Finite Group Databasebeta

← C2×#14542863 #17942531

Subgroups — C2×#14542863 #17942531

Order 4352.

7758 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542863C2132yesmaximal, direct product factor
2C2×#11763542C213yesmaximal, complemented
3C2×Q8×Dic34C211yesmaximal, characteristic, complemented
4C2×#11763514C213yesmaximal, complemented
5C2×#11763478C211yesmaximal, characteristic, complemented
6C2×#11763471C211yesmaximal, characteristic, complemented
7C2×#11763466C211yesmaximal, characteristic, complemented
8C2×#11763464C213yesmaximal, complemented
9C2×#11763460C213yesmaximal, complemented
10C2×#11763430C213yesmaximal, complemented
11C2×#11763424C213yesmaximal, complemented
12C2×#11763356C213yesmaximal, complemented
13C2×#11763337C213yesmaximal, complemented
14C2×#11763291C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D17C211yesmaximal, characteristic, complemented
16C2×C17×#520C211yesmaximal, characteristic, complemented
17C22×#63256C2211yescharacteristic
18C22×#63252C2216yes—
19C22×Q8×D17C2211yescharacteristic
20#11763542C22148yescomplemented
21Q8×Dic34C22116yescomplemented
22#11763514C22148yescomplemented
23#11763478C22116yescomplemented
24#11763471C22116yescomplemented
25#11763466C22116yescomplemented
26#11763464C22148yescomplemented
27#11763460C22148yescomplemented
28#11763430C22148yescomplemented
29#11763424C22148yescomplemented
30#11763356C22148yescomplemented
31C2×#10587555C2213yes—
32C2×#10587574C2213yes—
33C2×#10587574C2213yes—
34C2×#10587626C2213yes—
35#11763337C22148yescomplemented
36C2×#10587584C2213yes—
37C2×#10587565C2213yes—
38C2×#10587575C2213yes—
39C2×#10587561C2213yes—
40C2×#10587622C2213yes—
41C2×#10587571C2213yes—
42C2×#10587571C2216yes—
43C2×#10587580C2213yes—
44C2×#10587615C2216yes—
45C2×#10587569C2216yes—
46C2×#10587569C2213yes—
47C2×#10587583C2213yes—
48C2×#10587610C2216yes—
49C2×#10587610C2213yes—
50C2×#10587582C2216yes—
51C2×#10587582C2211yescharacteristic
52C2×#10587581C2213yes—
53C2×#10587616C2213yes—
54C2×#10587570C2213yes—
55C2×#10587624C2213yes—
56C2×#10587624C2213yes—
57#11763291C22116yescomplemented
58C2×Q8×Dic17C2211yescharacteristic
59C2×Q8×Dic17C2211yescharacteristic
60C2×C4×Dic34C2213yes—
61C2×C4×Dic34C2213yes—
62C2×#10587573C2213yes—
63C4×Q8×D17C22116yescomplemented
64C2×C4×D68C2213yes—
65C2×C4×D68C2213yes—
66C2×#10587579C2213yes—
67C2×C4×C22⋊D17C2216yes—
68C2×C4×C22⋊D17C2213yes—
69C2×C4×C22⋊D17C2213yes—
70C2×#10587558C2213yes—
71C2×C4⋊C4×D17C2213yes—
72C2×C4⋊C4×D17C2213yes—
73C2×C42×D17C2213yes—
74C22×#41×C17C2211yescharacteristic
75C17×#520C22116yescomplemented
76C2×C4×Q8×C17C2211yescharacteristic
77C2×C4×Q8×C17C2211yescharacteristic
78C2×C4×D4×C17C2213yes—
79C2×C4×D4×C17C2213yes—
80C2×C17×#117C2213yes—
81C22×C4⋊C4×C17C2213yes—
82C2×#41×C17—28no—
83C2×#41×C17C2318yes—
84C22×Q8×C17C2311yescharacteristic
85C22×D4×C17C2313yes—
86C23×C4×C17C2313yes—
87C23×C4×C17C2316yes—
88C22×C22⋊D17C2313yes—
89C22×C22⋊D17C2313yes—
90C22×C22⋊D17C2316yes—
91C2×#63256—28no—
92C2×#63256C2318yes—
93C2×Q8×D17—28no—
94C2×Q8×D17C2318yes—
95C2×#63252—424no—
96C2×#63252C23148yes—
97C22×D68C2313yes—
98C22×D68C2313yes—
99C22×C4×D17C2311yescharacteristic
100C22×C4×D17C2313yes—
101C22×C4×D17C2313yes—
102C22×C4×D17C2313yes—
103C22×C4×D17C2316yes—
104C22×Dic34C2313yes—
105C22×Dic34C2311yescharacteristic
106C22×Dic34C2316yes—
107C4×Q8×C17C2318yes—
108C4×Q8×C17C2318yes—
109C4×D4×C17C23124yes—
110C4×D4×C17C23124yes—
111C17×#117C23124yes—
112C2×C4⋊C4×C17C23124yes—
113C2×C4⋊C4×C17C2313yes—
114C2×C4⋊C4×C17C2313yes—
115C2×C4⋊C4×C17C2313yes—
116C2×C4⋊C4×C17C2311yescharacteristic
117C2×C22⋊C4×C17C2313yes—
118C2×C22⋊C4×C17C2313yes—
119C2×C42×C17C2313yes—
120C2×C42×C17C2313yes—
121C2×C22⋊Dic17C2313yes—
122C2×C22⋊Dic17C2316yes—
123C2×C22⋊Dic17C2313yes—
124Q8×Dic17C2318yes—
125Q8×Dic17C2318yes—
126#10587626C23124yes—
127#10587624C23124yes—
128#10587624C23124yes—
129#10587622C23124yes—
130#10587616C23124yes—
131#10587615C23148yes—
132C4×C22⋊D17C23124yes—
133C4×C22⋊D17C23124yes—
134C4×C22⋊D17C23148yes—
135C2×#63227C2313yes—
136C2×#63227C2313yes—
137C2×#63227C2311yescharacteristic
138C2×#63227C2313yes—
139C2×#63227C2316yes—
140C2×#63227C2311yescharacteristic
141C2×#63227C2313yes—
142C2×C4⋊Dic17C2313yes—
143C2×C4⋊Dic17C2313yes—
144C2×C4⋊Dic17C2313yes—
145C2×C4⋊Dic17C2313yes—
146#10587610C23148yes—
147#10587610C23124yes—
148C2×#63225C2313yes—
149C2×#63225C2316yes—
150C2×#63225C2311yescharacteristic
151C2×#63225C2311yescharacteristic
152C2×#63225C2313yes—
153C2×#63225C2313yes—
154C2×#63225C2313yes—
155C2×C4×Dic17C2313yes—
156C2×C4×Dic17C2313yes—
157C2×C4×Dic17C2313yes—
158C2×C4×Dic17C2313yes—
159#10587584C23124yes—
160#10587583C23124yes—
161#10587582C23148yes—
162#10587582C2318yes—
163#10587581C23124yes—
164#10587580C23124yes—
165#10587579C23124yes—
166C4⋊C4×D17C23124yes—
167C4⋊C4×D17C23124yes—
168#10587575C23124yes—
169#10587574C23124yes—
170#10587574C23124yes—
171#10587573C23124yes—
172#10587571C23124yes—
173#10587571C23148yes—
174#10587570C23124yes—
175#10587569C23124yes—
176#10587569C23148yes—
177#10587565C23124yes—
178#10587561C23124yes—
179C4×D68C23124yes—
180C4×D68C23124yes—
181#10587558C23124yes—
182C42×D17C23124yes—
183#10587555C23124yes—
184C4×Dic34C23124yes—
185C4×Dic34C23124yes—
186C24×C17C2413yes—
187C23×D17C2413yes—
188C23×D17C2411yescharacteristic
189#41×C17—232no—
190C2×Q8×C17#4118yescomplemented
191C2×Q8×C17C2414yes—
192C2×D4×C17—212no—
193C2×D4×C17C24112yes—
194C22×C4×C17—212no—
195C22×C4×C17—412no—
196C22×C4×C17C2413yes—
197C22×C4×C17C2411yescharacteristic
198C22×C4×C17C2413yes—
199C22×C4×C17C2411yescharacteristic
200C22×C4×C17C2411yescharacteristic
201C22×C4×C17C24112yes—
202C22×C4×C17C24124yes—
203C22×C4×C17C2413yes—
204C2×C22⋊D17—212no—
205C2×C22⋊D17—212no—
206C2×C22⋊D17—412no—
207C2×C22⋊D17C24112yes—
208C2×C22⋊D17C24112yes—
209C2×C22⋊D17C24124yes—
210C22×Dic17C2413yes—
211C22×Dic17C2413yes—
212C22×Dic17C2413yes—
213C22×Dic17C2411yescharacteristic
214C22×Dic17C2411yescharacteristic
215C22×Dic17C2411yescharacteristic
216#63256—232no—
217Q8×D17—232no—
218#63252—496no—
219C2×D68—212no—
220C2×D68—212no—
221C2×D68C24112yes—
222C2×D68C24112yes—
223C2×C4×D17—212no—
224C2×C4×D17—212no—
225C2×C4×D17—212no—
226C2×C4×D17—24no—
227C2×C4×D17—412no—
228C2×C4×D17C24112yes—
229C2×C4×D17C24112yes—
230C2×C4×D17C24112yes—
231C2×C4×D17C2414yes—
232C2×C4×D17C24124yes—
233C2×Dic34—212no—
234C2×Dic34—24no—
235C2×Dic34—412no—
236C2×Dic34C24112yes—
237C2×Dic34C2414yes—
238C2×Dic34C24124yes—
239C4⋊C4×C17C24112yes—
240C4⋊C4×C17C24112yes—
241C4⋊C4×C17C24112yes—
242C4⋊C4×C17C2414yes—
243C22⋊C4×C17C24112yes—
244C22⋊C4×C17C24112yes—
245C42×C17C24112yes—
246C42×C17C24112yes—
247C22⋊Dic17C24112yes—
248C22⋊Dic17C24112yes—
249C22⋊Dic17C24124yes—
250#63227C24112yes—
251#63227C24112yes—
252#63227C2414yes—
253#63227C24112yes—
254#63227C24124yes—
255#63227C2414yes—
256#63227C24112yes—
257C4⋊Dic17C24112yes—
258C4⋊Dic17C24112yes—
259C4⋊Dic17C24112yes—
260C4⋊Dic17C24112yes—
261#63225C24112yes—
262#63225C24124yes—
263#63225C24112yes—
264#63225C2414yes—
265#63225C24112yes—
266#63225C2414yes—
267#63225C24112yes—
268C4×Dic17C24112yes—
269C4×Dic17C24112yes—
270C4×Dic17C24112yes—
271C4×Dic17C24112yes—
272C2×#3522—171nomaximal, Sylow
273C23×C17—26no—
274C23×C17—26no—
275C23×C17—26no—
276C23×C17C2516yes—
277C23×C17C2511yescharacteristic
278C22×D17—22no—
279C22×D17—22no—
280C22×D17—26no—
281C22×D17—26no—
282C22×D17—26no—
283C22×D17H(5,𝔽2)14yes—
284C22×D17C2516yes—
285C22×D17C2512yes—
286Q8×C17C2×#41116yescomplemented
287D4×C17—224no—
288C2×C4×C17—22no—
289C2×C4×C17—26no—
290C2×C4×C17—26no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—224no—
294C2×C4×C17—424no—
295C2×C4×C17C2×#41112yes—
296C2×C4×C17C2512yes—
297C2×C4×C17C2512yes—
298C2×C4×C17C2516yes—
299C2×C4×C17C2516yes—
300C2×C4×C17C2512yes—
301C2×C4×C17C2516yes—
302C22⋊D17—224no—
303C22⋊D17—224no—
304C22⋊D17—424no—
305C2×Dic17—26no—
306C2×Dic17—22no—
307C2×Dic17—26no—
308C2×Dic17—26no—
309C2×Dic17—22no—
310C2×Dic172−1+414yes—
311C2×Dic17C2516yes—
312C2×Dic17C2512yes—
313C2×Dic17C2512yes—
314C2×Dic17C2516yes—
315C2×Dic17C2516yes—
316C2×Dic17C2512yes—
317D68—224no—
318D68—224no—
319C4×D17—224no—
320C4×D17—224no—
321C4×D17—224no—
322C4×D17—28no—
323C4×D17—424no—
324Dic34—224no—
325Dic34—28no—
326Dic34—424no—
327#3522—1732no—
328C2×#559—173no—
329C2×Q82—171no—
330C2×#554—173no—
331C2×#550—171no—
332C2×#548—171no—
333C2×#548—171no—
334C2×#547—173no—
335C2×#547—173no—
336C2×#542—173no—
337C2×#542—173no—
338C2×#532—173no—
339C2×#529—173no—
340C2×#520—171no—
341C2×#520D1711yescharacteristic, complemented
342C22×C4×Q8—171no—
343C22×C17—26no—
344C22×C17—26no—
345C22×C17—26no—
346C22×C17—412no—
347C22×C17C22×#4112yes—
348C22×C17C2×H(5,𝔽2)12yes—
349C22×C17C2×2−1+412yes—
350C22×C17C2611yescharacteristic
351C2×D17—22no—
352C2×D17—22no—
353C2×D17—28no—
354C2×D17—26no—
355C2×D17—26no—
356C2×D17—26no—
357C2×D17—412no—
358C2×D17C2×H(5,𝔽2)14yes—
359C4×C17—22no—
360C4×C17—26no—
361C4×C17—26no—
362C4×C17—22no—
363C4×C17—22no—
364C4×C17C22×#41112yes—
365Dic17—26no—
366Dic17—22no—
367Dic17—26no—
368Dic17—26no—
369Dic17—22no—
370Dic17C2×2−1+414yes—
371C22×#41—171no—
372C22×#41—176no—
373C22×#41C2×D1711yescharacteristic
374C23×Q8—171no—
375#559—1748no—
376Q82—1716no—
377#554—1748no—
378#550—1716no—
379#548—1716no—
380#548—1716no—
381#547—1748no—
382#547—1748no—
383#542—1748no—
384#542—1748no—
385#532—1748no—
386C2×C4⋊Q8—173no—
387C2×C4⋊Q8—173no—
388C2×C4⋊Q8—173no—
389C2×#127—173no—
390#529—1748no—
391C2×#126—173no—
392C2×#126—173no—
393C2×#125—173no—
394C2×#124—173no—
395C2×#124—173no—
396C2×#124—176no—
397C2×#124—173no—
398C2×#123—176no—
399C2×#123—173no—
400C2×#123—173no—
401C2×#123—176no—
402C2×C22⋊Q8—176no—
403C2×C22⋊Q8—173no—
404C2×C22⋊Q8—171no—
405C2×C22⋊Q8—176no—
406C2×C22⋊Q8—173no—
407C2×#121—173no—
408C2×#121—173no—
409C2×#121—173no—
410C2×#121—173no—
411C2×#121—173no—
412#520—1716no—
413#520C2×D17116yescomplemented
414C2×C4×Q8—171no—
415C2×C4×Q8—171no—
416C2×C4×Q8—1716no—
417C2×C4×Q8—173no—
418C2×C4×Q8—173no—
419C2×C4×Q8—173no—
420C2×C4×Q8C2×D1711yescharacteristic
421C2×C4×Q8C2×D1711yescharacteristic
422C2×C4×D4—173no—
423C2×C4×D4—173no—
424C2×C4×D4—176no—
425C2×C4×D4—173no—
426C2×C4×D4—173no—
427C2×C4×D4—173no—
428C2×C4×D4C2×D1713yes—
429C2×C4×D4C2×D1713yes—
430C2×#117—173no—
431C2×#117C2×D1713yes—
432C22×C4⋊C4—173no—
433C22×C4⋊C4—173no—
434C22×C4⋊C4C2×D1713yes—
435C22×C42—173no—
436C2×C17—46no—
437C2×C17#352214yescomplemented
438C2×C17C23×#4111yescharacteristic
439C2×C17C22×H(5,𝔽2)11yescharacteristic
440C2×C17C22×2−1+411yescharacteristic
441D17—24no—
442D17—46no—
443C2×#41—28no—
444C2×#41—178no—
445C2×#41—1748no—
446C2×#41—348no—
447C2×#41—6824no—
448C2×#41C22×D1718yes—
449C22×Q8—178no—
450C22×Q8—171no—
451C22×Q8—173no—
452C22×Q8—176no—
453C22×Q8—348no—
454C22×Q8C22×D1711yescharacteristic
455C22×D4—173no—
456C22×D4—173no—
457C22×D4—176no—
458C22×D4—173no—
459C22×D4—173no—
460C22×D4C22×D1713yes—
461C23×C4—173no—
462C23×C4—173no—
463C23×C4—173no—
464C23×C4—171no—
465C23×C4—176no—
466C23×C4C22×D1713yes—
467C23×C4C22×D1716yes—
468C4⋊Q8—1724no—
469C4⋊Q8—1724no—
470C4⋊Q8—1724no—
471#127—1724no—
472#126—1724no—
473#126—1724no—
474#125—1724no—
475#124—1724no—
476#124—1724no—
477#124—1748no—
478#124—1724no—
479#123—1748no—
480#123—1724no—
481#123—1724no—
482#123—1748no—
483C22⋊Q8—1748no—
484C22⋊Q8—1724no—
485C22⋊Q8—178no—
486C22⋊Q8—1748no—
487C22⋊Q8—1724no—
488#121—1724no—
489#121—1724no—
490#121—1724no—
491#121—1724no—
492#121—1724no—
493C4×Q8—178no—
494C4×Q8—178no—
495C4×Q8—1724no—
496C4×Q8—1724no—
497C4×Q8—1724no—
498C4×Q8C22×D1718yes—
499C4×Q8C22×D1718yes—
500C4×D4—1724no—
501C4×D4—1724no—
502C4×D4—1748no—
503C4×D4—1724no—
504C4×D4—1724no—
505C4×D4—1724no—
506C4×D4C22×D17124yes—
507C4×D4C22×D17124yes—
508#117—1724no—
509#117C22×D17124yes—
510C2×C4⋊C4—173no—
511C2×C4⋊C4—173no—
512C2×C4⋊C4—173no—
513C2×C4⋊C4—176no—
514C2×C4⋊C4—171no—
515C2×C4⋊C4—171no—
516C2×C4⋊C4—173no—
517C2×C4⋊C4—173no—
518C2×C4⋊C4—173no—
519C2×C4⋊C4—173no—
520C2×C4⋊C4—173no—
521C2×C4⋊C4—1724no—
522C2×C4⋊C4—1724no—
523C2×C4⋊C4C22×D1713yes—
524C2×C4⋊C4C22×D1713yes—
525C2×C4⋊C4C22×D1713yes—
526C2×C4⋊C4C22×D17124yes—
527C2×C4⋊C4C22×D1711yescharacteristic
528C2×C22⋊C4—173no—
529C2×C22⋊C4—176no—
530C2×C22⋊C4—173no—
531C2×C22⋊C4—173no—
532C2×C22⋊C4—173no—
533C2×C22⋊C4—171no—
534C2×C22⋊C4—171no—
535C2×C22⋊C4—173no—
536C2×C22⋊C4—176no—
537C2×C22⋊C4—173no—
538C2×C22⋊C4C22×D1713yes—
539C2×C22⋊C4C22×D1713yes—
540C2×C42—173no—
541C2×C42—173no—
542C2×C42—173no—
543C2×C42—173no—
544C2×C42—1724no—
545C2×C42C22×D1713yes—
546C2×C42C22×D1713yes—
547C17C2×#352211yescharacteristic, complemented, Sylow
548C24—171no—
549C24—173no—
550C24C23×D1713yes—
551#41—232no—
552#41—3432no—
553#41—6896no—
554C2×Q8—174no—
555C2×Q8—1712no—
556C2×Q8—1724no—
557C2×Q8—344no—
558C2×Q8—3432no—
559C2×Q8—3412no—
560C2×Q8—6812no—
561C2×Q8#6325218yescomplemented
562C2×Q8C23×D1714yes—
563C2×D4—212no—
564C2×D4—1712no—
565C2×D4—1712no—
566C2×D4—1724no—
567C2×D4—1712no—
568C2×D4—1712no—
569C2×D4—3412no—
570C2×D4—3412no—
571C2×D4—3412no—
572C2×D4—3412no—
573C2×D4—6812no—
574C2×D4C23×D17112yes—
575C22×C4—212no—
576C22×C4—412no—
577C22×C4—171no—
578C22×C4—171no—
579C22×C4—173no—
580C22×C4—173no—
581C22×C4—173no—
582C22×C4—171no—
583C22×C4—174no—
584C22×C4—1712no—
585C22×C4—1712no—
586C22×C4—1712no—
587C22×C4—1724no—
588C22×C4—344no—
589C22×C4—3412no—
590C22×C4—3412no—
591C22×C4—3412no—
592C22×C4—6812no—
593C22×C4C23×D17112yes—
594C22×C4C23×D1711yescharacteristic
595C22×C4C23×D1713yes—
596C22×C4C23×D1711yescharacteristic
597C22×C4C23×D1713yes—
598C22×C4C23×D1711yescharacteristic
599C22×C4C23×D17124yes—
600C22×C4C23×D1713yes—
601C4⋊C4—1712no—
602C4⋊C4—1712no—
603C4⋊C4—1712no—
604C4⋊C4—1724no—
605C4⋊C4—174no—
606C4⋊C4—174no—
607C4⋊C4—1712no—
608C4⋊C4—1712no—
609C4⋊C4—1712no—
610C4⋊C4—1712no—
611C4⋊C4—1712no—
612C4⋊C4C23×D17112yes—
613C4⋊C4C23×D17112yes—
614C4⋊C4C23×D17112yes—
615C4⋊C4C23×D1714yes—
616C22⋊C4—1712no—
617C22⋊C4—1724no—
618C22⋊C4—1712no—
619C22⋊C4—1712no—
620C22⋊C4—1712no—
621C22⋊C4—174no—
622C22⋊C4—174no—
623C22⋊C4—1712no—
624C22⋊C4—1724no—
625C22⋊C4—1712no—
626C22⋊C4C23×D17112yes—
627C22⋊C4C23×D17112yes—
628C42—1712no—
629C42—1712no—
630C42—1712no—
631C42—1712no—
632C42C23×D17112yes—
633C42C23×D17112yes—
634C23—26no—
635C23—26no—
636C23—26no—
637C23—174no—
638C23—172no—
639C23—176no—
640C23—342no—
641C23—342no—
642C23—346no—
643C23—346no—
644C23—346no—
645C23C24×D1716yes—
646C23C24×D1711yescharacteristic
647Q8—348no—
648Q8—3424no—
649Q8—6824no—
650Q8C2×#63252116yescomplemented
651D4—224no—
652D4—3424no—
653D4—3424no—
654D4—3424no—
655D4—3424no—
656D4—6824no—
657C2×C4—22no—
658C2×C4—26no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—224no—
663C2×C4—424no—
664C2×C4—174no—
665C2×C4—172no—
666C2×C4—172no—
667C2×C4—176no—
668C2×C4—176no—
669C2×C4—176no—
670C2×C4—172no—
671C2×C4—348no—
672C2×C4—3424no—
673C2×C4—342no—
674C2×C4—346no—
675C2×C4—346no—
676C2×C4—346no—
677C2×C4—342no—
678C2×C4—3424no—
679C2×C4—3424no—
680C2×C4—6824no—
681C2×C4C2×#63252112yes—
682C2×C4C24×D1712yes—
683C2×C4C24×D1716yes—
684C2×C4C24×D1712yes—
685C2×C4C24×D1716yes—
686C2×C4C24×D1712yes—
687C2×C4C24×D1716yes—
688C22—26no—
689C22—26no—
690C22—26no—
691C22—412no—
692C22—174no—
693C22—348no—
694C22—342no—
695C22—342no—
696C22—346no—
697C22—346no—
698C22—346no—
699C22—6812no—
700C22C22×#6325212yes—
701C22H(5,𝔽2)×D1712yes—
702C222−1+4×D1712yes—
703C22C25×D1711yescharacteristic
704C4—22no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—22no—
709C4—174no—
710C4—342no—
711C4—346no—
712C4—346no—
713C4—346no—
714C4—342no—
715C4C22×#63252112yes—
716C2—46no—
717C2—344no—
718C2—686no—
719C2#1454286314yesdirect product factor
720C2C23×#6325211yescharacteristic
721C2C2×H(5,𝔽2)×D1711yescharacteristic
722C2C2×2−1+4×D1711yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#520C2
socleC23×C17C25
hypercenterC2×#520D17
hypocenterC17C2×#3522
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #14542863C2direct (N × H)
2. C2×#11763542C2semidirect
3. C2×Q8×Dic34C2semidirect
4. C2×#11763514C2semidirect
5. C2×#11763478C2semidirect
6. C2×#11763471C2semidirect
7. C2×#11763466C2semidirect
8. C2×#11763464C2semidirect
9. C2×#11763460C2semidirect
10. C2×#11763430C2semidirect
11. C2×#11763424C2semidirect
12. C2×#11763356C2semidirect
13. C2×#11763337C2semidirect
14. C2×#11763291C2semidirect
15. C2×C4×Q8×D17C2semidirect
16. C2×C17×#520C2semidirect
20. #11763542C22semidirect
21. Q8×Dic34C22semidirect
22. #11763514C22semidirect
23. #11763478C22semidirect
24. #11763471C22semidirect
25. #11763466C22semidirect
26. #11763464C22semidirect
27. #11763460C22semidirect
28. #11763430C22semidirect
29. #11763424C22semidirect
30. #11763356C22semidirect
35. #11763337C22semidirect
57. #11763291C22semidirect
63. C4×Q8×D17C22semidirect
75. C17×#520C22semidirect
190. C2×Q8×C17#41semidirect
286. Q8×C17C2×#41semidirect
341. C2×#520D17semidirect
413. #520C2×D17semidirect
437. C2×C17#3522semidirect
547. C17C2×#3522semidirect
561. C2×Q8#63252semidirect
650. Q8C2×#63252semidirect
719. C2#14542863direct (N × H)

Maximal subgroups

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

subgroupindex
#145428632
C2×#117635422
C2×Q8×Dic342
C2×#117635142
C2×#117634782
C2×#117634712
C2×#117634662
C2×#117634642
C2×#117634602
C2×#117634302
C2×#117634242
C2×#117633562
C2×#117633372
C2×#117632912
C2×C4×Q8×D172
C2×C17×#5202
C2×#352217