Finite Group Databasebeta

← C2×#20254484 #27087635

Subgroups — C2×#20254484 #27087635

Order 12032.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689744C211yesmaximal, characteristic, complemented
2C2×#15689692C211yesmaximal, characteristic, complemented
3#20254484C2116yesmaximal, direct product factor
4C2×#15689512C211yesmaximal, characteristic, complemented
5C2×#15689507C211yesmaximal, characteristic, complemented
6C2×#15689483C211yesmaximal, characteristic, complemented
7C2×#15689470C211yesmaximal, characteristic, complemented
8C2×#15689346C211yesmaximal, characteristic, complemented
9C2×#15689324C211yesmaximal, characteristic, complemented
10C2×#15689339C211yesmaximal, characteristic, complemented
11C2×#15689319C211yesmaximal, characteristic, complemented
12C2×#15689287C211yesmaximal, characteristic, complemented
13C2×#15689270C211yesmaximal, characteristic, complemented
14C2×#15689276C211yesmaximal, characteristic, complemented
15C2×#15689259C211yesmaximal, characteristic, complemented
16C2×C47×#433C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C22×Dic188C2211yescharacteristic, complemented
20C22×#10625325C2211yescharacteristic
21C22×#10625325C2211yescharacteristic
22C22×#10625325C2211yescharacteristic, complemented
23C22×#10625325C2211yescharacteristic, complemented
24C22×D376C2211yescharacteristic
25C22×D376C2211yescharacteristic
26C22×D376C2211yescharacteristic, complemented
27#15689744—24no—
28#15689744C2218yescomplemented
29#15689692—24no—
30#15689692C2218yescomplemented
31C2×#13094024C2211yescharacteristic, complemented
32C2×#13094021C2211yescharacteristic
33C2×#13094021C2211yescharacteristic
34C2×#13094019—21no—
35C2×#13094012C2211yescharacteristic
36C2×#13094012C2211yescharacteristic
37C2×#13094012C2211yescharacteristic, complemented
38C2×#13094010—21no—
39C2×#13094006—21no—
40C2×#13094003C2211yescharacteristic
41C2×#13094002—21no—
42C2×#13093999—21no—
43C2×#13093999—21no—
44C2×#13093998C2211yescharacteristic
45C2×#13093994—21no—
46C2×#13093994—21no—
47C2×C4×Dic94C2211yescharacteristic, complemented
48C2×C4×D188C2211yescharacteristic, complemented
49#15689512C2218yescomplemented
50#15689507C2218yescomplemented
51#15689483C2218yescomplemented
52#15689470C2218yescomplemented
53#15689346C2218yescomplemented
54#15689339C2218yescomplemented
55#15689324C2218yescomplemented
56#15689319C2218yescomplemented
57#15689287C2218yescomplemented
58#15689276C2218yescomplemented
59#15689270C2218yescomplemented
60#15689259C2218yescomplemented
61C2×#13093949C2211yescharacteristic, complemented
62C2×#13093949C2211yescharacteristic, complemented
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic, complemented
68C2×#13093946C2211yescharacteristic, complemented
69C2×#117×C47C2211yescharacteristic
70C47×#433C2218yescomplemented
71C2×C4⋊C8×C47C2211yescharacteristic, complemented
72C2×C4⋊C8×C47C2211yescharacteristic, complemented
73C2×C22⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×#97×C47C2211yescharacteristic, complemented
76C2×C4×C8×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625350—22no—
79C2×#10625350—42no—
80C2×#10625350—42no—
81C2×#10625350C2314yes—
82C22×Dic94—21no—
83C22×Dic94C2311yescharacteristic
84C22×Dic94C2311yescharacteristic
85C22×D188—21no—
86C22×D188—22no—
87C22×D188—21no—
88C22×D188—21no—
89C22×D188—21no—
90C22×D188—21no—
91C22×D188—42no—
92C22×D188—42no—
93C22×D188C2311yescharacteristic
94C22×D188C2311yescharacteristic
95C22×D188C2311yescharacteristic
96C22×D188C2311yescharacteristic
97C22×D188C2314yes—
98C22×C22⋊D47—21no—
99C22×C22⋊D47—21no—
100C22×C4×D47—21no—
101C22×C4×D47—21no—
102C2×Dic188—42no—
103C2×Dic188C2314yescomplemented
104C2×#10625325—42no—
105C2×#10625325—42no—
106C2×#10625325—42no—
107C2×#10625325—42no—
108C2×#10625325C2314yes—
109C2×#10625325C2314yes—
110C2×#10625325C2314yescomplemented
111C2×#10625325C2314yescomplemented
112C2×D376—42no—
113C2×D376—42no—
114C2×D376—42no—
115C2×D376C2314yes—
116C2×D376C2314yes—
117C2×D376C2314yescomplemented
118#13094024—22no—
119#13094024C2314yescomplemented
120#13094021—22no—
121#13094021—22no—
122#13094021C2314yes—
123#13094021C2314yes—
124#13094019—28no—
125#13094012—22no—
126#13094012—22no—
127#13094012—22no—
128#13094012C2314yes—
129#13094012C2314yes—
130#13094012C2314yescomplemented
131#13094010—28no—
132#13094006—28no—
133#13094003—22no—
134#13094003C2314yes—
135#13094002—28no—
136#13093999—28no—
137#13093999—28no—
138#13093998—22no—
139#13093998C2314yes—
140#13093994—28no—
141#13093994—28no—
142C4×Dic94—22no—
143C4×Dic94C2314yescomplemented
144C4×D188—22no—
145C4×D188C2314yescomplemented
146C2×C4⋊Dic47—21no—
147C2×C4⋊Dic47C2311yescharacteristic
148C2×C4⋊Dic47C2311yescharacteristic
149C2×Dic47⋊C4—21no—
150C2×Dic47⋊C4—21no—
151C2×C22⋊Dic47—21no—
152C2×(C2×D47)⋊C4—21no—
153C2×(C2×D47)⋊C4—21no—
154C2×(C2×D47)⋊C4—21no—
155C2×(C2×D47)⋊C4—21no—
156C2×(C2×D47)⋊C4—21no—
157C2×(C2×D47)⋊C4—21no—
158C2×(C2×D47)⋊C4—21no—
159C2×(C2×D47)⋊C4—21no—
160C2×C4×Dic47—21no—
161#13093949C2314yescomplemented
162#13093949C2314yescomplemented
163#13093946C2314yes—
164#13093946C2314yes—
165#13093946C2314yes—
166#13093946C2314yes—
167#13093946C2314yescomplemented
168#13093946C2314yescomplemented
169C23×C4×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174#117×C47D414yes—
175#117×C47C2314yes—
176C2×C4⋊C4×C47D411yescharacteristic
177C2×C4⋊C4×C47D411yescharacteristic
178C2×C22⋊C4×C47D411yescharacteristic
179C2×C22⋊C4×C47D411yescharacteristic
180C2×C42×C47C2311yescharacteristic
181C2×C42×C47C2311yescharacteristic
182C4⋊C8×C47C2314yescomplemented
183C4⋊C8×C47C2314yescomplemented
184C22⋊C8×C47C2314yes—
185C22⋊C8×C47C2314yes—
186#97×C47C2314yescomplemented
187C4×C8×C47C2314yescomplemented
188C24×C47C2×D411yescharacteristic
189C23×D47—21no—
190C23×D47—21no—
191C23×D47—21no—
192C23×D47—21no—
193C23×D47—24no—
194C23×D47—44no—
195C23×D47—82no—
196C23×D47—82no—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D412yes—
205C22×C4×C47C2412yes—
206C22×C4×C47C2411yescharacteristic
207C2×C22⋊D47—24no—
208C2×C22⋊D47—24no—
209C2×C22⋊D47—44no—
210C2×C22⋊D47—82no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215#10625350—44no—
216#10625350—44no—
217#10625350—48no—
218C2×D188—22no—
219C2×D188—22no—
220C2×D188—22no—
221C2×D188—22no—
222C2×D188—22no—
223C2×D188—22no—
224C2×D188—22no—
225C2×D188—22no—
226C2×D188—21no—
227C2×D188—24no—
228C2×D188—21no—
229C2×D188—21no—
230C2×D188—21no—
231C2×D188—24no—
232C2×D188—24no—
233C2×D188—24no—
234C2×D188—24no—
235C2×D188—44no—
236C2×D188—44no—
237C2×D188—44no—
238C2×D188—48no—
239C2×D188—82no—
240C2×D188—82no—
241C2×D188—82no—
242C2×D188—82no—
243C2×D188C2412yes—
244C2×D188C2412yes—
245C2×D188C2412yes—
246C2×D188C2412yes—
247C2×C4×D47—24no—
248C2×C4×D47—24no—
249C2×C4×D47—44no—
250C2×C4×D47—82no—
251C2×Dic94—22no—
252C2×Dic94—22no—
253C2×Dic94—22no—
254C2×Dic94—22no—
255C2×Dic94—21no—
256C2×Dic94—21no—
257C2×Dic94—24no—
258C2×Dic94—82no—
259C2×Dic94C2412yes—
260C2×Dic94C2412yes—
261C2×C8×C47—22no—
262C2×C8×C47—22no—
263C2×C8×C47—22no—
264C2×C8×C47—22no—
265C2×C8×C47C2412yes—
266C2×C8×C47C2412yes—
267C2×C8×C47C2412yes—
268C2×C8×C47C2412yes—
269C4⋊C4×C47C2×D414yes—
270C4⋊C4×C47C2×D414yes—
271C22⋊C4×C47C2×D414yes—
272C22⋊C4×C47C2×D414yes—
273C42×C47C2×D412yes—
274C42×C47C2×D412yes—
275C42×C47C2412yes—
276C42×C47C2412yes—
277C22⋊Dic47—24no—
278(C2×D47)⋊C4—24no—
279(C2×D47)⋊C4—24no—
280(C2×D47)⋊C4—24no—
281(C2×D47)⋊C4—24no—
282(C2×D47)⋊C4—24no—
283(C2×D47)⋊C4—24no—
284(C2×D47)⋊C4—24no—
285(C2×D47)⋊C4—24no—
286C4⋊Dic47—24no—
287C4⋊Dic47—21no—
288C4⋊Dic47—21no—
289C4⋊Dic47C2412yes—
290C4⋊Dic47C2412yes—
291Dic47⋊C4—24no—
292Dic47⋊C4—24no—
293C4×Dic47—24no—
294Dic188—44no—
295D376—44no—
296D376—44no—
297D376—44no—
298#10625325—44no—
299#10625325—44no—
300#10625325—44no—
301#10625325—44no—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47C22×D412yes—
306C23×C47C22×D411yescharacteristic
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—22no—
311C22×D47—48no—
312C22×D47—42no—
313C22×D47—42no—
314C22×D47—42no—
315C22×D47—42no—
316C22×D47—42no—
317C22×D47—42no—
318C22×D47—42no—
319C22×D47—42no—
320C22×D47—42no—
321C22×D47—42no—
322C22×D47—42no—
323C22×D47—42no—
324C22×D47—84no—
325C22×D47—84no—
326C22×D47—816no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—24no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47C22×D412yes—
336C2×C4×C47C22×D412yes—
337C2×C4×C47C22×D412yes—
338C2×C4×C47C22×D412yes—
339C2×C4×C47C22×D412yes—
340C2×C4×C47C22×D411yescharacteristic
341C2×C4×C47H(5,𝔽2)12yes—
342C2×C4×C47H(5,𝔽2)12yes—
343C2×C4×C47C2511yescharacteristic
344C22⋊D47—48no—
345C22⋊D47—84no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—42no—
351C2×Dic47—42no—
352C2×Dic47—42no—
353C2×Dic47—42no—
354D188—22no—
355D188—22no—
356D188—22no—
357D188—22no—
358D188—22no—
359D188—22no—
360D188—22no—
361D188—22no—
362D188—48no—
363D188—42no—
364D188—42no—
365D188—42no—
366D188—42no—
367D188—84no—
368D188—84no—
369D188—84no—
370D188—84no—
371C4×D47—48no—
372C4×D47—84no—
373Dic94—22no—
374Dic94—22no—
375Dic94—22no—
376Dic94—22no—
377Dic94—42no—
378Dic94—42no—
379Dic94—84no—
380C8×C47—22no—
381C8×C47—22no—
382C8×C47—22no—
383C8×C47—22no—
384C2×#3224—471nomaximal, Sylow
385C22×C47—22no—
386C22×C47—22no—
387C22×C47—22no—
388C22×C47—44no—
389C22×C47#53512yes—
390C22×C47#57612yes—
391C22×C47#57712yes—
392C22×C47C23×D411yescharacteristic
393C2×D47—42no—
394C2×D47—42no—
395C2×D47—42no—
396C2×D47—42no—
397C2×D47—42no—
398C2×D47—42no—
399C2×D47—42no—
400C2×D47—42no—
401C2×D47—42no—
402C2×D47—42no—
403C2×D47—42no—
404C2×D47—42no—
405C2×D47—816no—
406C2×D47—84no—
407C2×D47—84no—
408C2×D47—84no—
409C2×D47—84no—
410C4×C47—22no—
411C4×C47—22no—
412C4×C47—22no—
413C4×C47—22no—
414C4×C47—22no—
415C4×C47#53512yes—
416C4×C47C2×H(5,𝔽2)11yescharacteristic
417C4×C47C2×H(5,𝔽2)11yescharacteristic
418Dic47—42no—
419Dic47—42no—
420Dic47—42no—
421Dic47—42no—
422C2×#542—471no—
423C2×#535—471no—
424#3224—4716no—
425C2×#496—471no—
426C2×#495—471no—
427C2×#489—471no—
428C2×#486—471no—
429C2×#464—471no—
430C2×#460—471no—
431C2×#463—471no—
432C2×#459—471no—
433C2×#452—471no—
434C2×#449—471no—
435C2×#450—471no—
436C2×#447—471no—
437C2×#433D4711yescharacteristic, complemented
438C2×C47—42no—
439C2×C47#322414yescomplemented
440C2×C47C2×#53511yescharacteristic
441C2×C47C2×#57611yescharacteristic
442C2×C47C2×#57711yescharacteristic
443D47—82no—
444D47—82no—
445D47—82no—
446D47—82no—
447C22×#41—471no—
448C23×D4—471no—
449C22×Q16—471no—
450C22×SD16—471no—
451C22×SD16—471no—
452C22×SD16—471no—
453C22×SD16—471no—
454C22×D8—471no—
455C22×D8—471no—
456C22×D8—471no—
457#542—478no—
458#542—944no—
459#535—478no—
460#535—944no—
461C2×C4⋊Q8—471no—
462C2×#127—471no—
463C2×#127—471no—
464C2×#126—941no—
465C2×#124—471no—
466C2×#124—471no—
467C2×#124—471no—
468C2×#124—941no—
469C2×#123—941no—
470C2×C22⋊Q8—471no—
471C2×C22⋊Q8—941no—
472C2×#121—471no—
473C2×#121—941no—
474C2×#121—941no—
475C2×#120—941no—
476C2×#120—941no—
477C2×C4×Q8—471no—
478C2×C4×D4—471no—
479C2×#117C2×D4711yescharacteristic
480#496—478no—
481#495—478no—
482#489—478no—
483#486—478no—
484#464—478no—
485#463—478no—
486#460—478no—
487#459—478no—
488#452—478no—
489#450—478no—
490#449—478no—
491#447—478no—
492#433C2×D4718yescomplemented
493C2×C4⋊C8C2×D4711yescharacteristic, complemented
494C2×C4⋊C8C2×D4711yescharacteristic, complemented
495C2×#103—471no—
496C2×#103—471no—
497C2×#102—471no—
498C2×#102—471no—
499C2×#102—471no—
500C2×#102—471no—
501C2×#102—471no—
502C2×#102—471no—
503C2×C22⋊C8C2×D4711yescharacteristic
504C2×C22⋊C8C2×D4711yescharacteristic
505C2×#97C2×D4711yescharacteristic, complemented
506C2×C4×C8C2×D4711yescharacteristic, complemented
507C47C2×#322411yescharacteristic, complemented, Sylow
508C25—941no—
509C2×#41—474no—
510C2×#41—942no—
511C2×#41—1882no—
512C2×#41—1882no—
513C22×Q8—471no—
514C22×Q8—471no—
515C22×Q8—941no—
516C22×D4—471no—
517C22×D4—471no—
518C22×D4—471no—
519C22×D4—471no—
520C22×D4—474no—
521C22×D4—941no—
522C22×D4—941no—
523C22×D4—941no—
524C22×D4—941no—
525C22×D4—941no—
526C22×D4—941no—
527C22×D4—941no—
528C22×D4—942no—
529C22×D4—1882no—
530C22×D4—1882no—
531C23×C4—941no—
532C23×C4—941no—
533C23×C4C22×D4711yescharacteristic
534C2×Q16—474no—
535C2×Q16—1882no—
536C2×SD16—474no—
537C2×SD16—474no—
538C2×SD16—474no—
539C2×SD16—474no—
540C2×SD16—1882no—
541C2×SD16—1882no—
542C2×SD16—1882no—
543C2×SD16—1882no—
544C2×D8—474no—
545C2×D8—474no—
546C2×D8—474no—
547C2×D8—1882no—
548C2×D8—1882no—
549C2×D8—1882no—
550C22×C8C22×D4711yescharacteristic
551C22×C8C22×D4711yescharacteristic
552C22×C8C22×D4711yescharacteristic
553C22×C8C22×D4711yescharacteristic
554C4⋊Q8—474no—
555C4⋊Q8—942no—
556#127—474no—
557#127—474no—
558#127—942no—
559#127—942no—
560#126—948no—
561#124—474no—
562#124—474no—
563#124—474no—
564#124—948no—
565#124—942no—
566#124—942no—
567#124—942no—
568#123—948no—
569C22⋊Q8—474no—
570C22⋊Q8—942no—
571C22⋊Q8—948no—
572#121—474no—
573#121—942no—
574#121—948no—
575#121—948no—
576#120—948no—
577#120—948no—
578C4×Q8—474no—
579C4×Q8—942no—
580C4×D4—474no—
581C4×D4—942no—
582#117D18814yes—
583#117C22×D4714yes—
584C2×C4⋊C4—471no—
585C2×C4⋊C4—471no—
586C2×C4⋊C4—941no—
587C2×C4⋊C4—941no—
588C2×C4⋊C4—941no—
589C2×C4⋊C4D18811yescharacteristic
590C2×C4⋊C4D18811yescharacteristic
591C2×C22⋊C4—941no—
592C2×C22⋊C4—941no—
593C2×C22⋊C4—941no—
594C2×C22⋊C4—941no—
595C2×C22⋊C4—941no—
596C2×C22⋊C4—941no—
597C2×C22⋊C4—941no—
598C2×C22⋊C4—941no—
599C2×C22⋊C4—941no—
600C2×C22⋊C4D18811yescharacteristic
601C2×C22⋊C4D18811yescharacteristic
602C2×C42—941no—
603C2×C42C22×D4711yescharacteristic
604C2×C42C22×D4711yescharacteristic
605C4⋊C8C22×D4714yescomplemented
606C4⋊C8C22×D4714yescomplemented
607#103—474no—
608#103—474no—
609#102—474no—
610#102—474no—
611#102—474no—
612#102—474no—
613#102—474no—
614#102—474no—
615C22⋊C8C22×D4714yes—
616C22⋊C8C22×D4714yes—
617#97C22×D4714yescomplemented
618C4×C8C22×D4714yescomplemented
619C24—944no—
620C24—941no—
621C24—941no—
622C24—941no—
623C24—941no—
624C24—3762no—
625C24—3762no—
626C24—1884no—
627C24C2×D18811yescharacteristic
628#41—1884no—
629#41—1884no—
630#41—1888no—
631C2×Q8—472no—
632C2×Q8—472no—
633C2×Q8—944no—
634C2×Q8—941no—
635C2×Q8—941no—
636C2×Q8—942no—
637C2×Q8—942no—
638C2×Q8—942no—
639C2×Q8—942no—
640C2×Q8—3762no—
641C2×D4—472no—
642C2×D4—472no—
643C2×D4—472no—
644C2×D4—472no—
645C2×D4—944no—
646C2×D4—944no—
647C2×D4—944no—
648C2×D4—944no—
649C2×D4—944no—
650C2×D4—944no—
651C2×D4—941no—
652C2×D4—944no—
653C2×D4—941no—
654C2×D4—941no—
655C2×D4—941no—
656C2×D4—942no—
657C2×D4—942no—
658C2×D4—942no—
659C2×D4—942no—
660C2×D4—942no—
661C2×D4—942no—
662C2×D4—942no—
663C2×D4—942no—
664C2×D4—3762no—
665C2×D4—3762no—
666C2×D4—3762no—
667C2×D4—3762no—
668C2×D4—3762no—
669C2×D4—1884no—
670C2×D4—1884no—
671C2×D4—1884no—
672C2×D4—1888no—
673C2×D4—1884no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—941no—
677C22×C4—941no—
678C22×C4—941no—
679C22×C4—941no—
680C22×C4—944no—
681C22×C4—944no—
682C22×C4—3762no—
683C22×C4—1884no—
684C22×C4C2×D18812yes—
685C22×C4C2×D18811yescharacteristic
686C22×C4C2×D18811yescharacteristic
687C22×C4C2×D18811yescharacteristic
688C22×C4C2×D18811yescharacteristic
689C22×C4C2×D18811yescharacteristic
690C22×C4C23×D4712yes—
691C22×C4C23×D4711yescharacteristic
692Q16—1884no—
693SD16—1884no—
694SD16—1884no—
695SD16—1884no—
696SD16—1884no—
697D8—1884no—
698D8—1884no—
699D8—1884no—
700C2×C8—22no—
701C2×C8—22no—
702C2×C8—22no—
703C2×C8—22no—
704C2×C8C23×D4712yes—
705C2×C8C23×D4712yes—
706C2×C8C23×D4712yes—
707C2×C8C23×D4712yes—
708C4⋊C4—472no—
709C4⋊C4—472no—
710C4⋊C4—944no—
711C4⋊C4—944no—
712C4⋊C4—941no—
713C4⋊C4—941no—
714C4⋊C4—944no—
715C4⋊C4C2×D18814yes—
716C4⋊C4C2×D18814yes—
717C22⋊C4—944no—
718C22⋊C4—944no—
719C22⋊C4—944no—
720C22⋊C4—944no—
721C22⋊C4—944no—
722C22⋊C4—944no—
723C22⋊C4—944no—
724C22⋊C4—944no—
725C22⋊C4—944no—
726C22⋊C4C2×D18814yes—
727C22⋊C4C2×D18814yes—
728C42—944no—
729C42C2×D18812yes—
730C42C2×D18812yes—
731C42C23×D4712yes—
732C42C23×D4712yes—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—942no—
737C23—942no—
738C23—942no—
739C23—942no—
740C23—3764no—
741C23—3764no—
742C23—37616no—
743C23—1888no—
744C23—1882no—
745C23—1882no—
746C23—1882no—
747C23—1882no—
748C23—1882no—
749C23—1882no—
750C23—1882no—
751C23—1882no—
752C23—1882no—
753C23—1882no—
754C23—1882no—
755C23—1882no—
756C23C22×D18812yes—
757C23C22×D18811yescharacteristic
758Q8—942no—
759Q8—942no—
760Q8—942no—
761Q8—942no—
762Q8—3764no—
763Q8—1882no—
764Q8—1882no—
765D4—942no—
766D4—942no—
767D4—942no—
768D4—942no—
769D4—942no—
770D4—942no—
771D4—942no—
772D4—942no—
773D4—3764no—
774D4—3764no—
775D4—3764no—
776D4—3764no—
777D4—3764no—
778D4—1888no—
779D4—1888no—
780D4—1882no—
781D4—1882no—
782D4—1882no—
783D4—1882no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—942no—
793C2×C4—942no—
794C2×C4—942no—
795C2×C4—942no—
796C2×C4—3764no—
797C2×C4—1888no—
798C2×C4—1882no—
799C2×C4—1882no—
800C2×C4—1882no—
801C2×C4—1882no—
802C2×C4C22×D18812yes—
803C2×C4C22×D18812yes—
804C2×C4C22×D18812yes—
805C2×C4C22×D18812yes—
806C2×C4C22×D18812yes—
807C2×C4C22×D18811yescharacteristic
808C2×C4#1309407012yes—
809C2×C4#1309407012yes—
810C2×C4C24×D4711yescharacteristic
811C8—22no—
812C8—22no—
813C8—22no—
814C8—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—37616no—
820C22—3764no—
821C22—3764no—
822C22—3764no—
823C22—3764no—
824C22—1882no—
825C22—1882no—
826C22—1882no—
827C22—1882no—
828C22—1882no—
829C22—1882no—
830C22—1882no—
831C22—1882no—
832C22—1882no—
833C22—1882no—
834C22—1882no—
835C22—1882no—
836C22#1568969212yes—
837C22#1568992812yes—
838C22#1568993512yes—
839C22C23×D18811yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—1882no—
846C4—1882no—
847C4—1882no—
848C4—1882no—
849C4#1568969212yes—
850C4C2×#1309407011yescharacteristic
851C4C2×#1309407011yescharacteristic
852C2—42no—
853C2—3762no—
854C2—3762no—
855C2—3762no—
856C2—3762no—
857C2#2025448414yesdirect product factor
858C2C2×#1568969211yescharacteristic
859C2C2×#1568992811yescharacteristic
860C2C2×#1568993511yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#433C2
socleC23×C47C22×D4
hypercenterC2×#433D47
hypocenterC47C2×#3224
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#15689744C2semidirect
2. C2×#15689692C2semidirect
3. #20254484C2direct (N × H)
4. C2×#15689512C2semidirect
5. C2×#15689507C2semidirect
6. C2×#15689483C2semidirect
7. C2×#15689470C2semidirect
8. C2×#15689346C2semidirect
9. C2×#15689324C2semidirect
10. C2×#15689339C2semidirect
11. C2×#15689319C2semidirect
12. C2×#15689287C2semidirect
13. C2×#15689270C2semidirect
14. C2×#15689276C2semidirect
15. C2×#15689259C2semidirect
16. C2×C47×#433C2semidirect
19. C22×Dic188C22semidirect
22. C22×#10625325C22semidirect
23. C22×#10625325C22semidirect
26. C22×D376C22semidirect
28. #15689744C22semidirect
30. #15689692C22semidirect
31. C2×#13094024C22semidirect
37. C2×#13094012C22semidirect
47. C2×C4×Dic94C22semidirect
48. C2×C4×D188C22semidirect
49. #15689512C22semidirect
50. #15689507C22semidirect
51. #15689483C22semidirect
52. #15689470C22semidirect
53. #15689346C22semidirect
54. #15689339C22semidirect
55. #15689324C22semidirect
56. #15689319C22semidirect
57. #15689287C22semidirect
58. #15689276C22semidirect
59. #15689270C22semidirect
60. #15689259C22semidirect
61. C2×#13093949C22semidirect
62. C2×#13093949C22semidirect
67. C2×#13093946C22semidirect
68. C2×#13093946C22semidirect
70. C47×#433C22semidirect
71. C2×C4⋊C8×C47C22semidirect
72. C2×C4⋊C8×C47C22semidirect
75. C2×#97×C47C22semidirect
76. C2×C4×C8×C47C22semidirect
103. C2×Dic188C23semidirect
110. C2×#10625325C23semidirect
111. C2×#10625325C23semidirect
117. C2×D376C23semidirect
119. #13094024C23semidirect
130. #13094012C23semidirect
143. C4×Dic94C23semidirect
145. C4×D188C23semidirect
161. #13093949C23semidirect
162. #13093949C23semidirect
167. #13093946C23semidirect
168. #13093946C23semidirect
182. C4⋊C8×C47C23semidirect
183. C4⋊C8×C47C23semidirect
186. #97×C47C23semidirect
187. C4×C8×C47C23semidirect
437. C2×#433D47semidirect
439. C2×C47#3224semidirect
492. #433C2×D47semidirect
493. C2×C4⋊C8C2×D47semidirect
494. C2×C4⋊C8C2×D47semidirect
505. C2×#97C2×D47semidirect
506. C2×C4×C8C2×D47semidirect
507. C47C2×#3224semidirect
605. C4⋊C8C22×D47semidirect
606. C4⋊C8C22×D47semidirect
617. #97C22×D47semidirect
618. C4×C8C22×D47semidirect
857. C2#20254484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897442
C2×#156896922
#202544842
C2×#156895122
C2×#156895072
C2×#156894832
C2×#156894702
C2×#156893462
C2×#156893242
C2×#156893392
C2×#156893192
C2×#156892872
C2×#156892702
C2×#156892762
C2×#156892592
C2×C47×#4332
C2×#322447