Finite Group Databasebeta

← C2×#22570141 #31723619

Subgroups — C2×#22570141 #31723619

Order 17152.

2346 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863909C211yesmaximal, characteristic
2C2×#117×D67C211yesmaximal, characteristic, complemented
3#22570141C2116yesmaximal, direct product factor
4C2×#16863736C211yesmaximal, characteristic, complemented
5C2×#16863735C211yesmaximal, characteristic, complemented
6C2×#16863734C211yesmaximal, characteristic, complemented
7C2×#16863723C211yesmaximal, characteristic, complemented
8C2×#16863722C211yesmaximal, characteristic, complemented
9C2×#16863721C211yesmaximal, characteristic, complemented
10C2×#16863720C211yesmaximal, characteristic, complemented
11C2×#16863437C211yesmaximal, characteristic, complemented
12C2×#16863435C211yesmaximal, characteristic, complemented
13C2×#16863396C211yesmaximal, characteristic, complemented
14C2×#16863396C211yesmaximal, characteristic, complemented
15C2×#16863358C211yesmaximal, characteristic, complemented
16C2×#485×C67C211yesmaximal, characteristic, complemented
17C22×#11761629C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C22×#11761611C2211yescharacteristic
20C22×#11761611C2211yescharacteristic
21#16863909—24no—
22#16863909C2218yes—
23C2×#14524028—21no—
24C2×#14524019C2211yescharacteristic
25C2×#14524018C2211yescharacteristic
26C2×#14524017C2211yescharacteristic
27C2×#14524013—21no—
28C2×#14524005—21no—
29C2×(C22⋊D67)⋊C4—21no—
30C2×#14524002C2211yescharacteristic
31C2×#14524001C2211yescharacteristic
32C2×#14524001C2211yescharacteristic
33C2×#14524001C2211yescharacteristic
34C2×#14524000—21no—
35C2×#14523999—21no—
36#117×D67—24no—
37#117×D67C2218yescomplemented
38C2×C4⋊C4×D67C2211yescharacteristic
39C2×C4⋊C4×D67C2211yescharacteristic
40C2×C22⋊C4×D67—21no—
41C2×C42×D67—21no—
42#16863736C2218yescomplemented
43#16863735C2218yescomplemented
44#16863734C2218yescomplemented
45#16863723C2218yescomplemented
46#16863722C2218yescomplemented
47#16863721C2218yescomplemented
48#16863720C2218yescomplemented
49#16863437C2218yescomplemented
50#16863435C2218yescomplemented
51C2×#14523977C2211yescharacteristic, complemented
52C2×#14523976C2211yescharacteristic, complemented
53C2×#14523976C2211yescharacteristic, complemented
54C2×#14523975C2211yescharacteristic, complemented
55C2×#14523974C2211yescharacteristic, complemented
56C2×#14523974C2211yescharacteristic, complemented
57#16863396C2218yescomplemented
58#16863396C2218yescomplemented
59C2×#14523967C2211yescharacteristic, complemented
60C2×#14523967C2211yescharacteristic, complemented
61C2×#14523965C2211yescharacteristic, complemented
62C2×#14523965C2211yescharacteristic, complemented
63C2×#14523963C2211yescharacteristic, complemented
64C2×#14523963C2211yescharacteristic, complemented
65#16863358C2218yescomplemented
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
78C2×#11761629—22no—
79C2×#11761629—24no—
80C2×#11761629—24no—
81C2×#11761629C2314yes—
82C22×D268—21no—
83C22×D268—21no—
84C22×D268C2311yescharacteristic
85C22×C22⋊D67—21no—
86C23×Dic67D411yescharacteristic
87C22×C4×D67—24no—
88C22×C4×D67—24no—
89C22×C4×D67—21no—
90C22×C4×D67—21no—
91C22×C4×D67—21no—
92C22×C4×D67D411yescharacteristic
93C22×C4×D67D414yes—
94C22×C4×D67D411yescharacteristic
95C22×C4×D67C2314yes—
96C22×C4×D67C2311yescharacteristic
97C22×C4×D67C2311yescharacteristic
98C2×#11761611—24no—
99C2×#11761611—24no—
100C2×#11761611C2314yes—
101C2×#11761611C2314yes—
102C22×C67⋊C8C2311yescharacteristic
103C22×C67⋊C8C2311yescharacteristic
104#14524028—28no—
105#14524019—22no—
106#14524019C2314yes—
107#14524018—22no—
108#14524018C2314yes—
109#14524017—22no—
110#14524017C2314yes—
111#14524013—28no—
112#14524005—28no—
113(C22⋊D67)⋊C4—28no—
114#14524002—22no—
115#14524002C2314yes—
116#14524001—22no—
117#14524001—22no—
118#14524001—22no—
119#14524001C2314yes—
120#14524001C2314yes—
121#14524001C2314yes—
122#14524000—28no—
123#14523999—28no—
124C2×C4⋊Dic67C2311yescharacteristic
125C2×C4⋊Dic67C2311yescharacteristic
126C2×C4⋊Dic67C2311yescharacteristic
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C2×Dic67⋊C4—21no—
130C4⋊C4×D67—22no—
131C4⋊C4×D67—22no—
132C4⋊C4×D67C2314yes—
133C4⋊C4×D67C2314yes—
134C2×C22⋊Dic67—21no—
135C2×(C2×D67)⋊C4—21no—
136C2×(C2×D67)⋊C4—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—
142C2×C4×Dic67—21no—
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#14523967C2314yescomplemented
154#14523967C2314yescomplemented
155#14523965C2314yescomplemented
156#14523965C2314yescomplemented
157#14523963C2314yescomplemented
158#14523963C2314yescomplemented
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—21no—
184C23×D67—42no—
185C23×D67—42no—
186C23×D67C2×D411yescharacteristic
187C23×D67C2×D411yescharacteristic
188C23×D67C2×D414yes—
189#11761629—28no—
190#11761629—28no—
191#11761629—48no—
192C2×D268—22no—
193C2×D268—22no—
194C2×D268—24no—
195C2×D268—24no—
196C2×D268—21no—
197C2×D268—44no—
198C2×D268—44no—
199C2×D268C2412yes—
200C2×C22⋊D67—24no—
201C2×C22⋊D67—44no—
202C22×Dic67—24no—
203C22×Dic67—21no—
204C22×Dic67—21no—
205C22×Dic67—21no—
206C22×Dic67C2×D411yescharacteristic
207C22×Dic67C2×D414yes—
208C22×Dic67C2×D411yescharacteristic
209C2×C4×D67—24no—
210C2×C4×D67—22no—
211C2×C4×D67—22no—
212C2×C4×D67—24no—
213C2×C4×D67—216no—
214C2×C4×D67—28no—
215C2×C4×D67—28no—
216C2×C4×D67—24no—
217C2×C4×D67—24no—
218C2×C4×D67—24no—
219C2×C4×D67—44no—
220C2×C4×D67—44no—
221C2×C4×D67—44no—
222C2×C4×D67C2×D414yes—
223C2×C4×D67C2×D414yes—
224C2×C4×D67C2×D412yes—
225C2×C4×D67C2×D412yes—
226C2×C4×D67#4114yes—
227C2×C4×D67#4114yes—
228C2×C4×D67C2412yes—
229C2×C4×D67C2412yes—
230#11761611—28no—
231#11761611—28no—
232C2×C67⋊C8—22no—
233C2×C67⋊C8—22no—
234C2×C67⋊C8C2412yes—
235C2×C67⋊C8C2412yes—
236C4⋊Dic67—21no—
237C4⋊Dic67—21no—
238C4⋊Dic67—21no—
239C4⋊Dic67C2412yes—
240C4⋊Dic67C2412yes—
241C4⋊Dic67C2412yes—
242Dic67⋊C4—24no—
243Dic67⋊C4—24no—
244Dic67⋊C4—24no—
245C22⋊Dic67—24no—
246(C2×D67)⋊C4—24no—
247(C2×D67)⋊C4—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—
255C4×Dic67—24no—
256C24×C67C2×D411yescharacteristic
257C2×Q8×C67—21no—
258C2×Q8×C67—22no—
259C2×Q8×C67—22no—
260C2×Q8×C67C2412yes—
261C22×C4×C67—22no—
262C22×C4×C67—22no—
263C22×C4×C67—21no—
264C22×C4×C67—21no—
265C22×C4×C67—21no—
266C22×C4×C67—21no—
267C22×C4×C67C2×D411yescharacteristic
268C22×C4×C67C2×D412yes—
269C22×C4×C67C2412yes—
270C22×C4×C67C2411yescharacteristic
271C2×C8×C67—22no—
272C2×C8×C67—22no—
273C2×C8×C67C2412yes—
274C2×C8×C67C2412yes—
275C4⋊C4×C67—24no—
276C4⋊C4×C67—21no—
277C4⋊C4×C67—21no—
278C4⋊C4×C67—21no—
279C4⋊C4×C67C2412yes—
280C4⋊C4×C67C2412yes—
281C4⋊C4×C67C2412yes—
282C22⋊C4×C67—24no—
283C22⋊C4×C67—24no—
284C42×C67—24no—
285C23×C67—22no—
286C23×C67—22no—
287C23×C67—22no—
288C23×C67C22×D412yes—
289C23×C67C22×D411yescharacteristic
290C22×D67—22no—
291C22×D67—22no—
292C22×D67—22no—
293C22×D67—22no—
294C22×D67—22no—
295C22×D67—28no—
296C22×D67—22no—
297C22×D67—44no—
298C22×D67—44no—
299C22×D67—416no—
300C22×D67—42no—
301C22×D67—42no—
302C22×D67—42no—
303C22×D67#12314yes—
304C22×D67C22×D412yes—
305C22×D67C22×D412yes—
306Q8×C67—22no—
307Q8×C67—22no—
308Q8×C67—42no—
309C2×C4×C67—22no—
310C2×C4×C67—24no—
311C2×C4×C67—22no—
312C2×C4×C67—22no—
313C2×C4×C67—22no—
314C2×C4×C67—22no—
315C2×C4×C67—22no—
316C2×C4×C67—22no—
317C2×C4×C67—42no—
318C2×C4×C67—42no—
319C2×C4×C67—42no—
320C2×C4×C67—42no—
321C2×C4×C67C22×D412yes—
322C2×C4×C67C22×D411yescharacteristic
323C2×C4×C67C2×#4112yes—
324C2×C4×C67C2×#4112yes—
325C2×C4×C67C2511yescharacteristic
326C22⋊D67—48no—
327C2×Dic67—22no—
328C2×Dic67—28no—
329C2×Dic67—22no—
330C2×Dic67—22no—
331C2×Dic67—22no—
332C2×Dic67—42no—
333C2×Dic67—42no—
334C2×Dic67—42no—
335C2×Dic67#12314yes—
336C2×Dic67C22×D412yes—
337C2×Dic67C22×D412yes—
338D268—22no—
339D268—22no—
340D268—48no—
341D268—48no—
342D268—42no—
343C4×D67—28no—
344C4×D67—24no—
345C4×D67—22no—
346C4×D67—22no—
347C4×D67—28no—
348C4×D67—48no—
349C4×D67—48no—
350C4×D67—48no—
351C4×D67#12318yes—
352C4×D67C2×#4114yes—
353C4×D67C2×#4114yes—
354C8×C67—22no—
355C8×C67—22no—
356C67⋊C8—22no—
357C67⋊C8—22no—
358C22×C67—22no—
359C22×C67—22no—
360C22×C67—22no—
361C22×C67—44no—
362C22×C67C2×#12312yes—
363C22×C67#57512yes—
364C22×C67#57512yes—
365C22×C67C23×D411yescharacteristic
366C2×D67—28no—
367C2×D67—22no—
368C2×D67—22no—
369C2×D67—22no—
370C2×D67—22no—
371C2×D67—22no—
372C2×D67—416no—
373C2×D67—44no—
374C2×D67—42no—
375C2×D67—42no—
376C2×D67—42no—
377C2×D67—84no—
378C2×D67C2×#12314yes—
379C4×C67—22no—
380C4×C67—42no—
381C4×C67—42no—
382C4×C67—42no—
383C4×C67—42no—
384C4×C67C2×#12312yes—
385C4×C67C22×#4111yescharacteristic
386C4×C67C22×#4111yescharacteristic
387Dic67—22no—
388Dic67—42no—
389Dic67—42no—
390Dic67—42no—
391Dic67C2×#12314yes—
392C2×#3093—671nomaximal, Sylow
393C2×C67—42no—
394C2×C67#309314yescomplemented
395C2×C67C22×#12311yescharacteristic
396C2×C67C2×#57511yescharacteristic
397C2×C67C2×#57511yescharacteristic
398D67—24no—
399D67—42no—
400D67—82no—
401C2×#525—671no—
402C22×#117—671no—
403#3093—6716no—
404C2×#485—671no—
405C2×#485—671no—
406C2×#485—671no—
407C2×#485D6711yescharacteristic, complemented
408C2×#482—671no—
409C2×#482—671no—
410C2×#482—671no—
411C2×#482—671no—
412C2×#428—671no—
413C2×#428—671no—
414C2×#417—671no—
415C2×#417—671no—
416C2×#407—671no—
417C67C2×#309311yescharacteristic, complemented, Sylow
418C22×#41—671no—
419C24×C4—671no—
420C22×M16—671no—
421C22×M16—671no—
422#525—678no—
423#525—1344no—
424C2×#123—1341no—
425C2×C22⋊Q8—671no—
426C2×C22⋊Q8C2×D6711yescharacteristic
427C2×#121—671no—
428C2×#121—671no—
429C2×#120—1341no—
430C2×C4×D4—1341no—
431C2×C4×D4—1341no—
432C2×#117—671no—
433C2×#117—678no—
434C2×#117—671no—
435C2×#117—671no—
436C2×#117—671no—
437C2×#117—1341no—
438C2×#117—1341no—
439C2×#117—1344no—
440C2×#117C2×D6711yescharacteristic
441C22×C4⋊C4—671no—
442C22×C4⋊C4—671no—
443C22×C22⋊C4—1341no—
444C22×C42—1341no—
445#485—678no—
446#485—678no—
447#485—678no—
448#485C2×D6718yescomplemented
449#482—678no—
450#482—678no—
451#482—678no—
452#482—678no—
453#428—678no—
454#428—678no—
455C2×#107—671no—
456C2×#107—671no—
457C2×#107—671no—
458C2×#107C2×D6711yescharacteristic, complemented
459C2×#106—671no—
460C2×#106—671no—
461C2×#106—671no—
462C2×#106C2×D6711yescharacteristic, complemented
463#417—678no—
464#417—678no—
465C2×#103—671no—
466C2×#103—671no—
467C2×#103C2×D6711yescharacteristic, complemented
468C2×#103C2×D6711yescharacteristic, complemented
469C2×#102—671no—
470C2×#102—671no—
471C2×#102—671no—
472C2×#102—671no—
473#407—678no—
474C2×C22⋊C8—671no—
475C2×C22⋊C8—671no—
476C2×C22⋊C8—671no—
477C2×C22⋊C8C2×D6711yescharacteristic
478C25—671no—
479C2×#41—674no—
480C2×#41—1344no—
481C2×#41—1344no—
482C2×#41—1342no—
483C22×Q8C22×D6711yescharacteristic
484C22×D4—671no—
485C22×D4—1341no—
486C22×D4—1341no—
487C22×D4—1341no—
488C23×C4—671no—
489C23×C4—671no—
490C23×C4—671no—
491C23×C4—674no—
492C23×C4—671no—
493C23×C4—671no—
494C23×C4—674no—
495C23×C4—1341no—
496C23×C4—1341no—
497C23×C4—1341no—
498C23×C4—1344no—
499C23×C4—1344no—
500C23×C4C22×D6711yescharacteristic
501C2×M16—674no—
502C2×M16—674no—
503C2×M16—1344no—
504C2×M16—1344no—
505C22×C8—671no—
506C22×C8—671no—
507C22×C8C22×D6711yescharacteristic
508C22×C8C22×D6711yescharacteristic
509#123—1348no—
510C22⋊Q8—22no—
511C22⋊Q8—674no—
512C22⋊Q8—1342no—
513C22⋊Q8C22×D6714yes—
514#121—674no—
515#121—674no—
516#121—1342no—
517#121—1342no—
518#120—1348no—
519C4×D4—1348no—
520C4×D4—1348no—
521#117—22no—
522#117—674no—
523#117—674no—
524#117—674no—
525#117—674no—
526#117—1348no—
527#117—1348no—
528#117—1342no—
529#117—1342no—
530#117—1342no—
531#117—1342no—
532#117C22×D6714yes—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—671no—
535C2×C4⋊C4—671no—
536C2×C4⋊C4—671no—
537C2×C4⋊C4—674no—
538C2×C4⋊C4—674no—
539C2×C4⋊C4—1342no—
540C2×C4⋊C4—1342no—
541C2×C4⋊C4—1341no—
542C2×C4⋊C4—1341no—
543C2×C4⋊C4—1341no—
544C2×C4⋊C4C22×D6711yescharacteristic
545C2×C4⋊C4C22×D6711yescharacteristic
546C2×C4⋊C4C22×D6711yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1348no—
550C2×C22⋊C4—1341no—
551C2×C22⋊C4—1341no—
552C2×C22⋊C4—1341no—
553C2×C22⋊C4—1341no—
554C2×C22⋊C4—1341no—
555C2×C22⋊C4—1341no—
556C2×C22⋊C4—1341no—
557C2×C42—21no—
558C2×C42—1348no—
559C2×C42—1341no—
560C2×C42—1341no—
561C2×C42—1341no—
562C2×C42—1341no—
563#107—674no—
564#107—674no—
565#107—674no—
566#107C22×D6714yescomplemented
567#106—674no—
568#106—674no—
569#106—674no—
570#106C22×D6714yescomplemented
571#103—674no—
572#103—674no—
573#103C22×D6714yescomplemented
574#103C22×D6714yescomplemented
575#102—674no—
576#102—674no—
577#102—674no—
578#102—674no—
579C22⋊C8—674no—
580C22⋊C8—674no—
581C22⋊C8—674no—
582C22⋊C8C22×D6714yes—
583C24—2682no—
584C24—2682no—
585C24—674no—
586C24—671no—
587C24—671no—
588C24—1344no—
589C24—1341no—
590C24D4×D6711yescharacteristic
591#41—2688no—
592#41—1348no—
593#41—1348no—
594C2×Q8—21no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8C23×D6712yes—
598C2×D4—2684no—
599C2×D4—2684no—
600C2×D4—2684no—
601C2×D4—672no—
602C2×D4—1344no—
603C2×D4—1344no—
604C2×D4—1344no—
605C2×D4—1341no—
606C2×D4—1342no—
607C2×D4—1342no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—2684no—
615C22×C4—2684no—
616C22×C4—2684no—
617C22×C4—671no—
618C22×C4—672no—
619C22×C4—674no—
620C22×C4—674no—
621C22×C4—672no—
622C22×C4—674no—
623C22×C4—671no—
624C22×C4—674no—
625C22×C4—674no—
626C22×C4—672no—
627C22×C4—672no—
628C22×C4—1344no—
629C22×C4—1344no—
630C22×C4—1344no—
631C22×C4—1344no—
632C22×C4—13416no—
633C22×C4—1348no—
634C22×C4—1348no—
635C22×C4—1344no—
636C22×C4—1341no—
637C22×C4—1341no—
638C22×C4—1341no—
639C22×C4—1344no—
640C22×C4—1342no—
641C22×C4—1342no—
642C22×C4D4×D6712yes—
643C22×C4D4×D6711yescharacteristic
644C22×C4C23×D6712yes—
645C22×C4C23×D6711yescharacteristic
646M16—1348no—
647M16—1348no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—672no—
651C2×C8—672no—
652C2×C8—1342no—
653C2×C8—1342no—
654C2×C8C23×D6712yes—
655C2×C8C23×D6712yes—
656C4⋊C4—24no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—672no—
661C4⋊C4—672no—
662C4⋊C4—672no—
663C4⋊C4—1344no—
664C4⋊C4—1344no—
665C4⋊C4—1344no—
666C4⋊C4—1341no—
667C4⋊C4—1341no—
668C4⋊C4—1341no—
669C4⋊C4C23×D6712yes—
670C4⋊C4C23×D6712yes—
671C4⋊C4C23×D6712yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—1344no—
675C22⋊C4—1344no—
676C22⋊C4—1344no—
677C22⋊C4—1344no—
678C22⋊C4—1344no—
679C22⋊C4—1344no—
680C22⋊C4—1344no—
681C42—24no—
682C42—1344no—
683C42—1344no—
684C42—1344no—
685C42—1344no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—2684no—
690C23—2684no—
691C23—26816no—
692C23—2682no—
693C23—2682no—
694C23—2682no—
695C23—674no—
696C23—672no—
697C23—672no—
698C23—1348no—
699C23—1342no—
700C23—1342no—
701C23—1342no—
702C23—1342no—
703C23—1342no—
704C23—1342no—
705C23C2×D4×D6712yes—
706C23C2×D4×D6711yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—42no—
710D4—2688no—
711D4—2688no—
712D4—2688no—
713D4—2682no—
714D4—1342no—
715D4—1342no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—2688no—
729C2×C4—2688no—
730C2×C4—2688no—
731C2×C4—2682no—
732C2×C4—2682no—
733C2×C4—2682no—
734C2×C4—674no—
735C2×C4—672no—
736C2×C4—678no—
737C2×C4—674no—
738C2×C4—674no—
739C2×C4—672no—
740C2×C4—1348no—
741C2×C4—1348no—
742C2×C4—1342no—
743C2×C4—1342no—
744C2×C4—1342no—
745C2×C4—1348no—
746C2×C4—1342no—
747C2×C4—1344no—
748C2×C4—1342no—
749C2×C4—1342no—
750C2×C4C2×D4×D6712yes—
751C2×C4C2×D4×D6711yescharacteristic
752C2×C4#41×D6712yes—
753C2×C4#41×D6712yes—
754C2×C4C24×D6711yescharacteristic
755C8—22no—
756C8—22no—
757C8—1342no—
758C8—1342no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—44no—
763C22—26816no—
764C22—2684no—
765C22—2682no—
766C22—2682no—
767C22—2682no—
768C22—5364no—
769C22—674no—
770C22—1342no—
771C22—1342no—
772C22—1342no—
773C22—1342no—
774C22—1342no—
775C22—1348no—
776C22#123×D6712yes—
777C22#1686419312yes—
778C22#1686419512yes—
779C22C22×D4×D6711yescharacteristic
780C4—22no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—2682no—
786C4—2682no—
787C4—2682no—
788C4—674no—
789C4—1342no—
790C4#123×D6712yes—
791C4C2×#41×D6711yescharacteristic
792C4C2×#41×D6711yescharacteristic
793C2—42no—
794C2—2682no—
795C2—5362no—
796C2—1344no—
797C2#2257014114yesdirect product factor
798C2C2×#123×D6711yescharacteristic
799C2C2×#1686419311yescharacteristic
800C2C2×#1686419511yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#485×C67C2
socleC23×C67C22×D4
prime radicalC2×#16863909C2
hypercenterC2×#485D67
hypocenterC67C2×#3093
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
2. C2×#117×D67C2semidirect
3. #22570141C2direct (N × H)
4. C2×#16863736C2semidirect
5. C2×#16863735C2semidirect
6. C2×#16863734C2semidirect
7. C2×#16863723C2semidirect
8. C2×#16863722C2semidirect
9. C2×#16863721C2semidirect
10. C2×#16863720C2semidirect
11. C2×#16863437C2semidirect
12. C2×#16863435C2semidirect
13. C2×#16863396C2semidirect
14. C2×#16863396C2semidirect
15. C2×#16863358C2semidirect
16. C2×#485×C67C2semidirect
37. #117×D67C22semidirect
42. #16863736C22semidirect
43. #16863735C22semidirect
44. #16863734C22semidirect
45. #16863723C22semidirect
46. #16863722C22semidirect
47. #16863721C22semidirect
48. #16863720C22semidirect
49. #16863437C22semidirect
50. #16863435C22semidirect
51. C2×#14523977C22semidirect
52. C2×#14523976C22semidirect
53. C2×#14523976C22semidirect
54. C2×#14523975C22semidirect
55. C2×#14523974C22semidirect
56. C2×#14523974C22semidirect
57. #16863396C22semidirect
58. #16863396C22semidirect
59. C2×#14523967C22semidirect
60. C2×#14523967C22semidirect
61. C2×#14523965C22semidirect
62. C2×#14523965C22semidirect
63. C2×#14523963C22semidirect
64. C2×#14523963C22semidirect
65. #16863358C22semidirect
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. #14523967C23semidirect
154. #14523967C23semidirect
155. #14523965C23semidirect
156. #14523965C23semidirect
157. #14523963C23semidirect
158. #14523963C23semidirect
177. #107×C67C23semidirect
178. #106×C67C23semidirect
179. #103×C67C23semidirect
180. #103×C67C23semidirect
394. C2×C67#3093semidirect
407. C2×#485D67semidirect
417. C67C2×#3093semidirect
448. #485C2×D67semidirect
458. C2×#107C2×D67semidirect
462. C2×#106C2×D67semidirect
467. C2×#103C2×D67semidirect
468. C2×#103C2×D67semidirect
566. #107C22×D67semidirect
570. #106C22×D67semidirect
573. #103C22×D67semidirect
574. #103C22×D67semidirect
797. C2#22570141direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168639092
C2×#117×D672
#225701412
C2×#168637362
C2×#168637352
C2×#168637342
C2×#168637232
C2×#168637222
C2×#168637212
C2×#168637202
C2×#168634372
C2×#168634352
C2×#168633962
C2×#168633582
C2×#485×C672
C2×#309367