Finite Group Databasebeta

← C2×#22570012 #31723349

Subgroups — C2×#22570012 #31723349

Order 17152.

2098 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×#16863952C211yesmaximal, characteristic
2C2×C4×Q8×D67C211yesmaximal, characteristic
3#22570012C2116yesmaximal, direct product factor
4C2×#16863704C211yesmaximal, characteristic, complemented
5C2×#16863703C211yesmaximal, characteristic, complemented
6C2×#16863700C211yesmaximal, characteristic, complemented
7C2×#16863690C211yesmaximal, characteristic, complemented
8C2×#16863689C211yesmaximal, characteristic, complemented
9C2×#16863680C211yesmaximal, characteristic, complemented
10C2×#16863679C211yesmaximal, characteristic, complemented
11C2×#16863437C211yesmaximal, characteristic
12C2×#16863435C211yesmaximal, characteristic
13C2×#16863418C211yesmaximal, characteristic
14C2×#16863403C211yesmaximal, characteristic
15C2×#16863403C211yesmaximal, characteristic
16C2×#479×C67C211yesmaximal, characteristic, complemented
17C22×Q8×D67C2211yescharacteristic
18C22×#11761611C2211yescharacteristic
19C22×#11761611C2211yescharacteristic
20#16863952—24no—
21#16863952C2218yes—
22C2×#14524042C2211yescharacteristic
23C2×#14524042C2211yescharacteristic
24C2×#14524035C2211yescharacteristic
25C2×#14524021—21no—
26C2×#14524021—21no—
27C2×Q8×Dic67C2211yescharacteristic
28C2×C4×Dic134—21no—
29C2×C4×Dic134C2211yescharacteristic
30C2×#14524008—21no—
31C2×#14524008—21no—
32C2×#14524008—21no—
33C2×#14524008C2211yescharacteristic
34C4×Q8×D67—24no—
35C4×Q8×D67C2218yes—
36C2×#14524001C2211yescharacteristic
37C2×#14524001C2211yescharacteristic
38C2×C4⋊C4×D67—21no—
39C2×C4⋊C4×D67C2211yescharacteristic
40C2×C42×D67—21no—
41C2×C42×D67C2211yescharacteristic
42#16863704C2218yescomplemented
43#16863703C2218yescomplemented
44#16863700C2218yescomplemented
45#16863690C2218yescomplemented
46#16863689C2218yescomplemented
47#16863680C2218yescomplemented
48#16863679C2218yescomplemented
49#16863437C2218yes—
50#16863435C2218yes—
51C2×#14523977C2211yescharacteristic
52C2×#14523976C2211yescharacteristic
53C2×#14523976C2211yescharacteristic
54C2×#14523975C2211yescharacteristic
55C2×#14523974C2211yescharacteristic
56C2×#14523974C2211yescharacteristic
57#16863418C2218yes—
58C2×C4⋊(C67⋊C8)C2211yescharacteristic
59C2×Dic67⋊C8C2211yescharacteristic
60C2×Dic67⋊C8C2211yescharacteristic
61#16863403C2218yes—
62#16863403C2218yes—
63C2×#14523968C2211yescharacteristic
64C2×#14523968C2211yescharacteristic
65C2×#14523967C2211yescharacteristic
66C2×#14523967C2211yescharacteristic
67C2×#14523966C2211yescharacteristic
68C2×#14523966C2211yescharacteristic
69C2×#125×C67C2211yescharacteristic
70C2×C4×Q8×C67C2211yescharacteristic
71#479×C67C2218yescomplemented
72C2×#107×C67C2211yescharacteristic
73C2×#106×C67C2211yescharacteristic
74C2×C4⋊C8×C67C2211yescharacteristic
75C2×#103×C67C2211yescharacteristic
76C2×#103×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134—21no—
79C22×Dic134—21no—
80C22×Dic134C2311yescharacteristic
81C2×Q8×D67—22no—
82C2×Q8×D67—24no—
83C2×Q8×D67Q818yescomplemented
84C2×Q8×D67C2314yes—
85C22×C4×D67—21no—
86C22×C4×D67—21no—
87C22×C4×D67D411yescharacteristic
88C22×C4×D67D411yescharacteristic
89C22×C4×D67C2311yescharacteristic
90C2×#11761611—24no—
91C2×#11761611—24no—
92C2×#11761611C2314yes—
93C2×#11761611C2314yes—
94C22×C67⋊C8C2311yescharacteristic
95C22×C67⋊C8C2311yescharacteristic
96#14524042—22no—
97#14524042—22no—
98#14524042C2314yes—
99#14524042C2314yes—
100#14524035—22no—
101#14524035C2314yes—
102#14524021—28no—
103#14524021—28no—
104Q8×Dic67—22no—
105Q8×Dic67C2314yes—
106C4×Dic134—28no—
107C4×Dic134—22no—
108C4×Dic134C2314yes—
109#14524008—22no—
110#14524008—28no—
111#14524008—28no—
112#14524008—28no—
113#14524008C2314yes—
114#14524001—22no—
115#14524001—22no—
116#14524001C2314yes—
117#14524001C2314yes—
118C2×C4⋊Dic67—21no—
119C2×C4⋊Dic67C2311yescharacteristic
120C2×C4⋊Dic67C2311yescharacteristic
121C2×C4⋊Dic67C2311yescharacteristic
122C2×Dic67⋊C4—21no—
123C2×Dic67⋊C4—21no—
124C2×Dic67⋊C4—21no—
125C2×Dic67⋊C4—21no—
126C2×Dic67⋊C4—21no—
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C4⋊C4×D67—28no—
130C4⋊C4×D67—22no—
131C4⋊C4×D67C2314yes—
132C2×(C2×D67)⋊C4—21no—
133C2×(C2×D67)⋊C4—21no—
134C2×C4×Dic67—21no—
135C2×C4×Dic67—21no—
136C2×C4×Dic67—21no—
137C2×C4×Dic67—21no—
138C2×C4×Dic67—21no—
139C2×C4×Dic67D411yescharacteristic
140C2×C4×Dic67D411yescharacteristic
141C2×C4×Dic67C2311yescharacteristic
142C42×D67—28no—
143C42×D67D414yes—
144C42×D67C2314yes—
145#14523977C2314yes—
146#14523976C2314yes—
147#14523976C2314yes—
148#14523975C2314yes—
149#14523974C2314yes—
150#14523974C2314yes—
151C4⋊(C67⋊C8)C2314yes—
152Dic67⋊C8C2314yes—
153Dic67⋊C8C2314yes—
154#14523968C2314yes—
155#14523968C2314yes—
156#14523967C2314yes—
157#14523967C2314yes—
158#14523966C2314yes—
159#14523966C2314yes—
160C22×Q8×C67C2311yescharacteristic
161C22×C8×C67C2311yescharacteristic
162C22×C8×C67C2311yescharacteristic
163#125×C67—22no—
164#125×C67C2314yes—
165C4×Q8×C67—22no—
166C4×Q8×C67C2314yes—
167C2×C4⋊C4×C67—21no—
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#107×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—24no—
187C2×Dic134—44no—
188C2×Dic134—44no—
189C2×Dic134C2×Q814yes—
190C2×Dic134C2412yes—
191Q8×D67—216no—
192Q8×D67—28no—
193Q8×D67C2×Q8116yescomplemented
194C22×Dic67—21no—
195C22×Dic67—21no—
196C22×Dic67—21no—
197C22×Dic67—21no—
198C22×Dic67C2×D411yescharacteristic
199C22×Dic67C2×D411yescharacteristic
200C22×Dic67C2×D411yescharacteristic
201C2×C4×D67—28no—
202C2×C4×D67—24no—
203C2×C4×D67—24no—
204C2×C4×D67—24no—
205C2×C4×D67—42no—
206C2×C4×D67—44no—
207C2×C4×D67C2×D414yes—
208C2×C4×D67C2×D414yes—
209C2×C4×D67C2×D412yes—
210C2×C4×D67C2×Q814yes—
211C2×C4×D67#4114yes—
212C2×C4×D67C2412yes—
213#11761611—28no—
214#11761611—28no—
215C2×C67⋊C8—22no—
216C2×C67⋊C8—22no—
217C2×C67⋊C8C2412yes—
218C2×C67⋊C8C2412yes—
219C4⋊Dic67—21no—
220C4⋊Dic67—21no—
221C4⋊Dic67—21no—
222C4⋊Dic67—24no—
223C4⋊Dic67C2412yes—
224C4⋊Dic67C2412yes—
225C4⋊Dic67C2412yes—
226Dic67⋊C4—24no—
227Dic67⋊C4—24no—
228Dic67⋊C4—24no—
229Dic67⋊C4—24no—
230Dic67⋊C4—24no—
231Dic67⋊C4—24no—
232Dic67⋊C4—24no—
233(C2×D67)⋊C4—24no—
234(C2×D67)⋊C4—24no—
235C4×Dic67—24no—
236C4×Dic67—24no—
237C4×Dic67—24no—
238C4×Dic67—24no—
239C4×Dic67—24no—
240C4×Dic67C2×D412yes—
241C4×Dic67C2×D414yes—
242C4×Dic67C2×D414yes—
243C4×Dic67C2412yes—
244C2×Q8×C67—21no—
245C2×Q8×C67—22no—
246C2×Q8×C67C2×Q814yes—
247C2×Q8×C67C2412yes—
248C22×C4×C67—21no—
249C22×C4×C67—21no—
250C22×C4×C67—21no—
251C22×C4×C67—21no—
252C22×C4×C67C2×D411yescharacteristic
253C22×C4×C67C2×D411yescharacteristic
254C22×C4×C67C2411yescharacteristic
255C2×C8×C67—22no—
256C2×C8×C67—22no—
257C2×C8×C67C2412yes—
258C2×C8×C67C2412yes—
259C4⋊C4×C67—24no—
260C4⋊C4×C67—24no—
261C4⋊C4×C67—24no—
262C4⋊C4×C67—21no—
263C4⋊C4×C67—21no—
264C4⋊C4×C67—21no—
265C4⋊C4×C67C2412yes—
266C4⋊C4×C67C2412yes—
267C4⋊C4×C67C2412yes—
268C42×C67—24no—
269C42×C67C2×D412yes—
270C42×C67C2412yes—
271C23×C67C22×D411yescharacteristic
272C22×D67—22no—
273C22×D67—22no—
274C22×D67C22⋊Q814yes—
275C22×D67C22×D412yes—
276Q8×C67—24no—
277Q8×C67—22no—
278Q8×C67C22×Q814yes—
279C2×C4×C67—24no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67—22no—
286C2×C4×C67—42no—
287C2×C4×C67—42no—
288C2×C4×C67—42no—
289C2×C4×C67C22×D412yes—
290C2×C4×C67C22×D412yes—
291C2×C4×C67C22×D411yescharacteristic
292C2×C4×C67C22×Q812yes—
293C2×C4×C67C2×#4112yes—
294C2×C4×C67C2511yescharacteristic
295C2×Dic67—24no—
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×Dic67#13714yes—
306C2×Dic67C22×D412yes—
307C2×Dic67C22×D412yes—
308C2×Dic67C22×D412yes—
309C4×D67—216no—
310C4×D67—28no—
311C4×D67—44no—
312C4×D67—48no—
313C4×D67C22⋊Q818yes—
314C4×D67C22×Q814yes—
315C4×D67C2×#4114yes—
316Dic134—24no—
317Dic134—22no—
318Dic134—216no—
319Dic134—48no—
320Dic134—48no—
321Dic134C22×Q814yes—
322C8×C67—22no—
323C8×C67—22no—
324C67⋊C8—22no—
325C67⋊C8—22no—
326C22×C67C2×C22⋊Q812yes—
327C22×C67C2×#13712yes—
328C22×C67#57512yes—
329C22×C67C23×D411yescharacteristic
330C2×D67—28no—
331C2×D67—22no—
332C2×D67—22no—
333C2×D67C2×C22⋊Q814yes—
334C4×C67—24no—
335C4×C67—22no—
336C4×C67—22no—
337C4×C67—42no—
338C4×C67—42no—
339C4×C67—42no—
340C4×C67C2×C22⋊Q812yes—
341C4×C67C23×Q811yescharacteristic
342C4×C67C22×#4111yescharacteristic
343Dic67—24no—
344Dic67—22no—
345Dic67—42no—
346Dic67—42no—
347Dic67—42no—
348Dic67C2×C22⋊Q814yes—
349Dic67C2×#13714yes—
350C2×#3078—671nomaximal, Sylow
351C2×C67#307814yescomplemented
352C2×C67C22×C22⋊Q811yescharacteristic
353C2×C67C22×#13711yescharacteristic
354C2×C67C2×#57511yescharacteristic
355D67—24no—
356C2×#533—671no—
357C22×C4×Q8—671no—
358#3078—6716no—
359C2×#479—671no—
360C2×#479—671no—
361C2×#479—671no—
362C2×#479D6711yescharacteristic, complemented
363C2×#477—671no—
364C2×#477—671no—
365C2×#475—671no—
366C2×#475—671no—
367C2×#428—671no—
368C2×#428—671no—
369C2×#423—671no—
370C2×#419—671no—
371C2×#419—671no—
372C67C2×#307811yescharacteristic, complemented, Sylow
373C23×Q8—671no—
374C22×M16—671no—
375C22×M16—671no—
376#533—678no—
377#533—1344no—
378C2×C4⋊Q8—671no—
379C2×C4⋊Q8—671no—
380C2×#125—671no—
381C2×#125C2×D6711yescharacteristic
382C2×C22⋊Q8—1341no—
383C2×C22⋊Q8—1341no—
384C2×C4×Q8—671no—
385C2×C4×Q8—678no—
386C2×C4×Q8—671no—
387C2×C4×Q8—671no—
388C2×C4×Q8—1341no—
389C2×C4×Q8—1341no—
390C2×C4×Q8—1341no—
391C2×C4×Q8—1341no—
392C2×C4×Q8—1344no—
393C2×C4×Q8C2×D6711yescharacteristic
394C2×#117—671no—
395C2×#117—671no—
396C22×C4⋊C4—671no—
397C22×C4⋊C4—1341no—
398C22×C42—671no—
399C22×C42—1341no—
400#479—678no—
401#479—678no—
402#479—678no—
403#479C2×D6718yescomplemented
404#477—678no—
405#477—678no—
406#475—678no—
407#475—678no—
408#428—678no—
409#428—678no—
410C2×#107—671no—
411C2×#107—671no—
412C2×#107—671no—
413C2×#107C2×D6711yescharacteristic
414C2×#106—671no—
415C2×#106—671no—
416C2×#106—671no—
417C2×#106C2×D6711yescharacteristic
418#423—678no—
419C2×C4⋊C8—671no—
420C2×C4⋊C8—671no—
421C2×C4⋊C8—671no—
422C2×C4⋊C8C2×D6711yescharacteristic
423#419—678no—
424#419—678no—
425C2×#103—671no—
426C2×#103—671no—
427C2×#103—671no—
428C2×#103—671no—
429C2×#103—671no—
430C2×#103—671no—
431C2×#103C2×D6711yescharacteristic
432C2×#103C2×D6711yescharacteristic
433C22×Q8—678no—
434C22×Q8—674no—
435C22×Q8—671no—
436C22×Q8—1341no—
437C22×Q8—1341no—
438C22×Q8—1341no—
439C22×Q8—1342no—
440C22×Q8—1344no—
441C22×Q8C22×D6711yescharacteristic
442C23×C4—671no—
443C23×C4—671no—
444C23×C4—671no—
445C23×C4—1341no—
446C23×C4—1341no—
447C2×M16—674no—
448C2×M16—674no—
449C2×M16—1344no—
450C2×M16—1344no—
451C22×C8—671no—
452C22×C8—671no—
453C22×C8C22×D6711yescharacteristic
454C22×C8C22×D6711yescharacteristic
455C4⋊Q8—674no—
456C4⋊Q8—674no—
457C4⋊Q8—1342no—
458C4⋊Q8—1342no—
459#125—22no—
460#125—674no—
461#125—1342no—
462#125C22×D6714yes—
463C22⋊Q8—1348no—
464C22⋊Q8—1348no—
465C4×Q8—22no—
466C4×Q8—674no—
467C4×Q8—674no—
468C4×Q8—674no—
469C4×Q8—1348no—
470C4×Q8—1348no—
471C4×Q8—1342no—
472C4×Q8—1348no—
473C4×Q8—1348no—
474C4×Q8—1342no—
475C4×Q8—1342no—
476C4×Q8C22×D6714yes—
477#117—674no—
478#117—674no—
479#117—1342no—
480#117—1342no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—671no—
485C2×C4⋊C4—671no—
486C2×C4⋊C4—671no—
487C2×C4⋊C4—674no—
488C2×C4⋊C4—1342no—
489C2×C4⋊C4—1348no—
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⋊C4—1341no—
498C2×C4⋊C4C22×D6711yescharacteristic
499C2×C4⋊C4C22×D6711yescharacteristic
500C2×C4⋊C4C22×D6711yescharacteristic
501C2×C22⋊C4—1341no—
502C2×C22⋊C4—1341no—
503C2×C42—21no—
504C2×C42—671no—
505C2×C42—671no—
506C2×C42—671no—
507C2×C42—674no—
508C2×C42—674no—
509C2×C42—1348no—
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#107C22×D6714yes—
520#106—674no—
521#106—674no—
522#106—674no—
523#106C22×D6714yes—
524C4⋊C8—674no—
525C4⋊C8—674no—
526C4⋊C8—674no—
527C4⋊C8C22×D6714yes—
528#103—674no—
529#103—674no—
530#103—674no—
531#103—674no—
532#103—674no—
533#103—674no—
534#103C22×D6714yes—
535#103C22×D6714yes—
536C24—671no—
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—2684no—
540C2×Q8—2684no—
541C2×Q8—6716no—
542C2×Q8—674no—
543C2×Q8—672no—
544C2×Q8—1344no—
545C2×Q8—1344no—
546C2×Q8—1344no—
547C2×Q8—1348no—
548C2×Q8—13416no—
549C2×Q8—1348no—
550C2×Q8—1341no—
551C2×Q8—1342no—
552C2×Q8Q8×D6714yes—
553C2×Q8C23×D6712yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—2682no—
559C22×C4—2684no—
560C22×C4—674no—
561C22×C4—671no—
562C22×C4—671no—
563C22×C4—672no—
564C22×C4—674no—
565C22×C4—674no—
566C22×C4—672no—
567C22×C4—671no—
568C22×C4—674no—
569C22×C4—1344no—
570C22×C4—1344no—
571C22×C4—1344no—
572C22×C4—1348no—
573C22×C4—1341no—
574C22×C4—1341no—
575C22×C4—1341no—
576C22×C4—1341no—
577C22×C4D4×D6711yescharacteristic
578C22×C4D4×D6711yescharacteristic
579C22×C4C23×D6711yescharacteristic
580M16—1348no—
581M16—1348no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—672no—
585C2×C8—672no—
586C2×C8—1342no—
587C2×C8—1342no—
588C2×C8C23×D6712yes—
589C2×C8C23×D6712yes—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—672no—
597C4⋊C4—672no—
598C4⋊C4—672no—
599C4⋊C4—1344no—
600C4⋊C4—1344no—
601C4⋊C4—1344no—
602C4⋊C4—1344no—
603C4⋊C4—1344no—
604C4⋊C4—1341no—
605C4⋊C4—1341no—
606C4⋊C4—1341no—
607C4⋊C4—1344no—
608C4⋊C4—1344no—
609C4⋊C4—1344no—
610C4⋊C4C23×D6712yes—
611C4⋊C4C23×D6712yes—
612C4⋊C4C23×D6712yes—
613C22⋊C4—1344no—
614C22⋊C4—1344no—
615C42—24no—
616C42—674no—
617C42—674no—
618C42—672no—
619C42—672no—
620C42—1344no—
621C42—1344no—
622C42—1344no—
623C42—1344no—
624C42—1344no—
625C42D4×D6712yes—
626C42C23×D6712yes—
627C23—674no—
628C23—672no—
629C23—1342no—
630C23—1342no—
631C23C2×D4×D6711yescharacteristic
632Q8—24no—
633Q8—22no—
634Q8—2688no—
635Q8—2688no—
636Q8—674no—
637Q8—13416no—
638Q8—1344no—
639Q8—1342no—
640Q8C2×Q8×D6714yes—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—2684no—
652C2×C4—2688no—
653C2×C4—2682no—
654C2×C4—2682no—
655C2×C4—2682no—
656C2×C4—674no—
657C2×C4—674no—
658C2×C4—672no—
659C2×C4—672no—
660C2×C4—678no—
661C2×C4—674no—
662C2×C4—674no—
663C2×C4—672no—
664C2×C4—1348no—
665C2×C4—13416no—
666C2×C4—1342no—
667C2×C4—1342no—
668C2×C4—1342no—
669C2×C4—1344no—
670C2×C4—1342no—
671C2×C4—1342no—
672C2×C4C2×D4×D6712yes—
673C2×C4C2×D4×D6712yes—
674C2×C4C2×D4×D6711yescharacteristic
675C2×C4C2×Q8×D6712yes—
676C2×C4#41×D6712yes—
677C2×C4C24×D6711yescharacteristic
678C8—22no—
679C8—22no—
680C8—1342no—
681C8—1342no—
682C22—674no—
683C22—1348no—
684C22—1342no—
685C22—1342no—
686C22C22⋊Q8×D6712yes—
687C22#137×D6712yes—
688C22#1686419312yes—
689C22C22×D4×D6711yescharacteristic
690C4—22no—
691C4—22no—
692C4—24no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—2682no—
697C4—2682no—
698C4—2682no—
699C4—674no—
700C4—674no—
701C4—1342no—
702C4—1344no—
703C4C22⋊Q8×D6712yes—
704C4C22×Q8×D6711yescharacteristic
705C4C2×#41×D6711yescharacteristic
706C2—1344no—
707C2#2257001214yesdirect product factor
708C2C2×C22⋊Q8×D6711yescharacteristic
709C2C2×#137×D6711yescharacteristic
710C2C2×#1686419311yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#479×C67C2
socleC23×C67C22×D4
prime radicalC23×D67C2×D4
hypercenterC2×#479D67
hypocenterC67C2×#3078
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. #22570012C2direct (N × H)
4. C2×#16863704C2semidirect
5. C2×#16863703C2semidirect
6. C2×#16863700C2semidirect
7. C2×#16863690C2semidirect
8. C2×#16863689C2semidirect
9. C2×#16863680C2semidirect
10. C2×#16863679C2semidirect
16. C2×#479×C67C2semidirect
42. #16863704C22semidirect
43. #16863703C22semidirect
44. #16863700C22semidirect
45. #16863690C22semidirect
46. #16863689C22semidirect
47. #16863680C22semidirect
48. #16863679C22semidirect
71. #479×C67C22semidirect
83. C2×Q8×D67Q8semidirect
193. Q8×D67C2×Q8semidirect
351. C2×C67#3078semidirect
362. C2×#479D67semidirect
372. C67C2×#3078semidirect
403. #479C2×D67semidirect
707. C2#22570012direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168639522
C2×C4×Q8×D672
#225700122
C2×#168637042
C2×#168637032
C2×#168637002
C2×#168636902
C2×#168636892
C2×#168636802
C2×#168636792
C2×#168634372
C2×#168634352
C2×#168634182
C2×#168634032
C2×#479×C672
C2×#307867