Finite Group Databasebeta

← C2×#20254101 #27086215

Subgroups — C2×#20254101 #27086215

Order 12032.

2234 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689675C211yesmaximal, characteristic, complemented
2C2×#15689668C211yesmaximal, characteristic
3#20254101C2116yesmaximal, direct product factor
4C2×#15689527C211yesmaximal, characteristic, complemented
5C2×#15689494C211yesmaximal, characteristic, complemented
6C2×#15689472C211yesmaximal, characteristic, complemented
7C2×#15689468C211yesmaximal, characteristic, complemented
8C2×#15689371C211yesmaximal, characteristic, complemented
9C2×#15689369C211yesmaximal, characteristic, complemented
10C2×#15689367C211yesmaximal, characteristic, complemented
11C2×#15689226C211yesmaximal, characteristic, complemented
12C2×#15689224C211yesmaximal, characteristic, complemented
13C2×#15689222C211yesmaximal, characteristic, complemented
14C2×#15689220C211yesmaximal, characteristic, complemented
15C2×M16×Dic47C211yesmaximal, characteristic, complemented
16C2×C47×#468C211yesmaximal, characteristic, complemented
17C22×#10625352—21no—
18C22×#10625325C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625329C2211yescharacteristic
22#15689675—24no—
23#15689675C2218yescomplemented
24#15689668—24no—
25#15689668C2218yes—
26C2×#13094023C2211yescharacteristic
27C2×#13094023C2211yescharacteristic
28C2×#13094022C2211yescharacteristic
29C2×#13094020C2211yescharacteristic
30C2×#13094014—21no—
31C2×#13094010—21no—
32C2×#13094003C2211yescharacteristic
33C2×#13094001—21no—
34C2×#13093998C2211yescharacteristic
35C2×#13093996—21no—
36C2×Q8×Dic47C2211yescharacteristic
37C2×#13093989—21no—
38C2×#13093989C2211yescharacteristic
39C2×D4×Dic47C2211yescharacteristic
40C2×#13093986C2211yescharacteristic
41C2×(C22⋊D47)⋊C4—21no—
42C2×#13093980—21no—
43C22×C4×Dic47C2211yescharacteristic
44#15689527C2218yescomplemented
45#15689494C2218yescomplemented
46#15689472C2218yescomplemented
47#15689468C2218yescomplemented
48#15689371C2218yescomplemented
49#15689369C2218yescomplemented
50#15689367C2218yescomplemented
51#15689226C2218yescomplemented
52#15689224C2218yescomplemented
53#15689222C2218yescomplemented
54#15689220C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093949C2211yescharacteristic
59C2×#13093948C2211yescharacteristic
60C2×#13093947C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093945C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64M16×Dic47C2218yescomplemented
65C2×#13093934C2211yescharacteristic
66C2×#13093934C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic
73C47×#468C2218yescomplemented
74C2×#107×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C2×#10625352—28no—
78C2×#10625352—48no—
79C22×Dic94—21no—
80C22×Dic94—21no—
81C22×Dic94C2311yescharacteristic
82C22×D188C2311yescharacteristic
83C22×C22⋊D47—21no—
84C22×C22⋊D47—21no—
85C22×C22⋊D47—21no—
86C23×Dic47—21no—
87C23×Dic47D411yescharacteristic
88C23×Dic47D411yescharacteristic
89C22×C4×D47—21no—
90C2×#10625325—24no—
91C2×#10625325C2314yes—
92C2×#10625335—24no—
93C2×#10625335C2314yes—
94C2×#10625336—24no—
95C2×#10625336C2314yes—
96C2×#10625329—24no—
97C2×#10625329C2314yes—
98C22×C47⋊C8C2311yescharacteristic
99C22×C47⋊C8C2311yescharacteristic
100#13094023—22no—
101#13094023—22no—
102#13094023C2314yes—
103#13094023C2314yes—
104#13094022—22no—
105#13094022C2314yes—
106#13094020—22no—
107#13094020C2314yes—
108#13094014—28no—
109#13094010—28no—
110#13094003—22no—
111#13094003C2314yes—
112#13094001—28no—
113#13093998—22no—
114#13093998C2314yes—
115#13093996—28no—
116Q8×Dic47—22no—
117Q8×Dic47C2314yes—
118#13093989—28no—
119#13093989—22no—
120#13093989C2314yes—
121D4×Dic47—22no—
122D4×Dic47C2314yes—
123#13093986—22no—
124#13093986C2314yes—
125(C22⋊D47)⋊C4—28no—
126#13093980—28no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47D411yescharacteristic
143C2×C4×Dic47D411yescharacteristic
144C2×C4×Dic47D414yes—
145C2×C4×Dic47C2311yescharacteristic
146C2×C4×Dic47C2311yescharacteristic
147C2×C4×Dic47C2314yes—
148#13093958C2314yes—
149#13093957C2314yes—
150#13093957C2314yes—
151#13093949C2314yes—
152#13093948C2314yes—
153#13093947C2314yes—
154#13093946C2314yes—
155#13093945C2314yes—
156#13093944C2314yes—
157#13093934C2314yes—
158#13093934C2314yes—
159C8×Dic47C2314yes—
160C8×Dic47C2314yes—
161C22×Q8×C47C2311yescharacteristic
162C22×D4×C47—21no—
163C22×D4×C47C2311yescharacteristic
164C23×C4×C47C2311yescharacteristic
165C2×SD16×C47—24no—
166C2×SD16×C47C2314yes—
167C2×M16×C47—24no—
168C2×M16×C47C2314yes—
169C22×C8×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C22⋊Q8×C47—22no—
172C22⋊Q8×C47C2314yes—
173#121×C47—22no—
174#121×C47C2314yes—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180#107×C47C2314yes—
181#103×C47C2314yes—
182#102×C47C2314yes—
183C24×C47—21no—
184C24×C47C2×D411yescharacteristic
185C23×D47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47C2412yes—
190C2×D4×C47—24no—
191C2×D4×C47—21no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—44no—
195C2×D4×C47C2412yes—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D412yes—
203C22×C4×C47C2412yes—
204C22×C4×C47C2411yescharacteristic
205C2×C22⋊D47—24no—
206C2×C22⋊D47—24no—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—44no—
209C2×C22⋊D47—44no—
210C2×C22⋊D47—44no—
211C22×Dic47—24no—
212C22×Dic47—24no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—24no—
217C22×Dic47—44no—
218C22×Dic47C2×D411yescharacteristic
219C22×Dic47C2×D411yescharacteristic
220C22×Dic47C2×D414yes—
221C22×Dic47C2×D414yes—
222C22×Dic47C2×D411yescharacteristic
223C22×Dic47C2×D411yescharacteristic
224#10625352—432no—
225C2×D188—22no—
226C2×D188—22no—
227C2×D188—21no—
228C2×D188C2412yes—
229C2×C4×D47—24no—
230C2×C4×D47—44no—
231C2×Dic94—22no—
232C2×Dic94—22no—
233C2×Dic94—21no—
234C2×Dic94—24no—
235C2×Dic94—24no—
236C2×Dic94—44no—
237C2×Dic94—44no—
238C2×Dic94C2412yes—
239SD16×C47—28no—
240M16×C47—28no—
241C2×C8×C47—22no—
242C2×C8×C47#4114yescomplemented
243C2×C8×C47C2412yes—
244C2×C8×C47C2412yes—
245C4⋊C4×C47—24no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47C2412yes—
249C4⋊C4×C47C2412yes—
250C22⋊C4×C47—24no—
251C22⋊C4×C47—24no—
252C22⋊Dic47—24no—
253C22⋊Dic47—24no—
254#10625336—28no—
255#10625335—28no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4—24no—
258C4⋊Dic47—21no—
259C4⋊Dic47—21no—
260C4⋊Dic47—24no—
261C4⋊Dic47C2412yes—
262C4⋊Dic47C2412yes—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4—24no—
268Dic47⋊C4—24no—
269C4×Dic47—24no—
270C4×Dic47—24no—
271C4×Dic47C2×D414yes—
272C4×Dic47C2×D412yes—
273C4×Dic47C2×D414yes—
274C4×Dic47C2×D412yes—
275C4×Dic47C2412yes—
276C4×Dic47C2412yes—
277#10625329—28no—
278C2×C47⋊C8—22no—
279C2×C47⋊C8#4114yescomplemented
280C2×C47⋊C8C2412yes—
281C2×C47⋊C8C2412yes—
282#10625325—28no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47—42no—
288C23×C47—42no—
289C23×C47—42no—
290C23×C47C22×D412yes—
291C23×C47C22×D411yescharacteristic
292C22×D47—22no—
293C22×D47—42no—
294C22×D47—42no—
295C22×D47—42no—
296Q8×C47—22no—
297Q8×C47—22no—
298Q8×C47—42no—
299D4×C47—22no—
300D4×C47—22no—
301D4×C47—48no—
302D4×C47—42no—
303C2×C4×C47—22no—
304C2×C4×C47—24no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47C22×D412yes—
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C2×#4112yes—
316C2×C4×C47C2×#4112yes—
317C2×C4×C47C2511yescharacteristic
318C22⋊D47—48no—
319C22⋊D47—48no—
320C22⋊D47—48no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—28no—
324C2×Dic47—28no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—48no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47AGL(1,ℤ/8)14yes—
333C2×Dic47#13714yes—
334C2×Dic47C22×D412yes—
335C2×Dic47C22×D412yes—
336C2×Dic47C22×D412yes—
337C2×Dic47C22×D412yes—
338D188—22no—
339D188—22no—
340D188—42no—
341C4×D47—48no—
342Dic94—22no—
343Dic94—22no—
344Dic94—42no—
345Dic94—48no—
346Dic94—48no—
347C8×C47—22no—
348C8×C47C2×#4114yescomplemented
349C47⋊C8—22no—
350C47⋊C8C2×#4114yescomplemented
351C2×#3182—471nomaximal, Sylow
352C22×C47—22no—
353C22×C47—22no—
354C22×C47—22no—
355C22×C47—44no—
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—84no—
360C22×C47#53212yes—
361C22×C47C2×AGL(1,ℤ/8)12yes—
362C22×C47C2×#13712yes—
363C22×C47C23×D411yescharacteristic
364C2×D47—42no—
365C2×D47—42no—
366C2×D47—42no—
367C2×D47—84no—
368C4×C47—22no—
369C4×C47—42no—
370C4×C47—42no—
371C4×C47—42no—
372C4×C47#53212yes—
373C4×C47C22×#4111yescharacteristic
374C4×C47C22×#4111yescharacteristic
375Dic47—22no—
376Dic47—22no—
377Dic47—42no—
378Dic47—42no—
379Dic47—42no—
380Dic47C2×AGL(1,ℤ/8)14yes—
381Dic47C2×#13714yes—
382C2×#533—471no—
383C2×#532—471no—
384#3182—4716no—
385C2×#500—471no—
386C2×#492—471no—
387C2×#487—471no—
388C2×#486—471no—
389C2×#468—471no—
390C2×#468—471no—
391C2×#468—471no—
392C2×#468D4711yescharacteristic, complemented
393C2×#440—471no—
394C2×#440—471no—
395C2×#440—471no—
396C2×#440—471no—
397C2×C4×M16—471no—
398C2×C47—42no—
399C2×C47—82no—
400C2×C47#318214yescomplemented
401C2×C47C2×#53211yescharacteristic
402C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
403C2×C47C22×#13711yescharacteristic
404D47—82no—
405C22×#41—941no—
406C22×SD16—471no—
407C22×SD16—471no—
408C22×SD16—471no—
409C22×SD16C2×D4711yescharacteristic
410C22×M16—471no—
411C22×M16C2×D4711yescharacteristic
412#533—478no—
413#533—944no—
414#532—478no—
415#532—944no—
416C2×C4⋊Q8—471no—
417C2×C4⋊Q8—471no—
418C2×C4⋊Q8—471no—
419C2×#127—471no—
420C2×#125—941no—
421C2×#124—941no—
422C2×C22⋊Q8—471no—
423C2×C22⋊Q8—941no—
424C2×C22⋊Q8C2×D4711yescharacteristic
425C2×#121—471no—
426C2×#121—941no—
427C2×#121C2×D4711yescharacteristic
428C2×C4×Q8—471no—
429C2×C4×Q8—471no—
430C2×C4×Q8—941no—
431C2×C4×D4—471no—
432C2×C4×D4—471no—
433C2×C4×D4—941no—
434C2×#117—941no—
435C22×C42—471no—
436#500—478no—
437#492—478no—
438#487—478no—
439#486—478no—
440#468—478no—
441#468—478no—
442#468—478no—
443#468C2×D4718yescomplemented
444#440—478no—
445#440—478no—
446#440—478no—
447#440—478no—
448C2×#107—471no—
449C2×#107—471no—
450C2×#107—471no—
451C2×#107C2×D4711yescharacteristic
452C2×#103—471no—
453C2×#103—471no—
454C2×#103—471no—
455C2×#103C2×D4711yescharacteristic
456C2×#102—471no—
457C2×#102—471no—
458C2×#102—471no—
459C2×#102C2×D4711yescharacteristic
460C4×M16—478no—
461C2×#97—471no—
462C2×#97—471no—
463C2×C4×C8—471no—
464C2×C4×C8—471no—
465C47C2×#318211yescharacteristic, complemented, Sylow
466C2×#41—948no—
467C2×#41—1888no—
468C22×Q8—471no—
469C22×Q8—941no—
470C22×Q8—941no—
471C22×Q8C22×D4711yescharacteristic
472C22×D4—21no—
473C22×D4—471no—
474C22×D4—941no—
475C22×D4—941no—
476C22×D4—941no—
477C22×D4C22×D4711yescharacteristic
478C23×C4—471no—
479C23×C4—471no—
480C23×C4—941no—
481C23×C4—941no—
482C23×C4C22×D4711yescharacteristic
483C2×SD16—24no—
484C2×SD16—474no—
485C2×SD16—474no—
486C2×SD16—474no—
487C2×SD16—944no—
488C2×SD16—944no—
489C2×SD16—944no—
490C2×SD16C22×D4714yes—
491C2×M16—24no—
492C2×M16—474no—
493C2×M16—944no—
494C2×M16C22×D4714yes—
495C22×C8—471no—
496C22×C8—471no—
497C22×C8C22×D4711yescharacteristic
498C22×C8C22×D4711yescharacteristic
499C4⋊Q8—474no—
500C4⋊Q8—474no—
501C4⋊Q8—474no—
502C4⋊Q8—942no—
503C4⋊Q8—942no—
504C4⋊Q8—942no—
505#127—474no—
506#127—942no—
507#125—948no—
508#124—948no—
509C22⋊Q8—22no—
510C22⋊Q8—474no—
511C22⋊Q8—948no—
512C22⋊Q8—942no—
513C22⋊Q8C22×D4714yes—
514#121—22no—
515#121—474no—
516#121—948no—
517#121—942no—
518#121C22×D4714yes—
519C4×Q8—474no—
520C4×Q8—474no—
521C4×Q8—942no—
522C4×Q8—948no—
523C4×Q8—942no—
524C4×D4—474no—
525C4×D4—474no—
526C4×D4—948no—
527C4×D4—942no—
528C4×D4—942no—
529#117—948no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—471no—
532C2×C4⋊C4—471no—
533C2×C4⋊C4—941no—
534C2×C4⋊C4—941no—
535C2×C4⋊C4—941no—
536C2×C4⋊C4—941no—
537C2×C4⋊C4—941no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4C22×D4711yescharacteristic
541C2×C4⋊C4C22×D4711yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—941no—
545C2×C22⋊C4—941no—
546C2×C22⋊C4—941no—
547C2×C22⋊C4—941no—
548C2×C42—471no—
549C2×C42—471no—
550C2×C42—474no—
551C2×C42—471no—
552C2×C42—471no—
553C2×C42—474no—
554C2×C42—941no—
555C2×C42—941no—
556#107—474no—
557#107—474no—
558#107—474no—
559#107C22×D4714yes—
560#103—474no—
561#103—474no—
562#103—474no—
563#103C22×D4714yes—
564#102—474no—
565#102—474no—
566#102—474no—
567#102C22×D4714yes—
568#97—474no—
569#97—474no—
570C4×C8—474no—
571C4×C8—474no—
572C24—21no—
573C24—941no—
574C24D4×D4711yescharacteristic
575#41—18832no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—472no—
580C2×Q8—944no—
581C2×Q8—944no—
582C2×Q8—941no—
583C2×Q8—942no—
584C2×Q8—942no—
585C2×Q8—1884no—
586C2×Q8—1884no—
587C2×Q8C23×D4712yes—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—44no—
593C2×D4—472no—
594C2×D4—944no—
595C2×D4—944no—
596C2×D4—944no—
597C2×D4—941no—
598C2×D4—942no—
599C2×D4—942no—
600C2×D4—1884no—
601C2×D4—1884no—
602C2×D4—1884no—
603C2×D4C23×D4712yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—471no—
610C22×C4—471no—
611C22×C4—474no—
612C22×C4—474no—
613C22×C4—471no—
614C22×C4—471no—
615C22×C4—944no—
616C22×C4—944no—
617C22×C4—944no—
618C22×C4—944no—
619C22×C4—941no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—1884no—
623C22×C4—1884no—
624C22×C4D4×D4712yes—
625C22×C4D4×D4711yescharacteristic
626C22×C4C23×D4712yes—
627C22×C4C23×D4711yescharacteristic
628SD16—28no—
629SD16—948no—
630SD16—948no—
631SD16—948no—
632M16—28no—
633M16—948no—
634C2×C8—22no—
635C2×C8—474no—
636C2×C8—472no—
637C2×C8—472no—
638C2×C8—942no—
639C2×C8#1062535214yescomplemented
640C2×C8C23×D4712yes—
641C2×C8C23×D4712yes—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—472no—
646C4⋊C4—472no—
647C4⋊C4—944no—
648C4⋊C4—944no—
649C4⋊C4—944no—
650C4⋊C4—944no—
651C4⋊C4—944no—
652C4⋊C4—944no—
653C4⋊C4—944no—
654C4⋊C4—941no—
655C4⋊C4—941no—
656C4⋊C4C23×D4712yes—
657C4⋊C4C23×D4712yes—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—944no—
661C22⋊C4—944no—
662C22⋊C4—944no—
663C22⋊C4—944no—
664C42—472no—
665C42—474no—
666C42—474no—
667C42—472no—
668C42—472no—
669C42—472no—
670C42—944no—
671C42—944no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—942no—
680C23—1882no—
681C23—1882no—
682C23—1882no—
683C23C2×D4×D4712yes—
684C23C2×D4×D4711yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—42no—
688Q8—942no—
689Q8—942no—
690Q8—1888no—
691Q8—1888no—
692Q8—1882no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—42no—
697D4—942no—
698D4—942no—
699D4—1888no—
700D4—1888no—
701D4—1888no—
702D4—1882no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—474no—
714C2×C4—474no—
715C2×C4—472no—
716C2×C4—472no—
717C2×C4—472no—
718C2×C4—472no—
719C2×C4—948no—
720C2×C4—948no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—1888no—
727C2×C4—1888no—
728C2×C4—1882no—
729C2×C4—1882no—
730C2×C4—1882no—
731C2×C4C2×D4×D4712yes—
732C2×C4C2×D4×D4711yescharacteristic
733C2×C4#41×D4712yes—
734C2×C4C2×#1062535212yes—
735C2×C4C24×D4711yescharacteristic
736C8—22no—
737C8—474no—
738C8—942no—
739C8C2×#1062535214yescomplemented
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—3764no—
749C22—1882no—
750C22—1882no—
751C22—1882no—
752C22#1568966812yes—
753C22AGL(1,ℤ/8)×D4712yes—
754C22#137×D4712yes—
755C22C22×D4×D4711yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—474no—
761C4—474no—
762C4—942no—
763C4—942no—
764C4—1882no—
765C4—1882no—
766C4—1882no—
767C4#1568966812yes—
768C4C2×#41×D4711yescharacteristic
769C4C22×#1062535211yescharacteristic
770C2—42no—
771C2—82no—
772C2—3762no—
773C2#2025410114yesdirect product factor
774C2C2×#1568966811yescharacteristic
775C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
776C2C2×#137×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#468C2
socleC23×C47C22×D4
prime radicalC2×#15689668C2
hypercenterC2×#468D47
hypocenterC47C2×#3182
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#15689675C2semidirect
3. #20254101C2direct (N × H)
4. C2×#15689527C2semidirect
5. C2×#15689494C2semidirect
6. C2×#15689472C2semidirect
7. C2×#15689468C2semidirect
8. C2×#15689371C2semidirect
9. C2×#15689369C2semidirect
10. C2×#15689367C2semidirect
11. C2×#15689226C2semidirect
12. C2×#15689224C2semidirect
13. C2×#15689222C2semidirect
14. C2×#15689220C2semidirect
15. C2×M16×Dic47C2semidirect
16. C2×C47×#468C2semidirect
23. #15689675C22semidirect
44. #15689527C22semidirect
45. #15689494C22semidirect
46. #15689472C22semidirect
47. #15689468C22semidirect
48. #15689371C22semidirect
49. #15689369C22semidirect
50. #15689367C22semidirect
51. #15689226C22semidirect
52. #15689224C22semidirect
53. #15689222C22semidirect
54. #15689220C22semidirect
64. M16×Dic47C22semidirect
73. C47×#468C22semidirect
242. C2×C8×C47#41semidirect
279. C2×C47⋊C8#41semidirect
348. C8×C47C2×#41semidirect
350. C47⋊C8C2×#41semidirect
392. C2×#468D47semidirect
400. C2×C47#3182semidirect
443. #468C2×D47semidirect
465. C47C2×#3182semidirect
639. C2×C8#10625352semidirect
739. C8C2×#10625352semidirect
773. C2#20254101direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896752
C2×#156896682
#202541012
C2×#156895272
C2×#156894942
C2×#156894722
C2×#156894682
C2×#156893712
C2×#156893692
C2×#156893672
C2×#156892262
C2×#156892242
C2×#156892222
C2×#156892202
C2×M16×Dic472
C2×C47×#4682
C2×#318247