Finite Group Databasebeta

← C2×#14542533 #17942751

Subgroups — C2×#14542533 #17942751

Order 4352.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542533C2132yesmaximal, direct product factor
2C2×#11763530C212yesmaximal, complemented
3C2×#11763517C212yesmaximal, complemented
4C2×#11763501C212yesmaximal, complemented
5C2×#11763496C214yesmaximal, complemented
6C2×#11763493C212yesmaximal, complemented
7C2×#11763482C214yesmaximal, complemented
8C2×#11763437C211yesmaximal, characteristic, complemented
9C2×#11763428C212yesmaximal, complemented
10C2×#11763420C212yesmaximal, complemented
11C2×#11763364C212yesmaximal, complemented
12C2×#11763338C212yesmaximal, complemented
13C2×#11763316C211yesmaximal, characteristic
14C22×#10587632C211yesmaximal, characteristic, complemented
15C2×#11763292C211yesmaximal, characteristic, complemented
16C2×#11763287C211yesmaximal, characteristic, complemented
17C2×#117×D17C211yesmaximal, characteristic, complemented
18C2×C17×#536C211yesmaximal, characteristic, complemented
19C23×C4×D17C2211yescharacteristic
20#11763530C22132yescomplemented
21#11763517C22132yescomplemented
22#11763501C22132yescomplemented
23#11763496C22164yescomplemented
24#11763493C22132yescomplemented
25#11763482C22164yescomplemented
26#11763437C22116yescomplemented
27#11763428C22132yescomplemented
28#11763420C22132yescomplemented
29#11763364C22132yescomplemented
30C2×#10587555C2212yescomplemented
31C2×#10587574C2212yescomplemented
32#11763338C22132yescomplemented
33C2×#10587584C2214yes—
34C2×#10587584C2214yes—
35C2×#10587565C2214yescomplemented
36C2×#10587565C2214yescomplemented
37C2×#10587556C2212yescomplemented
38C2×#10587576C2212yescomplemented
39C2×#10587576C2214yescomplemented
40C2×#10587575C2214yescomplemented
41C2×#10587575C2214yescomplemented
42C2×#10587571C2214yes—
43#11763316C22116yes—
44C2×#10587572C2214yes—
45C2×#10587569C2214yes—
46C2×#10587621C2212yes—
47C2×#10587583C2214yes—
48C2×#10587564C2214yes—
49C2×#10587564C2214yescomplemented
50C2×#10587632C2211yescharacteristic
51C2×#10587632C2212yes—
52C2×#10587632C2212yes—
53C2×#10587632C2212yes—
54C2×#10587632C2212yes—
55C2×#10587632C2211yescharacteristic
56C2×#10587632C22116yescomplemented
57C2×#10587624C2211yescharacteristic
58C2×#10587624C2211yescharacteristic
59C2×#10587623C2212yes—
60#11763292C22116yescomplemented
61#11763287C22116yescomplemented
62C2×Q8×Dic17C2212yescomplemented
63C2×Q8×Dic17C2212yescomplemented
64C2×Q8×Dic17C2212yescomplemented
65C2×Q8×Dic17C2212yescomplemented
66C2×Q8×Dic17C2212yescomplemented
67C2×#10587573C2214yescomplemented
68C2×D4×Dic17C2214yes—
69C2×D4×Dic17C2212yescomplemented
70C2×C4×C22⋊D17C2212yes—
71C2×C4×C22⋊D17C2212yes—
72C2×#10587567C2214yes—
73C2×#10587612C2211yescharacteristic
74C2×#10587612C2211yescharacteristic
75C2×#10587612C2214yes—
76C2×#10587612C2212yescomplemented
77C2×#10587578C2211yescharacteristic
78C2×#10587578C2211yescharacteristic
79C2×#10587578C2214yes—
80C2×#10587558C2212yes—
81C2×#10587563C2212yes—
82C2×#10587563C2214yescomplemented
83#117×D17C22116yescomplemented
84C22×C4⋊Dic17C2211yescharacteristic
85C22×C4⋊Dic17C2212yescomplemented
86C22×#63225C2212yes—
87C2×C4⋊C4×D17C2211yescharacteristic
88C2×C4⋊C4×D17C2211yescharacteristic
89C22×#63227C2212yes—
90C2×C22⋊C4×D17C2212yes—
91C2×C42×D17C2212yes—
92C22×#41×C17C2211yescharacteristic
93C23×Q8×C17C2211yescharacteristic
94C17×#536C22116yescomplemented
95C2×C17×C4⋊Q8C2212yescomplemented
96C2×C17×#124C2212yescomplemented
97C2×C17×#123C2214yes—
98C2×C17×C22⋊Q8C2212yescomplemented
99C2×C17×C22⋊Q8C2212yescomplemented
100C2×C17×#117C2211yescharacteristic
101C24×D17C2311yescharacteristic
102C2×#41×C17—28no—
103C2×#41×C17C2318yes—
104C22×Q8×C17—28no—
105C22×Q8×C17C2312yes—
106C22×Q8×C17C2312yes—
107C22×Q8×C17C2311yescharacteristic
108C22×Q8×C17C2318yes—
109C22×D4×C17C2312yes—
110C22×D4×C17C2311yescharacteristic
111C23×C4×C17C2312yes—
112C23×C4×C17C2312yes—
113C23×C4×C17C2311yescharacteristic
114C22×C22⋊D17C2312yes—
115C22×C22⋊D17C2312yes—
116C23×Dic17C2311yescharacteristic
117C23×Dic17C2312yes—
118C23×Dic17C2314yes—
119C22×C4×D17—28no—
120C22×C4×D17C2311yescharacteristic
121C22×C4×D17C2312yes—
122C22×C4×D17C2311yescharacteristic
123C22×C4×D17C2318yes—
124C22×C4×D17C2311yescharacteristic
125C22×C4×D17C2311yescharacteristic
126C22×C4×D17C2312yes—
127C22×Dic34C2314yes—
128C17×C4⋊Q8C23116yescomplemented
129C17×#124C23116yescomplemented
130C17×#123C23132yes—
131C17×C22⋊Q8C23116yescomplemented
132C17×C22⋊Q8C23116yescomplemented
133C17×#117C2318yes—
134C2×C4⋊C4×C17C2311yescharacteristic
135C2×C4⋊C4×C17C2311yescharacteristic
136C2×C4⋊C4×C17C2314yes—
137C2×C4⋊C4×C17C2314yes—
138C2×C22⋊C4×C17C2312yes—
139C2×C22⋊C4×C17C2314yes—
140C2×C22⋊C4×C17C2314yes—
141C2×C42×C17C2312yes—
142C2×C22⋊Dic17C2312yes—
143C2×C22⋊Dic17C2312yes—
144C2×C22⋊Dic17C2312yes—
145C2×C22⋊Dic17C2314yes—
146C2×C22⋊Dic17C2312yes—
147#10587632C23116yes—
148#10587632C23116yes—
149#10587632C23116yes—
150#10587632C23116yes—
151#10587632C2318yes—
152#10587632C2318yes—
153Q8×Dic17C23116yescomplemented
154Q8×Dic17C23116yescomplemented
155Q8×Dic17C23116yescomplemented
156Q8×Dic17C23116yescomplemented
157Q8×Dic17C23116yescomplemented
158#10587624C2318yes—
159#10587624C2318yes—
160#10587623C23116yes—
161#10587621C23116yes—
162D4×Dic17C23132yes—
163D4×Dic17C23116yescomplemented
164C4×C22⋊D17C23116yes—
165C4×C22⋊D17C23116yes—
166C2×#63227C23116yes—
167C2×#63227C2312yes—
168C2×#63227C2312yes—
169C2×#63227C2314yes—
170C2×#63227C2314yes—
171C2×#63227C2312yes—
172C2×#63227C2312yes—
173#10587612C23132yes—
174#10587612C2318yes—
175#10587612C2318yes—
176#10587612C23116yescomplemented
177C2×C4⋊Dic17C2311yescharacteristic
178C2×C4⋊Dic17C2311yescharacteristic
179C2×C4⋊Dic17C2312yes—
180C2×C4⋊Dic17C2312yes—
181C2×C4⋊Dic17C2318yes—
182C2×C4⋊Dic17C2314yes—
183C2×C4⋊Dic17C2314yes—
184C2×C4⋊Dic17C2311yescharacteristic
185C2×C4⋊Dic17C2311yescharacteristic
186C2×C4⋊Dic17C2314yes—
187C2×C4⋊Dic17C2314yes—
188C2×C4⋊Dic17C23116yescomplemented
189C2×#63225C23116yes—
190C2×#63225C2312yes—
191C2×#63225C2312yes—
192C2×#63225C2314yes—
193C2×#63225C2314yes—
194C2×#63225C2314yes—
195C2×#63225C2314yes—
196C2×#63225C2312yes—
197C2×#63225C2312yes—
198C2×C4×Dic17C2312yes—
199C2×C4×Dic17C2312yes—
200C2×C4×Dic17C2312yes—
201C2×C4×Dic17C2314yes—
202C2×C4×Dic17C2314yes—
203C2×C4×Dic17C2314yes—
204C2×C4×Dic17C2312yes—
205#10587584C23132yes—
206#10587584C23132yes—
207#10587583C23132yes—
208#10587578C23132yes—
209#10587578C2318yes—
210#10587578C2318yes—
211C4⋊C4×D17C2318yes—
212C4⋊C4×D17C2318yes—
213#10587576C23116yescomplemented
214#10587576C23132yescomplemented
215#10587575C23132yescomplemented
216#10587575C23132yescomplemented
217#10587574C23116yescomplemented
218#10587573C23132yescomplemented
219#10587572C23132yes—
220#10587571C23132yes—
221#10587569C23132yes—
222#10587567C23132yes—
223C22⋊C4×D17C23116yes—
224#10587565C23132yescomplemented
225#10587565C23132yescomplemented
226#10587564C23132yes—
227#10587564C23132yescomplemented
228#10587563C23116yes—
229#10587563C23132yescomplemented
230#10587558C23116yes—
231C42×D17C23116yes—
232#10587556C23116yescomplemented
233#10587555C23116yescomplemented
234C24×C17C2412yes—
235C24×C17C2411yescharacteristic
236C23×D17—24no—
237C23×D17—24no—
238C23×D17—42no—
239C23×D17C2411yescharacteristic
240C23×D17C2414yes—
241C23×D17C2411yescharacteristic
242#41×C17—232no—
243C2×Q8×C17—28no—
244C2×Q8×C17—28no—
245C2×Q8×C17—232no—
246C2×Q8×C17—24no—
247C2×Q8×C17C2418yes—
248C2×Q8×C17C2418yes—
249C2×Q8×C17C2414yes—
250C2×D4×C17—28no—
251C2×D4×C17—24no—
252C2×D4×C17C2418yes—
253C2×D4×C17C2414yes—
254C22×C4×C17—28no—
255C22×C4×C17—28no—
256C22×C4×C17#4118yes—
257C22×C4×C17C2418yes—
258C22×C4×C17C2418yes—
259C22×C4×C17C2412yes—
260C22×C4×C17C2412yes—
261C22×C4×C17C2412yes—
262C22×C4×C17C2414yes—
263C22×C4×C17C2411yescharacteristic
264C22×C4×C17C2411yescharacteristic
265C22×C4×C17C2414yes—
266C2×C22⋊D17—28no—
267C2×C22⋊D17—44no—
268C2×C22⋊D17C2418yes—
269C2×C22⋊D17C2418yes—
270C22×Dic17—24no—
271C22×Dic17—44no—
272C22×Dic17—48no—
273C22×Dic17C2412yes—
274C22×Dic17C2414yes—
275C22×Dic17C2414yes—
276C22×Dic17C2411yescharacteristic
277C22×Dic17C2411yescharacteristic
278C22×Dic17C2412yes—
279C22×Dic17C2412yes—
280C22×Dic17C2412yes—
281C22×Dic17C24116yes—
282C22×Dic17C2418yes—
283C2×C4×D17—28no—
284C2×C4×D17—24no—
285C2×C4×D17—24no—
286C2×C4×D17—24no—
287C2×C4×D17—24no—
288C2×C4×D17—232no—
289C2×C4×D17—44no—
290C2×C4×D17C2414yes—
291C2×C4×D17C2414yes—
292C2×C4×D17C2414yes—
293C2×C4×D17C2414yes—
294C2×C4×D17C2418yes—
295C2×C4×D17C2418yes—
296C2×Dic34—48no—
297C2×Dic34C24116yes—
298C4⋊C4×C17C2414yes—
299C4⋊C4×C17C2414yes—
300C4⋊C4×C17C24116yes—
301C4⋊C4×C17C24116yes—
302C22⋊C4×C17C24116yes—
303C22⋊C4×C17C24116yes—
304C22⋊C4×C17C2418yes—
305C42×C17C2418yes—
306C22⋊Dic17C2418yes—
307C22⋊Dic17C2418yes—
308C22⋊Dic17C2418yes—
309C22⋊Dic17C2418yes—
310C22⋊Dic17C24116yes—
311#63227C2418yes—
312#63227C2418yes—
313#63227C24116yes—
314#63227C24116yes—
315#63227C2418yes—
316#63227C2418yes—
317C4⋊Dic17C2414yes—
318C4⋊Dic17C2418yes—
319C4⋊Dic17C24116yes—
320C4⋊Dic17C2414yes—
321C4⋊Dic17C24116yes—
322C4⋊Dic17C24116yes—
323C4⋊Dic17C2418yes—
324C4⋊Dic17C24116yes—
325C4⋊Dic17C2414yes—
326C4⋊Dic17C2414yes—
327#63225C24116yes—
328#63225C24116yes—
329#63225C2418yes—
330#63225C2418yes—
331#63225C24116yes—
332#63225C24116yes—
333#63225C2418yes—
334#63225C2418yes—
335C4×Dic17C2418yes—
336C4×Dic17C2418yes—
337C4×Dic17C2418yes—
338C4×Dic17C24116yes—
339C4×Dic17C24116yes—
340C4×Dic17C24116yes—
341C4×Dic17C2418yes—
342C2×#3495—171nomaximal, Sylow
343C23×C17—22no—
344C23×C17—22no—
345C23×C17—24no—
346C23×C17—24no—
347C23×C17—24no—
348C23×C17C2×#4114yes—
349C23×C17C2514yes—
350C23×C17C2512yes—
351C23×C17C2511yescharacteristic
352C22×D17—22no—
353C22×D17—22no—
354C22×D17—28no—
355C22×D17—22no—
356C22×D17—22no—
357C22×D17—22no—
358C22×D17—28no—
359C22×D17—44no—
360C22×D17—416no—
361C22×D172−1+414yes—
362C22×D17C2512yes—
363C22×D17C2512yes—
364Q8×C17—216no—
365Q8×C17—216no—
366Q8×C17—28no—
367D4×C17—216no—
368D4×C17—28no—
369C2×C4×C17—24no—
370C2×C4×C17—216no—
371C2×C4×C17—28no—
372C2×C4×C17—24no—
373C2×C4×C17—24no—
374C2×C4×C17—216no—
375C2×C4×C17C2×#4114yes—
376C2×C4×C17C2×#4114yes—
377C2×C4×C17C2×#41116yes—
378C2×C4×C17C2514yes—
379C2×C4×C17C2514yes—
380C2×C4×C17C2518yes—
381C2×C4×C17C2514yes—
382C2×C4×C17C2512yes—
383C2×C4×C17C2512yes—
384C22⋊D17—216no—
385C22⋊D17—48no—
386C2×Dic17—28no—
387C2×Dic17—22no—
388C2×Dic17—22no—
389C2×Dic17—24no—
390C2×Dic17—24no—
391C2×Dic17—24no—
392C2×Dic17—28no—
393C2×Dic17—24no—
394C2×Dic17—48no—
395C2×Dic17—416no—
396C2×Dic17C2514yes—
397C2×Dic17C2514yes—
398C2×Dic17C2512yes—
399C2×Dic17C2512yes—
400C2×Dic17C2514yes—
401C2×Dic17C2518yes—
402C2×Dic17C2514yes—
403C4×D17—216no—
404C4×D17—28no—
405C4×D17—28no—
406C4×D17—28no—
407C4×D17—28no—
408C4×D17—48no—
409Dic34—416no—
410#3495—1732no—
411C2×#556—172no—
412C2×#554—172no—
413C2×#552—174no—
414C2×#552—172no—
415C2×#552—172no—
416C2×#551—174no—
417C2×#544—171no—
418C2×#542—172no—
419C2×#541—172no—
420C2×#536D1711yescharacteristic, complemented
421C2×#533—172no—
422C2×#529—172no—
423C2×#525—171no—
424C22×C22⋊Q8—171no—
425C2×#520—171no—
426C2×#519—171no—
427C22×#117—171no—
428C22×C17—22no—
429C22×C17—22no—
430C22×C17—28no—
431C22×C17—24no—
432C22×C17—24no—
433C22×C17—24no—
434C22×C17—48no—
435C22×C17C22×#4114yes—
436C22×C17C22×#4112yes—
437C22×C17C2×2−1+412yes—
438C22×C17#58512yes—
439C22×C17C2611yescharacteristic
440C2×D17—22no—
441C2×D17—22no—
442C2×D17—28no—
443C2×D17—22no—
444C2×D17—22no—
445C2×D17—22no—
446C2×D17—416no—
447C2×D17—44no—
448C2×D17C2×2−1+414yes—
449C4×C17—24no—
450C4×C17—28no—
451C4×C17—24no—
452C4×C17—24no—
453C4×C17C22×#4114yes—
454C4×C17C22×#4114yes—
455Dic17—22no—
456Dic17—22no—
457Dic17—24no—
458Dic17—24no—
459Dic17—24no—
460Dic17—28no—
461Dic17—24no—
462C22×#41C2×D1711yescharacteristic
463C23×Q8C2×D1711yescharacteristic
464C24×C4—171no—
465#556—1732no—
466#554—1732no—
467#552—1764no—
468#552—1732no—
469#552—1732no—
470#551—1764no—
471#544—1716no—
472#542—1732no—
473#541—1732no—
474#536C2×D17116yescomplemented
475#533—1732no—
476C2×C4⋊Q8—172no—
477C2×C4⋊Q8—172no—
478C2×C4⋊Q8C2×D1712yescomplemented
479#529—1732no—
480C2×#126—174no—
481C2×#126—174no—
482C2×#126—174no—
483C2×#126—174no—
484C2×#125—174no—
485C2×#125—174no—
486C2×#125—174no—
487C2×#125—172no—
488C2×#125—172no—
489C2×#124—174no—
490C2×#124C2×D1712yescomplemented
491#525—1716no—
492C2×#123—172no—
493C2×#123—174no—
494C2×#123—174no—
495C2×#123C2×D1714yes—
496C2×C22⋊Q8—172no—
497C2×C22⋊Q8—172no—
498C2×C22⋊Q8—172no—
499C2×C22⋊Q8—172no—
500C2×C22⋊Q8—171no—
501C2×C22⋊Q8—171no—
502C2×C22⋊Q8—1716no—
503C2×C22⋊Q8—174no—
504C2×C22⋊Q8—174no—
505C2×C22⋊Q8—174no—
506C2×C22⋊Q8C2×D1712yescomplemented
507C2×C22⋊Q8C2×D1712yescomplemented
508C2×#121—171no—
509C2×#121—171no—
510C2×#120—172no—
511#520—1716no—
512#519—1716no—
513C2×C4×Q8—172no—
514C2×C4×Q8—172no—
515C2×C4×Q8—172no—
516C2×C4×Q8—172no—
517C2×C4×Q8—172no—
518C2×C4×Q8—174no—
519C2×C4×D4—174no—
520C2×C4×D4—172no—
521C2×C4×D4—172no—
522C2×C4×D4—172no—
523C2×C4×D4—174no—
524C2×#117—171no—
525C2×#117—171no—
526C2×#117—174no—
527C2×#117—172no—
528C2×#117—1716no—
529C2×#117—171no—
530C2×#117—171no—
531C2×#117—174no—
532C2×#117—172no—
533C2×#117—174no—
534C2×#117—172no—
535C2×#117C2×D1711yescharacteristic
536C22×C4⋊C4—172no—
537C22×C4⋊C4—171no—
538C22×C4⋊C4—172no—
539C22×C4⋊C4—171no—
540C22×C4⋊C4—171no—
541C22×C22⋊C4—172no—
542C22×C22⋊C4—172no—
543C22×C42—172no—
544C2×C17—24no—
545C2×C17—44no—
546C2×C17#349514yescomplemented
547C2×C17C23×#4111yescharacteristic
548C2×C17C22×2−1+411yescharacteristic
549C2×C17C2×#58511yescharacteristic
550D17—24no—
551D17—42no—
552C25—171no—
553C2×#41—28no—
554C2×#41C22×D1718yes—
555C22×Q8—28no—
556C22×Q8—174no—
557C22×Q8C22×D1712yes—
558C22×Q8C22×D1712yes—
559C22×Q8C22×D1711yescharacteristic
560C22×Q8C22×D1718yes—
561C22×D4—172no—
562C22×D4—172no—
563C22×D4C22×D1712yes—
564C22×D4C22×D1711yescharacteristic
565C23×C4—171no—
566C23×C4—172no—
567C23×C4—174no—
568C23×C4—172no—
569C23×C4—171no—
570C23×C4—171no—
571C23×C4—171no—
572C23×C4—178no—
573C23×C4—171no—
574C23×C4—172no—
575C23×C4—348no—
576C23×C4C22×D1712yes—
577C23×C4C22×D1712yes—
578C23×C4C22×D1711yescharacteristic
579C4⋊Q8—1716no—
580C4⋊Q8—1716no—
581C4⋊Q8C22×D17116yescomplemented
582#126—1732no—
583#126—1732no—
584#126—1732no—
585#126—1732no—
586#125—1732no—
587#125—1732no—
588#125—1732no—
589#125—1716no—
590#125—1716no—
591#124—1732no—
592#124C22×D17116yescomplemented
593#123—1716no—
594#123—1732no—
595#123—1732no—
596#123C22×D17132yes—
597C22⋊Q8—1716no—
598C22⋊Q8—1716no—
599C22⋊Q8—1716no—
600C22⋊Q8—1716no—
601C22⋊Q8—178no—
602C22⋊Q8—178no—
603C22⋊Q8—1732no—
604C22⋊Q8—1732no—
605C22⋊Q8—1732no—
606C22⋊Q8C22×D17116yescomplemented
607C22⋊Q8C22×D17116yescomplemented
608#121—178no—
609#121—178no—
610#120—1716no—
611C4×Q8—1716no—
612C4×Q8—1716no—
613C4×Q8—1716no—
614C4×Q8—1716no—
615C4×Q8—1716no—
616C4×Q8—1732no—
617C4×D4—1716no—
618C4×D4—1732no—
619C4×D4—1716no—
620C4×D4—1716no—
621C4×D4—1732no—
622#117—178no—
623#117—178no—
624#117—1732no—
625#117—1716no—
626#117—178no—
627#117—178no—
628#117—1732no—
629#117—1716no—
630#117—1732no—
631#117—1716no—
632#117C22×D1718yes—
633C2×C4⋊C4—171no—
634C2×C4⋊C4—172no—
635C2×C4⋊C4—171no—
636C2×C4⋊C4—172no—
637C2×C4⋊C4—172no—
638C2×C4⋊C4—174no—
639C2×C4⋊C4—172no—
640C2×C4⋊C4—174no—
641C2×C4⋊C4—178no—
642C2×C4⋊C4—1716no—
643C2×C4⋊C4—174no—
644C2×C4⋊C4—1716no—
645C2×C4⋊C4—171no—
646C2×C4⋊C4—171no—
647C2×C4⋊C4—174no—
648C2×C4⋊C4—174no—
649C2×C4⋊C4—174no—
650C2×C4⋊C4—174no—
651C2×C4⋊C4—172no—
652C2×C4⋊C4—172no—
653C2×C4⋊C4—174no—
654C2×C4⋊C4—178no—
655C2×C4⋊C4—178no—
656C2×C4⋊C4C22×D1711yescharacteristic
657C2×C4⋊C4C22×D1711yescharacteristic
658C2×C4⋊C4C22×D1714yes—
659C2×C4⋊C4C22×D1714yes—
660C2×C22⋊C4—172no—
661C2×C22⋊C4—172no—
662C2×C22⋊C4—172no—
663C2×C22⋊C4—174no—
664C2×C22⋊C4—172no—
665C2×C22⋊C4—172no—
666C2×C22⋊C4—172no—
667C2×C22⋊C4—174no—
668C2×C22⋊C4—174no—
669C2×C22⋊C4—1716no—
670C2×C22⋊C4—172no—
671C2×C22⋊C4—172no—
672C2×C22⋊C4—1716no—
673C2×C22⋊C4C22×D1712yes—
674C2×C22⋊C4C22×D1714yes—
675C2×C22⋊C4C22×D1714yes—
676C2×C42—172no—
677C2×C42—172no—
678C2×C42—174no—
679C2×C42—174no—
680C2×C42—174no—
681C2×C42—172no—
682C2×C42—172no—
683C2×C42—1716no—
684C2×C42C22×D1712yes—
685C17C2×#349511yescharacteristic, complemented, Sylow
686C24—171no—
687C24—171no—
688C24—174no—
689C24—344no—
690C24—344no—
691C24—682no—
692C24C23×D1712yes—
693C24C23×D1711yescharacteristic
694#41—232no—
695C2×Q8—28no—
696C2×Q8—28no—
697C2×Q8—232no—
698C2×Q8—24no—
699C2×Q8—1716no—
700C2×Q8—688no—
701C2×Q8C23×D1718yes—
702C2×Q8C23×D1718yes—
703C2×Q8C23×D1714yes—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—178no—
707C2×D4—178no—
708C2×D4—348no—
709C2×D4—684no—
710C2×D4C23×D1718yes—
711C2×D4C23×D1714yes—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—174no—
715C22×C4—172no—
716C22×C4—171no—
717C22×C4—172no—
718C22×C4—172no—
719C22×C4—172no—
720C22×C4—174no—
721C22×C4—171no—
722C22×C4—178no—
723C22×C4—1716no—
724C22×C4—174no—
725C22×C4—178no—
726C22×C4—174no—
727C22×C4—174no—
728C22×C4—174no—
729C22×C4—178no—
730C22×C4—348no—
731C22×C4—344no—
732C22×C4—344no—
733C22×C4—344no—
734C22×C4—344no—
735C22×C4—344no—
736C22×C4—3432no—
737C22×C4—684no—
738C22×C4—688no—
739C22×C4—684no—
740C22×C4#6325418yes—
741C22×C4C23×D1718yes—
742C22×C4C23×D1718yes—
743C22×C4C23×D1714yes—
744C22×C4C23×D1712yes—
745C22×C4C23×D1712yes—
746C22×C4C23×D1712yes—
747C22×C4C23×D1714yes—
748C22×C4C23×D1711yescharacteristic
749C22×C4C23×D1711yescharacteristic
750C4⋊C4—174no—
751C4⋊C4—178no—
752C4⋊C4—174no—
753C4⋊C4—178no—
754C4⋊C4—178no—
755C4⋊C4—1716no—
756C4⋊C4—178no—
757C4⋊C4—1716no—
758C4⋊C4—1716no—
759C4⋊C4—174no—
760C4⋊C4—174no—
761C4⋊C4—1716no—
762C4⋊C4—1716no—
763C4⋊C4—1716no—
764C4⋊C4—1716no—
765C4⋊C4—178no—
766C4⋊C4—178no—
767C4⋊C4—1716no—
768C4⋊C4C23×D1714yes—
769C4⋊C4C23×D1714yes—
770C4⋊C4C23×D17116yes—
771C4⋊C4C23×D17116yes—
772C22⋊C4—178no—
773C22⋊C4—178no—
774C22⋊C4—178no—
775C22⋊C4—1716no—
776C22⋊C4—178no—
777C22⋊C4—178no—
778C22⋊C4—178no—
779C22⋊C4—1716no—
780C22⋊C4—1716no—
781C22⋊C4—178no—
782C22⋊C4—178no—
783C22⋊C4C23×D1718yes—
784C22⋊C4C23×D17116yes—
785C22⋊C4C23×D17116yes—
786C42—178no—
787C42—178no—
788C42—178no—
789C42—1716no—
790C42—1716no—
791C42—1716no—
792C42—178no—
793C42C23×D1718yes—
794C23—22no—
795C23—22no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—174no—
800C23—172no—
801C23—172no—
802C23—348no—
803C23—342no—
804C23—342no—
805C23—348no—
806C23—342no—
807C23—342no—
808C23—342no—
809C23—684no—
810C23—6816no—
811C23C2×#6325414yes—
812C23C24×D1714yes—
813C23C24×D1712yes—
814C23C24×D1711yescharacteristic
815Q8—216no—
816Q8—216no—
817Q8—28no—
818Q8—6816no—
819D4—216no—
820D4—28no—
821D4—3416no—
822D4—688no—
823C2×C4—24no—
824C2×C4—216no—
825C2×C4—28no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—216no—
829C2×C4—174no—
830C2×C4—172no—
831C2×C4—174no—
832C2×C4—174no—
833C2×C4—174no—
834C2×C4—178no—
835C2×C4—172no—
836C2×C4—3416no—
837C2×C4—348no—
838C2×C4—342no—
839C2×C4—342no—
840C2×C4—344no—
841C2×C4—344no—
842C2×C4—344no—
843C2×C4—348no—
844C2×C4—344no—
845C2×C4—348no—
846C2×C4—348no—
847C2×C4—348no—
848C2×C4—348no—
849C2×C4—688no—
850C2×C4—6816no—
851C2×C4—688no—
852C2×C4C2×#6325414yes—
853C2×C4C2×#6325414yes—
854C2×C4C2×#63254116yes—
855C2×C4C24×D1718yes—
856C2×C4C24×D1714yes—
857C2×C4C24×D1714yes—
858C2×C4C24×D1714yes—
859C2×C4C24×D1712yes—
860C2×C4C24×D1712yes—
861C22—28no—
862C22—22no—
863C22—22no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—48no—
868C22—174no—
869C22—348no—
870C22—342no—
871C22—342no—
872C22—342no—
873C22—342no—
874C22—342no—
875C22—6816no—
876C22—684no—
877C22C22×#6325414yes—
878C22C22×#6325412yes—
879C222−1+4×D1712yes—
880C22#1176364612yes—
881C22C25×D1711yescharacteristic
882C4—24no—
883C4—28no—
884C4—24no—
885C4—24no—
886C4—342no—
887C4—342no—
888C4—344no—
889C4—344no—
890C4—344no—
891C4—348no—
892C4—344no—
893C4C22×#6325414yes—
894C4C22×#6325414yes—
895C2—24no—
896C2—44no—
897C2—344no—
898C2—682no—
899C2#1454253314yesdirect product factor
900C2C23×#6325411yescharacteristic
901C2C2×2−1+4×D1711yescharacteristic
902C2C2×#1176364611yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#536C2
socleC23×C17C25
prime radicalC2×#11763316C2
hypercenterC2×#536D17
hypocenterC17C2×#3495
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. #14542533C2direct (N × H)
2. C2×#11763530C2semidirect
3. C2×#11763517C2semidirect
4. C2×#11763501C2semidirect
5. C2×#11763496C2semidirect
6. C2×#11763493C2semidirect
7. C2×#11763482C2semidirect
8. C2×#11763437C2semidirect
9. C2×#11763428C2semidirect
10. C2×#11763420C2semidirect
11. C2×#11763364C2semidirect
12. C2×#11763338C2semidirect
14. C22×#10587632C2semidirect
15. C2×#11763292C2semidirect
16. C2×#11763287C2semidirect
17. C2×#117×D17C2semidirect
18. C2×C17×#536C2semidirect
20. #11763530C22semidirect
21. #11763517C22semidirect
22. #11763501C22semidirect
23. #11763496C22semidirect
24. #11763493C22semidirect
25. #11763482C22semidirect
26. #11763437C22semidirect
27. #11763428C22semidirect
28. #11763420C22semidirect
29. #11763364C22semidirect
30. C2×#10587555C22semidirect
31. C2×#10587574C22semidirect
32. #11763338C22semidirect
35. C2×#10587565C22semidirect
36. C2×#10587565C22semidirect
37. C2×#10587556C22semidirect
38. C2×#10587576C22semidirect
39. C2×#10587576C22semidirect
40. C2×#10587575C22semidirect
41. C2×#10587575C22semidirect
49. C2×#10587564C22semidirect
56. C2×#10587632C22semidirect
60. #11763292C22semidirect
61. #11763287C22semidirect
62. C2×Q8×Dic17C22semidirect
63. C2×Q8×Dic17C22semidirect
64. C2×Q8×Dic17C22semidirect
65. C2×Q8×Dic17C22semidirect
66. C2×Q8×Dic17C22semidirect
67. C2×#10587573C22semidirect
69. C2×D4×Dic17C22semidirect
76. C2×#10587612C22semidirect
82. C2×#10587563C22semidirect
83. #117×D17C22semidirect
85. C22×C4⋊Dic17C22semidirect
94. C17×#536C22semidirect
95. C2×C17×C4⋊Q8C22semidirect
96. C2×C17×#124C22semidirect
98. C2×C17×C22⋊Q8C22semidirect
99. C2×C17×C22⋊Q8C22semidirect
128. C17×C4⋊Q8C23semidirect
129. C17×#124C23semidirect
131. C17×C22⋊Q8C23semidirect
132. C17×C22⋊Q8C23semidirect
153. Q8×Dic17C23semidirect
154. Q8×Dic17C23semidirect
155. Q8×Dic17C23semidirect
156. Q8×Dic17C23semidirect
157. Q8×Dic17C23semidirect
163. D4×Dic17C23semidirect
176. #10587612C23semidirect
188. C2×C4⋊Dic17C23semidirect
213. #10587576C23semidirect
214. #10587576C23semidirect
215. #10587575C23semidirect
216. #10587575C23semidirect
217. #10587574C23semidirect
218. #10587573C23semidirect
224. #10587565C23semidirect
225. #10587565C23semidirect
227. #10587564C23semidirect
229. #10587563C23semidirect
232. #10587556C23semidirect
233. #10587555C23semidirect
420. C2×#536D17semidirect
474. #536C2×D17semidirect
478. C2×C4⋊Q8C2×D17semidirect
490. C2×#124C2×D17semidirect
506. C2×C22⋊Q8C2×D17semidirect
507. C2×C22⋊Q8C2×D17semidirect
546. C2×C17#3495semidirect
581. C4⋊Q8C22×D17semidirect
592. #124C22×D17semidirect
606. C22⋊Q8C22×D17semidirect
607. C22⋊Q8C22×D17semidirect
685. C17C2×#3495semidirect
899. C2#14542533direct (N × H)

Maximal subgroups

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

subgroupindex
#145425332
C2×#117635302
C2×#117635172
C2×#117635012
C2×#117634962
C2×#117634932
C2×#117634822
C2×#117634372
C2×#117634282
C2×#117634202
C2×#117633642
C2×#117633382
C2×#117633162
C22×#105876322
C2×#117632922
C2×#117632872
C2×#117×D172
C2×C17×#5362
C2×#349517