Finite Group Databasebeta

← C2×#22565709 #31026368

Subgroups — C2×#22565709 #31026368

Order 17152.

2074 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22565709C2116yesmaximal, direct product factor
2C2×C67⋊#401C211yesmaximal, characteristic, complemented
3C2×#16863327C211yesmaximal, characteristic, complemented
4C2×#16863322C211yesmaximal, characteristic
5C2×#16863320C211yesmaximal, characteristic
6C2×#16863291C211yesmaximal, characteristic, complemented
7C2×#16863287C211yesmaximal, characteristic
8C2×#16863287C211yesmaximal, characteristic
9C2×#16863287C211yesmaximal, characteristic
10C2×#16863286C211yesmaximal, characteristic
11C2×#16863285C211yesmaximal, characteristic
12C2×#16863280C211yesmaximal, characteristic, complemented
13C2×#16863280C211yesmaximal, characteristic, complemented
14C2×#16863278C211yesmaximal, characteristic, complemented
15C2×C4×Dic67⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C4⋊C4×C67C211yesmaximal, characteristic, complemented
17C22×Dic67⋊C4C2211yescharacteristic
18C22×Dic67⋊C4C2211yescharacteristic
19C22×Dic67⋊C4C2211yescharacteristic
20C22×Dic67⋊C4C2211yescharacteristic
21C22×Dic67⋊C4C2211yescharacteristic
22C22×Dic67⋊C4C2211yescharacteristic
23C22×Dic67⋊C4C2211yescharacteristic
24C22×(C2×D67)⋊C4C2211yescharacteristic
25C22×(C2×D67)⋊C4C2211yescharacteristic
26C22×(C2×D67)⋊C4C2211yescharacteristic
27C22×(C2×D67)⋊C4C2211yescharacteristic
28C22×(C2×D67)⋊C4C2211yescharacteristic
29C22×(C2×D67)⋊C4C2211yescharacteristic
30C22×(C2×D67)⋊C4C2211yescharacteristic
31C22×C4×Dic67C2211yescharacteristic
32C22×C4×Dic67C2211yescharacteristic
33C67⋊#401C2218yescomplemented
34#16863327C2218yescomplemented
35#16863322C2218yes—
36#16863320C2218yes—
37#16863291C2218yescomplemented
38#16863287C2218yes—
39#16863287C2218yes—
40#16863287C2218yes—
41#16863286C2218yes—
42#16863285C2218yes—
43#16863280C2218yescomplemented
44#16863280C2218yescomplemented
45#16863278C2218yescomplemented
46C4×Dic67⋊C4C2218yescomplemented
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×C42×C67C2211yescharacteristic
62C22×C42×C67C2211yescharacteristic
63C22×C42×C67C2211yescharacteristic
64C4×C4⋊C4×C67C2218yescomplemented
65C2×#95×C67C2211yescharacteristic
66C2×#95×C67C2211yescharacteristic
67C24×D67C2311yescharacteristic
68C23×Dic67C2311yescharacteristic
69C23×Dic67C2311yescharacteristic
70C23×Dic67C2311yescharacteristic
71C23×Dic67C2311yescharacteristic
72C23×Dic67C2311yescharacteristic
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C2×Dic67⋊C4—24no—
76C2×Dic67⋊C4—24no—
77C2×Dic67⋊C4—24no—
78C2×Dic67⋊C4—24no—
79C2×Dic67⋊C4—24no—
80C2×Dic67⋊C4—24no—
81C2×Dic67⋊C4—42no—
82C2×Dic67⋊C4C2314yes—
83C2×Dic67⋊C4C2314yes—
84C2×Dic67⋊C4C2314yes—
85C2×Dic67⋊C4C2314yes—
86C2×Dic67⋊C4C2314yes—
87C2×Dic67⋊C4C2314yes—
88C2×Dic67⋊C4C2314yes—
89C2×(C2×D67)⋊C4—24no—
90C2×(C2×D67)⋊C4—24no—
91C2×(C2×D67)⋊C4—24no—
92C2×(C2×D67)⋊C4—24no—
93C2×(C2×D67)⋊C4—24no—
94C2×(C2×D67)⋊C4—42no—
95C2×(C2×D67)⋊C4—42no—
96C2×(C2×D67)⋊C4C2314yes—
97C2×(C2×D67)⋊C4C2314yes—
98C2×(C2×D67)⋊C4C2314yes—
99C2×(C2×D67)⋊C4C2314yes—
100C2×(C2×D67)⋊C4C2314yes—
101C2×(C2×D67)⋊C4C2314yes—
102C2×(C2×D67)⋊C4C2314yes—
103C2×C4×Dic67—24no—
104C2×C4×Dic67—42no—
105C2×C4×Dic67C2314yes—
106C2×C4×Dic67C2314yes—
107C67⋊#95C2314yes—
108C67⋊#95C2314yes—
109C67⋊#95C2314yes—
110C67⋊#95C2314yes—
111C67⋊#95C2314yes—
112C67⋊#95C2314yes—
113C67⋊#95C2314yes—
114C67⋊#95C2314yes—
115C67⋊#95C2314yes—
116C67⋊#95C2314yes—
117C67⋊#95C2314yes—
118C67⋊#95C2314yes—
119C23×C4×C67C2311yescharacteristic
120C23×C4×C67C2311yescharacteristic
121C23×C4×C67C2311yescharacteristic
122C23×C4×C67C2311yescharacteristic
123C23×C4×C67C2311yescharacteristic
124C23×C4×C67C2311yescharacteristic
125C23×C4×C67C2311yescharacteristic
126C2×C4⋊C4×C67—24no—
127C2×C4⋊C4×C67—24no—
128C2×C4⋊C4×C67C2314yes—
129C2×C4⋊C4×C67C2314yes—
130C2×C42×C67—24no—
131C2×C42×C67—42no—
132C2×C42×C67—42no—
133C2×C42×C67C2314yes—
134C2×C42×C67C2314yes—
135C2×C42×C67C2314yes—
136#95×C67C2314yes—
137#95×C67C2314yes—
138C23×D67—22no—
139C23×D67—22no—
140C23×D67—22no—
141C23×D67—22no—
142C23×D67—22no—
143C23×D67—22no—
144C23×D67—22no—
145C23×D67C2412yes—
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#4114yes—
166C22×Dic67#4114yes—
167C22×Dic67C2412yes—
168C22×Dic67C2412yes—
169C22×Dic67C2412yes—
170C22×Dic67C2412yes—
171C22×Dic67C2412yes—
172C22×Dic67C2412yes—
173C22×Dic67C2412yes—
174Dic67⋊C4—28no—
175Dic67⋊C4—28no—
176Dic67⋊C4—28no—
177Dic67⋊C4—28no—
178Dic67⋊C4—28no—
179Dic67⋊C4—28no—
180Dic67⋊C4—44no—
181(C2×D67)⋊C4—28no—
182(C2×D67)⋊C4—28no—
183(C2×D67)⋊C4—28no—
184(C2×D67)⋊C4—28no—
185(C2×D67)⋊C4—28no—
186(C2×D67)⋊C4—44no—
187(C2×D67)⋊C4—44no—
188C4×Dic67—28no—
189C4×Dic67—44no—
190C24×C67C2411yescharacteristic
191C22×C4×C67—22no—
192C22×C4×C67—22no—
193C22×C4×C67—22no—
194C22×C4×C67—22no—
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#4114yes—
210C22×C4×C67#4114yes—
211C22×C4×C67#4114yes—
212C22×C4×C67C2412yes—
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—28no—
221C42×C67—28no—
222C42×C67—44no—
223C42×C67—44no—
224C23×C67C2×#4112yes—
225C23×C67C2×#4112yes—
226C23×C67C2×#4112yes—
227C23×C67C2×#4112yes—
228C23×C67C2×#4112yes—
229C23×C67H(5,𝔽2)12yes—
230C23×C672−1+412yes—
231C23×C67C2511yescharacteristic
232C22×D67—22no—
233C22×D67—22no—
234C22×D67—22no—
235C22×D67—22no—
236C22×D67—22no—
237C22×D67—22no—
238C22×D67—22no—
239C22×D67—44no—
240C22×D67—44no—
241C22×D67—44no—
242C22×D67—44no—
243C22×D67—44no—
244C22×D67—44no—
245C22×D67—44no—
246C2×C4×C67—28no—
247C2×C4×C67—28no—
248C2×C4×C67—28no—
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—22no—
266C2×C4×C67—22no—
267C2×C4×C67—44no—
268C2×C4×C67—44no—
269C2×C4×C67—44no—
270C2×C4×C67—44no—
271C2×C4×C67C2×#4114yes—
272C2×C4×C67C2×#4114yes—
273C2×C4×C67C2×#4114yes—
274C2×Dic67—28no—
275C2×Dic67—28no—
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×Dic67C2×#4114yes—
301C2×Dic67C2×#4114yes—
302C22×C67#52914yes—
303C22×C67#52914yes—
304C22×C67#53914yes—
305C22×C67#55314yes—
306C22×C67#55314yes—
307C22×C67#55614yes—
308C22×C67#55614yes—
309C22×C67C22×#4111yescharacteristic
310C22×C67C22×#4111yescharacteristic
311C22×C67C22×#4111yescharacteristic
312C22×C67C22×#4111yescharacteristic
313C22×C67C22×#4111yescharacteristic
314C22×C67C2×H(5,𝔽2)11yescharacteristic
315C22×C67C2×2−1+411yescharacteristic
316C2×D67—42no—
317C2×D67—42no—
318C2×D67—42no—
319C2×D67—42no—
320C2×D67—42no—
321C2×D67—42no—
322C2×D67—42no—
323C2×D67—88no—
324C4×C67—24no—
325C4×C67—24no—
326C4×C67—24no—
327C4×C67—42no—
328C4×C67—42no—
329C4×C67—42no—
330C4×C67—42no—
331Dic67—24no—
332Dic67—24no—
333Dic67—42no—
334Dic67—42no—
335Dic67—42no—
336Dic67—42no—
337Dic67—42no—
338C2×#2594—671nomaximal, Sylow
339C2×C67#259418yescomplemented
340C2×C67C2×#52911yescharacteristic
341C2×C67C2×#52911yescharacteristic
342C2×C67C2×#53911yescharacteristic
343C2×C67C2×#55311yescharacteristic
344C2×C67C2×#55311yescharacteristic
345C2×C67C2×#55611yescharacteristic
346C2×C67C2×#55611yescharacteristic
347D67—82no—
348#2594—6716no—
349C2×#401—671no—
350C2×#398—671no—
351C2×#397—671no—
352C2×#396—671no—
353C2×#389—671no—
354C2×#388—671no—
355C2×#388—671no—
356C2×#388—671no—
357C2×#388—671no—
358C2×#388—671no—
359C2×#387—671no—
360C2×#387—671no—
361C2×#387—671no—
362C2×C4×C4⋊C4—671no—
363C2×C4×C4⋊C4D6711yescharacteristic, complemented
364C67C2×#259411yescharacteristic, complemented, Sylow
365C22×C4⋊C4—671no—
366C22×C4⋊C4—671no—
367C22×C4⋊C4—671no—
368C22×C4⋊C4—671no—
369C22×C4⋊C4—671no—
370C22×C4⋊C4—671no—
371C22×C4⋊C4—671no—
372C22×C4⋊C4C2×D6711yescharacteristic
373C22×C4⋊C4C2×D6711yescharacteristic
374C22×C22⋊C4—671no—
375C22×C22⋊C4—671no—
376C22×C22⋊C4—671no—
377C22×C22⋊C4—671no—
378C22×C22⋊C4—671no—
379C22×C22⋊C4—671no—
380C22×C22⋊C4—671no—
381C22×C42—671no—
382C22×C42—671no—
383C22×C42C2×D6711yescharacteristic
384C22×C42C2×D6711yescharacteristic
385C22×C42C2×D6711yescharacteristic
386#401—678no—
387#398—678no—
388#397—678no—
389#396—678no—
390#389—678no—
391#388—678no—
392#388—678no—
393#388—678no—
394#388—678no—
395#388—678no—
396#387—678no—
397#387—678no—
398#387—678no—
399C4×C4⋊C4—678no—
400C4×C4⋊C4C2×D6718yescomplemented
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×#95C2×D6711yescharacteristic
414C2×#95C2×D6711yescharacteristic
415C25—671no—
416C23×C4—671no—
417C23×C4—671no—
418C23×C4—671no—
419C23×C4—671no—
420C23×C4—671no—
421C23×C4—671no—
422C23×C4—671no—
423C23×C4C22×D6711yescharacteristic
424C23×C4C22×D6711yescharacteristic
425C23×C4C22×D6711yescharacteristic
426C23×C4C22×D6711yescharacteristic
427C23×C4C22×D6711yescharacteristic
428C23×C4C22×D6711yescharacteristic
429C23×C4C22×D6711yescharacteristic
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—2682no—
433C2×C4⋊C4—674no—
434C2×C4⋊C4—674no—
435C2×C4⋊C4—674no—
436C2×C4⋊C4—674no—
437C2×C4⋊C4—674no—
438C2×C4⋊C4—674no—
439C2×C4⋊C4—674no—
440C2×C4⋊C4—1344no—
441C2×C4⋊C4—1344no—
442C2×C4⋊C4—1344no—
443C2×C4⋊C4—1344no—
444C2×C4⋊C4—1344no—
445C2×C4⋊C4—1344no—
446C2×C4⋊C4C22×D6714yes—
447C2×C4⋊C4C22×D6714yes—
448C2×C22⋊C4—2682no—
449C2×C22⋊C4—2682no—
450C2×C22⋊C4—674no—
451C2×C22⋊C4—674no—
452C2×C22⋊C4—674no—
453C2×C22⋊C4—674no—
454C2×C22⋊C4—674no—
455C2×C22⋊C4—674no—
456C2×C22⋊C4—674no—
457C2×C22⋊C4—1344no—
458C2×C22⋊C4—1344no—
459C2×C22⋊C4—1344no—
460C2×C22⋊C4—1344no—
461C2×C22⋊C4—1344no—
462C2×C42—24no—
463C2×C42—42no—
464C2×C42—42no—
465C2×C42—2682no—
466C2×C42—674no—
467C2×C42—674no—
468C2×C42—1344no—
469C2×C42C22×D6714yes—
470C2×C42C22×D6714yes—
471C2×C42C22×D6714yes—
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#95C22×D6714yes—
485#95C22×D6714yes—
486C24—672no—
487C24—1342no—
488C24—1342no—
489C24—1342no—
490C24—1342no—
491C24—1342no—
492C24—1342no—
493C24—1342no—
494C24C23×D6711yescharacteristic
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
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—674no—
514C22×C4—674no—
515C22×C4—672no—
516C22×C4—672no—
517C22×C4—672no—
518C22×C4—672no—
519C22×C4—672no—
520C22×C4—672no—
521C22×C4—672no—
522C22×C4—1342no—
523C22×C4—1342no—
524C22×C4—1342no—
525C22×C4—1342no—
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#1176162814yes—
542C22×C4#1176162814yes—
543C22×C4#1176162814yes—
544C22×C4C23×D6712yes—
545C22×C4C23×D6712yes—
546C22×C4C23×D6712yes—
547C22×C4C23×D6712yes—
548C22×C4C23×D6712yes—
549C22×C4C23×D6712yes—
550C22×C4C23×D6712yes—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—2684no—
554C4⋊C4—1348no—
555C4⋊C4—1348no—
556C4⋊C4—1348no—
557C4⋊C4—1348no—
558C4⋊C4—1348no—
559C4⋊C4—1348no—
560C22⋊C4—2684no—
561C22⋊C4—2684no—
562C22⋊C4—1348no—
563C22⋊C4—1348no—
564C22⋊C4—1348no—
565C22⋊C4—1348no—
566C22⋊C4—1348no—
567C42—28no—
568C42—44no—
569C42—44no—
570C42—2684no—
571C42—1348no—
572C23—2684no—
573C23—2684no—
574C23—2684no—
575C23—2684no—
576C23—2684no—
577C23—2684no—
578C23—2684no—
579C23—1342no—
580C23—1342no—
581C23—1342no—
582C23—1342no—
583C23—1342no—
584C23—1342no—
585C23—1342no—
586C23#41×D6712yes—
587C23#41×D6712yes—
588C23C2×#1176162812yes—
589C23C2×#1176162812yes—
590C23C2×#1176162812yes—
591C23#1452408812yes—
592C23#1452409112yes—
593C23C24×D6711yescharacteristic
594C2×C4—28no—
595C2×C4—28no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—28no—
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—44no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—44no—
619C2×C4—2684no—
620C2×C4—2684no—
621C2×C4—2684no—
622C2×C4—2684no—
623C2×C4—2684no—
624C2×C4—674no—
625C2×C4—674no—
626C2×C4—1342no—
627C2×C4—1342no—
628C2×C4—1342no—
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—1348no—
642C2×C4—1348no—
643C2×C4—1342no—
644C2×C4—1342no—
645C2×C4—1342no—
646C2×C4—1342no—
647C2×C4C2×#1176162814yes—
648C2×C4C2×#1176162814yes—
649C2×C4C2×#1176162814yes—
650C22—2682no—
651C22—2682no—
652C22—2682no—
653C22—2682no—
654C22—2682no—
655C22—2682no—
656C22—2682no—
657C22—5368no—
658C22#1686392414yes—
659C22#1686393014yes—
660C22#1686399314yes—
661C22#1686409514yes—
662C22#1686409614yes—
663C22#1686411814yes—
664C22#1686411814yes—
665C22C2×#41×D6711yescharacteristic
666C22C2×#41×D6711yescharacteristic
667C22C22×#1176162811yescharacteristic
668C22C22×#1176162811yescharacteristic
669C22C22×#1176162811yescharacteristic
670C22C2×#1452408811yescharacteristic
671C22C2×#1452409111yescharacteristic
672C4—24no—
673C4—24no—
674C4—24no—
675C4—42no—
676C4—42no—
677C4—42no—
678C4—42no—
679C4—2682no—
680C4—2682no—
681C4—2682no—
682C4—2682no—
683C4—2682no—
684C4—1344no—
685C4—1344no—
686C2—5362no—
687C2#2256570918yesdirect product factor
688C2C2×#1686392411yescharacteristic
689C2C2×#1686393011yescharacteristic
690C2C2×#1686399311yescharacteristic
691C2C2×#1686409511yescharacteristic
692C2C2×#1686409611yescharacteristic
693C2C2×#1686411811yescharacteristic
694C2C2×#1686411811yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×C4×C4⋊C4×C67C2
socleC24×C67C24
prime radicalC24×D67C23
hypercenterC2×C4×C4⋊C4D67
hypocenterC67C2×#2594
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #22565709C2direct (N × H)
2. C2×C67⋊#401C2semidirect
3. C2×#16863327C2semidirect
6. C2×#16863291C2semidirect
12. C2×#16863280C2semidirect
13. C2×#16863280C2semidirect
14. C2×#16863278C2semidirect
15. C2×C4×Dic67⋊C4C2semidirect
16. C2×C4×C4⋊C4×C67C2semidirect
33. C67⋊#401C22semidirect
34. #16863327C22semidirect
37. #16863291C22semidirect
43. #16863280C22semidirect
44. #16863280C22semidirect
45. #16863278C22semidirect
46. C4×Dic67⋊C4C22semidirect
64. C4×C4⋊C4×C67C22semidirect
339. C2×C67#2594semidirect
363. C2×C4×C4⋊C4D67semidirect
364. C67C2×#2594semidirect
400. C4×C4⋊C4C2×D67semidirect
687. C2#22565709direct (N × H)

Maximal subgroups

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

subgroupindex
#225657092
C2×C67⋊#4012
C2×#168633272
C2×#168633222
C2×#168633202
C2×#168632912
C2×#168632872
C2×#168632862
C2×#168632852
C2×#168632802
C2×#168632782
C2×C4×Dic67⋊C42
C2×C4×C4⋊C4×C672
C2×#259467