Finite Group Databasebeta

← C2×#22571464 #31728022

Subgroups — C2×#22571464 #31728022

Order 17152.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864024C211yesmaximal, characteristic, complemented
2C2×#16864001C211yesmaximal, characteristic
3#22571464C2116yesmaximal, direct product factor
4C2×#16863805C211yesmaximal, characteristic, complemented
5C2×#16863798C211yesmaximal, characteristic, complemented
6C2×#16863761C211yesmaximal, characteristic, complemented
7C2×#16863743C211yesmaximal, characteristic, complemented
8C2×#16863715C211yesmaximal, characteristic, complemented
9C2×#16863721C211yesmaximal, characteristic, complemented
10C2×#16863721C211yesmaximal, characteristic, complemented
11C2×#16863710C211yesmaximal, characteristic, complemented
12C2×#16863697C211yesmaximal, characteristic, complemented
13C2×#16863697C211yesmaximal, characteristic, complemented
14C2×#16863687C211yesmaximal, characteristic, complemented
15C2×#16863677C211yesmaximal, characteristic, complemented
16C2×#433×C67C211yesmaximal, characteristic, complemented
17#16864024—24no—
18#16864024C2218yescomplemented
19#16864001—24no—
20#16864001C2218yes—
21C2×#14524043C2211yescharacteristic
22C2×#14524043C2211yescharacteristic
23C2×#14524042—21no—
24C2×#14524040C2211yescharacteristic
25C2×#14524035C2211yescharacteristic
26C2×#14524035C2211yescharacteristic
27C2×#14524035C2211yescharacteristic
28C2×#14524034—21no—
29C2×#14524028—21no—
30C2×#14524028—21no—
31C2×#14524020—21no—
32C2×#14524020—21no—
33C2×#14524017C2211yescharacteristic
34C2×#14524017C2211yescharacteristic
35C2×#14524016—21no—
36C2×#14524016—21no—
37C2×C4×D268C2211yescharacteristic
38C2×C4×D268C2211yescharacteristic
39C2×#14524002C2211yescharacteristic
40C22×C4⋊Dic67C2211yescharacteristic
41#16863805C2218yescomplemented
42#16863798C2218yescomplemented
43#16863761C2218yescomplemented
44#16863743C2218yescomplemented
45#16863721C2218yescomplemented
46#16863721C2218yescomplemented
47#16863715C2218yescomplemented
48#16863710C2218yescomplemented
49#16863697C2218yescomplemented
50#16863697C2218yescomplemented
51#16863687C2218yescomplemented
52#16863677C2218yescomplemented
53C2×#14523977C2211yescharacteristic
54C2×#14523977C2211yescharacteristic
55C2×#14523977C2211yescharacteristic
56C2×#14523977C2211yescharacteristic
57C2×#14523975C2211yescharacteristic
58C2×#14523975C2211yescharacteristic
59C2×#14523975C2211yescharacteristic
60C2×#14523975C2211yescharacteristic
61C2×#14523965C2211yescharacteristic
62C2×#14523965C2211yescharacteristic
63C2×#14523965C2211yescharacteristic
64C2×#14523965C2211yescharacteristic
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×D268—21no—
80C22×D268—21no—
81C22×D268C2311yescharacteristic
82C22×D268C2311yescharacteristic
83C22×C22⋊D67—21no—
84C22×C22⋊D67—21no—
85C23×Dic67—21no—
86C22×C4×D67—21no—
87C22×C4×D67—21no—
88#14524043—22no—
89#14524043—22no—
90#14524043C2314yes—
91#14524043C2314yes—
92#14524042—28no—
93#14524040—22no—
94#14524040C2314yes—
95#14524035—22no—
96#14524035—22no—
97#14524035—22no—
98#14524035C2314yes—
99#14524035C2314yes—
100#14524035C2314yes—
101#14524034—28no—
102#14524028—28no—
103#14524028—28no—
104#14524020—28no—
105#14524020—28no—
106#14524017—22no—
107#14524017—22no—
108#14524017C2314yes—
109#14524017C2314yes—
110#14524016—28no—
111#14524016—28no—
112C4×D268—22no—
113C4×D268—22no—
114C4×D268C2314yes—
115C4×D268C2314yes—
116#14524002—22no—
117#14524002C2314yes—
118C2×C4⋊Dic67—22no—
119C2×C4⋊Dic67—21no—
120C2×C4⋊Dic67—21no—
121C2×C4⋊Dic67—21no—
122C2×C4⋊Dic67C2314yes—
123C2×C4⋊Dic67C2311yescharacteristic
124C2×C4⋊Dic67C2311yescharacteristic
125C2×C4⋊Dic67C2311yescharacteristic
126C2×C4⋊Dic67C2311yescharacteristic
127C2×C4⋊Dic67C2311yescharacteristic
128C2×C4⋊Dic67C2311yescharacteristic
129C2×Dic67⋊C4—21no—
130C2×Dic67⋊C4—21no—
131C2×Dic67⋊C4—21no—
132C2×Dic67⋊C4—21no—
133C2×Dic67⋊C4—21no—
134C2×Dic67⋊C4—21no—
135C2×C22⋊Dic67—21no—
136C2×(C2×D67)⋊C4—21no—
137C2×(C2×D67)⋊C4—21no—
138C2×(C2×D67)⋊C4—21no—
139C2×(C2×D67)⋊C4—21no—
140C2×C4×Dic67—21no—
141#14523977C2314yes—
142#14523977C2314yes—
143#14523977C2314yes—
144#14523977C2314yes—
145#14523975C2314yes—
146#14523975C2314yes—
147#14523975C2314yes—
148#14523975C2314yes—
149#14523965C2314yes—
150#14523965C2314yes—
151#14523965C2314yes—
152#14523965C2314yes—
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—
177C23×D67—21no—
178C2×Dic134—24no—
179C2×Dic134—24no—
180C2×Dic134—82no—
181C2×Dic134—82no—
182C2×D268—22no—
183C2×D268—22no—
184C2×D268—22no—
185C2×D268—22no—
186C2×D268—21no—
187C2×D268—21no—
188C2×D268—24no—
189C2×D268—24no—
190C2×D268—82no—
191C2×D268—82no—
192C2×D268C2412yes—
193C2×D268C2412yes—
194C2×C22⋊D67—24no—
195C2×C22⋊D67—24no—
196C2×C22⋊D67—82no—
197C2×C22⋊D67—82no—
198C22×Dic67—21no—
199C22×Dic67—21no—
200C22×Dic67—21no—
201C22×Dic67—21no—
202C22×Dic67—21no—
203C22×Dic67—21no—
204C22×Dic67—24no—
205C22×Dic67—82no—
206C2×C4×D67—24no—
207C2×C4×D67—24no—
208C2×C4×D67—82no—
209C2×C4×D67—82no—
210C4⋊Dic67—24no—
211C4⋊Dic67—21no—
212C4⋊Dic67—21no—
213C4⋊Dic67—24no—
214C4⋊Dic67—24no—
215C4⋊Dic67—21no—
216C4⋊Dic67—21no—
217C4⋊Dic67—21no—
218C4⋊Dic67—21no—
219C4⋊Dic67C2412yes—
220C4⋊Dic67C2412yes—
221C4⋊Dic67C2412yes—
222C4⋊Dic67C2412yes—
223C4⋊Dic67C2412yes—
224C4⋊Dic67C2412yes—
225Dic67⋊C4—24no—
226Dic67⋊C4—24no—
227Dic67⋊C4—24no—
228Dic67⋊C4—24no—
229Dic67⋊C4—24no—
230Dic67⋊C4—24no—
231C22⋊Dic67—24no—
232(C2×D67)⋊C4—24no—
233(C2×D67)⋊C4—24no—
234(C2×D67)⋊C4—24no—
235(C2×D67)⋊C4—24no—
236C4×Dic67—24no—
237C24×C67C2×D411yescharacteristic
238C22×C4×C67—22no—
239C22×C4×C67—22no—
240C22×C4×C67C2×D411yescharacteristic
241C22×C4×C67C2×D411yescharacteristic
242C22×C4×C67C2×D411yescharacteristic
243C22×C4×C67C2×D411yescharacteristic
244C22×C4×C67C2×D411yescharacteristic
245C22×C4×C67C2×D412yes—
246C22×C4×C67C2412yes—
247C22×C4×C67C2411yescharacteristic
248C2×C8×C67—22no—
249C2×C8×C67—22no—
250C2×C8×C67—22no—
251C2×C8×C67—22no—
252C2×C8×C67C2412yes—
253C2×C8×C67C2412yes—
254C2×C8×C67C2412yes—
255C2×C8×C67C2412yes—
256C4⋊C4×C67C2×D414yes—
257C4⋊C4×C67C2×D414yes—
258C22⋊C4×C67C2×D414yes—
259C22⋊C4×C67C2×D414yes—
260C42×C67C2×D412yes—
261C42×C67C2×D412yes—
262C42×C67C2412yes—
263C42×C67C2412yes—
264C23×C67—22no—
265C23×C67—22no—
266C23×C67—22no—
267C23×C67C22×D412yes—
268C23×C67C22×D411yescharacteristic
269C22×D67—22no—
270C22×D67—22no—
271C22×D67—42no—
272C22×D67—42no—
273C22×D67—42no—
274C22×D67—42no—
275C22×D67—42no—
276C22×D67—42no—
277C2×C4×C67—22no—
278C2×C4×C67—22no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—24no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67C22×D412yes—
286C2×C4×C67C22×D412yes—
287C2×C4×C67C22×D412yes—
288C2×C4×C67C22×D412yes—
289C2×C4×C67C22×D412yes—
290C2×C4×C67C22×D411yescharacteristic
291C2×C4×C672−1+412yes—
292C2×C4×C672−1+412yes—
293C2×C4×C67C2511yescharacteristic
294C22⋊D67—84no—
295C22⋊D67—84no—
296C2×Dic67—22no—
297C2×Dic67—22no—
298C2×Dic67—22no—
299C2×Dic67—22no—
300C2×Dic67—22no—
301C2×Dic67—22no—
302C2×Dic67—42no—
303C2×Dic67—42no—
304C2×Dic67—42no—
305C2×Dic67—42no—
306C2×Dic67—42no—
307C2×Dic67—42no—
308C2×Dic67—84no—
309D268—22no—
310D268—22no—
311D268—22no—
312D268—22no—
313D268—42no—
314D268—42no—
315D268—84no—
316D268—84no—
317C4×D67—84no—
318C4×D67—84no—
319Dic134—84no—
320Dic134—84no—
321C8×C67—22no—
322C8×C67—22no—
323C8×C67—22no—
324C8×C67—22no—
325C22×C67—22no—
326C22×C67—22no—
327C22×C67—22no—
328C22×C67—44no—
329C22×C67#53612yes—
330C22×C67#57612yes—
331C22×C67#57712yes—
332C22×C67C23×D411yescharacteristic
333C2×D67—42no—
334C2×D67—42no—
335C2×D67—42no—
336C2×D67—42no—
337C2×D67—42no—
338C2×D67—42no—
339C2×D67—84no—
340C2×D67—84no—
341C4×C67—22no—
342C4×C67—22no—
343C4×C67—22no—
344C4×C67—22no—
345C4×C67—22no—
346C4×C67#53612yes—
347C4×C67C2×2−1+411yescharacteristic
348C4×C67C2×2−1+411yescharacteristic
349Dic67—42no—
350Dic67—42no—
351Dic67—42no—
352Dic67—42no—
353Dic67—42no—
354Dic67—42no—
355C2×#3241—671nomaximal, Sylow
356C2×C67—42no—
357C2×C67#324114yescomplemented
358C2×C67C2×#53611yescharacteristic
359C2×C67C2×#57611yescharacteristic
360C2×C67C2×#57711yescharacteristic
361D67—82no—
362D67—82no—
363C2×#544—671no—
364C2×#540—671no—
365#3241—6716no—
366C2×#501—671no—
367C2×#499—671no—
368C2×#490—671no—
369C2×#486—671no—
370C2×#481—671no—
371C2×#482—671no—
372C2×#482—671no—
373C2×#480—671no—
374C2×#478—671no—
375C2×#478—671no—
376C2×#476—671no—
377C2×#474—671no—
378C2×#433D6711yescharacteristic, complemented
379C67C2×#324111yescharacteristic, complemented, Sylow
380#544—678no—
381#544—1344no—
382#540—678no—
383#540—1344no—
384C2×C4⋊Q8—671no—
385C2×C4⋊Q8—671no—
386C2×C4⋊Q8—1341no—
387C2×#127—671no—
388C2×#125—671no—
389C2×#125—671no—
390C2×#125—671no—
391C2×#125—1341no—
392C2×#123—1341no—
393C2×#123—1341no—
394C2×C22⋊Q8—1341no—
395C2×C22⋊Q8—1341no—
396C2×#121—671no—
397C2×#121—671no—
398C2×#121—1341no—
399C2×#121—1341no—
400C2×C4×D4—671no—
401C2×C4×D4—671no—
402C2×#117—671no—
403C2×#117C2×D6711yescharacteristic
404C22×C4⋊C4—671no—
405#501—678no—
406#499—678no—
407#490—678no—
408#486—678no—
409#482—678no—
410#482—678no—
411#481—678no—
412#480—678no—
413#478—678no—
414#478—678no—
415#476—678no—
416#474—678no—
417#433C2×D6718yescomplemented
418C2×#107—671no—
419C2×#107—671no—
420C2×#107—671no—
421C2×#107—671no—
422C2×#106—671no—
423C2×#106—671no—
424C2×#106—671no—
425C2×#106—671no—
426C2×C4⋊C8C2×D6711yescharacteristic
427C2×C4⋊C8C2×D6711yescharacteristic
428C2×#102—671no—
429C2×#102—671no—
430C2×#102—671no—
431C2×#102—671no—
432C2×#102—671no—
433C2×#102—671no—
434C2×#102—671no—
435C2×#102—671no—
436C2×C22⋊C8C2×D6711yescharacteristic
437C2×C22⋊C8C2×D6711yescharacteristic
438C2×#97C2×D6711yescharacteristic
439C2×C4×C8C2×D6711yescharacteristic
440C22×Q8—1341no—
441C22×Q8—1341no—
442C22×D4—671no—
443C22×D4—671no—
444C22×D4—1341no—
445C22×D4—1341no—
446C22×D4—1341no—
447C22×D4—1341no—
448C23×C4—1341no—
449C23×C4—1341no—
450C23×C4—1341no—
451C23×C4C22×D6711yescharacteristic
452C22×C8C22×D6711yescharacteristic
453C22×C8C22×D6711yescharacteristic
454C22×C8C22×D6711yescharacteristic
455C22×C8C22×D6711yescharacteristic
456C4⋊Q8—674no—
457C4⋊Q8—674no—
458C4⋊Q8—1348no—
459C4⋊Q8—1342no—
460C4⋊Q8—1342no—
461#127—674no—
462#127—1342no—
463#125—674no—
464#125—674no—
465#125—674no—
466#125—1348no—
467#125—1342no—
468#125—1342no—
469#125—1342no—
470#123—1348no—
471#123—1348no—
472C22⋊Q8—1348no—
473C22⋊Q8—1348no—
474#121—674no—
475#121—674no—
476#121—1342no—
477#121—1342no—
478#121—1348no—
479#121—1348no—
480C4×D4—674no—
481C4×D4—674no—
482C4×D4—1342no—
483C4×D4—1342no—
484#117—674no—
485#117—1342no—
486#117D26814yes—
487#117C22×D6714yes—
488C2×C4⋊C4—671no—
489C2×C4⋊C4—671no—
490C2×C4⋊C4—674no—
491C2×C4⋊C4—671no—
492C2×C4⋊C4—671no—
493C2×C4⋊C4—671no—
494C2×C4⋊C4—671no—
495C2×C4⋊C4—1341no—
496C2×C4⋊C4—1342no—
497C2×C4⋊C4—1341no—
498C2×C4⋊C4—1341no—
499C2×C4⋊C4—1341no—
500C2×C4⋊C4—1341no—
501C2×C4⋊C4—1341no—
502C2×C4⋊C4—1341no—
503C2×C4⋊C4—1341no—
504C2×C4⋊C4—1341no—
505C2×C4⋊C4D26811yescharacteristic
506C2×C4⋊C4D26811yescharacteristic
507C2×C22⋊C4—1341no—
508C2×C22⋊C4—1341no—
509C2×C22⋊C4—1341no—
510C2×C22⋊C4—1341no—
511C2×C22⋊C4—1341no—
512C2×C22⋊C4D26811yescharacteristic
513C2×C22⋊C4D26811yescharacteristic
514C2×C42—1341no—
515C2×C42C22×D6711yescharacteristic
516C2×C42C22×D6711yescharacteristic
517#107—674no—
518#107—674no—
519#107—674no—
520#107—674no—
521#106—674no—
522#106—674no—
523#106—674no—
524#106—674no—
525C4⋊C8C22×D6714yes—
526C4⋊C8C22×D6714yes—
527#102—674no—
528#102—674no—
529#102—674no—
530#102—674no—
531#102—674no—
532#102—674no—
533#102—674no—
534#102—674no—
535C22⋊C8C22×D6714yes—
536C22⋊C8C22×D6714yes—
537#97C22×D6714yes—
538C4×C8C22×D6714yes—
539C24—1341no—
540C24—1341no—
541C24C2×D26811yescharacteristic
542C2×Q8—5362no—
543C2×Q8—5362no—
544C2×Q8—1344no—
545C2×Q8—1344no—
546C2×D4—5362no—
547C2×D4—5362no—
548C2×D4—5362no—
549C2×D4—5362no—
550C2×D4—672no—
551C2×D4—672no—
552C2×D4—1344no—
553C2×D4—1344no—
554C2×D4—1341no—
555C2×D4—1341no—
556C2×D4—1344no—
557C2×D4—1344no—
558C2×D4—1342no—
559C2×D4—1342no—
560C2×D4—1342no—
561C2×D4—1342no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—5362no—
565C22×C4—5362no—
566C22×C4—5362no—
567C22×C4—1341no—
568C22×C4—1341no—
569C22×C4—1341no—
570C22×C4—1341no—
571C22×C4—1341no—
572C22×C4—1341no—
573C22×C4—1344no—
574C22×C4—1344no—
575C22×C4—1344no—
576C22×C4C2×D26812yes—
577C22×C4C2×D26811yescharacteristic
578C22×C4C2×D26811yescharacteristic
579C22×C4C2×D26811yescharacteristic
580C22×C4C2×D26811yescharacteristic
581C22×C4C2×D26811yescharacteristic
582C22×C4C23×D6712yes—
583C22×C4C23×D6711yescharacteristic
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8C23×D6712yes—
589C2×C8C23×D6712yes—
590C2×C8C23×D6712yes—
591C2×C8C23×D6712yes—
592C4⋊C4—672no—
593C4⋊C4—672no—
594C4⋊C4—672no—
595C4⋊C4—672no—
596C4⋊C4—672no—
597C4⋊C4—672no—
598C4⋊C4—1344no—
599C4⋊C4—1341no—
600C4⋊C4—1341no—
601C4⋊C4—1341no—
602C4⋊C4—1341no—
603C4⋊C4—1341no—
604C4⋊C4—1341no—
605C4⋊C4—1344no—
606C4⋊C4—1344no—
607C4⋊C4—1344no—
608C4⋊C4—1344no—
609C4⋊C4—1344no—
610C4⋊C4—1344no—
611C4⋊C4—1344no—
612C4⋊C4—1344no—
613C4⋊C4C2×D26814yes—
614C4⋊C4C2×D26814yes—
615C22⋊C4—1344no—
616C22⋊C4—1344no—
617C22⋊C4—1344no—
618C22⋊C4—1344no—
619C22⋊C4—1344no—
620C22⋊C4C2×D26814yes—
621C22⋊C4C2×D26814yes—
622C42—1344no—
623C42C2×D26812yes—
624C42C2×D26812yes—
625C42C23×D6712yes—
626C42C23×D6712yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—2682no—
631C23—2682no—
632C23—2682no—
633C23—2682no—
634C23—2682no—
635C23—2682no—
636C23—1342no—
637C23—1342no—
638C23C22×D26812yes—
639C23C22×D26811yescharacteristic
640Q8—5364no—
641Q8—5364no—
642D4—2682no—
643D4—2682no—
644D4—5364no—
645D4—5364no—
646D4—5364no—
647D4—5364no—
648D4—1342no—
649D4—1342no—
650D4—1342no—
651D4—1342no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—2682no—
661C2×C4—2682no—
662C2×C4—2682no—
663C2×C4—2682no—
664C2×C4—2682no—
665C2×C4—2682no—
666C2×C4—5364no—
667C2×C4—5364no—
668C2×C4—5364no—
669C2×C4—1342no—
670C2×C4—1342no—
671C2×C4—1342no—
672C2×C4—1342no—
673C2×C4—1342no—
674C2×C4—1342no—
675C2×C4C22×D26812yes—
676C2×C4C22×D26812yes—
677C2×C4C22×D26812yes—
678C2×C4C22×D26812yes—
679C2×C4C22×D26812yes—
680C2×C4C22×D26811yescharacteristic
681C2×C4#1452409012yes—
682C2×C4#1452409012yes—
683C2×C4C24×D6711yescharacteristic
684C8—22no—
685C8—22no—
686C8—22no—
687C8—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—2682no—
693C22—2682no—
694C22—2682no—
695C22—2682no—
696C22—2682no—
697C22—2682no—
698C22—5364no—
699C22—5364no—
700C22#1686397212yes—
701C22#1686420112yes—
702C22#1686420812yes—
703C22C23×D26811yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—2682no—
710C4—2682no—
711C4—2682no—
712C4—2682no—
713C4—2682no—
714C4—2682no—
715C4#1686397212yes—
716C4C2×#1452409011yescharacteristic
717C4C2×#1452409011yescharacteristic
718C2—42no—
719C2—5362no—
720C2—5362no—
721C2#2257146414yesdirect product factor
722C2C2×#1686397211yescharacteristic
723C2C2×#1686420111yescharacteristic
724C2C2×#1686420811yescharacteristic
subgroupG/H
centerC23C22×D268
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#433×C67C2
socleC23×C67C22×D4
prime radicalC2×#16864001C2
hypercenterC2×#433D67
hypocenterC67C2×#3241
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. #22571464C2direct (N × H)
4. C2×#16863805C2semidirect
5. C2×#16863798C2semidirect
6. C2×#16863761C2semidirect
7. C2×#16863743C2semidirect
8. C2×#16863715C2semidirect
9. C2×#16863721C2semidirect
10. C2×#16863721C2semidirect
11. C2×#16863710C2semidirect
12. C2×#16863697C2semidirect
13. C2×#16863697C2semidirect
14. C2×#16863687C2semidirect
15. C2×#16863677C2semidirect
16. C2×#433×C67C2semidirect
18. #16864024C22semidirect
41. #16863805C22semidirect
42. #16863798C22semidirect
43. #16863761C22semidirect
44. #16863743C22semidirect
45. #16863721C22semidirect
46. #16863721C22semidirect
47. #16863715C22semidirect
48. #16863710C22semidirect
49. #16863697C22semidirect
50. #16863697C22semidirect
51. #16863687C22semidirect
52. #16863677C22semidirect
70. #433×C67C22semidirect
357. C2×C67#3241semidirect
378. C2×#433D67semidirect
379. C67C2×#3241semidirect
417. #433C2×D67semidirect
721. C2#22571464direct (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×#168640012
#225714642
C2×#168638052
C2×#168637982
C2×#168637612
C2×#168637432
C2×#168637152
C2×#168637212
C2×#168637102
C2×#168636972
C2×#168636872
C2×#168636772
C2×#433×C672
C2×#324167