Finite Group Databasebeta

← C2×#22570156 #31723636

Subgroups — C2×#22570156 #31723636

Order 17152.

2326 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D67C211yesmaximal, characteristic
2C2×#117×D67C211yesmaximal, characteristic
3#22570156C2116yesmaximal, direct product factor
4C2×#16863733C211yesmaximal, characteristic, complemented
5C2×#16863730C211yesmaximal, characteristic, complemented
6C2×#16863738C211yesmaximal, characteristic, complemented
7C2×#16863737C211yesmaximal, characteristic, complemented
8C2×#16863734C211yesmaximal, characteristic, complemented
9C2×#16863728C211yesmaximal, characteristic, complemented
10C2×#16863725C211yesmaximal, characteristic, complemented
11C2×#16863437C211yesmaximal, characteristic, complemented
12C2×#16863435C211yesmaximal, characteristic, complemented
13C2×#16863403C211yesmaximal, characteristic, complemented
14C2×#16863403C211yesmaximal, characteristic, complemented
15C2×#16863358C211yesmaximal, characteristic
16C2×#485×C67C211yesmaximal, characteristic, complemented
17C22×Q8×D67C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C22×#11761611C2211yescharacteristic
20C22×#11761611C2211yescharacteristic
21C2×#14524023C2211yescharacteristic
22C2×#14524022C2211yescharacteristic
23C2×#14524021—21no—
24C2×#14524020—21no—
25C2×#14524019C2211yescharacteristic
26C22⋊Q8×D67—24no—
27C22⋊Q8×D67C2218yes—
28C2×#14524002C2211yescharacteristic
29C2×#14524001C2211yescharacteristic
30C2×#14524001C2211yescharacteristic
31C2×#14524000—21no—
32C2×#14523999—21no—
33#117×D67—24no—
34#117×D67C2218yes—
35C2×C4⋊C4×D67—21no—
36C2×C4⋊C4×D67C2211yescharacteristic
37C2×C4⋊C4×D67C2211yescharacteristic
38C2×C4⋊C4×D67C2211yescharacteristic
39C2×C22⋊C4×D67—21no—
40C2×C22⋊C4×D67—21no—
41C2×C42×D67—21no—
42#16863738C2218yescomplemented
43#16863737C2218yescomplemented
44#16863734C2218yescomplemented
45#16863733C2218yescomplemented
46#16863730C2218yescomplemented
47#16863728C2218yescomplemented
48#16863725C2218yescomplemented
49#16863437C2218yescomplemented
50#16863435C2218yescomplemented
51C2×#14523977C2211yescharacteristic, complemented
52C2×#14523976C2211yescharacteristic, complemented
53C2×#14523976C2211yescharacteristic, complemented
54C2×#14523975C2211yescharacteristic, complemented
55C2×#14523974C2211yescharacteristic, complemented
56C2×#14523974C2211yescharacteristic, complemented
57#16863403C2218yescomplemented
58#16863403C2218yescomplemented
59C2×#14523968C2211yescharacteristic, complemented
60C2×#14523968C2211yescharacteristic, complemented
61C2×#14523967C2211yescharacteristic, complemented
62C2×#14523967C2211yescharacteristic, complemented
63C2×#14523966C2211yescharacteristic, complemented
64C2×#14523966C2211yescharacteristic, complemented
65#16863358C2218yes—
66C2×C22⋊(C67⋊C8)C2211yescharacteristic
67C2×(C2×D67)⋊C8C2211yescharacteristic
68C2×(C2×D67)⋊C8C2211yescharacteristic
69C2×C22⋊Q8×C67C2211yescharacteristic
70C2×#117×C67C2211yescharacteristic
71#485×C67C2218yescomplemented
72C2×#107×C67C2211yescharacteristic, complemented
73C2×#106×C67C2211yescharacteristic, complemented
74C2×#103×C67C2211yescharacteristic, complemented
75C2×#103×C67C2211yescharacteristic, complemented
76C2×C22⋊C8×C67C2211yescharacteristic
77C24×D67D411yescharacteristic
78C22×Dic134—21no—
79C22×Dic134C2311yescharacteristic
80C2×Q8×D67—22no—
81C2×Q8×D67—24no—
82C2×Q8×D67—24no—
83C2×Q8×D67C2314yes—
84C23×Dic67D411yescharacteristic
85C22×C4×D67—24no—
86C22×C4×D67—24no—
87C22×C4×D67—21no—
88C22×C4×D67—21no—
89C22×C4×D67—21no—
90C22×C4×D67—21no—
91C22×C4×D67D411yescharacteristic
92C22×C4×D67D411yescharacteristic
93C22×C4×D67D414yes—
94C22×C4×D67C2311yescharacteristic
95C22×C4×D67C2314yes—
96C22×C4×D67C2311yescharacteristic
97C2×#11761611—24no—
98C2×#11761611—24no—
99C2×#11761611C2314yes—
100C2×#11761611C2314yes—
101C22×C67⋊C8C2311yescharacteristic
102C22×C67⋊C8C2311yescharacteristic
103#14524023—22no—
104#14524023C2314yes—
105#14524022—22no—
106#14524022C2314yes—
107#14524021—28no—
108#14524020—28no—
109#14524019—22no—
110#14524019C2314yes—
111#14524002—22no—
112#14524002C2314yes—
113#14524001—22no—
114#14524001—22no—
115#14524001C2314yes—
116#14524001C2314yes—
117#14524000—28no—
118#14523999—28no—
119C2×C4⋊Dic67—21no—
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—
128C4⋊C4×D67—28no—
129C4⋊C4×D67—22no—
130C4⋊C4×D67—22no—
131C4⋊C4×D67—22no—
132C4⋊C4×D67C2314yes—
133C4⋊C4×D67C2314yes—
134C4⋊C4×D67C2314yes—
135C2×C22⋊Dic67—21no—
136C2×C22⋊Dic67—21no—
137C2×(C2×D67)⋊C4—21no—
138C2×(C2×D67)⋊C4—21no—
139C2×(C2×D67)⋊C4—21no—
140C2×(C2×D67)⋊C4—21no—
141C22⋊C4×D67—28no—
142C22⋊C4×D67—28no—
143C2×C4×Dic67—21no—
144C2×C4×Dic67—21no—
145C2×C4×Dic67—21no—
146C42×D67—28no—
147#14523977C2314yescomplemented
148#14523976C2314yescomplemented
149#14523976C2314yescomplemented
150#14523975C2314yescomplemented
151#14523974C2314yescomplemented
152#14523974C2314yescomplemented
153#14523968C2314yescomplemented
154#14523968C2314yescomplemented
155#14523967C2314yescomplemented
156#14523967C2314yescomplemented
157#14523966C2314yescomplemented
158#14523966C2314yescomplemented
159C22⋊(C67⋊C8)C2314yes—
160(C2×D67)⋊C8C2314yes—
161(C2×D67)⋊C8C2314yes—
162C22×Q8×C67C2311yescharacteristic
163C23×C4×C67C2311yescharacteristic
164C22×C8×C67C2311yescharacteristic
165C22×C8×C67C2311yescharacteristic
166C22⋊Q8×C67—22no—
167C22⋊Q8×C67C2314yes—
168#117×C67—22no—
169#117×C67C2314yes—
170C2×C4⋊C4×C67—21no—
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C4⋊C4×C67C2311yescharacteristic
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67—21no—
176C2×C42×C67—21no—
177#107×C67C2314yescomplemented
178#106×C67C2314yescomplemented
179#103×C67C2314yescomplemented
180#103×C67C2314yescomplemented
181C22⋊C8×C67C2314yes—
182C23×D67—24no—
183C23×D67—24no—
184C23×D67—42no—
185C23×D67C2×D414yes—
186C23×D67C2×D411yescharacteristic
187C23×D67C2×D411yescharacteristic
188C2×Dic134—22no—
189C2×Dic134—22no—
190C2×Dic134—21no—
191C2×Dic134—24no—
192C2×Dic134—44no—
193C2×Dic134C2412yes—
194Q8×D67—28no—
195Q8×D67—28no—
196Q8×D67—48no—
197C22×Dic67—24no—
198C22×Dic67—21no—
199C22×Dic67—21no—
200C22×Dic67—21no—
201C22×Dic67—21no—
202C22×Dic67C2×D411yescharacteristic
203C22×Dic67C2×D414yes—
204C22×Dic67C2×D411yescharacteristic
205C2×C4×D67—24no—
206C2×C4×D67—22no—
207C2×C4×D67—22no—
208C2×C4×D67—24no—
209C2×C4×D67—216no—
210C2×C4×D67—28no—
211C2×C4×D67—28no—
212C2×C4×D67—24no—
213C2×C4×D67—24no—
214C2×C4×D67—24no—
215C2×C4×D67—24no—
216C2×C4×D67—44no—
217C2×C4×D67—44no—
218C2×C4×D67—44no—
219C2×C4×D67—44no—
220C2×C4×D67C2×D414yes—
221C2×C4×D67C2×D414yes—
222C2×C4×D67C2×D412yes—
223C2×C4×D67C2×D412yes—
224C2×C4×D67#4114yes—
225C2×C4×D67#4114yes—
226C2×C4×D67C2412yes—
227C2×C4×D67C2412yes—
228#11761611—28no—
229#11761611—28no—
230C2×C67⋊C8—22no—
231C2×C67⋊C8—22no—
232C2×C67⋊C8C2412yes—
233C2×C67⋊C8C2412yes—
234C4⋊Dic67—21no—
235C4⋊Dic67—21no—
236C4⋊Dic67—21no—
237C4⋊Dic67—24no—
238C4⋊Dic67C2412yes—
239C4⋊Dic67C2412yes—
240C4⋊Dic67C2412yes—
241Dic67⋊C4—24no—
242Dic67⋊C4—24no—
243Dic67⋊C4—24no—
244Dic67⋊C4—24no—
245Dic67⋊C4—24no—
246C22⋊Dic67—24no—
247C22⋊Dic67—24no—
248(C2×D67)⋊C4—24no—
249(C2×D67)⋊C4—24no—
250(C2×D67)⋊C4—24no—
251(C2×D67)⋊C4—24no—
252C4×Dic67—24no—
253C4×Dic67—24no—
254C4×Dic67—24no—
255C24×C67C2×D411yescharacteristic
256C2×Q8×C67—21no—
257C2×Q8×C67—22no—
258C2×Q8×C67—22no—
259C2×Q8×C67C2412yes—
260C22×C4×C67—22no—
261C22×C4×C67—22no—
262C22×C4×C67—21no—
263C22×C4×C67—21no—
264C22×C4×C67—21no—
265C22×C4×C67—21no—
266C22×C4×C67C2×D411yescharacteristic
267C22×C4×C67C2×D412yes—
268C22×C4×C67C2412yes—
269C22×C4×C67C2411yescharacteristic
270C2×C8×C67—22no—
271C2×C8×C67—22no—
272C2×C8×C67C2412yes—
273C2×C8×C67C2412yes—
274C4⋊C4×C67—24no—
275C4⋊C4×C67—21no—
276C4⋊C4×C67—21no—
277C4⋊C4×C67—21no—
278C4⋊C4×C67C2412yes—
279C4⋊C4×C67C2412yes—
280C4⋊C4×C67C2412yes—
281C22⋊C4×C67—24no—
282C22⋊C4×C67—24no—
283C42×C67—24no—
284C23×C67—22no—
285C23×C67—22no—
286C23×C67—22no—
287C23×C67C22×D412yes—
288C23×C67C22×D411yescharacteristic
289C22×D67—22no—
290C22×D67—22no—
291C22×D67—22no—
292C22×D67—22no—
293C22×D67—28no—
294C22×D67—28no—
295C22×D67—44no—
296C22×D67—416no—
297C22×D67#12314yes—
298C22×D67#13714yes—
299C22×D67C22×D412yes—
300C22×D67C22×D412yes—
301Q8×C67—22no—
302Q8×C67—22no—
303Q8×C67—42no—
304C2×C4×C67—22no—
305C2×C4×C67—24no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—42no—
313C2×C4×C67—42no—
314C2×C4×C67—42no—
315C2×C4×C67—42no—
316C2×C4×C67C22×D412yes—
317C2×C4×C67C22×D411yescharacteristic
318C2×C4×C67C2×#4112yes—
319C2×C4×C67C2×#4112yes—
320C2×C4×C67C2511yescharacteristic
321C2×Dic67—22no—
322C2×Dic67—28no—
323C2×Dic67—22no—
324C2×Dic67—22no—
325C2×Dic67—22no—
326C2×Dic67—22no—
327C2×Dic67—42no—
328C2×Dic67—42no—
329C2×Dic67—42no—
330C2×Dic67—42no—
331C2×Dic67#12314yes—
332C2×Dic67C22×D412yes—
333C2×Dic67C22×D412yes—
334C4×D67—28no—
335C4×D67—24no—
336C4×D67—22no—
337C4×D67—22no—
338C4×D67—28no—
339C4×D67—48no—
340C4×D67—48no—
341C4×D67—48no—
342C4×D67—48no—
343C4×D67#12318yes—
344C4×D67C2×#4114yes—
345C4×D67C2×#4114yes—
346Dic134—22no—
347Dic134—22no—
348Dic134—42no—
349Dic134—48no—
350C8×C67—22no—
351C8×C67—22no—
352C67⋊C8—22no—
353C67⋊C8—22no—
354C22×C67—22no—
355C22×C67—22no—
356C22×C67—22no—
357C22×C67—44no—
358C22×C67C2×#12312yes—
359C22×C67C2×#13712yes—
360C22×C67#57512yes—
361C22×C67C23×D411yescharacteristic
362C2×D67—28no—
363C2×D67—28no—
364C2×D67—22no—
365C2×D67—22no—
366C2×D67—22no—
367C2×D67—22no—
368C2×D67—416no—
369C2×D67C2×#12314yes—
370C2×D67C2×#13714yes—
371C4×C67—22no—
372C4×C67—42no—
373C4×C67—42no—
374C4×C67—42no—
375C4×C67—42no—
376C4×C67C2×#12312yes—
377C4×C67C22×#4111yescharacteristic
378C4×C67C22×#4111yescharacteristic
379Dic67—22no—
380Dic67—42no—
381Dic67—42no—
382Dic67—42no—
383Dic67—42no—
384Dic67C2×#12314yes—
385C2×#3095—671nomaximal, Sylow
386C2×C67—42no—
387C2×C67#309514yescomplemented
388C2×C67C22×#12311yescharacteristic
389C2×C67C22×#13711yescharacteristic
390C2×C67C2×#57511yescharacteristic
391D67—24no—
392D67—24no—
393C22×C22⋊Q8—671no—
394C22×#117—671no—
395#3095—6716no—
396C2×#484—671no—
397C2×#484—671no—
398C2×#485—671no—
399C2×#485—671no—
400C2×#485—671no—
401C2×#485D6711yescharacteristic, complemented
402C2×#483—671no—
403C2×#483—671no—
404C2×#428—671no—
405C2×#428—671no—
406C2×#419—671no—
407C2×#419—671no—
408C2×#407—671no—
409C67C2×#309511yescharacteristic, complemented, Sylow
410C23×Q8—671no—
411C24×C4—671no—
412C22×M16—671no—
413C22×M16—671no—
414C2×C22⋊Q8—671no—
415C2×C22⋊Q8—671no—
416C2×C22⋊Q8—678no—
417C2×C22⋊Q8—671no—
418C2×C22⋊Q8—1341no—
419C2×C22⋊Q8—1341no—
420C2×C22⋊Q8—1344no—
421C2×C22⋊Q8C2×D6711yescharacteristic
422C2×#117—671no—
423C2×#117—678no—
424C2×#117—671no—
425C2×#117—671no—
426C2×#117—1341no—
427C2×#117—1341no—
428C2×#117—1344no—
429C2×#117C2×D6711yescharacteristic
430C22×C4⋊C4—671no—
431C22×C4⋊C4—671no—
432C22×C4⋊C4—671no—
433C22×C4⋊C4—1341no—
434C22×C22⋊C4—1341no—
435C22×C22⋊C4—1341no—
436C22×C42—1341no—
437#485—678no—
438#485—678no—
439#485—678no—
440#485C2×D6718yescomplemented
441#484—678no—
442#484—678no—
443#483—678no—
444#483—678no—
445#428—678no—
446#428—678no—
447C2×#107—671no—
448C2×#107—671no—
449C2×#107—671no—
450C2×#107C2×D6711yescharacteristic, complemented
451C2×#106—671no—
452C2×#106—671no—
453C2×#106—671no—
454C2×#106C2×D6711yescharacteristic, complemented
455#419—678no—
456#419—678no—
457C2×#103—671no—
458C2×#103—671no—
459C2×#103—671no—
460C2×#103—671no—
461C2×#103—671no—
462C2×#103—671no—
463C2×#103C2×D6711yescharacteristic, complemented
464C2×#103C2×D6711yescharacteristic, complemented
465#407—678no—
466C2×C22⋊C8—671no—
467C2×C22⋊C8—671no—
468C2×C22⋊C8—671no—
469C2×C22⋊C8C2×D6711yescharacteristic
470C25—671no—
471C22×Q8—674no—
472C22×Q8—671no—
473C22×Q8—1341no—
474C22×Q8—1344no—
475C22×Q8—1344no—
476C22×Q8—1342no—
477C22×Q8C22×D6711yescharacteristic
478C23×C4—671no—
479C23×C4—671no—
480C23×C4—671no—
481C23×C4—674no—
482C23×C4—671no—
483C23×C4—671no—
484C23×C4—674no—
485C23×C4—1341no—
486C23×C4—1341no—
487C23×C4—1341no—
488C23×C4—1341no—
489C23×C4—1344no—
490C23×C4—1344no—
491C23×C4C22×D6711yescharacteristic
492C2×M16—674no—
493C2×M16—674no—
494C2×M16—1344no—
495C2×M16—1344no—
496C22×C8—671no—
497C22×C8—671no—
498C22×C8C22×D6711yescharacteristic
499C22×C8C22×D6711yescharacteristic
500C22⋊Q8—22no—
501C22⋊Q8—674no—
502C22⋊Q8—674no—
503C22⋊Q8—674no—
504C22⋊Q8—1348no—
505C22⋊Q8—1348no—
506C22⋊Q8—1342no—
507C22⋊Q8—1342no—
508C22⋊Q8—1342no—
509C22⋊Q8C22×D6714yes—
510#117—22no—
511#117—674no—
512#117—674no—
513#117—674no—
514#117—1348no—
515#117—1348no—
516#117—1342no—
517#117—1342no—
518#117—1342no—
519#117C22×D6714yes—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—671no—
522C2×C4⋊C4—671no—
523C2×C4⋊C4—671no—
524C2×C4⋊C4—674no—
525C2×C4⋊C4—674no—
526C2×C4⋊C4—674no—
527C2×C4⋊C4—1342no—
528C2×C4⋊C4—1342no—
529C2×C4⋊C4—1342no—
530C2×C4⋊C4—1348no—
531C2×C4⋊C4—1341no—
532C2×C4⋊C4—1341no—
533C2×C4⋊C4—1341no—
534C2×C4⋊C4—1341no—
535C2×C4⋊C4—1341no—
536C2×C4⋊C4—1341no—
537C2×C4⋊C4C22×D6711yescharacteristic
538C2×C4⋊C4C22×D6711yescharacteristic
539C2×C4⋊C4C22×D6711yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—1348no—
543C2×C22⋊C4—1348no—
544C2×C22⋊C4—1341no—
545C2×C22⋊C4—1341no—
546C2×C22⋊C4—1341no—
547C2×C22⋊C4—1341no—
548C2×C22⋊C4—1341no—
549C2×C22⋊C4—1341no—
550C2×C42—21no—
551C2×C42—1348no—
552C2×C42—1341no—
553C2×C42—1341no—
554C2×C42—1341no—
555#107—674no—
556#107—674no—
557#107—674no—
558#107C22×D6714yescomplemented
559#106—674no—
560#106—674no—
561#106—674no—
562#106C22×D6714yescomplemented
563#103—674no—
564#103—674no—
565#103—674no—
566#103—674no—
567#103—674no—
568#103—674no—
569#103C22×D6714yescomplemented
570#103C22×D6714yescomplemented
571C22⋊C8—674no—
572C22⋊C8—674no—
573C22⋊C8—674no—
574C22⋊C8C22×D6714yes—
575C24—2682no—
576C24—674no—
577C24—671no—
578C24—671no—
579C24—1344no—
580C24—1344no—
581C24D4×D6711yescharacteristic
582C2×Q8—21no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—2684no—
586C2×Q8—2688no—
587C2×Q8—672no—
588C2×Q8—1344no—
589C2×Q8—1348no—
590C2×Q8—1348no—
591C2×Q8—1342no—
592C2×Q8—1342no—
593C2×Q8—1341no—
594C2×Q8C23×D6712yes—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—2684no—
602C22×C4—2684no—
603C22×C4—2684no—
604C22×C4—2684no—
605C22×C4—671no—
606C22×C4—672no—
607C22×C4—674no—
608C22×C4—674no—
609C22×C4—672no—
610C22×C4—674no—
611C22×C4—671no—
612C22×C4—674no—
613C22×C4—674no—
614C22×C4—672no—
615C22×C4—672no—
616C22×C4—1344no—
617C22×C4—1344no—
618C22×C4—1344no—
619C22×C4—1344no—
620C22×C4—1344no—
621C22×C4—13416no—
622C22×C4—1348no—
623C22×C4—1348no—
624C22×C4—1344no—
625C22×C4—1341no—
626C22×C4—1341no—
627C22×C4—1341no—
628C22×C4—1341no—
629C22×C4—1344no—
630C22×C4—1342no—
631C22×C4—1342no—
632C22×C4D4×D6712yes—
633C22×C4D4×D6711yescharacteristic
634C22×C4C23×D6712yes—
635C22×C4C23×D6711yescharacteristic
636M16—1348no—
637M16—1348no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—672no—
641C2×C8—672no—
642C2×C8—1342no—
643C2×C8—1342no—
644C2×C8C23×D6712yes—
645C2×C8C23×D6712yes—
646C4⋊C4—24no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—672no—
651C4⋊C4—672no—
652C4⋊C4—672no—
653C4⋊C4—1344no—
654C4⋊C4—1344no—
655C4⋊C4—1344no—
656C4⋊C4—1344no—
657C4⋊C4—1344no—
658C4⋊C4—1341no—
659C4⋊C4—1341no—
660C4⋊C4—1341no—
661C4⋊C4—1344no—
662C4⋊C4C23×D6712yes—
663C4⋊C4C23×D6712yes—
664C4⋊C4C23×D6712yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—1344no—
668C22⋊C4—1344no—
669C22⋊C4—1344no—
670C22⋊C4—1344no—
671C22⋊C4—1344no—
672C22⋊C4—1344no—
673C42—24no—
674C42—1344no—
675C42—1344no—
676C42—1344no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—2684no—
681C23—26816no—
682C23—674no—
683C23—674no—
684C23—672no—
685C23—672no—
686C23—1348no—
687C23—1348no—
688C23—1342no—
689C23—1342no—
690C23—1342no—
691C23—1342no—
692C23C2×D4×D6712yes—
693C23C2×D4×D6711yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—42no—
697Q8—2688no—
698Q8—2682no—
699Q8—1342no—
700Q8—1342no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—2688no—
714C2×C4—2688no—
715C2×C4—2688no—
716C2×C4—2688no—
717C2×C4—2682no—
718C2×C4—2682no—
719C2×C4—2682no—
720C2×C4—2682no—
721C2×C4—674no—
722C2×C4—672no—
723C2×C4—678no—
724C2×C4—674no—
725C2×C4—674no—
726C2×C4—672no—
727C2×C4—1348no—
728C2×C4—1348no—
729C2×C4—1342no—
730C2×C4—1342no—
731C2×C4—1342no—
732C2×C4—1342no—
733C2×C4—1348no—
734C2×C4—1342no—
735C2×C4—1344no—
736C2×C4—1342no—
737C2×C4—1342no—
738C2×C4C2×D4×D6712yes—
739C2×C4C2×D4×D6711yescharacteristic
740C2×C4#41×D6712yes—
741C2×C4#41×D6712yes—
742C2×C4C24×D6711yescharacteristic
743C8—22no—
744C8—22no—
745C8—1342no—
746C8—1342no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—44no—
751C22—26816no—
752C22—674no—
753C22—674no—
754C22—1342no—
755C22—1342no—
756C22—1342no—
757C22—1342no—
758C22—1348no—
759C22—1348no—
760C22#123×D6712yes—
761C22#137×D6712yes—
762C22#1686419312yes—
763C22C22×D4×D6711yescharacteristic
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—2682no—
770C4—2682no—
771C4—2682no—
772C4—2682no—
773C4—674no—
774C4—1342no—
775C4#123×D6712yes—
776C4C2×#41×D6711yescharacteristic
777C4C2×#41×D6711yescharacteristic
778C2—42no—
779C2—1344no—
780C2—1344no—
781C2#2257015614yesdirect product factor
782C2C2×#123×D6711yescharacteristic
783C2C2×#137×D6711yescharacteristic
784C2C2×#1686419311yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#485×C67C2
socleC23×C67C22×D4
prime radicalC24×D67D4
hypercenterC2×#485D67
hypocenterC67C2×#3095
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #22570156C2direct (N × H)
4. C2×#16863733C2semidirect
5. C2×#16863730C2semidirect
6. C2×#16863738C2semidirect
7. C2×#16863737C2semidirect
8. C2×#16863734C2semidirect
9. C2×#16863728C2semidirect
10. C2×#16863725C2semidirect
11. C2×#16863437C2semidirect
12. C2×#16863435C2semidirect
13. C2×#16863403C2semidirect
14. C2×#16863403C2semidirect
16. C2×#485×C67C2semidirect
42. #16863738C22semidirect
43. #16863737C22semidirect
44. #16863734C22semidirect
45. #16863733C22semidirect
46. #16863730C22semidirect
47. #16863728C22semidirect
48. #16863725C22semidirect
49. #16863437C22semidirect
50. #16863435C22semidirect
51. C2×#14523977C22semidirect
52. C2×#14523976C22semidirect
53. C2×#14523976C22semidirect
54. C2×#14523975C22semidirect
55. C2×#14523974C22semidirect
56. C2×#14523974C22semidirect
57. #16863403C22semidirect
58. #16863403C22semidirect
59. C2×#14523968C22semidirect
60. C2×#14523968C22semidirect
61. C2×#14523967C22semidirect
62. C2×#14523967C22semidirect
63. C2×#14523966C22semidirect
64. C2×#14523966C22semidirect
71. #485×C67C22semidirect
72. C2×#107×C67C22semidirect
73. C2×#106×C67C22semidirect
74. C2×#103×C67C22semidirect
75. C2×#103×C67C22semidirect
147. #14523977C23semidirect
148. #14523976C23semidirect
149. #14523976C23semidirect
150. #14523975C23semidirect
151. #14523974C23semidirect
152. #14523974C23semidirect
153. #14523968C23semidirect
154. #14523968C23semidirect
155. #14523967C23semidirect
156. #14523967C23semidirect
157. #14523966C23semidirect
158. #14523966C23semidirect
177. #107×C67C23semidirect
178. #106×C67C23semidirect
179. #103×C67C23semidirect
180. #103×C67C23semidirect
387. C2×C67#3095semidirect
401. C2×#485D67semidirect
409. C67C2×#3095semidirect
440. #485C2×D67semidirect
450. C2×#107C2×D67semidirect
454. C2×#106C2×D67semidirect
463. C2×#103C2×D67semidirect
464. C2×#103C2×D67semidirect
558. #107C22×D67semidirect
562. #106C22×D67semidirect
569. #103C22×D67semidirect
570. #103C22×D67semidirect
781. C2#22570156direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D672
C2×#117×D672
#225701562
C2×#168637332
C2×#168637302
C2×#168637382
C2×#168637372
C2×#168637342
C2×#168637282
C2×#168637252
C2×#168634372
C2×#168634352
C2×#168634032
C2×#168633582
C2×#485×C672
C2×#309567