Finite Group Databasebeta

← C2×#20254225 #27086904

Subgroups — C2×#20254225 #27086904

Order 12032.

2362 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic, complemented
2#20254225C2116yesmaximal, direct product factor
3C2×#15689464C211yesmaximal, characteristic, complemented
4C2×#15689461C211yesmaximal, characteristic, complemented
5C2×#15689447C211yesmaximal, characteristic, complemented
6C2×#15689444C211yesmaximal, characteristic, complemented
7C2×#15689379C211yesmaximal, characteristic, complemented
8C2×#15689374C211yesmaximal, characteristic, complemented
9C2×#15689371C211yesmaximal, characteristic, complemented
10C2×#15689367C211yesmaximal, characteristic, complemented
11C2×#15689285C211yesmaximal, characteristic, complemented
12C2×#15689283C211yesmaximal, characteristic, complemented
13C2×#15689268C211yesmaximal, characteristic, complemented
14C2×#15689266C211yesmaximal, characteristic, complemented
15C2×#15689087C211yesmaximal, characteristic, complemented
16C2×C47×#525C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625337C2211yescharacteristic, complemented
19C22×#10625335C2211yescharacteristic, complemented
20C22×#10625336C2211yescharacteristic, complemented
21C22×#10625334C2211yescharacteristic, complemented
22C22×#10625329C2211yescharacteristic
23C22×#10625329C2211yescharacteristic
24#15689634—24no—
25#15689634C2218yescomplemented
26C2×#13094007—21no—
27C2×#13094003C2211yescharacteristic
28C2×#13094003C2211yescharacteristic
29C2×#13093998C2211yescharacteristic
30C2×#13093998C2211yescharacteristic
31C2×#13093993—21no—
32C2×C4×C22⋊D47—21no—
33C2×C4×C22⋊D47—21no—
34C2×#13093983C2211yescharacteristic
35#15689464C2218yescomplemented
36#15689461C2218yescomplemented
37#15689447C2218yescomplemented
38#15689444C2218yescomplemented
39#15689379C2218yescomplemented
40#15689374C2218yescomplemented
41#15689371C2218yescomplemented
42#15689367C2218yescomplemented
43#15689285C2218yescomplemented
44#15689283C2218yescomplemented
45#15689268C2218yescomplemented
46#15689266C2218yescomplemented
47C2×#13093957C2211yescharacteristic, complemented
48C2×#13093957C2211yescharacteristic, complemented
49C2×#13093955C2211yescharacteristic, complemented
50C2×#13093955C2211yescharacteristic, complemented
51C2×#13093948C2211yescharacteristic, complemented
52C2×#13093948C2211yescharacteristic, complemented
53C2×#13093947C2211yescharacteristic, complemented
54C2×#13093947C2211yescharacteristic, complemented
55C2×#13093945C2211yescharacteristic, complemented
56C2×#13093945C2211yescharacteristic, complemented
57C2×#13093944C2211yescharacteristic, complemented
58C2×#13093944C2211yescharacteristic, complemented
59#15689087C2218yescomplemented
60C2×C22⋊(C47⋊C8)C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×C22⋊(C47⋊C8)C2211yescharacteristic
63C2×C22⋊(C47⋊C8)C2211yescharacteristic
64C22×#41×C47C2211yescharacteristic
65C24×C4×C47C2211yescharacteristic
66C47×#525—24no—
67C47×#525C2218yescomplemented
68C2×#123×C47—21no—
69C2×C22⋊Q8×C47C2211yescharacteristic
70C2×C22⋊Q8×C47C2211yescharacteristic
71C2×#121×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic
73C2×#120×C47—21no—
74C2×C4×D4×C47—21no—
75C2×C4×D4×C47—21no—
76C2×#117×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—42no—
79C2×#10625350—42no—
80C2×#10625350C2314yes—
81C22×Dic94C2311yescharacteristic
82C22×D188C2311yescharacteristic
83C22×C22⋊D47—21no—
84C22×C22⋊D47—21no—
85C22×C22⋊D47—21no—
86C22×C4×D47—21no—
87C2×#10625337—42no—
88C2×#10625337C2314yescomplemented
89C2×#10625335—42no—
90C2×#10625335C2314yescomplemented
91C2×#10625336—42no—
92C2×#10625336C2314yescomplemented
93C2×#10625334—42no—
94C2×#10625334C2314yescomplemented
95C2×#10625329—42no—
96C2×#10625329—42no—
97C2×#10625329C2314yes—
98C2×#10625329C2314yes—
99C22×C47⋊C8C2311yescharacteristic
100C22×C47⋊C8C2311yescharacteristic
101C22×C47⋊C8C2311yescharacteristic
102C22×C47⋊C8C2311yescharacteristic
103#13094007—28no—
104#13094003—22no—
105#13094003—22no—
106#13094003C2314yes—
107#13094003C2314yes—
108#13093998—22no—
109#13093998—22no—
110#13093998C2314yes—
111#13093998C2314yes—
112#13093993—28no—
113C4×C22⋊D47—28no—
114C4×C22⋊D47—28no—
115#13093983—22no—
116#13093983C2314yes—
117C2×C4⋊Dic47C2311yescharacteristic
118C2×C4⋊Dic47C2311yescharacteristic
119C2×Dic47⋊C4—21no—
120C2×Dic47⋊C4—21no—
121C2×C22⋊Dic47—21no—
122C2×C22⋊Dic47—21no—
123C2×C22⋊Dic47—21no—
124C2×(C2×D47)⋊C4—21no—
125C2×(C2×D47)⋊C4—21no—
126C2×C4×Dic47—21no—
127#13093957C2314yescomplemented
128#13093957C2314yescomplemented
129#13093955C2314yescomplemented
130#13093955C2314yescomplemented
131#13093948C2314yescomplemented
132#13093948C2314yescomplemented
133#13093947C2314yescomplemented
134#13093947C2314yescomplemented
135#13093945C2314yescomplemented
136#13093945C2314yescomplemented
137#13093944C2314yescomplemented
138#13093944C2314yescomplemented
139C22⋊(C47⋊C8)C2314yes—
140C22⋊(C47⋊C8)C2314yes—
141C22⋊(C47⋊C8)C2314yes—
142C22⋊(C47⋊C8)C2314yes—
143C25×C47D411yescharacteristic
144C2×#41×C47—22no—
145C2×#41×C47—42no—
146C2×#41×C47—42no—
147C2×#41×C47C2314yes—
148C22×Q8×C47C2311yescharacteristic
149C22×D4×C47—21no—
150C22×D4×C47—21no—
151C22×D4×C47—21no—
152C22×D4×C47C2311yescharacteristic
153C23×C4×C47—21no—
154C23×C4×C47—42no—
155C23×C4×C47—42no—
156C23×C4×C47D411yescharacteristic
157C23×C4×C47D411yescharacteristic
158C23×C4×C47D411yescharacteristic
159C23×C4×C47D414yes—
160C23×C4×C47C2311yescharacteristic
161C23×C4×C47C2311yescharacteristic
162C23×C4×C47C2311yescharacteristic
163C23×C4×C47C2314yes—
164#123×C47—28no—
165C22⋊Q8×C47—22no—
166C22⋊Q8×C47—22no—
167C22⋊Q8×C47C2314yes—
168C22⋊Q8×C47C2314yes—
169#121×C47—22no—
170#121×C47—22no—
171#121×C47C2314yes—
172#121×C47C2314yes—
173#120×C47—28no—
174C4×D4×C47—28no—
175C4×D4×C47—28no—
176#117×C47—22no—
177#117×C47C2314yes—
178C2×C4⋊C4×C47—21no—
179C2×C4⋊C4×C47—21no—
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C4⋊C4×C47C2311yescharacteristic
182C2×C22⋊C4×C47—21no—
183C2×C22⋊C4×C47—21no—
184C2×C22⋊C4×C47—21no—
185C2×C22⋊C4×C47—21no—
186C2×C22⋊C4×C47—21no—
187C2×C42×C47—21no—
188C24×C47—21no—
189C24×C47—42no—
190C24×C47—42no—
191C24×C47—42no—
192C24×C47C2×D411yescharacteristic
193C24×C47C2×D411yescharacteristic
194C24×C47C2×D411yescharacteristic
195C24×C47C2×D414yes—
196C23×D47—21no—
197#41×C47—44no—
198#41×C47—44no—
199#41×C47—48no—
200C2×Q8×C47—21no—
201C2×Q8×C47—22no—
202C2×Q8×C47—22no—
203C2×Q8×C47C2412yes—
204C2×D4×C47—24no—
205C2×D4×C47—24no—
206C2×D4×C47—24no—
207C2×D4×C47—21no—
208C2×D4×C47—22no—
209C2×D4×C47—22no—
210C2×D4×C47—44no—
211C2×D4×C47—44no—
212C2×D4×C47—44no—
213C2×D4×C47C2412yes—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47—22no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—24no—
224C22×C4×C47—48no—
225C22×C4×C47—44no—
226C22×C4×C47—44no—
227C22×C4×C47—42no—
228C22×C4×C47—42no—
229C22×C4×C47—42no—
230C22×C4×C47—44no—
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47C2×D412yes—
235C22×C4×C47C2×D412yes—
236C22×C4×C47C2×D412yes—
237C22×C4×C47C2×D414yes—
238C22×C4×C47C2×D414yes—
239C22×C4×C47C2×D414yes—
240C22×C4×C47C2412yes—
241C22×C4×C47C2412yes—
242C22×C4×C47C2412yes—
243C22×C4×C47C2411yescharacteristic
244C2×C22⋊D47—24no—
245C2×C22⋊D47—24no—
246C2×C22⋊D47—24no—
247C2×C22⋊D47—44no—
248C2×C22⋊D47—44no—
249C2×C22⋊D47—44no—
250C22×Dic47—21no—
251C22×Dic47—21no—
252C22×Dic47—21no—
253#10625350—44no—
254#10625350—44no—
255#10625350—48no—
256C2×D188—22no—
257C2×D188—22no—
258C2×D188—21no—
259C2×D188C2412yes—
260C2×C4×D47—24no—
261C2×C4×D47—44no—
262C2×Dic94—22no—
263C2×Dic94—22no—
264C2×Dic94—21no—
265C2×Dic94C2412yes—
266C4⋊C4×C47—24no—
267C4⋊C4×C47—24no—
268C4⋊C4×C47—21no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47C2412yes—
271C4⋊C4×C47C2412yes—
272C22⋊C4×C47—24no—
273C22⋊C4×C47—24no—
274C22⋊C4×C47—24no—
275C22⋊C4×C47—24no—
276C22⋊C4×C47—24no—
277C42×C47—24no—
278C22⋊Dic47—24no—
279C22⋊Dic47—24no—
280C22⋊Dic47—24no—
281#10625337—44no—
282#10625336—44no—
283#10625335—44no—
284#10625334—44no—
285(C2×D47)⋊C4—24no—
286(C2×D47)⋊C4—24no—
287C4⋊Dic47—21no—
288C4⋊Dic47—21no—
289C4⋊Dic47C2412yes—
290C4⋊Dic47C2412yes—
291Dic47⋊C4—24no—
292Dic47⋊C4—24no—
293C4×Dic47—24no—
294#10625329—44no—
295#10625329—44no—
296C2×C47⋊C8—22no—
297C2×C47⋊C8—22no—
298C2×C47⋊C8—22no—
299C2×C47⋊C8—22no—
300C2×C47⋊C8C2412yes—
301C2×C47⋊C8C2412yes—
302C2×C47⋊C8C2412yes—
303C2×C47⋊C8C2412yes—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—44no—
315C23×C47—44no—
316C23×C47—44no—
317C23×C47—416no—
318C23×C47—42no—
319C23×C47—42no—
320C23×C47—42no—
321C23×C47C22×D412yes—
322C23×C47C22×D412yes—
323C23×C47C22×D412yes—
324C23×C47C22×D411yescharacteristic
325C22×D47—22no—
326C22×D47—42no—
327C22×D47—42no—
328C22×D47—42no—
329Q8×C47—22no—
330Q8×C47—22no—
331Q8×C47—42no—
332D4×C47—22no—
333D4×C47—22no—
334D4×C47—48no—
335D4×C47—48no—
336D4×C47—48no—
337D4×C47—42no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—24no—
342C2×C4×C47—24no—
343C2×C4×C47—24no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—44no—
354C2×C4×C47—44no—
355C2×C4×C47—44no—
356C2×C4×C47—48no—
357C2×C4×C47—42no—
358C2×C4×C47—42no—
359C2×C4×C47—42no—
360C2×C4×C47C22×D412yes—
361C2×C4×C47C22×D412yes—
362C2×C4×C47C22×D412yes—
363C2×C4×C47C22×D411yescharacteristic
364C2×C4×C47H(5,𝔽2)12yes—
365C2×C4×C47H(5,𝔽2)12yes—
366C2×C4×C47C2511yescharacteristic
367C22⋊D47—48no—
368C22⋊D47—48no—
369C22⋊D47—48no—
370C2×Dic47—22no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—42no—
374C2×Dic47—42no—
375C2×Dic47—42no—
376D188—22no—
377D188—22no—
378D188—42no—
379C4×D47—48no—
380Dic94—22no—
381Dic94—22no—
382Dic94—42no—
383C47⋊C8—22no—
384C47⋊C8—22no—
385C47⋊C8—22no—
386C47⋊C8—22no—
387C2×#3197—471nomaximal, Sylow
388C22×C47—22no—
389C22×C47—22no—
390C22×C47—22no—
391C22×C47—22no—
392C22×C47—22no—
393C22×C47—22no—
394C22×C47—22no—
395C22×C47—22no—
396C22×C47—22no—
397C22×C47—416no—
398C22×C47—44no—
399C22×C47—44no—
400C22×C47—44no—
401C22×C47—42no—
402C22×C47—42no—
403C22×C47—42no—
404C22×C47—84no—
405C22×C47#53412yes—
406C22×C47#57512yes—
407C22×C47#57512yes—
408C22×C47C23×D411yescharacteristic
409C2×D47—42no—
410C2×D47—42no—
411C2×D47—42no—
412C2×D47—84no—
413C4×C47—22no—
414C4×C47—22no—
415C4×C47—22no—
416C4×C47—42no—
417C4×C47—42no—
418C4×C47—42no—
419C4×C47#53412yes—
420C4×C47C2×H(5,𝔽2)11yescharacteristic
421C4×C47C2×H(5,𝔽2)11yescharacteristic
422Dic47—42no—
423Dic47—42no—
424Dic47—42no—
425C2×#525—471no—
426C2×#525D4711yescharacteristic, complemented
427#3197—4716no—
428C2×#485—471no—
429C2×#485—471no—
430C2×#482—471no—
431C2×#482—471no—
432C2×#470—471no—
433C2×#469—471no—
434C2×#468—471no—
435C2×#468—471no—
436C2×#452—471no—
437C2×#452—471no—
438C2×#449—471no—
439C2×#449—471no—
440C2×#407—471no—
441C2×C47—42no—
442C2×C47—42no—
443C2×C47—42no—
444C2×C47—82no—
445C2×C47#319714yescomplemented
446C2×C47C2×#53411yescharacteristic
447C2×C47C2×#57511yescharacteristic
448C2×C47C2×#57511yescharacteristic
449D47—82no—
450C22×#41—471no—
451C22×#41C2×D4711yescharacteristic
452C24×C4C2×D4711yescharacteristic
453C22×Q16—471no—
454C22×SD16—471no—
455C22×SD16—471no—
456C22×D8—471no—
457C22×M16—471no—
458C22×M16—471no—
459#525—24no—
460#525—478no—
461#525—944no—
462#525C2×D4718yescomplemented
463C2×#123—21no—
464C2×#123—941no—
465C2×C22⋊Q8—471no—
466C2×C22⋊Q8—471no—
467C2×C22⋊Q8C2×D4711yescharacteristic
468C2×C22⋊Q8C2×D4711yescharacteristic
469C2×#121—471no—
470C2×#121—471no—
471C2×#121C2×D4711yescharacteristic
472C2×#121C2×D4711yescharacteristic
473C2×#120—21no—
474C2×#120—941no—
475C2×C4×D4—21no—
476C2×C4×D4—21no—
477C2×C4×D4—941no—
478C2×C4×D4—941no—
479C2×#117—471no—
480C2×#117C2×D4711yescharacteristic
481#485—478no—
482#485—478no—
483#482—478no—
484#482—478no—
485#470—478no—
486#469—478no—
487#468—478no—
488#468—478no—
489#452—478no—
490#452—478no—
491#449—478no—
492#449—478no—
493C2×#107—471no—
494C2×#107—471no—
495C2×#106—471no—
496C2×#106—471no—
497C2×#103—471no—
498C2×#103—471no—
499C2×#103—471no—
500C2×#103—471no—
501C2×#102—471no—
502C2×#102—471no—
503C2×#102—471no—
504C2×#102—471no—
505#407—478no—
506C2×C22⋊C8—471no—
507C2×C22⋊C8—471no—
508C2×C22⋊C8—471no—
509C2×C22⋊C8—471no—
510C47C2×#319711yescharacteristic, complemented, Sylow
511C25C22⋊D4711yescharacteristic
512C2×#41—22no—
513C2×#41—42no—
514C2×#41—42no—
515C2×#41—474no—
516C2×#41—942no—
517C2×#41—1882no—
518C2×#41—1882no—
519C2×#41C22×D4714yes—
520C22×Q8—471no—
521C22×Q8C22×D4711yescharacteristic
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—471no—
526C22×D4—941no—
527C22×D4—941no—
528C22×D4—941no—
529C22×D4C22×D4711yescharacteristic
530C23×C4—21no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4—941no—
534C23×C4C22⋊D4711yescharacteristic
535C23×C4C22⋊D4711yescharacteristic
536C23×C4C22⋊D4711yescharacteristic
537C23×C4C22⋊D4714yes—
538C23×C4C22×D4711yescharacteristic
539C23×C4C22×D4711yescharacteristic
540C23×C4C22×D4711yescharacteristic
541C23×C4C22×D4714yes—
542C2×Q16—474no—
543C2×Q16—1882no—
544C2×SD16—474no—
545C2×SD16—474no—
546C2×SD16—1882no—
547C2×SD16—1882no—
548C2×D8—474no—
549C2×D8—1882no—
550C2×M16—474no—
551C2×M16—474no—
552C2×M16—1882no—
553C2×M16—1882no—
554C22×C8—471no—
555C22×C8—471no—
556C22×C8—471no—
557C22×C8—471no—
558#123—28no—
559#123—948no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—474no—
563C22⋊Q8—474no—
564C22⋊Q8—942no—
565C22⋊Q8—942no—
566C22⋊Q8C22×D4714yes—
567C22⋊Q8C22×D4714yes—
568#121—22no—
569#121—22no—
570#121—474no—
571#121—474no—
572#121—942no—
573#121—942no—
574#121C22×D4714yes—
575#121C22×D4714yes—
576#120—28no—
577#120—948no—
578C4×D4—28no—
579C4×D4—28no—
580C4×D4—948no—
581C4×D4—948no—
582#117—22no—
583#117—474no—
584#117—942no—
585#117C22×D4714yes—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—471no—
589C2×C4⋊C4—471no—
590C2×C4⋊C4—941no—
591C2×C4⋊C4—941no—
592C2×C4⋊C4C22×D4711yescharacteristic
593C2×C4⋊C4C22×D4711yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—941no—
600C2×C22⋊C4—941no—
601C2×C22⋊C4—941no—
602C2×C22⋊C4—941no—
603C2×C22⋊C4—941no—
604C2×C42—21no—
605C2×C42—941no—
606#107—474no—
607#107—474no—
608#106—474no—
609#106—474no—
610#103—474no—
611#103—474no—
612#103—474no—
613#103—474no—
614#102—474no—
615#102—474no—
616#102—474no—
617#102—474no—
618C22⋊C8—474no—
619C22⋊C8—474no—
620C22⋊C8—474no—
621C22⋊C8—474no—
622C24—21no—
623C24—42no—
624C24—42no—
625C24—42no—
626C24—941no—
627C24C2×C22⋊D4711yescharacteristic
628C24C2×C22⋊D4711yescharacteristic
629C24C2×C22⋊D4711yescharacteristic
630C24C2×C22⋊D4714yes—
631#41—44no—
632#41—44no—
633#41—48no—
634#41—1884no—
635#41—1884no—
636#41—1888no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—472no—
641C2×Q8—941no—
642C2×Q8—942no—
643C2×Q8—942no—
644C2×Q8C23×D4712yes—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—44no—
652C2×D4—44no—
653C2×D4—44no—
654C2×D4—472no—
655C2×D4—944no—
656C2×D4—944no—
657C2×D4—944no—
658C2×D4—941no—
659C2×D4—942no—
660C2×D4—942no—
661C2×D4—1884no—
662C2×D4—1884no—
663C2×D4—1884no—
664C2×D4C23×D4712yes—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—24no—
675C22×C4—48no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—44no—
682C22×C4—941no—
683C22×C4—941no—
684C22×C4—941no—
685C22×C4—944no—
686C22×C4—1884no—
687C22×C4C2×C22⋊D4712yes—
688C22×C4C2×C22⋊D4712yes—
689C22×C4C2×C22⋊D4712yes—
690C22×C4C2×C22⋊D4711yescharacteristic
691C22×C4C2×C22⋊D4711yescharacteristic
692C22×C4C2×C22⋊D4711yescharacteristic
693C22×C4C2×C22⋊D4714yes—
694C22×C4C2×C22⋊D4714yes—
695C22×C4C2×C22⋊D4714yes—
696C22×C4C23×D4712yes—
697C22×C4C23×D4712yes—
698C22×C4C23×D4712yes—
699C22×C4C23×D4711yescharacteristic
700Q16—1884no—
701SD16—1884no—
702SD16—1884no—
703D8—1884no—
704M16—1884no—
705M16—1884no—
706C2×C8—472no—
707C2×C8—472no—
708C2×C8—472no—
709C2×C8—472no—
710C2×C8—942no—
711C2×C8—942no—
712C2×C8—942no—
713C2×C8—942no—
714C4⋊C4—24no—
715C4⋊C4—24no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—472no—
719C4⋊C4—472no—
720C4⋊C4—944no—
721C4⋊C4—944no—
722C4⋊C4—941no—
723C4⋊C4—941no—
724C4⋊C4C23×D4712yes—
725C4⋊C4C23×D4712yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—944no—
732C22⋊C4—944no—
733C22⋊C4—944no—
734C22⋊C4—944no—
735C22⋊C4—944no—
736C42—24no—
737C42—944no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—416no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—942no—
756C23—1882no—
757C23—1882no—
758C23—1882no—
759C23C22×C22⋊D4712yes—
760C23C22×C22⋊D4712yes—
761C23C22×C22⋊D4712yes—
762C23C22×C22⋊D4711yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—42no—
766Q8—942no—
767Q8—942no—
768Q8—1882no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—48no—
773D4—48no—
774D4—42no—
775D4—942no—
776D4—942no—
777D4—1888no—
778D4—1888no—
779D4—1888no—
780D4—1882no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—48no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—942no—
804C2×C4—942no—
805C2×C4—942no—
806C2×C4—1888no—
807C2×C4—1882no—
808C2×C4—1882no—
809C2×C4—1882no—
810C2×C4C22×C22⋊D4712yes—
811C2×C4C22×C22⋊D4712yes—
812C2×C4C22×C22⋊D4712yes—
813C2×C4C22×C22⋊D4711yescharacteristic
814C2×C4#1309406912yes—
815C2×C4#1309406912yes—
816C2×C4C24×D4711yescharacteristic
817C8—942no—
818C8—942no—
819C8—942no—
820C8—942no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—416no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—84no—
838C22—3764no—
839C22—1882no—
840C22—1882no—
841C22—1882no—
842C22#1568968212yes—
843C22#1568992112yes—
844C22#1568992112yes—
845C22C23×C22⋊D4711yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—1882no—
853C4—1882no—
854C4—1882no—
855C4#1568968212yes—
856C4C2×#1309406911yescharacteristic
857C4C2×#1309406911yescharacteristic
858C2—42no—
859C2—42no—
860C2—42no—
861C2—82no—
862C2—3762no—
863C2#2025422514yesdirect product factor
864C2C2×#1568968211yescharacteristic
865C2C2×#1568992111yescharacteristic
866C2C2×#1568992111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#525C2
socleC23×C47C22×D4
hypercenterC2×#525D47
hypocenterC47C2×#3197
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#15689634C2semidirect
2. #20254225C2direct (N × H)
3. C2×#15689464C2semidirect
4. C2×#15689461C2semidirect
5. C2×#15689447C2semidirect
6. C2×#15689444C2semidirect
7. C2×#15689379C2semidirect
8. C2×#15689374C2semidirect
9. C2×#15689371C2semidirect
10. C2×#15689367C2semidirect
11. C2×#15689285C2semidirect
12. C2×#15689283C2semidirect
13. C2×#15689268C2semidirect
14. C2×#15689266C2semidirect
15. C2×#15689087C2semidirect
16. C2×C47×#525C2semidirect
18. C22×#10625337C22semidirect
19. C22×#10625335C22semidirect
20. C22×#10625336C22semidirect
21. C22×#10625334C22semidirect
25. #15689634C22semidirect
35. #15689464C22semidirect
36. #15689461C22semidirect
37. #15689447C22semidirect
38. #15689444C22semidirect
39. #15689379C22semidirect
40. #15689374C22semidirect
41. #15689371C22semidirect
42. #15689367C22semidirect
43. #15689285C22semidirect
44. #15689283C22semidirect
45. #15689268C22semidirect
46. #15689266C22semidirect
47. C2×#13093957C22semidirect
48. C2×#13093957C22semidirect
49. C2×#13093955C22semidirect
50. C2×#13093955C22semidirect
51. C2×#13093948C22semidirect
52. C2×#13093948C22semidirect
53. C2×#13093947C22semidirect
54. C2×#13093947C22semidirect
55. C2×#13093945C22semidirect
56. C2×#13093945C22semidirect
57. C2×#13093944C22semidirect
58. C2×#13093944C22semidirect
59. #15689087C22semidirect
67. C47×#525C22semidirect
88. C2×#10625337C23semidirect
90. C2×#10625335C23semidirect
92. C2×#10625336C23semidirect
94. C2×#10625334C23semidirect
127. #13093957C23semidirect
128. #13093957C23semidirect
129. #13093955C23semidirect
130. #13093955C23semidirect
131. #13093948C23semidirect
132. #13093948C23semidirect
133. #13093947C23semidirect
134. #13093947C23semidirect
135. #13093945C23semidirect
136. #13093945C23semidirect
137. #13093944C23semidirect
138. #13093944C23semidirect
426. C2×#525D47semidirect
445. C2×C47#3197semidirect
462. #525C2×D47semidirect
510. C47C2×#3197semidirect
863. C2#20254225direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896342
#202542252
C2×#156894642
C2×#156894612
C2×#156894472
C2×#156894442
C2×#156893792
C2×#156893742
C2×#156893712
C2×#156893672
C2×#156892852
C2×#156892832
C2×#156892682
C2×#156892662
C2×#156890872
C2×C47×#5252
C2×#319747