Finite Group Databasebeta

← C2×#22570438 #31724110

Subgroups — C2×#22570438 #31724110

Order 17152.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864017C211yesmaximal, characteristic
2#22570438C2116yesmaximal, direct product factor
3C2×#16863737C211yesmaximal, characteristic, complemented
4C2×#16863720C211yesmaximal, characteristic
5C2×#16863691C211yesmaximal, characteristic, complemented
6C2×#16863681C211yesmaximal, characteristic, complemented
7C2×#16863618C211yesmaximal, characteristic, complemented
8C2×#16863618C211yesmaximal, characteristic, complemented
9C2×#16863552C211yesmaximal, characteristic, complemented
10C2×#16863535C211yesmaximal, characteristic
11C2×#16863501C211yesmaximal, characteristic, complemented
12C2×#16863494C211yesmaximal, characteristic, complemented
13C2×C4×#11761618C211yesmaximal, characteristic, complemented
14C2×C4×#11761615C211yesmaximal, characteristic, complemented
15C2×#16863457C211yesmaximal, characteristic, complemented
16C2×#519×C67C211yesmaximal, characteristic, complemented
17C22×#11761618C2211yescharacteristic
18C22×#11761618C2211yescharacteristic
19C22×#11761615C2211yescharacteristic
20C22×#11761615C2211yescharacteristic
21#16864017—24no—
22#16864017C2218yes—
23C2×#14524043C2211yescharacteristic
24C2×#14524038—21no—
25C2×#14524031C2211yescharacteristic
26C2×#14524029—21no—
27C2×#14524025—21no—
28C2×#14524022C2211yescharacteristic
29C2×#14524021—21no—
30C2×#14524017C2211yescharacteristic
31C2×C4×Dic134C2211yescharacteristic
32C2×C4×D268C2211yescharacteristic
33#16863737C2218yescomplemented
34#16863720C2218yes—
35#16863691C2218yescomplemented
36#16863681C2218yescomplemented
37#16863618C2218yescomplemented
38#16863618C2218yescomplemented
39#16863552C2218yescomplemented
40#16863535C2218yes—
41#16863501C2218yescomplemented
42#16863494C2218yescomplemented
43C4×#11761618C2218yescomplemented
44C4×#11761615C2218yescomplemented
45#16863457C2218yescomplemented
46C2×#14523976C2211yescharacteristic
47C2×#14523976C2211yescharacteristic
48C2×#14523974C2211yescharacteristic
49C2×#14523974C2211yescharacteristic
50C2×C4⋊(C67⋊C8)C2211yescharacteristic
51C2×C4⋊(C67⋊C8)C2211yescharacteristic
52C2×#14523967C2211yescharacteristic
53C2×#14523967C2211yescharacteristic
54C2×#14523967C2211yescharacteristic
55C2×#14523967C2211yescharacteristic
56C2×#14523966C2211yescharacteristic
57C2×#14523966C2211yescharacteristic
58C2×#14523963C2211yescharacteristic
59C2×#14523963C2211yescharacteristic
60C2×C22⋊(C67⋊C8)C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×#14523954C2211yescharacteristic
63C2×C4×C67⋊C8C2211yescharacteristic
64C23×Q8×C67C2211yescharacteristic
65#519×C67—24no—
66#519×C67C2218yescomplemented
67C2×C4×Q8×C67—21no—
68C2×C4×Q8×C67—21no—
69C2×C4×Q8×C67C2211yescharacteristic
70C2×C4×Q8×C67C2211yescharacteristic
71C2×C4×Q8×C67C2211yescharacteristic
72C2×C4×Q8×C67C2211yescharacteristic
73C2×#117×C67—21no—
74C2×#117×C67—21no—
75C2×#117×C67C2211yescharacteristic
76C2×#117×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134C2311yescharacteristic
79C22×D268C2311yescharacteristic
80C22×C22⋊D67—21no—
81C22×C4×D67—21no—
82C2×#11761618—24no—
83C2×#11761618—24no—
84C2×#11761618C2314yes—
85C2×#11761618C2314yes—
86C2×#11761615—24no—
87C2×#11761615—24no—
88C2×#11761615C2314yes—
89C2×#11761615C2314yes—
90C22×C67⋊C8C2311yescharacteristic
91C22×C67⋊C8C2311yescharacteristic
92C22×C67⋊C8C2311yescharacteristic
93C22×C67⋊C8C2311yescharacteristic
94#14524043—22no—
95#14524043C2314yes—
96#14524038—28no—
97#14524031—22no—
98#14524031C2314yes—
99#14524029—28no—
100#14524025—28no—
101#14524022—22no—
102#14524022C2314yes—
103#14524021—28no—
104#14524017—22no—
105#14524017C2314yes—
106C4×Dic134—22no—
107C4×Dic134C2314yes—
108C4×D268—22no—
109C4×D268C2314yes—
110C2×C4⋊Dic67—21no—
111C2×C4⋊Dic67C2311yescharacteristic
112C2×C4⋊Dic67C2311yescharacteristic
113C2×Dic67⋊C4—21no—
114C2×Dic67⋊C4—21no—
115C2×C22⋊Dic67—21no—
116C2×(C2×D67)⋊C4—21no—
117C2×(C2×D67)⋊C4—21no—
118C2×(C2×D67)⋊C4—21no—
119C2×(C2×D67)⋊C4—21no—
120C2×C4×Dic67—21no—
121#14523976C2314yes—
122#14523976C2314yes—
123#14523974C2314yes—
124#14523974C2314yes—
125C4⋊(C67⋊C8)C2314yes—
126C4⋊(C67⋊C8)C2314yes—
127#14523967C2314yes—
128#14523967C2314yes—
129#14523967C2314yes—
130#14523967C2314yes—
131#14523966C2314yes—
132#14523966C2314yes—
133#14523963C2314yes—
134#14523963C2314yes—
135C22⋊(C67⋊C8)C2314yes—
136C22⋊(C67⋊C8)C2314yes—
137#14523954C2314yes—
138C4×C67⋊C8C2314yes—
139C22×Q8×C67—24no—
140C22×Q8×C67—24no—
141C22×Q8×C67—21no—
142C22×Q8×C67—22no—
143C22×Q8×C67C2314yes—
144C22×Q8×C67C2311yescharacteristic
145C22×Q8×C67C2311yescharacteristic
146C23×C4×C67—21no—
147C23×C4×C67C2311yescharacteristic
148C4×Q8×C67—28no—
149C4×Q8×C67—28no—
150C4×Q8×C67—22no—
151C4×Q8×C67—22no—
152C4×Q8×C67—22no—
153C4×Q8×C67—22no—
154C4×Q8×C67C2314yes—
155C4×Q8×C67C2314yes—
156C4×Q8×C67C2314yes—
157C4×Q8×C67C2314yes—
158#117×C67—22no—
159#117×C67—28no—
160#117×C67—28no—
161#117×C67D414yes—
162#117×C67C2314yes—
163#117×C67C2314yes—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67D411yescharacteristic
169C2×C4⋊C4×C67D411yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C22⋊C4×C67—21no—
173C2×C22⋊C4×C67D411yescharacteristic
174C2×C22⋊C4×C67D411yescharacteristic
175C2×C42×C67—21no—
176C2×C42×C67—21no—
177C2×C42×C67—21no—
178C2×C42×C67—21no—
179C2×C42×C67—21no—
180C2×C42×C67C2311yescharacteristic
181C2×C42×C67C2311yescharacteristic
182C23×D67—21no—
183C2×Dic134—22no—
184C2×Dic134—22no—
185C2×Dic134—21no—
186C2×Dic134—24no—
187C2×Dic134—82no—
188C2×Dic134C2412yes—
189C2×D268—22no—
190C2×D268—22no—
191C2×D268—21no—
192C2×D268C2412yes—
193C2×C22⋊D67—24no—
194C2×C22⋊D67—82no—
195C22×Dic67—21no—
196C22×Dic67—21no—
197C22×Dic67—21no—
198C2×C4×D67—24no—
199C2×C4×D67—82no—
200#11761618—28no—
201#11761618—28no—
202#11761615—28no—
203#11761615—28no—
204C2×C67⋊C8—22no—
205C2×C67⋊C8—22no—
206C2×C67⋊C8—22no—
207C2×C67⋊C8—22no—
208C2×C67⋊C8C2412yes—
209C2×C67⋊C8C2412yes—
210C2×C67⋊C8C2412yes—
211C2×C67⋊C8C2412yes—
212C4⋊Dic67—24no—
213C4⋊Dic67—21no—
214C4⋊Dic67—21no—
215C4⋊Dic67C2412yes—
216C4⋊Dic67C2412yes—
217Dic67⋊C4—24no—
218Dic67⋊C4—24no—
219C22⋊Dic67—24no—
220(C2×D67)⋊C4—24no—
221(C2×D67)⋊C4—24no—
222(C2×D67)⋊C4—24no—
223(C2×D67)⋊C4—24no—
224C4×Dic67—24no—
225C24×C67C2×D411yescharacteristic
226C2×Q8×C67—216no—
227C2×Q8×C67—28no—
228C2×Q8×C67—28no—
229C2×Q8×C67—28no—
230C2×Q8×C67—24no—
231C2×Q8×C67—21no—
232C2×Q8×C67—21no—
233C2×Q8×C67—22no—
234C2×Q8×C67—22no—
235C2×Q8×C67#4114yes—
236C2×Q8×C67#4114yes—
237C2×Q8×C67C2412yes—
238C2×Q8×C67C2412yes—
239C22×C4×C67—28no—
240C22×C4×C67—21no—
241C22×C4×C67—21no—
242C22×C4×C67—24no—
243C22×C4×C67—22no—
244C22×C4×C67—22no—
245C22×C4×C67—21no—
246C22×C4×C67—21no—
247C22×C4×C67C2×D411yescharacteristic
248C22×C4×C67C2×D411yescharacteristic
249C22×C4×C67C2×D411yescharacteristic
250C22×C4×C67C2×D411yescharacteristic
251C22×C4×C67C2×D411yescharacteristic
252C22×C4×C67C2×D412yes—
253C22×C4×C67C2412yes—
254C22×C4×C67C2411yescharacteristic
255C4⋊C4×C67—24no—
256C4⋊C4×C67—24no—
257C4⋊C4×C67—24no—
258C4⋊C4×C67—24no—
259C4⋊C4×C67—21no—
260C4⋊C4×C67—21no—
261C4⋊C4×C67C2×D414yes—
262C4⋊C4×C67C2×D414yes—
263C4⋊C4×C67C2412yes—
264C4⋊C4×C67C2412yes—
265C22⋊C4×C67—24no—
266C22⋊C4×C67C2×D414yes—
267C22⋊C4×C67C2×D414yes—
268C42×C67—24no—
269C42×C67—24no—
270C42×C67—24no—
271C42×C67—24no—
272C42×C67—24no—
273C42×C67C2×D412yes—
274C42×C67C2×D412yes—
275C42×C67C2412yes—
276C42×C67C2412yes—
277C23×C67—22no—
278C23×C67—22no—
279C23×C67—22no—
280C23×C67C22×D412yes—
281C23×C67C22×D411yescharacteristic
282C22×D67—22no—
283C22×D67—42no—
284C22×D67—42no—
285C22×D67—42no—
286Q8×C67—216no—
287Q8×C67—24no—
288Q8×C67—24no—
289Q8×C67—22no—
290Q8×C67—22no—
291Q8×C67C2×#4114yes—
292Q8×C67C2×#4114yes—
293C2×C4×C67—216no—
294C2×C4×C67—24no—
295C2×C4×C67—24no—
296C2×C4×C67—22no—
297C2×C4×C67—22no—
298C2×C4×C67—22no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—24no—
304C2×C4×C67—22no—
305C2×C4×C67—22no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—42no—
309C2×C4×C67—42no—
310C2×C4×C67C22×D412yes—
311C2×C4×C67C22×D412yes—
312C2×C4×C67C22×D412yes—
313C2×C4×C67C22×D412yes—
314C2×C4×C67C22×D412yes—
315C2×C4×C67C22×D411yescharacteristic
316C2×C4×C67C2×#4112yes—
317C2×C4×C67C2×#4112yes—
318C2×C4×C67C2511yescharacteristic
319C22⋊D67—84no—
320C2×Dic67—22no—
321C2×Dic67—22no—
322C2×Dic67—22no—
323C2×Dic67—42no—
324C2×Dic67—42no—
325C2×Dic67—42no—
326D268—22no—
327D268—22no—
328D268—42no—
329C4×D67—84no—
330Dic134—22no—
331Dic134—22no—
332Dic134—42no—
333Dic134—84no—
334C67⋊C8—22no—
335C67⋊C8—22no—
336C67⋊C8—22no—
337C67⋊C8—22no—
338C22×C67—22no—
339C22×C67—22no—
340C22×C67—22no—
341C22×C67—44no—
342C22×C67#52512yes—
343C22×C67#57712yes—
344C22×C67#57812yes—
345C22×C67C23×D411yescharacteristic
346C2×D67—42no—
347C2×D67—42no—
348C2×D67—42no—
349C2×D67—84no—
350C4×C67—24no—
351C4×C67—24no—
352C4×C67—22no—
353C4×C67—22no—
354C4×C67—22no—
355C4×C67—22no—
356C4×C67—22no—
357C4×C67—42no—
358C4×C67—42no—
359C4×C67#52512yes—
360C4×C67C22×#4111yescharacteristic
361C4×C67C22×#4111yescharacteristic
362Dic67—42no—
363Dic67—42no—
364Dic67—42no—
365C2×#3121—671nomaximal, Sylow
366C2×C67—42no—
367C2×C67#312114yescomplemented
368C2×C67C2×#52511yescharacteristic
369C2×C67C2×#57711yescharacteristic
370C2×C67C2×#57811yescharacteristic
371D67—82no—
372C2×#542—671no—
373C2×#519D6711yescharacteristic, complemented
374#3121—6716no—
375C2×#485—671no—
376C2×#482—671no—
377C2×#477—671no—
378C2×#475—671no—
379C2×#464—671no—
380C2×#464—671no—
381C2×#451—671no—
382C2×#448—671no—
383C2×#441—671no—
384C2×#440—671no—
385C2×C4×Q16—671no—
386C2×C4×SD16—671no—
387C2×#433—671no—
388C67C2×#312111yescharacteristic, complemented, Sylow
389C23×Q8C2×D6711yescharacteristic
390C22×Q16—671no—
391C22×Q16—671no—
392C22×SD16—671no—
393C22×SD16—671no—
394#542—678no—
395#542—1344no—
396C2×C4⋊Q8—671no—
397C2×#126—1341no—
398C2×#124—671no—
399C2×#124—1341no—
400C2×#123—1341no—
401C2×C22⋊Q8—671no—
402C2×C22⋊Q8—1341no—
403C2×#121—671no—
404#519—24no—
405#519C2×D6718yescomplemented
406C2×C4×Q8—21no—
407C2×C4×Q8—21no—
408C2×C4×Q8—671no—
409C2×C4×Q8C2×D6711yescharacteristic
410C2×C4×Q8C2×D6711yescharacteristic
411C2×C4×Q8C2×D6711yescharacteristic
412C2×C4×Q8C2×D6711yescharacteristic
413C2×C4×D4—671no—
414C2×#117—21no—
415C2×#117—21no—
416C2×#117C2×D6711yescharacteristic
417C2×#117C2×D6711yescharacteristic
418#485—678no—
419#482—678no—
420#477—678no—
421#475—678no—
422#464—678no—
423#464—678no—
424#451—678no—
425#448—678no—
426#441—678no—
427#440—678no—
428C4×Q16—678no—
429C4×SD16—678no—
430#433—678no—
431C2×#107—671no—
432C2×#107—671no—
433C2×#106—671no—
434C2×#106—671no—
435C2×C4⋊C8—671no—
436C2×C4⋊C8—671no—
437C2×#103—671no—
438C2×#103—671no—
439C2×#103—671no—
440C2×#103—671no—
441C2×#103—671no—
442C2×#103—671no—
443C2×#102—671no—
444C2×#102—671no—
445C2×C22⋊C8—671no—
446C2×C22⋊C8—671no—
447C2×#97—671no—
448C2×C4×C8—671no—
449C22×Q8—24no—
450C22×Q8—24no—
451C22×Q8—21no—
452C22×Q8—22no—
453C22×Q8—671no—
454C22×Q8—1341no—
455C22×Q8C22×D6714yes—
456C22×Q8C22×D6711yescharacteristic
457C22×Q8C22×D6711yescharacteristic
458C22×D4—671no—
459C22×D4—1341no—
460C23×C4—21no—
461C23×C4—1341no—
462C23×C4C22×D6711yescharacteristic
463C2×Q16—674no—
464C2×Q16—674no—
465C2×Q16—1344no—
466C2×Q16—1344no—
467C2×SD16—674no—
468C2×SD16—674no—
469C2×SD16—1344no—
470C2×SD16—1344no—
471C22×C8—671no—
472C22×C8—671no—
473C22×C8—671no—
474C22×C8—671no—
475C4⋊Q8—674no—
476C4⋊Q8—1342no—
477#126—1348no—
478#124—674no—
479#124—1348no—
480#124—1342no—
481#123—1348no—
482C22⋊Q8—674no—
483C22⋊Q8—1342no—
484C22⋊Q8—1348no—
485#121—674no—
486#121—1342no—
487C4×Q8—28no—
488C4×Q8—28no—
489C4×Q8—22no—
490C4×Q8—22no—
491C4×Q8—22no—
492C4×Q8—22no—
493C4×Q8—674no—
494C4×Q8—1342no—
495C4×Q8C22×D6714yes—
496C4×Q8C22×D6714yes—
497C4×Q8C22×D6714yes—
498C4×Q8C22×D6714yes—
499C4×D4—674no—
500C4×D4—1342no—
501#117—22no—
502#117—28no—
503#117—28no—
504#117C22⋊D6714yes—
505#117C22×D6714yes—
506#117C22×D6714yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—671no—
512C2×C4⋊C4—671no—
513C2×C4⋊C4—1341no—
514C2×C4⋊C4—1341no—
515C2×C4⋊C4—1341no—
516C2×C4⋊C4C22⋊D6711yescharacteristic
517C2×C4⋊C4C22⋊D6711yescharacteristic
518C2×C4⋊C4C22×D6711yescharacteristic
519C2×C4⋊C4C22×D6711yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—1341no—
522C2×C22⋊C4—1341no—
523C2×C22⋊C4—1341no—
524C2×C22⋊C4—1341no—
525C2×C22⋊C4—1341no—
526C2×C22⋊C4C22⋊D6711yescharacteristic
527C2×C22⋊C4C22⋊D6711yescharacteristic
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—21no—
531C2×C42—21no—
532C2×C42—21no—
533C2×C42—1341no—
534C2×C42C22×D6711yescharacteristic
535C2×C42C22×D6711yescharacteristic
536#107—674no—
537#107—674no—
538#106—674no—
539#106—674no—
540C4⋊C8—674no—
541C4⋊C8—674no—
542#103—674no—
543#103—674no—
544#103—674no—
545#103—674no—
546#103—674no—
547#103—674no—
548#102—674no—
549#102—674no—
550C22⋊C8—674no—
551C22⋊C8—674no—
552#97—674no—
553C4×C8—674no—
554C24—1341no—
555C24C2×C22⋊D6711yescharacteristic
556C2×Q8—216no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—24no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—5362no—
566C2×Q8—672no—
567C2×Q8—1342no—
568C2×Q8—1342no—
569C2×Q8—1341no—
570C2×Q8—1344no—
571C2×Q8#1176162814yes—
572C2×Q8#1176162814yes—
573C2×Q8C23×D6712yes—
574C2×Q8C23×D6712yes—
575C2×D4—5362no—
576C2×D4—672no—
577C2×D4—1344no—
578C2×D4—1341no—
579C2×D4—1342no—
580C2×D4—1342no—
581C22×C4—28no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—5362no—
590C22×C4—1341no—
591C22×C4—1341no—
592C22×C4—1341no—
593C22×C4—1344no—
594C22×C4C2×C22⋊D6712yes—
595C22×C4C2×C22⋊D6711yescharacteristic
596C22×C4C2×C22⋊D6711yescharacteristic
597C22×C4C2×C22⋊D6711yescharacteristic
598C22×C4C2×C22⋊D6711yescharacteristic
599C22×C4C2×C22⋊D6711yescharacteristic
600C22×C4C23×D6712yes—
601C22×C4C23×D6711yescharacteristic
602Q16—1348no—
603Q16—1348no—
604SD16—1348no—
605SD16—1348no—
606C2×C8—672no—
607C2×C8—672no—
608C2×C8—672no—
609C2×C8—672no—
610C2×C8—1342no—
611C2×C8—1342no—
612C2×C8—1342no—
613C2×C8—1342no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—672no—
621C4⋊C4—672no—
622C4⋊C4—1341no—
623C4⋊C4—1341no—
624C4⋊C4—1344no—
625C4⋊C4—1344no—
626C4⋊C4—1344no—
627C4⋊C4C2×C22⋊D6714yes—
628C4⋊C4C2×C22⋊D6714yes—
629C4⋊C4C23×D6712yes—
630C4⋊C4C23×D6712yes—
631C22⋊C4—24no—
632C22⋊C4—1344no—
633C22⋊C4—1344no—
634C22⋊C4—1344no—
635C22⋊C4—1344no—
636C22⋊C4—1344no—
637C22⋊C4C2×C22⋊D6714yes—
638C22⋊C4C2×C22⋊D6714yes—
639C42—24no—
640C42—24no—
641C42—24no—
642C42—24no—
643C42—24no—
644C42—1344no—
645C42C2×C22⋊D6712yes—
646C42C2×C22⋊D6712yes—
647C42C23×D6712yes—
648C42C23×D6712yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—2682no—
653C23—2682no—
654C23—2682no—
655C23—1342no—
656C23C22×C22⋊D6712yes—
657C23C22×C22⋊D6711yescharacteristic
658Q8—216no—
659Q8—24no—
660Q8—24no—
661Q8—22no—
662Q8—22no—
663Q8—2682no—
664Q8—5364no—
665Q8—1342no—
666Q8—1342no—
667Q8C2×#1176162814yes—
668Q8C2×#1176162814yes—
669D4—2682no—
670D4—5364no—
671D4—1342no—
672D4—1342no—
673C2×C4—216no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—2682no—
691C2×C4—2682no—
692C2×C4—2682no—
693C2×C4—5364no—
694C2×C4—1342no—
695C2×C4—1342no—
696C2×C4—1342no—
697C2×C4C22×C22⋊D6712yes—
698C2×C4C22×C22⋊D6712yes—
699C2×C4C22×C22⋊D6712yes—
700C2×C4C22×C22⋊D6712yes—
701C2×C4C22×C22⋊D6712yes—
702C2×C4C22×C22⋊D6711yescharacteristic
703C2×C4C2×#1176162812yes—
704C2×C4C2×#1176162812yes—
705C2×C4C24×D6711yescharacteristic
706C8—1342no—
707C8—1342no—
708C8—1342no—
709C8—1342no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—2682no—
715C22—2682no—
716C22—2682no—
717C22—5364no—
718C22#1686390712yes—
719C22#1686420412yes—
720C22#1686421112yes—
721C22C23×C22⋊D6711yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—24no—
727C4—24no—
728C4—22no—
729C4—42no—
730C4—42no—
731C4—2682no—
732C4—2682no—
733C4—2682no—
734C4#1686390712yes—
735C4C22×#1176162811yescharacteristic
736C4C22×#1176162811yescharacteristic
737C2—42no—
738C2—5362no—
739C2#2257043814yesdirect product factor
740C2C2×#1686390711yescharacteristic
741C2C2×#1686420411yescharacteristic
742C2C2×#1686421111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#519×C67C2
socleC23×C67C22×D4
prime radicalC2×#14524017C22
hypercenterC2×#519D67
hypocenterC67C2×#3121
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. #22570438C2direct (N × H)
3. C2×#16863737C2semidirect
5. C2×#16863691C2semidirect
6. C2×#16863681C2semidirect
7. C2×#16863618C2semidirect
8. C2×#16863618C2semidirect
9. C2×#16863552C2semidirect
11. C2×#16863501C2semidirect
12. C2×#16863494C2semidirect
13. C2×C4×#11761618C2semidirect
14. C2×C4×#11761615C2semidirect
15. C2×#16863457C2semidirect
16. C2×#519×C67C2semidirect
33. #16863737C22semidirect
35. #16863691C22semidirect
36. #16863681C22semidirect
37. #16863618C22semidirect
38. #16863618C22semidirect
39. #16863552C22semidirect
41. #16863501C22semidirect
42. #16863494C22semidirect
43. C4×#11761618C22semidirect
44. C4×#11761615C22semidirect
45. #16863457C22semidirect
66. #519×C67C22semidirect
367. C2×C67#3121semidirect
373. C2×#519D67semidirect
388. C67C2×#3121semidirect
405. #519C2×D67semidirect
739. C2#22570438direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640172
#225704382
C2×#168637372
C2×#168637202
C2×#168636912
C2×#168636812
C2×#168636182
C2×#168635522
C2×#168635352
C2×#168635012
C2×#168634942
C2×C4×#117616182
C2×C4×#117616152
C2×#168634572
C2×#519×C672
C2×#312167