Finite Group Databasebeta

← C2×#14541353 #17913012

Subgroups — C2×#14541353 #17913012

Order 4352.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763499C211yesmaximal, characteristic
2#14541353C2116yesmaximal, direct product factor
3C2×#11763208C211yesmaximal, characteristic, complemented
4C2×#11763144C211yesmaximal, characteristic, complemented
5C2×#11763142C211yesmaximal, characteristic, complemented
6C2×#11763150C211yesmaximal, characteristic, complemented
7C2×#11763147C211yesmaximal, characteristic, complemented
8C2×#11763116C211yesmaximal, characteristic, complemented
9C2×#11763113C211yesmaximal, characteristic, complemented
10C2×#11763065C211yesmaximal, characteristic, complemented
11C2×#11763065C211yesmaximal, characteristic, complemented
12C2×C4×#63231C211yesmaximal, characteristic, complemented
13C2×#11762887C211yesmaximal, characteristic
14C2×#11762852C211yesmaximal, characteristic, complemented
15C2×#11762849C211yesmaximal, characteristic, complemented
16C2×C17×#552C211yesmaximal, characteristic
17C22×#63231C2211yescharacteristic
18C22×#63223C2211yescharacteristic
19C22×#63223C2211yescharacteristic
20#11763499—24no—
21#11763499C2218yes—
22C2×#10587565—21no—
23C2×#10587556C2211yescharacteristic
24C2×#10587575—21no—
25C2×#10587621—21no—
26C2×#10587610C2211yescharacteristic
27C2×#10587610C2211yescharacteristic
28C2×C4×Dic34C2211yescharacteristic
29C2×#10587612C2211yescharacteristic
30C2×#10587563—21no—
31C22×C4⋊Dic17C2211yescharacteristic
32#11763208C2218yescomplemented
33#11763150C2218yescomplemented
34#11763147C2218yescomplemented
35#11763144C2218yescomplemented
36#11763142C2218yescomplemented
37#11763116C2218yescomplemented
38#11763113C2218yescomplemented
39#11763065C2218yescomplemented
40#11763065C2218yescomplemented
41C4×#63231C2218yescomplemented
42#11762887C2218yes—
43#11762852C2218yescomplemented
44#11762849C2218yescomplemented
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587478C2211yescharacteristic
48C2×#10587478C2211yescharacteristic
49C2×#10587478C2211yescharacteristic
50C2×#10587479C2211yescharacteristic
51C2×#10587479C2211yescharacteristic
52C2×#10587479C2211yescharacteristic
53C2×#10587479C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×#10587506C2211yescharacteristic
56C2×#10587506C2211yescharacteristic
57C2×#10587506C2211yescharacteristic
58C2×#10587481C2211yescharacteristic
59C2×#10587481C2211yescharacteristic
60C2×#10587481C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#552—24no—
65C17×#552C2218yes—
66C2×C17×#126—21no—
67C2×C17×#125—21no—
68C2×C17×#125C2211yescharacteristic
69C2×C17×#123—21no—
70C2×C17×C22⋊Q8C2211yescharacteristic
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×D4×C17C2211yescharacteristic
74C2×C17×#117—21no—
75C2×C17×#117C2211yescharacteristic
76C22×C4⋊C4×C17C2211yescharacteristic
77C22×Q8×C17C2311yescharacteristic
78C22×D4×C17D411yescharacteristic
79C23×C4×C17—21no—
80C23×C4×C17C2311yescharacteristic
81C23×C4×C17C2311yescharacteristic
82C23×Dic17—21no—
83C22×Dic34C2311yescharacteristic
84C17×#126—28no—
85C17×#125—28no—
86C17×#125—22no—
87C17×#125C2314yes—
88C17×#123—28no—
89C17×C22⋊Q8—22no—
90C17×C22⋊Q8—22no—
91C17×C22⋊Q8C2314yes—
92C17×C22⋊Q8C2314yes—
93C4×Q8×C17—22no—
94C4×Q8×C17C2314yes—
95C4×D4×C17D414yes—
96C4×D4×C17C2314yes—
97C17×#117—22no—
98C17×#117—28no—
99C17×#117C2314yes—
100C2×C4⋊C4×C17—21no—
101C2×C4⋊C4×C17—22no—
102C2×C4⋊C4×C17—21no—
103C2×C4⋊C4×C17—21no—
104C2×C4⋊C4×C17—21no—
105C2×C4⋊C4×C17—21no—
106C2×C4⋊C4×C17—21no—
107C2×C4⋊C4×C17D411yescharacteristic
108C2×C4⋊C4×C17C2311yescharacteristic
109C2×C4⋊C4×C17C2311yescharacteristic
110C2×C4⋊C4×C17C2314yes—
111C2×C4⋊C4×C17C2311yescharacteristic
112C2×C22⋊C4×C17—21no—
113C2×C22⋊C4×C17—21no—
114C2×C22⋊C4×C17—21no—
115C2×C22⋊C4×C17D411yescharacteristic
116C2×C22⋊C4×C17D411yescharacteristic
117C2×C42×C17—21no—
118C2×C42×C17—21no—
119C2×C42×C17C2311yescharacteristic
120C2×C22⋊Dic17—21no—
121C2×C22⋊Dic17—21no—
122C2×C22⋊Dic17—21no—
123C2×#63231—24no—
124C2×#63231C2314yes—
125#10587621—28no—
126#10587612—22no—
127#10587612C2314yes—
128C2×C4⋊Dic17—22no—
129C2×C4⋊Dic17—21no—
130C2×C4⋊Dic17C2314yes—
131C2×C4⋊Dic17C2311yescharacteristic
132C2×C4⋊Dic17C2311yescharacteristic
133C2×C4⋊Dic17C2311yescharacteristic
134#10587610—22no—
135#10587610—22no—
136#10587610C2314yes—
137#10587610C2314yes—
138C2×#63225—21no—
139C2×#63225—21no—
140C2×#63225—21no—
141C2×#63225—21no—
142C2×#63225—21no—
143C2×C4×Dic17—21no—
144C2×C4×Dic17—21no—
145C2×#63223—24no—
146C2×#63223—24no—
147C2×#63223C2314yes—
148C2×#63223C2314yes—
149C22×#3622C2311yescharacteristic
150C22×#3622C2311yescharacteristic
151C22×#3622C2311yescharacteristic
152C22×#3622C2311yescharacteristic
153#10587575—28no—
154#10587565—28no—
155#10587563—28no—
156#10587556—22no—
157#10587556C2314yes—
158C4×Dic34—22no—
159C4×Dic34C2314yes—
160#10587506C2314yes—
161#10587506C2314yes—
162#10587506C2314yes—
163C22⋊#3622C2314yes—
164C22⋊#3622C2314yes—
165#10587481C2314yes—
166#10587481C2314yes—
167#10587481C2314yes—
168#10587479C2314yes—
169#10587479C2314yes—
170#10587479C2314yes—
171#10587479C2314yes—
172#10587478C2314yes—
173#10587478C2314yes—
174#10587478C2314yes—
175#10587478C2314yes—
176#10587478C2314yes—
177C4⋊#3622C2314yes—
178C4×#3622C2314yes—
179C24×C17C2×D411yescharacteristic
180C24×C17C2×D411yescharacteristic
181C2×Q8×C17—21no—
182C2×Q8×C17—22no—
183C2×Q8×C17—22no—
184C2×Q8×C17C2412yes—
185C2×D4×C17—42no—
186C2×D4×C17C2×D414yes—
187C22×C4×C17—22no—
188C22×C4×C17—22no—
189C22×C4×C17—22no—
190C22×C4×C17—22no—
191C22×C4×C17—24no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—44no—
197C22×C4×C17C2×D412yes—
198C22×C4×C17C2×D412yes—
199C22×C4×C17C2×D411yescharacteristic
200C22×C4×C17C2×D411yescharacteristic
201C22×C4×C17C2×D411yescharacteristic
202C22×C4×C17C2×D411yescharacteristic
203C22×C4×C17C2412yes—
204C22×C4×C17C2412yes—
205C22×C4×C17C2411yescharacteristic
206C22×Dic17—21no—
207C22×Dic17—24no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—44no—
212C2×Dic34—22no—
213C2×Dic34—22no—
214C2×Dic34—21no—
215C2×Dic34C2412yes—
216C4⋊C4×C17—21no—
217C4⋊C4×C17—21no—
218C4⋊C4×C17—24no—
219C4⋊C4×C17—24no—
220C4⋊C4×C17—24no—
221C4⋊C4×C17—24no—
222C4⋊C4×C17—24no—
223C4⋊C4×C17—24no—
224C4⋊C4×C17—21no—
225C4⋊C4×C17C2×D414yes—
226C4⋊C4×C17C2412yes—
227C4⋊C4×C17C2412yes—
228C4⋊C4×C17C2412yes—
229C22⋊C4×C17—24no—
230C22⋊C4×C17—24no—
231C22⋊C4×C17—24no—
232C22⋊C4×C17C2×D414yes—
233C22⋊C4×C17C2×D414yes—
234C42×C17—24no—
235C42×C17—24no—
236C42×C17C2×D412yes—
237C42×C17C2412yes—
238C22⋊Dic17—24no—
239C22⋊Dic17—24no—
240C22⋊Dic17—24no—
241#63231—28no—
242C4⋊Dic17—21no—
243C4⋊Dic17—21no—
244C4⋊Dic17—21no—
245C4⋊Dic17—24no—
246C4⋊Dic17C2412yes—
247C4⋊Dic17C2412yes—
248C4⋊Dic17C2412yes—
249#63225—24no—
250#63225—24no—
251#63225—24no—
252#63225—24no—
253#63225—24no—
254C4×Dic17—24no—
255C4×Dic17—24no—
256#63223—28no—
257#63223—28no—
258C2×#3622—22no—
259C2×#3622—22no—
260C2×#3622—22no—
261C2×#3622#4114yes—
262C2×#3622C2412yes—
263C2×#3622C2412yes—
264C2×#3622C2412yes—
265C2×#3622C2412yes—
266C2×#3352—171nomaximal, Sylow
267C23×C17—22no—
268C23×C17—22no—
269C23×C17—22no—
270C23×C17—22no—
271C23×C17—22no—
272C23×C17—22no—
273C23×C17C22×D412yes—
274C23×C17C22×D412yes—
275C23×C17C22×D411yescharacteristic
276Q8×C17—22no—
277Q8×C17—22no—
278Q8×C17—42no—
279D4×C17—44no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—24no—
285C2×C4×C17—24no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—48no—
295C2×C4×C17—42no—
296C2×C4×C17—42no—
297C2×C4×C17—42no—
298C2×C4×C17—42no—
299C2×C4×C17C22×D412yes—
300C2×C4×C17C22×D412yes—
301C2×C4×C17C22×D412yes—
302C2×C4×C17C22×D412yes—
303C2×C4×C17C22×D411yescharacteristic
304C2×C4×C17C2×#4112yes—
305C2×C4×C172−1+412yes—
306C2×C4×C17C2511yescharacteristic
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—22no—
311C2×Dic17—48no—
312C2×Dic17—42no—
313C2×Dic17—42no—
314C2×Dic17—42no—
315C2×Dic17—42no—
316Dic34—22no—
317Dic34—22no—
318Dic34—42no—
319#3622—22no—
320#3622—22no—
321#3622—22no—
322#3622C2×#4114yes—
323C2×#552—171no—
324C2×#552D1711yescharacteristic
325#3352—1716no—
326C2×#499—171no—
327C2×#484—171no—
328C2×#484—171no—
329C2×#485—171no—
330C2×#485—171no—
331C2×#479—171no—
332C2×#479—171no—
333C2×#470—171no—
334C2×#470—171no—
335C2×C4×Q16—171no—
336C2×#436—171no—
337C2×#428—171no—
338C2×#428—171no—
339C22×C17—22no—
340C22×C17—22no—
341C22×C17—22no—
342C22×C17—22no—
343C22×C17—22no—
344C22×C17—22no—
345C22×C17—44no—
346C22×C17—44no—
347C22×C17#54712yes—
348C22×C17#57512yes—
349C22×C17#57812yes—
350C22×C17C23×D411yescharacteristic
351C4×C17—22no—
352C4×C17—22no—
353C4×C17—22no—
354C4×C17—22no—
355C4×C17—42no—
356C4×C17—42no—
357C4×C17—42no—
358C4×C17—42no—
359C4×C17#54712yes—
360C4×C17C22×#4111yescharacteristic
361C4×C17C2×2−1+411yescharacteristic
362Dic17—42no—
363Dic17—42no—
364Dic17—42no—
365Dic17—42no—
366C22×Q16—171no—
367C22×M16—171no—
368C22×M16—171no—
369#552—24no—
370#552—178no—
371#552—344no—
372#552C2×D1718yes—
373C2×#126—21no—
374C2×#126—341no—
375C2×#125—21no—
376C2×#125—171no—
377C2×#125—341no—
378C2×#125C2×D1711yescharacteristic
379C2×#123—21no—
380C2×#123—341no—
381C2×C22⋊Q8—171no—
382C2×C22⋊Q8—171no—
383C2×C22⋊Q8C2×D1711yescharacteristic
384C2×C22⋊Q8C2×D1711yescharacteristic
385C2×C4×Q8—171no—
386C2×C4×Q8C2×D1711yescharacteristic
387C2×C4×D4C2×D1711yescharacteristic
388C2×#117—21no—
389C2×#117—171no—
390C2×#117—341no—
391C2×#117C2×D1711yescharacteristic
392C22×C4⋊C4—171no—
393C22×C4⋊C4C2×D1711yescharacteristic
394#499—178no—
395#485—178no—
396#485—178no—
397#484—178no—
398#484—178no—
399#479—178no—
400#479—178no—
401#470—178no—
402#470—178no—
403C4×Q16—178no—
404#436—178no—
405#428—178no—
406#428—178no—
407C2×#107—171no—
408C2×#107—171no—
409C2×#107—171no—
410C2×#107—171no—
411C2×#107—171no—
412C2×#106—171no—
413C2×#106—171no—
414C2×#106—171no—
415C2×#106—171no—
416C2×C4⋊C8—171no—
417C2×#103—171no—
418C2×#103—171no—
419C2×#103—171no—
420C2×#103—171no—
421C2×#103—171no—
422C2×#103—171no—
423C2×C22⋊C8—171no—
424C2×C22⋊C8—171no—
425C2×C4×C8—171no—
426C2×C17—42no—
427C2×C17—42no—
428C2×C17#335214yescomplemented
429C2×C17C2×#54711yescharacteristic
430C2×C17C2×#57511yescharacteristic
431C2×C17C2×#57811yescharacteristic
432C22×Q8—171no—
433C22×Q8C22×D1711yescharacteristic
434C22×D4C22⋊D1711yescharacteristic
435C23×C4—21no—
436C23×C4—341no—
437C23×C4C22×D1711yescharacteristic
438C23×C4C22×D1711yescharacteristic
439C2×Q16—174no—
440C2×Q16—344no—
441C2×M16—174no—
442C2×M16—174no—
443C2×M16—344no—
444C2×M16—344no—
445C22×C8—171no—
446C22×C8—171no—
447C22×C8—171no—
448C22×C8—171no—
449#126—28no—
450#126—348no—
451#125—28no—
452#125—22no—
453#125—174no—
454#125—348no—
455#125—342no—
456#125C22×D1714yes—
457#123—28no—
458#123—348no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—174no—
462C22⋊Q8—174no—
463C22⋊Q8—342no—
464C22⋊Q8—342no—
465C22⋊Q8C22×D1714yes—
466C22⋊Q8C22×D1714yes—
467C4×Q8—22no—
468C4×Q8—174no—
469C4×Q8—342no—
470C4×Q8C22×D1714yes—
471C4×D4C22⋊D1714yes—
472C4×D4C22×D1714yes—
473#117—22no—
474#117—28no—
475#117—174no—
476#117—342no—
477#117—348no—
478#117C22×D1714yes—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—171no—
487C2×C4⋊C4—171no—
488C2×C4⋊C4—174no—
489C2×C4⋊C4—171no—
490C2×C4⋊C4—341no—
491C2×C4⋊C4—342no—
492C2×C4⋊C4—341no—
493C2×C4⋊C4—341no—
494C2×C4⋊C4—341no—
495C2×C4⋊C4—341no—
496C2×C4⋊C4—341no—
497C2×C4⋊C4C22⋊D1711yescharacteristic
498C2×C4⋊C4C22×D1711yescharacteristic
499C2×C4⋊C4C22×D1711yescharacteristic
500C2×C4⋊C4C22×D1714yes—
501C2×C4⋊C4C22×D1711yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—341no—
506C2×C22⋊C4—341no—
507C2×C22⋊C4—341no—
508C2×C22⋊C4C22⋊D1711yescharacteristic
509C2×C22⋊C4C22⋊D1711yescharacteristic
510C2×C42—21no—
511C2×C42—21no—
512C2×C42—341no—
513C2×C42—341no—
514C2×C42C22×D1711yescharacteristic
515#107—174no—
516#107—174no—
517#107—174no—
518#107—174no—
519#107—174no—
520#106—174no—
521#106—174no—
522#106—174no—
523#106—174no—
524C4⋊C8—174no—
525#103—174no—
526#103—174no—
527#103—174no—
528#103—174no—
529#103—174no—
530#103—174no—
531C22⋊C8—174no—
532C22⋊C8—174no—
533C4×C8—174no—
534C17C2×#335211yescharacteristic, complemented, Sylow
535C24C2×C22⋊D1711yescharacteristic
536C24C2×C22⋊D1711yescharacteristic
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—172no—
541C2×Q8—341no—
542C2×Q8—342no—
543C2×Q8—342no—
544C2×Q8C23×D1712yes—
545C2×D4—42no—
546C2×D4C2×C22⋊D1714yes—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—44no—
557C22×C4—344no—
558C22×C4—341no—
559C22×C4—341no—
560C22×C4—341no—
561C22×C4—341no—
562C22×C4—684no—
563C22×C4C2×C22⋊D1712yes—
564C22×C4C2×C22⋊D1712yes—
565C22×C4C2×C22⋊D1711yescharacteristic
566C22×C4C2×C22⋊D1711yescharacteristic
567C22×C4C2×C22⋊D1711yescharacteristic
568C22×C4C2×C22⋊D1711yescharacteristic
569C22×C4C23×D1712yes—
570C22×C4C23×D1712yes—
571C22×C4C23×D1711yescharacteristic
572Q16—348no—
573M16—348no—
574M16—348no—
575C2×C8—174no—
576C2×C8—172no—
577C2×C8—172no—
578C2×C8—172no—
579C2×C8—172no—
580C2×C8—342no—
581C2×C8—342no—
582C2×C8—342no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—21no—
592C4⋊C4—172no—
593C4⋊C4—172no—
594C4⋊C4—172no—
595C4⋊C4—341no—
596C4⋊C4—341no—
597C4⋊C4—344no—
598C4⋊C4—341no—
599C4⋊C4—344no—
600C4⋊C4—344no—
601C4⋊C4—344no—
602C4⋊C4—344no—
603C4⋊C4—344no—
604C4⋊C4C2×C22⋊D1714yes—
605C4⋊C4C23×D1712yes—
606C4⋊C4C23×D1712yes—
607C4⋊C4C23×D1712yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—344no—
612C22⋊C4—344no—
613C22⋊C4—344no—
614C22⋊C4C2×C22⋊D1714yes—
615C22⋊C4C2×C22⋊D1714yes—
616C42—24no—
617C42—24no—
618C42—344no—
619C42—344no—
620C42C2×C22⋊D1712yes—
621C42C23×D1712yes—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23C22×C22⋊D1712yes—
629C23C22×C22⋊D1712yes—
630C23C22×C22⋊D1711yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—42no—
634Q8—342no—
635Q8—342no—
636Q8—682no—
637D4—44no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—342no—
658C2×C4—342no—
659C2×C4—342no—
660C2×C4—342no—
661C2×C4—688no—
662C2×C4—682no—
663C2×C4—682no—
664C2×C4—682no—
665C2×C4—682no—
666C2×C4#41×D1712yes—
667C2×C4#1058769712yes—
668C2×C4C22×C22⋊D1712yes—
669C2×C4C22×C22⋊D1712yes—
670C2×C4C22×C22⋊D1712yes—
671C2×C4C22×C22⋊D1712yes—
672C2×C4C22×C22⋊D1711yescharacteristic
673C2×C4C24×D1711yescharacteristic
674C8—174no—
675C8—342no—
676C8—342no—
677C8—342no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—44no—
685C22—44no—
686C22#1176345812yes—
687C22#1176360712yes—
688C22#1176362412yes—
689C22C23×C22⋊D1711yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—682no—
699C4—682no—
700C4—682no—
701C4—682no—
702C4#1176345812yes—
703C4C2×#41×D1711yescharacteristic
704C4C2×#1058769711yescharacteristic
705C2—42no—
706C2—42no—
707C2#1454135314yesdirect product factor
708C2C2×#1176345811yescharacteristic
709C2C2×#1176360711yescharacteristic
710C2C2×#1176362411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#552C2
socleC23×C17C22×D4
prime radicalC22×D4×C17D4
hypercenterC2×#552D17
hypocenterC17C2×#3352
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #14541353C2direct (N × H)
3. C2×#11763208C2semidirect
4. C2×#11763144C2semidirect
5. C2×#11763142C2semidirect
6. C2×#11763150C2semidirect
7. C2×#11763147C2semidirect
8. C2×#11763116C2semidirect
9. C2×#11763113C2semidirect
10. C2×#11763065C2semidirect
11. C2×#11763065C2semidirect
12. C2×C4×#63231C2semidirect
14. C2×#11762852C2semidirect
15. C2×#11762849C2semidirect
32. #11763208C22semidirect
33. #11763150C22semidirect
34. #11763147C22semidirect
35. #11763144C22semidirect
36. #11763142C22semidirect
37. #11763116C22semidirect
38. #11763113C22semidirect
39. #11763065C22semidirect
40. #11763065C22semidirect
41. C4×#63231C22semidirect
43. #11762852C22semidirect
44. #11762849C22semidirect
428. C2×C17#3352semidirect
534. C17C2×#3352semidirect
707. C2#14541353direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634992
#145413532
C2×#117632082
C2×#117631442
C2×#117631422
C2×#117631502
C2×#117631472
C2×#117631162
C2×#117631132
C2×#117630652
C2×C4×#632312
C2×#117628872
C2×#117628522
C2×#117628492
C2×C17×#5522
C2×#335217