414yes—
346#63225C24116yes—
347#63225C2414yes—
348#63225C24116yes—
349#63225C2414yes—
350#63225C2414yes—
351#63225C24116yes—
352#63225C24116yes—
353#63225C24116yes—
354#63225C24116yes—
355#63225C24116yes—
356C4×Dic17C24116yes—
357C4×Dic17C2414yes—
358C4×Dic17C2414yes—
359C4×Dic17C2414yes—
360C4×Dic17C2414yes—
361C4×Dic17C24116yes—
362C4×Dic17C24116yes—
363C4×Dic17C2414yes—
364C4×Dic17C2414yes—
365C4×Dic17C24116yes—
366C2×#3509—171nomaximal, Sylow
367C23×C17—22no—
368C23×C17—22no—
369C23×C17—22no—
370C23×C17C2512yes—
371C23×C17C2511yescharacteristic
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—22no—
375C22×D17—22no—
376C22×D17—22no—
377C22×D17C2×#4114yes—
378C22×D17C2512yes—
379C22×D17C2512yes—
380Q8×C17—216no—
381Q8×C17—216no—
382C2×C4×C17—28no—
383C2×C4×C17—22no—
384C2×C4×C17—22no—
385C2×C4×C17—22no—
386C2×C4×C17—28no—
387C2×C4×C17—28no—
388C2×C4×C17—28no—
389C2×C4×C17—28no—
390C2×C4×C17C2×#4114yes—
391C2×C4×C172−1+414yes—
392C2×C4×C172−1+414yes—
393C2×C4×C17C2512yes—
394C2×C4×C17C2512yes—
395C2×C4×C17C2512yes—
396C2×C4×C17C2518yes—
397C2×C4×C17C2518yes—
398C2×C4×C17C2512yes—
399C2×C4×C17C2512yes—
400C2×C4×C17C2512yes—
401C22⋊D17—28no—
402C22⋊D17—28no—
403C2×Dic17—28no—
404C2×Dic17—22no—
405C2×Dic17—28no—
406C2×Dic17—22no—
407C2×Dic17—22no—
408C2×Dic17—22no—
409C2×Dic17—22no—
410C2×Dic17C2×#4114yes—
411C2×Dic17C2518yes—
412C2×Dic17C2518yes—
413C2×Dic17C2512yes—
414C2×Dic17C2512yes—
415C2×Dic17C2512yes—
416C2×Dic17C2512yes—
417C2×Dic17C2512yes—
418C2×Dic17C2512yes—
419D68—28no—
420C4×D17—232no—
421C4×D17—28no—
422C4×D17—28no—
423C4×D17—28no—
424C4×D17—28no—
425C4×D17—28no—
426C4×D17C2×#41116yes—
427Dic34—216no—
428Dic34—216no—
429Dic34—28no—
430Dic34—232no—
431#3509—1732no—
432C2×#557—172no—
433C2×#557—172no—
434C2×#556—172no—
435C2×#556—172no—
436C2×#552—172no—
437C2×#552—172no—
438C2×#552—172no—
439C2×#552—172no—
440C2×#541—172no—
441C2×#541—172no—
442C2×#536—172no—
443C2×#533—171no—
444C2×#533—171no—
445C2×#533—171no—
446C2×#533—171no—
447C2×#533D1711yescharacteristic, complemented
448C22×C4⋊Q8—171no—
449C2×#519—172no—
450C2×C4×#41—171no—
451C22×C17—22no—
452C22×C17—22no—
453C22×C17—22no—
454C22×C17—44no—
455C22×C17C22×#4112yes—
456C22×C17C2×2−1+412yes—
457C22×C17C2×2−1+412yes—
458C22×C17C2611yescharacteristic
459C2×D17—22no—
460C2×D17—22no—
461C2×D17—28no—
462C2×D17—22no—
463C2×D17—22no—
464C2×D17—22no—
465C2×D17—44no—
466C2×D17C22×#4114yes—
467C4×C17—28no—
468C4×C17—22no—
469C4×C17—22no—
470C4×C17—22no—
471C4×C17—28no—
472C4×C17C22×#4114yes—
473C4×C17C2×2−1+414yes—
474C4×C17C2×2−1+414yes—
475Dic17—28no—
476Dic17—22no—
477Dic17—28no—
478Dic17—22no—
479Dic17—22no—
480Dic17—22no—
481Dic17—22no—
482Dic17C22×#4114yes—
483C22×#41—171no—
484C23×Q8—172no—
485#557—1732no—
486#557—1732no—
487#556—1732no—
488#556—1732no—
489#552—1732no—
490#552—1732no—
491#552—1732no—
492#552—1732no—
493#541—1732no—
494#541—1732no—
495#536—1732no—
496#533—1716no—
497#533—1716no—
498#533—1716no—
499#533—1716no—
500#533C2×D17116yescomplemented
501C2×C4⋊Q8—172no—
502C2×C4⋊Q8—1716no—
503C2×C4⋊Q8—172no—
504C2×C4⋊Q8—172no—
505C2×C4⋊Q8—174no—
506C2×C4⋊Q8—171no—
507C2×C4⋊Q8—171no—
508C2×C4⋊Q8C2×D1711yescharacteristic
509C2×C4⋊Q8C2×D1711yescharacteristic
510C2×#126—174no—
511C2×#126—174no—
512C2×#126—174no—
513C2×#126—174no—
514C2×#125—172no—
515C2×#125—172no—
516C2×#125—172no—
517C2×#125—174no—
518C2×#125—174no—
519C2×#125—174no—
520C2×#125—172no—
521C2×#125—174no—
522C2×#125C2×D1712yes—
523C2×#124—174no—
524C2×#123—174no—
525C2×#123—174no—
526C2×C22⋊Q8—172no—
527C2×C22⋊Q8—172no—
528C2×C22⋊Q8—172no—
529C2×C22⋊Q8—172no—
530C2×C22⋊Q8—172no—
531C2×C22⋊Q8—172no—
532C2×C22⋊Q8—172no—
533C2×C22⋊Q8—172no—
534C2×C22⋊Q8C2×D1712yes—
535C2×C22⋊Q8C2×D1712yes—
536#519—1732no—
537C4×#41—1716no—
538C2×C4×Q8—172no—
539C2×C4×Q8—172no—
540C2×C4×Q8—172no—
541C2×C4×Q8—172no—
542C2×C4×Q8—174no—
543C2×C4×Q8—172no—
544C2×C4×Q8—172no—
545C2×C4×Q8—171no—
546C2×C4×Q8—171no—
547C2×C4×Q8—172no—
548C2×C4×Q8—174no—
549C2×C4×Q8—172no—
550C2×C4×Q8C2×D1712yes—
551C2×C4×Q8C2×D1712yes—
552C2×C4×D4—171no—
553C2×C4×D4—171no—
554C2×C4×D4—171no—
555C2×C4×D4—171no—
556C2×C4×D4—171no—
557C2×C4×D4—171no—
558C2×#117—171no—
559C2×#117—172no—
560C2×#117—172no—
561C2×#117—174no—
562C2×#117—172no—
563C2×#117—172no—
564C2×#117—171no—
565C2×#117—171no—
566C2×#117—174no—
567C2×#117C2×D1712yes—
568C22×C4⋊C4—172no—
569C22×C4⋊C4—172no—
570C22×C42—171no—
571C22×C42—171no—
572C22×C42C2×D1711yescharacteristic
573C2×C17—42no—
574C2×C17#350914yescomplemented
575C2×C17C23×#4111yescharacteristic
576C2×C17C22×2−1+411yescharacteristic
577C2×C17C22×2−1+411yescharacteristic
578D17—24no—
579D17—42no—
580C2×#41—178no—
581C2×#41—348no—
582C22×Q8—1716no—
583C22×Q8—172no—
584C22×Q8—172no—
585C22×Q8—174no—
586C22×Q8—171no—
587C22×Q8—3416no—
588C22×Q8C22×D1712yes—
589C22×Q8C22×D1712yes—
590C22×D4—171no—
591C22×D4—171no—
592C22×D4—171no—
593C23×C4—171no—
594C23×C4—174no—
595C23×C4—171no—
596C23×C4—171no—
597C23×C4—171no—
598C23×C4—171no—
599C23×C4—171no—
600C23×C4C22×D1711yescharacteristic
601C23×C4C22×D1711yescharacteristic
602C23×C4C22×D1711yescharacteristic
603C4⋊Q8—1716no—
604C4⋊Q8—1716no—
605C4⋊Q8—1716no—
606C4⋊Q8—1732no—
607C4⋊Q8—178no—
608C4⋊Q8—178no—
609C4⋊Q8C22×D1718yes—
610C4⋊Q8C22×D1718yes—
611#126—1732no—
612#126—1732no—
613#126—1732no—
614#126—1732no—
615#125—1716no—
616#125—1716no—
617#125—1716no—
618#125—1732no—
619#125—1732no—
620#125—1732no—
621#125—1716no—
622#125—1732no—
623#125C22×D17116yes—
624#124—1732no—
625#123—1732no—
626#123—1732no—
627C22⋊Q8—1716no—
628C22⋊Q8—1716no—
629C22⋊Q8—1716no—
630C22⋊Q8—1716no—
631C22⋊Q8—1716no—
632C22⋊Q8—1716no—
633C22⋊Q8—1716no—
634C22⋊Q8—1716no—
635C22⋊Q8C22×D17116yes—
636C22⋊Q8C22×D17116yes—
637C4×Q8—1716no—
638C4×Q8—1716no—
639C4×Q8—1716no—
640C4×Q8—1716no—
641C4×Q8—1732no—
642C4×Q8—1716no—
643C4×Q8—1716no—
644C4×Q8—178no—
645C4×Q8—178no—
646C4×Q8—1716no—
647C4×Q8—1732no—
648C4×Q8—1716no—
649C4×Q8C22×D17116yes—
650C4×Q8C22×D17116yes—
651C4×D4—178no—
652C4×D4—178no—
653C4×D4—178no—
654C4×D4—178no—
655C4×D4—178no—
656C4×D4—178no—
657#117—178no—
658#117—1716no—
659#117—1716no—
660#117—1732no—
661#117—1716no—
662#117—1716no—
663#117—178no—
664#117—178no—
665#117—1732no—
666#117C22×D17116yes—
667C2×C4⋊C4—172no—
668C2×C4⋊C4—172no—
669C2×C4⋊C4—174no—
670C2×C4⋊C4—174no—
671C2×C4⋊C4—172no—
672C2×C4⋊C4—171no—
673C2×C4⋊C4—171no—
674C2×C4⋊C4—171no—
675C2×C4⋊C4—171no—
676C2×C4⋊C4—171no—
677C2×C4⋊C4—171no—
678C2×C4⋊C4—172no—
679C2×C4⋊C4—174no—
680C2×C4⋊C4—174no—
681C2×C4⋊C4—174no—
682C2×C4⋊C4—174no—
683C2×C4⋊C4—174no—
684C2×C4⋊C4—174no—
685C2×C4⋊C4—174no—
686C2×C4⋊C4—174no—
687C2×C4⋊C4—1716no—
688C2×C4⋊C4—1716no—
689C2×C4⋊C4C22×D1712yes—
690C2×C4⋊C4C22×D1712yes—
691C2×C4⋊C4C22×D1712yes—
692C2×C4⋊C4C22×D1712yes—
693C2×C4⋊C4C22×D1714yes—
694C2×C4⋊C4C22×D1714yes—
695C2×C22⋊C4—171no—
696C2×C22⋊C4—171no—
697C2×C22⋊C4—174no—
698C2×C22⋊C4—171no—
699C2×C22⋊C4—171no—
700C2×C22⋊C4—174no—
701C2×C22⋊C4—171no—
702C2×C22⋊C4—171no—
703C2×C22⋊C4—174no—
704C2×C22⋊C4—174no—
705C2×C22⋊C4C22×D1714yes—
706C2×C42—171no—
707C2×C42—174no—
708C2×C42—174no—
709C2×C42—174no—
710C2×C42—171no—
711C2×C42—174no—
712C2×C42—171no—
713C2×C42—171no—
714C2×C42—171no—
715C2×C42—171no—
716C2×C42—178no—
717C2×C42—178no—
718C2×C42C22×D1711yescharacteristic
719C2×C42C22×D1714yes—
720C2×C42C22×D1711yescharacteristic
721C2×C42C22×D1711yescharacteristic
722C2×C42C22×D1718yes—
723C2×C42C22×D1711yescharacteristic
724C17C2×#350911yescharacteristic, complemented, Sylow
725C24—171no—
726C24—171no—
727C24C23×D1711yescharacteristic
728#41—3432no—
729C2×Q8—28no—
730C2×Q8—28no—
731C2×Q8—178no—
732C2×Q8—178no—
733C2×Q8—1716no—
734C2×Q8—174no—
735C2×Q8—3416no—
736C2×Q8—344no—
737C2×Q8—3464no—
738C2×Q8—348no—
739C2×Q8—348no—
740C2×Q8C23×D1718yes—
741C2×Q8C23×D1718yes—
742C2×D4—174no—
743C2×D4—174no—
744C2×D4—174no—
745C2×D4—344no—
746C2×D4—344no—
747C2×D4—344no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—171no—
752C22×C4—178no—
753C22×C4—174no—
754C22×C4—171no—
755C22×C4—171no—
756C22×C4—174no—
757C22×C4—171no—
758C22×C4—171no—
759C22×C4—174no—
760C22×C4—171no—
761C22×C4—174no—
762C22×C4—174no—
763C22×C4—174no—
764C22×C4—174no—
765C22×C4—174no—
766C22×C4—1716no—
767C22×C4—3416no—
768C22×C4—344no—
769C22×C4—344no—
770C22×C4—344no—
771C22×C4—344no—
772C22×C4—344no—
773C22×C4C23×D1714yes—
774C22×C4C23×D1714yes—
775C22×C4C23×D1714yes—
776C22×C4C23×D1711yescharacteristic
777C22×C4C23×D1714yes—
778C22×C4C23×D1714yes—
779C22×C4C23×D1711yescharacteristic
780C22×C4C23×D1711yescharacteristic
781C22×C4C23×D1711yescharacteristic
782C22×C4C23×D1711yescharacteristic
783C22×C4C23×D1711yescharacteristic
784C4⋊C4—178no—
785C4⋊C4—178no—
786C4⋊C4—1716no—
787C4⋊C4—1716no—
788C4⋊C4—178no—
789C4⋊C4—174no—
790C4⋊C4—174no—
791C4⋊C4—174no—
792C4⋊C4—174no—
793C4⋊C4—174no—
794C4⋊C4—174no—
795C4⋊C4—178no—
796C4⋊C4—1716no—
797C4⋊C4—1716no—
798C4⋊C4—1716no—
799C4⋊C4—1716no—
800C4⋊C4—1716no—
801C4⋊C4—1716no—
802C4⋊C4—1716no—
803C4⋊C4—1716no—
804C4⋊C4C23×D1718yes—
805C4⋊C4C23×D1718yes—
806C4⋊C4C23×D1718yes—
807C4⋊C4C23×D1718yes—
808C4⋊C4C23×D17116yes—
809C4⋊C4C23×D17116yes—
810C22⋊C4—174no—
811C22⋊C4—174no—
812C22⋊C4—1716no—
813C22⋊C4—174no—
814C22⋊C4—174no—
815C22⋊C4—1716no—
816C22⋊C4—174no—
817C22⋊C4—174no—
818C22⋊C4—1716no—
819C22⋊C4—1716no—
820C22⋊C4C23×D17116yes—
821C42—174no—
822C42—174no—
823C42—174no—
824C42—174no—
825C42—174no—
826C42—174no—
827C42—1716no—
828C42—1716no—
829C42—1716no—
830C42—1716no—
831C42C23×D1714yes—
832C42C23×D1714yes—
833C42C23×D1714yes—
834C42C23×D1714yes—
835C42C23×D17116yes—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—174no—
840C23—172no—
841C23—172no—
842C23—342no—
843C23—342no—
844C23—342no—
845C23—342no—
846C23—342no—
847C23C24×D1712yes—
848C23C24×D1711yescharacteristic
849Q8—216no—
850Q8—216no—
851Q8—3432no—
852Q8—348no—
853Q8—3416no—
854Q8—3416no—
855D4—348no—
856D4—348no—
857D4—348no—
858C2×C4—22no—
859C2×C4—28no—
860C2×C4—22no—
861C2×C4—28no—
862C2×C4—22no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—174no—
867C2×C4—172no—
868C2×C4—1716no—
869C2×C4—172no—
870C2×C4—172no—
871C2×C4—178no—
872C2×C4—172no—
873C2×C4—172no—
874C2×C4—178no—
875C2×C4—172no—
876C2×C4—3432no—
877C2×C4—342no—
878C2×C4—348no—
879C2×C4—342no—
880C2×C4—342no—
881C2×C4—342no—
882C2×C4—342no—
883C2×C4—348no—
884C2×C4—348no—
885C2×C4—348no—
886C2×C4—348no—
887C2×C4—348no—
888C2×C4—348no—
889C2×C4#1058769414yes—
890C2×C4#41×D1714yes—
891C2×C4#1058769714yes—
892C2×C4C24×D1712yes—
893C2×C4C24×D1718yes—
894C2×C4C24×D1718yes—
895C2×C4C24×D1712yes—
896C2×C4C24×D1712yes—
897C2×C4C24×D1712yes—
898C2×C4C24×D1712yes—
899C2×C4C24×D1712yes—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—44no—
904C22—174no—
905C22—348no—
906C22—342no—
907C22—342no—
908C22—342no—
909C22—342no—
910C22—342no—
911C22—684no—
912C22C2×#41×D1712yes—
913C22C2×#1058769712yes—
914C22C2×#1058769412yes—
915C22C25×D1711yescharacteristic
916C4—22no—
917C4—28no—
918C4—22no—
919C4—28no—
920C4—22no—
921C4—174no—
922C4—342no—
923C4—348no—
924C4—342no—
925C4—342no—
926C4—342no—
927C4—342no—
928C4—348no—
929C4C2×#41×D1714yes—
930C4C2×#1058769714yes—
931C4C2×#1058769414yes—
932C2—42no—
933C2—344no—
934C2—682no—
935C2#1454266314yesdirect product factor
936C2C22×#41×D1711yescharacteristic
937C2C22×#1058769711yescharacteristic
938C2C22×#1058769411yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#533C2
socleC23×C17C25
prime radicalC22×#63252C22
hypercenterC2×#533D17
hypocenterC17C2×#3509
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #14542663C2direct (N × H)
2. C2×#11763536C2semidirect
3. C2×#11763535C2semidirect
4. C2×#11763530C2semidirect
5. C2×#11763527C2semidirect
6. C2×#11763500C2semidirect
7. C2×#11763498C2semidirect
8. C2×#11763497C2semidirect
9. C2×#11763493C2semidirect
10. C2×#11763419C2semidirect
11. C2×#11763417C2semidirect
13. C2×#11763366C2semidirect
14. C2×#11763364C2semidirect
15. C2×#11763364C2semidirect
16. C2×#11763364C2semidirect
17. C2×C4⋊Q8×D17C2semidirect
18. C2×#11763285C2semidirect
20. C2×C17×#533C2semidirect
23. #11763536C22semidirect
24. #11763535C22semidirect
25. #11763530C22semidirect
26. #11763527C22semidirect
27. #11763500C22semidirect
28. #11763498C22semidirect
29. #11763497C22semidirect
30. #11763493C22semidirect
31. #11763419C22semidirect
32. #11763417C22semidirect
34. #11763366C22semidirect
35. #11763364C22semidirect
36. #11763364C22semidirect
37. #11763364C22semidirect
44. C4⋊Q8×D17C22semidirect
68. #11763285C22semidirect
101. C17×#533C22semidirect
447. C2×#533D17semidirect
500. #533C2×D17semidirect
574. C2×C17#3509semidirect
724. C17C2×#3509semidirect
935. C2#14542663direct (N × H)

Maximal subgroups

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

subgroupindex
#145426632
C2×#117635362
C2×#117635352
C2×#117635302
C2×#117635272
C2×#117635002
C2×#117634982
C2×#117634972
C2×#117634932
C2×#117634192
C2×#117634172
C2×#117633822
C2×#117633662
C2×#117633642
C2×C4⋊Q8×D172
C2×#117632852
C2×C4×#632522
C2×C17×#5332
C2×#350917