Finite Group Databasebeta

← C2×#22568440 #31062091

Subgroups — C2×#22568440 #31062091

Order 17152.

1914 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22568440C2116yesmaximal, direct product factor
2C2×C67⋊#401C211yesmaximal, characteristic, complemented
3C2×#16863335C211yesmaximal, characteristic, complemented
4C2×#16863334C211yesmaximal, characteristic, complemented
5C2×#16863332C211yesmaximal, characteristic
6C2×#16863326C211yesmaximal, characteristic, complemented
7C2×#16863324C211yesmaximal, characteristic
8C2×#16863324C211yesmaximal, characteristic
9C2×#16863321C211yesmaximal, characteristic
10C2×#16863317C211yesmaximal, characteristic, complemented
11C2×#16863316C211yesmaximal, characteristic, complemented
12C2×#16863308C211yesmaximal, characteristic
13C2×#16863292C211yesmaximal, characteristic, complemented
14C2×#16863289C211yesmaximal, characteristic
15C2×#16863282C211yesmaximal, characteristic, complemented
16C2×#396×C67C211yesmaximal, characteristic
17C23×Dic134C2211yescharacteristic
18C22×C4⋊Dic67C2211yescharacteristic
19C22×C4⋊Dic67C2211yescharacteristic
20C22×C4⋊Dic67C2211yescharacteristic
21C22×Dic67⋊C4C2211yescharacteristic
22C22×Dic67⋊C4C2211yescharacteristic
23C22×Dic67⋊C4C2211yescharacteristic
24C22×Dic67⋊C4C2211yescharacteristic
25C22×C22⋊Dic67C2211yescharacteristic
26C22×C22⋊Dic67C2211yescharacteristic
27C22×C22⋊Dic67C2211yescharacteristic
28C22×C22⋊Dic67C2211yescharacteristic
29C22×C4×Dic67C2211yescharacteristic
30C67⋊#401C2218yescomplemented
31#16863335C2218yescomplemented
32#16863334C2218yescomplemented
33#16863332C2218yes—
34#16863326C2218yescomplemented
35#16863324C2218yes—
36#16863324C2218yes—
37#16863321C2218yes—
38#16863317C2218yescomplemented
39#16863316C2218yescomplemented
40#16863308C2218yes—
41#16863292C2218yescomplemented
42#16863289C2218yes—
43#16863282C2218yescomplemented
44C2×C67⋊#95C2211yescharacteristic
45C2×C67⋊#95C2211yescharacteristic
46C2×C67⋊#95C2211yescharacteristic
47C2×C67⋊#95C2211yescharacteristic
48C2×C67⋊#95C2211yescharacteristic
49C2×C67⋊#95C2211yescharacteristic
50C2×C67⋊#95C2211yescharacteristic
51C2×C67⋊#95C2211yescharacteristic
52C2×C67⋊#95C2211yescharacteristic
53C2×C67⋊#95C2211yescharacteristic
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C22×C4⋊C4×C67C2211yescharacteristic
60C22×C4⋊C4×C67C2211yescharacteristic
61C22×C4⋊C4×C67C2211yescharacteristic
62C22×C22⋊C4×C67C2211yescharacteristic
63C22×C22⋊C4×C67C2211yescharacteristic
64C22×C22⋊C4×C67C2211yescharacteristic
65#396×C67C2218yes—
66C2×#95×C67C2211yescharacteristic
67C22×Dic134—42no—
68C22×Dic134—42no—
69C22×Dic134—42no—
70C22×Dic134C2314yes—
71C23×Dic67C2311yescharacteristic
72C23×Dic67C2311yescharacteristic
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C2×C4⋊Dic67—24no—
80C2×C4⋊Dic67—42no—
81C2×C4⋊Dic67—42no—
82C2×C4⋊Dic67C2314yes—
83C2×C4⋊Dic67C2314yes—
84C2×C4⋊Dic67C2314yes—
85C2×Dic67⋊C4—42no—
86C2×Dic67⋊C4—42no—
87C2×Dic67⋊C4—42no—
88C2×Dic67⋊C4—42no—
89C2×Dic67⋊C4C2314yes—
90C2×Dic67⋊C4C2314yes—
91C2×Dic67⋊C4C2314yes—
92C2×Dic67⋊C4C2314yes—
93C2×C22⋊Dic67—42no—
94C2×C22⋊Dic67—42no—
95C2×C22⋊Dic67—42no—
96C2×C22⋊Dic67—42no—
97C2×C22⋊Dic67C2314yes—
98C2×C22⋊Dic67C2314yes—
99C2×C22⋊Dic67C2314yes—
100C2×C22⋊Dic67C2314yes—
101C2×C4×Dic67—42no—
102C2×C4×Dic67C2314yes—
103C67⋊#95C2314yes—
104C67⋊#95C2314yes—
105C67⋊#95C2314yes—
106C67⋊#95C2314yes—
107C67⋊#95C2314yes—
108C67⋊#95C2314yes—
109C67⋊#95C2314yes—
110C67⋊#95C2314yes—
111C67⋊#95C2314yes—
112C67⋊#95C2314yes—
113C67⋊#95C2314yes—
114C67⋊#95C2314yes—
115C67⋊#95C2314yes—
116C67⋊#95C2314yes—
117C67⋊#95C2314yes—
118C25×C67C2311yescharacteristic
119C23×C4×C67C2311yescharacteristic
120C23×C4×C67C2311yescharacteristic
121C23×C4×C67C2311yescharacteristic
122C23×C4×C67C2311yescharacteristic
123C23×C4×C67C2311yescharacteristic
124C23×C4×C67C2311yescharacteristic
125C2×C4⋊C4×C67—24no—
126C2×C4⋊C4×C67—42no—
127C2×C4⋊C4×C67—42no—
128C2×C4⋊C4×C67C2314yes—
129C2×C4⋊C4×C67C2314yes—
130C2×C4⋊C4×C67C2314yes—
131C2×C22⋊C4×C67—24no—
132C2×C22⋊C4×C67—42no—
133C2×C22⋊C4×C67—42no—
134C2×C22⋊C4×C67C2314yes—
135C2×C22⋊C4×C67C2314yes—
136C2×C22⋊C4×C67C2314yes—
137#95×C67C2314yes—
138C2×Dic134—44no—
139C2×Dic134—44no—
140C2×Dic134—44no—
141C2×Dic134—416no—
142C22×Dic67—22no—
143C22×Dic67—22no—
144C22×Dic67—22no—
145C22×Dic67—22no—
146C22×Dic67—22no—
147C22×Dic67—22no—
148C22×Dic67—22no—
149C22×Dic67—22no—
150C22×Dic67—22no—
151C22×Dic67—22no—
152C22×Dic67—22no—
153C22×Dic67—22no—
154C22×Dic67—22no—
155C22×Dic67—22no—
156C22×Dic67—22no—
157C22×Dic67—22no—
158C22×Dic67—22no—
159C22×Dic67—22no—
160C22×Dic67—22no—
161C22×Dic67—22no—
162C22×Dic67—22no—
163C22×Dic67—22no—
164C22×Dic67—22no—
165C22×Dic67—22no—
166C22×Dic67C2412yes—
167C22×Dic67C2412yes—
168C22×Dic67C2412yes—
169C22×Dic67C2412yes—
170C22×Dic67C2412yes—
171C22×Dic67C2412yes—
172C22×Dic67C2412yes—
173C22×Dic67C2412yes—
174C4⋊Dic67—28no—
175C4⋊Dic67—44no—
176C4⋊Dic67—44no—
177Dic67⋊C4—44no—
178Dic67⋊C4—44no—
179Dic67⋊C4—44no—
180Dic67⋊C4—44no—
181C22⋊Dic67—44no—
182C22⋊Dic67—44no—
183C22⋊Dic67—44no—
184C22⋊Dic67—44no—
185C4×Dic67—44no—
186C24×C67—22no—
187C24×C67—22no—
188C24×C67—22no—
189C24×C67—22no—
190C24×C67—22no—
191C24×C67—22no—
192C24×C67—22no—
193C24×C67C2412yes—
194C24×C67C2411yescharacteristic
195C22×C4×C67—22no—
196C22×C4×C67—22no—
197C22×C4×C67—22no—
198C22×C4×C67—22no—
199C22×C4×C67—22no—
200C22×C4×C67—22no—
201C22×C4×C67—22no—
202C22×C4×C67—22no—
203C22×C4×C67—22no—
204C22×C4×C67—22no—
205C22×C4×C67—22no—
206C22×C4×C67—22no—
207C22×C4×C67—22no—
208C22×C4×C67—22no—
209C22×C4×C67—22no—
210C22×C4×C67—22no—
211C22×C4×C67—22no—
212C22×C4×C67#4114yes—
213C22×C4×C67C2412yes—
214C22×C4×C67C2412yes—
215C22×C4×C67C2412yes—
216C22×C4×C67C2412yes—
217C22×C4×C67C2412yes—
218C22×C4×C67C2412yes—
219C4⋊C4×C67—28no—
220C4⋊C4×C67—44no—
221C4⋊C4×C67—44no—
222C22⋊C4×C67—28no—
223C22⋊C4×C67—44no—
224C22⋊C4×C67—44no—
225C23×C67—22no—
226C23×C67—22no—
227C23×C67—22no—
228C23×C67—22no—
229C23×C67—22no—
230C23×C67—22no—
231C23×C67—22no—
232C23×C67—44no—
233C23×C67—44no—
234C23×C67—44no—
235C23×C67—44no—
236C23×C67—44no—
237C23×C67—44no—
238C23×C67—44no—
239C23×C67C2×#4112yes—
240C23×C67H(5,𝔽2)12yes—
241C23×C67H(5,𝔽2)12yes—
242C23×C67H(5,𝔽2)12yes—
243C23×C672−1+412yes—
244C23×C672−1+412yes—
245C23×C672−1+412yes—
246C23×C67C2511yescharacteristic
247C2×C4×C67—28no—
248C2×C4×C67—22no—
249C2×C4×C67—22no—
250C2×C4×C67—22no—
251C2×C4×C67—22no—
252C2×C4×C67—22no—
253C2×C4×C67—22no—
254C2×C4×C67—22no—
255C2×C4×C67—22no—
256C2×C4×C67—22no—
257C2×C4×C67—22no—
258C2×C4×C67—22no—
259C2×C4×C67—22no—
260C2×C4×C67—22no—
261C2×C4×C67—22no—
262C2×C4×C67—22no—
263C2×C4×C67—22no—
264C2×C4×C67—22no—
265C2×C4×C67—44no—
266C2×C4×C67—44no—
267C2×C4×C67—44no—
268C2×C4×C67—44no—
269C2×C4×C67—44no—
270C2×C4×C67C2×#4114yes—
271C2×Dic67—22no—
272C2×Dic67—22no—
273C2×Dic67—22no—
274C2×Dic67—22no—
275C2×Dic67—22no—
276C2×Dic67—22no—
277C2×Dic67—22no—
278C2×Dic67—22no—
279C2×Dic67—22no—
280C2×Dic67—22no—
281C2×Dic67—22no—
282C2×Dic67—22no—
283C2×Dic67—22no—
284C2×Dic67—22no—
285C2×Dic67—22no—
286C2×Dic67—22no—
287C2×Dic67—22no—
288C2×Dic67—22no—
289C2×Dic67—22no—
290C2×Dic67—22no—
291C2×Dic67—22no—
292C2×Dic67—22no—
293C2×Dic67—22no—
294C2×Dic67—22no—
295C2×Dic67—44no—
296C2×Dic67—44no—
297C2×Dic67—44no—
298C2×Dic67—44no—
299C2×Dic67—44no—
300C2×Dic67—44no—
301C2×Dic67—44no—
302C2×Dic67—44no—
303Dic134—416no—
304C22×C67—42no—
305C22×C67—42no—
306C22×C67—42no—
307C22×C67—42no—
308C22×C67—42no—
309C22×C67—42no—
310C22×C67—42no—
311C22×C67—88no—
312C22×C67#53914yes—
313C22×C67#54214yes—
314C22×C67#54214yes—
315C22×C67#56014yes—
316C22×C67#56314yes—
317C22×C67#56314yes—
318C22×C67#56314yes—
319C22×C67C22×#4111yescharacteristic
320C22×C67C2×H(5,𝔽2)11yescharacteristic
321C22×C67C2×H(5,𝔽2)11yescharacteristic
322C22×C67C2×H(5,𝔽2)11yescharacteristic
323C22×C67C2×2−1+411yescharacteristic
324C22×C67C2×2−1+411yescharacteristic
325C22×C67C2×2−1+411yescharacteristic
326C4×C67—24no—
327C4×C67—42no—
328C4×C67—42no—
329C4×C67—42no—
330C4×C67—42no—
331C4×C67—42no—
332Dic67—42no—
333Dic67—42no—
334Dic67—42no—
335Dic67—42no—
336Dic67—42no—
337Dic67—42no—
338Dic67—42no—
339Dic67—42no—
340C2×#2838—671nomaximal, Sylow
341C2×C67—82no—
342C2×C67#283818yescomplemented
343C2×C67C2×#53911yescharacteristic
344C2×C67C2×#54211yescharacteristic
345C2×C67C2×#54211yescharacteristic
346C2×C67C2×#56011yescharacteristic
347C2×C67C2×#56311yescharacteristic
348C2×C67C2×#56311yescharacteristic
349C2×C67C2×#56311yescharacteristic
350#2838—6716no—
351C2×#401—671no—
352C2×#400—671no—
353C2×#400—671no—
354C2×#399—671no—
355C2×#398—671no—
356C2×#397—671no—
357C2×#397—671no—
358C2×#397—671no—
359C2×#396D6711yescharacteristic
360C2×#395—671no—
361C2×#395—671no—
362C2×#393—671no—
363C2×#389—671no—
364C2×#388—671no—
365C2×#387—671no—
366C67C2×#283811yescharacteristic, complemented, Sylow
367C23×Q8—671no—
368C22×C4⋊C4—671no—
369C22×C4⋊C4—671no—
370C22×C4⋊C4—671no—
371C22×C4⋊C4—671no—
372C22×C4⋊C4—671no—
373C22×C4⋊C4—671no—
374C22×C4⋊C4—671no—
375C22×C4⋊C4C2×D6711yescharacteristic
376C22×C4⋊C4C2×D6711yescharacteristic
377C22×C4⋊C4C2×D6711yescharacteristic
378C22×C22⋊C4—671no—
379C22×C22⋊C4—671no—
380C22×C22⋊C4—671no—
381C22×C22⋊C4—671no—
382C22×C22⋊C4C2×D6711yescharacteristic
383C22×C22⋊C4C2×D6711yescharacteristic
384C22×C22⋊C4C2×D6711yescharacteristic
385C22×C42—671no—
386#401—678no—
387#400—678no—
388#400—678no—
389#399—678no—
390#398—678no—
391#397—678no—
392#397—678no—
393#397—678no—
394#396C2×D6718yes—
395#395—678no—
396#395—678no—
397#393—678no—
398#389—678no—
399#388—678no—
400#387—678no—
401C2×#95—671no—
402C2×#95—671no—
403C2×#95—671no—
404C2×#95—671no—
405C2×#95—671no—
406C2×#95—671no—
407C2×#95—671no—
408C2×#95—671no—
409C2×#95—671no—
410C2×#95—671no—
411C2×#95—671no—
412C2×#95—671no—
413C2×#95—671no—
414C2×#95—671no—
415C2×#95—671no—
416C2×#95C2×D6711yescharacteristic
417C25C22×D6711yescharacteristic
418C22×Q8—2682no—
419C22×Q8—2682no—
420C22×Q8—2682no—
421C22×Q8—674no—
422C23×C4—671no—
423C23×C4—671no—
424C23×C4—671no—
425C23×C4—671no—
426C23×C4—671no—
427C23×C4—671no—
428C23×C4—671no—
429C23×C4—671no—
430C23×C4C22×D6711yescharacteristic
431C23×C4C22×D6711yescharacteristic
432C23×C4C22×D6711yescharacteristic
433C23×C4C22×D6711yescharacteristic
434C23×C4C22×D6711yescharacteristic
435C23×C4C22×D6711yescharacteristic
436C2×C4⋊C4—24no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—42no—
439C2×C4⋊C4—2682no—
440C2×C4⋊C4—2682no—
441C2×C4⋊C4—2682no—
442C2×C4⋊C4—2682no—
443C2×C4⋊C4—2682no—
444C2×C4⋊C4—2682no—
445C2×C4⋊C4—674no—
446C2×C4⋊C4—674no—
447C2×C4⋊C4—674no—
448C2×C4⋊C4—674no—
449C2×C4⋊C4—674no—
450C2×C4⋊C4—674no—
451C2×C4⋊C4—674no—
452C2×C4⋊C4—1344no—
453C2×C4⋊C4C22×D6714yes—
454C2×C4⋊C4C22×D6714yes—
455C2×C4⋊C4C22×D6714yes—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—2682no—
460C2×C22⋊C4—2682no—
461C2×C22⋊C4—2682no—
462C2×C22⋊C4—2682no—
463C2×C22⋊C4—674no—
464C2×C22⋊C4—674no—
465C2×C22⋊C4—674no—
466C2×C22⋊C4—674no—
467C2×C22⋊C4C22×D6714yes—
468C2×C22⋊C4C22×D6714yes—
469C2×C22⋊C4C22×D6714yes—
470C2×C42—2682no—
471C2×C42—674no—
472#95—674no—
473#95—674no—
474#95—674no—
475#95—674no—
476#95—674no—
477#95—674no—
478#95—674no—
479#95—674no—
480#95—674no—
481#95—674no—
482#95—674no—
483#95—674no—
484#95—674no—
485#95—674no—
486#95—674no—
487#95C22×D6714yes—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24C23×D6712yes—
496C24C23×D6711yescharacteristic
497C2×Q8—2684no—
498C2×Q8—2684no—
499C2×Q8—2684no—
500C2×Q8—26816no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—672no—
519C22×C4—672no—
520C22×C4—672no—
521C22×C4—672no—
522C22×C4—672no—
523C22×C4—672no—
524C22×C4—672no—
525C22×C4—672no—
526C22×C4—1342no—
527C22×C4—1342no—
528C22×C4—1342no—
529C22×C4—1342no—
530C22×C4—1342no—
531C22×C4—1342no—
532C22×C4—1342no—
533C22×C4—1342no—
534C22×C4—1342no—
535C22×C4—1342no—
536C22×C4—1342no—
537C22×C4—1342no—
538C22×C4—1342no—
539C22×C4—1342no—
540C22×C4—1342no—
541C22×C4—1342no—
542C22×C4—1342no—
543C22×C4—1342no—
544C22×C4—1342no—
545C22×C4—1342no—
546C22×C4—1342no—
547C22×C4—1342no—
548C22×C4—1342no—
549C22×C4—1342no—
550C22×C4#1176162714yes—
551C22×C4C23×D6712yes—
552C22×C4C23×D6712yes—
553C22×C4C23×D6712yes—
554C22×C4C23×D6712yes—
555C22×C4C23×D6712yes—
556C22×C4C23×D6712yes—
557C4⋊C4—28no—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C4⋊C4—2684no—
561C4⋊C4—2684no—
562C4⋊C4—2684no—
563C4⋊C4—2684no—
564C4⋊C4—2684no—
565C4⋊C4—2684no—
566C4⋊C4—1348no—
567C22⋊C4—28no—
568C22⋊C4—44no—
569C22⋊C4—44no—
570C22⋊C4—2684no—
571C22⋊C4—2684no—
572C22⋊C4—2684no—
573C22⋊C4—2684no—
574C42—2684no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—44no—
583C23—44no—
584C23—44no—
585C23—44no—
586C23—44no—
587C23—44no—
588C23—44no—
589C23C2×#1176162712yes—
590C23#1452408812yes—
591C23#1452408812yes—
592C23#1452408912yes—
593C23#1452409012yes—
594C23#1452409012yes—
595C23#1452409112yes—
596C23C24×D6711yescharacteristic
597Q8—26816no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—28no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—44no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—2684no—
622C2×C4—2684no—
623C2×C4—2684no—
624C2×C4—2684no—
625C2×C4—2684no—
626C2×C4—2684no—
627C2×C4—2684no—
628C2×C4—2684no—
629C2×C4—1342no—
630C2×C4—1342no—
631C2×C4—1342no—
632C2×C4—1342no—
633C2×C4—1342no—
634C2×C4—1342no—
635C2×C4—1342no—
636C2×C4—1342no—
637C2×C4—1342no—
638C2×C4—1342no—
639C2×C4—1342no—
640C2×C4—1342no—
641C2×C4—1342no—
642C2×C4—1342no—
643C2×C4—1342no—
644C2×C4—1342no—
645C2×C4—1342no—
646C2×C4—1342no—
647C2×C4—1342no—
648C2×C4—1342no—
649C2×C4—1342no—
650C2×C4—1342no—
651C2×C4—1342no—
652C2×C4—1342no—
653C2×C4C2×#1176162714yes—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—88no—
662C22#1686399114yes—
663C22#1686401314yes—
664C22#1686401914yes—
665C22#1686413414yes—
666C22#1686414714yes—
667C22#1686414714yes—
668C22#1686414814yes—
669C22C22×#1176162711yescharacteristic
670C22C2×#1452408811yescharacteristic
671C22C2×#1452408811yescharacteristic
672C22C2×#1452408911yescharacteristic
673C22C2×#1452409011yescharacteristic
674C22C2×#1452409011yescharacteristic
675C22C2×#1452409111yescharacteristic
676C4—24no—
677C4—42no—
678C4—42no—
679C4—42no—
680C4—42no—
681C4—42no—
682C4—2682no—
683C4—2682no—
684C4—2682no—
685C4—2682no—
686C4—2682no—
687C4—2682no—
688C4—2682no—
689C4—2682no—
690C2—82no—
691C2#2256844018yesdirect product factor
692C2C2×#1686399111yescharacteristic
693C2C2×#1686401311yescharacteristic
694C2C2×#1686401911yescharacteristic
695C2C2×#1686413411yescharacteristic
696C2C2×#1686414711yescharacteristic
697C2C2×#1686414711yescharacteristic
698C2C2×#1686414811yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#396×C67C2
socleC24×C67C24
prime radicalC25×C67C23
hypercenterC2×#396D67
hypocenterC67C2×#2838
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #22568440C2direct (N × H)
2. C2×C67⋊#401C2semidirect
3. C2×#16863335C2semidirect
4. C2×#16863334C2semidirect
6. C2×#16863326C2semidirect
10. C2×#16863317C2semidirect
11. C2×#16863316C2semidirect
13. C2×#16863292C2semidirect
15. C2×#16863282C2semidirect
30. C67⋊#401C22semidirect
31. #16863335C22semidirect
32. #16863334C22semidirect
34. #16863326C22semidirect
38. #16863317C22semidirect
39. #16863316C22semidirect
41. #16863292C22semidirect
43. #16863282C22semidirect
342. C2×C67#2838semidirect
366. C67C2×#2838semidirect
691. C2#22568440direct (N × H)

Maximal subgroups

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

subgroupindex
#225684402
C2×C67⋊#4012
C2×#168633352
C2×#168633342
C2×#168633322
C2×#168633262
C2×#168633242
C2×#168633212
C2×#168633172
C2×#168633162
C2×#168633082
C2×#168632922
C2×#168632892
C2×#168632822
C2×#396×C672
C2×#283867