Finite Group Databasebeta

← C2×#14540212 #17907252

Subgroups — C2×#14540212 #17907252

Order 4352.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763430C211yesmaximal, characteristic
2C2×#11763421C211yesmaximal, characteristic, complemented
3#14540212C2116yesmaximal, direct product factor
4C2×#11763117C211yesmaximal, characteristic, complemented
5C2×#11763105C211yesmaximal, characteristic, complemented
6C2×#11763095C211yesmaximal, characteristic, complemented
7C2×#11763110C211yesmaximal, characteristic, complemented
8C2×#11763067C211yesmaximal, characteristic, complemented
9C2×#11763055C211yesmaximal, characteristic
10C2×#11763050C211yesmaximal, characteristic, complemented
11C2×#11763038C211yesmaximal, characteristic
12C2×#11763032C211yesmaximal, characteristic, complemented
13C2×#11763032C211yesmaximal, characteristic, complemented
14C2×#11763020C211yesmaximal, characteristic, complemented
15C2×#11763015C211yesmaximal, characteristic, complemented
16C2×C17×#424C211yesmaximal, characteristic, complemented
17C22×Dic68C2211yescharacteristic
18C22×Dic68C2211yescharacteristic
19C22×#63219C2211yescharacteristic
20C22×#63219C2211yescharacteristic
21#11763430—24no—
22#11763430C2218yes—
23#11763421—24no—
24#11763421C2218yescomplemented
25C2×#10587555C2211yescharacteristic
26C2×#10587555C2211yescharacteristic
27C2×#10587584—21no—
28C2×#10587565—21no—
29C2×#10587565—21no—
30C2×#10587556C2211yescharacteristic
31C2×#10587575—21no—
32C2×#10587575—21no—
33C2×#10587561C2211yescharacteristic
34C2×#10587571—21no—
35C2×#10587569—21no—
36C2×#10587610C2211yescharacteristic
37C2×#10587610C2211yescharacteristic
38C2×#10587610C2211yescharacteristic
39C2×#10587582—21no—
40C2×#10587616C2211yescharacteristic
41C2×C4×Dic34C2211yescharacteristic
42C2×C4×Dic34C2211yescharacteristic
43C2×C4×Dic34C2211yescharacteristic
44C2×C4×D68C2211yescharacteristic
45#11763117C2218yescomplemented
46#11763110C2218yescomplemented
47#11763105C2218yescomplemented
48#11763095C2218yescomplemented
49#11763067C2218yescomplemented
50#11763055C2218yes—
51#11763050C2218yescomplemented
52#11763038C2218yes—
53#11763032C2218yescomplemented
54#11763032C2218yescomplemented
55#11763020C2218yescomplemented
56#11763015C2218yescomplemented
57C2×#10587489C2211yescharacteristic
58C2×#10587489C2211yescharacteristic
59C2×#10587488C2211yescharacteristic
60C2×#10587488C2211yescharacteristic
61C2×#10587487C2211yescharacteristic
62C2×#10587487C2211yescharacteristic
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587487C2211yescharacteristic
66C2×#10587487C2211yescharacteristic
67C2×#10587492C2211yescharacteristic
68C2×#10587492C2211yescharacteristic
69C22×M16×C17C2211yescharacteristic
70C23×C8×C17C2211yescharacteristic
71C2×C17×#117C2211yescharacteristic
72C17×#424C2218yescomplemented
73C2×C17×C4⋊C8C2211yescharacteristic
74C2×C17×C4⋊C8C2211yescharacteristic
75C2×C17×C4⋊C8C2211yescharacteristic
76C2×C17×C4⋊C8C2211yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C22×C22⋊D17—21no—
79C22×D68C2311yescharacteristic
80C22×C4×D17—21no—
81C22×Dic34—21no—
82C22×Dic34C2311yescharacteristic
83C22×Dic34C2311yescharacteristic
84C22×Dic34C2311yescharacteristic
85C2×M16×C17—42no—
86C2×M16×C17C2314yes—
87C22×C8×C17—42no—
88C22×C8×C17C2311yescharacteristic
89C22×C8×C17C2311yescharacteristic
90C22×C8×C17C2311yescharacteristic
91C22×C8×C17C2311yescharacteristic
92C22×C8×C17C2314yes—
93C17×#117D414yes—
94C17×#117C2314yes—
95C2×C4⋊C4×C17D411yescharacteristic
96C2×C4⋊C4×C17D411yescharacteristic
97C2×C22⋊C4×C17D411yescharacteristic
98C2×C22⋊C4×C17D411yescharacteristic
99C2×C42×C17C2311yescharacteristic
100C2×C42×C17C2311yescharacteristic
101C2×C22⋊Dic17—21no—
102C2×C22⋊Dic17—21no—
103C2×C22⋊Dic17—21no—
104#10587616—22no—
105#10587616C2314yes—
106C2×#63227—21no—
107C2×#63227—21no—
108C2×#63227—21no—
109C2×#63227—21no—
110C2×C4⋊Dic17—21no—
111C2×C4⋊Dic17—21no—
112C2×C4⋊Dic17—21no—
113C2×C4⋊Dic17C2311yescharacteristic
114C2×C4⋊Dic17C2311yescharacteristic
115C2×C4⋊Dic17C2311yescharacteristic
116C2×C4⋊Dic17C2311yescharacteristic
117#10587610—22no—
118#10587610—22no—
119#10587610—22no—
120#10587610C2314yes—
121#10587610C2314yes—
122#10587610C2314yes—
123C2×#63225—21no—
124C2×#63225—21no—
125C2×#63225—21no—
126C2×#63225—21no—
127C2×#63225—21no—
128C2×#63225—21no—
129C2×#63225—21no—
130C2×#63225—21no—
131C2×C4×Dic17—21no—
132C2×C4×Dic17—21no—
133C2×C4×Dic17—21no—
134C2×Dic68—42no—
135C2×Dic68—42no—
136C2×Dic68C2314yes—
137C2×Dic68C2314yes—
138C2×#63219—42no—
139C2×#63219—42no—
140C2×#63219C2314yes—
141C2×#63219C2314yes—
142#10587584—28no—
143#10587582—28no—
144#10587575—28no—
145#10587575—28no—
146#10587571—28no—
147#10587569—28no—
148#10587565—28no—
149#10587565—28no—
150#10587561—22no—
151#10587561C2314yes—
152C4×D68—22no—
153C4×D68C2314yes—
154#10587556—22no—
155#10587556C2314yes—
156#10587555—22no—
157#10587555—22no—
158#10587555C2314yes—
159#10587555C2314yes—
160C4×Dic34—22no—
161C4×Dic34—22no—
162C4×Dic34—22no—
163C4×Dic34C2314yes—
164C4×Dic34C2314yes—
165C4×Dic34C2314yes—
166C17×C4⋊C8C2314yes—
167C17×C4⋊C8C2314yes—
168C17×C4⋊C8C2314yes—
169C17×C4⋊C8C2314yes—
170#10587492C2314yes—
171#10587492C2314yes—
172#10587489C2314yes—
173#10587489C2314yes—
174#10587488C2314yes—
175#10587488C2314yes—
176#10587487C2314yes—
177#10587487C2314yes—
178#10587487C2314yes—
179#10587487C2314yes—
180#10587487C2314yes—
181#10587487C2314yes—
182C24×C17C2×D411yescharacteristic
183C23×D17—21no—
184C22×C4×C17—22no—
185C22×C4×C17—22no—
186C22×C4×C17C2×D411yescharacteristic
187C22×C4×C17C2×D411yescharacteristic
188C22×C4×C17C2×D411yescharacteristic
189C22×C4×C17C2×D412yes—
190C22×C4×C17C2×D411yescharacteristic
191C22×C4×C17C2×D411yescharacteristic
192C22×C4×C17C2412yes—
193C22×C4×C17C2411yescharacteristic
194C2×C22⋊D17—24no—
195C2×C22⋊D17—82no—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C2×D68—22no—
204C2×D68—22no—
205C2×D68—21no—
206C2×D68C2412yes—
207C2×C4×D17—24no—
208C2×C4×D17—82no—
209C2×Dic34—22no—
210C2×Dic34—22no—
211C2×Dic34—22no—
212C2×Dic34—22no—
213C2×Dic34—22no—
214C2×Dic34—22no—
215C2×Dic34—21no—
216C2×Dic34—21no—
217C2×Dic34—21no—
218C2×Dic34—24no—
219C2×Dic34—82no—
220C2×Dic34C2412yes—
221C2×Dic34C2412yes—
222C2×Dic34C2412yes—
223M16×C17—44no—
224C2×C8×C17—22no—
225C2×C8×C17—22no—
226C2×C8×C17—22no—
227C2×C8×C17—22no—
228C2×C8×C17—44no—
229C2×C8×C17C2412yes—
230C2×C8×C17C2412yes—
231C2×C8×C17C2412yes—
232C2×C8×C17C2412yes—
233C4⋊C4×C17C2×D414yes—
234C4⋊C4×C17C2×D414yes—
235C22⋊C4×C17C2×D414yes—
236C22⋊C4×C17C2×D414yes—
237C42×C17C2×D412yes—
238C42×C17C2×D412yes—
239C42×C17C2412yes—
240C42×C17C2412yes—
241C22⋊Dic17—24no—
242C22⋊Dic17—24no—
243C22⋊Dic17—24no—
244#63227—24no—
245#63227—24no—
246#63227—24no—
247#63227—24no—
248C4⋊Dic17—21no—
249C4⋊Dic17—21no—
250C4⋊Dic17—21no—
251C4⋊Dic17—21no—
252C4⋊Dic17—24no—
253C4⋊Dic17—24no—
254C4⋊Dic17—24no—
255C4⋊Dic17C2412yes—
256C4⋊Dic17C2412yes—
257C4⋊Dic17C2412yes—
258C4⋊Dic17C2412yes—
259#63225—24no—
260#63225—24no—
261#63225—24no—
262#63225—24no—
263#63225—24no—
264#63225—24no—
265#63225—24no—
266#63225—24no—
267C4×Dic17—24no—
268C4×Dic17—24no—
269C4×Dic17—24no—
270Dic68—44no—
271Dic68—44no—
272#63219—44no—
273#63219—44no—
274C2×#3258—171nomaximal, Sylow
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—22no—
278C23×C17C22×D412yes—
279C23×C17C22×D411yescharacteristic
280C22×D17—22no—
281C22×D17—42no—
282C22×D17—42no—
283C22×D17—42no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—24no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17C22×D412yes—
293C2×C4×C17C22×D412yes—
294C2×C4×C17C22×D412yes—
295C2×C4×C17C22×D412yes—
296C2×C4×C17C22×D412yes—
297C2×C4×C17C22×D411yescharacteristic
298C2×C4×C17H(5,𝔽2)12yes—
299C2×C4×C172−1+412yes—
300C2×C4×C17C2511yescharacteristic
301C22⋊D17—84no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—42no—
310C2×Dic17—42no—
311C2×Dic17—42no—
312C2×Dic17—42no—
313C2×Dic17—42no—
314C2×Dic17—42no—
315C2×Dic17—42no—
316D68—22no—
317D68—22no—
318D68—42no—
319C4×D17—84no—
320Dic34—22no—
321Dic34—22no—
322Dic34—22no—
323Dic34—22no—
324Dic34—22no—
325Dic34—22no—
326Dic34—42no—
327Dic34—42no—
328Dic34—42no—
329Dic34—84no—
330C8×C17—22no—
331C8×C17—22no—
332C8×C17—22no—
333C8×C17—22no—
334C2×#542—171no—
335C2×#541—171no—
336#3258—1716no—
337C2×#479—171no—
338C2×#477—171no—
339C2×#475—171no—
340C2×#478—171no—
341C2×#470—171no—
342C2×#468—171no—
343C2×#467—171no—
344C2×#465—171no—
345C2×#464—171no—
346C2×#464—171no—
347C2×#462—171no—
348C2×#461—171no—
349C2×#424D1711yescharacteristic, complemented
350C22×C17—22no—
351C22×C17—22no—
352C22×C17—22no—
353C22×C17—44no—
354C22×C17#53712yes—
355C22×C17#57712yes—
356C22×C17#57812yes—
357C22×C17C23×D411yescharacteristic
358C2×D17—42no—
359C2×D17—42no—
360C2×D17—42no—
361C2×D17—84no—
362C4×C17—22no—
363C4×C17—22no—
364C4×C17—22no—
365C4×C17—22no—
366C4×C17—22no—
367C4×C17#53712yes—
368C4×C17C2×H(5,𝔽2)11yescharacteristic
369C4×C17C2×2−1+411yescharacteristic
370Dic17—42no—
371Dic17—42no—
372Dic17—42no—
373Dic17—42no—
374Dic17—42no—
375Dic17—42no—
376Dic17—42no—
377C22×Q16—171no—
378C22×Q16—171no—
379C22×SD16—171no—
380C22×SD16—171no—
381C22×M16C2×D1711yescharacteristic
382C23×C8C2×D1711yescharacteristic
383#542—178no—
384#542—344no—
385#541—178no—
386#541—344no—
387C2×C4⋊Q8—171no—
388C2×C4⋊Q8—171no—
389C2×#126—341no—
390C2×#126—341no—
391C2×#126—341no—
392C2×#125—171no—
393C2×#125—341no—
394C2×#125—341no—
395C2×#124—171no—
396C2×#124—341no—
397C2×#123—341no—
398C2×C22⋊Q8—171no—
399C2×C22⋊Q8—171no—
400C2×C22⋊Q8—171no—
401C2×C22⋊Q8—341no—
402C2×#121—171no—
403C2×C4×Q8—171no—
404C2×C4×Q8—171no—
405C2×C4×Q8—171no—
406C2×C4×D4—171no—
407C2×#117C2×D1711yescharacteristic
408#479—178no—
409#478—178no—
410#477—178no—
411#475—178no—
412#470—178no—
413#468—178no—
414#467—178no—
415#465—178no—
416#464—178no—
417#464—178no—
418#462—178no—
419#461—178no—
420C2×#107—171no—
421C2×#107—171no—
422C2×#106—171no—
423C2×#106—171no—
424#424C2×D1718yescomplemented
425C2×C4⋊C8C2×D1711yescharacteristic
426C2×C4⋊C8C2×D1711yescharacteristic
427C2×C4⋊C8C2×D1711yescharacteristic
428C2×C4⋊C8C2×D1711yescharacteristic
429C2×#103—171no—
430C2×#103—171no—
431C2×#103—171no—
432C2×#103—171no—
433C2×#103—171no—
434C2×#103—171no—
435C2×#102—171no—
436C2×#102—171no—
437C2×C17—42no—
438C2×C17#325814yescomplemented
439C2×C17C2×#53711yescharacteristic
440C2×C17C2×#57711yescharacteristic
441C2×C17C2×#57811yescharacteristic
442D17—82no—
443C22×Q8—171no—
444C22×Q8—171no—
445C22×Q8—171no—
446C22×Q8—341no—
447C22×D4—171no—
448C22×D4—341no—
449C23×C4—341no—
450C23×C4C22×D1711yescharacteristic
451C2×Q16—174no—
452C2×Q16—174no—
453C2×Q16—682no—
454C2×Q16—682no—
455C2×SD16—174no—
456C2×SD16—174no—
457C2×SD16—682no—
458C2×SD16—682no—
459C2×M16—42no—
460C2×M16C22×D1714yes—
461C22×C8—42no—
462C22×C8C22×D1711yescharacteristic
463C22×C8C22×D1711yescharacteristic
464C22×C8C22×D1711yescharacteristic
465C22×C8C22×D1711yescharacteristic
466C22×C8C22×D1714yes—
467C4⋊Q8—174no—
468C4⋊Q8—174no—
469C4⋊Q8—342no—
470C4⋊Q8—342no—
471#126—348no—
472#126—348no—
473#126—348no—
474#125—174no—
475#125—348no—
476#125—348no—
477#125—342no—
478#124—174no—
479#124—348no—
480#124—342no—
481#123—348no—
482C22⋊Q8—174no—
483C22⋊Q8—174no—
484C22⋊Q8—174no—
485C22⋊Q8—342no—
486C22⋊Q8—342no—
487C22⋊Q8—342no—
488C22⋊Q8—348no—
489#121—174no—
490#121—342no—
491C4×Q8—174no—
492C4×Q8—174no—
493C4×Q8—174no—
494C4×Q8—342no—
495C4×Q8—342no—
496C4×Q8—342no—
497C4×D4—174no—
498C4×D4—342no—
499#117D6814yes—
500#117C22×D1714yes—
501C2×C4⋊C4—171no—
502C2×C4⋊C4—171no—
503C2×C4⋊C4—171no—
504C2×C4⋊C4—171no—
505C2×C4⋊C4—341no—
506C2×C4⋊C4—341no—
507C2×C4⋊C4—341no—
508C2×C4⋊C4—341no—
509C2×C4⋊C4—341no—
510C2×C4⋊C4—341no—
511C2×C4⋊C4—341no—
512C2×C4⋊C4—341no—
513C2×C4⋊C4—341no—
514C2×C4⋊C4—341no—
515C2×C4⋊C4—341no—
516C2×C4⋊C4D6811yescharacteristic
517C2×C4⋊C4D6811yescharacteristic
518C2×C22⋊C4—341no—
519C2×C22⋊C4—341no—
520C2×C22⋊C4—341no—
521C2×C22⋊C4—341no—
522C2×C22⋊C4—341no—
523C2×C22⋊C4—341no—
524C2×C22⋊C4—341no—
525C2×C22⋊C4D6811yescharacteristic
526C2×C22⋊C4D6811yescharacteristic
527C2×C42—341no—
528C2×C42—341no—
529C2×C42—341no—
530C2×C42C22×D1711yescharacteristic
531C2×C42C22×D1711yescharacteristic
532#107—174no—
533#107—174no—
534#106—174no—
535#106—174no—
536C4⋊C8C22×D1714yes—
537C4⋊C8C22×D1714yes—
538C4⋊C8C22×D1714yes—
539C4⋊C8C22×D1714yes—
540#103—174no—
541#103—174no—
542#103—174no—
543#103—174no—
544#103—174no—
545#103—174no—
546#102—174no—
547#102—174no—
548C17C2×#325811yescharacteristic, complemented, Sylow
549C24—341no—
550C24C2×D6811yescharacteristic
551C2×Q8—172no—
552C2×Q8—172no—
553C2×Q8—172no—
554C2×Q8—341no—
555C2×Q8—341no—
556C2×Q8—341no—
557C2×Q8—344no—
558C2×Q8—342no—
559C2×Q8—342no—
560C2×Q8—342no—
561C2×Q8—342no—
562C2×Q8—342no—
563C2×Q8—342no—
564C2×Q8—1362no—
565C2×D4—172no—
566C2×D4—344no—
567C2×D4—341no—
568C2×D4—342no—
569C2×D4—342no—
570C2×D4—1362no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—341no—
576C22×C4—341no—
577C22×C4—341no—
578C22×C4—341no—
579C22×C4—341no—
580C22×C4—344no—
581C22×C4—1362no—
582C22×C4C2×D6812yes—
583C22×C4C2×D6811yescharacteristic
584C22×C4C2×D6811yescharacteristic
585C22×C4C2×D6811yescharacteristic
586C22×C4C2×D6811yescharacteristic
587C22×C4C2×D6811yescharacteristic
588C22×C4C23×D1712yes—
589C22×C4C23×D1711yescharacteristic
590Q16—684no—
591Q16—684no—
592SD16—684no—
593SD16—684no—
594M16—44no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—44no—
600C2×C8C23×D1712yes—
601C2×C8C23×D1712yes—
602C2×C8C23×D1712yes—
603C2×C8C23×D1712yes—
604C4⋊C4—172no—
605C4⋊C4—172no—
606C4⋊C4—172no—
607C4⋊C4—172no—
608C4⋊C4—341no—
609C4⋊C4—341no—
610C4⋊C4—341no—
611C4⋊C4—341no—
612C4⋊C4—344no—
613C4⋊C4—344no—
614C4⋊C4—344no—
615C4⋊C4—344no—
616C4⋊C4—344no—
617C4⋊C4—344no—
618C4⋊C4—344no—
619C4⋊C4—344no—
620C4⋊C4—344no—
621C4⋊C4—344no—
622C4⋊C4—344no—
623C4⋊C4C2×D6814yes—
624C4⋊C4C2×D6814yes—
625C22⋊C4—344no—
626C22⋊C4—344no—
627C22⋊C4—344no—
628C22⋊C4—344no—
629C22⋊C4—344no—
630C22⋊C4—344no—
631C22⋊C4—344no—
632C22⋊C4C2×D6814yes—
633C22⋊C4C2×D6814yes—
634C42—344no—
635C42—344no—
636C42—344no—
637C42C2×D6812yes—
638C42C2×D6812yes—
639C42C23×D1712yes—
640C42C23×D1712yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—342no—
645C23—682no—
646C23—682no—
647C23—682no—
648C23C22×D6812yes—
649C23C22×D6811yescharacteristic
650Q8—342no—
651Q8—342no—
652Q8—342no—
653Q8—342no—
654Q8—342no—
655Q8—342no—
656Q8—682no—
657Q8—682no—
658Q8—682no—
659Q8—1364no—
660D4—342no—
661D4—342no—
662D4—682no—
663D4—1364no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—342no—
673C2×C4—342no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—342no—
677C2×C4—342no—
678C2×C4—342no—
679C2×C4—682no—
680C2×C4—682no—
681C2×C4—682no—
682C2×C4—682no—
683C2×C4—682no—
684C2×C4—682no—
685C2×C4—682no—
686C2×C4—1364no—
687C2×C4C22×D6812yes—
688C2×C4C22×D6812yes—
689C2×C4C22×D6812yes—
690C2×C4C22×D6812yes—
691C2×C4C22×D6812yes—
692C2×C4C22×D6811yescharacteristic
693C2×C4#1058769112yes—
694C2×C4#1058769412yes—
695C2×C4C24×D1711yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—682no—
705C22—682no—
706C22—682no—
707C22—1364no—
708C22#1176339012yes—
709C22#1176362112yes—
710C22#1176362612yes—
711C22C23×D6811yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—682no—
718C4—682no—
719C4—682no—
720C4—682no—
721C4—682no—
722C4—682no—
723C4—682no—
724C4#1176339012yes—
725C4C2×#1058769111yescharacteristic
726C4C2×#1058769411yescharacteristic
727C2—42no—
728C2—1362no—
729C2#1454021214yesdirect product factor
730C2C2×#1176339011yescharacteristic
731C2C2×#1176362111yescharacteristic
732C2C2×#1176362611yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#424C2
socleC23×C17C22×D4
prime radicalC2×#10587616C22
hypercenterC2×#424D17
hypocenterC17C2×#3258
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. C2×#11763421C2semidirect
3. #14540212C2direct (N × H)
4. C2×#11763117C2semidirect
5. C2×#11763105C2semidirect
6. C2×#11763095C2semidirect
7. C2×#11763110C2semidirect
8. C2×#11763067C2semidirect
10. C2×#11763050C2semidirect
12. C2×#11763032C2semidirect
13. C2×#11763032C2semidirect
14. C2×#11763020C2semidirect
15. C2×#11763015C2semidirect
16. C2×C17×#424C2semidirect
24. #11763421C22semidirect
45. #11763117C22semidirect
46. #11763110C22semidirect
47. #11763105C22semidirect
48. #11763095C22semidirect
49. #11763067C22semidirect
51. #11763050C22semidirect
53. #11763032C22semidirect
54. #11763032C22semidirect
55. #11763020C22semidirect
56. #11763015C22semidirect
72. C17×#424C22semidirect
349. C2×#424D17semidirect
424. #424C2×D17semidirect
438. C2×C17#3258semidirect
548. C17C2×#3258semidirect
729. C2#14540212direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634302
C2×#117634212
#145402122
C2×#117631172
C2×#117631052
C2×#117630952
C2×#117631102
C2×#117630672
C2×#117630552
C2×#117630502
C2×#117630382
C2×#117630322
C2×#117630202
C2×#117630152
C2×C17×#4242
C2×#325817