Finite Group Databasebeta

← C2×#20254497 #27087673

Subgroups — C2×#20254497 #27087673

Order 12032.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689744C211yesmaximal, characteristic, complemented
2#20254497C2116yesmaximal, direct product factor
3C2×#15689515C211yesmaximal, characteristic, complemented
4C2×#15689505C211yesmaximal, characteristic, complemented
5C2×#15689482C211yesmaximal, characteristic, complemented
6C2×#15689473C211yesmaximal, characteristic, complemented
7C2×#15689342C211yesmaximal, characteristic, complemented
8C2×#15689330C211yesmaximal, characteristic, complemented
9C2×#15689335C211yesmaximal, characteristic, complemented
10C2×#15689325C211yesmaximal, characteristic, complemented
11C2×#15689285C211yesmaximal, characteristic, complemented
12C2×#15689268C211yesmaximal, characteristic
13C2×#15689279C211yesmaximal, characteristic, complemented
14C2×#15689262C211yesmaximal, characteristic, complemented
15C2×#15689184C211yesmaximal, characteristic, complemented
16C2×C47×#536C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×#10625336C2211yescharacteristic
22C22×#10625336C2211yescharacteristic
23C22×#10625336C2211yescharacteristic
24C22×#10625334C2211yescharacteristic
25#15689744—24no—
26#15689744C2218yescomplemented
27C2×#13094024C2211yescharacteristic
28C2×#13094019—21no—
29C2×#13094012C2211yescharacteristic
30C2×#13094010—21no—
31C2×#13094006—21no—
32C2×#13094003C2211yescharacteristic
33C2×#13094002—21no—
34C2×#13093998C2211yescharacteristic
35C2×C4×Dic94C2211yescharacteristic
36C2×C4×D188C2211yescharacteristic
37#15689515C2218yescomplemented
38#15689505C2218yescomplemented
39#15689482C2218yescomplemented
40#15689473C2218yescomplemented
41#15689342C2218yescomplemented
42#15689335C2218yescomplemented
43#15689330C2218yescomplemented
44#15689325C2218yescomplemented
45#15689285C2218yescomplemented
46#15689279C2218yescomplemented
47#15689268C2218yes—
48#15689262C2218yescomplemented
49#15689184C2218yescomplemented
50C2×C4⋊(C47⋊C8)C2211yescharacteristic
51C2×C4⋊(C47⋊C8)C2211yescharacteristic
52C2×#13093948C2211yescharacteristic
53C2×#13093948C2211yescharacteristic
54C2×#13093948C2211yescharacteristic
55C2×#13093948C2211yescharacteristic
56C2×#13093948C2211yescharacteristic
57C2×#13093948C2211yescharacteristic
58C2×#13093945C2211yescharacteristic
59C2×#13093945C2211yescharacteristic
60C2×C22⋊(C47⋊C8)C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×#13093935C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C22×#41×C47C2211yescharacteristic
65C23×Q8×C47C2211yescharacteristic
66C47×#536—24no—
67C47×#536C2218yescomplemented
68C2×C4⋊Q8×C47C2211yescharacteristic
69C2×C4⋊Q8×C47C2211yescharacteristic
70C2×#124×C47C2211yescharacteristic
71C2×#124×C47C2211yescharacteristic
72C2×#123×C47—21no—
73C2×#123×C47—21no—
74C2×C22⋊Q8×C47—21no—
75C2×C22⋊Q8×C47—21no—
76C2×#117×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C4×D47—21no—
82C2×#10625337—42no—
83C2×#10625337—42no—
84C2×#10625337—42no—
85C2×#10625337C2314yes—
86C2×#10625337C2314yes—
87C2×#10625337C2314yes—
88C2×#10625335—42no—
89C2×#10625335C2314yes—
90C2×#10625336—42no—
91C2×#10625336—42no—
92C2×#10625336—42no—
93C2×#10625336C2314yes—
94C2×#10625336C2314yes—
95C2×#10625336C2314yes—
96C2×#10625334—42no—
97C2×#10625334C2314yes—
98C22×C47⋊C8C2311yescharacteristic
99C22×C47⋊C8C2311yescharacteristic
100C22×C47⋊C8C2311yescharacteristic
101C22×C47⋊C8C2311yescharacteristic
102#13094024—22no—
103#13094024C2314yes—
104#13094019—28no—
105#13094012—22no—
106#13094012C2314yes—
107#13094010—28no—
108#13094006—28no—
109#13094003—22no—
110#13094003C2314yes—
111#13094002—28no—
112#13093998—22no—
113#13093998C2314yes—
114C4×Dic94—22no—
115C4×Dic94C2314yes—
116C4×D188—22no—
117C4×D188C2314yes—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47C2311yescharacteristic
120C2×C4⋊Dic47C2311yescharacteristic
121C2×Dic47⋊C4—21no—
122C2×Dic47⋊C4—21no—
123C2×C22⋊Dic47—21no—
124C2×(C2×D47)⋊C4—21no—
125C2×(C2×D47)⋊C4—21no—
126C2×(C2×D47)⋊C4—21no—
127C2×(C2×D47)⋊C4—21no—
128C2×C4×Dic47—21no—
129C4⋊(C47⋊C8)C2314yes—
130C4⋊(C47⋊C8)C2314yes—
131#13093948C2314yes—
132#13093948C2314yes—
133#13093948C2314yes—
134#13093948C2314yes—
135#13093948C2314yes—
136#13093948C2314yes—
137#13093945C2314yes—
138#13093945C2314yes—
139C22⋊(C47⋊C8)C2314yes—
140C22⋊(C47⋊C8)C2314yes—
141#13093935C2314yes—
142C4×C47⋊C8C2314yes—
143C2×#41×C47—22no—
144C2×#41×C47—42no—
145C2×#41×C47—42no—
146C2×#41×C47C2314yes—
147C22×Q8×C47—21no—
148C22×Q8×C47—22no—
149C22×Q8×C47—42no—
150C22×Q8×C47—42no—
151C22×Q8×C47C2311yescharacteristic
152C22×Q8×C47C2311yescharacteristic
153C22×Q8×C47C2311yescharacteristic
154C22×Q8×C47C2314yes—
155C22×D4×C47—21no—
156C22×D4×C47C2311yescharacteristic
157C23×C4×C47—21no—
158C23×C4×C47—21no—
159C23×C4×C47C2311yescharacteristic
160C4⋊Q8×C47—22no—
161C4⋊Q8×C47—22no—
162C4⋊Q8×C47C2314yes—
163C4⋊Q8×C47C2314yes—
164#124×C47—22no—
165#124×C47—22no—
166#124×C47C2314yes—
167#124×C47C2314yes—
168#123×C47—28no—
169#123×C47—28no—
170C22⋊Q8×C47—28no—
171C22⋊Q8×C47—28no—
172#117×C47D414yes—
173#117×C47C2314yes—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47—21no—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47D411yescharacteristic
179C2×C4⋊C4×C47D411yescharacteristic
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182C2×C22⋊C4×C47—21no—
183C2×C22⋊C4×C47—21no—
184C2×C22⋊C4×C47D411yescharacteristic
185C2×C22⋊C4×C47D411yescharacteristic
186C2×C42×C47C2311yescharacteristic
187C2×C42×C47C2311yescharacteristic
188C24×C47—21no—
189C24×C47C2×D411yescharacteristic
190C23×D47—21no—
191#41×C47—44no—
192#41×C47—44no—
193#41×C47—48no—
194C2×Q8×C47—24no—
195C2×Q8×C47—21no—
196C2×Q8×C47—21no—
197C2×Q8×C47—21no—
198C2×Q8×C47—22no—
199C2×Q8×C47—22no—
200C2×Q8×C47—22no—
201C2×Q8×C47—22no—
202C2×Q8×C47—22no—
203C2×Q8×C47—22no—
204C2×Q8×C47—44no—
205C2×Q8×C47—44no—
206C2×Q8×C47—44no—
207C2×Q8×C47—48no—
208C2×Q8×C47C2412yes—
209C2×Q8×C47C2412yes—
210C2×Q8×C47C2412yes—
211C2×D4×C47—24no—
212C2×D4×C47—21no—
213C2×D4×C47—22no—
214C2×D4×C47—22no—
215C2×D4×C47—44no—
216C2×D4×C47C2412yes—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—24no—
223C22×C4×C47—24no—
224C22×C4×C47—44no—
225C22×C4×C47—44no—
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D412yes—
232C22×C4×C47C2412yes—
233C22×C4×C47C2411yescharacteristic
234C2×C22⋊D47—24no—
235C2×C22⋊D47—82no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—21no—
239C2×D188—22no—
240C2×D188—22no—
241C2×D188—21no—
242C2×D188C2412yes—
243C2×C4×D47—24no—
244C2×C4×D47—82no—
245C2×Dic94—22no—
246C2×Dic94—22no—
247C2×Dic94—21no—
248C2×Dic94—24no—
249C2×Dic94—82no—
250C2×Dic94C2412yes—
251C4⋊C4×C47—24no—
252C4⋊C4×C47—24no—
253C4⋊C4×C47—24no—
254C4⋊C4×C47—24no—
255C4⋊C4×C47C2×D414yes—
256C4⋊C4×C47C2×D414yes—
257C22⋊C4×C47—24no—
258C22⋊C4×C47—24no—
259C22⋊C4×C47—24no—
260C22⋊C4×C47—24no—
261C22⋊C4×C47C2×D414yes—
262C22⋊C4×C47C2×D414yes—
263C42×C47C2×D412yes—
264C42×C47C2×D412yes—
265C42×C47C2412yes—
266C42×C47C2412yes—
267C22⋊Dic47—24no—
268#10625337—44no—
269#10625337—44no—
270#10625337—44no—
271#10625336—44no—
272#10625336—44no—
273#10625336—44no—
274#10625335—44no—
275#10625334—44no—
276(C2×D47)⋊C4—24no—
277(C2×D47)⋊C4—24no—
278(C2×D47)⋊C4—24no—
279(C2×D47)⋊C4—24no—
280C4⋊Dic47—24no—
281C4⋊Dic47—21no—
282C4⋊Dic47—21no—
283C4⋊Dic47C2412yes—
284C4⋊Dic47C2412yes—
285Dic47⋊C4—24no—
286Dic47⋊C4—24no—
287C4×Dic47—24no—
288C2×C47⋊C8—22no—
289C2×C47⋊C8—22no—
290C2×C47⋊C8—22no—
291C2×C47⋊C8—22no—
292C2×C47⋊C8C2412yes—
293C2×C47⋊C8C2412yes—
294C2×C47⋊C8C2412yes—
295C2×C47⋊C8C2412yes—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—42no—
301C23×C47—42no—
302C23×C47—42no—
303C23×C47C22×D412yes—
304C23×C47C22×D411yescharacteristic
305C22×D47—22no—
306C22×D47—42no—
307C22×D47—42no—
308C22×D47—42no—
309Q8×C47—22no—
310Q8×C47—22no—
311Q8×C47—22no—
312Q8×C47—22no—
313Q8×C47—22no—
314Q8×C47—22no—
315Q8×C47—48no—
316Q8×C47—42no—
317Q8×C47—42no—
318Q8×C47—42no—
319D4×C47—22no—
320D4×C47—22no—
321D4×C47—48no—
322D4×C47—42no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—24no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—48no—
335C2×C4×C47—48no—
336C2×C4×C47—42no—
337C2×C4×C47—42no—
338C2×C4×C47—42no—
339C2×C4×C47C22×D412yes—
340C2×C4×C47C22×D412yes—
341C2×C4×C47C22×D412yes—
342C2×C4×C47C22×D412yes—
343C2×C4×C47C22×D412yes—
344C2×C4×C47C22×D411yescharacteristic
345C2×C4×C47H(5,𝔽2)12yes—
346C2×C4×C47H(5,𝔽2)12yes—
347C2×C4×C47C2511yescharacteristic
348C22⋊D47—84no—
349C2×Dic47—22no—
350C2×Dic47—22no—
351C2×Dic47—22no—
352C2×Dic47—42no—
353C2×Dic47—42no—
354C2×Dic47—42no—
355D188—22no—
356D188—22no—
357D188—42no—
358C4×D47—84no—
359Dic94—22no—
360Dic94—22no—
361Dic94—42no—
362Dic94—84no—
363C47⋊C8—22no—
364C47⋊C8—22no—
365C47⋊C8—22no—
366C47⋊C8—22no—
367C2×#3225—471nomaximal, Sylow
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—44no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—84no—
376C22×C47#53512yes—
377C22×C47#57712yes—
378C22×C47#57812yes—
379C22×C47C23×D411yescharacteristic
380C2×D47—42no—
381C2×D47—42no—
382C2×D47—42no—
383C2×D47—84no—
384C4×C47—22no—
385C4×C47—22no—
386C4×C47—22no—
387C4×C47—22no—
388C4×C47—22no—
389C4×C47—42no—
390C4×C47—42no—
391C4×C47—42no—
392C4×C47#53512yes—
393C4×C47C2×H(5,𝔽2)11yescharacteristic
394C4×C47C2×H(5,𝔽2)11yescharacteristic
395Dic47—42no—
396Dic47—42no—
397Dic47—42no—
398C2×#542—471no—
399C2×#536D4711yescharacteristic, complemented
400#3225—4716no—
401C2×#497—471no—
402C2×#495—471no—
403C2×#489—471no—
404C2×#487—471no—
405C2×#464—471no—
406C2×#462—471no—
407C2×#463—471no—
408C2×#461—471no—
409C2×#452—471no—
410C2×#449—471no—
411C2×#451—471no—
412C2×#448—471no—
413C2×#433—471no—
414C2×C47—42no—
415C2×C47—82no—
416C2×C47#322514yescomplemented
417C2×C47C2×#53511yescharacteristic
418C2×C47C2×#57711yescharacteristic
419C2×C47C2×#57811yescharacteristic
420D47—82no—
421C22×#41C2×D4711yescharacteristic
422C23×Q8C2×D4711yescharacteristic
423C22×Q16—471no—
424C22×Q16—471no—
425C22×Q16—471no—
426C22×SD16—471no—
427C22×SD16—471no—
428C22×SD16—471no—
429C22×SD16—471no—
430C22×D8—471no—
431#542—478no—
432#542—944no—
433#536—24no—
434#536C2×D4718yescomplemented
435C2×C4⋊Q8—471no—
436C2×C4⋊Q8C2×D4711yescharacteristic
437C2×C4⋊Q8C2×D4711yescharacteristic
438C2×#126—941no—
439C2×#124—471no—
440C2×#124—941no—
441C2×#124C2×D4711yescharacteristic
442C2×#124C2×D4711yescharacteristic
443C2×#123—21no—
444C2×#123—21no—
445C2×#123—941no—
446C2×C22⋊Q8—21no—
447C2×C22⋊Q8—21no—
448C2×C22⋊Q8—471no—
449C2×C22⋊Q8—941no—
450C2×#121—471no—
451C2×C4×Q8—471no—
452C2×C4×D4—471no—
453C2×#117C2×D4711yescharacteristic
454#497—478no—
455#495—478no—
456#489—478no—
457#487—478no—
458#464—478no—
459#463—478no—
460#462—478no—
461#461—478no—
462#452—478no—
463#451—478no—
464#449—478no—
465#448—478no—
466#433—478no—
467C2×C4⋊C8—471no—
468C2×C4⋊C8—471no—
469C2×#103—471no—
470C2×#103—471no—
471C2×#103—471no—
472C2×#103—471no—
473C2×#103—471no—
474C2×#103—471no—
475C2×#102—471no—
476C2×#102—471no—
477C2×C22⋊C8—471no—
478C2×C22⋊C8—471no—
479C2×#97—471no—
480C2×C4×C8—471no—
481C47C2×#322511yescharacteristic, complemented, Sylow
482C2×#41—22no—
483C2×#41—42no—
484C2×#41—42no—
485C2×#41C22×D4714yes—
486C22×Q8—21no—
487C22×Q8—22no—
488C22×Q8—42no—
489C22×Q8—42no—
490C22×Q8—471no—
491C22×Q8—941no—
492C22×Q8C22×D4711yescharacteristic
493C22×Q8C22×D4711yescharacteristic
494C22×Q8C22×D4711yescharacteristic
495C22×Q8C22×D4714yes—
496C22×D4—21no—
497C22×D4—471no—
498C22×D4—941no—
499C22×D4C22×D4711yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—941no—
503C23×C4C22×D4711yescharacteristic
504C2×Q16—474no—
505C2×Q16—474no—
506C2×Q16—474no—
507C2×Q16—1882no—
508C2×Q16—1882no—
509C2×Q16—1882no—
510C2×SD16—474no—
511C2×SD16—474no—
512C2×SD16—474no—
513C2×SD16—474no—
514C2×SD16—1882no—
515C2×SD16—1882no—
516C2×SD16—1882no—
517C2×SD16—1882no—
518C2×D8—474no—
519C2×D8—1882no—
520C22×C8—471no—
521C22×C8—471no—
522C22×C8—471no—
523C22×C8—471no—
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526C4⋊Q8—474no—
527C4⋊Q8—942no—
528C4⋊Q8C22×D4714yes—
529C4⋊Q8C22×D4714yes—
530#126—948no—
531#124—22no—
532#124—22no—
533#124—474no—
534#124—948no—
535#124—942no—
536#124C22×D4714yes—
537#124C22×D4714yes—
538#123—28no—
539#123—28no—
540#123—948no—
541C22⋊Q8—28no—
542C22⋊Q8—28no—
543C22⋊Q8—474no—
544C22⋊Q8—942no—
545C22⋊Q8—948no—
546#121—474no—
547#121—942no—
548C4×Q8—474no—
549C4×Q8—942no—
550C4×D4—474no—
551C4×D4—942no—
552#117C22⋊D4714yes—
553#117C22×D4714yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—471no—
559C2×C4⋊C4—471no—
560C2×C4⋊C4—941no—
561C2×C4⋊C4—941no—
562C2×C4⋊C4—941no—
563C2×C4⋊C4C22⋊D4711yescharacteristic
564C2×C4⋊C4C22⋊D4711yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—941no—
570C2×C22⋊C4—941no—
571C2×C22⋊C4—941no—
572C2×C22⋊C4—941no—
573C2×C22⋊C4—941no—
574C2×C22⋊C4C22⋊D4711yescharacteristic
575C2×C22⋊C4C22⋊D4711yescharacteristic
576C2×C42—941no—
577C2×C42C22×D4711yescharacteristic
578C2×C42C22×D4711yescharacteristic
579C4⋊C8—474no—
580C4⋊C8—474no—
581#103—474no—
582#103—474no—
583#103—474no—
584#103—474no—
585#103—474no—
586#103—474no—
587#102—474no—
588#102—474no—
589C22⋊C8—474no—
590C22⋊C8—474no—
591#97—474no—
592C4×C8—474no—
593C24—21no—
594C24—941no—
595C24C2×C22⋊D4711yescharacteristic
596#41—44no—
597#41—44no—
598#41—48no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—44no—
610C2×Q8—44no—
611C2×Q8—44no—
612C2×Q8—48no—
613C2×Q8—472no—
614C2×Q8—944no—
615C2×Q8—941no—
616C2×Q8—942no—
617C2×Q8—942no—
618C2×Q8—3762no—
619C2×Q8C23×D4712yes—
620C2×Q8C23×D4712yes—
621C2×Q8C23×D4712yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—44no—
627C2×D4—472no—
628C2×D4—944no—
629C2×D4—941no—
630C2×D4—942no—
631C2×D4—942no—
632C2×D4—3762no—
633C2×D4C23×D4712yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—24no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—941no—
644C22×C4—941no—
645C22×C4—941no—
646C22×C4—944no—
647C22×C4—3762no—
648C22×C4C2×C22⋊D4712yes—
649C22×C4C2×C22⋊D4711yescharacteristic
650C22×C4C2×C22⋊D4711yescharacteristic
651C22×C4C2×C22⋊D4711yescharacteristic
652C22×C4C2×C22⋊D4711yescharacteristic
653C22×C4C2×C22⋊D4711yescharacteristic
654C22×C4C23×D4712yes—
655C22×C4C23×D4711yescharacteristic
656Q16—1884no—
657Q16—1884no—
658Q16—1884no—
659SD16—1884no—
660SD16—1884no—
661SD16—1884no—
662SD16—1884no—
663D8—1884no—
664C2×C8—472no—
665C2×C8—472no—
666C2×C8—472no—
667C2×C8—472no—
668C2×C8—942no—
669C2×C8—942no—
670C2×C8—942no—
671C2×C8—942no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—472no—
677C4⋊C4—472no—
678C4⋊C4—944no—
679C4⋊C4—944no—
680C4⋊C4—941no—
681C4⋊C4—941no—
682C4⋊C4—944no—
683C4⋊C4C2×C22⋊D4714yes—
684C4⋊C4C2×C22⋊D4714yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—944no—
690C22⋊C4—944no—
691C22⋊C4—944no—
692C22⋊C4—944no—
693C22⋊C4—944no—
694C22⋊C4C2×C22⋊D4714yes—
695C22⋊C4C2×C22⋊D4714yes—
696C42—944no—
697C42C2×C22⋊D4712yes—
698C42C2×C22⋊D4712yes—
699C42C23×D4712yes—
700C42C23×D4712yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—942no—
709C23—1882no—
710C23—1882no—
711C23—1882no—
712C23C22×C22⋊D4712yes—
713C23C22×C22⋊D4711yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—48no—
721Q8—42no—
722Q8—42no—
723Q8—42no—
724Q8—942no—
725Q8—942no—
726Q8—3764no—
727Q8—1882no—
728D4—22no—
729D4—22no—
730D4—48no—
731D4—42no—
732D4—942no—
733D4—942no—
734D4—3764no—
735D4—1882no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—3764no—
756C2×C4—1882no—
757C2×C4—1882no—
758C2×C4—1882no—
759C2×C4C22×C22⋊D4712yes—
760C2×C4C22×C22⋊D4712yes—
761C2×C4C22×C22⋊D4712yes—
762C2×C4C22×C22⋊D4712yes—
763C2×C4C22×C22⋊D4712yes—
764C2×C4C22×C22⋊D4711yescharacteristic
765C2×C4#1309406912yes—
766C2×C4#1309406912yes—
767C2×C4C24×D4711yescharacteristic
768C8—942no—
769C8—942no—
770C8—942no—
771C8—942no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—3764no—
781C22—1882no—
782C22—1882no—
783C22—1882no—
784C22#1568969012yes—
785C22#1568993112yes—
786C22#1568993812yes—
787C22C23×C22⋊D4711yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—1882no—
797C4—1882no—
798C4—1882no—
799C4#1568969012yes—
800C4C2×#1309406911yescharacteristic
801C4C2×#1309406911yescharacteristic
802C2—42no—
803C2—82no—
804C2—3762no—
805C2#2025449714yesdirect product factor
806C2C2×#1568969011yescharacteristic
807C2C2×#1568993111yescharacteristic
808C2C2×#1568993811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#536C2
socleC23×C47C22×D4
prime radicalC2×#15689268C2
hypercenterC2×#536D47
hypocenterC47C2×#3225
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#15689744C2semidirect
2. #20254497C2direct (N × H)
3. C2×#15689515C2semidirect
4. C2×#15689505C2semidirect
5. C2×#15689482C2semidirect
6. C2×#15689473C2semidirect
7. C2×#15689342C2semidirect
8. C2×#15689330C2semidirect
9. C2×#15689335C2semidirect
10. C2×#15689325C2semidirect
11. C2×#15689285C2semidirect
13. C2×#15689279C2semidirect
14. C2×#15689262C2semidirect
15. C2×#15689184C2semidirect
16. C2×C47×#536C2semidirect
26. #15689744C22semidirect
37. #15689515C22semidirect
38. #15689505C22semidirect
39. #15689482C22semidirect
40. #15689473C22semidirect
41. #15689342C22semidirect
42. #15689335C22semidirect
43. #15689330C22semidirect
44. #15689325C22semidirect
45. #15689285C22semidirect
46. #15689279C22semidirect
48. #15689262C22semidirect
49. #15689184C22semidirect
67. C47×#536C22semidirect
399. C2×#536D47semidirect
416. C2×C47#3225semidirect
434. #536C2×D47semidirect
481. C47C2×#3225semidirect
805. C2#20254497direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897442
#202544972
C2×#156895152
C2×#156895052
C2×#156894822
C2×#156894732
C2×#156893422
C2×#156893302
C2×#156893352
C2×#156893252
C2×#156892852
C2×#156892682
C2×#156892792
C2×#156892622
C2×#156891842
C2×C47×#5362
C2×#322547