Finite Group Databasebeta

← C2×#22572741 #31734460

Subgroups — C2×#22572741 #31734460

Order 17152.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864116C211yesmaximal, characteristic
2C2×#16864086C211yesmaximal, characteristic
3#22572741C2116yesmaximal, direct product factor
4C2×#16863805C211yesmaximal, characteristic, complemented
5C2×#16863732C211yesmaximal, characteristic, complemented
6C2×#16863738C211yesmaximal, characteristic, complemented
7C2×#16863738C211yesmaximal, characteristic, complemented
8C2×#16863738C211yesmaximal, characteristic, complemented
9C2×#16863704C211yesmaximal, characteristic, complemented
10C2×#16863692C211yesmaximal, characteristic, complemented
11C2×#16863654C211yesmaximal, characteristic, complemented
12C2×#16863637C211yesmaximal, characteristic, complemented
13C2×#16863504C211yesmaximal, characteristic, complemented
14C2×#16863438C211yesmaximal, characteristic, complemented
15C2×#16863434C211yesmaximal, characteristic, complemented
16C2×#435×C67C211yesmaximal, characteristic
17C22×Dic268C2211yescharacteristic
18#16864116—24no—
19#16864116C2218yes—
20#16864086—24no—
21#16864086C2218yes—
22C2×#14524043C2211yescharacteristic
23C2×#14524036—21no—
24C2×#14524036—21no—
25C2×#14524036—21no—
26C2×#14524035C2211yescharacteristic
27C2×#14524033—21no—
28C2×#14524030—21no—
29C2×#14524024—21no—
30C2×#14524022C2211yescharacteristic
31C2×#14524022C2211yescharacteristic
32C2×#14524022C2211yescharacteristic
33C2×#14524022C2211yescharacteristic
34C2×C4×Dic134C2211yescharacteristic
35C2×C4×Dic134C2211yescharacteristic
36C2×#14524008—21no—
37C2×#14524002C2211yescharacteristic
38C2×#14524002C2211yescharacteristic
39C2×#14524002C2211yescharacteristic
40C2×#14523999—21no—
41C22×C4⋊Dic67C2211yescharacteristic
42#16863805C2218yescomplemented
43#16863738C2218yescomplemented
44#16863738C2218yescomplemented
45#16863738C2218yescomplemented
46#16863732C2218yescomplemented
47#16863704C2218yescomplemented
48#16863692C2218yescomplemented
49#16863654C2218yescomplemented
50#16863637C2218yescomplemented
51#16863504C2218yescomplemented
52#16863438C2218yescomplemented
53#16863434C2218yescomplemented
54C2×#14523977C2211yescharacteristic
55C2×#14523977C2211yescharacteristic
56C2×#14523977C2211yescharacteristic
57C2×#14523977C2211yescharacteristic
58C2×#14523977C2211yescharacteristic
59C2×#14523975C2211yescharacteristic
60C2×#14523975C2211yescharacteristic
61C2×#14523975C2211yescharacteristic
62C2×#14523975C2211yescharacteristic
63C2×#14523968C2211yescharacteristic
64C2×#14523968C2211yescharacteristic
65C2×#14523968C2211yescharacteristic
66C2×#14523968C2211yescharacteristic
67C2×#14523968C2211yescharacteristic
68C2×#14523968C2211yescharacteristic
69C22×M16×C67C2211yescharacteristic
70C23×C8×C67C2211yescharacteristic
71C2×C4×D4×C67C2211yescharacteristic
72#435×C67C2218yes—
73C2×C4⋊C8×C67C2211yescharacteristic
74C2×C22⋊C8×C67C2211yescharacteristic
75C2×C22⋊C8×C67C2211yescharacteristic
76C2×#97×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134C2311yescharacteristic
79C22×Dic134C2311yescharacteristic
80C23×Dic67—21no—
81C2×Dic268—24no—
82C2×Dic268C2314yes—
83#14524043—22no—
84#14524043C2314yes—
85#14524036—28no—
86#14524036—28no—
87#14524036—28no—
88#14524035—22no—
89#14524035C2314yes—
90#14524033—28no—
91#14524030—28no—
92#14524024—28no—
93#14524022—22no—
94#14524022—22no—
95#14524022—22no—
96#14524022—22no—
97#14524022C2314yes—
98#14524022C2314yes—
99#14524022C2314yes—
100#14524022C2314yes—
101C4×Dic134—22no—
102C4×Dic134—22no—
103C4×Dic134C2314yes—
104C4×Dic134C2314yes—
105#14524008—28no—
106#14524002—22no—
107#14524002—22no—
108#14524002—22no—
109#14524002C2314yes—
110#14524002C2314yes—
111#14524002C2314yes—
112#14523999—28no—
113C2×C4⋊Dic67—22no—
114C2×C4⋊Dic67—21no—
115C2×C4⋊Dic67—21no—
116C2×C4⋊Dic67C2314yes—
117C2×C4⋊Dic67C2311yescharacteristic
118C2×C4⋊Dic67C2311yescharacteristic
119C2×C4⋊Dic67C2311yescharacteristic
120C2×C4⋊Dic67C2311yescharacteristic
121C2×C4⋊Dic67C2311yescharacteristic
122C2×C4⋊Dic67C2311yescharacteristic
123C2×Dic67⋊C4—21no—
124C2×Dic67⋊C4—21no—
125C2×Dic67⋊C4—21no—
126C2×Dic67⋊C4—21no—
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C2×Dic67⋊C4—21no—
130C2×Dic67⋊C4—21no—
131C2×C22⋊Dic67—21no—
132C2×C22⋊Dic67—21no—
133C2×C22⋊Dic67—21no—
134C2×C22⋊Dic67—21no—
135C2×C22⋊Dic67—21no—
136C2×C22⋊Dic67—21no—
137C2×C22⋊Dic67—21no—
138C2×C4×Dic67—21no—
139C2×C4×Dic67—21no—
140C2×C4×Dic67—21no—
141C2×C4×Dic67—21no—
142C2×C4×Dic67—21no—
143#14523977C2314yes—
144#14523977C2314yes—
145#14523977C2314yes—
146#14523977C2314yes—
147#14523977C2314yes—
148#14523975C2314yes—
149#14523975C2314yes—
150#14523975C2314yes—
151#14523975C2314yes—
152#14523968C2314yes—
153#14523968C2314yes—
154#14523968C2314yes—
155#14523968C2314yes—
156#14523968C2314yes—
157#14523968C2314yes—
158C22×D4×C67D411yescharacteristic
159C23×C4×C67C2311yescharacteristic
160C23×C4×C67C2311yescharacteristic
161C2×M16×C67—24no—
162C2×M16×C67C2314yes—
163C22×C8×C67—24no—
164C22×C8×C67C2314yes—
165C22×C8×C67C2311yescharacteristic
166C22×C8×C67C2311yescharacteristic
167C22×C8×C67C2311yescharacteristic
168C22×C8×C67C2311yescharacteristic
169C4×D4×C67D414yes—
170C4×D4×C67C2314yes—
171C2×C4⋊C4×C67D411yescharacteristic
172C2×C22⋊C4×C67D411yescharacteristic
173C2×C22⋊C4×C67D411yescharacteristic
174C2×C42×C67C2311yescharacteristic
175C4⋊C8×C67C2314yes—
176C22⋊C8×C67C2314yes—
177C22⋊C8×C67C2314yes—
178#97×C67C2314yes—
179C2×Dic134—22no—
180C2×Dic134—22no—
181C2×Dic134—22no—
182C2×Dic134—22no—
183C2×Dic134—24no—
184C2×Dic134—21no—
185C2×Dic134—21no—
186C2×Dic134—44no—
187C2×Dic134C2412yes—
188C2×Dic134C2412yes—
189C22×Dic67—21no—
190C22×Dic67—21no—
191C22×Dic67—21no—
192C22×Dic67—21no—
193C22×Dic67—21no—
194C22×Dic67—21no—
195C22×Dic67—21no—
196C22×Dic67—21no—
197C22×Dic67—24no—
198C22×Dic67—44no—
199Dic268—28no—
200C4⋊Dic67—21no—
201C4⋊Dic67—21no—
202C4⋊Dic67—24no—
203C4⋊Dic67—24no—
204C4⋊Dic67—21no—
205C4⋊Dic67—21no—
206C4⋊Dic67—21no—
207C4⋊Dic67—21no—
208C4⋊Dic67C2412yes—
209C4⋊Dic67C2412yes—
210C4⋊Dic67C2412yes—
211C4⋊Dic67C2412yes—
212C4⋊Dic67C2412yes—
213C4⋊Dic67C2412yes—
214Dic67⋊C4—24no—
215Dic67⋊C4—24no—
216Dic67⋊C4—24no—
217Dic67⋊C4—24no—
218Dic67⋊C4—24no—
219Dic67⋊C4—24no—
220Dic67⋊C4—24no—
221Dic67⋊C4—24no—
222C22⋊Dic67—24no—
223C22⋊Dic67—24no—
224C22⋊Dic67—24no—
225C22⋊Dic67—24no—
226C22⋊Dic67—24no—
227C22⋊Dic67—24no—
228C22⋊Dic67—24no—
229C4×Dic67—24no—
230C4×Dic67—24no—
231C4×Dic67—24no—
232C4×Dic67—24no—
233C4×Dic67—24no—
234C24×C67C2×D411yescharacteristic
235C24×C67C2×D411yescharacteristic
236C2×D4×C67—42no—
237C2×D4×C67C2×D414yes—
238C22×C4×C67—22no—
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67—22no—
242C22×C4×C67C2×D411yescharacteristic
243C22×C4×C67C2×D411yescharacteristic
244C22×C4×C67C2×D411yescharacteristic
245C22×C4×C67C2×D411yescharacteristic
246C22×C4×C67C2×D412yes—
247C22×C4×C67C2×D412yes—
248C22×C4×C67C2412yes—
249C22×C4×C67C2412yes—
250C22×C4×C67C2411yescharacteristic
251M16×C67—28no—
252C2×C8×C67—22no—
253C2×C8×C67—22no—
254C2×C8×C67—22no—
255C2×C8×C67—28no—
256C2×C8×C67#4114yes—
257C2×C8×C67C2412yes—
258C2×C8×C67C2412yes—
259C2×C8×C67C2412yes—
260C2×C8×C67C2412yes—
261C4⋊C4×C67C2×D414yes—
262C22⋊C4×C67C2×D414yes—
263C22⋊C4×C67C2×D414yes—
264C42×C67C2×D412yes—
265C42×C67C2412yes—
266C23×C67—22no—
267C23×C67—22no—
268C23×C67—22no—
269C23×C67—22no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67C22×D412yes—
273C23×C67C22×D412yes—
274C23×C67C22×D411yescharacteristic
275D4×C67—44no—
276C2×C4×C67—22no—
277C2×C4×C67—22no—
278C2×C4×C67—22no—
279C2×C4×C67—22no—
280C2×C4×C67—24no—
281C2×C4×C67—24no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67—22no—
286C2×C4×C67C22×D412yes—
287C2×C4×C67C22×D412yes—
288C2×C4×C67C22×D412yes—
289C2×C4×C67C22×D412yes—
290C2×C4×C67C22×D411yescharacteristic
291C2×C4×C67C2×#4112yes—
292C2×C4×C672−1+412yes—
293C2×C4×C67C2511yescharacteristic
294C2×Dic67—22no—
295C2×Dic67—22no—
296C2×Dic67—22no—
297C2×Dic67—22no—
298C2×Dic67—22no—
299C2×Dic67—22no—
300C2×Dic67—22no—
301C2×Dic67—22no—
302C2×Dic67—48no—
303C2×Dic67—42no—
304C2×Dic67—42no—
305C2×Dic67—42no—
306C2×Dic67—42no—
307C2×Dic67—42no—
308C2×Dic67—42no—
309C2×Dic67—42no—
310C2×Dic67—42no—
311Dic134—22no—
312Dic134—22no—
313Dic134—22no—
314Dic134—22no—
315Dic134—48no—
316Dic134—42no—
317Dic134—42no—
318C8×C67—22no—
319C8×C67—22no—
320C8×C67—22no—
321C8×C67C2×#4114yes—
322C22×C67—22no—
323C22×C67—22no—
324C22×C67—22no—
325C22×C67—22no—
326C22×C67—22no—
327C22×C67—22no—
328C22×C67—44no—
329C22×C67—44no—
330C22×C67#54712yes—
331C22×C67#57512yes—
332C22×C67#57812yes—
333C22×C67C23×D411yescharacteristic
334C4×C67—22no—
335C4×C67—22no—
336C4×C67—22no—
337C4×C67—22no—
338C4×C67#54712yes—
339C4×C67C22×#4111yescharacteristic
340C4×C67C2×2−1+411yescharacteristic
341Dic67—42no—
342Dic67—42no—
343Dic67—42no—
344Dic67—42no—
345Dic67—42no—
346Dic67—42no—
347Dic67—42no—
348Dic67—42no—
349C2×#3349—671nomaximal, Sylow
350C2×C67—42no—
351C2×C67—42no—
352C2×C67#334914yescomplemented
353C2×C67C2×#54711yescharacteristic
354C2×C67C2×#57511yescharacteristic
355C2×C67C2×#57811yescharacteristic
356C2×#556—671no—
357C2×#552—671no—
358#3349—6716no—
359C2×#501—671no—
360C2×#484—671no—
361C2×#485—671no—
362C2×#485—671no—
363C2×#485—671no—
364C2×#479—671no—
365C2×#477—671no—
366C2×#470—671no—
367C2×#467—671no—
368C2×#441—671no—
369C2×#435D6711yescharacteristic
370C2×#428—671no—
371C2×#427—671no—
372C67C2×#334911yescharacteristic, complemented, Sylow
373C22×Q16—671no—
374C22×M16C2×D6711yescharacteristic
375C23×C8C2×D6711yescharacteristic
376#556—678no—
377#556—1344no—
378#552—678no—
379#552—1344no—
380C2×C4⋊Q8—671no—
381C2×#126—1341no—
382C2×#126—1341no—
383C2×#126—1341no—
384C2×#125—671no—
385C2×#125—1341no—
386C2×#124—1341no—
387C2×#123—1341no—
388C2×C22⋊Q8—671no—
389C2×C22⋊Q8—671no—
390C2×C22⋊Q8—671no—
391C2×C22⋊Q8—671no—
392C2×C4×Q8—671no—
393C2×C4×Q8—671no—
394C2×C4×Q8—1341no—
395C2×C4×D4C2×D6711yescharacteristic
396C2×#117—671no—
397C2×#117—671no—
398C2×#117—671no—
399C2×#117—1341no—
400C22×C4⋊C4—671no—
401#501—678no—
402#485—678no—
403#485—678no—
404#485—678no—
405#484—678no—
406#479—678no—
407#477—678no—
408#470—678no—
409#467—678no—
410#441—678no—
411#435C2×D6718yes—
412#428—678no—
413#427—678no—
414C2×#107—671no—
415C2×#107—671no—
416C2×#107—671no—
417C2×#107—671no—
418C2×#107—671no—
419C2×#106—671no—
420C2×#106—671no—
421C2×#106—671no—
422C2×#106—671no—
423C2×C4⋊C8C2×D6711yescharacteristic
424C2×#103—671no—
425C2×#103—671no—
426C2×#103—671no—
427C2×#103—671no—
428C2×#103—671no—
429C2×#103—671no—
430C2×C22⋊C8C2×D6711yescharacteristic
431C2×C22⋊C8C2×D6711yescharacteristic
432C2×#97C2×D6711yescharacteristic
433C22×Q8—671no—
434C22×Q8—671no—
435C22×Q8—1341no—
436C22×D4D26811yescharacteristic
437C23×C4—1341no—
438C23×C4C22×D6711yescharacteristic
439C23×C4C22×D6711yescharacteristic
440C2×Q16—674no—
441C2×Q16—1344no—
442C2×M16—24no—
443C2×M16C22×D6714yes—
444C22×C8—24no—
445C22×C8C22×D6711yescharacteristic
446C22×C8C22×D6714yes—
447C22×C8C22×D6711yescharacteristic
448C22×C8C22×D6711yescharacteristic
449C22×C8C22×D6711yescharacteristic
450C4⋊Q8—674no—
451C4⋊Q8—1342no—
452#126—1348no—
453#126—1348no—
454#126—1348no—
455#125—674no—
456#125—1348no—
457#125—1342no—
458#124—1348no—
459#123—1348no—
460C22⋊Q8—674no—
461C22⋊Q8—674no—
462C22⋊Q8—674no—
463C22⋊Q8—674no—
464C22⋊Q8—1342no—
465C22⋊Q8—1342no—
466C22⋊Q8—1342no—
467C22⋊Q8—1342no—
468C4×Q8—674no—
469C4×Q8—674no—
470C4×Q8—1348no—
471C4×Q8—1342no—
472C4×Q8—1342no—
473C4×D4D26814yes—
474C4×D4C22×D6714yes—
475#117—674no—
476#117—674no—
477#117—674no—
478#117—1342no—
479#117—1342no—
480#117—1342no—
481#117—1348no—
482C2×C4⋊C4—671no—
483C2×C4⋊C4—671no—
484C2×C4⋊C4—674no—
485C2×C4⋊C4—671no—
486C2×C4⋊C4—671no—
487C2×C4⋊C4—671no—
488C2×C4⋊C4—671no—
489C2×C4⋊C4—1341no—
490C2×C4⋊C4—1342no—
491C2×C4⋊C4—1341no—
492C2×C4⋊C4—1341no—
493C2×C4⋊C4—1341no—
494C2×C4⋊C4—1341no—
495C2×C4⋊C4—1341no—
496C2×C4⋊C4—1341no—
497C2×C4⋊C4—1341no—
498C2×C4⋊C4—1341no—
499C2×C4⋊C4—1341no—
500C2×C4⋊C4D26811yescharacteristic
501C2×C22⋊C4—1341no—
502C2×C22⋊C4—1341no—
503C2×C22⋊C4—1341no—
504C2×C22⋊C4—1341no—
505C2×C22⋊C4—1341no—
506C2×C22⋊C4—1341no—
507C2×C22⋊C4—1341no—
508C2×C22⋊C4D26811yescharacteristic
509C2×C22⋊C4D26811yescharacteristic
510C2×C42—1341no—
511C2×C42—1341no—
512C2×C42—1341no—
513C2×C42—1341no—
514C2×C42—1341no—
515C2×C42C22×D6711yescharacteristic
516#107—674no—
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—
526#103—674no—
527#103—674no—
528#103—674no—
529#103—674no—
530#103—674no—
531#103—674no—
532C22⋊C8C22×D6714yes—
533C22⋊C8C22×D6714yes—
534#97C22×D6714yes—
535C24C2×D26811yescharacteristic
536C24C2×D26811yescharacteristic
537C2×Q8—2684no—
538C2×Q8—672no—
539C2×Q8—672no—
540C2×Q8—1342no—
541C2×Q8—1342no—
542C2×Q8—1342no—
543C2×Q8—1342no—
544C2×Q8—1341no—
545C2×Q8—1341no—
546C2×Q8—1344no—
547C2×D4—42no—
548C2×D4C2×D26814yes—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—2684no—
554C22×C4—1344no—
555C22×C4—1341no—
556C22×C4—1341no—
557C22×C4—1341no—
558C22×C4—1341no—
559C22×C4—1341no—
560C22×C4—1341no—
561C22×C4—1341no—
562C22×C4—1341no—
563C22×C4C2×D26812yes—
564C22×C4C2×D26812yes—
565C22×C4C2×D26811yescharacteristic
566C22×C4C2×D26811yescharacteristic
567C22×C4C2×D26811yescharacteristic
568C22×C4C2×D26811yescharacteristic
569C22×C4C23×D6712yes—
570C22×C4C23×D6712yes—
571C22×C4C23×D6711yescharacteristic
572Q16—1348no—
573M16—28no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—28no—
578C2×C8#1176162714yes—
579C2×C8C23×D6712yes—
580C2×C8C23×D6712yes—
581C2×C8C23×D6712yes—
582C2×C8C23×D6712yes—
583C4⋊C4—672no—
584C4⋊C4—672no—
585C4⋊C4—672no—
586C4⋊C4—672no—
587C4⋊C4—672no—
588C4⋊C4—672no—
589C4⋊C4—1341no—
590C4⋊C4—1341no—
591C4⋊C4—1344no—
592C4⋊C4—1341no—
593C4⋊C4—1341no—
594C4⋊C4—1341no—
595C4⋊C4—1341no—
596C4⋊C4—1344no—
597C4⋊C4—1344no—
598C4⋊C4—1344no—
599C4⋊C4—1344no—
600C4⋊C4—1344no—
601C4⋊C4—1344no—
602C4⋊C4—1344no—
603C4⋊C4—1344no—
604C4⋊C4—1344no—
605C4⋊C4C2×D26814yes—
606C22⋊C4—1344no—
607C22⋊C4—1344no—
608C22⋊C4—1344no—
609C22⋊C4—1344no—
610C22⋊C4—1344no—
611C22⋊C4—1344no—
612C22⋊C4—1344no—
613C22⋊C4C2×D26814yes—
614C22⋊C4C2×D26814yes—
615C42—1344no—
616C42—1344no—
617C42—1344no—
618C42—1344no—
619C42—1344no—
620C42C2×D26812yes—
621C42C23×D6712yes—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23C22×D26812yes—
629C23C22×D26812yes—
630C23C22×D26811yescharacteristic
631Q8—2688no—
632Q8—2682no—
633Q8—2682no—
634Q8—1342no—
635Q8—1342no—
636Q8—1342no—
637Q8—1342no—
638D4—44no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—2688no—
650C2×C4—2682no—
651C2×C4—2682no—
652C2×C4—2682no—
653C2×C4—2682no—
654C2×C4—2682no—
655C2×C4—2682no—
656C2×C4—2682no—
657C2×C4—2682no—
658C2×C4—1342no—
659C2×C4—1342no—
660C2×C4—1342no—
661C2×C4—1342no—
662C2×C4—1342no—
663C2×C4—1342no—
664C2×C4—1342no—
665C2×C4—1342no—
666C2×C4C22×D26812yes—
667C2×C4C22×D26812yes—
668C2×C4C22×D26812yes—
669C2×C4C22×D26812yes—
670C2×C4C22×D26811yescharacteristic
671C2×C4C2×#1176162712yes—
672C2×C4#1452409012yes—
673C2×C4C24×D6711yescharacteristic
674C8—22no—
675C8—22no—
676C8—22no—
677C8C2×#1176162714yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—44no—
685C22—44no—
686C22#1686405012yes—
687C22#1686419612yes—
688C22#1686421312yes—
689C22C23×D26811yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—2682no—
695C4—2682no—
696C4—2682no—
697C4—2682no—
698C4—2682no—
699C4—2682no—
700C4—2682no—
701C4—2682no—
702C4#1686405012yes—
703C4C22×#1176162711yescharacteristic
704C4C2×#1452409011yescharacteristic
705C2—42no—
706C2—42no—
707C2#2257274114yesdirect product factor
708C2C2×#1686405011yescharacteristic
709C2C2×#1686419611yescharacteristic
710C2C2×#1686421311yescharacteristic
subgroupG/H
centerC23C22×D268
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#435×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×C67D4
hypercenterC2×#435D67
hypocenterC67C2×#3349
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #22572741C2direct (N × H)
4. C2×#16863805C2semidirect
5. C2×#16863732C2semidirect
6. C2×#16863738C2semidirect
7. C2×#16863738C2semidirect
8. C2×#16863738C2semidirect
9. C2×#16863704C2semidirect
10. C2×#16863692C2semidirect
11. C2×#16863654C2semidirect
12. C2×#16863637C2semidirect
13. C2×#16863504C2semidirect
14. C2×#16863438C2semidirect
15. C2×#16863434C2semidirect
42. #16863805C22semidirect
43. #16863738C22semidirect
44. #16863738C22semidirect
45. #16863738C22semidirect
46. #16863732C22semidirect
47. #16863704C22semidirect
48. #16863692C22semidirect
49. #16863654C22semidirect
50. #16863637C22semidirect
51. #16863504C22semidirect
52. #16863438C22semidirect
53. #16863434C22semidirect
352. C2×C67#3349semidirect
372. C67C2×#3349semidirect
707. C2#22572741direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641162
C2×#168640862
#225727412
C2×#168638052
C2×#168637322
C2×#168637382
C2×#168637042
C2×#168636922
C2×#168636542
C2×#168636372
C2×#168635042
C2×#168634382
C2×#168634342
C2×#435×C672
C2×#334967