Finite Group Databasebeta

← C2×#22572367 #31732519

Subgroups — C2×#22572367 #31732519

Order 17152.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864111C211yesmaximal, characteristic, complemented
2C2×#16864042C211yesmaximal, characteristic, complemented
3#22572367C2116yesmaximal, direct product factor
4C2×#16863756C211yesmaximal, characteristic, complemented
5C2×#16863738C211yesmaximal, characteristic, complemented
6C2×#16863721C211yesmaximal, characteristic, complemented
7C2×#16863677C211yesmaximal, characteristic, complemented
8C2×#16863642C211yesmaximal, characteristic, complemented
9C2×#16863632C211yesmaximal, characteristic, complemented
10C2×#16863612C211yesmaximal, characteristic, complemented
11C2×#16863543C211yesmaximal, characteristic, complemented
12C2×#16863532C211yesmaximal, characteristic, complemented
13C2×#16863509C211yesmaximal, characteristic, complemented
14C2×#16863402C211yesmaximal, characteristic, complemented
15C2×#16863393C211yesmaximal, characteristic, complemented
16C2×#435×C67C211yesmaximal, characteristic, complemented
17C22×#11761628C2211yescharacteristic
18C23×D268C2211yescharacteristic
19C22×#11761617C2211yescharacteristic, complemented
20C22×D536C2211yescharacteristic
21C22×D536C2211yescharacteristic
22#16864111—24no—
23#16864111C2218yescomplemented
24#16864042—24no—
25#16864042C2218yescomplemented
26C2×#14524043C2211yescharacteristic, complemented
27C2×#14524031C2211yescharacteristic
28C2×#14524029—21no—
29C2×#14524029—21no—
30C2×#14524028—21no—
31C2×#14524022C2211yescharacteristic
32C2×#14524017C2211yescharacteristic
33C2×#14524017C2211yescharacteristic
34C2×#14524017C2211yescharacteristic, complemented
35C2×#14524016—21no—
36C2×#14524014—21no—
37C2×#14524011—21no—
38C2×C4×D268C2211yescharacteristic
39C2×C4×D268C2211yescharacteristic, complemented
40C2×#14524002C2211yescharacteristic
41C2×#14524002C2211yescharacteristic, complemented
42C2×#14524001—21no—
43C2×C22⋊C4×D67—21no—
44#16863756C2218yescomplemented
45#16863738C2218yescomplemented
46#16863721C2218yescomplemented
47#16863677C2218yescomplemented
48#16863642C2218yescomplemented
49#16863632C2218yescomplemented
50#16863612C2218yescomplemented
51#16863543C2218yescomplemented
52#16863532C2218yescomplemented
53#16863509C2218yescomplemented
54C2×#14523977C2211yescharacteristic, complemented
55C2×#14523977C2211yescharacteristic, complemented
56C2×#14523975C2211yescharacteristic, complemented
57#16863402C2218yescomplemented
58#16863393C2218yescomplemented
59C2×#14523968C2211yescharacteristic, complemented
60C2×#14523968C2211yescharacteristic, complemented
61C2×#14523968C2211yescharacteristic, complemented
62C2×#14523965C2211yescharacteristic
63C2×#14523965C2211yescharacteristic
64C2×#14523965C2211yescharacteristic
65C2×#14523965C2211yescharacteristic
66C2×#14523965C2211yescharacteristic
67C2×#14523965C2211yescharacteristic
68C2×#14523965C2211yescharacteristic, complemented
69C22×M16×C67C2211yescharacteristic
70C23×C8×C67C2211yescharacteristic, complemented
71C2×C4×D4×C67C2211yescharacteristic
72#435×C67C2218yescomplemented
73C2×C4⋊C8×C67C2211yescharacteristic, complemented
74C2×C22⋊C8×C67C2211yescharacteristic
75C2×C22⋊C8×C67C2211yescharacteristic, complemented
76C2×#97×C67C2211yescharacteristic, complemented
77C24×D67—21no—
78C2×#11761628—24no—
79C2×#11761628—22no—
80C2×#11761628—42no—
81C2×#11761628C2314yes—
82C22×Dic134—21no—
83C22×Dic134C2311yescharacteristic
84C22×D268—24no—
85C22×D268—22no—
86C22×D268—21no—
87C22×D268—42no—
88C22×D268C2311yescharacteristic
89C22×D268C2311yescharacteristic
90C22×D268C2314yes—
91C22×D268C2311yescharacteristic
92C22×C22⋊D67—21no—
93C22×C22⋊D67—21no—
94C22×C22⋊D67—21no—
95C22×C22⋊D67—21no—
96C22×C4×D67—21no—
97C22×C4×D67—21no—
98C22×C4×D67—21no—
99C2×#11761617—42no—
100C2×#11761617C2314yescomplemented
101C2×D536—24no—
102C2×D536—42no—
103C2×D536C2314yes—
104C2×D536C2314yes—
105#14524043—22no—
106#14524043C2314yescomplemented
107#14524031—22no—
108#14524031C2314yes—
109#14524029—28no—
110#14524029—28no—
111#14524028—28no—
112#14524022—22no—
113#14524022C2314yes—
114#14524017—22no—
115#14524017—22no—
116#14524017—22no—
117#14524017C2314yes—
118#14524017C2314yes—
119#14524017C2314yescomplemented
120#14524016—28no—
121#14524014—28no—
122#14524011—28no—
123C4×D268—22no—
124C4×D268—22no—
125C4×D268C2314yes—
126C4×D268C2314yescomplemented
127#14524002—22no—
128#14524002—22no—
129#14524002C2314yes—
130#14524002C2314yescomplemented
131#14524001—28no—
132C2×C4⋊Dic67—21no—
133C2×C4⋊Dic67C2311yescharacteristic
134C2×C4⋊Dic67C2311yescharacteristic
135C2×C4⋊Dic67C2311yescharacteristic
136C2×C4⋊Dic67C2311yescharacteristic
137C2×Dic67⋊C4—21no—
138C2×C22⋊Dic67—21no—
139C2×C22⋊Dic67—21no—
140C2×C22⋊Dic67—21no—
141C2×(C2×D67)⋊C4—21no—
142C2×(C2×D67)⋊C4—21no—
143C2×(C2×D67)⋊C4—21no—
144C2×(C2×D67)⋊C4—21no—
145C2×(C2×D67)⋊C4—21no—
146C2×(C2×D67)⋊C4—21no—
147C2×(C2×D67)⋊C4—21no—
148C22⋊C4×D67—28no—
149C2×C4×Dic67—21no—
150C2×C4×Dic67—21no—
151#14523977C2314yescomplemented
152#14523977C2314yescomplemented
153#14523975C2314yescomplemented
154#14523968C2314yescomplemented
155#14523968C2314yescomplemented
156#14523968C2314yescomplemented
157#14523965C2314yes—
158#14523965C2314yes—
159#14523965C2314yes—
160#14523965C2314yes—
161#14523965C2314yes—
162#14523965C2314yes—
163#14523965C2314yescomplemented
164C22×D4×C67D411yescharacteristic
165C23×C4×C67C2311yescharacteristic
166C23×C4×C67C2311yescharacteristic
167C2×M16×C67—42no—
168C2×M16×C67C2314yes—
169C22×C8×C67—42no—
170C22×C8×C67C2311yescharacteristic
171C22×C8×C67C2311yescharacteristic
172C22×C8×C67C2311yescharacteristic
173C22×C8×C67C2311yescharacteristic
174C22×C8×C67C2314yescomplemented
175C4×D4×C67D414yes—
176C4×D4×C67C2314yes—
177C2×C4⋊C4×C67D411yescharacteristic
178C2×C22⋊C4×C67D411yescharacteristic
179C2×C22⋊C4×C67D411yescharacteristic
180C2×C42×C67C2311yescharacteristic
181C4⋊C8×C67C2314yescomplemented
182C22⋊C8×C67C2314yes—
183C22⋊C8×C67C2314yescomplemented
184#97×C67C2314yescomplemented
185C23×D67—21no—
186C23×D67—21no—
187C23×D67—21no—
188C23×D67—24no—
189C23×D67—44no—
190C23×D67—44no—
191C23×D67—82no—
192#11761628—28no—
193#11761628—44no—
194#11761628—48no—
195C2×Dic134—22no—
196C2×Dic134—22no—
197C2×Dic134—21no—
198C2×Dic134—24no—
199C2×Dic134—82no—
200C2×Dic134C2412yes—
201C2×D268—21no—
202C2×D268—22no—
203C2×D268—22no—
204C2×D268—22no—
205C2×D268—22no—
206C2×D268—22no—
207C2×D268—28no—
208C2×D268—21no—
209C2×D268—24no—
210C2×D268—21no—
211C2×D268—44no—
212C2×D268—48no—
213C2×D268—44no—
214C2×D268#4114yes—
215C2×D268C2412yes—
216C2×D268C2412yes—
217C2×D268C2412yes—
218C2×C22⋊D67—24no—
219C2×C22⋊D67—24no—
220C2×C22⋊D67—24no—
221C2×C22⋊D67—24no—
222C2×C22⋊D67—44no—
223C2×C22⋊D67—82no—
224C2×C22⋊D67—82no—
225C2×C22⋊D67—82no—
226C22×Dic67—21no—
227C22×Dic67—21no—
228C22×Dic67—21no—
229C22×Dic67—21no—
230C22×Dic67—21no—
231C2×C4×D67—24no—
232C2×C4×D67—24no—
233C2×C4×D67—24no—
234C2×C4×D67—44no—
235C2×C4×D67—44no—
236C2×C4×D67—82no—
237#11761617—44no—
238D536—28no—
239D536—44no—
240C4⋊Dic67—24no—
241C4⋊Dic67—21no—
242C4⋊Dic67—21no—
243C4⋊Dic67—21no—
244C4⋊Dic67—21no—
245C4⋊Dic67C2412yes—
246C4⋊Dic67C2412yes—
247C4⋊Dic67C2412yes—
248C4⋊Dic67C2412yes—
249Dic67⋊C4—24no—
250C22⋊Dic67—24no—
251C22⋊Dic67—24no—
252C22⋊Dic67—24no—
253(C2×D67)⋊C4—24no—
254(C2×D67)⋊C4—24no—
255(C2×D67)⋊C4—24no—
256(C2×D67)⋊C4—24no—
257(C2×D67)⋊C4—24no—
258(C2×D67)⋊C4—24no—
259(C2×D67)⋊C4—24no—
260C4×Dic67—24no—
261C4×Dic67—24no—
262C24×C67C2×D411yescharacteristic
263C24×C67C2×D411yescharacteristic
264C2×D4×C67—42no—
265C2×D4×C67C2×D414yes—
266C22×C4×C67—22no—
267C22×C4×C67—22no—
268C22×C4×C67—22no—
269C22×C4×C67—22no—
270C22×C4×C67C2×D411yescharacteristic
271C22×C4×C67C2×D411yescharacteristic
272C22×C4×C67C2×D411yescharacteristic
273C22×C4×C67C2×D411yescharacteristic
274C22×C4×C67C2×D412yes—
275C22×C4×C67C2×D412yes—
276C22×C4×C67C2412yes—
277C22×C4×C67C2412yes—
278C22×C4×C67C2411yescharacteristic
279M16×C67—44no—
280C2×C8×C67—22no—
281C2×C8×C67—22no—
282C2×C8×C67—22no—
283C2×C8×C67—22no—
284C2×C8×C67—44no—
285C2×C8×C67C2412yes—
286C2×C8×C67C2412yes—
287C2×C8×C67C2412yes—
288C2×C8×C67C2412yes—
289C4⋊C4×C67C2×D414yes—
290C22⋊C4×C67C2×D414yes—
291C22⋊C4×C67C2×D414yes—
292C42×C67C2×D412yes—
293C42×C67C2412yes—
294C23×C67—22no—
295C23×C67—22no—
296C23×C67—22no—
297C23×C67—22no—
298C23×C67—22no—
299C23×C67—22no—
300C23×C67C22×D412yes—
301C23×C67C22×D412yes—
302C23×C67C22×D411yescharacteristic
303C22×D67—24no—
304C22×D67—22no—
305C22×D67—22no—
306C22×D67—22no—
307C22×D67—48no—
308C22×D67—42no—
309C22×D67—42no—
310C22×D67—48no—
311C22×D67—42no—
312C22×D67—42no—
313C22×D67—42no—
314C22×D67—42no—
315C22×D67—42no—
316C22×D67—42no—
317C22×D67—84no—
318C22×D67—816no—
319D4×C67—44no—
320C2×C4×C67—22no—
321C2×C4×C67—22no—
322C2×C4×C67—22no—
323C2×C4×C67—22no—
324C2×C4×C67—24no—
325C2×C4×C67—24no—
326C2×C4×C67—22no—
327C2×C4×C67—22no—
328C2×C4×C67—22no—
329C2×C4×C67—22no—
330C2×C4×C67C22×D412yes—
331C2×C4×C67C22×D412yes—
332C2×C4×C67C22×D412yes—
333C2×C4×C67C22×D412yes—
334C2×C4×C67C22×D411yescharacteristic
335C2×C4×C67C2×#4112yes—
336C2×C4×C67H(5,𝔽2)12yes—
337C2×C4×C67C2511yescharacteristic
338C22⋊D67—48no—
339C22⋊D67—84no—
340C22⋊D67—84no—
341C22⋊D67—84no—
342C2×Dic67—22no—
343C2×Dic67—22no—
344C2×Dic67—22no—
345C2×Dic67—22no—
346C2×Dic67—22no—
347C2×Dic67—42no—
348C2×Dic67—42no—
349C2×Dic67—42no—
350C2×Dic67—42no—
351C2×Dic67—42no—
352D268—24no—
353D268—22no—
354D268—22no—
355D268—22no—
356D268—22no—
357D268—22no—
358D268—48no—
359D268—42no—
360D268—42no—
361D268C2×#4114yes—
362C4×D67—48no—
363C4×D67—48no—
364C4×D67—84no—
365Dic134—22no—
366Dic134—22no—
367Dic134—42no—
368Dic134—84no—
369C8×C67—22no—
370C8×C67—22no—
371C8×C67—22no—
372C8×C67—22no—
373C22×C67—22no—
374C22×C67—22no—
375C22×C67—22no—
376C22×C67—22no—
377C22×C67—22no—
378C22×C67—22no—
379C22×C67—44no—
380C22×C67—44no—
381C22×C67#54612yes—
382C22×C67#57512yes—
383C22×C67#57612yes—
384C22×C67C23×D411yescharacteristic
385C2×D67—24no—
386C2×D67—48no—
387C2×D67—42no—
388C2×D67—42no—
389C2×D67—42no—
390C2×D67—42no—
391C2×D67—42no—
392C2×D67—42no—
393C2×D67—42no—
394C2×D67—42no—
395C2×D67—816no—
396C2×D67—84no—
397C2×D67—84no—
398C4×C67—22no—
399C4×C67—22no—
400C4×C67—22no—
401C4×C67—22no—
402C4×C67#54612yes—
403C4×C67C22×#4111yescharacteristic
404C4×C67C2×H(5,𝔽2)11yescharacteristic
405Dic67—42no—
406Dic67—42no—
407Dic67—42no—
408Dic67—42no—
409Dic67—42no—
410C2×#3319—671nomaximal, Sylow
411C2×C67—42no—
412C2×C67—42no—
413C2×C67#331914yescomplemented
414C2×C67C2×#54611yescharacteristic
415C2×C67C2×#57511yescharacteristic
416C2×C67C2×#57611yescharacteristic
417D67—44no—
418D67—82no—
419D67—82no—
420C2×#555—671no—
421C2×#546—671no—
422#3319—6716no—
423C2×#489—671no—
424C2×#485—671no—
425C2×#482—671no—
426C2×#474—671no—
427C2×#468—671no—
428C2×#466—671no—
429C2×#463—671no—
430C2×#449—671no—
431C2×#447—671no—
432C2×#442—671no—
433C2×#435D6711yescharacteristic, complemented
434C2×#418—671no—
435C2×#416—671no—
436C67C2×#331911yescharacteristic, complemented, Sylow
437C22×#41—671no—
438C23×D4—671no—
439C22×SD16—671no—
440C22×D8—671no—
441C22×D8—671no—
442C22×M16C2×D6711yescharacteristic
443C23×C8C2×D6711yescharacteristic, complemented
444#555—678no—
445#555—1344no—
446#546—678no—
447#546—1344no—
448C2×C4⋊Q8—671no—
449C2×#124—671no—
450C2×#124—1341no—
451C2×#124—1341no—
452C2×#123—1341no—
453C2×C22⋊Q8—671no—
454C2×#121—671no—
455C2×#121—671no—
456C2×#121—671no—
457C2×#121—1341no—
458C2×#121—1341no—
459C2×#120—1341no—
460C2×C4×D4—671no—
461C2×C4×D4—671no—
462C2×C4×D4C2×D6711yescharacteristic
463C2×#117—671no—
464C2×#117—671no—
465C2×#117—1341no—
466C22×C22⋊C4—1341no—
467#489—678no—
468#485—678no—
469#482—678no—
470#474—678no—
471#468—678no—
472#466—678no—
473#463—678no—
474#449—678no—
475#447—678no—
476#442—678no—
477#435C2×D6718yescomplemented
478C2×#107—671no—
479C2×#107—671no—
480C2×#106—671no—
481C2×C4⋊C8C2×D6711yescharacteristic, complemented
482#418—678no—
483#416—678no—
484C2×#103—671no—
485C2×#103—671no—
486C2×#103—671no—
487C2×#102—671no—
488C2×#102—671no—
489C2×#102—671no—
490C2×#102—671no—
491C2×#102—671no—
492C2×#102—671no—
493C2×#102—671no—
494C2×C22⋊C8C2×D6711yescharacteristic
495C2×C22⋊C8C2×D6711yescharacteristic, complemented
496C2×#97C2×D6711yescharacteristic, complemented
497C25—1341no—
498C2×#41—2682no—
499C2×#41—674no—
500C2×#41—1344no—
501C2×#41—1342no—
502C22×Q8—671no—
503C22×Q8—1341no—
504C22×D4—2682no—
505C22×D4—674no—
506C22×D4—671no—
507C22×D4—671no—
508C22×D4—671no—
509C22×D4—1344no—
510C22×D4—1341no—
511C22×D4—1341no—
512C22×D4—1341no—
513C22×D4—1341no—
514C22×D4—1341no—
515C22×D4—1342no—
516C22×D4D26811yescharacteristic
517C23×C4—1341no—
518C23×C4—1341no—
519C23×C4—1341no—
520C23×C4C22×D6711yescharacteristic
521C23×C4C22×D6711yescharacteristic
522C2×SD16—2682no—
523C2×SD16—674no—
524C2×D8—2682no—
525C2×D8—674no—
526C2×D8—674no—
527C2×D8—1344no—
528C2×M16—42no—
529C2×M16C22×D6714yes—
530C22×C8—42no—
531C22×C8C22×D6711yescharacteristic
532C22×C8C22×D6711yescharacteristic
533C22×C8C22×D6711yescharacteristic
534C22×C8C22×D6711yescharacteristic
535C22×C8C22×D6714yescomplemented
536C4⋊Q8—674no—
537C4⋊Q8—1342no—
538#124—674no—
539#124—1348no—
540#124—1348no—
541#124—1342no—
542#123—1348no—
543C22⋊Q8—674no—
544C22⋊Q8—1342no—
545#121—674no—
546#121—674no—
547#121—674no—
548#121—1348no—
549#121—1342no—
550#121—1342no—
551#121—1342no—
552#121—1348no—
553#120—1348no—
554C4×D4—674no—
555C4×D4—674no—
556C4×D4—1342no—
557C4×D4—1342no—
558C4×D4D26814yes—
559C4×D4C22×D6714yes—
560#117—674no—
561#117—674no—
562#117—1342no—
563#117—1342no—
564#117—1348no—
565C2×C4⋊C4—671no—
566C2×C4⋊C4—671no—
567C2×C4⋊C4—671no—
568C2×C4⋊C4—671no—
569C2×C4⋊C4—1341no—
570C2×C4⋊C4—1341no—
571C2×C4⋊C4D26811yescharacteristic
572C2×C22⋊C4—1341no—
573C2×C22⋊C4—1341no—
574C2×C22⋊C4—1341no—
575C2×C22⋊C4—1341no—
576C2×C22⋊C4—1341no—
577C2×C22⋊C4—1341no—
578C2×C22⋊C4—1341no—
579C2×C22⋊C4—1341no—
580C2×C22⋊C4—1341no—
581C2×C22⋊C4—1341no—
582C2×C22⋊C4—1348no—
583C2×C22⋊C4D26811yescharacteristic
584C2×C22⋊C4D26811yescharacteristic
585C2×C42—1341no—
586C2×C42—1341no—
587C2×C42C22×D6711yescharacteristic
588#107—674no—
589#107—674no—
590#106—674no—
591C4⋊C8C22×D6714yescomplemented
592#103—674no—
593#103—674no—
594#103—674no—
595#102—674no—
596#102—674no—
597#102—674no—
598#102—674no—
599#102—674no—
600#102—674no—
601#102—674no—
602C22⋊C8C22×D6714yes—
603C22⋊C8C22×D6714yescomplemented
604#97C22×D6714yescomplemented
605C24—2684no—
606C24—2684no—
607C24—5362no—
608C24—1341no—
609C24—1341no—
610C24—1344no—
611C24—1341no—
612C24C2×D26811yescharacteristic
613C24C2×D26811yescharacteristic
614#41—2688no—
615#41—2684no—
616#41—1348no—
617C2×Q8—5362no—
618C2×Q8—672no—
619C2×Q8—1342no—
620C2×Q8—1342no—
621C2×Q8—1341no—
622C2×Q8—1344no—
623C2×D4—42no—
624C2×D4—2684no—
625C2×D4—2688no—
626C2×D4—2684no—
627C2×D4—2684no—
628C2×D4—5362no—
629C2×D4—5362no—
630C2×D4—5362no—
631C2×D4—674no—
632C2×D4—672no—
633C2×D4—672no—
634C2×D4—672no—
635C2×D4—1348no—
636C2×D4—1344no—
637C2×D4—1344no—
638C2×D4—1344no—
639C2×D4—1344no—
640C2×D4—1341no—
641C2×D4—1344no—
642C2×D4—1341no—
643C2×D4—1341no—
644C2×D4—1342no—
645C2×D4—1342no—
646C2×D4—1342no—
647C2×D4—1342no—
648C2×D4—1342no—
649C2×D4C2×D26814yes—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—2684no—
655C22×C4—2684no—
656C22×C4—5362no—
657C22×C4—1341no—
658C22×C4—1341no—
659C22×C4—1341no—
660C22×C4—1341no—
661C22×C4—1341no—
662C22×C4—1344no—
663C22×C4—1344no—
664C22×C4—1344no—
665C22×C4C2×D26812yes—
666C22×C4C2×D26812yes—
667C22×C4C2×D26811yescharacteristic
668C22×C4C2×D26811yescharacteristic
669C22×C4C2×D26811yescharacteristic
670C22×C4C2×D26811yescharacteristic
671C22×C4C23×D6712yes—
672C22×C4C23×D6712yes—
673C22×C4C23×D6711yescharacteristic
674SD16—2684no—
675D8—2684no—
676D8—1348no—
677M16—44no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—44no—
683C2×C8C23×D6712yes—
684C2×C8C23×D6712yes—
685C2×C8C23×D6712yes—
686C2×C8C23×D6712yes—
687C4⋊C4—672no—
688C4⋊C4—672no—
689C4⋊C4—672no—
690C4⋊C4—672no—
691C4⋊C4—1341no—
692C4⋊C4—1341no—
693C4⋊C4—1341no—
694C4⋊C4—1341no—
695C4⋊C4—1344no—
696C4⋊C4—1344no—
697C4⋊C4C2×D26814yes—
698C22⋊C4—1344no—
699C22⋊C4—1344no—
700C22⋊C4—1344no—
701C22⋊C4—1344no—
702C22⋊C4—1344no—
703C22⋊C4—1344no—
704C22⋊C4—1344no—
705C22⋊C4—1344no—
706C22⋊C4—1344no—
707C22⋊C4—1344no—
708C22⋊C4C2×D26814yes—
709C22⋊C4C2×D26814yes—
710C42—1344no—
711C42—1344no—
712C42C2×D26812yes—
713C42C23×D6712yes—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—2688no—
721C23—2688no—
722C23—2682no—
723C23—2682no—
724C23—2682no—
725C23—2682no—
726C23—2682no—
727C23—2682no—
728C23—2682no—
729C23—2682no—
730C23—5364no—
731C23—53616no—
732C23—1342no—
733C23—1342no—
734C23—1344no—
735C23—1342no—
736C23C22×D26812yes—
737C23C22×D26812yes—
738C23C22×D26811yescharacteristic
739Q8—2682no—
740Q8—5364no—
741Q8—1342no—
742Q8—1342no—
743D4—44no—
744D4—2688no—
745D4—2688no—
746D4—2682no—
747D4—2682no—
748D4—5364no—
749D4—5364no—
750D4—5364no—
751D4—674no—
752D4—1344no—
753D4—1342no—
754D4—1342no—
755D4—1342no—
756D4—1342no—
757D4—1342no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—2688no—
769C2×C4—2688no—
770C2×C4—2682no—
771C2×C4—2682no—
772C2×C4—2682no—
773C2×C4—2682no—
774C2×C4—2682no—
775C2×C4—5364no—
776C2×C4—1342no—
777C2×C4—1342no—
778C2×C4—1342no—
779C2×C4—1342no—
780C2×C4—1342no—
781C2×C4C22×D26812yes—
782C2×C4C22×D26812yes—
783C2×C4C22×D26812yes—
784C2×C4C22×D26812yes—
785C2×C4C22×D26811yescharacteristic
786C2×C4#41×D6712yes—
787C2×C4#1452408812yes—
788C2×C4C24×D6711yescharacteristic
789C8—22no—
790C8—22no—
791C8—22no—
792C8—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—2688no—
802C22—2682no—
803C22—2682no—
804C22—2682no—
805C22—2682no—
806C22—2682no—
807C22—2682no—
808C22—2682no—
809C22—2682no—
810C22—53616no—
811C22—5364no—
812C22—5364no—
813C22—1344no—
814C22#1686404112yes—
815C22#1686419612yes—
816C22#1686420112yes—
817C22C23×D26811yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—2682no—
823C4—2682no—
824C4—2682no—
825C4—2682no—
826C4—2682no—
827C4#1686404112yes—
828C4C2×#41×D6711yescharacteristic
829C4C2×#1452408811yescharacteristic
830C2—42no—
831C2—42no—
832C2—2684no—
833C2—5362no—
834C2—5362no—
835C2#2257236714yesdirect product factor
836C2C2×#1686404111yescharacteristic
837C2C2×#1686419611yescharacteristic
838C2C2×#1686420111yescharacteristic
subgroupG/H
centerC23C22×D268
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#435×C67C2
socleC23×C67C22×D4
hypercenterC2×#435D67
hypocenterC67C2×#3319
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16864111C2semidirect
2. C2×#16864042C2semidirect
3. #22572367C2direct (N × H)
4. C2×#16863756C2semidirect
5. C2×#16863738C2semidirect
6. C2×#16863721C2semidirect
7. C2×#16863677C2semidirect
8. C2×#16863642C2semidirect
9. C2×#16863632C2semidirect
10. C2×#16863612C2semidirect
11. C2×#16863543C2semidirect
12. C2×#16863532C2semidirect
13. C2×#16863509C2semidirect
14. C2×#16863402C2semidirect
15. C2×#16863393C2semidirect
16. C2×#435×C67C2semidirect
19. C22×#11761617C22semidirect
23. #16864111C22semidirect
25. #16864042C22semidirect
26. C2×#14524043C22semidirect
34. C2×#14524017C22semidirect
39. C2×C4×D268C22semidirect
41. C2×#14524002C22semidirect
44. #16863756C22semidirect
45. #16863738C22semidirect
46. #16863721C22semidirect
47. #16863677C22semidirect
48. #16863642C22semidirect
49. #16863632C22semidirect
50. #16863612C22semidirect
51. #16863543C22semidirect
52. #16863532C22semidirect
53. #16863509C22semidirect
54. C2×#14523977C22semidirect
55. C2×#14523977C22semidirect
56. C2×#14523975C22semidirect
57. #16863402C22semidirect
58. #16863393C22semidirect
59. C2×#14523968C22semidirect
60. C2×#14523968C22semidirect
61. C2×#14523968C22semidirect
68. C2×#14523965C22semidirect
70. C23×C8×C67C22semidirect
72. #435×C67C22semidirect
73. C2×C4⋊C8×C67C22semidirect
75. C2×C22⋊C8×C67C22semidirect
76. C2×#97×C67C22semidirect
100. C2×#11761617C23semidirect
106. #14524043C23semidirect
119. #14524017C23semidirect
126. C4×D268C23semidirect
130. #14524002C23semidirect
151. #14523977C23semidirect
152. #14523977C23semidirect
153. #14523975C23semidirect
154. #14523968C23semidirect
155. #14523968C23semidirect
156. #14523968C23semidirect
163. #14523965C23semidirect
174. C22×C8×C67C23semidirect
181. C4⋊C8×C67C23semidirect
183. C22⋊C8×C67C23semidirect
184. #97×C67C23semidirect
413. C2×C67#3319semidirect
433. C2×#435D67semidirect
436. C67C2×#3319semidirect
443. C23×C8C2×D67semidirect
477. #435C2×D67semidirect
481. C2×C4⋊C8C2×D67semidirect
495. C2×C22⋊C8C2×D67semidirect
496. C2×#97C2×D67semidirect
535. C22×C8C22×D67semidirect
591. C4⋊C8C22×D67semidirect
603. C22⋊C8C22×D67semidirect
604. #97C22×D67semidirect
835. C2#22572367direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641112
C2×#168640422
#225723672
C2×#168637562
C2×#168637382
C2×#168637212
C2×#168636772
C2×#168636422
C2×#168636322
C2×#168636122
C2×#168635432
C2×#168635322
C2×#168635092
C2×#168634022
C2×#168633932
C2×#435×C672
C2×#331967