Finite Group Databasebeta

← C2×#20254238 #27086929

Subgroups — C2×#20254238 #27086929

Order 12032.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689702C211yesmaximal, characteristic, complemented
2C2×#15689692C211yesmaximal, characteristic, complemented
3#20254238C2116yesmaximal, direct product factor
4C2×#15689443C211yesmaximal, characteristic, complemented
5C2×#15689464C211yesmaximal, characteristic, complemented
6C2×#15689438C211yesmaximal, characteristic, complemented
7C2×#15689375C211yesmaximal, characteristic, complemented
8C2×#15689370C211yesmaximal, characteristic, complemented
9C2×#15689358C211yesmaximal, characteristic, complemented
10C2×#15689353C211yesmaximal, characteristic, complemented
11C2×#15689269C211yesmaximal, characteristic, complemented
12C2×#15689269C211yesmaximal, characteristic, complemented
13C2×#15689276C211yesmaximal, characteristic, complemented
14C2×#15689256C211yesmaximal, characteristic, complemented
15C2×#15689088C211yesmaximal, characteristic, complemented
16C2×C47×#482C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625352C2211yescharacteristic, complemented
19C23×D188C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×#10625325C2211yescharacteristic
22C22×#10625334C2211yescharacteristic
23C22×#10625334C2211yescharacteristic
24C22×#10625324C2211yescharacteristic, complemented
25C22×C8×D47C2211yescharacteristic, complemented
26#15689702—24no—
27#15689702C2218yescomplemented
28#15689692—24no—
29#15689692C2218yescomplemented
30C2×#13094021—21no—
31C2×#13094012—21no—
32C2×#13094004C2211yescharacteristic, complemented
33C2×#13094003C2211yescharacteristic
34C2×#13094001—21no—
35C2×#13093999C2211yescharacteristic
36C2×#13093999C2211yescharacteristic
37C2×#13093999C2211yescharacteristic
38C2×#13093999C2211yescharacteristic
39C2×#13093997—21no—
40C2×#13093996—21no—
41C2×#13093995—21no—
42C2×#13093995C2211yescharacteristic, complemented
43C2×#13093994—21no—
44C2×#13093994—21no—
45C2×C4⋊C4×D47C2211yescharacteristic, complemented
46#15689464C2218yescomplemented
47#15689443C2218yescomplemented
48#15689438C2218yescomplemented
49#15689375C2218yescomplemented
50#15689370C2218yescomplemented
51#15689358C2218yescomplemented
52#15689353C2218yescomplemented
53#15689276C2218yescomplemented
54#15689269C2218yescomplemented
55#15689269C2218yescomplemented
56#15689256C2218yescomplemented
57C2×#13093957C2211yescharacteristic, complemented
58C2×#13093955C2211yescharacteristic, complemented
59C2×#13093947C2211yescharacteristic, complemented
60C2×#13093947C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65#15689088C2218yescomplemented
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
69C2×#121×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C47×#482C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#102×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic
77C24×D47—21no—
78C2×#10625350—42no—
79C2×#10625350—42no—
80C2×#10625350D414yes—
81C2×#10625350C2314yes—
82C2×#10625352—22no—
83C2×#10625352—42no—
84C2×#10625352—42no—
85C2×#10625352C2314yescomplemented
86C22×Dic94D411yescharacteristic
87C22×Dic94C2311yescharacteristic
88C22×D188—21no—
89C22×D188—22no—
90C22×D188—21no—
91C22×D188—21no—
92C22×D188—21no—
93C22×D188—21no—
94C22×D188—42no—
95C22×D188—42no—
96C22×D188D411yescharacteristic
97C22×D188C2311yescharacteristic
98C22×D188C2311yescharacteristic
99C22×D188C2314yes—
100C22×C22⋊D47—21no—
101C22×C22⋊D47—21no—
102C22×C22⋊D47D411yescharacteristic
103C22×C22⋊D47D411yescharacteristic
104C23×Dic47—21no—
105C22×C4×D47—21no—
106C22×C4×D47C2311yescharacteristic
107C22×C4×D47C2311yescharacteristic
108C2×#10625325—42no—
109C2×#10625325—42no—
110C2×#10625325C2314yes—
111C2×#10625325C2314yes—
112C2×#10625334—42no—
113C2×#10625334—42no—
114C2×#10625334C2314yes—
115C2×#10625334C2314yes—
116C2×#10625324—42no—
117C2×#10625324C2314yescomplemented
118C22×C47⋊C8C2311yescharacteristic
119C22×C47⋊C8C2311yescharacteristic
120C2×C8×D47—42no—
121C2×C8×D47C2314yescomplemented
122#13094021—28no—
123#13094012—28no—
124#13094004—22no—
125#13094004C2314yescomplemented
126#13094003—22no—
127#13094003C2314yes—
128#13094001—28no—
129#13093999—22no—
130#13093999—22no—
131#13093999—22no—
132#13093999—22no—
133#13093999C2314yes—
134#13093999C2314yes—
135#13093999C2314yes—
136#13093999C2314yes—
137#13093997—28no—
138#13093996—28no—
139#13093995—28no—
140#13093995—22no—
141#13093995C2314yescomplemented
142#13093994—28no—
143#13093994—28no—
144C2×C4⋊Dic47—21no—
145C2×C4⋊Dic47C2311yescharacteristic
146C2×Dic47⋊C4—21no—
147C2×Dic47⋊C4—21no—
148C4⋊C4×D47—22no—
149C4⋊C4×D47C2314yescomplemented
150C2×C22⋊Dic47—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—
157#13093957C2314yescomplemented
158#13093955C2314yescomplemented
159#13093947C2314yescomplemented
160#13093947C2314yescomplemented
161#13093946C2314yes—
162#13093946C2314yes—
163#13093944C2314yes—
164#13093944C2314yes—
165C22⋊(C47⋊C8)C2314yes—
166(C2×D47)⋊C8C2314yescomplemented
167(C2×D47)⋊C8C2314yescomplemented
168C22×D4×C47—21no—
169C22×D4×C47C2311yescharacteristic
170C23×C4×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173#121×C47—22no—
174#121×C47C2314yes—
175#117×C47—22no—
176#117×C47C2314yes—
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182C2×C42×C47—21no—
183#107×C47C2314yescomplemented
184#106×C47C2314yescomplemented
185#102×C47C2314yescomplemented
186#102×C47C2314yescomplemented
187C22⋊C8×C47C2314yes—
188C24×C47—21no—
189C24×C47C2×D411yescharacteristic
190C23×D47—21no—
191C23×D47—21no—
192C23×D47—24no—
193C23×D47—44no—
194C23×D47—82no—
195C23×D47—82no—
196C23×D47C2×D411yescharacteristic
197C23×D47C2×D411yescharacteristic
198C2×D4×C47—24no—
199C2×D4×C47—21no—
200C2×D4×C47—22no—
201C2×D4×C47—22no—
202C2×D4×C47—82no—
203C2×D4×C47C2412yes—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D412yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2411yescharacteristic
213C2×C22⋊D47—24no—
214C2×C22⋊D47—24no—
215C2×C22⋊D47—42no—
216C2×C22⋊D47—42no—
217C2×C22⋊D47—44no—
218C2×C22⋊D47—82no—
219C2×C22⋊D47C2×D414yes—
220C2×C22⋊D47C2×D414yes—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—24no—
224C22×Dic47—44no—
225C22×Dic47C2×D411yescharacteristic
226C22×Dic47C2×D411yescharacteristic
227#10625352—44no—
228#10625352—44no—
229#10625352—48no—
230#10625350—48no—
231#10625350—44no—
232#10625350—44no—
233C2×D188—22no—
234C2×D188—22no—
235C2×D188—22no—
236C2×D188—22no—
237C2×D188—21no—
238C2×D188—21no—
239C2×D188—24no—
240C2×D188—24no—
241C2×D188—24no—
242C2×D188—24no—
243C2×D188—24no—
244C2×D188—44no—
245C2×D188—44no—
246C2×D188—42no—
247C2×D188—44no—
248C2×D188—48no—
249C2×D188—82no—
250C2×D188—82no—
251C2×D188—82no—
252C2×D188—82no—
253C2×D188C2×D414yes—
254C2×D188C2412yes—
255C2×D188C2412yes—
256C2×C4×D47—22no—
257C2×C4×D47—22no—
258C2×C4×D47—22no—
259C2×C4×D47—22no—
260C2×C4×D47—24no—
261C2×C4×D47—82no—
262C2×C4×D47C2×D412yes—
263C2×C4×D47C2×D412yes—
264C2×C4×D47C2412yes—
265C2×C4×D47C2412yes—
266C2×Dic94—22no—
267C2×Dic94—22no—
268C2×Dic94—21no—
269C2×Dic94—42no—
270C2×Dic94C2×D414yes—
271C2×Dic94C2412yes—
272C2×C8×C47—22no—
273C2×C8×C47—22no—
274C2×C8×C47C2412yes—
275C2×C8×C47C2412yes—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47C2412yes—
280C4⋊C4×C47C2412yes—
281C4⋊C4×C47C2412yes—
282C22⋊C4×C47—24no—
283C22⋊C4×C47—24no—
284C42×C47—24no—
285C22⋊Dic47—24no—
286C22⋊Dic47—24no—
287#10625334—44no—
288#10625334—44no—
289(C2×D47)⋊C4—24no—
290(C2×D47)⋊C4—24no—
291(C2×D47)⋊C4—24no—
292(C2×D47)⋊C4—24no—
293(C2×D47)⋊C4—24no—
294C4⋊Dic47—21no—
295C4⋊Dic47—24no—
296C4⋊Dic47C2412yes—
297Dic47⋊C4—24no—
298Dic47⋊C4—24no—
299C2×C47⋊C8—22no—
300C2×C47⋊C8—22no—
301C2×C47⋊C8C2412yes—
302C2×C47⋊C8C2412yes—
303#10625325—44no—
304#10625325—44no—
305#10625324—44no—
306C8×D47—44no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—42no—
312C23×C47—42no—
313C23×C47—42no—
314C23×C47C22×D412yes—
315C23×C47C22×D411yescharacteristic
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—48no—
325C22×D47—42no—
326C22×D47—42no—
327C22×D47—42no—
328C22×D47—42no—
329C22×D47—42no—
330C22×D47—42no—
331C22×D47—84no—
332C22×D47—84no—
333C22×D47—816no—
334C22×D47C22×D412yes—
335C22×D47C22×D412yes—
336D4×C47—22no—
337D4×C47—22no—
338D4×C47—42no—
339D4×C47—84no—
340C2×C4×C47—22no—
341C2×C4×C47—24no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—42no—
348C2×C4×C47—42no—
349C2×C4×C47—42no—
350C2×C4×C47C22×D412yes—
351C2×C4×C47C22×D411yescharacteristic
352C2×C4×C47H(5,𝔽2)12yes—
353C2×C4×C47H(5,𝔽2)12yes—
354C2×C4×C47C2511yescharacteristic
355C22⋊D47—44no—
356C22⋊D47—44no—
357C22⋊D47—48no—
358C22⋊D47—84no—
359C2×Dic47—22no—
360C2×Dic47—22no—
361C2×Dic47—22no—
362C2×Dic47—22no—
363C2×Dic47—48no—
364C2×Dic47—42no—
365C2×Dic47—42no—
366C2×Dic47C22×D412yes—
367C2×Dic47C22×D412yes—
368D188—22no—
369D188—22no—
370D188—22no—
371D188—22no—
372D188—44no—
373D188—48no—
374D188—42no—
375D188—42no—
376D188—84no—
377D188—84no—
378D188—84no—
379D188—84no—
380C4×D47—24no—
381C4×D47—24no—
382C4×D47—22no—
383C4×D47—22no—
384C4×D47—22no—
385C4×D47—22no—
386C4×D47—84no—
387Dic94—22no—
388Dic94—22no—
389Dic94—44no—
390Dic94—42no—
391C8×C47—22no—
392C8×C47—22no—
393C47⋊C8—22no—
394C47⋊C8—22no—
395C2×#3198—471nomaximal, Sylow
396C22×C47—22no—
397C22×C47—22no—
398C22×C47—22no—
399C22×C47—44no—
400C22×C47—42no—
401C22×C47—42no—
402C22×C47—42no—
403C22×C47—84no—
404C22×C47#53412yes—
405C22×C47#57612yes—
406C22×C47#57712yes—
407C22×C47C23×D411yescharacteristic
408C2×D47—22no—
409C2×D47—22no—
410C2×D47—22no—
411C2×D47—22no—
412C2×D47—22no—
413C2×D47—22no—
414C2×D47—44no—
415C2×D47—44no—
416C2×D47—42no—
417C2×D47—42no—
418C2×D47—42no—
419C2×D47—42no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—816no—
423C2×D47—84no—
424C2×D47—84no—
425C4×C47—22no—
426C4×C47—42no—
427C4×C47—42no—
428C4×C47—42no—
429C4×C47#53412yes—
430C4×C47C2×H(5,𝔽2)11yescharacteristic
431C4×C47C2×H(5,𝔽2)11yescharacteristic
432Dic47—22no—
433Dic47—22no—
434Dic47—42no—
435Dic47—42no—
436C2×#537—471no—
437C2×#535—471no—
438#3198—4716no—
439C2×#481—471no—
440C2×#485—471no—
441C2×#482D4711yescharacteristic, complemented
442C2×#480—471no—
443C2×#469—471no—
444C2×#468—471no—
445C2×#466—471no—
446C2×#465—471no—
447C2×#449—471no—
448C2×#449—471no—
449C2×#450—471no—
450C2×#447—471no—
451C2×#408—471no—
452C2×C47—42no—
453C2×C47—82no—
454C2×C47#319814yescomplemented
455C2×C47C2×#53411yescharacteristic
456C2×C47C2×#57611yescharacteristic
457C2×C47C2×#57711yescharacteristic
458D47—42no—
459D47—42no—
460D47—82no—
461D47—82no—
462C22×#41—471no—
463C22×#41—471no—
464C23×D4—471no—
465C22×SD16—471no—
466C22×SD16—471no—
467C22×D8—471no—
468C22×D8—471no—
469C22×M16—471no—
470C23×C8—471no—
471#537—478no—
472#537—944no—
473#535—478no—
474#535—944no—
475C2×#127—941no—
476C2×#124—941no—
477C2×C22⋊Q8—471no—
478C2×C22⋊Q8—471no—
479C2×C22⋊Q8—941no—
480C2×#121—471no—
481C2×#121—471no—
482C2×#121—471no—
483C2×#121—471no—
484C2×#121—471no—
485C2×#121—941no—
486C2×#121—941no—
487C2×#121—941no—
488C2×#121C2×D4711yescharacteristic
489C2×#120—941no—
490C2×#120—941no—
491C2×#117C2×D4711yescharacteristic
492C22×C4⋊C4—471no—
493#485—478no—
494#482C2×D4718yescomplemented
495#481—478no—
496#480—478no—
497#469—478no—
498#468—478no—
499#466—478no—
500#465—478no—
501#450—478no—
502#449—478no—
503#449—478no—
504#447—478no—
505C2×#107—471no—
506C2×#107C2×D4711yescharacteristic, complemented
507C2×#106—471no—
508C2×#106C2×D4711yescharacteristic, complemented
509C2×#103—471no—
510C2×#103—471no—
511C2×#102—471no—
512C2×#102—471no—
513C2×#102—471no—
514C2×#102—471no—
515C2×#102C2×D4711yescharacteristic, complemented
516C2×#102C2×D4711yescharacteristic, complemented
517#408—478no—
518C2×C22⋊C8—471no—
519C2×C22⋊C8—471no—
520C2×C22⋊C8—471no—
521C2×C22⋊C8C2×D4711yescharacteristic
522C47C2×#319811yescharacteristic, complemented, Sylow
523C25—941no—
524C2×#41—474no—
525C2×#41—474no—
526C2×#41—474no—
527C2×#41—942no—
528C2×#41—1882no—
529C2×#41—1882no—
530C2×#41—1882no—
531C2×#41—1882no—
532C22×Q8—471no—
533C22×Q8—471no—
534C22×D4—21no—
535C22×D4—471no—
536C22×D4—471no—
537C22×D4—471no—
538C22×D4—471no—
539C22×D4—471no—
540C22×D4—474no—
541C22×D4—941no—
542C22×D4—941no—
543C22×D4—941no—
544C22×D4—941no—
545C22×D4—941no—
546C22×D4—941no—
547C22×D4—941no—
548C22×D4—942no—
549C22×D4—1882no—
550C22×D4—1882no—
551C22×D4C22×D4711yescharacteristic
552C23×C4—471no—
553C23×C4—471no—
554C23×C4—941no—
555C23×C4—941no—
556C23×C4C22×D4711yescharacteristic
557C2×SD16—474no—
558C2×SD16—474no—
559C2×SD16—1882no—
560C2×SD16—1882no—
561C2×D8—474no—
562C2×D8—474no—
563C2×D8—1882no—
564C2×D8—1882no—
565C2×M16—474no—
566C2×M16—1882no—
567C22×C8—471no—
568C22×C8—471no—
569C22×C8—474no—
570C22×C8—1882no—
571C22×C8C22×D4711yescharacteristic
572C22×C8C22×D4711yescharacteristic
573#127—948no—
574#124—948no—
575C22⋊Q8—474no—
576C22⋊Q8—474no—
577C22⋊Q8—948no—
578C22⋊Q8—942no—
579C22⋊Q8—942no—
580#121—22no—
581#121—474no—
582#121—474no—
583#121—474no—
584#121—474no—
585#121—474no—
586#121—948no—
587#121—942no—
588#121—942no—
589#121—942no—
590#121—942no—
591#121—942no—
592#121—948no—
593#121—948no—
594#121C22×D4714yes—
595#120—948no—
596#120—948no—
597#117—22no—
598#117C22×D4714yes—
599C2×C4⋊C4—471no—
600C2×C4⋊C4—474no—
601C2×C4⋊C4—942no—
602C2×C4⋊C4—941no—
603C2×C4⋊C4—941no—
604C2×C4⋊C4—941no—
605C2×C4⋊C4C22×D4711yescharacteristic
606C2×C4⋊C4C22×D4711yescharacteristic
607C2×C4⋊C4C22×D4711yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—941no—
611C2×C22⋊C4—941no—
612C2×C22⋊C4—941no—
613C2×C22⋊C4—941no—
614C2×C22⋊C4—941no—
615C2×C22⋊C4—941no—
616C2×C22⋊C4—941no—
617C2×C42—21no—
618#107—474no—
619#107C22×D4714yescomplemented
620#106—474no—
621#106C22×D4714yescomplemented
622#103—474no—
623#103—474no—
624#102—474no—
625#102—474no—
626#102—474no—
627#102—474no—
628#102C22×D4714yescomplemented
629#102C22×D4714yescomplemented
630C22⋊C8—474no—
631C22⋊C8—474no—
632C22⋊C8—474no—
633C22⋊C8C22×D4714yes—
634C24—21no—
635C24—471no—
636C24—471no—
637C24—944no—
638C24—941no—
639C24—941no—
640C24—3762no—
641C24—3762no—
642C24—1884no—
643C24D4×D4711yescharacteristic
644#41—1888no—
645#41—1884no—
646#41—1884no—
647#41—1884no—
648#41—1884no—
649#41—1888no—
650C2×Q8—474no—
651C2×Q8—472no—
652C2×Q8—941no—
653C2×Q8—942no—
654C2×Q8—942no—
655C2×Q8—1882no—
656C2×D4—24no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—82no—
661C2×D4—474no—
662C2×D4—474no—
663C2×D4—474no—
664C2×D4—472no—
665C2×D4—472no—
666C2×D4—944no—
667C2×D4—944no—
668C2×D4—944no—
669C2×D4—944no—
670C2×D4—944no—
671C2×D4—944no—
672C2×D4—941no—
673C2×D4—941no—
674C2×D4—944no—
675C2×D4—942no—
676C2×D4—942no—
677C2×D4—942no—
678C2×D4—942no—
679C2×D4—3762no—
680C2×D4—3762no—
681C2×D4—3762no—
682C2×D4—3762no—
683C2×D4—3762no—
684C2×D4—1884no—
685C2×D4—1884no—
686C2×D4—1882no—
687C2×D4—1884no—
688C2×D4—1888no—
689C2×D4—1882no—
690C2×D4—1882no—
691C2×D4—1884no—
692C2×D4C23×D4712yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—471no—
699C22×C4—471no—
700C22×C4—472no—
701C22×C4—472no—
702C22×C4—472no—
703C22×C4—472no—
704C22×C4—944no—
705C22×C4—944no—
706C22×C4—942no—
707C22×C4—942no—
708C22×C4—942no—
709C22×C4—942no—
710C22×C4—941no—
711C22×C4—941no—
712C22×C4—3762no—
713C22×C4—1884no—
714C22×C4D4×D4712yes—
715C22×C4D4×D4711yescharacteristic
716C22×C4C23×D4712yes—
717C22×C4C23×D4711yescharacteristic
718SD16—1884no—
719SD16—1884no—
720D8—1884no—
721D8—1884no—
722M16—1884no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—472no—
726C2×C8—472no—
727C2×C8—942no—
728C2×C8—942no—
729C2×C8—1884no—
730C2×C8C23×D4712yes—
731C2×C8C23×D4712yes—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—472no—
736C4⋊C4—944no—
737C4⋊C4—944no—
738C4⋊C4—944no—
739C4⋊C4—941no—
740C4⋊C4C23×D4712yes—
741C4⋊C4C23×D4712yes—
742C4⋊C4C23×D4712yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—944no—
746C22⋊C4—944no—
747C22⋊C4—944no—
748C22⋊C4—944no—
749C22⋊C4—944no—
750C22⋊C4—944no—
751C22⋊C4—944no—
752C42—24no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—472no—
761C23—472no—
762C23—942no—
763C23—942no—
764C23—942no—
765C23—942no—
766C23—942no—
767C23—942no—
768C23—942no—
769C23—942no—
770C23—3764no—
771C23—3764no—
772C23—37616no—
773C23—1888no—
774C23—1882no—
775C23—1882no—
776C23—1882no—
777C23—1882no—
778C23—1882no—
779C23—1882no—
780C23C2×D4×D4712yes—
781C23C2×D4×D4711yescharacteristic
782Q8—942no—
783Q8—942no—
784Q8—1884no—
785Q8—1882no—
786D4—22no—
787D4—22no—
788D4—42no—
789D4—84no—
790D4—942no—
791D4—942no—
792D4—942no—
793D4—942no—
794D4—3764no—
795D4—3764no—
796D4—3764no—
797D4—3764no—
798D4—3764no—
799D4—1884no—
800D4—1888no—
801D4—1884no—
802D4—1884no—
803D4—1888no—
804D4—1882no—
805D4—1882no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—472no—
817C2×C4—472no—
818C2×C4—942no—
819C2×C4—942no—
820C2×C4—944no—
821C2×C4—944no—
822C2×C4—942no—
823C2×C4—942no—
824C2×C4—942no—
825C2×C4—942no—
826C2×C4—942no—
827C2×C4—942no—
828C2×C4—3764no—
829C2×C4—1888no—
830C2×C4—1882no—
831C2×C4—1882no—
832C2×C4C2×D4×D4712yes—
833C2×C4C2×D4×D4711yescharacteristic
834C2×C4#1309407012yes—
835C2×C4#1309407012yes—
836C2×C4C24×D4711yescharacteristic
837C8—22no—
838C8—22no—
839C8—942no—
840C8—942no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—84no—
849C22—942no—
850C22—942no—
851C22—942no—
852C22—942no—
853C22—942no—
854C22—942no—
855C22—37616no—
856C22—3764no—
857C22—3764no—
858C22—1882no—
859C22—1882no—
860C22—1882no—
861C22—1882no—
862C22—1882no—
863C22—1882no—
864C22—1884no—
865C22—1884no—
866C22#1568968412yes—
867C22#1568992712yes—
868C22#1568993012yes—
869C22C22×D4×D4711yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—942no—
875C4—942no—
876C4—1882no—
877C4—1882no—
878C4#1568968412yes—
879C4C2×#1309407011yescharacteristic
880C4C2×#1309407011yescharacteristic
881C2—42no—
882C2—82no—
883C2—3762no—
884C2—3762no—
885C2—1882no—
886C2—1882no—
887C2#2025423814yesdirect product factor
888C2C2×#1568968411yescharacteristic
889C2C2×#1568992711yescharacteristic
890C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#482C2
socleC23×C47C22×D4
hypercenterC2×#482D47
hypocenterC47C2×#3198
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#15689702C2semidirect
2. C2×#15689692C2semidirect
3. #20254238C2direct (N × H)
4. C2×#15689443C2semidirect
5. C2×#15689464C2semidirect
6. C2×#15689438C2semidirect
7. C2×#15689375C2semidirect
8. C2×#15689370C2semidirect
9. C2×#15689358C2semidirect
10. C2×#15689353C2semidirect
11. C2×#15689269C2semidirect
12. C2×#15689269C2semidirect
13. C2×#15689276C2semidirect
14. C2×#15689256C2semidirect
15. C2×#15689088C2semidirect
16. C2×C47×#482C2semidirect
18. C22×#10625352C22semidirect
24. C22×#10625324C22semidirect
25. C22×C8×D47C22semidirect
27. #15689702C22semidirect
29. #15689692C22semidirect
32. C2×#13094004C22semidirect
42. C2×#13093995C22semidirect
45. C2×C4⋊C4×D47C22semidirect
46. #15689464C22semidirect
47. #15689443C22semidirect
48. #15689438C22semidirect
49. #15689375C22semidirect
50. #15689370C22semidirect
51. #15689358C22semidirect
52. #15689353C22semidirect
53. #15689276C22semidirect
54. #15689269C22semidirect
55. #15689269C22semidirect
56. #15689256C22semidirect
57. C2×#13093957C22semidirect
58. C2×#13093955C22semidirect
59. C2×#13093947C22semidirect
60. C2×#13093947C22semidirect
65. #15689088C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
71. C47×#482C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×#102×C47C22semidirect
75. C2×#102×C47C22semidirect
85. C2×#10625352C23semidirect
117. C2×#10625324C23semidirect
121. C2×C8×D47C23semidirect
125. #13094004C23semidirect
141. #13093995C23semidirect
149. C4⋊C4×D47C23semidirect
157. #13093957C23semidirect
158. #13093955C23semidirect
159. #13093947C23semidirect
160. #13093947C23semidirect
166. (C2×D47)⋊C8C23semidirect
167. (C2×D47)⋊C8C23semidirect
183. #107×C47C23semidirect
184. #106×C47C23semidirect
185. #102×C47C23semidirect
186. #102×C47C23semidirect
441. C2×#482D47semidirect
454. C2×C47#3198semidirect
494. #482C2×D47semidirect
506. C2×#107C2×D47semidirect
508. C2×#106C2×D47semidirect
515. C2×#102C2×D47semidirect
516. C2×#102C2×D47semidirect
522. C47C2×#3198semidirect
619. #107C22×D47semidirect
621. #106C22×D47semidirect
628. #102C22×D47semidirect
629. #102C22×D47semidirect
887. C2#20254238direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897022
C2×#156896922
#202542382
C2×#156894432
C2×#156894642
C2×#156894382
C2×#156893752
C2×#156893702
C2×#156893582
C2×#156893532
C2×#156892692
C2×#156892762
C2×#156892562
C2×#156890882
C2×C47×#4822
C2×#319847