Finite Group Databasebeta

← C2×#14542766 #17942510

Subgroups — C2×#14542766 #17942510

Order 4352.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542766C2132yesmaximal, direct product factor
2C2×#11763538C211yesmaximal, characteristic, complemented
3C2×#11763528C213yesmaximal, complemented
4C2×#11763516C213yesmaximal, complemented
5C2×#11763511C213yesmaximal, complemented
6C2×#11763501C213yesmaximal, complemented
7C2×Q8×C22⋊D17C211yesmaximal, characteristic, complemented
8C2×#11763466C211yesmaximal, characteristic, complemented
9C2×#11763428C213yesmaximal, complemented
10C2×#11763419C213yesmaximal, complemented
11C2×#11763340C213yesmaximal, complemented
12C2×#11763339C213yesmaximal, complemented
13C2×#11763292C211yesmaximal, characteristic, complemented
14C2×#11763285C211yesmaximal, characteristic, complemented
15C22×Q8×Dic17C211yesmaximal, characteristic, complemented
16C2×C17×#548C211yesmaximal, characteristic, complemented
17C22×Q8×D17C2211yescharacteristic
18#11763538C22116yescomplemented
19#11763528C22148yescomplemented
20#11763516C22148yescomplemented
21#11763511C22148yescomplemented
22#11763501C22148yescomplemented
23Q8×C22⋊D17C22116yescomplemented
24#11763466C22116yescomplemented
25#11763428C22148yescomplemented
26#11763419C22148yescomplemented
27C2×#10587555C2213yes—
28C2×#10587630C2213yes—
29#11763340C22148yescomplemented
30#11763339C22148yescomplemented
31C2×#10587584C2213yes—
32C2×#10587565C2216yes—
33C2×#10587565C2216yes—
34C2×#10587565C2213yes—
35C2×#10587576C2213yes—
36C2×#10587576C2213yes—
37C2×#10587576C2216yes—
38C2×#10587575C2213yes—
39C2×#10587622C2213yes—
40C2×#10587571C2213yes—
41C2×#10587572C2216yes—
42C2×#10587572C2211yescharacteristic
43C2×#10587621C2213yes—
44C2×#10587610C2213yes—
45C2×#10587610C2213yes—
46C2×#10587564C2216yes—
47C2×#10587564C2213yes—
48C2×#10587632C2213yes—
49C2×#10587625C2213yes—
50C2×#10587624C2213yes—
51#11763292C22116yescomplemented
52#11763285C22116yescomplemented
53C2×Q8×Dic17C2211yescharacteristic
54C2×Q8×Dic17C2211yescharacteristic
55C2×Q8×Dic17C2213yes—
56C2×Q8×Dic17C2211yescharacteristic
57C2×Q8×Dic17C2213yes—
58C2×Q8×Dic17C22116yescomplemented
59C2×C4×Dic34C2213yes—
60C2×C4×Dic34C2213yes—
61C2×#10587573C2213yes—
62C2×D4×Dic17C2213yes—
63C2×D4×Dic17C2213yes—
64C2×D4×Dic17C2216yes—
65C2×C4×C22⋊D17C2213yes—
66C2×C4×C22⋊D17C2213yes—
67C2×#10587612C2213yes—
68C2×#10587578C2213yes—
69C2×#10587558C2213yes—
70C2×#10587563C2216yes—
71C22×C4⋊Dic17C2213yes—
72C22×C4⋊Dic17C2213yes—
73C22×C4×Dic17C2213yes—
74C22×#41×C17C2211yescharacteristic
75C23×Q8×C17C2211yescharacteristic
76C17×#548C22116yescomplemented
77C2×C17×#124C2213yes—
78C2×C17×C22⋊Q8C2213yes—
79C2×C17×#121C2213yes—
80C2×C4×Q8×C17C2211yescharacteristic
81C2×C4×D4×C17C2213yes—
82C2×#41×C17—28no—
83C2×#41×C17C2318yes—
84C22×Q8×C17—28no—
85C22×Q8×C17C2318yes—
86C22×Q8×C17C2313yes—
87C22×Q8×C17C2311yescharacteristic
88C22×D4×C17C2313yes—
89C22×D4×C17C2313yes—
90C23×C4×C17C2313yes—
91C23×C4×C17C2313yes—
92C22×C22⋊D17C2311yescharacteristic
93C22×C22⋊D17C2313yes—
94C23×Dic17C2311yescharacteristic
95C23×Dic17C2313yes—
96C23×Dic17C2316yes—
97C2×Q8×D17—28no—
98C2×Q8×D17C2318yes—
99C22×C4×D17C2313yes—
100C22×Dic34C2313yes—
101C22×Dic34C2313yes—
102C17×#124C23124yes—
103C17×C22⋊Q8C23124yes—
104C17×#121C23124yes—
105C4×Q8×C17C2318yes—
106C4×D4×C17C23124yes—
107C2×C4⋊C4×C17C2313yes—
108C2×C4⋊C4×C17C2313yes—
109C2×C22⋊C4×C17C2311yescharacteristic
110C2×C22⋊C4×C17C2313yes—
111C2×C22⋊C4×C17C2316yes—
112C2×C42×C17C2313yes—
113C2×C22⋊Dic17C2313yes—
114C2×C22⋊Dic17C2313yes—
115C2×C22⋊Dic17C2313yes—
116C2×C22⋊Dic17C2313yes—
117C2×C22⋊Dic17C2316yes—
118#10587632C23124yes—
119Q8×Dic17C2318yes—
120Q8×Dic17C2318yes—
121Q8×Dic17C23124yes—
122Q8×Dic17C2318yes—
123Q8×Dic17C23124yes—
124#10587630C23124yes—
125#10587625C23124yes—
126#10587624C23124yes—
127#10587622C23124yes—
128#10587621C23124yes—
129D4×Dic17C23148yes—
130D4×Dic17C23124yes—
131D4×Dic17C23124yes—
132C4×C22⋊D17C23124yes—
133C4×C22⋊D17C23124yes—
134C2×#63227C2311yescharacteristic
135C2×#63227C2313yes—
136C2×#63227C2311yescharacteristic
137C2×#63227C2313yes—
138#10587612C23124yes—
139C2×C4⋊Dic17C23124yes—
140C2×C4⋊Dic17C23124yes—
141C2×C4⋊Dic17C2313yes—
142C2×C4⋊Dic17C2313yes—
143C2×C4⋊Dic17C2313yes—
144C2×C4⋊Dic17C2313yes—
145C2×C4⋊Dic17C2316yes—
146C2×C4⋊Dic17C2311yescharacteristic
147C2×C4⋊Dic17C2316yes—
148C2×C4⋊Dic17C2311yescharacteristic
149#10587610C23124yes—
150#10587610C23124yes—
151C2×#63225C2313yes—
152C2×#63225C2316yes—
153C2×#63225C2313yes—
154C2×#63225C2313yes—
155C2×#63225C2313yes—
156C2×#63225C2313yes—
157C2×#63225C2313yes—
158C2×C4×Dic17C2313yes—
159C2×C4×Dic17C2313yes—
160C2×C4×Dic17C2313yes—
161C2×C4×Dic17C2313yes—
162C2×C4×Dic17C23124yes—
163C2×C4×Dic17C2316yes—
164C2×C4×Dic17C2313yes—
165#10587584C23124yes—
166#10587578C23124yes—
167#10587576C23148yes—
168#10587576C23124yes—
169#10587576C23124yes—
170#10587575C23124yes—
171#10587573C23124yes—
172#10587572C23148yes—
173#10587572C2318yes—
174#10587571C23124yes—
175#10587565C23148yes—
176#10587565C23124yes—
177#10587565C23148yes—
178#10587564C23124yes—
179#10587564C23148yes—
180#10587563C23148yes—
181#10587558C23124yes—
182#10587555C23124yes—
183C4×Dic34C23124yes—
184C4×Dic34C23124yes—
185C24×C17C2413yes—
186C24×C17C2411yescharacteristic
187C23×D17C2411yescharacteristic
188#41×C17—232no—
189C2×Q8×C17—232no—
190C2×Q8×C17—212no—
191C2×Q8×C17#4118yes—
192C2×Q8×C17C24112yes—
193C2×Q8×C17C2414yes—
194C2×D4×C17—212no—
195C2×D4×C17—212no—
196C2×D4×C17C24112yes—
197C2×D4×C17C24112yes—
198C22×C4×C17—212no—
199C22×C4×C17—212no—
200C22×C4×C17C24112yes—
201C22×C4×C17C2411yescharacteristic
202C22×C4×C17C2411yescharacteristic
203C22×C4×C17C2413yes—
204C22×C4×C17C24112yes—
205C22×C4×C17C2413yes—
206C22×C4×C17C2413yes—
207C2×C22⋊D17—24no—
208C2×C22⋊D17—46no—
209C2×C22⋊D17C2414yes—
210C2×C22⋊D17C24112yes—
211C22×Dic17—24no—
212C22×Dic17—412no—
213C22×Dic17—46no—
214C22×Dic17C2413yes—
215C22×Dic17C2413yes—
216C22×Dic17C2413yes—
217C22×Dic17C2413yes—
218C22×Dic17C2414yes—
219C22×Dic17C2411yescharacteristic
220C22×Dic17C2411yescharacteristic
221C22×Dic17C2411yescharacteristic
222C22×Dic17C24124yes—
223C22×Dic17C24112yes—
224Q8×D17—232no—
225C2×C4×D17—212no—
226C2×C4×D17C24112yes—
227C2×Dic34—212no—
228C2×Dic34—46no—
229C2×Dic34C24112yes—
230C2×Dic34C24112yes—
231C4⋊C4×C17C24112yes—
232C4⋊C4×C17C24112yes—
233C22⋊C4×C17C24124yes—
234C22⋊C4×C17C24112yes—
235C22⋊C4×C17C2414yes—
236C42×C17C24112yes—
237C22⋊Dic17C24112yes—
238C22⋊Dic17C24124yes—
239C22⋊Dic17C24112yes—
240C22⋊Dic17C24112yes—
241C22⋊Dic17C24112yes—
242#63227C2414yes—
243#63227C24112yes—
244#63227C24112yes—
245#63227C2414yes—
246C4⋊Dic17C2414yes—
247C4⋊Dic17C24112yes—
248C4⋊Dic17C24124yes—
249C4⋊Dic17C24112yes—
250C4⋊Dic17C24112yes—
251C4⋊Dic17C24124yes—
252C4⋊Dic17C24112yes—
253C4⋊Dic17C2414yes—
254#63225C24112yes—
255#63225C24112yes—
256#63225C24112yes—
257#63225C24112yes—
258#63225C24124yes—
259#63225C24112yes—
260#63225C24112yes—
261C4×Dic17C24124yes—
262C4×Dic17C24112yes—
263C4×Dic17C24112yes—
264C4×Dic17C24112yes—
265C4×Dic17C24112yes—
266C4×Dic17C24112yes—
267C2×#3516—171nomaximal, Sylow
268C23×C17—22no—
269C23×C17—22no—
270C23×C17—26no—
271C23×C17—26no—
272C23×C17—26no—
273C23×C172−1+414yes—
274C23×C17C2516yes—
275C23×C17C2512yes—
276C23×C17C2511yescharacteristic
277C22×D17—22no—
278C22×D17—22no—
279C22×D17—22no—
280C22×D17C2512yes—
281Q8×C17—224no—
282Q8×C17C2×#41116yes—
283D4×C17—224no—
284D4×C17—224no—
285C2×C4×C17—22no—
286C2×C4×C17—26no—
287C2×C4×C17—26no—
288C2×C4×C17—22no—
289C2×C4×C17—224no—
290C2×C4×C17—224no—
291C2×C4×C17C2×#41112yes—
292C2×C4×C17C2512yes—
293C2×C4×C17C2516yes—
294C2×C4×C17C2516yes—
295C2×C4×C17C2512yes—
296C2×C4×C17C2516yes—
297C22⋊D17—28no—
298C22⋊D17—412no—
299C2×Dic17—26no—
300C2×Dic17—28no—
301C2×Dic17—22no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—26no—
305C2×Dic17—26no—
306C2×Dic17—26no—
307C2×Dic17—424no—
308C2×Dic17—412no—
309C2×Dic17C2516yes—
310C2×Dic17C2512yes—
311C2×Dic17C2512yes—
312C2×Dic17C2512yes—
313C2×Dic17C2516yes—
314C2×Dic17C2516yes—
315C2×Dic17C2516yes—
316C4×D17—224no—
317Dic34—224no—
318Dic34—412no—
319#3516—1732no—
320C2×#557—171no—
321C2×#556—173no—
322C2×#554—173no—
323C2×#553—173no—
324C2×#552—173no—
325C2×D4×Q8—171no—
326C2×#548—171no—
327C2×#548D1711yescharacteristic, complemented
328C2×#542—173no—
329C2×#541—173no—
330C2×#529—173no—
331C2×#529—173no—
332C2×#520—171no—
333C2×#519—171no—
334C22×C4×Q8—171no—
335C22×C17—22no—
336C22×C17—22no—
337C22×C17—28no—
338C22×C17—26no—
339C22×C17—26no—
340C22×C17—26no—
341C22×C17—412no—
342C22×C17C22×#4112yes—
343C22×C17C2×2−1+414yes—
344C22×C17C2×2−1+412yes—
345C22×C17#58512yes—
346C22×C17C2611yescharacteristic
347C2×D17—22no—
348C2×D17—22no—
349C2×D17—22no—
350C2×D17—44no—
351C4×C17—22no—
352C4×C17—26no—
353C4×C17—26no—
354C4×C17—22no—
355C4×C17C22×#41112yes—
356Dic17—26no—
357Dic17—22no—
358Dic17—22no—
359Dic17—22no—
360Dic17—26no—
361Dic17—26no—
362Dic17—26no—
363C22×#41C2×D1711yescharacteristic
364C23×Q8—171no—
365C23×Q8C2×D1711yescharacteristic
366#557—1716no—
367#556—1748no—
368#554—1748no—
369#553—1748no—
370#552—1748no—
371D4×Q8—1716no—
372#548—1716no—
373#548C2×D17116yescomplemented
374#542—1748no—
375#541—1748no—
376C2×C4⋊Q8—173no—
377C2×C4⋊Q8—173no—
378#529—1748no—
379#529—1748no—
380C2×#126—173no—
381C2×#126—176no—
382C2×#126—173no—
383C2×#126—176no—
384C2×#125—173no—
385C2×#125—173no—
386C2×#125—176no—
387C2×#125—173no—
388C2×#124—173no—
389C2×#124—173no—
390C2×#124C2×D1713yes—
391C2×#123—173no—
392C2×#123—171no—
393C2×#123—176no—
394C2×C22⋊Q8—173no—
395C2×C22⋊Q8—173no—
396C2×C22⋊Q8—173no—
397C2×C22⋊Q8—173no—
398C2×C22⋊Q8—176no—
399C2×C22⋊Q8C2×D1713yes—
400C2×#121—173no—
401C2×#121—173no—
402C2×#121C2×D1713yes—
403#520—1716no—
404#519—1716no—
405C2×C4×Q8—171no—
406C2×C4×Q8—173no—
407C2×C4×Q8—171no—
408C2×C4×Q8—173no—
409C2×C4×Q8—171no—
410C2×C4×Q8—1716no—
411C2×C4×Q8—173no—
412C2×C4×Q8—173no—
413C2×C4×Q8—173no—
414C2×C4×Q8C2×D1711yescharacteristic
415C2×C4×D4—173no—
416C2×C4×D4—173no—
417C2×C4×D4—176no—
418C2×C4×D4—173no—
419C2×C4×D4—173no—
420C2×C4×D4C2×D1713yes—
421C2×#117—173no—
422C2×#117—173no—
423C2×#117—176no—
424C2×#117—173no—
425C22×C4⋊C4—173no—
426C22×C4⋊C4—173no—
427C22×C42—173no—
428C2×C17—24no—
429C2×C17—46no—
430C2×C17#351614yescomplemented
431C2×C17C23×#4111yescharacteristic
432C2×C17C22×2−1+411yescharacteristic
433C2×C17C2×#58511yescharacteristic
434D17—42no—
435C2×#41—28no—
436C2×#41C22×D1718yes—
437C22×Q8—28no—
438C22×Q8—178no—
439C22×Q8—173no—
440C22×Q8—173no—
441C22×Q8—348no—
442C22×Q8C22×D1713yes—
443C22×Q8C22×D1718yes—
444C22×Q8C22×D1711yescharacteristic
445C22×D4—171no—
446C22×D4—173no—
447C22×D4C22×D1713yes—
448C22×D4C22×D1713yes—
449C23×C4—171no—
450C23×C4—173no—
451C23×C4—176no—
452C23×C4—173no—
453C23×C4C22×D1713yes—
454C23×C4C22×D1713yes—
455C4⋊Q8—1724no—
456C4⋊Q8—1724no—
457#126—1724no—
458#126—1748no—
459#126—1724no—
460#126—1748no—
461#125—1724no—
462#125—1724no—
463#125—1748no—
464#125—1724no—
465#124—1724no—
466#124—1724no—
467#124C22×D17124yes—
468#123—1724no—
469#123—178no—
470#123—1748no—
471C22⋊Q8—1724no—
472C22⋊Q8—1724no—
473C22⋊Q8—1724no—
474C22⋊Q8—1724no—
475C22⋊Q8—1748no—
476C22⋊Q8C22×D17124yes—
477#121—1724no—
478#121—1724no—
479#121C22×D17124yes—
480C4×Q8—178no—
481C4×Q8—1724no—
482C4×Q8—178no—
483C4×Q8—1724no—
484C4×Q8—178no—
485C4×Q8—1724no—
486C4×Q8—1724no—
487C4×Q8—1724no—
488C4×Q8C22×D1718yes—
489C4×D4—1724no—
490C4×D4—1724no—
491C4×D4—1748no—
492C4×D4—1724no—
493C4×D4—1724no—
494C4×D4C22×D17124yes—
495#117—1724no—
496#117—1724no—
497#117—1748no—
498#117—1724no—
499C2×C4⋊C4—173no—
500C2×C4⋊C4—173no—
501C2×C4⋊C4—173no—
502C2×C4⋊C4—173no—
503C2×C4⋊C4—176no—
504C2×C4⋊C4—1724no—
505C2×C4⋊C4—1724no—
506C2×C4⋊C4—171no—
507C2×C4⋊C4—173no—
508C2×C4⋊C4—173no—
509C2×C4⋊C4—173no—
510C2×C4⋊C4—176no—
511C2×C4⋊C4—173no—
512C2×C4⋊C4—176no—
513C2×C4⋊C4—173no—
514C2×C4⋊C4—171no—
515C2×C4⋊C4—173no—
516C2×C4⋊C4C22×D1713yes—
517C2×C4⋊C4C22×D1713yes—
518C2×C22⋊C4—173no—
519C2×C22⋊C4—173no—
520C2×C22⋊C4—173no—
521C2×C22⋊C4—173no—
522C2×C22⋊C4—176no—
523C2×C22⋊C4—173no—
524C2×C22⋊C4—171no—
525C2×C22⋊C4—171no—
526C2×C22⋊C4—173no—
527C2×C22⋊C4C22×D1716yes—
528C2×C22⋊C4C22×D1711yescharacteristic
529C2×C22⋊C4C22×D1713yes—
530C2×C42—173no—
531C2×C42—176no—
532C2×C42—173no—
533C2×C42—173no—
534C2×C42—173no—
535C2×C42—173no—
536C2×C42—1724no—
537C2×C42C22×D1713yes—
538C17C2×#351611yescharacteristic, complemented, Sylow
539C24—171no—
540C24C23×D1713yes—
541C24C23×D1711yescharacteristic
542#41—232no—
543C2×Q8—232no—
544C2×Q8—212no—
545C2×Q8—1712no—
546C2×Q8—1712no—
547C2×Q8—3432no—
548C2×Q8—3412no—
549C2×Q8—686no—
550C2×Q8#6325418yes—
551C2×Q8C23×D17112yes—
552C2×Q8C23×D1714yes—
553C2×D4—212no—
554C2×D4—212no—
555C2×D4—174no—
556C2×D4—1712no—
557C2×D4—344no—
558C2×D4—686no—
559C2×D4C23×D17112yes—
560C2×D4C23×D17112yes—
561C22×C4—212no—
562C22×C4—212no—
563C22×C4—174no—
564C22×C4—171no—
565C22×C4—171no—
566C22×C4—173no—
567C22×C4—171no—
568C22×C4—173no—
569C22×C4—173no—
570C22×C4—173no—
571C22×C4—1712no—
572C22×C4—1724no—
573C22×C4—1712no—
574C22×C4—344no—
575C22×C4—3412no—
576C22×C4—6812no—
577C22×C4—686no—
578C22×C4C23×D17112yes—
579C22×C4C23×D17112yes—
580C22×C4C23×D1713yes—
581C22×C4C23×D1713yes—
582C22×C4C23×D1711yescharacteristic
583C22×C4C23×D1711yescharacteristic
584C22×C4C23×D1713yes—
585C4⋊C4—1712no—
586C4⋊C4—1712no—
587C4⋊C4—1712no—
588C4⋊C4—1712no—
589C4⋊C4—1724no—
590C4⋊C4—174no—
591C4⋊C4—1712no—
592C4⋊C4—1712no—
593C4⋊C4—1712no—
594C4⋊C4—1724no—
595C4⋊C4—1712no—
596C4⋊C4—1724no—
597C4⋊C4—1712no—
598C4⋊C4—174no—
599C4⋊C4—1712no—
600C4⋊C4C23×D17112yes—
601C4⋊C4C23×D17112yes—
602C22⋊C4—1712no—
603C22⋊C4—1712no—
604C22⋊C4—1712no—
605C22⋊C4—1712no—
606C22⋊C4—1724no—
607C22⋊C4—1712no—
608C22⋊C4—174no—
609C22⋊C4—174no—
610C22⋊C4—1712no—
611C22⋊C4C23×D17124yes—
612C22⋊C4C23×D1714yes—
613C22⋊C4C23×D17112yes—
614C42—1712no—
615C42—1712no—
616C42—1712no—
617C42—1712no—
618C42—1724no—
619C42—1712no—
620C42C23×D17112yes—
621C23—22no—
622C23—22no—
623C23—26no—
624C23—26no—
625C23—26no—
626C23—172no—
627C23—342no—
628C23—342no—
629C23—342no—
630C23#1058769714yes—
631C23C24×D1716yes—
632C23C24×D1712yes—
633C23C24×D1711yescharacteristic
634Q8—224no—
635Q8—3424no—
636Q8—6812no—
637Q8C2×#63254116yes—
638D4—224no—
639D4—224no—
640D4—348no—
641D4—6812no—
642C2×C4—22no—
643C2×C4—26no—
644C2×C4—26no—
645C2×C4—22no—
646C2×C4—224no—
647C2×C4—224no—
648C2×C4—172no—
649C2×C4—172no—
650C2×C4—176no—
651C2×C4—172no—
652C2×C4—176no—
653C2×C4—176no—
654C2×C4—176no—
655C2×C4—346no—
656C2×C4—348no—
657C2×C4—342no—
658C2×C4—342no—
659C2×C4—342no—
660C2×C4—346no—
661C2×C4—346no—
662C2×C4—346no—
663C2×C4—3424no—
664C2×C4—6824no—
665C2×C4—6812no—
666C2×C4C2×#63254112yes—
667C2×C4C24×D1716yes—
668C2×C4C24×D1716yes—
669C2×C4C24×D1712yes—
670C2×C4C24×D1712yes—
671C2×C4C24×D1716yes—
672C22—28no—
673C22—22no—
674C22—22no—
675C22—26no—
676C22—26no—
677C22—26no—
678C22—412no—
679C22—342no—
680C22—342no—
681C22—342no—
682C22—684no—
683C22C22×#6325412yes—
684C22C2×#1058769714yes—
685C22C2×#1058769712yes—
686C22#1176364612yes—
687C22C25×D1711yescharacteristic
688C4—22no—
689C4—26no—
690C4—26no—
691C4—22no—
692C4—346no—
693C4—342no—
694C4—342no—
695C4—342no—
696C4—346no—
697C4—346no—
698C4—346no—
699C4C22×#63254112yes—
700C2—24no—
701C2—46no—
702C2—682no—
703C2#1454276614yesdirect product factor
704C2C23×#6325411yescharacteristic
705C2C22×#1058769711yescharacteristic
706C2C2×#1176364611yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#548C2
socleC23×C17C25
hypercenterC2×#548D17
hypocenterC17C2×#3516
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #14542766C2direct (N × H)
2. C2×#11763538C2semidirect
3. C2×#11763528C2semidirect
4. C2×#11763516C2semidirect
5. C2×#11763511C2semidirect
6. C2×#11763501C2semidirect
7. C2×Q8×C22⋊D17C2semidirect
8. C2×#11763466C2semidirect
9. C2×#11763428C2semidirect
10. C2×#11763419C2semidirect
11. C2×#11763340C2semidirect
12. C2×#11763339C2semidirect
13. C2×#11763292C2semidirect
14. C2×#11763285C2semidirect
15. C22×Q8×Dic17C2semidirect
16. C2×C17×#548C2semidirect
18. #11763538C22semidirect
19. #11763528C22semidirect
20. #11763516C22semidirect
21. #11763511C22semidirect
22. #11763501C22semidirect
23. Q8×C22⋊D17C22semidirect
24. #11763466C22semidirect
25. #11763428C22semidirect
26. #11763419C22semidirect
29. #11763340C22semidirect
30. #11763339C22semidirect
51. #11763292C22semidirect
52. #11763285C22semidirect
58. C2×Q8×Dic17C22semidirect
76. C17×#548C22semidirect
327. C2×#548D17semidirect
373. #548C2×D17semidirect
430. C2×C17#3516semidirect
538. C17C2×#3516semidirect
703. C2#14542766direct (N × H)

Maximal subgroups

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

subgroupindex
#145427662
C2×#117635382
C2×#117635282
C2×#117635162
C2×#117635112
C2×#117635012
C2×Q8×C22⋊D172
C2×#117634662
C2×#117634282
C2×#117634192
C2×#117633402
C2×#117633392
C2×#117632922
C2×#117632852
C22×Q8×Dic172
C2×C17×#5482
C2×#351617