Finite Group Databasebeta

← #33108577

Subgroups — #33108577

Order 18688.

1066 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic73C211yesmaximal, characteristic, complemented
2C22×#14556523C211yesmaximal, characteristic, complemented
3#22612951C211yesmaximal, characteristic
4#22612940C211yesmaximal, characteristic, complemented
5#22610787C211yesmaximal, characteristic, complemented
6#22610660C211yesmaximal, characteristic, complemented
7#22610567C211yesmaximal, characteristic, complemented
8#22610560C211yesmaximal, characteristic, complemented
9#22610249C211yesmaximal, characteristic
10#22610239C211yesmaximal, characteristic, complemented
11#22610201C211yesmaximal, characteristic, complemented
12#22610194C211yesmaximal, characteristic, complemented
13#106×Dic73C211yesmaximal, characteristic, complemented
14C8×C22⋊Dic73C211yesmaximal, characteristic, complemented
15C2×#465×C73C211yesmaximal, characteristic
16C2×Q8×Dic73C2211yescharacteristic
17C2×D4×Dic73—21no—
18C2×D4×Dic73C2211yescharacteristic
19C22×C4⋊Dic73C2211yescharacteristic
20C22×C4⋊Dic73C2211yescharacteristic
21SD16×Dic73—24no—
22C2×#14556523—24no—
23C2×#14556523C2211yescharacteristic
24C2×#14556523C2211yescharacteristic
25C2×#14556523C2211yescharacteristic
26C2×#14556523C2211yescharacteristic
27C2×#14556515C2211yescharacteristic
28C2×#14556515C2211yescharacteristic
29C2×#14556512C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×C22⋊#10596831C2211yescharacteristic
32C2×C8×Dic73C2211yescharacteristic
33C2×C8×Dic73C2211yescharacteristic
34#17988494C2211yescharacteristic
35#17988490C2211yescharacteristic
36#17988486—21no—
37#17988486C2211yescharacteristic
38#17988486C2211yescharacteristic
39#17988480—21no—
40#17988473—21no—
41#17988467—21no—
42#17988462—21no—
43#17988462—21no—
44C4⋊C4×Dic73C2211yescharacteristic
45C4⋊C4×Dic73C2211yescharacteristic
46C22⋊C4×Dic73—21no—
47C4×C22⋊Dic73C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C22×SD16×C73C2211yescharacteristic
55C23×C8×C73C2211yescharacteristic
56C2×C22⋊Q8×C73C2211yescharacteristic
57C2×#121×C73C2211yescharacteristic
58#465×C73C418yescomplemented
59C2×#106×C73C2211yescharacteristic
60C2×#103×C73C2211yescharacteristic
61C2×#102×C73C2211yescharacteristic
62C23×Dic73—21no—
63C23×Dic73—21no—
64C23×Dic73—21no—
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67Q8×Dic73—22no—
68Q8×Dic73—41no—
69D4×Dic73—22no—
70D4×Dic73—41no—
71D4×Dic73—44no—
72C2×C4⋊Dic73—22no—
73C2×C4⋊Dic73—22no—
74C2×C4⋊Dic73—21no—
75C2×C4⋊Dic73—21no—
76C2×C4⋊Dic73—21no—
77C2×C4⋊Dic73—21no—
78C2×C4⋊Dic73—21no—
79C2×C4⋊Dic73—41no—
80C2×C4⋊Dic73—41no—
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×C22⋊Dic73—21no—
86C2×C22⋊Dic73—21no—
87C2×C22⋊Dic73—21no—
88C2×C22⋊Dic73D411yescharacteristic
89C2×C22⋊Dic73D411yescharacteristic
90C2×C4×Dic73—21no—
91C2×C4×Dic73—21no—
92C2×C4×Dic73—21no—
93C2×C4×Dic73C2311yescharacteristic
94C2×C4×Dic73C2311yescharacteristic
95#14556523—22no—
96#14556523—22no—
97#14556523—22no—
98#14556523D414yescomplemented
99#14556515—22no—
100#14556515—41no—
101#14556512—22no—
102#14556512—41no—
103C22⋊#10596831—22no—
104C8×Dic73—22no—
105C8×Dic73—22no—
106#14556498—21no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110#14556498—21no—
111#14556498—21no—
112#14556498D411yescharacteristic
113#14556498D411yescharacteristic
114C22×Q8×C73C2311yescharacteristic
115C22×D4×C73—21no—
116C22×D4×C73C2311yescharacteristic
117C23×C4×C73C2311yescharacteristic
118C2×SD16×C73—22no—
119C2×SD16×C73—22no—
120C2×SD16×C73C2×C414yescomplemented
121C22×C8×C73—22no—
122C22×C8×C73—22no—
123C22×C8×C73C2×C414yescomplemented
124C22×C8×C73C2311yescharacteristic
125C22×C8×C73C2311yescharacteristic
126C22⋊Q8×C73—22no—
127C22⋊Q8×C73C2×C414yescomplemented
128#121×C73—22no—
129#121×C73C2×C414yes—
130C2×C4⋊C4×C73—21no—
131C2×C4⋊C4×C73C2311yescharacteristic
132C2×C4⋊C4×C73C2311yescharacteristic
133C2×C22⋊C4×C73—21no—
134C2×C22⋊C4×C73—21no—
135#106×C73C2×C414yescomplemented
136#103×C73C2×C414yescomplemented
137#102×C73C2×C414yescomplemented
138C22×Dic73—21no—
139C22×Dic73—21no—
140C22×Dic73—21no—
141C22×Dic73—21no—
142C22×Dic73—42no—
143C22×Dic73—42no—
144C22×Dic73—42no—
145C22×Dic73—42no—
146C22×Dic73—42no—
147C22×Dic73—42no—
148C22×Dic73—81no—
149C22×Dic73—81no—
150C22×Dic73—81no—
151C22×Dic73C2×D411yescharacteristic
152C22×Dic73C2×D411yescharacteristic
153C22×Dic73C2×D411yescharacteristic
154C22×Dic73C2×D411yescharacteristic
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C4⋊Dic73—21no—
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—42no—
168C4⋊Dic73—42no—
169C4⋊Dic73—42no—
170C4⋊Dic73—42no—
171C4⋊Dic73—81no—
172C4⋊Dic73C2×D412yes—
173C4⋊Dic73C2×D412yes—
174C22⋊Dic73—22no—
175C22⋊Dic73—42no—
176C22⋊Dic73—42no—
177C22⋊Dic73—81no—
178C22⋊Dic73SD1614yescomplemented
179C4×Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—42no—
184C4×Dic73—42no—
185C4×Dic73—81no—
186C24×C73—21no—
187C24×C73C2×D411yescharacteristic
188C2×Q8×C73—21no—
189C2×Q8×C73—21no—
190C2×Q8×C73—21no—
191C2×Q8×C73—21no—
192C2×Q8×C73—21no—
193C2×Q8×C73C22×C412yes—
194C2×D4×C73—24no—
195C2×D4×C73—21no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—42no—
201C2×D4×C73—42no—
202C2×D4×C73C22×C412yes—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73C22×C412yes—
211C22×C4×C73C2×D411yescharacteristic
212C22×C4×C73#4112yes—
213C22×C4×C73C2411yescharacteristic
214SD16×C73—28no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—28no—
218C2×C8×C73C22×C412yes—
219C2×C8×C73C22×C412yes—
220C2×C8×C73C2×D412yes—
221C2×C8×C73#4112yes—
222C4⋊C4×C73—24no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73C22×C412yes—
226C4⋊C4×C73C22×C412yes—
227C22⋊C4×C73—24no—
228C22⋊C4×C73—24no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—22no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73C4×D412yes—
241C23×C73C2×SD1612yes—
242C23×C73#13512yes—
243C23×C73C22×D411yescharacteristic
244Q8×C73—22no—
245Q8×C73—22no—
246Q8×C73—41no—
247Q8×C73—41no—
248D4×C73—22no—
249D4×C73—22no—
250D4×C73—48no—
251D4×C73—41no—
252D4×C73—41no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—22no—
261C2×C4×C73—22no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73C4×D412yes—
269C2×C4×C73C23×C411yescharacteristic
270C2×C4×C73C22×D411yescharacteristic
271C2×C4×C73C2×#4111yescharacteristic
272C2×C4×C73C2×#4111yescharacteristic
273C2×C4×C73H(5,𝔽2)11yescharacteristic
274C2×C4×C732−1+411yescharacteristic
275C2×Dic73—21no—
276C2×Dic73—21no—
277C2×Dic73—21no—
278C2×Dic73—21no—
279C2×Dic73—21no—
280C2×Dic73—22no—
281C2×Dic73—22no—
282C2×Dic73—21no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—21no—
286C2×Dic73—21no—
287C2×Dic73—41no—
288C2×Dic73—41no—
289C2×Dic73—41no—
290C2×Dic73—41no—
291C2×Dic73—41no—
292C2×Dic73—41no—
293C2×Dic73—41no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297C2×Dic73—84no—
298C2×Dic73—84no—
299C2×Dic73—84no—
300C2×Dic73C2×SD1612yes—
301C2×Dic73C2×SD1612yes—
302C8×C73—22no—
303C8×C73C4×D414yescomplemented
304#10596831—41no—
305#10596831—41no—
306C22×C73—22no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—22no—
310C22×C73—22no—
311C22×C73—22no—
312C22×C73—42no—
313C22×C73—42no—
314C22×C73—42no—
315C22×C73—81no—
316C22×C73—81no—
317C22×C73—81no—
318C22×C73—81no—
319C22×C73C4×SD1614yescomplemented
320C22×C73C2×C4×D411yescharacteristic
321C22×C73D4211yescharacteristic
322C22×C73#54711yescharacteristic
323C22×C73C22×SD1611yescharacteristic
324C22×C73C2×#13511yescharacteristic
325C22×C73#57711yescharacteristic
326C22×C73#57711yescharacteristic
327C4×C73—22no—
328C4×C73—42no—
329C4×C73—42no—
330C4×C73—42no—
331C4×C73C2×C4×D411yescharacteristic
332C4×C73#52011yescharacteristic
333C4×C73#54811yescharacteristic
334C4×C73#55311yescharacteristic
335Dic73—22no—
336Dic73—22no—
337Dic73—41no—
338Dic73—42no—
339Dic73—41no—
340Dic73—42no—
341Dic73—81no—
342Dic73—81no—
343#23022—731nomaximal, Sylow
344C2×C73—24no—
345C2×C73—82no—
346C2×C73#236111yescharacteristic
347C2×C73C2×C4×SD1611yescharacteristic
348C2×C73#295211yescharacteristic
349C2×C73D4×SD1611yescharacteristic
350C2×C73#328211yescharacteristic
351C2×C73#333511yescharacteristic
352C2×C73#333711yescharacteristic
353C2×#465D7311yescharacteristic
354C2×C4×SD16—731no—
355C22×#106—731no—
356#2361—731no—
357#2360—731no—
358#1968—731no—
359#1941—731no—
360#1927—731no—
361#1926—731no—
362#1874—731no—
363#1872—731no—
364#1865—731no—
365#1864—731no—
366C4×#106—731no—
367C8×C22⋊C4—731no—
368C73#2302211yescharacteristic, complemented, Sylow
369C22×SD16C2×D7311yescharacteristic
370C23×C8C2×D7311yescharacteristic
371C2×C22⋊Q8C2×D7311yescharacteristic
372C2×#121C2×D7311yescharacteristic
373C2×C4×Q8—731no—
374C2×C4×D4—731no—
375C2×C4×D4—1461no—
376C22×C4⋊C4—731no—
377C22×C4⋊C4—731no—
378#465Dic7318yescomplemented
379C4×SD16—1464no—
380C2×#106—731no—
381C2×#106—731no—
382C2×#106—731no—
383C2×#106—731no—
384C2×#106—1464no—
385C2×#106C2×D7311yescharacteristic
386C2×#103—731no—
387C2×#103—731no—
388C2×#103C2×D7311yescharacteristic
389C2×#102—731no—
390C2×#102—731no—
391C2×#102C2×D7311yescharacteristic
392C2×C22⋊C8—731no—
393C2×C4×C8—731no—
394C2×C4×C8—731no—
395#391—731no—
396#390—731no—
397#389—731no—
398#389—731no—
399#389—1461no—
400#388—1461no—
401#387—1461no—
402#386—1461no—
403#385—1461no—
404#385—1461no—
405C4×C4⋊C4—731no—
406C4×C4⋊C4—731no—
407C4×C22⋊C4—731no—
408C4×C22⋊C4—1461no—
409#340—731no—
410#340—731no—
411#340—731no—
412#340—731no—
413#336—731no—
414#336—731no—
415C22×Q8C22×D7311yescharacteristic
416C22×D4—21no—
417C22×D4C22×D7311yescharacteristic
418C23×C4—1461no—
419C23×C4—1461no—
420C23×C4—1461no—
421C23×C4C22×D7311yescharacteristic
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16C2×Dic7314yescomplemented
425C22×C8—22no—
426C22×C8—22no—
427C22×C8—731no—
428C22×C8—731no—
429C22×C8C2×Dic7314yescomplemented
430C22×C8C22×D7311yescharacteristic
431C22×C8C22×D7311yescharacteristic
432C22⋊Q8—22no—
433C22⋊Q8C2×Dic7314yescomplemented
434#121—22no—
435#121C2×Dic7314yes—
436C4×Q8—2921no—
437C4×Q8—1462no—
438C4×D4—2924no—
439C4×D4—2921no—
440C4×D4—1462no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—2921no—
443C2×C4⋊C4—2921no—
444C2×C4⋊C4—731no—
445C2×C4⋊C4—731no—
446C2×C4⋊C4—731no—
447C2×C4⋊C4—731no—
448C2×C4⋊C4—1461no—
449C2×C4⋊C4—1461no—
450C2×C4⋊C4—1461no—
451C2×C4⋊C4—1461no—
452C2×C4⋊C4—1462no—
453C2×C4⋊C4—1462no—
454C2×C4⋊C4—1461no—
455C2×C4⋊C4C22×D7311yescharacteristic
456C2×C4⋊C4C22×D7311yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—731no—
460C2×C22⋊C4—731no—
461C2×C22⋊C4—1461no—
462C2×C22⋊C4—1461no—
463C2×C22⋊C4—1461no—
464C2×C42—731no—
465C2×C42—731no—
466C2×C42—1461no—
467C2×C42—1461no—
468C2×C42—1461no—
469#106—734no—
470#106—1462no—
471#106—1462no—
472#106—1462no—
473#106C2×Dic7314yescomplemented
474#103—2921no—
475#103—1462no—
476#103C2×Dic7314yescomplemented
477#102—2921no—
478#102—1462no—
479#102C2×Dic7314yescomplemented
480C22⋊C8—1462no—
481C4×C8—1462no—
482C4×C8—1462no—
483#95—731no—
484#95—731no—
485#95—1461no—
486#95—1461no—
487#95—1461no—
488#95—1461no—
489#95—1461no—
490#95—1461no—
491C24—21no—
492C24D4×D7311yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8C22×Dic7312yes—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4C22×Dic7312yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—2922no—
516C22×C4—2922no—
517C22×C4—2922no—
518C22×C4—2922no—
519C22×C4—2922no—
520C22×C4—2922no—
521C22×C4—5841no—
522C22×C4—5841no—
523C22×C4—5841no—
524C22×C4—731no—
525C22×C4—731no—
526C22×C4—731no—
527C22×C4—731no—
528C22×C4—1461no—
529C22×C4—1461no—
530C22×C4—1461no—
531C22×C4—1461no—
532C22×C4C22×Dic7312yes—
533C22×C4D4×D7311yescharacteristic
534C22×C4#1192402712yes—
535C22×C4C23×D7311yescharacteristic
536SD16—28no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—28no—
540C2×C8—1461no—
541C2×C8—1461no—
542C2×C8—1461no—
543C2×C8—1461no—
544C2×C8—1461no—
545C2×C8—1461no—
546C2×C8C22×Dic7312yes—
547C2×C8C22×Dic7312yes—
548C2×C8D4×D7312yes—
549C2×C8#1192402712yes—
550C4⋊C4—24no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—2922no—
554C4⋊C4—2922no—
555C4⋊C4—2922no—
556C4⋊C4—2922no—
557C4⋊C4—5841no—
558C4⋊C4—732no—
559C4⋊C4—732no—
560C4⋊C4—1461no—
561C4⋊C4—1461no—
562C4⋊C4—1461no—
563C4⋊C4—1461no—
564C4⋊C4—1461no—
565C4⋊C4—1461no—
566C4⋊C4C22×Dic7312yes—
567C4⋊C4C22×Dic7312yes—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—2922no—
571C22⋊C4—2922no—
572C22⋊C4—5841no—
573C22⋊C4—734no—
574C22⋊C4—1462no—
575C42—2922no—
576C42—2922no—
577C42—5841no—
578C42—1461no—
579C42—1461no—
580C42—1461no—
581C42—1461no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23D4×Dic7312yes—
594C23SD16×D7312yes—
595C23#1455661212yes—
596C23C2×D4×D7311yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—41no—
600Q8—41no—
601D4—22no—
602D4—22no—
603D4—48no—
604D4—41no—
605D4—41no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—2921no—
622C2×C4—2921no—
623C2×C4—2921no—
624C2×C4—2921no—
625C2×C4—2921no—
626C2×C4—2921no—
627C2×C4—2921no—
628C2×C4—2921no—
629C2×C4—2921no—
630C2×C4—2921no—
631C2×C4—5844no—
632C2×C4—5844no—
633C2×C4—5844no—
634C2×C4—732no—
635C2×C4—732no—
636C2×C4—1461no—
637C2×C4—1461no—
638C2×C4—1462no—
639C2×C4—1461no—
640C2×C4—1462no—
641C2×C4—1461no—
642C2×C4—1461no—
643C2×C4—1461no—
644C2×C4—1461no—
645C2×C4—1461no—
646C2×C4—1461no—
647C2×C4—1461no—
648C2×C4D4×Dic7312yes—
649C2×C4C23×Dic7311yescharacteristic
650C2×C4C2×D4×D7311yescharacteristic
651C2×C4C2×#1192402711yescharacteristic
652C2×C4C2×#1192402711yescharacteristic
653C2×C4#1455663711yescharacteristic
654C2×C4#1455663811yescharacteristic
655C8—22no—
656C8—2921no—
657C8—2921no—
658C8D4×Dic7314yescomplemented
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22SD16×Dic7314yescomplemented
673C22C2×D4×Dic7311yescharacteristic
674C22#1798922111yescharacteristic
675C22#1798923711yescharacteristic
676C22C2×SD16×D7311yescharacteristic
677C22C2×#1455661211yescharacteristic
678C22#1798939411yescharacteristic
679C22#1798939411yescharacteristic
680C4—22no—
681C4—42no—
682C4—42no—
683C4—42no—
684C4—2921no—
685C4—2922no—
686C4—2922no—
687C4—2921no—
688C4—5841no—
689C4—5841no—
690C4—1462no—
691C4—1462no—
692C4C2×D4×Dic7311yescharacteristic
693C4#1798907011yescharacteristic
694C4#1798924311yescharacteristic
695C4#1798928911yescharacteristic
696C2—24no—
697C2—82no—
698C2#2261295111yescharacteristic
699C2C2×SD16×Dic7311yescharacteristic
700C2#2261881511yescharacteristic
701C2#2262162411yescharacteristic
702C2#2262163511yescharacteristic
703C2#2262228311yescharacteristic
704C2#2262231611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#465×C73C2
socleC23×C73C22×D4
prime radicalC2×#121×C73C22
cosocleC22×C4×C73C24
hypercenterC2×#465D73
hypocenterC73#23022
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic73C2semidirect
2. C22×#14556523C2semidirect
4. #22612940C2semidirect
5. #22610787C2semidirect
6. #22610660C2semidirect
7. #22610567C2semidirect
8. #22610560C2semidirect
10. #22610239C2semidirect
11. #22610201C2semidirect
12. #22610194C2semidirect
13. #106×Dic73C2semidirect
14. C8×C22⋊Dic73C2semidirect
58. #465×C73C4semidirect
98. #14556523D4semidirect
120. C2×SD16×C73C2×C4semidirect
123. C22×C8×C73C2×C4semidirect
127. C22⋊Q8×C73C2×C4semidirect
135. #106×C73C2×C4semidirect
136. #103×C73C2×C4semidirect
137. #102×C73C2×C4semidirect
178. C22⋊Dic73SD16semidirect
303. C8×C73C4×D4semidirect
319. C22×C73C4×SD16semidirect
368. C73#23022semidirect
378. #465Dic73semidirect
424. C2×SD16C2×Dic73semidirect
429. C22×C8C2×Dic73semidirect
433. C22⋊Q8C2×Dic73semidirect
473. #106C2×Dic73semidirect
476. #103C2×Dic73semidirect
479. #102C2×Dic73semidirect
658. C8D4×Dic73semidirect
672. C22SD16×Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic732
C22×#145565232
#226129512
#226129402
#226107872
#226106602
#226105672
#226105602
#226102492
#226102392
#226102012
#226101942
#106×Dic732
C8×C22⋊Dic732
C2×#465×C732
#2302273