Finite Group Databasebeta

← C2×#22569995 #31723330

Subgroups — C2×#22569995 #31723330

Order 17152.

2162 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863949C211yesmaximal, characteristic, complemented
2C2×#16863864C211yesmaximal, characteristic
3#22569995C2116yesmaximal, direct product factor
4C2×#16863706C211yesmaximal, characteristic, complemented
5C2×#16863702C211yesmaximal, characteristic, complemented
6C2×#16863690C211yesmaximal, characteristic, complemented
7C2×#16863680C211yesmaximal, characteristic, complemented
8C2×#16863699C211yesmaximal, characteristic, complemented
9C2×#16863695C211yesmaximal, characteristic, complemented
10C2×#16863685C211yesmaximal, characteristic, complemented
11C2×#16863675C211yesmaximal, characteristic, complemented
12C2×#16863432C211yesmaximal, characteristic, complemented
13C22×Dic67⋊C8C211yesmaximal, characteristic, complemented
14C2×#16863393C211yesmaximal, characteristic
15C2×#16863390C211yesmaximal, characteristic
16C2×#427×C67C211yesmaximal, characteristic, complemented
17C22×#11761628C2211yescharacteristic
18C23×C67⋊C8C2211yescharacteristic
19#16863949—24no—
20#16863949C2218yescomplemented
21C2×#14524042C2211yescharacteristic
22C2×#14524042C2211yescharacteristic
23C2×#14524034C2211yescharacteristic
24C2×#14524034C2211yescharacteristic
25C2×#14524020—21no—
26C2×#14524020—21no—
27#16863864—24no—
28#16863864C2218yes—
29C2×C4×Dic134—21no—
30C2×C4×Dic134—21no—
31C2×#14524008C2211yescharacteristic
32C2×#14524008C2211yescharacteristic
33C2×#14524005C2211yescharacteristic
34C2×#14524005C2211yescharacteristic
35C2×(C22⋊D67)⋊C4—21no—
36C2×(C22⋊D67)⋊C4—21no—
37C2×#14524002C2211yescharacteristic
38C2×#14524000—21no—
39C22×C4×Dic67C2211yescharacteristic
40C2×C42×D67—21no—
41#16863706C2218yescomplemented
42#16863702C2218yescomplemented
43#16863699C2218yescomplemented
44#16863695C2218yescomplemented
45#16863690C2218yescomplemented
46#16863685C2218yescomplemented
47#16863680C2218yescomplemented
48#16863675C2218yescomplemented
49#16863432C2218yescomplemented
50C2×#14523976C2211yescharacteristic
51C2×#14523976C2211yescharacteristic
52C2×#14523974C2211yescharacteristic
53C2×#14523974C2211yescharacteristic
54C2×Dic67⋊C8C2211yescharacteristic
55C2×Dic67⋊C8C2211yescharacteristic
56C2×Dic67⋊C8C2211yescharacteristic
57C2×Dic67⋊C8C2211yescharacteristic
58C2×Dic67⋊C8C2218yescomplemented
59#16863393C2218yes—
60#16863390C2218yes—
61C2×#14523968C2211yescharacteristic
62C2×#14523968C2211yescharacteristic
63C2×#14523966C2211yescharacteristic
64C2×#14523966C2211yescharacteristic
65C2×#14523965C2211yescharacteristic
66C2×#14523965C2211yescharacteristic
67C2×#14523963C2211yescharacteristic
68C2×#14523963C2211yescharacteristic
69C23×C8×C67C2211yescharacteristic
70C2×#117×C67C2211yescharacteristic
71C2×#117×C67C2211yescharacteristic
72#427×C67C2218yescomplemented
73C2×#107×C67C2211yescharacteristic
74C2×#107×C67C2211yescharacteristic
75C2×#106×C67C2211yescharacteristic
76C2×#106×C67C2211yescharacteristic
77C2×#11761628—22no—
78C2×#11761628—24no—
79C2×#11761628Q818yescomplemented
80C2×#11761628C2314yes—
81C22×Dic134—21no—
82C22×Dic134—21no—
83C22×Dic134C2311yescharacteristic
84C22×D268C2311yescharacteristic
85C22×C22⋊D67—21no—
86C23×Dic67D411yescharacteristic
87C23×Dic67D411yescharacteristic
88C22×C4×D67—21no—
89C22×C4×D67—21no—
90C22×C4×D67—21no—
91C22×C67⋊C8—24no—
92C22×C67⋊C8C2311yescharacteristic
93C22×C67⋊C8C2311yescharacteristic
94C22×C67⋊C8C2314yes—
95#14524042—22no—
96#14524042—22no—
97#14524042C2314yes—
98#14524042C2314yes—
99#14524034—22no—
100#14524034—22no—
101#14524034C2314yes—
102#14524034C2314yes—
103#14524020—28no—
104#14524020—28no—
105C4×Dic134—28no—
106C4×Dic134—28no—
107#14524008—22no—
108#14524008—22no—
109#14524008C2314yes—
110#14524008C2314yes—
111#14524005—22no—
112#14524005—22no—
113#14524005C2314yes—
114#14524005C2314yes—
115(C22⋊D67)⋊C4—28no—
116(C22⋊D67)⋊C4—28no—
117#14524002—22no—
118#14524002C2314yes—
119#14524000—28no—
120C2×C4⋊Dic67—21no—
121C2×C4⋊Dic67—21no—
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×C22⋊Dic67—21no—
131C2×(C2×D67)⋊C4—21no—
132C2×(C2×D67)⋊C4—21no—
133C2×C4×Dic67—21no—
134C2×C4×Dic67—21no—
135C2×C4×Dic67—21no—
136C2×C4×Dic67D411yescharacteristic
137C2×C4×Dic67D411yescharacteristic
138C2×C4×Dic67D414yes—
139C2×C4×Dic67C2311yescharacteristic
140C2×C4×Dic67C2311yescharacteristic
141C2×C4×Dic67C2314yes—
142C42×D67—28no—
143#14523976C2314yes—
144#14523976C2314yes—
145#14523974C2314yes—
146#14523974C2314yes—
147Dic67⋊C8C2314yes—
148Dic67⋊C8C2314yes—
149Dic67⋊C8C2314yes—
150Dic67⋊C8C2314yes—
151#14523968C2314yes—
152#14523968C2314yes—
153#14523966C2314yes—
154#14523966C2314yes—
155#14523965C2314yes—
156#14523965C2314yes—
157#14523963C2314yes—
158#14523963C2314yes—
159C23×C4×C67C2311yescharacteristic
160C22×C8×C67—24no—
161C22×C8×C67C2311yescharacteristic
162C22×C8×C67C2311yescharacteristic
163C22×C8×C67C2314yes—
164#117×C67—22no—
165#117×C67—22no—
166#117×C67C2314yes—
167#117×C67C2314yes—
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C4⋊C4×C67C2311yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C22⋊C4×C67—21no—
173C2×C22⋊C4×C67—21no—
174C2×C42×C67—21no—
175C2×C42×C67—21no—
176#107×C67C2314yes—
177#107×C67C2314yes—
178#106×C67C2314yes—
179#106×C67C2314yes—
180C23×D67—21no—
181#11761628—216no—
182#11761628—28no—
183#11761628C2×Q8116yescomplemented
184C2×Dic134—21no—
185C2×Dic134—22no—
186C2×Dic134—24no—
187C2×Dic134—24no—
188C2×Dic134—44no—
189C2×Dic134—44no—
190C2×Dic134C2×Q814yes—
191C2×Dic134C2412yes—
192C2×D268—21no—
193C2×D268—22no—
194C2×D268C2×Q814yes—
195C2×D268C2412yes—
196C2×C22⋊D67—28no—
197C2×C22⋊D67—24no—
198C22×Dic67—21no—
199C22×Dic67—24no—
200C22×Dic67—21no—
201C22×Dic67—21no—
202C22×Dic67—42no—
203C22×Dic67C2×D411yescharacteristic
204C22×Dic67C2×D411yescharacteristic
205C22×Dic67C2×D411yescharacteristic
206C22×Dic67C2×D414yes—
207C22×Dic67C2×D414yes—
208C22×Dic67C2×D411yescharacteristic
209C2×C4×D67—28no—
210C2×C4×D67—24no—
211C2×C4×D67—24no—
212C2×C4×D67—24no—
213C2×C4×D67—44no—
214C2×C4×D67—44no—
215C2×C67⋊C8—22no—
216C2×C67⋊C8—22no—
217C2×C67⋊C8—28no—
218C2×C67⋊C8C2412yes—
219C2×C67⋊C8C2412yes—
220C4⋊Dic67—21no—
221C4⋊Dic67—21no—
222C4⋊Dic67—24no—
223C4⋊Dic67—24no—
224C4⋊Dic67C2412yes—
225C4⋊Dic67C2412yes—
226Dic67⋊C4—24no—
227Dic67⋊C4—24no—
228Dic67⋊C4—24no—
229Dic67⋊C4—24no—
230Dic67⋊C4—24no—
231Dic67⋊C4—24no—
232C22⋊Dic67—24no—
233(C2×D67)⋊C4—24no—
234(C2×D67)⋊C4—24no—
235C4×Dic67—24no—
236C4×Dic67—24no—
237C4×Dic67—24no—
238C4×Dic67C2×D414yes—
239C4×Dic67C2×D414yes—
240C4×Dic67C2×D412yes—
241C4×Dic67C2×D412yes—
242C4×Dic67C2412yes—
243C4×Dic67C2412yes—
244C24×C67C2×D411yescharacteristic
245C22×C4×C67—21no—
246C22×C4×C67—21no—
247C22×C4×C67—21no—
248C22×C4×C67—21no—
249C22×C4×C67C2×D412yes—
250C22×C4×C67C2×D411yescharacteristic
251C22×C4×C67C2×Q814yes—
252C22×C4×C67#4114yes—
253C22×C4×C67C2411yescharacteristic
254C22×C4×C67C2412yes—
255C2×C8×C67—22no—
256C2×C8×C67—22no—
257C2×C8×C67—28no—
258C2×C8×C67C2412yes—
259C2×C8×C67C2412yes—
260C4⋊C4×C67—21no—
261C4⋊C4×C67—21no—
262C4⋊C4×C67—21no—
263C4⋊C4×C67—21no—
264C4⋊C4×C67C2412yes—
265C4⋊C4×C67C2412yes—
266C4⋊C4×C67C2412yes—
267C4⋊C4×C67C2412yes—
268C22⋊C4×C67—24no—
269C22⋊C4×C67—24no—
270C42×C67—24no—
271C42×C67—24no—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67C22⋊Q814yes—
275C23×C67C22×D412yes—
276C23×C67C22×D411yescharacteristic
277C22×D67—24no—
278C22×D67—22no—
279C22×D67—42no—
280C22×D67—42no—
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×C67—42no—
289C2×C4×C67C22⋊Q814yes—
290C2×C4×C67C22⋊Q818yes—
291C2×C4×C67C22×D412yes—
292C2×C4×C67C22×D411yescharacteristic
293C2×C4×C67C22×Q812yes—
294C2×C4×C67C22×Q814yes—
295C2×C4×C67C2×#4112yes—
296C2×C4×C67C2×#4114yes—
297C2×C4×C67C2511yescharacteristic
298C22⋊D67—216no—
299C2×Dic67—24no—
300C2×Dic67—22no—
301C2×Dic67—22no—
302C2×Dic67—22no—
303C2×Dic67—22no—
304C2×Dic67—28no—
305C2×Dic67—22no—
306C2×Dic67—22no—
307C2×Dic67—44no—
308C2×Dic67—42no—
309C2×Dic67—42no—
310C2×Dic67#13514yes—
311C2×Dic67C22×D412yes—
312C2×Dic67C22×D412yes—
313C2×Dic67C22×D412yes—
314C2×Dic67C22×D412yes—
315D268—24no—
316D268—22no—
317D268C22×Q814yes—
318C4×D67—216no—
319C4×D67—48no—
320C4×D67—48no—
321Dic134—24no—
322Dic134—22no—
323Dic134—48no—
324Dic134—48no—
325Dic134C22×Q814yes—
326C8×C67—22no—
327C8×C67—22no—
328C67⋊C8—22no—
329C67⋊C8—22no—
330C22×C67—28no—
331C22×C67—22no—
332C22×C67—22no—
333C22×C67C2×C22⋊Q814yes—
334C22×C67C2×C22⋊Q812yes—
335C22×C67C2×#13512yes—
336C22×C67#57512yes—
337C22×C67C23×D411yescharacteristic
338C2×D67—24no—
339C2×D67—48no—
340C2×D67—42no—
341C2×D67—42no—
342C4×C67—42no—
343C4×C67—42no—
344C4×C67—42no—
345C4×C67—42no—
346C4×C67C2×C22⋊Q812yes—
347C4×C67C2×C22⋊Q814yes—
348C4×C67C23×Q811yescharacteristic
349C4×C67C22×#4111yescharacteristic
350Dic67—24no—
351Dic67—22no—
352Dic67—22no—
353Dic67—22no—
354Dic67—42no—
355Dic67—42no—
356Dic67C2×#13514yes—
357C2×#3076—671nomaximal, Sylow
358C2×C67—24no—
359C2×C67#307614yescomplemented
360C2×C67C22×C22⋊Q811yescharacteristic
361C2×C67C22×#13511yescharacteristic
362C2×C67C2×#57511yescharacteristic
363D67—44no—
364C2×#533—671no—
365C2×C4×#41—671no—
366#3076—6716no—
367C2×#479—671no—
368C2×#479—671no—
369C2×#477—671no—
370C2×#475—671no—
371C2×#478—671no—
372C2×#478—671no—
373C2×#476—671no—
374C2×#474—671no—
375C2×#427—671no—
376C2×#427D6711yescharacteristic, complemented
377C22×C4⋊C8—671no—
378C2×#416—671no—
379C2×#416—671no—
380C67C2×#307611yescharacteristic, complemented, Sylow
381C22×#41—671no—
382C23×C8—671no—
383C23×C8C2×D6711yescharacteristic
384#533—678no—
385#533—1344no—
386C2×C4⋊Q8—671no—
387C2×C4⋊Q8—671no—
388C2×#125—671no—
389C2×#125—671no—
390C2×C22⋊Q8—1341no—
391C2×C22⋊Q8—1341no—
392C4×#41—678no—
393C4×#41—1344no—
394C2×C4×Q8—671no—
395C2×C4×Q8—671no—
396C2×C4×Q8—1341no—
397C2×C4×Q8—1341no—
398C2×C4×D4—671no—
399C2×C4×D4—671no—
400C2×C4×D4—1341no—
401C2×C4×D4—1341no—
402C2×#117—671no—
403C2×#117—1341no—
404C2×#117C2×D6711yescharacteristic
405C2×#117C2×D6711yescharacteristic
406C22×C42—671no—
407C22×C42—1341no—
408#479—678no—
409#479—678no—
410#478—678no—
411#478—678no—
412#477—678no—
413#476—678no—
414#475—678no—
415#474—678no—
416#427—678no—
417#427C2×D6718yescomplemented
418C2×#107—671no—
419C2×#107—671no—
420C2×#107C2×D6711yescharacteristic
421C2×#107C2×D6711yescharacteristic
422C2×#106—671no—
423C2×#106—671no—
424C2×#106C2×D6711yescharacteristic
425C2×#106C2×D6711yescharacteristic
426C2×C4⋊C8—671no—
427C2×C4⋊C8—671no—
428C2×C4⋊C8—671no—
429C2×C4⋊C8—671no—
430C2×C4⋊C8—678no—
431#416—678no—
432#416—678no—
433C2×#103—671no—
434C2×#103—671no—
435C2×#103—671no—
436C2×#103—671no—
437C2×#102—671no—
438C2×#102—671no—
439C2×#102—671no—
440C2×#102—671no—
441C2×#41—678no—
442C2×#41—674no—
443C2×#41—1342no—
444C2×#41—1344no—
445C22×Q8—671no—
446C22×Q8—1341no—
447C22×Q8—1341no—
448C22×D4—671no—
449C22×D4—1341no—
450C23×C4—671no—
451C23×C4—671no—
452C23×C4—1341no—
453C23×C4—1341no—
454C23×C4—1341no—
455C23×C4C22×D6711yescharacteristic
456C22×C8—24no—
457C22×C8—671no—
458C22×C8—671no—
459C22×C8—674no—
460C22×C8—1344no—
461C22×C8C22×D6711yescharacteristic
462C22×C8C22×D6711yescharacteristic
463C22×C8C22×D6714yes—
464C4⋊Q8—674no—
465C4⋊Q8—674no—
466C4⋊Q8—1342no—
467C4⋊Q8—1342no—
468#125—674no—
469#125—674no—
470#125—1342no—
471#125—1342no—
472C22⋊Q8—1348no—
473C22⋊Q8—1348no—
474C4×Q8—674no—
475C4×Q8—674no—
476C4×Q8—1348no—
477C4×Q8—1348no—
478C4×Q8—1342no—
479C4×Q8—1342no—
480C4×D4—674no—
481C4×D4—674no—
482C4×D4—1342no—
483C4×D4—1342no—
484C4×D4—1348no—
485C4×D4—1348no—
486#117—22no—
487#117—22no—
488#117—674no—
489#117—1348no—
490#117—1342no—
491#117C22×D6714yes—
492#117C22×D6714yes—
493C2×C4⋊C4—671no—
494C2×C4⋊C4—671no—
495C2×C4⋊C4—1341no—
496C2×C4⋊C4—1341no—
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⋊C4C22×D6711yescharacteristic
504C2×C4⋊C4C22×D6711yescharacteristic
505C2×C4⋊C4C22×D6711yescharacteristic
506C2×C4⋊C4C22×D6711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—1341no—
510C2×C22⋊C4—1341no—
511C2×C22⋊C4—1341no—
512C2×C42—21no—
513C2×C42—21no—
514C2×C42—674no—
515C2×C42—671no—
516C2×C42—671no—
517C2×C42—671no—
518C2×C42—671no—
519C2×C42—674no—
520C2×C42—1348no—
521C2×C42—1341no—
522C2×C42—1341no—
523C2×C42—1341no—
524#107—674no—
525#107—674no—
526#107C22×D6714yes—
527#107C22×D6714yes—
528#106—674no—
529#106—674no—
530#106C22×D6714yes—
531#106C22×D6714yes—
532C4⋊C8—674no—
533C4⋊C8—674no—
534C4⋊C8—674no—
535C4⋊C8—674no—
536#103—674no—
537#103—674no—
538#103—674no—
539#103—674no—
540#102—674no—
541#102—674no—
542#102—674no—
543#102—674no—
544C24—1341no—
545C24D4×D6711yescharacteristic
546#41—6716no—
547#41—13416no—
548#41—1348no—
549C2×Q8—2684no—
550C2×Q8—2684no—
551C2×Q8—674no—
552C2×Q8—672no—
553C2×Q8—1344no—
554C2×Q8—1344no—
555C2×Q8—1341no—
556C2×Q8—1342no—
557C2×D4—674no—
558C2×D4—672no—
559C2×D4—1348no—
560C2×D4—1344no—
561C2×D4—1341no—
562C2×D4—1342no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—2684no—
568C22×C4—2684no—
569C22×C4—2682no—
570C22×C4—674no—
571C22×C4—671no—
572C22×C4—671no—
573C22×C4—671no—
574C22×C4—671no—
575C22×C4—674no—
576C22×C4—1344no—
577C22×C4—1344no—
578C22×C4—1341no—
579C22×C4—1341no—
580C22×C4—1344no—
581C22×C4—1341no—
582C22×C4—1348no—
583C22×C4—1344no—
584C22×C4D4×D6712yes—
585C22×C4D4×D6711yescharacteristic
586C22×C4Q8×D6714yes—
587C22×C4#1176162814yes—
588C22×C4C23×D6711yescharacteristic
589C22×C4C23×D6712yes—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—672no—
594C2×C8—672no—
595C2×C8—1342no—
596C2×C8—1342no—
597C2×C8—1348no—
598C2×C8C23×D6712yes—
599C2×C8C23×D6712yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—672no—
605C4⋊C4—672no—
606C4⋊C4—1344no—
607C4⋊C4—1344no—
608C4⋊C4—1344no—
609C4⋊C4—1344no—
610C4⋊C4—1344no—
611C4⋊C4—1344no—
612C4⋊C4—1344no—
613C4⋊C4—1344no—
614C4⋊C4—1341no—
615C4⋊C4—1341no—
616C4⋊C4C23×D6712yes—
617C4⋊C4C23×D6712yes—
618C4⋊C4C23×D6712yes—
619C4⋊C4C23×D6712yes—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—1344no—
623C22⋊C4—1344no—
624C22⋊C4—1344no—
625C42—24no—
626C42—24no—
627C42—674no—
628C42—674no—
629C42—672no—
630C42—672no—
631C42—672no—
632C42—672no—
633C42—1344no—
634C42—1344no—
635C42—1344no—
636C23—22no—
637C23—22no—
638C23—2682no—
639C23—2682no—
640C23—1344no—
641C23—1342no—
642C23#1452402114yes—
643C23C2×D4×D6712yes—
644C23C2×D4×D6711yescharacteristic
645Q8—2688no—
646Q8—2688no—
647Q8—674no—
648Q8—1344no—
649Q8—1342no—
650D4—674no—
651D4—13416no—
652D4—1344no—
653D4—1342no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—2688no—
663C2×C4—2688no—
664C2×C4—2682no—
665C2×C4—2682no—
666C2×C4—2684no—
667C2×C4—674no—
668C2×C4—672no—
669C2×C4—672no—
670C2×C4—672no—
671C2×C4—672no—
672C2×C4—1342no—
673C2×C4—1342no—
674C2×C4—1348no—
675C2×C4—1344no—
676C2×C4—1342no—
677C2×C4—1342no—
678C2×C4—1342no—
679C2×C4—1342no—
680C2×C4—13416no—
681C2×C4#1452402114yes—
682C2×C4#1452402118yes—
683C2×C4C2×D4×D6712yes—
684C2×C4C2×D4×D6711yescharacteristic
685C2×C4C2×Q8×D6712yes—
686C2×C4C2×Q8×D6714yes—
687C2×C4C2×#1176162812yes—
688C2×C4C2×#1176162814yes—
689C2×C4C24×D6711yescharacteristic
690C8—22no—
691C8—22no—
692C8—1342no—
693C8—1342no—
694C22—28no—
695C22—22no—
696C22—22no—
697C22—2688no—
698C22—2682no—
699C22—2682no—
700C22—1344no—
701C22C2×#1452402114yes—
702C22C2×#1452402112yes—
703C22#135×D6712yes—
704C22#1686419312yes—
705C22C22×D4×D6711yescharacteristic
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—2682no—
711C4—2682no—
712C4—674no—
713C4—1342no—
714C4—1342no—
715C4—1342no—
716C4—1344no—
717C4C2×#1452402114yes—
718C4C2×#1452402112yes—
719C4C22×Q8×D6711yescharacteristic
720C4C22×#1176162811yescharacteristic
721C2—24no—
722C2—2684no—
723C2#2256999514yesdirect product factor
724C2C22×#1452402111yescharacteristic
725C2C2×#135×D6711yescharacteristic
726C2C2×#1686419311yescharacteristic
subgroupG/H
centerC22×C4D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#427×C67C2
socleC23×C67C22×D4
prime radicalC22×#11761628C22
hypercenterC2×#427D67
hypocenterC67C2×#3076
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
1. C2×#16863949C2semidirect
3. #22569995C2direct (N × H)
4. C2×#16863706C2semidirect
5. C2×#16863702C2semidirect
6. C2×#16863690C2semidirect
7. C2×#16863680C2semidirect
8. C2×#16863699C2semidirect
9. C2×#16863695C2semidirect
10. C2×#16863685C2semidirect
11. C2×#16863675C2semidirect
12. C2×#16863432C2semidirect
13. C22×Dic67⋊C8C2semidirect
16. C2×#427×C67C2semidirect
20. #16863949C22semidirect
41. #16863706C22semidirect
42. #16863702C22semidirect
43. #16863699C22semidirect
44. #16863695C22semidirect
45. #16863690C22semidirect
46. #16863685C22semidirect
47. #16863680C22semidirect
48. #16863675C22semidirect
49. #16863432C22semidirect
58. C2×Dic67⋊C8C22semidirect
72. #427×C67C22semidirect
79. C2×#11761628Q8semidirect
183. #11761628C2×Q8semidirect
359. C2×C67#3076semidirect
376. C2×#427D67semidirect
380. C67C2×#3076semidirect
417. #427C2×D67semidirect
723. C2#22569995direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168639492
C2×#168638642
#225699952
C2×#168637062
C2×#168637022
C2×#168636902
C2×#168636802
C2×#168636992
C2×#168636952
C2×#168636852
C2×#168636752
C2×#168634322
C22×Dic67⋊C82
C2×#168633932
C2×#168633902
C2×#427×C672
C2×#307667