Finite Group Databasebeta

← C2×#20254784 #27089161

Subgroups — C2×#20254784 #27089161

Order 12032.

1930 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689657C211yesmaximal, characteristic, complemented
2#20254784C2116yesmaximal, direct product factor
3C2×#15689430C211yesmaximal, characteristic, complemented
4C2×#15689427C211yesmaximal, characteristic, complemented
5C2×#15689423C211yesmaximal, characteristic, complemented
6C2×#15689420C211yesmaximal, characteristic, complemented
7C2×#15689379C211yesmaximal, characteristic, complemented
8C2×#15689374C211yesmaximal, characteristic
9C2×#15689371C211yesmaximal, characteristic, complemented
10C2×#15689367C211yesmaximal, characteristic, complemented
11C2×#15689345C211yesmaximal, characteristic, complemented
12C2×#15689342C211yesmaximal, characteristic, complemented
13C2×#15689338C211yesmaximal, characteristic, complemented
14C2×#15689335C211yesmaximal, characteristic, complemented
15C2×#15689147C211yesmaximal, characteristic, complemented
16C2×C47×#529C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625335C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21C22×#10625329C2211yescharacteristic
22C22×#10625329C2211yescharacteristic
23#15689657—24no—
24#15689657C2218yescomplemented
25C2×#13094018—21no—
26C2×#13094016C2211yescharacteristic
27C2×#13094012C2211yescharacteristic
28C2×#13094007—21no—
29C2×#13094003C2211yescharacteristic
30C2×#13093998C2211yescharacteristic
31C2×C4×Dic94C2211yescharacteristic
32C2×C4×D188C2211yescharacteristic
33C2×C4×C22⋊D47—21no—
34C2×#13093981—21no—
35#15689430C2218yescomplemented
36#15689427C2218yescomplemented
37#15689423C2218yescomplemented
38#15689420C2218yescomplemented
39#15689379C2218yescomplemented
40#15689374C2218yes—
41#15689371C2218yescomplemented
42#15689367C2218yescomplemented
43#15689345C2218yescomplemented
44#15689342C2218yescomplemented
45#15689338C2218yescomplemented
46#15689335C2218yescomplemented
47C2×#13093957C2211yescharacteristic
48C2×#13093957C2211yescharacteristic
49C2×#13093955C2211yescharacteristic
50C2×#13093955C2211yescharacteristic
51#15689147C2218yescomplemented
52C2×C4⋊(C47⋊C8)C2211yescharacteristic
53C2×C4⋊(C47⋊C8)C2211yescharacteristic
54C2×C4⋊(C47⋊C8)C2211yescharacteristic
55C2×C4⋊(C47⋊C8)C2211yescharacteristic
56C2×#13093948C2211yescharacteristic
57C2×#13093948C2211yescharacteristic
58C2×#13093947C2211yescharacteristic
59C2×#13093947C2211yescharacteristic
60C2×#13093945C2211yescharacteristic
61C2×#13093945C2211yescharacteristic
62C2×#13093944C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C47×#529—24no—
65C47×#529C2218yescomplemented
66C2×#126×C47—21no—
67C2×#125×C47C2211yescharacteristic
68C2×#124×C47C2211yescharacteristic
69C2×#123×C47—21no—
70C2×C22⋊Q8×C47C2211yescharacteristic
71C2×#121×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic
73C2×C4×D4×C47—21no—
74C2×C4×D4×C47C2211yescharacteristic
75C2×#117×C47—21no—
76C22×C42×C47C2211yescharacteristic
77C22×Dic94C2311yescharacteristic
78C22×D188C2311yescharacteristic
79C22×C22⋊D47—21no—
80C22×C4×D47—21no—
81C2×#10625337—42no—
82C2×#10625337C2314yes—
83C2×#10625335—42no—
84C2×#10625335C2314yes—
85C2×#10625336—42no—
86C2×#10625336C2314yes—
87C2×#10625334—42no—
88C2×#10625334C2314yes—
89C2×#10625329—42no—
90C2×#10625329—42no—
91C2×#10625329C2314yes—
92C2×#10625329C2314yes—
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97#13094018—28no—
98#13094016—22no—
99#13094016C2314yes—
100#13094012—22no—
101#13094012C2314yes—
102#13094007—28no—
103#13094003—22no—
104#13094003C2314yes—
105#13093998—22no—
106#13093998C2314yes—
107C4×Dic94—22no—
108C4×Dic94C2314yes—
109C4×D188—22no—
110C4×D188C2314yes—
111C4×C22⋊D47—28no—
112#13093981—28no—
113C2×C4⋊Dic47C2311yescharacteristic
114C2×C4⋊Dic47C2311yescharacteristic
115C2×Dic47⋊C4—21no—
116C2×Dic47⋊C4—21no—
117C2×Dic47⋊C4—21no—
118C2×Dic47⋊C4—21no—
119C2×C22⋊Dic47—21no—
120C2×(C2×D47)⋊C4—21no—
121C2×(C2×D47)⋊C4—21no—
122C2×(C2×D47)⋊C4—21no—
123C2×(C2×D47)⋊C4—21no—
124C2×C4×Dic47—21no—
125#13093957C2314yes—
126#13093957C2314yes—
127#13093955C2314yes—
128#13093955C2314yes—
129C4⋊(C47⋊C8)C2314yes—
130C4⋊(C47⋊C8)C2314yes—
131C4⋊(C47⋊C8)C2314yes—
132C4⋊(C47⋊C8)C2314yes—
133#13093948C2314yes—
134#13093948C2314yes—
135#13093947C2314yes—
136#13093947C2314yes—
137#13093945C2314yes—
138#13093945C2314yes—
139#13093944C2314yes—
140#13093944C2314yes—
141C22×Q8×C47C2311yescharacteristic
142C22×D4×C47—21no—
143C22×D4×C47C2311yescharacteristic
144C23×C4×C47—21no—
145C23×C4×C47D411yescharacteristic
146C23×C4×C47D411yescharacteristic
147C23×C4×C47C2311yescharacteristic
148#126×C47—28no—
149#125×C47—22no—
150#125×C47C2314yes—
151#124×C47—22no—
152#124×C47C2314yes—
153#123×C47—28no—
154C22⋊Q8×C47—22no—
155C22⋊Q8×C47C2314yes—
156#121×C47—22no—
157#121×C47C2314yes—
158C4×Q8×C47—22no—
159C4×Q8×C47C2314yes—
160C4×D4×C47—28no—
161C4×D4×C47—22no—
162C4×D4×C47C2314yes—
163#117×C47—28no—
164C2×C4⋊C4×C47—21no—
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47—21no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C22⋊C4×C47—21no—
171C2×C22⋊C4×C47—21no—
172C2×C22⋊C4×C47—21no—
173C2×C22⋊C4×C47—21no—
174C2×C22⋊C4×C47—21no—
175C2×C42×C47—21no—
176C2×C42×C47D411yescharacteristic
177C2×C42×C47D411yescharacteristic
178C2×C42×C47D414yes—
179C2×C42×C47C2311yescharacteristic
180C2×C42×C47C2311yescharacteristic
181C2×C42×C47C2314yes—
182C24×C47—21no—
183C24×C47C2×D411yescharacteristic
184C23×D47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47C2412yes—
189C2×D4×C47—24no—
190C2×D4×C47—21no—
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47—44no—
194C2×D4×C47C2412yes—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—24no—
201C22×C4×C47—42no—
202C22×C4×C47—42no—
203C22×C4×C47—44no—
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D412yes—
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D414yes—
211C22×C4×C47C2×D414yes—
212C22×C4×C47C2412yes—
213C22×C4×C47C2411yescharacteristic
214C2×C22⋊D47—24no—
215C2×C22⋊D47—44no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C2×D188—22no—
220C2×D188—22no—
221C2×D188—21no—
222C2×D188C2412yes—
223C2×C4×D47—24no—
224C2×C4×D47—44no—
225C2×Dic94—22no—
226C2×Dic94—22no—
227C2×Dic94—21no—
228C2×Dic94C2412yes—
229C4⋊C4×C47—24no—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—24no—
232C4⋊C4×C47—24no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C22⋊C4×C47—24no—
238C22⋊C4×C47—24no—
239C22⋊C4×C47—24no—
240C22⋊C4×C47—24no—
241C22⋊C4×C47—24no—
242C42×C47—24no—
243C42×C47C2×D414yes—
244C42×C47C2×D412yes—
245C42×C47C2×D412yes—
246C42×C47C2×D414yes—
247C42×C47C2412yes—
248C42×C47C2412yes—
249C22⋊Dic47—24no—
250#10625337—44no—
251#10625336—44no—
252#10625335—44no—
253#10625334—44no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4—24no—
258C4⋊Dic47—21no—
259C4⋊Dic47—21no—
260C4⋊Dic47C2412yes—
261C4⋊Dic47C2412yes—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266C4×Dic47—24no—
267#10625329—44no—
268#10625329—44no—
269C2×C47⋊C8—22no—
270C2×C47⋊C8—22no—
271C2×C47⋊C8—22no—
272C2×C47⋊C8—22no—
273C2×C47⋊C8C2412yes—
274C2×C47⋊C8C2412yes—
275C2×C47⋊C8C2412yes—
276C2×C47⋊C8C2412yes—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47C22×D412yes—
285C23×C47C22×D411yescharacteristic
286C22×D47—22no—
287C22×D47—42no—
288C22×D47—42no—
289C22×D47—42no—
290Q8×C47—22no—
291Q8×C47—22no—
292Q8×C47—42no—
293D4×C47—22no—
294D4×C47—22no—
295D4×C47—48no—
296D4×C47—42no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—24no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—44no—
309C2×C4×C47—44no—
310C2×C4×C47—48no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47C22×D412yes—
315C2×C4×C47C22×D412yes—
316C2×C4×C47C22×D412yes—
317C2×C4×C47C22×D412yes—
318C2×C4×C47C22×D412yes—
319C2×C4×C47C22×D411yescharacteristic
320C2×C4×C47H(5,𝔽2)12yes—
321C2×C4×C472−1+412yes—
322C2×C4×C47C2511yescharacteristic
323C22⋊D47—48no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330D188—22no—
331D188—22no—
332D188—42no—
333C4×D47—48no—
334Dic94—22no—
335Dic94—22no—
336Dic94—42no—
337C47⋊C8—22no—
338C47⋊C8—22no—
339C47⋊C8—22no—
340C47⋊C8—22no—
341C2×#3256—471nomaximal, Sylow
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—44no—
346C22×C47—42no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—84no—
350C22×C47#53712yes—
351C22×C47#57512yes—
352C22×C47#57512yes—
353C22×C47C23×D411yescharacteristic
354C2×D47—42no—
355C2×D47—42no—
356C2×D47—42no—
357C2×D47—84no—
358C4×C47—22no—
359C4×C47—22no—
360C4×C47—22no—
361C4×C47—22no—
362C4×C47—22no—
363C4×C47—42no—
364C4×C47—42no—
365C4×C47—42no—
366C4×C47#53712yes—
367C4×C47C2×H(5,𝔽2)11yescharacteristic
368C4×C47C2×2−1+411yescharacteristic
369Dic47—42no—
370Dic47—42no—
371Dic47—42no—
372C2×#529—471no—
373C2×#529D4711yescharacteristic, complemented
374#3256—4716no—
375C2×#479—471no—
376C2×#479—471no—
377C2×#478—471no—
378C2×#478—471no—
379C2×#470—471no—
380C2×#469—471no—
381C2×#468—471no—
382C2×#468—471no—
383C2×#464—471no—
384C2×#464—471no—
385C2×#463—471no—
386C2×#463—471no—
387C2×#423—471no—
388C2×C47—42no—
389C2×C47—82no—
390C2×C47#325614yescomplemented
391C2×C47C2×#53711yescharacteristic
392C2×C47C2×#57511yescharacteristic
393C2×C47C2×#57511yescharacteristic
394D47—82no—
395C22×Q16—471no—
396C22×SD16—471no—
397C22×SD16—471no—
398C22×D8—471no—
399C22×M16—471no—
400C22×M16—471no—
401#529—24no—
402#529—478no—
403#529—944no—
404#529C2×D4718yescomplemented
405C2×#126—21no—
406C2×#126—941no—
407C2×#125—471no—
408C2×#125C2×D4711yescharacteristic
409C2×#124—471no—
410C2×#124C2×D4711yescharacteristic
411C2×#123—21no—
412C2×#123—941no—
413C2×C22⋊Q8—471no—
414C2×C22⋊Q8C2×D4711yescharacteristic
415C2×#121—471no—
416C2×#121C2×D4711yescharacteristic
417C2×C4×Q8—471no—
418C2×C4×Q8C2×D4711yescharacteristic
419C2×C4×D4—21no—
420C2×C4×D4—471no—
421C2×C4×D4—941no—
422C2×C4×D4C2×D4711yescharacteristic
423C2×#117—21no—
424C2×#117—941no—
425C22×C42C2×D4711yescharacteristic
426#479—478no—
427#479—478no—
428#478—478no—
429#478—478no—
430#470—478no—
431#469—478no—
432#468—478no—
433#468—478no—
434#464—478no—
435#464—478no—
436#463—478no—
437#463—478no—
438C2×#107—471no—
439C2×#107—471no—
440C2×#106—471no—
441C2×#106—471no—
442#423—478no—
443C2×C4⋊C8—471no—
444C2×C4⋊C8—471no—
445C2×C4⋊C8—471no—
446C2×C4⋊C8—471no—
447C2×#103—471no—
448C2×#103—471no—
449C2×#103—471no—
450C2×#103—471no—
451C2×#102—471no—
452C2×#102—471no—
453C2×#102—471no—
454C2×#102—471no—
455C47C2×#325611yescharacteristic, complemented, Sylow
456C22×Q8—471no—
457C22×Q8C22×D4711yescharacteristic
458C22×D4—21no—
459C22×D4—471no—
460C22×D4—941no—
461C22×D4C22×D4711yescharacteristic
462C23×C4—21no—
463C23×C4—941no—
464C23×C4C22⋊D4711yescharacteristic
465C23×C4C22⋊D4711yescharacteristic
466C23×C4C22×D4711yescharacteristic
467C2×Q16—474no—
468C2×Q16—1882no—
469C2×SD16—474no—
470C2×SD16—474no—
471C2×SD16—1882no—
472C2×SD16—1882no—
473C2×D8—474no—
474C2×D8—1882no—
475C2×M16—474no—
476C2×M16—474no—
477C2×M16—1882no—
478C2×M16—1882no—
479C22×C8—471no—
480C22×C8—471no—
481C22×C8—471no—
482C22×C8—471no—
483#126—28no—
484#126—948no—
485#125—22no—
486#125—474no—
487#125—942no—
488#125C22×D4714yes—
489#124—22no—
490#124—474no—
491#124—942no—
492#124C22×D4714yes—
493#123—28no—
494#123—948no—
495C22⋊Q8—22no—
496C22⋊Q8—474no—
497C22⋊Q8—942no—
498C22⋊Q8C22×D4714yes—
499#121—22no—
500#121—474no—
501#121—942no—
502#121C22×D4714yes—
503C4×Q8—22no—
504C4×Q8—474no—
505C4×Q8—942no—
506C4×Q8C22×D4714yes—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—474no—
510C4×D4—948no—
511C4×D4—942no—
512C4×D4C22×D4714yes—
513#117—28no—
514#117—948no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—471no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—941no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4C22×D4711yescharacteristic
526C2×C4⋊C4C22×D4711yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C22⋊C4—941no—
537C2×C42—21no—
538C2×C42—941no—
539C2×C42C22⋊D4711yescharacteristic
540C2×C42C22⋊D4711yescharacteristic
541C2×C42C22⋊D4714yes—
542C2×C42C22×D4711yescharacteristic
543C2×C42C22×D4711yescharacteristic
544C2×C42C22×D4714yes—
545#107—474no—
546#107—474no—
547#106—474no—
548#106—474no—
549C4⋊C8—474no—
550C4⋊C8—474no—
551C4⋊C8—474no—
552C4⋊C8—474no—
553#103—474no—
554#103—474no—
555#103—474no—
556#103—474no—
557#102—474no—
558#102—474no—
559#102—474no—
560#102—474no—
561C24—21no—
562C24—941no—
563C24C2×C22⋊D4711yescharacteristic
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—472no—
568C2×Q8—941no—
569C2×Q8—942no—
570C2×Q8—942no—
571C2×Q8C23×D4712yes—
572C2×D4—24no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—44no—
577C2×D4—472no—
578C2×D4—944no—
579C2×D4—941no—
580C2×D4—942no—
581C2×D4—942no—
582C2×D4—1884no—
583C2×D4C23×D4712yes—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—944no—
597C22×C4—1884no—
598C22×C4C2×C22⋊D4712yes—
599C22×C4C2×C22⋊D4711yescharacteristic
600C22×C4C2×C22⋊D4711yescharacteristic
601C22×C4C2×C22⋊D4711yescharacteristic
602C22×C4C2×C22⋊D4711yescharacteristic
603C22×C4C2×C22⋊D4711yescharacteristic
604C22×C4C2×C22⋊D4714yes—
605C22×C4C2×C22⋊D4714yes—
606C22×C4C23×D4712yes—
607C22×C4C23×D4711yescharacteristic
608Q16—1884no—
609SD16—1884no—
610SD16—1884no—
611D8—1884no—
612M16—1884no—
613M16—1884no—
614C2×C8—472no—
615C2×C8—472no—
616C2×C8—472no—
617C2×C8—472no—
618C2×C8—942no—
619C2×C8—942no—
620C2×C8—942no—
621C2×C8—942no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—472no—
629C4⋊C4—472no—
630C4⋊C4—944no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4—944no—
634C4⋊C4—941no—
635C4⋊C4—941no—
636C4⋊C4C23×D4712yes—
637C4⋊C4C23×D4712yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—944no—
644C22⋊C4—944no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C22⋊C4—944no—
648C42—24no—
649C42—944no—
650C42C2×C22⋊D4714yes—
651C42C2×C22⋊D4712yes—
652C42C2×C22⋊D4712yes—
653C42C2×C22⋊D4714yes—
654C42C23×D4712yes—
655C42C23×D4712yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—942no—
664C23—1882no—
665C23—1882no—
666C23—1882no—
667C23C22×C22⋊D4712yes—
668C23C22×C22⋊D4711yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—942no—
673Q8—942no—
674Q8—1882no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—42no—
679D4—942no—
680D4—942no—
681D4—1888no—
682D4—1882no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—1888no—
704C2×C4—1882no—
705C2×C4—1882no—
706C2×C4—1882no—
707C2×C4C22×C22⋊D4712yes—
708C2×C4C22×C22⋊D4712yes—
709C2×C4C22×C22⋊D4712yes—
710C2×C4C22×C22⋊D4712yes—
711C2×C4C22×C22⋊D4712yes—
712C2×C4C22×C22⋊D4711yescharacteristic
713C2×C4#1309407012yes—
714C2×C4#1309407112yes—
715C2×C4C24×D4711yescharacteristic
716C8—942no—
717C8—942no—
718C8—942no—
719C8—942no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—3764no—
729C22—1882no—
730C22—1882no—
731C22—1882no—
732C22#1568970112yes—
733C22#1568992112yes—
734C22#1568992112yes—
735C22C23×C22⋊D4711yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—1882no—
745C4—1882no—
746C4—1882no—
747C4#1568970112yes—
748C4C2×#1309407011yescharacteristic
749C4C2×#1309407111yescharacteristic
750C2—42no—
751C2—82no—
752C2—3762no—
753C2#2025478414yesdirect product factor
754C2C2×#1568970111yescharacteristic
755C2C2×#1568992111yescharacteristic
756C2C2×#1568992111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#529C2
socleC23×C47C22×D4
prime radicalC2×#15689374C2
hypercenterC2×#529D47
hypocenterC47C2×#3256
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#15689657C2semidirect
2. #20254784C2direct (N × H)
3. C2×#15689430C2semidirect
4. C2×#15689427C2semidirect
5. C2×#15689423C2semidirect
6. C2×#15689420C2semidirect
7. C2×#15689379C2semidirect
9. C2×#15689371C2semidirect
10. C2×#15689367C2semidirect
11. C2×#15689345C2semidirect
12. C2×#15689342C2semidirect
13. C2×#15689338C2semidirect
14. C2×#15689335C2semidirect
15. C2×#15689147C2semidirect
16. C2×C47×#529C2semidirect
24. #15689657C22semidirect
35. #15689430C22semidirect
36. #15689427C22semidirect
37. #15689423C22semidirect
38. #15689420C22semidirect
39. #15689379C22semidirect
41. #15689371C22semidirect
42. #15689367C22semidirect
43. #15689345C22semidirect
44. #15689342C22semidirect
45. #15689338C22semidirect
46. #15689335C22semidirect
51. #15689147C22semidirect
65. C47×#529C22semidirect
373. C2×#529D47semidirect
390. C2×C47#3256semidirect
404. #529C2×D47semidirect
455. C47C2×#3256semidirect
753. C2#20254784direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896572
#202547842
C2×#156894302
C2×#156894272
C2×#156894232
C2×#156894202
C2×#156893792
C2×#156893742
C2×#156893712
C2×#156893672
C2×#156893452
C2×#156893422
C2×#156893382
C2×#156893352
C2×#156891472
C2×C47×#5292
C2×#325647