Finite Group Databasebeta

← C2×#22571509 #31728070

Subgroups — C2×#22571509 #31728070

Order 17152.

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×#16864024C211yesmaximal, characteristic, complemented
2C2×#16864017C211yesmaximal, characteristic
3#22571509C2116yesmaximal, direct product factor
4C2×#16863805C211yesmaximal, characteristic, complemented
5C2×#16863794C211yesmaximal, characteristic, complemented
6C2×#16863756C211yesmaximal, characteristic, complemented
7C2×#16863751C211yesmaximal, characteristic, complemented
8C2×#16863715C211yesmaximal, characteristic
9C2×#16863738C211yesmaximal, characteristic, complemented
10C2×#16863721C211yesmaximal, characteristic
11C2×#16863727C211yesmaximal, characteristic, complemented
12C2×#16863704C211yesmaximal, characteristic, complemented
13C2×#16863682C211yesmaximal, characteristic, complemented
14C2×#16863697C211yesmaximal, characteristic, complemented
15C2×#16863687C211yesmaximal, characteristic, complemented
16C2×#433×C67C211yesmaximal, characteristic, complemented
17#16864024—24no—
18#16864024C2218yescomplemented
19#16864017—24no—
20#16864017C2218yes—
21C2×#14524043C2211yescharacteristic
22C2×#14524043C2211yescharacteristic
23C2×#14524043C2211yescharacteristic
24C2×#14524042—21no—
25C2×#14524038—21no—
26C2×#14524035C2211yescharacteristic
27C2×#14524035C2211yescharacteristic
28C2×#14524034—21no—
29C2×#14524031C2211yescharacteristic
30C2×#14524029—21no—
31C2×#14524025—21no—
32C2×#14524022C2211yescharacteristic
33C2×#14524021—21no—
34C2×#14524020—21no—
35C2×#14524020—21no—
36C2×#14524017C2211yescharacteristic
37C2×C4×Dic134C2211yescharacteristic
38C2×C4×D268C2211yescharacteristic
39C2×#14524002C2211yescharacteristic
40C22×C4⋊Dic67C2211yescharacteristic
41#16863805C2218yescomplemented
42#16863794C2218yescomplemented
43#16863756C2218yescomplemented
44#16863751C2218yescomplemented
45#16863738C2218yescomplemented
46#16863727C2218yescomplemented
47#16863721C2218yes—
48#16863715C2218yes—
49#16863704C2218yescomplemented
50#16863697C2218yescomplemented
51#16863687C2218yescomplemented
52#16863682C2218yescomplemented
53C2×#14523977C2211yescharacteristic
54C2×#14523977C2211yescharacteristic
55C2×#14523975C2211yescharacteristic
56C2×#14523975C2211yescharacteristic
57C2×#14523975C2211yescharacteristic
58C2×#14523975C2211yescharacteristic
59C2×#14523975C2211yescharacteristic
60C2×#14523975C2211yescharacteristic
61C2×#14523968C2211yescharacteristic
62C2×#14523968C2211yescharacteristic
63C2×#14523968C2211yescharacteristic
64C2×#14523968C2211yescharacteristic
65C2×#14523965C2211yescharacteristic
66C2×#14523965C2211yescharacteristic
67C2×#14523965C2211yescharacteristic
68C2×#14523965C2211yescharacteristic
69C2×#117×C67C2211yescharacteristic
70#433×C67C2218yescomplemented
71C2×C4⋊C8×C67C2211yescharacteristic
72C2×C4⋊C8×C67C2211yescharacteristic
73C2×C22⋊C8×C67C2211yescharacteristic
74C2×C22⋊C8×C67C2211yescharacteristic
75C2×#97×C67C2211yescharacteristic
76C2×C4×C8×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134—21no—
79C22×Dic134—21no—
80C22×Dic134C2311yescharacteristic
81C22×D268C2311yescharacteristic
82C22×C22⋊D67—21no—
83C23×Dic67—21no—
84C22×C4×D67—21no—
85#14524043—22no—
86#14524043—22no—
87#14524043—22no—
88#14524043C2314yes—
89#14524043C2314yes—
90#14524043C2314yes—
91#14524042—28no—
92#14524038—28no—
93#14524035—22no—
94#14524035—22no—
95#14524035C2314yes—
96#14524035C2314yes—
97#14524034—28no—
98#14524031—22no—
99#14524031C2314yes—
100#14524029—28no—
101#14524025—28no—
102#14524022—22no—
103#14524022C2314yes—
104#14524021—28no—
105#14524020—28no—
106#14524020—28no—
107#14524017—22no—
108#14524017C2314yes—
109C4×Dic134—22no—
110C4×Dic134C2314yes—
111C4×D268—22no—
112C4×D268C2314yes—
113#14524002—22no—
114#14524002C2314yes—
115C2×C4⋊Dic67—22no—
116C2×C4⋊Dic67—21no—
117C2×C4⋊Dic67—21no—
118C2×C4⋊Dic67—21no—
119C2×C4⋊Dic67—21no—
120C2×C4⋊Dic67C2314yes—
121C2×C4⋊Dic67C2311yescharacteristic
122C2×C4⋊Dic67C2311yescharacteristic
123C2×C4⋊Dic67C2311yescharacteristic
124C2×C4⋊Dic67C2311yescharacteristic
125C2×C4⋊Dic67C2311yescharacteristic
126C2×C4⋊Dic67C2311yescharacteristic
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C2×Dic67⋊C4—21no—
130C2×Dic67⋊C4—21no—
131C2×Dic67⋊C4—21no—
132C2×Dic67⋊C4—21no—
133C2×C22⋊Dic67—21no—
134C2×C22⋊Dic67—21no—
135C2×(C2×D67)⋊C4—21no—
136C2×(C2×D67)⋊C4—21no—
137C2×(C2×D67)⋊C4—21no—
138C2×(C2×D67)⋊C4—21no—
139C2×C4×Dic67—21no—
140C2×C4×Dic67—21no—
141#14523977C2314yes—
142#14523977C2314yes—
143#14523975C2314yes—
144#14523975C2314yes—
145#14523975C2314yes—
146#14523975C2314yes—
147#14523975C2314yes—
148#14523975C2314yes—
149#14523968C2314yes—
150#14523968C2314yes—
151#14523968C2314yes—
152#14523968C2314yes—
153#14523965C2314yes—
154#14523965C2314yes—
155#14523965C2314yes—
156#14523965C2314yes—
157C23×C4×C67C2311yescharacteristic
158C22×C8×C67C2311yescharacteristic
159C22×C8×C67C2311yescharacteristic
160C22×C8×C67C2311yescharacteristic
161C22×C8×C67C2311yescharacteristic
162#117×C67D414yes—
163#117×C67C2314yes—
164C2×C4⋊C4×C67D411yescharacteristic
165C2×C4⋊C4×C67D411yescharacteristic
166C2×C22⋊C4×C67D411yescharacteristic
167C2×C22⋊C4×C67D411yescharacteristic
168C2×C42×C67C2311yescharacteristic
169C2×C42×C67C2311yescharacteristic
170C4⋊C8×C67C2314yes—
171C4⋊C8×C67C2314yes—
172C22⋊C8×C67C2314yes—
173C22⋊C8×C67C2314yes—
174#97×C67C2314yes—
175C4×C8×C67C2314yes—
176C23×D67—21no—
177C2×Dic134—22no—
178C2×Dic134—22no—
179C2×Dic134—21no—
180C2×Dic134—24no—
181C2×Dic134—24no—
182C2×Dic134—24no—
183C2×Dic134—82no—
184C2×Dic134—82no—
185C2×Dic134—82no—
186C2×Dic134C2412yes—
187C2×D268—22no—
188C2×D268—22no—
189C2×D268—21no—
190C2×D268C2412yes—
191C2×C22⋊D67—24no—
192C2×C22⋊D67—82no—
193C22×Dic67—21no—
194C22×Dic67—21no—
195C22×Dic67—21no—
196C22×Dic67—21no—
197C22×Dic67—21no—
198C22×Dic67—21no—
199C22×Dic67—21no—
200C22×Dic67—24no—
201C22×Dic67—82no—
202C2×C4×D67—24no—
203C2×C4×D67—82no—
204C4⋊Dic67—24no—
205C4⋊Dic67—21no—
206C4⋊Dic67—21no—
207C4⋊Dic67—24no—
208C4⋊Dic67—24no—
209C4⋊Dic67—24no—
210C4⋊Dic67—21no—
211C4⋊Dic67—21no—
212C4⋊Dic67—21no—
213C4⋊Dic67—21no—
214C4⋊Dic67C2412yes—
215C4⋊Dic67C2412yes—
216C4⋊Dic67C2412yes—
217C4⋊Dic67C2412yes—
218C4⋊Dic67C2412yes—
219C4⋊Dic67C2412yes—
220Dic67⋊C4—24no—
221Dic67⋊C4—24no—
222Dic67⋊C4—24no—
223Dic67⋊C4—24no—
224Dic67⋊C4—24no—
225Dic67⋊C4—24no—
226C22⋊Dic67—24no—
227C22⋊Dic67—24no—
228(C2×D67)⋊C4—24no—
229(C2×D67)⋊C4—24no—
230(C2×D67)⋊C4—24no—
231(C2×D67)⋊C4—24no—
232C4×Dic67—24no—
233C4×Dic67—24no—
234C24×C67C2×D411yescharacteristic
235C22×C4×C67—22no—
236C22×C4×C67—22no—
237C22×C4×C67C2×D411yescharacteristic
238C22×C4×C67C2×D411yescharacteristic
239C22×C4×C67C2×D411yescharacteristic
240C22×C4×C67C2×D411yescharacteristic
241C22×C4×C67C2×D411yescharacteristic
242C22×C4×C67C2×D412yes—
243C22×C4×C67C2412yes—
244C22×C4×C67C2411yescharacteristic
245C2×C8×C67—22no—
246C2×C8×C67—22no—
247C2×C8×C67—22no—
248C2×C8×C67—22no—
249C2×C8×C67C2412yes—
250C2×C8×C67C2412yes—
251C2×C8×C67C2412yes—
252C2×C8×C67C2412yes—
253C4⋊C4×C67C2×D414yes—
254C4⋊C4×C67C2×D414yes—
255C22⋊C4×C67C2×D414yes—
256C22⋊C4×C67C2×D414yes—
257C42×C67C2×D412yes—
258C42×C67C2×D412yes—
259C42×C67C2412yes—
260C42×C67C2412yes—
261C23×C67—22no—
262C23×C67—22no—
263C23×C67—22no—
264C23×C67C22×D412yes—
265C23×C67C22×D411yescharacteristic
266C22×D67—22no—
267C22×D67—42no—
268C22×D67—42no—
269C22×D67—42no—
270C2×C4×C67—22no—
271C2×C4×C67—22no—
272C2×C4×C67—22no—
273C2×C4×C67—22no—
274C2×C4×C67—22no—
275C2×C4×C67—24no—
276C2×C4×C67—22no—
277C2×C4×C67—22no—
278C2×C4×C67C22×D412yes—
279C2×C4×C67C22×D412yes—
280C2×C4×C67C22×D412yes—
281C2×C4×C67C22×D412yes—
282C2×C4×C67C22×D412yes—
283C2×C4×C67C22×D411yescharacteristic
284C2×C4×C672−1+412yes—
285C2×C4×C672−1+412yes—
286C2×C4×C67C2511yescharacteristic
287C22⋊D67—84no—
288C2×Dic67—22no—
289C2×Dic67—22no—
290C2×Dic67—22no—
291C2×Dic67—22no—
292C2×Dic67—22no—
293C2×Dic67—22no—
294C2×Dic67—22no—
295C2×Dic67—42no—
296C2×Dic67—42no—
297C2×Dic67—42no—
298C2×Dic67—42no—
299C2×Dic67—42no—
300C2×Dic67—42no—
301C2×Dic67—42no—
302C2×Dic67—84no—
303D268—22no—
304D268—22no—
305D268—42no—
306C4×D67—84no—
307Dic134—22no—
308Dic134—22no—
309Dic134—42no—
310Dic134—84no—
311Dic134—84no—
312Dic134—84no—
313C8×C67—22no—
314C8×C67—22no—
315C8×C67—22no—
316C8×C67—22no—
317C22×C67—22no—
318C22×C67—22no—
319C22×C67—22no—
320C22×C67—44no—
321C22×C67#53612yes—
322C22×C67#57712yes—
323C22×C67#57712yes—
324C22×C67C23×D411yescharacteristic
325C2×D67—42no—
326C2×D67—42no—
327C2×D67—42no—
328C2×D67—84no—
329C4×C67—22no—
330C4×C67—22no—
331C4×C67—22no—
332C4×C67—22no—
333C4×C67—22no—
334C4×C67#53612yes—
335C4×C67C2×2−1+411yescharacteristic
336C4×C67C2×2−1+411yescharacteristic
337Dic67—42no—
338Dic67—42no—
339Dic67—42no—
340Dic67—42no—
341Dic67—42no—
342Dic67—42no—
343Dic67—42no—
344C2×#3244—671nomaximal, Sylow
345C2×C67—42no—
346C2×C67#324414yescomplemented
347C2×C67C2×#53611yescharacteristic
348C2×C67C2×#57711yescharacteristic
349C2×C67C2×#57711yescharacteristic
350D67—82no—
351C2×#544—671no—
352C2×#542—671no—
353#3244—6716no—
354C2×#501—671no—
355C2×#498—671no—
356C2×#489—671no—
357C2×#488—671no—
358C2×#481—671no—
359C2×#485—671no—
360C2×#482—671no—
361C2×#483—671no—
362C2×#479—671no—
363C2×#475—671no—
364C2×#478—671no—
365C2×#476—671no—
366C2×#433D6711yescharacteristic, complemented
367C67C2×#324411yescharacteristic, complemented, Sylow
368#544—678no—
369#544—1344no—
370#542—678no—
371#542—1344no—
372C2×C4⋊Q8—671no—
373C2×C4⋊Q8—671no—
374C2×C4⋊Q8—671no—
375C2×C4⋊Q8—1341no—
376C2×#126—1341no—
377C2×#125—671no—
378C2×#125—671no—
379C2×#125—1341no—
380C2×#124—671no—
381C2×#124—1341no—
382C2×#123—1341no—
383C2×C22⋊Q8—671no—
384C2×C22⋊Q8—1341no—
385C2×C22⋊Q8—1341no—
386C2×C22⋊Q8—1341no—
387C2×#121—671no—
388C2×C4×Q8—671no—
389C2×C4×D4—671no—
390C2×#117—671no—
391C2×#117C2×D6711yescharacteristic
392C22×C4⋊C4—671no—
393#501—678no—
394#498—678no—
395#489—678no—
396#488—678no—
397#485—678no—
398#483—678no—
399#482—678no—
400#481—678no—
401#479—678no—
402#478—678no—
403#476—678no—
404#475—678no—
405#433C2×D6718yescomplemented
406C2×#107—671no—
407C2×#107—671no—
408C2×#106—671no—
409C2×#106—671no—
410C2×#106—671no—
411C2×#106—671no—
412C2×#106—671no—
413C2×#106—671no—
414C2×C4⋊C8C2×D6711yescharacteristic
415C2×C4⋊C8C2×D6711yescharacteristic
416C2×#103—671no—
417C2×#103—671no—
418C2×#103—671no—
419C2×#103—671no—
420C2×#102—671no—
421C2×#102—671no—
422C2×#102—671no—
423C2×#102—671no—
424C2×C22⋊C8C2×D6711yescharacteristic
425C2×C22⋊C8C2×D6711yescharacteristic
426C2×#97C2×D6711yescharacteristic
427C2×C4×C8C2×D6711yescharacteristic
428C22×Q8—671no—
429C22×Q8—1341no—
430C22×Q8—1341no—
431C22×Q8—1341no—
432C22×D4—671no—
433C22×D4—1341no—
434C23×C4—1341no—
435C23×C4—1341no—
436C23×C4C22×D6711yescharacteristic
437C22×C8C22×D6711yescharacteristic
438C22×C8C22×D6711yescharacteristic
439C22×C8C22×D6711yescharacteristic
440C22×C8C22×D6711yescharacteristic
441C4⋊Q8—674no—
442C4⋊Q8—674no—
443C4⋊Q8—674no—
444C4⋊Q8—1348no—
445C4⋊Q8—1342no—
446C4⋊Q8—1342no—
447C4⋊Q8—1342no—
448#126—1348no—
449#125—674no—
450#125—674no—
451#125—1348no—
452#125—1342no—
453#125—1342no—
454#124—674no—
455#124—1348no—
456#124—1342no—
457#123—1348no—
458C22⋊Q8—674no—
459C22⋊Q8—1342no—
460C22⋊Q8—1348no—
461C22⋊Q8—1348no—
462C22⋊Q8—1348no—
463#121—674no—
464#121—1342no—
465C4×Q8—674no—
466C4×Q8—1342no—
467C4×D4—674no—
468C4×D4—1342no—
469#117—674no—
470#117—1342no—
471#117D26814yes—
472#117C22×D6714yes—
473C2×C4⋊C4—671no—
474C2×C4⋊C4—671no—
475C2×C4⋊C4—674no—
476C2×C4⋊C4—671no—
477C2×C4⋊C4—671no—
478C2×C4⋊C4—671no—
479C2×C4⋊C4—671no—
480C2×C4⋊C4—1341no—
481C2×C4⋊C4—1342no—
482C2×C4⋊C4—1341no—
483C2×C4⋊C4—1341no—
484C2×C4⋊C4—1341no—
485C2×C4⋊C4—1341no—
486C2×C4⋊C4—1341no—
487C2×C4⋊C4—1341no—
488C2×C4⋊C4—1341no—
489C2×C4⋊C4—1341no—
490C2×C4⋊C4—1341no—
491C2×C4⋊C4D26811yescharacteristic
492C2×C4⋊C4D26811yescharacteristic
493C2×C22⋊C4—1341no—
494C2×C22⋊C4—1341no—
495C2×C22⋊C4—1341no—
496C2×C22⋊C4—1341no—
497C2×C22⋊C4—1341no—
498C2×C22⋊C4—1341no—
499C2×C22⋊C4D26811yescharacteristic
500C2×C22⋊C4D26811yescharacteristic
501C2×C42—1341no—
502C2×C42—1341no—
503C2×C42C22×D6711yescharacteristic
504C2×C42C22×D6711yescharacteristic
505#107—674no—
506#107—674no—
507#106—674no—
508#106—674no—
509#106—674no—
510#106—674no—
511#106—674no—
512#106—674no—
513C4⋊C8C22×D6714yes—
514C4⋊C8C22×D6714yes—
515#103—674no—
516#103—674no—
517#103—674no—
518#103—674no—
519#102—674no—
520#102—674no—
521#102—674no—
522#102—674no—
523C22⋊C8C22×D6714yes—
524C22⋊C8C22×D6714yes—
525#97C22×D6714yes—
526C4×C8C22×D6714yes—
527C24—1341no—
528C24C2×D26811yescharacteristic
529C2×Q8—5362no—
530C2×Q8—5362no—
531C2×Q8—5362no—
532C2×Q8—672no—
533C2×Q8—1342no—
534C2×Q8—1342no—
535C2×Q8—1341no—
536C2×Q8—1344no—
537C2×Q8—1344no—
538C2×Q8—1344no—
539C2×D4—5362no—
540C2×D4—672no—
541C2×D4—1344no—
542C2×D4—1341no—
543C2×D4—1342no—
544C2×D4—1342no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—5362no—
548C22×C4—5362no—
549C22×C4—1341no—
550C22×C4—1341no—
551C22×C4—1341no—
552C22×C4—1341no—
553C22×C4—1341no—
554C22×C4—1341no—
555C22×C4—1341no—
556C22×C4—1344no—
557C22×C4—1344no—
558C22×C4C2×D26812yes—
559C22×C4C2×D26811yescharacteristic
560C22×C4C2×D26811yescharacteristic
561C22×C4C2×D26811yescharacteristic
562C22×C4C2×D26811yescharacteristic
563C22×C4C2×D26811yescharacteristic
564C22×C4C23×D6712yes—
565C22×C4C23×D6711yescharacteristic
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8C23×D6712yes—
571C2×C8C23×D6712yes—
572C2×C8C23×D6712yes—
573C2×C8C23×D6712yes—
574C4⋊C4—672no—
575C4⋊C4—672no—
576C4⋊C4—672no—
577C4⋊C4—672no—
578C4⋊C4—672no—
579C4⋊C4—672no—
580C4⋊C4—1344no—
581C4⋊C4—1341no—
582C4⋊C4—1341no—
583C4⋊C4—1341no—
584C4⋊C4—1341no—
585C4⋊C4—1341no—
586C4⋊C4—1341no—
587C4⋊C4—1344no—
588C4⋊C4—1344no—
589C4⋊C4—1344no—
590C4⋊C4—1344no—
591C4⋊C4—1344no—
592C4⋊C4—1344no—
593C4⋊C4—1344no—
594C4⋊C4—1344no—
595C4⋊C4—1344no—
596C4⋊C4C2×D26814yes—
597C4⋊C4C2×D26814yes—
598C22⋊C4—1344no—
599C22⋊C4—1344no—
600C22⋊C4—1344no—
601C22⋊C4—1344no—
602C22⋊C4—1344no—
603C22⋊C4—1344no—
604C22⋊C4C2×D26814yes—
605C22⋊C4C2×D26814yes—
606C42—1344no—
607C42—1344no—
608C42C2×D26812yes—
609C42C2×D26812yes—
610C42C23×D6712yes—
611C42C23×D6712yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—2682no—
616C23—2682no—
617C23—2682no—
618C23—1342no—
619C23C22×D26812yes—
620C23C22×D26811yescharacteristic
621Q8—2682no—
622Q8—5364no—
623Q8—5364no—
624Q8—5364no—
625Q8—1342no—
626Q8—1342no—
627D4—2682no—
628D4—5364no—
629D4—1342no—
630D4—1342no—
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—2682no—
640C2×C4—2682no—
641C2×C4—2682no—
642C2×C4—2682no—
643C2×C4—2682no—
644C2×C4—2682no—
645C2×C4—2682no—
646C2×C4—5364no—
647C2×C4—5364no—
648C2×C4—1342no—
649C2×C4—1342no—
650C2×C4—1342no—
651C2×C4—1342no—
652C2×C4—1342no—
653C2×C4—1342no—
654C2×C4—1342no—
655C2×C4C22×D26812yes—
656C2×C4C22×D26812yes—
657C2×C4C22×D26812yes—
658C2×C4C22×D26812yes—
659C2×C4C22×D26812yes—
660C2×C4C22×D26811yescharacteristic
661C2×C4#1452409012yes—
662C2×C4#1452409012yes—
663C2×C4C24×D6711yescharacteristic
664C8—22no—
665C8—22no—
666C8—22no—
667C8—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—2682no—
673C22—2682no—
674C22—2682no—
675C22—5364no—
676C22#1686397212yes—
677C22#1686420812yes—
678C22#1686420812yes—
679C22C23×D26811yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—2682no—
686C4—2682no—
687C4—2682no—
688C4—2682no—
689C4—2682no—
690C4—2682no—
691C4—2682no—
692C4#1686397212yes—
693C4C2×#1452409011yescharacteristic
694C4C2×#1452409011yescharacteristic
695C2—42no—
696C2—5362no—
697C2#2257150914yesdirect product factor
698C2C2×#1686397211yescharacteristic
699C2C2×#1686420811yescharacteristic
700C2C2×#1686420811yescharacteristic
subgroupG/H
centerC23C22×D268
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#433×C67C2
socleC23×C67C22×D4
prime radicalC2×#14524017C22
hypercenterC2×#433D67
hypocenterC67C2×#3244
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16864024C2semidirect
3. #22571509C2direct (N × H)
4. C2×#16863805C2semidirect
5. C2×#16863794C2semidirect
6. C2×#16863756C2semidirect
7. C2×#16863751C2semidirect
9. C2×#16863738C2semidirect
11. C2×#16863727C2semidirect
12. C2×#16863704C2semidirect
13. C2×#16863682C2semidirect
14. C2×#16863697C2semidirect
15. C2×#16863687C2semidirect
16. C2×#433×C67C2semidirect
18. #16864024C22semidirect
41. #16863805C22semidirect
42. #16863794C22semidirect
43. #16863756C22semidirect
44. #16863751C22semidirect
45. #16863738C22semidirect
46. #16863727C22semidirect
49. #16863704C22semidirect
50. #16863697C22semidirect
51. #16863687C22semidirect
52. #16863682C22semidirect
70. #433×C67C22semidirect
346. C2×C67#3244semidirect
366. C2×#433D67semidirect
367. C67C2×#3244semidirect
405. #433C2×D67semidirect
697. C2#22571509direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640242
C2×#168640172
#225715092
C2×#168638052
C2×#168637942
C2×#168637562
C2×#168637512
C2×#168637152
C2×#168637382
C2×#168637212
C2×#168637272
C2×#168637042
C2×#168636822
C2×#168636972
C2×#168636872
C2×#433×C672
C2×#324467