Finite Group Databasebeta

← C2×#20253045 #27083476

Subgroups — C2×#20253045 #27083476

Order 12032.

2806 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094045C211yesmaximal, characteristic, complemented
2C22×#13094030C211yesmaximal, characteristic, complemented
3C2×#15689703C211yesmaximal, characteristic, complemented
4C2×#15689702C211yesmaximal, characteristic, complemented
5#20253045C2116yesmaximal, direct product factor
6C2×#15689380C211yesmaximal, characteristic, complemented
7C2×#15689379C211yesmaximal, characteristic, complemented
8C2×#15689375C211yesmaximal, characteristic, complemented
9C2×#15689374C211yesmaximal, characteristic, complemented
10C2×#15689353C211yesmaximal, characteristic, complemented
11C2×#15689352C211yesmaximal, characteristic, complemented
12C2×#15689349C211yesmaximal, characteristic, complemented
13C2×#106×D47C211yesmaximal, characteristic, complemented
14C2×#15689123C211yesmaximal, characteristic, complemented
15C2×#15689121C211yesmaximal, characteristic, complemented
16C2×C47×#465C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625350C2211yescharacteristic
19C22×#10625352C2211yescharacteristic
20C2×#13094045—28no—
21C2×#13094045C2218yescomplemented
22C22×#10625337C2211yescharacteristic
23C22×#10625325C2211yescharacteristic
24C22×#10625334C2211yescharacteristic
25C2×#13094030—28no—
26C2×#13094030C2218yescomplemented
27C22×#10625329C2211yescharacteristic
28C22×#10625324C2211yescharacteristic
29C22×#10625324C2211yescharacteristic
30C22×C8×D47C2211yescharacteristic
31C22×C8×D47C2211yescharacteristic
32#15689703—24no—
33#15689703C2218yescomplemented
34#15689702—24no—
35#15689702C2218yescomplemented
36C2×#13094004C2211yescharacteristic
37C2×#13094003C2211yescharacteristic
38C2×#13094002—21no—
39C2×#13094001—21no—
40C2×#13094000C2211yescharacteristic
41C2×#13093999—21no—
42C2×#13093999C2211yescharacteristic
43C2×#13093998C2211yescharacteristic
44C2×#13093997—21no—
45C2×#13093997—21no—
46C2×#13093997—21no—
47C2×#13093996—21no—
48C2×#13093995—21no—
49C2×#13093995C2211yescharacteristic
50C2×C4⋊C4×D47C2211yescharacteristic
51C2×C4⋊C4×D47C2211yescharacteristic
52#15689380C2218yescomplemented
53#15689379C2218yescomplemented
54#15689375C2218yescomplemented
55#15689374C2218yescomplemented
56#15689353C2218yescomplemented
57#15689352C2218yescomplemented
58#15689349C2218yescomplemented
59C2×#13093956C2211yescharacteristic
60C2×#13093955C2211yescharacteristic
61C2×#13093955C2211yescharacteristic
62#106×D47C2218yescomplemented
63#15689123C2218yescomplemented
64#15689121C2218yescomplemented
65C2×#13093949C2211yescharacteristic
66C2×#13093948C2211yescharacteristic
67C2×#13093947C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C2×#13093945C2211yescharacteristic
70C2×#13093944C2211yescharacteristic
71C22×SD16×C47C2211yescharacteristic
72C23×C8×C47C2211yescharacteristic
73C2×C22⋊Q8×C47C2211yescharacteristic
74C2×#121×C47C2211yescharacteristic
75C47×#465C2218yescomplemented
76C2×#106×C47C2211yescharacteristic
77C2×#103×C47C2211yescharacteristic
78C2×#102×C47C2211yescharacteristic
79C2×#10625354—22no—
80C2×#10625354—24no—
81C2×#10625354—24no—
82C2×#10625354C2314yes—
83C2×#10625350—24no—
84C2×#10625350—24no—
85C2×#10625350D414yes—
86C2×#10625350C2314yes—
87C2×#10625352—24no—
88C2×#10625352—22no—
89C2×#10625352—24no—
90C2×#10625352C2314yes—
91C22×Dic94D411yescharacteristic
92C22×Dic94C2311yescharacteristic
93C22×D188—21no—
94C22×D188—21no—
95C22×D188D411yescharacteristic
96C22×D188C2311yescharacteristic
97C22×C22⋊D47—21no—
98C22×C22⋊D47—21no—
99C22×C22⋊D47—21no—
100C22×C22⋊D47D411yescharacteristic
101C22×C22⋊D47D411yescharacteristic
102C23×Dic47—21no—
103C22×C4×D47—21no—
104C22×C4×D47—21no—
105C22×C4×D47—21no—
106C22×C4×D47C2311yescharacteristic
107C22×C4×D47C2311yescharacteristic
108#13094045—232no—
109C2×#10625337—24no—
110C2×#10625337C2314yes—
111C2×#10625325—24no—
112C2×#10625325C2314yes—
113C2×#10625334—24no—
114C2×#10625334C2314yes—
115#13094030—232no—
116C2×#10625329—24no—
117C2×#10625329C2314yes—
118C2×#10625324—24no—
119C2×#10625324—24no—
120C2×#10625324C2314yes—
121C2×#10625324C2314yes—
122C22×C47⋊C8C2311yescharacteristic
123C22×C47⋊C8C2311yescharacteristic
124C2×C8×D47—24no—
125C2×C8×D47D418yescomplemented
126C2×C8×D47C2314yes—
127C2×C8×D47C2314yes—
128#13094004—22no—
129#13094004C2314yes—
130#13094003—22no—
131#13094003C2314yes—
132#13094002—28no—
133#13094001—28no—
134#13094000—22no—
135#13094000C2314yes—
136#13093999—28no—
137#13093999—22no—
138#13093999C2314yes—
139#13093998—22no—
140#13093998C2314yes—
141#13093997—28no—
142#13093997—28no—
143#13093997—28no—
144#13093996—28no—
145#13093995—28no—
146#13093995—22no—
147#13093995C2314yes—
148C2×C4⋊Dic47—21no—
149C2×C4⋊Dic47C2311yescharacteristic
150C2×C4⋊Dic47C2311yescharacteristic
151C2×Dic47⋊C4—21no—
152C2×Dic47⋊C4—21no—
153C2×Dic47⋊C4—21no—
154C2×Dic47⋊C4—21no—
155C4⋊C4×D47—22no—
156C4⋊C4×D47—22no—
157C4⋊C4×D47C2314yes—
158C4⋊C4×D47C2314yes—
159C2×C22⋊Dic47—21no—
160C2×C22⋊Dic47—21no—
161C2×(C2×D47)⋊C4—21no—
162C2×(C2×D47)⋊C4—21no—
163C2×(C2×D47)⋊C4—21no—
164C2×(C2×D47)⋊C4—21no—
165#13093956C2314yes—
166#13093955C2314yes—
167#13093955C2314yes—
168#13093949C2314yes—
169#13093948C2314yes—
170#13093947C2314yes—
171#13093946C2314yes—
172#13093945C2314yes—
173#13093944C2314yes—
174C22×Q8×C47C2311yescharacteristic
175C22×D4×C47—21no—
176C22×D4×C47C2311yescharacteristic
177C23×C4×C47C2311yescharacteristic
178C2×SD16×C47—24no—
179C2×SD16×C47C2314yes—
180C22×C8×C47—24no—
181C22×C8×C47C2314yes—
182C22×C8×C47C2311yescharacteristic
183C22×C8×C47C2311yescharacteristic
184C22⋊Q8×C47—22no—
185C22⋊Q8×C47C2314yes—
186#121×C47—22no—
187#121×C47C2314yes—
188C2×C4⋊C4×C47—21no—
189C2×C4⋊C4×C47C2311yescharacteristic
190C2×C4⋊C4×C47C2311yescharacteristic
191C2×C22⋊C4×C47—21no—
192C2×C22⋊C4×C47—21no—
193#106×C47C2314yes—
194#103×C47C2314yes—
195#102×C47C2314yes—
196C24×C47—21no—
197C24×C47C2×D411yescharacteristic
198C23×D47—21no—
199C23×D47C2×D411yescharacteristic
200C23×D47C2×D411yescharacteristic
201C2×Q8×C47—21no—
202C2×Q8×C47—22no—
203C2×Q8×C47—22no—
204C2×Q8×C47C2412yes—
205C2×D4×C47—24no—
206C2×D4×C47—22no—
207C2×D4×C47—21no—
208C2×D4×C47—22no—
209C2×D4×C47—82no—
210C2×D4×C47C2412yes—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D412yes—
218C22×C4×C47C2412yes—
219C22×C4×C47C2411yescharacteristic
220C2×C22⋊D47—24no—
221C2×C22⋊D47—24no—
222C2×C22⋊D47—24no—
223C2×C22⋊D47—24no—
224C2×C22⋊D47—24no—
225C2×C22⋊D47—44no—
226C2×C22⋊D47—82no—
227C2×C22⋊D47—82no—
228C2×C22⋊D47C2×D414yes—
229C2×C22⋊D47C2×D414yes—
230C22×Dic47—21no—
231C22×Dic47—21no—
232C22×Dic47—21no—
233C22×Dic47—24no—
234C22×Dic47—44no—
235C22×Dic47C2×D411yescharacteristic
236C22×Dic47C2×D411yescharacteristic
237#10625354—28no—
238#10625354—28no—
239#10625354—48no—
240#10625352—28no—
241#10625352—28no—
242#10625352—48no—
243#10625350—216no—
244#10625350—28no—
245#10625350—28no—
246C2×D188—24no—
247C2×D188—22no—
248C2×D188—22no—
249C2×D188—24no—
250C2×D188—21no—
251C2×D188—24no—
252C2×D188—44no—
253C2×D188—82no—
254C2×D188C2×D414yes—
255C2×D188C2412yes—
256C2×C4×D47—22no—
257C2×C4×D47—22no—
258C2×C4×D47—24no—
259C2×C4×D47—24no—
260C2×C4×D47—24no—
261C2×C4×D47—44no—
262C2×C4×D47—82no—
263C2×C4×D47—82no—
264C2×C4×D47C2×D412yes—
265C2×C4×D47C2×D412yes—
266C2×C4×D47C2×D414yes—
267C2×C4×D47#4114yes—
268C2×C4×D47C2412yes—
269C2×C4×D47C2412yes—
270C2×Dic94—24no—
271C2×Dic94—22no—
272C2×Dic94—22no—
273C2×Dic94—21no—
274C2×Dic94C2×D414yes—
275C2×Dic94C2412yes—
276SD16×C47—28no—
277C2×C8×C47—22no—
278C2×C8×C47—28no—
279C2×C8×C47C2×D414yes—
280C2×C8×C47C2412yes—
281C2×C8×C47C2412yes—
282C4⋊C4×C47—24no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47—21no—
285C4⋊C4×C47C2412yes—
286C4⋊C4×C47C2412yes—
287C22⋊C4×C47—24no—
288C22⋊C4×C47—24no—
289C22⋊Dic47—24no—
290C22⋊Dic47—24no—
291#10625337—28no—
292#10625334—28no—
293(C2×D47)⋊C4—24no—
294(C2×D47)⋊C4—24no—
295(C2×D47)⋊C4—24no—
296(C2×D47)⋊C4—24no—
297C4⋊Dic47—21no—
298C4⋊Dic47—21no—
299C4⋊Dic47—24no—
300C4⋊Dic47C2412yes—
301C4⋊Dic47C2412yes—
302Dic47⋊C4—24no—
303Dic47⋊C4—24no—
304Dic47⋊C4—24no—
305Dic47⋊C4—24no—
306#10625329—28no—
307C2×C47⋊C8—22no—
308C2×C47⋊C8C2×D414yes—
309C2×C47⋊C8C2412yes—
310C2×C47⋊C8C2412yes—
311#10625325—28no—
312#10625324—28no—
313#10625324—28no—
314C8×D47—28no—
315C8×D47C2×D4116yescomplemented
316C23×C47—22no—
317C23×C47—22no—
318C23×C47—22no—
319C23×C47—22no—
320C23×C47—42no—
321C23×C47—42no—
322C23×C47—42no—
323C23×C47C22×D412yes—
324C23×C47C22×D411yescharacteristic
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—22no—
331C22×D47—42no—
332C22×D47—42no—
333C22×D47—42no—
334C22×D47#12114yes—
335C22×D47C22×D412yes—
336C22×D47C22×D412yes—
337Q8×C47—22no—
338Q8×C47—22no—
339Q8×C47—42no—
340D4×C47—22no—
341D4×C47—22no—
342D4×C47—42no—
343D4×C47—84no—
344C2×C4×C47—22no—
345C2×C4×C47—24no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—42no—
352C2×C4×C47—42no—
353C2×C4×C47—42no—
354C2×C4×C47C22×D412yes—
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47C22×D412yes—
357C2×C4×C47C2×#4112yes—
358C2×C4×C47C2511yescharacteristic
359C22⋊D47—28no—
360C22⋊D47—28no—
361C22⋊D47—48no—
362C22⋊D47—84no—
363C22⋊D47—84no—
364C2×Dic47—22no—
365C2×Dic47—22no—
366C2×Dic47—22no—
367C2×Dic47—22no—
368C2×Dic47—42no—
369C2×Dic47—42no—
370C2×Dic47—42no—
371C2×Dic47—48no—
372C2×Dic47#12114yes—
373C2×Dic47C22×D412yes—
374C2×Dic47C22×D412yes—
375D188—28no—
376D188—22no—
377D188—22no—
378D188—48no—
379D188—42no—
380D188—84no—
381C4×D47—24no—
382C4×D47—22no—
383C4×D47—22no—
384C4×D47—48no—
385C4×D47—84no—
386C4×D47—84no—
387C4×D47#12118yes—
388C4×D47C22×D414yes—
389C4×D47C2×#4114yes—
390Dic94—28no—
391Dic94—22no—
392Dic94—22no—
393Dic94—42no—
394C8×C47—22no—
395C8×C47C22×D414yes—
396C47⋊C8—22no—
397C47⋊C8C22×D414yes—
398C2×#3060—471nomaximal, Sylow
399C22×C47—22no—
400C22×C47—22no—
401C22×C47—22no—
402C22×C47—44no—
403C22×C47—42no—
404C22×C47—42no—
405C22×C47—42no—
406C22×C47—84no—
407C22×C47C2×#12112yes—
408C22×C47#57712yes—
409C22×C47#57712yes—
410C22×C47C23×D411yescharacteristic
411C2×D47—28no—
412C2×D47—22no—
413C2×D47—22no—
414C2×D47—22no—
415C2×D47—22no—
416C2×D47—22no—
417C2×D47—44no—
418C2×D47—42no—
419C2×D47—42no—
420C2×D47—42no—
421C2×D47—84no—
422C2×D47C2×#12114yes—
423C4×C47—22no—
424C4×C47—42no—
425C4×C47—42no—
426C4×C47—42no—
427C4×C47C2×#12112yes—
428C4×C47C23×D411yescharacteristic
429C4×C47C22×#4111yescharacteristic
430Dic47—22no—
431Dic47—42no—
432Dic47—42no—
433Dic47—42no—
434Dic47C2×#12114yes—
435C22×#135—471no—
436C22×#131—471no—
437C2×#537—471no—
438C2×#537—471no—
439#3060—4716no—
440C2×#470—471no—
441C2×#470—471no—
442C2×#469—471no—
443C2×#469—471no—
444C2×#465—471no—
445C2×#465—471no—
446C2×#465—471no—
447C2×#465D4711yescharacteristic, complemented
448C22×#106—471no—
449C2×#417—471no—
450C2×#417—471no—
451C2×C47—42no—
452C2×C47—82no—
453C2×C47#306014yescomplemented
454C2×C47C22×#12111yescharacteristic
455C2×C47C2×#57711yescharacteristic
456C2×C47C2×#57711yescharacteristic
457D47—24no—
458D47—42no—
459D47—82no—
460C22×#41—471no—
461C22×#41—471no—
462C22×#41—471no—
463C2×#135—478no—
464C2×#135—948no—
465C22×Q16—471no—
466C22×SD16—471no—
467C22×SD16C2×D4711yescharacteristic
468C22×D8—471no—
469C2×#131—478no—
470C2×#131—948no—
471C22×M16—471no—
472C22×M16—471no—
473C22×M16—471no—
474C23×C8—471no—
475C23×C8—471no—
476C23×C8C2×D4711yescharacteristic
477#537—478no—
478#537—478no—
479#537—944no—
480#537—944no—
481C2×C22⋊Q8—471no—
482C2×C22⋊Q8—471no—
483C2×C22⋊Q8—471no—
484C2×C22⋊Q8—941no—
485C2×C22⋊Q8—941no—
486C2×C22⋊Q8C2×D4711yescharacteristic
487C2×#121—471no—
488C2×#121—471no—
489C2×#121—471no—
490C2×#121—941no—
491C2×#121—941no—
492C2×#121—941no—
493C2×#121—941no—
494C2×#121—941no—
495C2×#121—941no—
496C2×#121C2×D4711yescharacteristic
497C22×C4⋊C4—471no—
498C22×C4⋊C4—471no—
499#470—478no—
500#470—478no—
501#469—478no—
502#469—478no—
503#465—478no—
504#465—478no—
505#465—478no—
506#465C2×D4718yescomplemented
507C2×#106—471no—
508C2×#106—471no—
509C2×#106—471no—
510C2×#106—478no—
511C2×#106C2×D4711yescharacteristic
512#417—478no—
513#417—478no—
514C2×#103—471no—
515C2×#103—471no—
516C2×#103—471no—
517C2×#103C2×D4711yescharacteristic
518C2×#102—471no—
519C2×#102—471no—
520C2×#102—471no—
521C2×#102C2×D4711yescharacteristic
522C47C2×#306011yescharacteristic, complemented, Sylow
523C2×#41—474no—
524C2×#41—474no—
525C2×#41—474no—
526C2×#41—474no—
527C2×#41—944no—
528C2×#41—944no—
529C2×#41—942no—
530C2×#41—942no—
531C2×#41—944no—
532C2×#41—944no—
533C2×#41—944no—
534C2×#41—944no—
535C22×Q8—471no—
536C22×Q8—471no—
537C22×Q8C22×D4711yescharacteristic
538C22×D4—21no—
539C22×D4—471no—
540C22×D4—471no—
541C22×D4—471no—
542C22×D4—471no—
543C22×D4—941no—
544C22×D4—941no—
545C22×D4—941no—
546C22×D4—941no—
547C22×D4—941no—
548C22×D4C22×D4711yescharacteristic
549C23×C4—471no—
550C23×C4—471no—
551C23×C4—941no—
552C23×C4—941no—
553C23×C4—941no—
554C23×C4—941no—
555C23×C4C22×D4711yescharacteristic
556#135—9432no—
557C2×Q16—474no—
558C2×Q16—944no—
559C2×SD16—24no—
560C2×SD16—474no—
561C2×SD16—944no—
562C2×SD16C22×D4714yes—
563C2×D8—474no—
564C2×D8—944no—
565#131—9432no—
566C2×M16—474no—
567C2×M16—474no—
568C2×M16—474no—
569C2×M16—944no—
570C2×M16—944no—
571C2×M16—944no—
572C22×C8—24no—
573C22×C8—471no—
574C22×C8—478no—
575C22×C8—474no—
576C22×C8—471no—
577C22×C8—474no—
578C22×C8—944no—
579C22×C8C22×D4711yescharacteristic
580C22×C8C22×D4714yes—
581C22×C8C22×D4711yescharacteristic
582C22⋊Q8—22no—
583C22⋊Q8—474no—
584C22⋊Q8—474no—
585C22⋊Q8—474no—
586C22⋊Q8—948no—
587C22⋊Q8—942no—
588C22⋊Q8—948no—
589C22⋊Q8—942no—
590C22⋊Q8—942no—
591C22⋊Q8C22×D4714yes—
592#121—22no—
593#121—474no—
594#121—474no—
595#121—474no—
596#121—948no—
597#121—948no—
598#121—948no—
599#121—942no—
600#121—948no—
601#121—942no—
602#121—948no—
603#121—948no—
604#121—942no—
605#121C22×D4714yes—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—471no—
608C2×C4⋊C4—471no—
609C2×C4⋊C4—474no—
610C2×C4⋊C4—474no—
611C2×C4⋊C4—942no—
612C2×C4⋊C4—942no—
613C2×C4⋊C4—941no—
614C2×C4⋊C4—941no—
615C2×C4⋊C4—941no—
616C2×C4⋊C4—941no—
617C2×C4⋊C4—941no—
618C2×C4⋊C4C22×D4711yescharacteristic
619C2×C4⋊C4C22×D4711yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—941no—
623C2×C22⋊C4—941no—
624C2×C22⋊C4—941no—
625C2×C22⋊C4—941no—
626C2×C22⋊C4—941no—
627C2×C22⋊C4—941no—
628#106—474no—
629#106—474no—
630#106—474no—
631#106C22×D4714yes—
632#103—474no—
633#103—474no—
634#103—474no—
635#103C22×D4714yes—
636#102—474no—
637#102—474no—
638#102—474no—
639#102C22×D4714yes—
640C24—21no—
641C24—471no—
642C24—471no—
643C24—941no—
644C24D4×D4711yescharacteristic
645#41—948no—
646#41—9416no—
647#41—948no—
648#41—948no—
649#41—948no—
650#41—948no—
651#41—948no—
652#41—1888no—
653#41—1888no—
654C2×Q8—21no—
655C2×Q8—22no—
656C2×Q8—22no—
657C2×Q8—474no—
658C2×Q8—472no—
659C2×Q8—944no—
660C2×Q8—941no—
661C2×Q8—942no—
662C2×Q8—942no—
663C2×Q8C23×D4712yes—
664C2×D4—24no—
665C2×D4—22no—
666C2×D4—21no—
667C2×D4—22no—
668C2×D4—82no—
669C2×D4—474no—
670C2×D4—474no—
671C2×D4—474no—
672C2×D4—472no—
673C2×D4—944no—
674C2×D4—944no—
675C2×D4—944no—
676C2×D4—944no—
677C2×D4—944no—
678C2×D4—944no—
679C2×D4—944no—
680C2×D4—944no—
681C2×D4—942no—
682C2×D4—941no—
683C2×D4—942no—
684C2×D4—3762no—
685C2×D4—3762no—
686C2×D4—3762no—
687C2×D4—1884no—
688C2×D4—1884no—
689C2×D4C23×D4712yes—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—471no—
696C22×C4—472no—
697C22×C4—474no—
698C22×C4—474no—
699C22×C4—472no—
700C22×C4—471no—
701C22×C4—472no—
702C22×C4—472no—
703C22×C4—944no—
704C22×C4—944no—
705C22×C4—944no—
706C22×C4—944no—
707C22×C4—942no—
708C22×C4—942no—
709C22×C4—941no—
710C22×C4—941no—
711C22×C4—941no—
712C22×C4—3762no—
713C22×C4—3762no—
714C22×C4—1884no—
715C22×C4—1884no—
716C22×C4D4×D4712yes—
717C22×C4D4×D4711yescharacteristic
718C22×C4C23×D4712yes—
719C22×C4C23×D4711yescharacteristic
720Q16—948no—
721SD16—28no—
722SD16—948no—
723D8—948no—
724M16—948no—
725M16—948no—
726M16—948no—
727C2×C8—22no—
728C2×C8—28no—
729C2×C8—474no—
730C2×C8—472no—
731C2×C8—4716no—
732C2×C8—472no—
733C2×C8—942no—
734C2×C8—948no—
735C2×C8D4×D4714yes—
736C2×C8C23×D4712yes—
737C2×C8C23×D4712yes—
738C4⋊C4—24no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—472no—
742C4⋊C4—472no—
743C4⋊C4—944no—
744C4⋊C4—944no—
745C4⋊C4—944no—
746C4⋊C4—944no—
747C4⋊C4—944no—
748C4⋊C4—941no—
749C4⋊C4—941no—
750C4⋊C4C23×D4712yes—
751C4⋊C4C23×D4712yes—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—944no—
755C22⋊C4—944no—
756C22⋊C4—944no—
757C22⋊C4—944no—
758C22⋊C4—944no—
759C22⋊C4—944no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—474no—
768C23—472no—
769C23—472no—
770C23—942no—
771C23—942no—
772C23—942no—
773C23—942no—
774C23—942no—
775C23—942no—
776C23—1882no—
777C23—1882no—
778C23—1882no—
779C23C2×D4×D4712yes—
780C23C2×D4×D4711yescharacteristic
781Q8—22no—
782Q8—22no—
783Q8—42no—
784Q8—948no—
785Q8—942no—
786Q8—942no—
787Q8—1882no—
788D4—22no—
789D4—22no—
790D4—42no—
791D4—84no—
792D4—948no—
793D4—948no—
794D4—948no—
795D4—942no—
796D4—942no—
797D4—3764no—
798D4—3764no—
799D4—3764no—
800D4—1888no—
801D4—1888no—
802D4—1882no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—474no—
814C2×C4—472no—
815C2×C4—478no—
816C2×C4—474no—
817C2×C4—474no—
818C2×C4—472no—
819C2×C4—942no—
820C2×C4—944no—
821C2×C4—942no—
822C2×C4—942no—
823C2×C4—942no—
824C2×C4—942no—
825C2×C4—942no—
826C2×C4—3764no—
827C2×C4—3764no—
828C2×C4—1888no—
829C2×C4—1888no—
830C2×C4—1882no—
831C2×C4—1882no—
832C2×C4—1882no—
833C2×C4C2×D4×D4712yes—
834C2×C4C2×D4×D4711yescharacteristic
835C2×C4C2×D4×D4712yes—
836C2×C4#41×D4712yes—
837C2×C4C24×D4711yescharacteristic
838C8—22no—
839C8—474no—
840C8—942no—
841C8C2×D4×D4714yes—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—44no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—84no—
850C22—474no—
851C22—942no—
852C22—942no—
853C22—948no—
854C22—942no—
855C22—942no—
856C22—942no—
857C22—3764no—
858C22—1882no—
859C22—1882no—
860C22—1882no—
861C22—1884no—
862C22#121×D4712yes—
863C22#1568992912yes—
864C22#1568993012yes—
865C22C22×D4×D4711yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—474no—
871C4—942no—
872C4—1882no—
873C4—1882no—
874C4—1882no—
875C4#121×D4712yes—
876C4C22×D4×D4711yescharacteristic
877C4C2×#41×D4711yescharacteristic
878C2—42no—
879C2—82no—
880C2—944no—
881C2—3762no—
882C2—1882no—
883C2#2025304514yesdirect product factor
884C2C2×#121×D4711yescharacteristic
885C2C2×#1568992911yescharacteristic
886C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#465C2
socleC23×C47C22×D4
hypercenterC2×#465D47
hypocenterC47C2×#3060
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C22×#13094045C2semidirect
2. C22×#13094030C2semidirect
3. C2×#15689703C2semidirect
4. C2×#15689702C2semidirect
5. #20253045C2direct (N × H)
6. C2×#15689380C2semidirect
7. C2×#15689379C2semidirect
8. C2×#15689375C2semidirect
9. C2×#15689374C2semidirect
10. C2×#15689353C2semidirect
11. C2×#15689352C2semidirect
12. C2×#15689349C2semidirect
13. C2×#106×D47C2semidirect
14. C2×#15689123C2semidirect
15. C2×#15689121C2semidirect
16. C2×C47×#465C2semidirect
21. C2×#13094045C22semidirect
26. C2×#13094030C22semidirect
33. #15689703C22semidirect
35. #15689702C22semidirect
52. #15689380C22semidirect
53. #15689379C22semidirect
54. #15689375C22semidirect
55. #15689374C22semidirect
56. #15689353C22semidirect
57. #15689352C22semidirect
58. #15689349C22semidirect
62. #106×D47C22semidirect
63. #15689123C22semidirect
64. #15689121C22semidirect
75. C47×#465C22semidirect
125. C2×C8×D47D4semidirect
315. C8×D47C2×D4semidirect
447. C2×#465D47semidirect
453. C2×C47#3060semidirect
506. #465C2×D47semidirect
522. C47C2×#3060semidirect
883. C2#20253045direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940452
C22×#130940302
C2×#156897032
C2×#156897022
#202530452
C2×#156893802
C2×#156893792
C2×#156893752
C2×#156893742
C2×#156893532
C2×#156893522
C2×#156893492
C2×#106×D472
C2×#156891232
C2×#156891212
C2×C47×#4652
C2×#306047