Finite Group Databasebeta

← C2×#14538632 #17901902

Subgroups — C2×#14538632 #17901902

Order 4352.

2094 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763436C211yesmaximal, characteristic, complemented
2C2×#11763291C211yesmaximal, characteristic
3#14538632C2116yesmaximal, direct product factor
4C2×#11763116C211yesmaximal, characteristic, complemented
5C2×#11763114C211yesmaximal, characteristic, complemented
6C2×#11763102C211yesmaximal, characteristic, complemented
7C2×#11763112C211yesmaximal, characteristic, complemented
8C2×#11763110C211yesmaximal, characteristic, complemented
9C2×#11763088C211yesmaximal, characteristic, complemented
10C2×#11763086C211yesmaximal, characteristic, complemented
11C2×#11762850C211yesmaximal, characteristic, complemented
12C2×#107×D17C211yesmaximal, characteristic, complemented
13C2×#11762834C211yesmaximal, characteristic, complemented
14C2×#11762809C211yesmaximal, characteristic
15C2×#11762804C211yesmaximal, characteristic
16C2×C17×#477C211yesmaximal, characteristic, complemented
17C22×#63256C2211yescharacteristic
18C22×#63218C2211yescharacteristic
19C22×C8×D17C2211yescharacteristic
20#11763436—24no—
21#11763436C2218yescomplemented
22C2×#10587574C2211yescharacteristic
23C2×#10587630—21no—
24C2×#10587556C2211yescharacteristic
25C2×#10587576C2211yescharacteristic
26C2×#10587575—21no—
27C2×#10587582—21no—
28C2×#10587632—21no—
29#11763291—24no—
30#11763291C2218yes—
31C2×Q8×Dic17C2211yescharacteristic
32C2×C4×D68—21no—
33C2×C4×D68C2211yescharacteristic
34C2×#10587579—21no—
35C2×#10587579C2211yescharacteristic
36C2×#10587578C2211yescharacteristic
37C2×#10587558—21no—
38C2×#10587558C2211yescharacteristic
39C2×C4⋊C4×D17—21no—
40C2×C4⋊C4×D17C2211yescharacteristic
41C2×C4⋊C4×D17C2211yescharacteristic
42#11763116C2218yescomplemented
43#11763114C2218yescomplemented
44#11763112C2218yescomplemented
45#11763110C2218yescomplemented
46#11763102C2218yescomplemented
47#11763088C2218yescomplemented
48#11763086C2218yescomplemented
49#11762850C2218yescomplemented
50C2×#10587489C2211yescharacteristic
51C2×#10587478C2211yescharacteristic
52C2×#10587478C2211yescharacteristic
53C2×#10587478C2211yescharacteristic
54#107×D17C2218yescomplemented
55C2×#10587488C2211yescharacteristic
56C2×#10587479C2211yescharacteristic
57#11762834C2218yescomplemented
58C2×C4⋊#3622C2211yescharacteristic
59C2×#10587485C2211yescharacteristic
60C2×#10587485C2211yescharacteristic
61#11762809C2218yes—
62#11762804C2218yes—
63C2×#10587506C2211yescharacteristic
64C2×#10587506C2211yescharacteristic
65C2×#10587492C2211yescharacteristic
66C2×#10587492C2211yescharacteristic
67C2×#10587480C2211yescharacteristic
68C2×#10587480C2211yescharacteristic
69C2×C17×C4⋊Q8C2211yescharacteristic
70C2×C4×Q8×C17C2211yescharacteristic
71C17×#477C2218yescomplemented
72C2×C17×#107C2211yescharacteristic
73C2×C17×#107C2211yescharacteristic
74C2×C17×C4⋊C8C2211yescharacteristic
75C2×C17×#103C2211yescharacteristic
76C2×C17×#103C2211yescharacteristic
77C22×Q8×C17—21no—
78C22×Q8×C17C2311yescharacteristic
79C2×#63256—22no—
80C2×#63256—24no—
81C2×#63256Q818yescomplemented
82C2×#63256C2314yes—
83C22×D68—21no—
84C22×D68C2311yescharacteristic
85C22×C4×D17—21no—
86C22×C4×D17—21no—
87C22×C4×D17—21no—
88C22×C4×D17—21no—
89C22×C4×D17—21no—
90C22×C4×D17C2311yescharacteristic
91C22×Dic34—21no—
92C22×C8×C17C2311yescharacteristic
93C22×C8×C17C2311yescharacteristic
94C17×C4⋊Q8—22no—
95C17×C4⋊Q8C2314yes—
96C4×Q8×C17—22no—
97C4×Q8×C17C2314yes—
98C2×C4⋊C4×C17—21no—
99C2×C4⋊C4×C17—21no—
100C2×C4⋊C4×C17C2311yescharacteristic
101C2×C4⋊C4×C17C2311yescharacteristic
102C2×C4⋊C4×C17C2311yescharacteristic
103C2×C42×C17—21no—
104C2×C42×C17C2311yescharacteristic
105#10587632—28no—
106Q8×Dic17—22no—
107Q8×Dic17C2314yes—
108#10587630—28no—
109C2×#63227—21no—
110C2×#63227—21no—
111C2×#63227—21no—
112C2×#63227D411yescharacteristic
113C2×#63227D411yescharacteristic
114C2×C4⋊Dic17—21no—
115C2×C4⋊Dic17—21no—
116C2×C4⋊Dic17C2311yescharacteristic
117C2×C4⋊Dic17C2311yescharacteristic
118C2×C4⋊Dic17C2311yescharacteristic
119C2×#63225—21no—
120C2×#63225—21no—
121C2×#63225—21no—
122C2×#63225—21no—
123C2×#63225—21no—
124C2×#63225—21no—
125C2×#63225D411yescharacteristic
126C2×#63225D411yescharacteristic
127C2×C4×Dic17—21no—
128C2×C4×Dic17—21no—
129C2×C4×Dic17C2311yescharacteristic
130C22×#3622C2311yescharacteristic
131C22×#3622C2311yescharacteristic
132C2×#63218—24no—
133C2×#63218C2314yes—
134C2×C8×D17—24no—
135C2×C8×D17C2314yes—
136#10587582—28no—
137#10587579—28no—
138#10587579—22no—
139#10587579C2314yes—
140#10587578—22no—
141#10587578C2314yes—
142C4⋊C4×D17—28no—
143C4⋊C4×D17—22no—
144C4⋊C4×D17—22no—
145C4⋊C4×D17C2314yes—
146C4⋊C4×D17C2314yes—
147#10587576—22no—
148#10587576C2314yes—
149#10587575—28no—
150#10587574—22no—
151#10587574C2314yes—
152C4×D68—28no—
153C4×D68—22no—
154C4×D68C2314yes—
155#10587558—28no—
156#10587558D414yes—
157#10587558C2314yes—
158#10587556—22no—
159#10587556C2314yes—
160C17×#107C2314yes—
161C17×#107C2314yes—
162C17×C4⋊C8C2314yes—
163C17×#103C2314yes—
164C17×#103C2314yes—
165#10587506C2314yes—
166#10587506C2314yes—
167#10587492C2314yes—
168#10587492C2314yes—
169#10587489C2314yes—
170#10587488C2314yes—
171#10587485C2314yes—
172#10587485C2314yes—
173#10587480C2314yes—
174#10587480C2314yes—
175#10587479C2314yes—
176#10587478C2314yes—
177#10587478C2314yes—
178#10587478C2314yes—
179C4⋊#3622C2314yes—
180C23×D17—21no—
181C23×D17C2×D411yescharacteristic
182C2×Q8×C17—21no—
183C2×Q8×C17—24no—
184C2×Q8×C17—22no—
185C2×Q8×C17—82no—
186C2×Q8×C17C2×Q814yes—
187C2×Q8×C17C2412yes—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17C2×D411yescharacteristic
193C22×C4×C17C2×D411yescharacteristic
194C22×C4×C17C2411yescharacteristic
195C22×Dic17—21no—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17C2×D411yescharacteristic
199C22×Dic17C2×D411yescharacteristic
200C22×Dic17C2×D411yescharacteristic
201#63256—216no—
202#63256—28no—
203#63256C2×Q8116yescomplemented
204C2×D68—28no—
205C2×D68—24no—
206C2×D68—21no—
207C2×D68—22no—
208C2×D68C2×Q814yes—
209C2×D68C2412yes—
210C2×C4×D17—28no—
211C2×C4×D17—24no—
212C2×C4×D17—24no—
213C2×C4×D17—24no—
214C2×C4×D17—24no—
215C2×C4×D17—24no—
216C2×C4×D17—82no—
217C2×C4×D17—82no—
218C2×C4×D17—82no—
219C2×C4×D17—82no—
220C2×C4×D17C2×D412yes—
221C2×C4×D17C2×Q814yes—
222C2×C4×D17#4114yes—
223C2×C4×D17C2412yes—
224C2×Dic34—24no—
225C2×Dic34—82no—
226C2×C8×C17—22no—
227C2×C8×C17—22no—
228C2×C8×C17C2412yes—
229C2×C8×C17C2412yes—
230C4⋊C4×C17—21no—
231C4⋊C4×C17—21no—
232C4⋊C4×C17—24no—
233C4⋊C4×C17—24no—
234C4⋊C4×C17—21no—
235C4⋊C4×C17C2412yes—
236C4⋊C4×C17C2412yes—
237C4⋊C4×C17C2412yes—
238C42×C17—24no—
239C42×C17C2×D412yes—
240C42×C17C2412yes—
241#63227—24no—
242#63227—24no—
243#63227—24no—
244#63227C2×D414yes—
245#63227C2×D414yes—
246C4⋊Dic17—21no—
247C4⋊Dic17—21no—
248C4⋊Dic17—21no—
249C4⋊Dic17—24no—
250C4⋊Dic17—24no—
251C4⋊Dic17C2412yes—
252C4⋊Dic17C2412yes—
253C4⋊Dic17C2412yes—
254#63225—24no—
255#63225—24no—
256#63225—24no—
257#63225—24no—
258#63225—24no—
259#63225—24no—
260#63225C2×D414yes—
261#63225C2×D414yes—
262C4×Dic17—24no—
263C4×Dic17—24no—
264C4×Dic17C2×D412yes—
265C4×Dic17C2412yes—
266C2×#3622—22no—
267C2×#3622—22no—
268C2×#3622C2412yes—
269C2×#3622C2412yes—
270#63218—28no—
271C8×D17—28no—
272C2×#3083—171nomaximal, Sylow
273C23×C17C22×D411yescharacteristic
274C22×D17—22no—
275C22×D17—22no—
276C22×D17—24no—
277C22×D17—22no—
278C22×D17—42no—
279C22×D17—42no—
280C22×D17C22⋊Q814yes—
281C22×D17C22×D412yes—
282Q8×C17—24no—
283Q8×C17—22no—
284Q8×C17—84no—
285Q8×C17C22×Q814yes—
286C2×C4×C17—24no—
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—42no—
294C2×C4×C17—42no—
295C2×C4×C17—42no—
296C2×C4×C17C22×D412yes—
297C2×C4×C17C22×D412yes—
298C2×C4×C17C22×D411yescharacteristic
299C2×C4×C17C22×Q812yes—
300C2×C4×C17C2×#4112yes—
301C2×C4×C17C2511yescharacteristic
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—42no—
308C2×Dic17—42no—
309C2×Dic17—42no—
310C2×Dic17C22⋊Q814yes—
311C2×Dic17C22×D412yes—
312C2×Dic17C22×D412yes—
313C2×Dic17C22×D412yes—
314D68—216no—
315D68—24no—
316D68—22no—
317D68C22×Q814yes—
318C4×D17—216no—
319C4×D17—84no—
320C4×D17—84no—
321C4×D17—84no—
322C4×D17—84no—
323C4×D17C22⋊Q818yes—
324C4×D17C22×Q814yes—
325C4×D17C2×#4114yes—
326Dic34—84no—
327C8×C17—22no—
328C8×C17—22no—
329#3622—22no—
330#3622—22no—
331C2×#544—171no—
332C2×#520—171no—
333#3083—1716no—
334C2×#479—171no—
335C2×#479—171no—
336C2×#477—171no—
337C2×#477D1711yescharacteristic, complemented
338C2×#478—171no—
339C2×#478—171no—
340C2×#474—171no—
341C2×#474—171no—
342C2×#428—171no—
343C22×#107—171no—
344C2×#424—171no—
345C2×#417—171no—
346C2×#416—171no—
347C22×C17C2×C22⋊Q812yes—
348C22×C17#57612yes—
349C22×C17#57812yes—
350C22×C17C23×D411yescharacteristic
351C2×D17—28no—
352C2×D17—22no—
353C2×D17—22no—
354C2×D17—24no—
355C2×D17—48no—
356C2×D17—42no—
357C2×D17—42no—
358C2×D17C2×C22⋊Q814yes—
359C4×C17—24no—
360C4×C17—22no—
361C4×C17—22no—
362C4×C17—42no—
363C4×C17—42no—
364C4×C17—42no—
365C4×C17C2×C22⋊Q812yes—
366C4×C17C23×Q811yescharacteristic
367C4×C17C22×#4111yescharacteristic
368Dic17—22no—
369Dic17—22no—
370Dic17—42no—
371Dic17—42no—
372Dic17—42no—
373Dic17C2×C22⋊Q814yes—
374C22×#41—171no—
375C22×M16—171no—
376C23×C8—171no—
377#544—178no—
378#544—344no—
379C2×C4⋊Q8—171no—
380C2×C4⋊Q8—341no—
381C2×C4⋊Q8C2×D1711yescharacteristic
382C2×#125—171no—
383C2×#125—171no—
384C2×#125—341no—
385C2×C22⋊Q8—341no—
386C2×C22⋊Q8—341no—
387#520—178no—
388#520—344no—
389C2×C4×Q8—171no—
390C2×C4×Q8C2×D1711yescharacteristic
391C2×C4×D4—171no—
392C2×C4×D4—171no—
393C2×C4×D4—341no—
394C2×C4×D4—341no—
395C2×#117—171no—
396C2×#117—171no—
397C2×#117—341no—
398C22×C4⋊C4—171no—
399C22×C4⋊C4—171no—
400C22×C4⋊C4—341no—
401#479—178no—
402#479—178no—
403#478—178no—
404#478—178no—
405#477—178no—
406#477C2×D1718yescomplemented
407#474—178no—
408#474—178no—
409#428—178no—
410C2×#107—171no—
411C2×#107—171no—
412C2×#107—171no—
413C2×#107—171no—
414C2×#107—178no—
415C2×#107C2×D1711yescharacteristic
416C2×#107C2×D1711yescharacteristic
417C2×#106—171no—
418C2×#106—171no—
419#424—178no—
420C2×C4⋊C8—171no—
421C2×C4⋊C8—171no—
422C2×C4⋊C8—171no—
423C2×C4⋊C8C2×D1711yescharacteristic
424#417—178no—
425#416—178no—
426C2×#103—171no—
427C2×#103—171no—
428C2×#103C2×D1711yescharacteristic
429C2×#103C2×D1711yescharacteristic
430C2×#102—171no—
431C2×#102—171no—
432C2×#102—171no—
433C2×#102—171no—
434C2×C17#308314yescomplemented
435C2×C17C22×C22⋊Q811yescharacteristic
436C2×C17C2×#57611yescharacteristic
437C2×C17C2×#57811yescharacteristic
438D17—24no—
439D17—44no—
440C2×#41—178no—
441C2×#41—174no—
442C2×#41—342no—
443C2×#41—344no—
444C22×Q8—21no—
445C22×Q8—341no—
446C22×Q8C22×D1711yescharacteristic
447C22×D4—171no—
448C22×D4—341no—
449C23×C4—171no—
450C23×C4—341no—
451C23×C4—341no—
452C23×C4—341no—
453C23×C4—341no—
454C23×C4—341no—
455C2×M16—174no—
456C2×M16—344no—
457C22×C8—171no—
458C22×C8—171no—
459C22×C8—174no—
460C22×C8—344no—
461C22×C8C22×D1711yescharacteristic
462C22×C8C22×D1711yescharacteristic
463C4⋊Q8—22no—
464C4⋊Q8—174no—
465C4⋊Q8—342no—
466C4⋊Q8—348no—
467C4⋊Q8C22×D1714yes—
468#125—174no—
469#125—174no—
470#125—342no—
471#125—348no—
472#125—342no—
473C22⋊Q8—348no—
474C22⋊Q8—348no—
475C4×Q8—22no—
476C4×Q8—174no—
477C4×Q8—342no—
478C4×Q8C22×D1714yes—
479C4×D4—174no—
480C4×D4—174no—
481C4×D4—348no—
482C4×D4—342no—
483C4×D4—348no—
484C4×D4—342no—
485#117—174no—
486#117—174no—
487#117—174no—
488#117—348no—
489#117—342no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—171no—
493C2×C4⋊C4—171no—
494C2×C4⋊C4—171no—
495C2×C4⋊C4—171no—
496C2×C4⋊C4—171no—
497C2×C4⋊C4—174no—
498C2×C4⋊C4—174no—
499C2×C4⋊C4—348no—
500C2×C4⋊C4—342no—
501C2×C4⋊C4—342no—
502C2×C4⋊C4—341no—
503C2×C4⋊C4—341no—
504C2×C4⋊C4—341no—
505C2×C4⋊C4—341no—
506C2×C4⋊C4—341no—
507C2×C4⋊C4—341no—
508C2×C4⋊C4—341no—
509C2×C4⋊C4—341no—
510C2×C4⋊C4C22×D1711yescharacteristic
511C2×C4⋊C4C22×D1711yescharacteristic
512C2×C4⋊C4C22×D1711yescharacteristic
513C2×C22⋊C4—171no—
514C2×C22⋊C4—171no—
515C2×C22⋊C4—341no—
516C2×C22⋊C4—341no—
517C2×C22⋊C4—341no—
518C2×C42—21no—
519C2×C42—171no—
520C2×C42—341no—
521C2×C42—341no—
522C2×C42C22×D1711yescharacteristic
523#107—174no—
524#107—174no—
525#107—174no—
526#107—174no—
527#107C22×D1714yes—
528#107C22×D1714yes—
529#106—174no—
530#106—174no—
531C4⋊C8—174no—
532C4⋊C8—174no—
533C4⋊C8—174no—
534C4⋊C8C22×D1714yes—
535#103—174no—
536#103—174no—
537#103C22×D1714yes—
538#103C22×D1714yes—
539#102—174no—
540#102—174no—
541#102—174no—
542#102—174no—
543C17C2×#308311yescharacteristic, complemented, Sylow
544C24—171no—
545C24—341no—
546#41—1716no—
547#41—3416no—
548#41—348no—
549C2×Q8—21no—
550C2×Q8—24no—
551C2×Q8—22no—
552C2×Q8—82no—
553C2×Q8—344no—
554C2×Q8—1362no—
555C2×Q8Q8×D1714yes—
556C2×Q8C23×D1712yes—
557C2×D4—174no—
558C2×D4—172no—
559C2×D4—344no—
560C2×D4—348no—
561C2×D4—341no—
562C2×D4—342no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—171no—
568C22×C4—172no—
569C22×C4—174no—
570C22×C4—174no—
571C22×C4—172no—
572C22×C4—171no—
573C22×C4—171no—
574C22×C4—344no—
575C22×C4—348no—
576C22×C4—344no—
577C22×C4—344no—
578C22×C4—344no—
579C22×C4—341no—
580C22×C4—341no—
581C22×C4—341no—
582C22×C4—344no—
583C22×C4—1362no—
584C22×C4—1362no—
585C22×C4—1362no—
586C22×C4—1362no—
587C22×C4D4×D1711yescharacteristic
588C22×C4D4×D1711yescharacteristic
589C22×C4C23×D1711yescharacteristic
590M16—348no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—172no—
594C2×C8—172no—
595C2×C8—348no—
596C2×C8—342no—
597C2×C8—342no—
598C2×C8C23×D1712yes—
599C2×C8C23×D1712yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—174no—
606C4⋊C4—174no—
607C4⋊C4—172no—
608C4⋊C4—172no—
609C4⋊C4—172no—
610C4⋊C4—344no—
611C4⋊C4—344no—
612C4⋊C4—344no—
613C4⋊C4—344no—
614C4⋊C4—344no—
615C4⋊C4—344no—
616C4⋊C4—341no—
617C4⋊C4—341no—
618C4⋊C4—341no—
619C4⋊C4—344no—
620C4⋊C4—344no—
621C4⋊C4C23×D1712yes—
622C4⋊C4C23×D1712yes—
623C4⋊C4C23×D1712yes—
624C22⋊C4—174no—
625C22⋊C4—174no—
626C22⋊C4—344no—
627C22⋊C4—344no—
628C22⋊C4—344no—
629C42—24no—
630C42—172no—
631C42—172no—
632C42—344no—
633C42—344no—
634C42D4×D1712yes—
635C42C23×D1712yes—
636C23—174no—
637C23—172no—
638C23—342no—
639C23—342no—
640C23—344no—
641C23—342no—
642C23—682no—
643C23—682no—
644C23C2×D4×D1711yescharacteristic
645Q8—24no—
646Q8—22no—
647Q8—84no—
648Q8—1364no—
649Q8C2×Q8×D1714yes—
650D4—174no—
651D4—3416no—
652D4—344no—
653D4—342no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—174no—
665C2×C4—172no—
666C2×C4—178no—
667C2×C4—174no—
668C2×C4—174no—
669C2×C4—172no—
670C2×C4—172no—
671C2×C4—3416no—
672C2×C4—342no—
673C2×C4—342no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—342no—
677C2×C4—682no—
678C2×C4—682no—
679C2×C4—682no—
680C2×C4—1364no—
681C2×C4—1364no—
682C2×C4—1364no—
683C2×C4—1364no—
684C2×C4C2×D4×D1712yes—
685C2×C4C2×D4×D1712yes—
686C2×C4C2×D4×D1711yescharacteristic
687C2×C4C2×Q8×D1712yes—
688C2×C4#41×D1712yes—
689C2×C4C24×D1711yescharacteristic
690C8—22no—
691C8—22no—
692C8—342no—
693C8—342no—
694C22—174no—
695C22—348no—
696C22—342no—
697C22—342no—
698C22—344no—
699C22—688no—
700C22—682no—
701C22—682no—
702C22C22⋊Q8×D1712yes—
703C22#1176361312yes—
704C22#1176362212yes—
705C22C22×D4×D1711yescharacteristic
706C4—22no—
707C4—24no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—174no—
713C4—342no—
714C4—342no—
715C4—682no—
716C4—682no—
717C4—682no—
718C4C22⋊Q8×D1712yes—
719C4C22×Q8×D1711yescharacteristic
720C4C2×#41×D1711yescharacteristic
721C2—344no—
722C2—684no—
723C2#1453863214yesdirect product factor
724C2C2×C22⋊Q8×D1711yescharacteristic
725C2C2×#1176361311yescharacteristic
726C2C2×#1176362211yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#477C2
socleC23×C17C22×D4
prime radicalC22×#63256C22
hypercenterC2×#477D17
hypocenterC17C2×#3083
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#11763436C2semidirect
3. #14538632C2direct (N × H)
4. C2×#11763116C2semidirect
5. C2×#11763114C2semidirect
6. C2×#11763102C2semidirect
7. C2×#11763112C2semidirect
8. C2×#11763110C2semidirect
9. C2×#11763088C2semidirect
10. C2×#11763086C2semidirect
11. C2×#11762850C2semidirect
12. C2×#107×D17C2semidirect
13. C2×#11762834C2semidirect
16. C2×C17×#477C2semidirect
21. #11763436C22semidirect
42. #11763116C22semidirect
43. #11763114C22semidirect
44. #11763112C22semidirect
45. #11763110C22semidirect
46. #11763102C22semidirect
47. #11763088C22semidirect
48. #11763086C22semidirect
49. #11762850C22semidirect
54. #107×D17C22semidirect
57. #11762834C22semidirect
71. C17×#477C22semidirect
81. C2×#63256Q8semidirect
203. #63256C2×Q8semidirect
337. C2×#477D17semidirect
406. #477C2×D17semidirect
434. C2×C17#3083semidirect
543. C17C2×#3083semidirect
723. C2#14538632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634362
C2×#117632912
#145386322
C2×#117631162
C2×#117631142
C2×#117631022
C2×#117631122
C2×#117631102
C2×#117630882
C2×#117630862
C2×#117628502
C2×#107×D172
C2×#117628342
C2×#117628092
C2×#117628042
C2×C17×#4772
C2×#308317