Finite Group Databasebeta

← C2×#14540061 #17906539

Subgroups — C2×#14540061 #17906539

Order 4352.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763437C211yesmaximal, characteristic, complemented
2#14540061C2116yesmaximal, direct product factor
3C2×#11763215C211yesmaximal, characteristic, complemented
4C2×#11763212C211yesmaximal, characteristic, complemented
5C2×#11763168C211yesmaximal, characteristic, complemented
6C2×#11763163C211yesmaximal, characteristic, complemented
7C2×#11763142C211yesmaximal, characteristic, complemented
8C2×#11763147C211yesmaximal, characteristic, complemented
9C2×#11763130C211yesmaximal, characteristic
10C2×#11763120C211yesmaximal, characteristic
11C2×#11763116C211yesmaximal, characteristic, complemented
12C2×#11763104C211yesmaximal, characteristic, complemented
13C2×#11763109C211yesmaximal, characteristic, complemented
14C2×#11763089C211yesmaximal, characteristic, complemented
15C2×#11762870C211yesmaximal, characteristic, complemented
16C2×C17×#542C211yesmaximal, characteristic
17#11763437—24no—
18#11763437C2218yescomplemented
19C2×#10587555C2211yescharacteristic
20C2×#10587555C2211yescharacteristic
21C2×#10587574—21no—
22C2×#10587556C2211yescharacteristic
23C2×#10587556C2211yescharacteristic
24C2×#10587576—21no—
25C2×#10587564—21no—
26C2×#10587564—21no—
27C2×#10587612C2211yescharacteristic
28C22×C4⋊Dic17C2211yescharacteristic
29#11763215C2218yescomplemented
30#11763212C2218yescomplemented
31#11763168C2218yescomplemented
32#11763163C2218yescomplemented
33#11763147C2218yescomplemented
34#11763142C2218yescomplemented
35#11763130C2218yes—
36#11763120C2218yes—
37#11763116C2218yescomplemented
38#11763109C2218yescomplemented
39#11763104C2218yescomplemented
40#11763089C2218yescomplemented
41#11762870C2218yescomplemented
42C2×#10587478C2211yescharacteristic
43C2×#10587478C2211yescharacteristic
44C2×#10587478C2211yescharacteristic
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587478C2211yescharacteristic
48C2×#10587479C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×C4⋊#3622C2211yescharacteristic
51C2×C4⋊#3622C2211yescharacteristic
52C2×#10587506C2211yescharacteristic
53C2×#10587506C2211yescharacteristic
54C2×#10587506C2211yescharacteristic
55C2×#10587506C2211yescharacteristic
56C2×#10587503C2211yescharacteristic
57C2×#10587503C2211yescharacteristic
58C2×#10587503C2211yescharacteristic
59C2×#10587503C2211yescharacteristic
60C2×C22⋊#3622C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#542—24no—
65C17×#542C2218yes—
66C2×C17×C4⋊Q8C2211yescharacteristic
67C2×C17×#126—21no—
68C2×C17×#124—21no—
69C2×C17×#124C2211yescharacteristic
70C2×C17×#123—21no—
71C2×C17×C22⋊Q8—21no—
72C2×C17×C22⋊Q8C2211yescharacteristic
73C2×C17×#121C2211yescharacteristic
74C2×C4×Q8×C17C2211yescharacteristic
75C2×C4×D4×C17C2211yescharacteristic
76C2×C17×#117C2211yescharacteristic
77C22×Q8×C17—21no—
78C22×Q8×C17C2311yescharacteristic
79C22×D4×C17—21no—
80C22×D4×C17C2311yescharacteristic
81C23×C4×C17—21no—
82C23×C4×C17C2311yescharacteristic
83C23×Dic17—21no—
84C22×Dic34—21no—
85C22×Dic34—21no—
86C17×C4⋊Q8—22no—
87C17×C4⋊Q8C2314yes—
88C17×#126—28no—
89C17×#124—28no—
90C17×#124—22no—
91C17×#124C2314yes—
92C17×#123—28no—
93C17×C22⋊Q8—22no—
94C17×C22⋊Q8—28no—
95C17×C22⋊Q8C2314yes—
96C17×#121—22no—
97C17×#121C2314yes—
98C4×Q8×C17—22no—
99C4×Q8×C17C2314yes—
100C4×D4×C17—22no—
101C4×D4×C17C2314yes—
102C17×#117D414yes—
103C17×#117C2314yes—
104C2×C4⋊C4×C17—21no—
105C2×C4⋊C4×C17—21no—
106C2×C4⋊C4×C17—21no—
107C2×C4⋊C4×C17D411yescharacteristic
108C2×C4⋊C4×C17D411yescharacteristic
109C2×C4⋊C4×C17C2311yescharacteristic
110C2×C4⋊C4×C17C2311yescharacteristic
111C2×C22⋊C4×C17—21no—
112C2×C22⋊C4×C17—21no—
113C2×C22⋊C4×C17—21no—
114C2×C22⋊C4×C17—21no—
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17D411yescharacteristic
117C2×C22⋊C4×C17D411yescharacteristic
118C2×C42×C17—21no—
119C2×C42×C17C2311yescharacteristic
120C2×C42×C17C2311yescharacteristic
121C2×C22⋊Dic17—21no—
122#10587612—22no—
123#10587612C2314yes—
124C2×C4⋊Dic17—21no—
125C2×C4⋊Dic17—22no—
126C2×C4⋊Dic17—21no—
127C2×C4⋊Dic17—21no—
128C2×C4⋊Dic17C2311yescharacteristic
129C2×C4⋊Dic17C2311yescharacteristic
130C2×C4⋊Dic17C2314yes—
131C2×C4⋊Dic17C2311yescharacteristic
132C2×C4⋊Dic17C2311yescharacteristic
133C2×#63225—21no—
134C2×#63225—21no—
135C2×#63225—21no—
136C2×#63225—21no—
137C2×C4×Dic17—21no—
138C22×#3622C2311yescharacteristic
139C22×#3622C2311yescharacteristic
140C22×#3622C2311yescharacteristic
141C22×#3622C2311yescharacteristic
142#10587576—28no—
143#10587574—28no—
144#10587564—28no—
145#10587564—28no—
146#10587556—22no—
147#10587556—22no—
148#10587556C2314yes—
149#10587556C2314yes—
150#10587555—22no—
151#10587555—22no—
152#10587555C2314yes—
153#10587555C2314yes—
154#10587506C2314yes—
155#10587506C2314yes—
156#10587506C2314yes—
157#10587506C2314yes—
158#10587503C2314yes—
159#10587503C2314yes—
160#10587503C2314yes—
161#10587503C2314yes—
162C22⋊#3622C2314yes—
163C22⋊#3622C2314yes—
164#10587479C2314yes—
165#10587479C2314yes—
166#10587478C2314yes—
167#10587478C2314yes—
168#10587478C2314yes—
169#10587478C2314yes—
170#10587478C2314yes—
171#10587478C2314yes—
172C4⋊#3622C2314yes—
173C4⋊#3622C2314yes—
174#10587474C2314yes—
175C4×#3622C2314yes—
176C24×C17—21no—
177C24×C17C2×D411yescharacteristic
178C2×Q8×C17—21no—
179C2×Q8×C17—24no—
180C2×Q8×C17—22no—
181C2×Q8×C17—22no—
182C2×Q8×C17—82no—
183C2×Q8×C17C2412yes—
184C2×D4×C17—24no—
185C2×D4×C17—21no—
186C2×D4×C17—22no—
187C2×D4×C17—22no—
188C2×D4×C17—82no—
189C2×D4×C17C2412yes—
190C22×C4×C17—22no—
191C22×C4×C17—22no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—24no—
196C22×C4×C17—82no—
197C22×C4×C17C2×D412yes—
198C22×C4×C17C2×D411yescharacteristic
199C22×C4×C17C2×D411yescharacteristic
200C22×C4×C17C2×D411yescharacteristic
201C22×C4×C17C2×D411yescharacteristic
202C22×C4×C17C2×D411yescharacteristic
203C22×C4×C17C2412yes—
204C22×C4×C17C2411yescharacteristic
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—24no—
210C22×Dic17—82no—
211C2×Dic34—24no—
212C2×Dic34—24no—
213C2×Dic34—82no—
214C2×Dic34—82no—
215C4⋊C4×C17—24no—
216C4⋊C4×C17—24no—
217C4⋊C4×C17—21no—
218C4⋊C4×C17—24no—
219C4⋊C4×C17—21no—
220C4⋊C4×C17C2×D414yes—
221C4⋊C4×C17C2×D414yes—
222C4⋊C4×C17C2412yes—
223C4⋊C4×C17C2412yes—
224C22⋊C4×C17—24no—
225C22⋊C4×C17—24no—
226C22⋊C4×C17—24no—
227C22⋊C4×C17—24no—
228C22⋊C4×C17—24no—
229C22⋊C4×C17C2×D414yes—
230C22⋊C4×C17C2×D414yes—
231C42×C17—24no—
232C42×C17C2×D412yes—
233C42×C17C2×D412yes—
234C42×C17C2412yes—
235C42×C17C2412yes—
236C22⋊Dic17—24no—
237C4⋊Dic17—21no—
238C4⋊Dic17—21no—
239C4⋊Dic17—21no—
240C4⋊Dic17—24no—
241C4⋊Dic17—24no—
242C4⋊Dic17—21no—
243C4⋊Dic17—24no—
244C4⋊Dic17C2412yes—
245C4⋊Dic17C2412yes—
246C4⋊Dic17C2412yes—
247C4⋊Dic17C2412yes—
248#63225—24no—
249#63225—24no—
250#63225—24no—
251#63225—24no—
252C4×Dic17—24no—
253C2×#3622—22no—
254C2×#3622—22no—
255C2×#3622—22no—
256C2×#3622—22no—
257C2×#3622C2412yes—
258C2×#3622C2412yes—
259C2×#3622C2412yes—
260C2×#3622C2412yes—
261C2×#3243—171nomaximal, Sylow
262C23×C17—22no—
263C23×C17—22no—
264C23×C17—22no—
265C23×C17—22no—
266C23×C17—42no—
267C23×C17—42no—
268C23×C17—42no—
269C23×C17C22×D412yes—
270C23×C17C22×D411yescharacteristic
271Q8×C17—22no—
272Q8×C17—22no—
273Q8×C17—42no—
274Q8×C17—84no—
275D4×C17—22no—
276D4×C17—22no—
277D4×C17—42no—
278D4×C17—84no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—24no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—42no—
291C2×C4×C17—42no—
292C2×C4×C17—42no—
293C2×C4×C17—84no—
294C2×C4×C17C22×D412yes—
295C2×C4×C17C22×D412yes—
296C2×C4×C17C22×D412yes—
297C2×C4×C17C22×D412yes—
298C2×C4×C17C22×D412yes—
299C2×C4×C17C22×D411yescharacteristic
300C2×C4×C172−1+412yes—
301C2×C4×C172−1+412yes—
302C2×C4×C17C2511yescharacteristic
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—42no—
308C2×Dic17—42no—
309C2×Dic17—42no—
310C2×Dic17—42no—
311C2×Dic17—84no—
312Dic34—84no—
313Dic34—84no—
314#3622—22no—
315#3622—22no—
316#3622—22no—
317#3622—22no—
318C2×#544—171no—
319C2×#542D1711yescharacteristic
320#3243—1716no—
321C2×#501—171no—
322C2×#500—171no—
323C2×#489—171no—
324C2×#488—171no—
325C2×#484—171no—
326C2×#485—171no—
327C2×#482—171no—
328C2×#480—171no—
329C2×#479—171no—
330C2×#477—171no—
331C2×#478—171no—
332C2×#474—171no—
333C2×#433—171no—
334C22×C17—22no—
335C22×C17—22no—
336C22×C17—22no—
337C22×C17—44no—
338C22×C17—42no—
339C22×C17—42no—
340C22×C17—42no—
341C22×C17—84no—
342C22×C17#53612yes—
343C22×C17#57612yes—
344C22×C17#57812yes—
345C22×C17C23×D411yescharacteristic
346C4×C17—22no—
347C4×C17—22no—
348C4×C17—22no—
349C4×C17—22no—
350C4×C17—22no—
351C4×C17—42no—
352C4×C17—42no—
353C4×C17—42no—
354C4×C17#53612yes—
355C4×C17C2×2−1+411yescharacteristic
356C4×C17C2×2−1+411yescharacteristic
357Dic17—42no—
358Dic17—42no—
359Dic17—42no—
360Dic17—42no—
361#544—178no—
362#544—344no—
363#542—24no—
364#542C2×D1718yes—
365C2×C4⋊Q8—171no—
366C2×C4⋊Q8—171no—
367C2×C4⋊Q8—341no—
368C2×C4⋊Q8C2×D1711yescharacteristic
369C2×#126—21no—
370C2×#125—171no—
371C2×#125—171no—
372C2×#125—341no—
373C2×#124—21no—
374C2×#124C2×D1711yescharacteristic
375C2×#123—21no—
376C2×C22⋊Q8—21no—
377C2×C22⋊Q8—341no—
378C2×C22⋊Q8—341no—
379C2×C22⋊Q8C2×D1711yescharacteristic
380C2×#121C2×D1711yescharacteristic
381C2×C4×Q8C2×D1711yescharacteristic
382C2×C4×D4C2×D1711yescharacteristic
383C2×#117—171no—
384C2×#117C2×D1711yescharacteristic
385C22×C4⋊C4—171no—
386#501—178no—
387#500—178no—
388#489—178no—
389#488—178no—
390#485—178no—
391#484—178no—
392#482—178no—
393#480—178no—
394#479—178no—
395#478—178no—
396#477—178no—
397#474—178no—
398#433—178no—
399C2×#107—171no—
400C2×#107—171no—
401C2×#107—171no—
402C2×#107—171no—
403C2×#107—171no—
404C2×#107—171no—
405C2×#106—171no—
406C2×#106—171no—
407C2×C4⋊C8—171no—
408C2×C4⋊C8—171no—
409C2×#103—171no—
410C2×#103—171no—
411C2×#103—171no—
412C2×#103—171no—
413C2×#102—171no—
414C2×#102—171no—
415C2×#102—171no—
416C2×#102—171no—
417C2×C22⋊C8—171no—
418C2×C22⋊C8—171no—
419C2×#97—171no—
420C2×C4×C8—171no—
421C2×C17—42no—
422C2×C17—82no—
423C2×C17#324314yescomplemented
424C2×C17C2×#53611yescharacteristic
425C2×C17C2×#57611yescharacteristic
426C2×C17C2×#57811yescharacteristic
427C22×Q8—21no—
428C22×Q8—341no—
429C22×Q8—341no—
430C22×Q8C22×D1711yescharacteristic
431C22×D4—21no—
432C22×D4C22×D1711yescharacteristic
433C23×C4—21no—
434C23×C4—341no—
435C23×C4C22×D1711yescharacteristic
436C22×C8—171no—
437C22×C8—171no—
438C22×C8—171no—
439C22×C8—171no—
440C4⋊Q8—22no—
441C4⋊Q8—174no—
442C4⋊Q8—174no—
443C4⋊Q8—348no—
444C4⋊Q8—342no—
445C4⋊Q8—342no—
446C4⋊Q8C22×D1714yes—
447#126—28no—
448#125—174no—
449#125—174no—
450#125—348no—
451#125—342no—
452#125—342no—
453#124—28no—
454#124—22no—
455#124C22×D1714yes—
456#123—28no—
457C22⋊Q8—22no—
458C22⋊Q8—28no—
459C22⋊Q8—348no—
460C22⋊Q8—348no—
461C22⋊Q8C22×D1714yes—
462#121—22no—
463#121C22×D1714yes—
464C4×Q8—22no—
465C4×Q8C22×D1714yes—
466C4×D4—22no—
467C4×D4C22×D1714yes—
468#117—174no—
469#117—342no—
470#117C22⋊D1714yes—
471#117C22×D1714yes—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—171no—
476C2×C4⋊C4—171no—
477C2×C4⋊C4—174no—
478C2×C4⋊C4—171no—
479C2×C4⋊C4—171no—
480C2×C4⋊C4—341no—
481C2×C4⋊C4—342no—
482C2×C4⋊C4—341no—
483C2×C4⋊C4—341no—
484C2×C4⋊C4—341no—
485C2×C4⋊C4—341no—
486C2×C4⋊C4—341no—
487C2×C4⋊C4—341no—
488C2×C4⋊C4C22⋊D1711yescharacteristic
489C2×C4⋊C4C22⋊D1711yescharacteristic
490C2×C4⋊C4C22×D1711yescharacteristic
491C2×C4⋊C4C22×D1711yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—341no—
498C2×C22⋊C4C22⋊D1711yescharacteristic
499C2×C22⋊C4C22⋊D1711yescharacteristic
500C2×C42—21no—
501C2×C42—341no—
502C2×C42C22×D1711yescharacteristic
503C2×C42C22×D1711yescharacteristic
504#107—174no—
505#107—174no—
506#107—174no—
507#107—174no—
508#107—174no—
509#107—174no—
510#106—174no—
511#106—174no—
512C4⋊C8—174no—
513C4⋊C8—174no—
514#103—174no—
515#103—174no—
516#103—174no—
517#103—174no—
518#102—174no—
519#102—174no—
520#102—174no—
521#102—174no—
522C22⋊C8—174no—
523C22⋊C8—174no—
524#97—174no—
525C4×C8—174no—
526C17C2×#324311yescharacteristic, complemented, Sylow
527C24—21no—
528C24C2×C22⋊D1711yescharacteristic
529C2×Q8—21no—
530C2×Q8—24no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—82no—
534C2×Q8—344no—
535C2×Q8—344no—
536C2×Q8—1362no—
537C2×Q8—1362no—
538C2×Q8C23×D1712yes—
539C2×D4—24no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—21no—
543C2×D4—82no—
544C2×D4C23×D1712yes—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—82no—
552C22×C4—341no—
553C22×C4—341no—
554C22×C4—341no—
555C22×C4—341no—
556C22×C4—344no—
557C22×C4—1362no—
558C22×C4C2×C22⋊D1712yes—
559C22×C4C2×C22⋊D1711yescharacteristic
560C22×C4C2×C22⋊D1711yescharacteristic
561C22×C4C2×C22⋊D1711yescharacteristic
562C22×C4C2×C22⋊D1711yescharacteristic
563C22×C4C2×C22⋊D1711yescharacteristic
564C22×C4C23×D1712yes—
565C22×C4C23×D1711yescharacteristic
566C2×C8—172no—
567C2×C8—172no—
568C2×C8—172no—
569C2×C8—172no—
570C2×C8—342no—
571C2×C8—342no—
572C2×C8—342no—
573C2×C8—342no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—172no—
580C4⋊C4—172no—
581C4⋊C4—172no—
582C4⋊C4—172no—
583C4⋊C4—344no—
584C4⋊C4—341no—
585C4⋊C4—341no—
586C4⋊C4—341no—
587C4⋊C4—341no—
588C4⋊C4—344no—
589C4⋊C4—344no—
590C4⋊C4—344no—
591C4⋊C4—344no—
592C4⋊C4—344no—
593C4⋊C4—344no—
594C4⋊C4C2×C22⋊D1714yes—
595C4⋊C4C2×C22⋊D1714yes—
596C4⋊C4C23×D1712yes—
597C4⋊C4C23×D1712yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—344no—
604C22⋊C4C2×C22⋊D1714yes—
605C22⋊C4C2×C22⋊D1714yes—
606C42—24no—
607C42—344no—
608C42C2×C22⋊D1712yes—
609C42C2×C22⋊D1712yes—
610C42C23×D1712yes—
611C42C23×D1712yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23C22×C22⋊D1712yes—
620C23C22×C22⋊D1711yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—42no—
624Q8—84no—
625Q8—1364no—
626Q8—1364no—
627D4—22no—
628D4—22no—
629D4—42no—
630D4—84no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—84no—
646C2×C4—342no—
647C2×C4—342no—
648C2×C4—342no—
649C2×C4—342no—
650C2×C4—682no—
651C2×C4—682no—
652C2×C4—682no—
653C2×C4—682no—
654C2×C4—1364no—
655C2×C4#1058769712yes—
656C2×C4#1058769712yes—
657C2×C4C22×C22⋊D1712yes—
658C2×C4C22×C22⋊D1712yes—
659C2×C4C22×C22⋊D1712yes—
660C2×C4C22×C22⋊D1712yes—
661C2×C4C22×C22⋊D1712yes—
662C2×C4C22×C22⋊D1711yescharacteristic
663C2×C4C24×D1711yescharacteristic
664C8—342no—
665C8—342no—
666C8—342no—
667C8—342no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—84no—
676C22#1176338012yes—
677C22#1176361212yes—
678C22#1176362412yes—
679C22C23×C22⋊D1711yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—682no—
689C4—682no—
690C4—682no—
691C4—682no—
692C4#1176338012yes—
693C4C2×#1058769711yescharacteristic
694C4C2×#1058769711yescharacteristic
695C2—42no—
696C2—82no—
697C2#1454006114yesdirect product factor
698C2C2×#1176338011yescharacteristic
699C2C2×#1176361211yescharacteristic
700C2C2×#1176362411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#542C2
socleC23×C17C22×D4
prime radicalC2×C17×#121C22
hypercenterC2×#542D17
hypocenterC17C2×#3243
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#11763437C2semidirect
2. #14540061C2direct (N × H)
3. C2×#11763215C2semidirect
4. C2×#11763212C2semidirect
5. C2×#11763168C2semidirect
6. C2×#11763163C2semidirect
7. C2×#11763142C2semidirect
8. C2×#11763147C2semidirect
11. C2×#11763116C2semidirect
12. C2×#11763104C2semidirect
13. C2×#11763109C2semidirect
14. C2×#11763089C2semidirect
15. C2×#11762870C2semidirect
18. #11763437C22semidirect
29. #11763215C22semidirect
30. #11763212C22semidirect
31. #11763168C22semidirect
32. #11763163C22semidirect
33. #11763147C22semidirect
34. #11763142C22semidirect
37. #11763116C22semidirect
38. #11763109C22semidirect
39. #11763104C22semidirect
40. #11763089C22semidirect
41. #11762870C22semidirect
423. C2×C17#3243semidirect
526. C17C2×#3243semidirect
697. C2#14540061direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634372
#145400612
C2×#117632152
C2×#117632122
C2×#117631682
C2×#117631632
C2×#117631422
C2×#117631472
C2×#117631302
C2×#117631202
C2×#117631162
C2×#117631042
C2×#117631092
C2×#117630892
C2×#117628702
C2×C17×#5422
C2×#324317