Finite Group Databasebeta

← C2×#22570044 #31723395

Subgroups — C2×#22570044 #31723395

Order 17152.

2018 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864023C211yesmaximal, characteristic
2C2×#16863872C211yesmaximal, characteristic
3#22570044C2116yesmaximal, direct product factor
4C2×#16863706C211yesmaximal, characteristic, complemented
5C2×#16863704C211yesmaximal, characteristic, complemented
6C2×#16863703C211yesmaximal, characteristic, complemented
7C2×#16863701C211yesmaximal, characteristic, complemented
8C2×#16863689C211yesmaximal, characteristic, complemented
9C2×#16863688C211yesmaximal, characteristic, complemented
10C2×#16863680C211yesmaximal, characteristic, complemented
11C2×#16863435C211yesmaximal, characteristic
12C2×#16863431C211yesmaximal, characteristic
13C2×#16863421C211yesmaximal, characteristic
14C2×#16863403C211yesmaximal, characteristic
15C2×#103×D67C211yesmaximal, characteristic
16C2×#475×C67C211yesmaximal, characteristic, complemented
17C22×Q8×D67C2211yescharacteristic
18C22×#11761611C2211yescharacteristic
19C22×C8×D67C2211yescharacteristic
20#16864023—24no—
21#16864023C2218yes—
22C2×#14524042C2211yescharacteristic
23C2×#14524041—21no—
24C2×#14524035C2211yescharacteristic
25C2×#14524034C2211yescharacteristic
26C2×#14524033—21no—
27C2×#14524021—21no—
28C2×#14524019—21no—
29#16863872—24no—
30#16863872C2218yes—
31C2×Q8×Dic67C2211yescharacteristic
32C2×C4×Dic134—21no—
33C2×C4×Dic134C2211yescharacteristic
34C2×#14524008—21no—
35C2×#14524008C2211yescharacteristic
36C2×#14524001—21no—
37C2×#14524001C2211yescharacteristic
38C2×#14524001C2211yescharacteristic
39C2×#14524000—21no—
40C2×#14524000C2211yescharacteristic
41C2×C4⋊C4×D67C2211yescharacteristic
42#16863706C2218yescomplemented
43#16863704C2218yescomplemented
44#16863703C2218yescomplemented
45#16863701C2218yescomplemented
46#16863689C2218yescomplemented
47#16863688C2218yescomplemented
48#16863680C2218yescomplemented
49#16863435C2218yes—
50#16863431C2218yes—
51C2×#14523977C2211yescharacteristic
52C2×#14523976C2211yescharacteristic
53C2×#14523976C2211yescharacteristic
54C2×#14523976C2211yescharacteristic
55C2×#14523975C2211yescharacteristic
56C2×#14523974C2211yescharacteristic
57#16863421C2218yes—
58C2×C4⋊(C67⋊C8)C2211yescharacteristic
59C2×Dic67⋊C8C2211yescharacteristic
60C2×Dic67⋊C8C2211yescharacteristic
61#16863403C2218yes—
62C2×#14523968C2211yescharacteristic
63C2×#14523968C2211yescharacteristic
64C2×#14523967C2211yescharacteristic
65C2×#14523967C2211yescharacteristic
66C2×#14523966C2211yescharacteristic
67C2×#14523966C2211yescharacteristic
68#103×D67C2218yes—
69C2×C4⋊Q8×C67C2211yescharacteristic
70C2×C4×Q8×C67C2211yescharacteristic
71#475×C67C2218yescomplemented
72C2×#106×C67C2211yescharacteristic
73C2×#106×C67C2211yescharacteristic
74C2×C4⋊C8×C67C2211yescharacteristic
75C2×#103×C67C2211yescharacteristic
76C2×#103×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134—21no—
79C22×Dic134C2311yescharacteristic
80C2×Q8×D67—22no—
81C2×Q8×D67—24no—
82C2×Q8×D67Q818yescomplemented
83C2×Q8×D67C2314yes—
84C22×C4×D67—21no—
85C22×C4×D67—21no—
86C22×C4×D67C2311yescharacteristic
87C2×#11761611—24no—
88C2×#11761611C2314yes—
89C22×C67⋊C8C2311yescharacteristic
90C22×C67⋊C8C2311yescharacteristic
91C2×C8×D67—24no—
92C2×C8×D67C2314yes—
93#14524042—22no—
94#14524042C2314yes—
95#14524041—28no—
96#14524035—22no—
97#14524035C2314yes—
98#14524034—22no—
99#14524034C2314yes—
100#14524033—28no—
101#14524021—28no—
102#14524019—28no—
103Q8×Dic67—22no—
104Q8×Dic67C2314yes—
105C4×Dic134—28no—
106C4×Dic134—22no—
107C4×Dic134C2314yes—
108#14524008—28no—
109#14524008—22no—
110#14524008C2314yes—
111#14524001—22no—
112#14524001—22no—
113#14524001—28no—
114#14524001C2314yes—
115#14524001C2314yes—
116#14524000—28no—
117#14524000D414yes—
118#14524000C2314yes—
119C2×C4⋊Dic67—21no—
120C2×C4⋊Dic67—21no—
121C2×C4⋊Dic67C2311yescharacteristic
122C2×C4⋊Dic67C2311yescharacteristic
123C2×C4⋊Dic67C2311yescharacteristic
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×Dic67⋊C4D411yescharacteristic
132C2×Dic67⋊C4D411yescharacteristic
133C4⋊C4×D67—22no—
134C4⋊C4×D67C2314yes—
135C2×(C2×D67)⋊C4—21no—
136C2×(C2×D67)⋊C4—21no—
137C2×(C2×D67)⋊C4D411yescharacteristic
138C2×(C2×D67)⋊C4D411yescharacteristic
139C2×C4×Dic67—21no—
140C2×C4×Dic67—21no—
141C2×C4×Dic67—21no—
142C2×C4×Dic67—21no—
143C2×C4×Dic67—21no—
144C2×C4×Dic67C2311yescharacteristic
145#14523977C2314yes—
146#14523976C2314yes—
147#14523976C2314yes—
148#14523976C2314yes—
149#14523975C2314yes—
150#14523974C2314yes—
151C4⋊(C67⋊C8)C2314yes—
152Dic67⋊C8C2314yes—
153Dic67⋊C8C2314yes—
154#14523968C2314yes—
155#14523968C2314yes—
156#14523967C2314yes—
157#14523967C2314yes—
158#14523966C2314yes—
159#14523966C2314yes—
160C22×Q8×C67—21no—
161C22×Q8×C67C2311yescharacteristic
162C22×C8×C67C2311yescharacteristic
163C22×C8×C67C2311yescharacteristic
164C4⋊Q8×C67—22no—
165C4⋊Q8×C67C2314yes—
166C4×Q8×C67—22no—
167C4×Q8×C67C2314yes—
168C2×C4⋊C4×C67—21no—
169C2×C4⋊C4×C67—21no—
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C42×C67—21no—
174C2×C42×C67C2311yescharacteristic
175#106×C67C2314yes—
176#106×C67C2314yes—
177C4⋊C8×C67C2314yes—
178#103×C67C2314yes—
179#103×C67C2314yes—
180C23×D67C2×D411yescharacteristic
181C2×Dic134—21no—
182C2×Dic134—22no—
183C2×Dic134—28no—
184C2×Dic134—24no—
185C2×Dic134—24no—
186C2×Dic134—82no—
187C2×Dic134C2×Q814yes—
188C2×Dic134C2412yes—
189Q8×D67—216no—
190Q8×D67—28no—
191Q8×D67C2×Q8116yescomplemented
192C22×Dic67—21no—
193C22×Dic67—21no—
194C22×Dic67—21no—
195C22×Dic67—21no—
196C22×Dic67C2×D411yescharacteristic
197C22×Dic67C2×D411yescharacteristic
198C22×Dic67C2×D411yescharacteristic
199C2×C4×D67—28no—
200C2×C4×D67—24no—
201C2×C4×D67—24no—
202C2×C4×D67—82no—
203C2×C4×D67C2×D412yes—
204C2×C4×D67C2×Q814yes—
205C2×C4×D67#4114yes—
206C2×C4×D67C2412yes—
207#11761611—28no—
208C2×C67⋊C8—22no—
209C2×C67⋊C8—22no—
210C2×C67⋊C8C2412yes—
211C2×C67⋊C8C2412yes—
212C8×D67—28no—
213C4⋊Dic67—21no—
214C4⋊Dic67—21no—
215C4⋊Dic67—21no—
216C4⋊Dic67—24no—
217C4⋊Dic67—24no—
218C4⋊Dic67C2412yes—
219C4⋊Dic67C2412yes—
220C4⋊Dic67C2412yes—
221Dic67⋊C4—24no—
222Dic67⋊C4—24no—
223Dic67⋊C4—24no—
224Dic67⋊C4—24no—
225Dic67⋊C4—24no—
226Dic67⋊C4—24no—
227Dic67⋊C4—24no—
228Dic67⋊C4C2×D414yes—
229Dic67⋊C4C2×D414yes—
230(C2×D67)⋊C4—24no—
231(C2×D67)⋊C4—24no—
232(C2×D67)⋊C4C2×D414yes—
233(C2×D67)⋊C4C2×D414yes—
234C4×Dic67—24no—
235C4×Dic67—24no—
236C4×Dic67—24no—
237C4×Dic67—24no—
238C4×Dic67—24no—
239C4×Dic67C2×D412yes—
240C4×Dic67C2412yes—
241C2×Q8×C67—21no—
242C2×Q8×C67—24no—
243C2×Q8×C67—22no—
244C2×Q8×C67—82no—
245C2×Q8×C67C2×Q814yes—
246C2×Q8×C67C2412yes—
247C22×C4×C67—21no—
248C22×C4×C67—21no—
249C22×C4×C67—21no—
250C22×C4×C67—21no—
251C22×C4×C67C2×D411yescharacteristic
252C22×C4×C67C2×D411yescharacteristic
253C22×C4×C67C2411yescharacteristic
254C2×C8×C67—22no—
255C2×C8×C67—22no—
256C2×C8×C67C2412yes—
257C2×C8×C67C2412yes—
258C4⋊C4×C67—24no—
259C4⋊C4×C67—24no—
260C4⋊C4×C67—21no—
261C4⋊C4×C67—21no—
262C4⋊C4×C67—21no—
263C4⋊C4×C67C2412yes—
264C4⋊C4×C67C2412yes—
265C4⋊C4×C67C2412yes—
266C42×C67—24no—
267C42×C67C2×D412yes—
268C42×C67C2412yes—
269C23×C67C22×D411yescharacteristic
270C22×D67—22no—
271C22×D67—22no—
272C22×D67C22⋊Q814yes—
273C22×D67C22×D412yes—
274Q8×C67—24no—
275Q8×C67—22no—
276Q8×C67—84no—
277Q8×C67C22×Q814yes—
278C2×C4×C67—24no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67—42no—
286C2×C4×C67—42no—
287C2×C4×C67—42no—
288C2×C4×C67C22×D412yes—
289C2×C4×C67C22×D412yes—
290C2×C4×C67C22×D411yescharacteristic
291C2×C4×C67C22×Q812yes—
292C2×C4×C67C2×#4112yes—
293C2×C4×C67C2511yescharacteristic
294C2×Dic67—24no—
295C2×Dic67—22no—
296C2×Dic67—22no—
297C2×Dic67—22no—
298C2×Dic67—22no—
299C2×Dic67—22no—
300C2×Dic67—22no—
301C2×Dic67—42no—
302C2×Dic67—42no—
303C2×Dic67—42no—
304C2×Dic67C22⋊Q814yes—
305C2×Dic67C22×D412yes—
306C2×Dic67C22×D412yes—
307C2×Dic67C22×D412yes—
308C4×D67—216no—
309C4×D67—84no—
310C4×D67C22⋊Q818yes—
311C4×D67C22×Q814yes—
312C4×D67C2×#4114yes—
313Dic134—24no—
314Dic134—22no—
315Dic134—216no—
316Dic134—84no—
317Dic134C22×Q814yes—
318C8×C67—22no—
319C8×C67—22no—
320C67⋊C8—22no—
321C67⋊C8—22no—
322C22×C67C2×C22⋊Q812yes—
323C22×C67#57712yes—
324C22×C67#57812yes—
325C22×C67C23×D411yescharacteristic
326C2×D67—28no—
327C2×D67—22no—
328C2×D67—22no—
329C2×D67C2×C22⋊Q814yes—
330C4×C67—24no—
331C4×C67—22no—
332C4×C67—22no—
333C4×C67—42no—
334C4×C67—42no—
335C4×C67—42no—
336C4×C67C2×C22⋊Q812yes—
337C4×C67C23×Q811yescharacteristic
338C4×C67C22×#4111yescharacteristic
339Dic67—24no—
340Dic67—22no—
341Dic67—22no—
342Dic67—42no—
343Dic67—42no—
344Dic67—42no—
345Dic67C2×C22⋊Q814yes—
346C2×#3082—671nomaximal, Sylow
347C2×C67#308214yescomplemented
348C2×C67C22×C22⋊Q811yescharacteristic
349C2×C67C2×#57711yescharacteristic
350C2×C67C2×#57811yescharacteristic
351D67—24no—
352C2×#544—671no—
353C2×#519—671no—
354#3082—6716no—
355C2×#479—671no—
356C2×#479—671no—
357C2×#479—671no—
358C2×#479—671no—
359C2×#477—671no—
360C2×#477—671no—
361C2×#475—671no—
362C2×#475D6711yescharacteristic, complemented
363C2×#428—671no—
364C2×#427—671no—
365C2×#424—671no—
366C2×#419—671no—
367C22×#103—671no—
368C67C2×#308211yescharacteristic, complemented, Sylow
369C23×Q8—671no—
370C22×M16—671no—
371C23×C8—671no—
372#544—678no—
373#544—1344no—
374C2×C4⋊Q8—671no—
375C2×C4⋊Q8—1341no—
376C2×C4⋊Q8C2×D6711yescharacteristic
377C2×#125—671no—
378C2×#125—671no—
379C2×#125—1341no—
380C2×C22⋊Q8—1341no—
381C2×C22⋊Q8—1341no—
382#519—678no—
383#519—1344no—
384C2×C4×Q8—671no—
385C2×C4×Q8—671no—
386C2×C4×Q8—671no—
387C2×C4×Q8—1341no—
388C2×C4×Q8—1341no—
389C2×C4×Q8C2×D6711yescharacteristic
390C2×#117—671no—
391C2×#117—671no—
392C2×#117—671no—
393C2×#117—1341no—
394C2×#117—1341no—
395C22×C4⋊C4—671no—
396#479—678no—
397#479—678no—
398#479—678no—
399#479—678no—
400#477—678no—
401#477—678no—
402#475—678no—
403#475C2×D6718yescomplemented
404#428—678no—
405#427—678no—
406C2×#107—671no—
407C2×#107—671no—
408C2×#107—671no—
409C2×#107—671no—
410C2×#106—671no—
411C2×#106—671no—
412C2×#106C2×D6711yescharacteristic
413C2×#106C2×D6711yescharacteristic
414#424—678no—
415C2×C4⋊C8—671no—
416C2×C4⋊C8—671no—
417C2×C4⋊C8—671no—
418C2×C4⋊C8C2×D6711yescharacteristic
419#419—678no—
420C2×#103—671no—
421C2×#103—671no—
422C2×#103—671no—
423C2×#103—671no—
424C2×#103—671no—
425C2×#103—671no—
426C2×#103—678no—
427C2×#103C2×D6711yescharacteristic
428C2×#103C2×D6711yescharacteristic
429C22×Q8—21no—
430C22×Q8—678no—
431C22×Q8—674no—
432C22×Q8—671no—
433C22×Q8—1341no—
434C22×Q8—1341no—
435C22×Q8—1342no—
436C22×Q8—1344no—
437C22×Q8C22×D6711yescharacteristic
438C23×C4—671no—
439C23×C4—1341no—
440C23×C4—1341no—
441C2×M16—674no—
442C2×M16—1344no—
443C22×C8—671no—
444C22×C8—671no—
445C22×C8—674no—
446C22×C8—1344no—
447C22×C8C22×D6711yescharacteristic
448C22×C8C22×D6711yescharacteristic
449C4⋊Q8—22no—
450C4⋊Q8—674no—
451C4⋊Q8—1342no—
452C4⋊Q8—1348no—
453C4⋊Q8C22×D6714yes—
454#125—674no—
455#125—674no—
456#125—1342no—
457#125—1348no—
458#125—1342no—
459C22⋊Q8—1348no—
460C22⋊Q8—1348no—
461C4×Q8—22no—
462C4×Q8—674no—
463C4×Q8—674no—
464C4×Q8—674no—
465C4×Q8—1348no—
466C4×Q8—1342no—
467C4×Q8—1342no—
468C4×Q8—1348no—
469C4×Q8—1342no—
470C4×Q8C22×D6714yes—
471#117—674no—
472#117—674no—
473#117—674no—
474#117—674no—
475#117—1348no—
476#117—1348no—
477#117—1342no—
478#117—1342no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—671no—
482C2×C4⋊C4—671no—
483C2×C4⋊C4—671no—
484C2×C4⋊C4—671no—
485C2×C4⋊C4—671no—
486C2×C4⋊C4—674no—
487C2×C4⋊C4—1342no—
488C2×C4⋊C4—1341no—
489C2×C4⋊C4—1341no—
490C2×C4⋊C4—1341no—
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⋊C4C22×D6711yescharacteristic
498C2×C4⋊C4C22×D6711yescharacteristic
499C2×C4⋊C4C22×D6711yescharacteristic
500C2×C22⋊C4—671no—
501C2×C22⋊C4—671no—
502C2×C22⋊C4—1341no—
503C2×C22⋊C4—1341no—
504C2×C42—21no—
505C2×C42—671no—
506C2×C42—1341no—
507C2×C42—1341no—
508C2×C42—1341no—
509C2×C42—1341no—
510C2×C42—1341no—
511C2×C42C22×D6711yescharacteristic
512#107—674no—
513#107—674no—
514#107—674no—
515#107—674no—
516#106—674no—
517#106—674no—
518#106C22×D6714yes—
519#106C22×D6714yes—
520C4⋊C8—674no—
521C4⋊C8—674no—
522C4⋊C8—674no—
523C4⋊C8C22×D6714yes—
524#103—674no—
525#103—674no—
526#103—674no—
527#103—674no—
528#103—674no—
529#103—674no—
530#103C22×D6714yes—
531#103C22×D6714yes—
532C24—671no—
533C2×Q8—21no—
534C2×Q8—24no—
535C2×Q8—22no—
536C2×Q8—82no—
537C2×Q8—5362no—
538C2×Q8—6716no—
539C2×Q8—674no—
540C2×Q8—672no—
541C2×Q8—1344no—
542C2×Q8—1344no—
543C2×Q8—1348no—
544C2×Q8—13416no—
545C2×Q8—1348no—
546C2×Q8—1341no—
547C2×Q8—1342no—
548C2×Q8Q8×D6714yes—
549C2×Q8C23×D6712yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—5362no—
555C22×C4—671no—
556C22×C4—672no—
557C22×C4—674no—
558C22×C4—674no—
559C22×C4—672no—
560C22×C4—671no—
561C22×C4—671no—
562C22×C4—1344no—
563C22×C4—1344no—
564C22×C4—1348no—
565C22×C4—1341no—
566C22×C4—1341no—
567C22×C4—1341no—
568C22×C4—1341no—
569C22×C4D4×D6711yescharacteristic
570C22×C4D4×D6711yescharacteristic
571C22×C4C23×D6711yescharacteristic
572M16—1348no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—672no—
576C2×C8—672no—
577C2×C8—1348no—
578C2×C8—1342no—
579C2×C8—1342no—
580C2×C8C23×D6712yes—
581C2×C8C23×D6712yes—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—674no—
588C4⋊C4—674no—
589C4⋊C4—672no—
590C4⋊C4—672no—
591C4⋊C4—672no—
592C4⋊C4—1344no—
593C4⋊C4—1344no—
594C4⋊C4—1344no—
595C4⋊C4—1344no—
596C4⋊C4—1344no—
597C4⋊C4—1344no—
598C4⋊C4—1341no—
599C4⋊C4—1341no—
600C4⋊C4—1341no—
601C4⋊C4—1344no—
602C4⋊C4—1344no—
603C4⋊C4—1344no—
604C4⋊C4C23×D6712yes—
605C4⋊C4C23×D6712yes—
606C4⋊C4C23×D6712yes—
607C22⋊C4—674no—
608C22⋊C4—674no—
609C22⋊C4—1344no—
610C22⋊C4—1344no—
611C42—24no—
612C42—672no—
613C42—672no—
614C42—1344no—
615C42—1344no—
616C42—1344no—
617C42—1344no—
618C42—1344no—
619C42D4×D6712yes—
620C42C23×D6712yes—
621C23—674no—
622C23—672no—
623C23—1342no—
624C23—1342no—
625C23C2×D4×D6711yescharacteristic
626Q8—24no—
627Q8—22no—
628Q8—84no—
629Q8—5364no—
630Q8—674no—
631Q8—13416no—
632Q8—1344no—
633Q8—1342no—
634Q8C2×Q8×D6714yes—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—2682no—
646C2×C4—2682no—
647C2×C4—2682no—
648C2×C4—5364no—
649C2×C4—674no—
650C2×C4—672no—
651C2×C4—678no—
652C2×C4—674no—
653C2×C4—674no—
654C2×C4—672no—
655C2×C4—672no—
656C2×C4—13416no—
657C2×C4—1342no—
658C2×C4—1342no—
659C2×C4—1342no—
660C2×C4—1344no—
661C2×C4—1342no—
662C2×C4—1342no—
663C2×C4—1342no—
664C2×C4C2×D4×D6712yes—
665C2×C4C2×D4×D6712yes—
666C2×C4C2×D4×D6711yescharacteristic
667C2×C4C2×Q8×D6712yes—
668C2×C4#41×D6712yes—
669C2×C4C24×D6711yescharacteristic
670C8—22no—
671C8—22no—
672C8—1342no—
673C8—1342no—
674C22—674no—
675C22—1348no—
676C22—1342no—
677C22—1342no—
678C22C22⋊Q8×D6712yes—
679C22#1686420212yes—
680C22#1686421212yes—
681C22C22×D4×D6711yescharacteristic
682C4—22no—
683C4—24no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—2682no—
689C4—2682no—
690C4—2682no—
691C4—674no—
692C4—1342no—
693C4—1344no—
694C4—1342no—
695C4C22⋊Q8×D6712yes—
696C4C22×Q8×D6711yescharacteristic
697C4C2×#41×D6711yescharacteristic
698C2—1344no—
699C2#2257004414yesdirect product factor
700C2C2×C22⋊Q8×D6711yescharacteristic
701C2C2×#1686420211yescharacteristic
702C2C2×#1686421211yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#475×C67C2
socleC23×C67C22×D4
prime radicalC23×D67C2×D4
hypercenterC2×#475D67
hypocenterC67C2×#3082
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #22570044C2direct (N × H)
4. C2×#16863706C2semidirect
5. C2×#16863704C2semidirect
6. C2×#16863703C2semidirect
7. C2×#16863701C2semidirect
8. C2×#16863689C2semidirect
9. C2×#16863688C2semidirect
10. C2×#16863680C2semidirect
16. C2×#475×C67C2semidirect
42. #16863706C22semidirect
43. #16863704C22semidirect
44. #16863703C22semidirect
45. #16863701C22semidirect
46. #16863689C22semidirect
47. #16863688C22semidirect
48. #16863680C22semidirect
71. #475×C67C22semidirect
82. C2×Q8×D67Q8semidirect
191. Q8×D67C2×Q8semidirect
347. C2×C67#3082semidirect
362. C2×#475D67semidirect
368. C67C2×#3082semidirect
403. #475C2×D67semidirect
699. C2#22570044direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640232
C2×#168638722
#225700442
C2×#168637062
C2×#168637042
C2×#168637032
C2×#168637012
C2×#168636892
C2×#168636882
C2×#168636802
C2×#168634352
C2×#168634312
C2×#168634212
C2×#168634032
C2×#103×D672
C2×#475×C672
C2×#308267