Finite Group Databasebeta

← C2×#20252242 #27080409

Subgroups — C2×#20252242 #27080409

Order 12032.

2870 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
1C22×SD16×D47C211yesmaximal, characteristic
2C2×#15689599C211yesmaximal, characteristic, complemented
3C2×#15689595C211yesmaximal, characteristic
4#20252242C2116yesmaximal, direct product factor
5C2×#15689226C211yesmaximal, characteristic, complemented
6C2×#15689223C211yesmaximal, characteristic, complemented
7C2×#15689221C211yesmaximal, characteristic, complemented
8C2×#15689220C211yesmaximal, characteristic, complemented
9C2×C4×#10625325C211yesmaximal, characteristic, complemented
10C2×SD16×Dic47C211yesmaximal, characteristic, complemented
11C2×#15689210C211yesmaximal, characteristic, complemented
12C2×#15689158C211yesmaximal, characteristic, complemented
13C2×#15689130C211yesmaximal, characteristic, complemented
14C2×#15689126C211yesmaximal, characteristic
15C2×#15689077C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C47C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×#10625336C2211yescharacteristic
22C2×SD16×D47C4116yescomplemented
23C2×SD16×D47C2218yes—
24C22×#10625324C2211yescharacteristic
25C22×C8×D47C2211yescharacteristic
26#15689599—24no—
27#15689599C2218yescomplemented
28#15689595—24no—
29#15689595C2218yes—
30C2×Q8×Dic47C2211yescharacteristic, complemented
31C2×C4×Dic94—21no—
32C2×C4×Dic94C2211yescharacteristic, complemented
33C2×#13093989—21no—
34C2×#13093989C2211yescharacteristic, complemented
35C2×C4×D188C2211yescharacteristic
36C2×D4×Dic47C2211yescharacteristic
37C2×#13093986C2211yescharacteristic
38C2×C4×C22⋊D47—21no—
39C2×(C22⋊D47)⋊C4—21no—
40C2×#13093982—21no—
41C2×#13093982C2211yescharacteristic
42C2×#13093982C2211yescharacteristic
43C2×#13093981—21no—
44C2×#13093981C2211yescharacteristic
45C22×(C2×D47)⋊C4—21no—
46C2×C22⋊C4×D47—21no—
47#15689226C2218yescomplemented
48#15689223C2218yescomplemented
49#15689221C2218yescomplemented
50#15689220C2218yescomplemented
51C4×#10625325C2218yescomplemented
52SD16×Dic47C2218yescomplemented
53#15689210C2218yescomplemented
54#15689158C2218yescomplemented
55C2×#13093957C2211yescharacteristic, complemented
56C2×#13093957C2211yescharacteristic, complemented
57C2×#13093956C2211yescharacteristic, complemented
58#15689130C2218yescomplemented
59#15689126C2218yes—
60C2×#13093949C2211yescharacteristic, complemented
61C2×#13093948C2211yescharacteristic, complemented
62C2×#13093947C2211yescharacteristic, complemented
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66#15689077C2218yescomplemented
67C2×#13093935C2211yescharacteristic, complemented
68C2×#13093934C2211yescharacteristic, complemented
69C2×C8×Dic47C2211yescharacteristic, complemented
70C22×SD16×C47C2211yescharacteristic
71C2×C4×Q8×C47C2211yescharacteristic, complemented
72C2×C4×D4×C47C2211yescharacteristic
73C4×SD16×C47C2218yescomplemented
74C2×#106×C47C2211yescharacteristic, complemented
75C2×#103×C47C2211yescharacteristic, complemented
76C2×#102×C47C2211yescharacteristic
77C2×C4×C8×C47C2211yescharacteristic, complemented
78C24×D47—21no—
79C22×Dic94—21no—
80C22×Dic94C2311yescharacteristic
81C2×Q8×D47—22no—
82C2×Q8×D47—24no—
83C2×Q8×D47C2×C418yescomplemented
84C2×Q8×D47C2314yes—
85C22×D188C2311yescharacteristic
86C22×C22⋊D47—21no—
87C2×D4×D47—22no—
88C2×D4×D47—24no—
89C2×D4×D47C2×C418yes—
90C2×D4×D47C2314yes—
91C23×Dic47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47—21no—
95C22×C4×D47C2311yescharacteristic
96C2×#10625325C2×C418yescomplemented
97C2×#10625325C2314yes—
98C2×#10625335C2×C418yescomplemented
99C2×#10625335C2314yes—
100C2×#10625336C2×C418yescomplemented
101C2×#10625336C2314yes—
102SD16×D47C2×C4164yescomplemented
103C2×#10625324—24no—
104C2×#10625324C2314yes—
105C22×C47⋊C8C2311yescharacteristic
106C22×C47⋊C8C2311yescharacteristic
107C2×C8×D47C2×C418yescomplemented
108C2×C8×D47C2314yes—
109Q8×Dic47—22no—
110Q8×Dic47C2314yescomplemented
111C4×Dic94—22no—
112C4×Dic94—28no—
113C4×Dic94C2314yescomplemented
114#13093989—28no—
115#13093989—22no—
116#13093989C2314yescomplemented
117C4×D188—22no—
118C4×D188C2314yes—
119D4×Dic47—22no—
120D4×Dic47C2314yes—
121#13093986—22no—
122#13093986C2314yes—
123C4×C22⋊D47—28no—
124(C22⋊D47)⋊C4—28no—
125#13093982—22no—
126#13093982—22no—
127#13093982—28no—
128#13093982C2314yes—
129#13093982C2314yes—
130#13093981—28no—
131#13093981D414yes—
132#13093981C2314yes—
133C2×C4⋊Dic47—21no—
134C2×C4⋊Dic47C2311yescharacteristic
135C2×C4⋊Dic47C2311yescharacteristic
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4D411yescharacteristic
139C2×Dic47⋊C4D411yescharacteristic
140C2×C22⋊Dic47—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—28no—
146C2×(C2×D47)⋊C4D411yescharacteristic
147C2×(C2×D47)⋊C4D411yescharacteristic
148C22⋊C4×D47—28no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151C2×C4×Dic47—21no—
152C2×C4×Dic47—21no—
153C2×C4×Dic47—21no—
154C2×C4×Dic47C2311yescharacteristic
155#13093957C2314yescomplemented
156#13093957C2314yescomplemented
157#13093956C2314yescomplemented
158#13093949C2314yescomplemented
159#13093948C2314yescomplemented
160#13093947C2314yescomplemented
161#13093946C2314yes—
162#13093945C2314yes—
163#13093944C2314yes—
164#13093935C2314yescomplemented
165#13093934C2314yescomplemented
166C8×Dic47C2314yescomplemented
167C22×Q8×C47C2311yescharacteristic
168C22×D4×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C2×SD16×C47C2×C418yescomplemented
171C2×SD16×C47C2314yes—
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174C4×Q8×C47—22no—
175C4×Q8×C47C2314yescomplemented
176C4×D4×C47—22no—
177C4×D4×C47C2314yes—
178C2×C4⋊C4×C47—21no—
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47—21no—
182C2×C42×C47—21no—
183C2×C42×C47C2311yescharacteristic
184#106×C47C2314yescomplemented
185#103×C47C2314yescomplemented
186#102×C47C2314yes—
187C4×C8×C47C2314yescomplemented
188C24×C47—21no—
189C23×D47—21no—
190C23×D47—28no—
191C23×D47—24no—
192C23×D47—82no—
193C23×D47—82no—
194C23×D47C2×D411yescharacteristic
195C2×Q8×C47—21no—
196C2×Q8×C47—22no—
197C2×Q8×C47C22×C414yes—
198C2×Q8×C47C2412yes—
199C2×D4×C47—21no—
200C2×D4×C47—22no—
201C2×D4×C47C22×C414yes—
202C2×D4×C47C2412yes—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—24no—
207C22×C4×C47—82no—
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2411yescharacteristic
211C2×C22⋊D47—28no—
212C2×C22⋊D47—24no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—24no—
217C22×Dic47—82no—
218C22×Dic47C2×D411yescharacteristic
219C22×Dic47C2×D411yescharacteristic
220C22×Dic47C2×D411yescharacteristic
221Q8×D47—216no—
222Q8×D47—28no—
223Q8×D47C22×C4116yescomplemented
224D4×D47—216no—
225D4×D47—28no—
226D4×D47C22×C4116yes—
227C2×D188—21no—
228C2×D188—22no—
229C2×D188C22×C414yes—
230C2×D188C2412yes—
231C2×C4×D47—28no—
232C2×C4×D47—24no—
233C2×C4×D47—24no—
234C2×C4×D47—24no—
235C2×C4×D47—82no—
236C2×C4×D47—82no—
237C2×C4×D47C22×C414yes—
238C2×C4×D47C2×D412yes—
239C2×C4×D47#4114yes—
240C2×C4×D47C2412yes—
241C2×Dic94—21no—
242C2×Dic94—22no—
243C2×Dic94—28no—
244C2×Dic94—24no—
245C2×Dic94C22×C414yes—
246C2×Dic94C2412yes—
247SD16×C47C22×C4116yescomplemented
248C2×C8×C47—22no—
249C2×C8×C47C22×C414yes—
250C2×C8×C47C2412yes—
251C2×C8×C47C2412yes—
252C4⋊C4×C47—24no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47C2412yes—
256C4⋊C4×C47C2412yes—
257C22⋊C4×C47—24no—
258C42×C47—24no—
259C42×C47C2×D412yes—
260C42×C47C2412yes—
261C22⋊Dic47—24no—
262#10625336C22×C4116yescomplemented
263#10625335C22×C4116yescomplemented
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4C2×D414yes—
269(C2×D47)⋊C4C2×D414yes—
270C4⋊Dic47—21no—
271C4⋊Dic47—21no—
272C4⋊Dic47—24no—
273C4⋊Dic47C2412yes—
274C4⋊Dic47C2412yes—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4C2×D414yes—
278Dic47⋊C4C2×D414yes—
279C4×Dic47—24no—
280C4×Dic47—24no—
281C4×Dic47—24no—
282C4×Dic47—24no—
283C4×Dic47—24no—
284C4×Dic47C2×D412yes—
285C4×Dic47C2412yes—
286C2×C47⋊C8—22no—
287C2×C47⋊C8C22×C414yes—
288C2×C47⋊C8C2412yes—
289C2×C47⋊C8C2412yes—
290#10625325C22×C4116yescomplemented
291#10625324—28no—
292C8×D47C22×C4116yescomplemented
293C23×C47—24no—
294C23×C47—22no—
295C23×C47—42no—
296C23×C47—42no—
297C23×C47C22×D411yescharacteristic
298C22×D47—22no—
299C22×D47—22no—
300C22×D47—24no—
301C22×D47—22no—
302C22×D47—216no—
303C22×D47—42no—
304C22×D47—42no—
305C22×D47—816no—
306C22×D47—84no—
307C22×D47—84no—
308C22×D47C4×D414yes—
309C22×D47C22×D412yes—
310Q8×C47—24no—
311Q8×C47—22no—
312Q8×C47C23×C414yes—
313D4×C47—24no—
314D4×C47—22no—
315D4×C47C23×C414yes—
316C2×C4×C47—24no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—42no—
323C2×C4×C47—42no—
324C2×C4×C47—84no—
325C2×C4×C47C23×C412yes—
326C2×C4×C47C22×D412yes—
327C2×C4×C47C22×D412yes—
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C2×#4112yes—
330C2×C4×C47C2511yescharacteristic
331C22⋊D47—216no—
332C2×Dic47—24no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—42no—
339C2×Dic47—42no—
340C2×Dic47—84no—
341C2×Dic47C4×D414yes—
342C2×Dic47C22×D412yes—
343C2×Dic47C22×D412yes—
344C2×Dic47C22×D412yes—
345D188—24no—
346D188—22no—
347D188C23×C414yes—
348C4×D47—216no—
349C4×D47—84no—
350C4×D47—84no—
351C4×D47C4×D418yes—
352C4×D47C23×C414yes—
353C4×D47C2×#4114yes—
354Dic94—24no—
355Dic94—22no—
356Dic94—216no—
357Dic94C23×C414yes—
358C8×C47—22no—
359C8×C47C23×C414yes—
360C47⋊C8—22no—
361C47⋊C8C23×C414yes—
362C2×#2949—471nomaximal, Sylow
363C22×C47—24no—
364C22×C47—48no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47C2×C4×D412yes—
368C22×C47#57712yes—
369C22×C47#57712yes—
370C22×C47C23×D411yescharacteristic
371C2×D47—28no—
372C2×D47—22no—
373C2×D47—22no—
374C2×D47—24no—
375C2×D47—48no—
376C2×D47—42no—
377C2×D47—42no—
378C2×D47—816no—
379C2×D47C2×C4×D414yes—
380C4×C47—24no—
381C4×C47—22no—
382C4×C47—22no—
383C4×C47—42no—
384C4×C47—42no—
385C4×C47C2×C4×D412yes—
386C4×C47C24×C411yescharacteristic
387C4×C47C22×#4111yescharacteristic
388Dic47—24no—
389Dic47—22no—
390Dic47—22no—
391Dic47—42no—
392Dic47—42no—
393Dic47C2×C4×D414yes—
394C23×SD16—471no—
395C2×#519—471no—
396C2×#518—471no—
397#2949—4716no—
398C2×#440—471no—
399C2×#440—471no—
400C2×#440—471no—
401C2×#440—471no—
402C2×C4×SD16—471no—
403C2×C4×SD16—471no—
404C2×C4×SD16—471no—
405C2×C4×SD16D4711yescharacteristic, complemented
406C2×#427—471no—
407C2×#419—471no—
408C2×#418—471no—
409C2×#405—471no—
410C2×C47—44no—
411C2×C47#294914yescomplemented
412C2×C47C22×C4×D411yescharacteristic
413C2×C47C2×#57711yescharacteristic
414C2×C47C2×#57711yescharacteristic
415D47—24no—
416D47—44no—
417C23×Q8—471no—
418C23×D4—471no—
419C22×SD16—471no—
420C22×SD16—471no—
421C22×SD16—4716no—
422C22×SD16—478no—
423C22×SD16—471no—
424C22×SD16C2×D4711yescharacteristic
425C22×M16—471no—
426C23×C8—471no—
427#519—478no—
428#519—944no—
429#518—478no—
430#518—944no—
431C2×C4×Q8—471no—
432C2×C4×Q8—471no—
433C2×C4×Q8—471no—
434C2×C4×Q8—941no—
435C2×C4×Q8—941no—
436C2×C4×Q8C2×D4711yescharacteristic, complemented
437C2×C4×D4—471no—
438C2×C4×D4—471no—
439C2×C4×D4—471no—
440C2×C4×D4—941no—
441C2×C4×D4—941no—
442C2×C4×D4C2×D4711yescharacteristic
443C2×#117—471no—
444C2×#117—471no—
445C2×#117—471no—
446C2×#117—941no—
447C2×#117—941no—
448C22×C22⋊C4—941no—
449C22×C22⋊C4—941no—
450#440—478no—
451#440—478no—
452#440—478no—
453#440—478no—
454C4×SD16—478no—
455C4×SD16—478no—
456C4×SD16—478no—
457C4×SD16C2×D4718yescomplemented
458#427—478no—
459C2×#107—471no—
460C2×#107—471no—
461C2×#106—471no—
462C2×#106C2×D4711yescharacteristic, complemented
463#419—478no—
464#418—478no—
465C2×#103—471no—
466C2×#103—471no—
467C2×#103—471no—
468C2×#103C2×D4711yescharacteristic, complemented
469C2×#102—471no—
470C2×#102—471no—
471C2×#102—471no—
472C2×#102C2×D4711yescharacteristic
473#405—478no—
474C2×#97—471no—
475C2×#97—471no—
476C2×C4×C8—471no—
477C2×C4×C8C2×D4711yescharacteristic, complemented
478C47C2×#294911yescharacteristic, complemented, Sylow
479C25—941no—
480C22×Q8—478no—
481C22×Q8—474no—
482C22×Q8—471no—
483C22×Q8—941no—
484C22×Q8—942no—
485C22×Q8—944no—
486C22×Q8C22×D4711yescharacteristic
487C22×D4—478no—
488C22×D4—474no—
489C22×D4—471no—
490C22×D4—942no—
491C22×D4—944no—
492C22×D4—941no—
493C22×D4C22×D4711yescharacteristic
494C23×C4—21no—
495C23×C4—471no—
496C23×C4—941no—
497C23×C4—941no—
498C23×C4—941no—
499C23×C4—941no—
500C2×SD16—478no—
501C2×SD16—474no—
502C2×SD16—478no—
503C2×SD16—474no—
504C2×SD16—4764no—
505C2×SD16—478no—
506C2×SD16—474no—
507C2×SD16C4×D4718yescomplemented
508C2×SD16C22×D4714yes—
509C2×M16—474no—
510C2×M16—944no—
511C22×C8—471no—
512C22×C8—478no—
513C22×C8—474no—
514C22×C8—471no—
515C22×C8C22×D4711yescharacteristic
516C22×C8C22×D4711yescharacteristic
517C4×Q8—22no—
518C4×Q8—474no—
519C4×Q8—474no—
520C4×Q8—474no—
521C4×Q8—948no—
522C4×Q8—942no—
523C4×Q8—942no—
524C4×Q8—948no—
525C4×Q8—942no—
526C4×Q8C22×D4714yescomplemented
527C4×D4—22no—
528C4×D4—474no—
529C4×D4—474no—
530C4×D4—474no—
531C4×D4—942no—
532C4×D4—942no—
533C4×D4—948no—
534C4×D4—948no—
535C4×D4—942no—
536C4×D4C22×D4714yes—
537#117—474no—
538#117—474no—
539#117—474no—
540#117—474no—
541#117—948no—
542#117—948no—
543#117—942no—
544#117—942no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—471no—
547C2×C4⋊C4—471no—
548C2×C4⋊C4—471no—
549C2×C4⋊C4—471no—
550C2×C4⋊C4—941no—
551C2×C4⋊C4—941no—
552C2×C4⋊C4—941no—
553C2×C4⋊C4C22×D4711yescharacteristic
554C2×C4⋊C4C22×D4711yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—471no—
557C2×C22⋊C4—471no—
558C2×C22⋊C4—948no—
559C2×C22⋊C4—948no—
560C2×C22⋊C4—941no—
561C2×C22⋊C4—941no—
562C2×C22⋊C4—941no—
563C2×C22⋊C4—941no—
564C2×C22⋊C4—941no—
565C2×C42—21no—
566C2×C42—471no—
567C2×C42—941no—
568C2×C42—941no—
569C2×C42—941no—
570C2×C42—941no—
571C2×C42—941no—
572C2×C42C22×D4711yescharacteristic
573#107—474no—
574#107—474no—
575#106—474no—
576#106C22×D4714yescomplemented
577#103—474no—
578#103—474no—
579#103—474no—
580#103C22×D4714yescomplemented
581#102—474no—
582#102—474no—
583#102—474no—
584#102C22×D4714yes—
585#97—474no—
586#97—474no—
587C4×C8—474no—
588C4×C8C22×D4714yescomplemented
589C24—21no—
590C24—471no—
591C24—944no—
592C24—948no—
593C24—941no—
594C24—3762no—
595C24—3762no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—4716no—
599C2×Q8—474no—
600C2×Q8—472no—
601C2×Q8—944no—
602C2×Q8—948no—
603C2×Q8—9416no—
604C2×Q8—948no—
605C2×Q8—941no—
606C2×Q8—942no—
607C2×Q8C2×C4×D4714yes—
608C2×Q8C23×D4712yes—
609C2×D4—21no—
610C2×D4—22no—
611C2×D4—4716no—
612C2×D4—474no—
613C2×D4—472no—
614C2×D4—9416no—
615C2×D4—948no—
616C2×D4—944no—
617C2×D4—948no—
618C2×D4—941no—
619C2×D4—942no—
620C2×D4C2×C4×D4714yes—
621C2×D4C23×D4712yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—82no—
627C22×C4—471no—
628C22×C4—474no—
629C22×C4—472no—
630C22×C4—474no—
631C22×C4—472no—
632C22×C4—471no—
633C22×C4—471no—
634C22×C4—944no—
635C22×C4—944no—
636C22×C4—948no—
637C22×C4—944no—
638C22×C4—941no—
639C22×C4—941no—
640C22×C4—941no—
641C22×C4—944no—
642C22×C4—3762no—
643C22×C4—3762no—
644C22×C4—3762no—
645C22×C4D4×D4711yescharacteristic
646C22×C4D4×D4711yescharacteristic
647C22×C4C23×D4711yescharacteristic
648SD16—4716no—
649SD16—4716no—
650SD16—4716no—
651SD16C2×C4×D47116yescomplemented
652M16—948no—
653C2×C8—22no—
654C2×C8—474no—
655C2×C8—472no—
656C2×C8—4716no—
657C2×C8—472no—
658C2×C8—942no—
659C2×C8C2×C4×D4714yes—
660C2×C8C23×D4712yes—
661C2×C8C23×D4712yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—474no—
666C4⋊C4—474no—
667C4⋊C4—472no—
668C4⋊C4—472no—
669C4⋊C4—944no—
670C4⋊C4—944no—
671C4⋊C4—944no—
672C4⋊C4—941no—
673C4⋊C4—941no—
674C4⋊C4C23×D4712yes—
675C4⋊C4C23×D4712yes—
676C22⋊C4—24no—
677C22⋊C4—474no—
678C22⋊C4—474no—
679C22⋊C4—944no—
680C22⋊C4—944no—
681C22⋊C4—944no—
682C22⋊C4—944no—
683C22⋊C4—944no—
684C42—24no—
685C42—472no—
686C42—472no—
687C42—944no—
688C42—944no—
689C42—944no—
690C42—944no—
691C42—944no—
692C42D4×D4712yes—
693C42C23×D4712yes—
694C23—24no—
695C23—22no—
696C23—42no—
697C23—42no—
698C23—474no—
699C23—472no—
700C23—9416no—
701C23—942no—
702C23—942no—
703C23—944no—
704C23—942no—
705C23—37616no—
706C23—3764no—
707C23—3764no—
708C23—1882no—
709C23—1882no—
710C23C2×D4×D4711yescharacteristic
711Q8—24no—
712Q8—22no—
713Q8—474no—
714Q8—9416no—
715Q8—944no—
716Q8—942no—
717Q8C22×C4×D4714yes—
718D4—24no—
719D4—22no—
720D4—474no—
721D4—9416no—
722D4—944no—
723D4—942no—
724D4C22×C4×D4714yes—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—84no—
734C2×C4—474no—
735C2×C4—472no—
736C2×C4—478no—
737C2×C4—474no—
738C2×C4—474no—
739C2×C4—472no—
740C2×C4—472no—
741C2×C4—9416no—
742C2×C4—944no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—942no—
747C2×C4—942no—
748C2×C4—3764no—
749C2×C4—3764no—
750C2×C4—3764no—
751C2×C4—1882no—
752C2×C4—1882no—
753C2×C4C22×C4×D4712yes—
754C2×C4C2×D4×D4712yes—
755C2×C4C2×D4×D4712yes—
756C2×C4C2×D4×D4711yescharacteristic
757C2×C4#41×D4712yes—
758C2×C4C24×D4711yescharacteristic
759C8—22no—
760C8—474no—
761C8—942no—
762C8C22×C4×D4714yes—
763C22—24no—
764C22—48no—
765C22—42no—
766C22—42no—
767C22—474no—
768C22—948no—
769C22—942no—
770C22—942no—
771C22—944no—
772C22—37616no—
773C22—1888no—
774C22—1882no—
775C22—1882no—
776C22C4×D4×D4712yes—
777C22#1568992912yes—
778C22#1568993012yes—
779C22C22×D4×D4711yescharacteristic
780C4—24no—
781C4—22no—
782C4—22no—
783C4—42no—
784C4—42no—
785C4—474no—
786C4—944no—
787C4—942no—
788C4—942no—
789C4—1882no—
790C4—1882no—
791C4C4×D4×D4712yes—
792C4C23×C4×D4711yescharacteristic
793C4C2×#41×D4711yescharacteristic
794C2—44no—
795C2—944no—
796C2—1884no—
797C2#2025224214yesdirect product factor
798C2C2×C4×D4×D4711yescharacteristic
799C2C2×#1568992911yescharacteristic
800C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C4×SD16×C47C2
socleC23×C47C22×D4
prime radicalC22×D4×D47C22
cosocleC2×C4×C47C25
hypercenterC2×C4×SD16D47
hypocenterC47C2×#2949
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#15689599C2semidirect
4. #20252242C2direct (N × H)
5. C2×#15689226C2semidirect
6. C2×#15689223C2semidirect
7. C2×#15689221C2semidirect
8. C2×#15689220C2semidirect
9. C2×C4×#10625325C2semidirect
10. C2×SD16×Dic47C2semidirect
11. C2×#15689210C2semidirect
12. C2×#15689158C2semidirect
13. C2×#15689130C2semidirect
15. C2×#15689077C2semidirect
16. C2×C4×SD16×C47C2semidirect
22. C2×SD16×D47C4semidirect
27. #15689599C22semidirect
30. C2×Q8×Dic47C22semidirect
32. C2×C4×Dic94C22semidirect
34. C2×#13093989C22semidirect
47. #15689226C22semidirect
48. #15689223C22semidirect
49. #15689221C22semidirect
50. #15689220C22semidirect
51. C4×#10625325C22semidirect
52. SD16×Dic47C22semidirect
53. #15689210C22semidirect
54. #15689158C22semidirect
55. C2×#13093957C22semidirect
56. C2×#13093957C22semidirect
57. C2×#13093956C22semidirect
58. #15689130C22semidirect
60. C2×#13093949C22semidirect
61. C2×#13093948C22semidirect
62. C2×#13093947C22semidirect
66. #15689077C22semidirect
67. C2×#13093935C22semidirect
68. C2×#13093934C22semidirect
69. C2×C8×Dic47C22semidirect
71. C2×C4×Q8×C47C22semidirect
73. C4×SD16×C47C22semidirect
74. C2×#106×C47C22semidirect
75. C2×#103×C47C22semidirect
77. C2×C4×C8×C47C22semidirect
83. C2×Q8×D47C2×C4semidirect
96. C2×#10625325C2×C4semidirect
98. C2×#10625335C2×C4semidirect
100. C2×#10625336C2×C4semidirect
102. SD16×D47C2×C4semidirect
107. C2×C8×D47C2×C4semidirect
110. Q8×Dic47C23semidirect
113. C4×Dic94C23semidirect
116. #13093989C23semidirect
155. #13093957C23semidirect
156. #13093957C23semidirect
157. #13093956C23semidirect
158. #13093949C23semidirect
159. #13093948C23semidirect
160. #13093947C23semidirect
164. #13093935C23semidirect
165. #13093934C23semidirect
166. C8×Dic47C23semidirect
170. C2×SD16×C47C2×C4semidirect
175. C4×Q8×C47C23semidirect
184. #106×C47C23semidirect
185. #103×C47C23semidirect
187. C4×C8×C47C23semidirect
223. Q8×D47C22×C4semidirect
247. SD16×C47C22×C4semidirect
262. #10625336C22×C4semidirect
263. #10625335C22×C4semidirect
290. #10625325C22×C4semidirect
292. C8×D47C22×C4semidirect
405. C2×C4×SD16D47semidirect
411. C2×C47#2949semidirect
436. C2×C4×Q8C2×D47semidirect
457. C4×SD16C2×D47semidirect
462. C2×#106C2×D47semidirect
468. C2×#103C2×D47semidirect
477. C2×C4×C8C2×D47semidirect
478. C47C2×#2949semidirect
507. C2×SD16C4×D47semidirect
526. C4×Q8C22×D47semidirect
576. #106C22×D47semidirect
580. #103C22×D47semidirect
588. C4×C8C22×D47semidirect
651. SD16C2×C4×D47semidirect
797. C2#20252242direct (N × H)

Maximal subgroups

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

subgroupindex
C22×SD16×D472
C2×#156895992
C2×#156895952
#202522422
C2×#156892262
C2×#156892232
C2×#156892212
C2×#156892202
C2×C4×#106253252
C2×SD16×Dic472
C2×#156892102
C2×#156891582
C2×#156891302
C2×#156891262
C2×#156890772
C2×C4×SD16×C472
C2×#294947