Finite Group Databasebeta

← #27079780

Subgroups — #27079780

Order 12032.

4812 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689959C211yesmaximal, characteristic
2C2×#15689889C212yesmaximal, complemented
3#20251869C214yesmaximal, complemented
4#20251868C214yesmaximal, complemented
5#20251865C214yesmaximal, complemented
6#20251864C214yesmaximal, complemented
7C2×#15689107C211yesmaximal, characteristic, complemented
8C2×#15689105C212yesmaximal, complemented
9#413×D47C218yesmaximal, complemented
10C2×C47×#413C211yesmaximal, characteristic, complemented
11#15689959—24no—
12#15689959—24no—
13#15689959—24no—
14#15689959—24no—
15C2×#13094072C2212yes—
16C2×#13094071C412yes—
17C2×#13094071C2212yes—
18C2×#13094070C412yes—
19C2×#13094070C2212yes—
20C2×#13094069C414yes—
21C2×#13094069C2212yes—
22C22×#10625350C414yes—
23C22×#10625350C2211yescharacteristic
24C22×#10625350C2211yescharacteristic
25C2×#41×D47C414yes—
26C2×#41×D47C2214yes—
27#15689889—24no—
28#15689889—24no—
29#15689889C2218yescomplemented
30#15689889C2218yescomplemented
31C2×#13094032—24no—
32C2×#13094030—24no—
33C22×#10625329C2212yescomplemented
34C2×M16×D47C2218yescomplemented
35#15689107C2214yescomplemented
36#15689107C2214yescomplemented
37#15689106C22116yescomplemented
38#15689105C2218yescomplemented
39#15689105C2218yescomplemented
40#15689104C22116yescomplemented
41C2×#13093943C2212yescomplemented
42C2×#13093942C2214yescomplemented
43#101×D47C22116yescomplemented
44C2×#13093941C2212yescomplemented
45C2×#13093940C2214yescomplemented
46#100×D47C22116yescomplemented
47C22×#41×C47C2211yescharacteristic
48C22×M16×C47C2212yescomplemented
49C47×#413C2214yescomplemented
50C47×#413C2214yescomplemented
51C2×#101×C47C2212yescomplemented
52C2×#100×C47C2212yescomplemented
53#13094072—28no—
54#13094072—28no—
55#13094071—28no—
56#13094071—28no—
57#13094071—28no—
58#13094071—28no—
59#13094070—28no—
60#13094070—28no—
61#13094070—28no—
62#13094070—28no—
63#13094069—216no—
64#13094069—216no—
65#13094069—28no—
66#13094069—28no—
67C2×#10625354C2×C414yes—
68C2×#10625354C2314yes—
69C2×#10625350—22no—
70C2×#10625350—22no—
71C2×#10625350—22no—
72C2×#10625350—22no—
73C2×#10625350—28no—
74C2×#10625350—28no—
75C2×#10625350—28no—
76C2×#10625350—28no—
77C2×#10625350C2×C418yes—
78C2×#10625350C2×C412yes—
79C2×#10625350C2×C418yes—
80C2×#10625350C2×C414yes—
81C2×#10625350C2×C414yes—
82C2×#10625350C2×C412yes—
83C2×#10625350C2×C412yes—
84C2×#10625350C2×C412yes—
85C2×#10625350D414yes—
86C2×#10625350D414yes—
87C2×#10625350D414yes—
88C2×#10625350D414yes—
89C2×#10625350C2312yes—
90C2×#10625350C2312yes—
91C2×#10625350C2312yes—
92C2×#10625350C2312yes—
93C2×#10625352C2×C418yes—
94C2×#10625352C2×C414yes—
95C2×#10625352C2×C418yes—
96C2×#10625352C2314yes—
97#41×D47—216no—
98#41×D47—216no—
99#41×D47—216no—
100#41×D47—216no—
101C22×Dic94C2×C414yes—
102C22×Dic94C2×C411yescharacteristic
103C22×Dic94C2311yescharacteristic
104C2×Q8×D47C2×C414yes—
105C2×Q8×D47C2314yes—
106C22×D188C2×C414yes—
107C22×D188C2×C411yescharacteristic
108C22×D188C2311yescharacteristic
109C22×C22⋊D47C2×C418yes—
110C22×C22⋊D47C2×C412yes—
111C22×C22⋊D47C2×C412yes—
112C2×D4×D47C2×C418yes—
113C2×D4×D47C2×C414yes—
114C2×D4×D47C2×C418yes—
115C2×D4×D47C2314yes—
116C22×C4×D47C2×C412yes—
117C22×C4×D47C2×C418yes—
118C22×C4×D47C2312yes—
119#13094032—216no—
120#13094032—216no—
121#13094030—216no—
122#13094030—216no—
123C2×#10625329—22no—
124C2×#10625329—22no—
125C2×#10625329—22no—
126C2×#10625329C2314yes—
127C2×#10625329C2314yes—
128C2×#10625329C2314yes—
129C2×#10625324—28no—
130M16×D47—216no—
131M16×D47C23132yes—
132C22×C47⋊C8—22no—
133C2×C8×D47—28no—
134#13093943C2318yes—
135#13093942C23116yes—
136#13093941C2318yes—
137#13093940C23116yes—
138C2×#41×C47—22no—
139C2×#41×C47—22no—
140C2×#41×C47—22no—
141C2×#41×C47—22no—
142C2×#41×C47C2×C412yes—
143C2×#41×C47C2×C412yes—
144C2×#41×C47C2312yes—
145C2×#41×C47C2312yes—
146C22×Q8×C47C2311yescharacteristic
147C22×D4×C47C2×C412yes—
148C22×D4×C47C2311yescharacteristic
149C23×C4×C47C2×C412yes—
150C23×C4×C47C2311yescharacteristic
151C2×M16×C47—22no—
152C2×M16×C47—22no—
153C2×M16×C47—22no—
154C2×M16×C47C2314yes—
155C2×M16×C47C2314yes—
156C2×M16×C47C2314yes—
157C22×C8×C47—22no—
158#101×C47C2318yes—
159#100×C47C2318yes—
160C24×C47C22×C412yes—
161C24×C47C22×C411yescharacteristic
162C23×D47C22×C412yes—
163C23×D47C22×C418yes—
164C23×D47C22×C412yes—
165#41×C47—24no—
166#41×C47—24no—
167#41×C47—24no—
168#41×C47—24no—
169#41×C47—24no—
170#41×C47—24no—
171#41×C47—24no—
172#41×C47—24no—
173C2×Q8×C47—22no—
174C2×Q8×C47—22no—
175C2×Q8×C47C22×C412yes—
176C2×Q8×C47C2412yes—
177C2×D4×C47—24no—
178C2×D4×C47—24no—
179C2×D4×C47—22no—
180C2×D4×C47—22no—
181C2×D4×C47C22×C414yes—
182C2×D4×C47C22×C414yes—
183C2×D4×C47C22×C412yes—
184C2×D4×C47C2412yes—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47C22×C412yes—
190C22×C4×C47C22×C414yes—
191C22×C4×C47C22×C414yes—
192C22×C4×C47C22×C411yescharacteristic
193C22×C4×C47C22×C411yescharacteristic
194C22×C4×C47C22×C411yescharacteristic
195C22×C4×C47C2×D412yes—
196C22×C4×C47C2×D412yes—
197C22×C4×C47C2×D412yes—
198C22×C4×C47C2×D412yes—
199C22×C4×C47C2411yescharacteristic
200C22×C4×C47C2411yescharacteristic
201C22×C4×C47C2411yescharacteristic
202C2×C22⋊D47—24no—
203C2×C22⋊D47—24no—
204C2×C22⋊D47—216no—
205C2×C22⋊D47—216no—
206C2×C22⋊D47C22⋊C418yes—
207C2×C22⋊D47C22⋊C418yes—
208C2×C22⋊D47C22×C414yes—
209C2×C22⋊D47C22×C418yes—
210C2×C22⋊D47C22×C418yes—
211C2×C22⋊D47C22×C414yes—
212C2×C22⋊D47C22×C414yes—
213C2×C22⋊D47C22×C414yes—
214C22×Dic47C22×C418yes—
215C22×Dic47C22×C412yes—
216C22×Dic47C22×C412yes—
217#10625354—216no—
218#10625354—216no—
219Q8×D47—216no—
220Q8×D47—216no—
221#10625352—232no—
222#10625352—232no—
223#10625352—216no—
224#10625352—216no—
225D4×D47—232no—
226D4×D47—232no—
227D4×D47—216no—
228D4×D47—216no—
229#10625350—22no—
230#10625350—22no—
231#10625350—22no—
232#10625350—22no—
233#10625350—24no—
234#10625350—24no—
235#10625350—24no—
236#10625350—24no—
237#10625350—24no—
238#10625350—24no—
239#10625350—216no—
240#10625350—216no—
241#10625350—28no—
242#10625350—28no—
243#10625350—216no—
244#10625350—216no—
245#10625350—28no—
246#10625350—28no—
247#10625350C22⋊C418yes—
248#10625350C22⋊C418yes—
249#10625350C22⋊C414yes—
250#10625350C22⋊C414yes—
251#10625350C22⋊C414yes—
252#10625350C22⋊C414yes—
253#10625350C2×D418yes—
254#10625350C2×D418yes—
255#10625350C2×D418yes—
256#10625350C2×D418yes—
257C2×D188—22no—
258C2×D188—22no—
259C2×D188—28no—
260C2×D188—28no—
261C2×D188C22⋊C414yes—
262C2×D188C22⋊C414yes—
263C2×D188C22×C418yes—
264C2×D188C22×C412yes—
265C2×D188C22×C412yes—
266C2×D188C22×C412yes—
267C2×D188C2412yes—
268C2×C4×D47—24no—
269C2×C4×D47—24no—
270C2×C4×D47—216no—
271C2×C4×D47—216no—
272C2×C4×D47C22×C414yes—
273C2×C4×D47C22×C418yes—
274C2×C4×D47C22×C414yes—
275C2×C4×D47C22×C418yes—
276C2×C4×D47C22×C414yes—
277C2×C4×D47C2×D418yes—
278C2×C4×D47C2×D418yes—
279C2×C4×D47C2414yes—
280C2×Dic94—22no—
281C2×Dic94—22no—
282C2×Dic94—28no—
283C2×Dic94—28no—
284C2×Dic94C22⋊C414yes—
285C2×Dic94C22⋊C414yes—
286C2×Dic94C22×C418yes—
287C2×Dic94C22×C412yes—
288C2×Dic94C22×C412yes—
289C2×Dic94C22×C412yes—
290C2×Dic94C2412yes—
291M16×C47—24no—
292M16×C47—24no—
293M16×C47—24no—
294M16×C47C2418yes—
295C2×C8×C47—24no—
296C2×C8×C47—24no—
297C2×C8×C47—24no—
298#10625329—24no—
299#10625329—24no—
300#10625329—24no—
301#10625329C2418yes—
302C2×C47⋊C8—24no—
303C2×C47⋊C8—24no—
304C2×C47⋊C8—24no—
305#10625324—232no—
306C8×D47—232no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—81no—
310C23×C47—82no—
311C23×C47C2×C22⋊C412yes—
312C23×C47C2×C22⋊C412yes—
313C23×C47C23×C414yes—
314C23×C47C23×C411yescharacteristic
315C23×C47C23×C411yescharacteristic
316C23×C47C23×C411yescharacteristic
317C22×D47—24no—
318C22×D47—216no—
319C22×D47—82no—
320C22×D47—88no—
321C22×D47—82no—
322C22×D47C2×C22⋊C418yes—
323C22×D47C23×C414yes—
324C22×D47C23×C414yes—
325Q8×C47—24no—
326Q8×C47—24no—
327D4×C47—28no—
328D4×C47—28no—
329D4×C47—24no—
330D4×C47—24no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—24no—
334C2×C4×C47—24no—
335C2×C4×C47—24no—
336C2×C4×C47—24no—
337C2×C4×C47C2×C22⋊C412yes—
338C2×C4×C47C2×C22⋊C412yes—
339C2×C4×C47C2×C22⋊C412yes—
340C2×C4×C47C2×C22⋊C412yes—
341C2×C4×C47C2×C22⋊C411yescharacteristic
342C2×C4×C47C2×C22⋊C411yescharacteristic
343C2×C4×C47C2×C22⋊C411yescharacteristic
344C2×C4×C47C2×C22⋊C411yescharacteristic
345C2×C4×C47C23×C414yes—
346C2×C4×C47C23×C411yescharacteristic
347C2×C4×C47C23×C411yescharacteristic
348C2×C4×C47C23×C411yescharacteristic
349C2×C4×C47C22×D412yes—
350C2×C4×C47C22×D412yes—
351C2×C4×C47C22×D412yes—
352C2×C4×C47C22×D412yes—
353C2×C4×C47C22×D412yes—
354C2×C4×C47C22×D412yes—
355C2×C4×C47C2511yescharacteristic
356C22⋊D47—24no—
357C22⋊D47—24no—
358C22⋊D47—28no—
359C22⋊D47—216no—
360C22⋊D47—216no—
361C22⋊D47C2×C22⋊C418yes—
362C22⋊D47C2×C22⋊C418yes—
363C22⋊D47C2×C22⋊C4116yes—
364C2×Dic47—24no—
365C2×Dic47—216no—
366C2×Dic47C2×C22⋊C418yes—
367C2×Dic47C23×C414yes—
368C2×Dic47C23×C414yes—
369D188—216no—
370D188—22no—
371D188—22no—
372D188—24no—
373D188C2×C22⋊C414yes—
374D188C2×C22⋊C414yes—
375D188C2×C22⋊C418yes—
376C4×D47—216no—
377C4×D47—24no—
378C4×D47—24no—
379C4×D47—28no—
380C4×D47—216no—
381C4×D47C2×C22⋊C418yes—
382C4×D47C2×C22⋊C418yes—
383C4×D47C22×D4116yes—
384Dic94—22no—
385Dic94—22no—
386Dic94—24no—
387Dic94—216no—
388Dic94C2×C22⋊C414yes—
389Dic94C2×C22⋊C414yes—
390Dic94C2×C22⋊C418yes—
391C8×C47—28no—
392C47⋊C8—28no—
393#60076—471nomaximal, Sylow
394C22×C47—24no—
395C22×C47—41no—
396C22×C47—41no—
397C22×C47—41no—
398C22×C47—42no—
399C22×C47—42no—
400C22×C47—44no—
401C22×C47—82no—
402C22×C47—82no—
403C22×C47C22×C22⋊C412yes—
404C22×C47C22×C22⋊C412yes—
405C22×C47C22×C22⋊C411yescharacteristic
406C22×C47C22×C22⋊C411yescharacteristic
407C22×C47C24×C411yescharacteristic
408C2×D47—24no—
409C2×D47—44no—
410C2×D47—48no—
411C2×D47—44no—
412C2×D47—816no—
413C2×D47—84no—
414C2×D47C22×C22⋊C418yes—
415C4×C47—24no—
416C4×C47C22×C22⋊C411yescharacteristic
417C4×C47C22×C22⋊C411yescharacteristic
418C4×C47C22×C22⋊C412yes—
419C4×C47C22×C22⋊C411yescharacteristic
420C4×C47C22×C22⋊C411yescharacteristic
421C4×C47C23×D412yes—
422Dic47—24no—
423Dic47C22×C22⋊C418yes—
424C2×#585—471no—
425C2×#568—472no—
426#2889—474no—
427#2889—474no—
428#2888—474no—
429#2888—474no—
430C2×#413—478no—
431C2×#413—471no—
432C2×#413—472no—
433C2×#413D4711yescharacteristic, complemented
434C2×C47—21no—
435C2×C47—22no—
436C2×C47—22no—
437C2×C47—21no—
438C2×C47—21no—
439C2×C47—44no—
440C2×C47C23×C22⋊C411yescharacteristic
441D47—28no—
442D47—44no—
443#585—944no—
444#585—944no—
445#585—944no—
446#585—944no—
447C2×2−1+4—472no—
448C2×2−1+4—472no—
449C2×2−1+4—472no—
450C2×H(5,𝔽2)—472no—
451C2×H(5,𝔽2)—472no—
452C2×H(5,𝔽2)—474no—
453C2×H(5,𝔽2)—472no—
454C22×#41—474no—
455C22×#41—474no—
456C22×#41—474no—
457C22×#41—471no—
458C22×#41—471no—
459C22×#41C2×D4711yescharacteristic
460#568—478no—
461#568—478no—
462#568—944no—
463#568—944no—
464C2×#131—944no—
465C2×#131—944no—
466C22×M16—472no—
467C22×M16—478no—
468C22×M16C2×D4712yescomplemented
469#413—474no—
470#413—474no—
471#413—478no—
472#413—478no—
473#413—4716no—
474#413—4716no—
475#413C2×D4714yescomplemented
476#413C2×D4714yescomplemented
477C2×#101—472no—
478C2×#101—474no—
479C2×#101—4716no—
480C2×#101C2×D4712yescomplemented
481C2×#100—472no—
482C2×#100—474no—
483C2×#100—4716no—
484C2×#100C2×D4712yescomplemented
485C47#6007611yescharacteristic, complemented, Sylow
4862−1+4—948no—
4872−1+4—948no—
4882−1+4—948no—
4892−1+4—948no—
4902−1+4—948no—
4912−1+4—948no—
492H(5,𝔽2)—9416no—
493H(5,𝔽2)—9416no—
494H(5,𝔽2)—948no—
495H(5,𝔽2)—948no—
496H(5,𝔽2)—948no—
497H(5,𝔽2)—948no—
498H(5,𝔽2)—948no—
499H(5,𝔽2)—948no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—474no—
505C2×#41—474no—
506C2×#41—478no—
507C2×#41—478no—
508C2×#41—474no—
509C2×#41—474no—
510C2×#41—472no—
511C2×#41—472no—
512C2×#41—478no—
513C2×#41—472no—
514C2×#41—474no—
515C2×#41—474no—
516C2×#41—478no—
517C2×#41—472no—
518C2×#41—474no—
519C2×#41—474no—
520C2×#41—474no—
521C2×#41—474no—
522C2×#41—472no—
523C2×#41—472no—
524C2×#41—472no—
525C2×#41—472no—
526C2×#41—948no—
527C2×#41—948no—
528C2×#41—948no—
529C2×#41—948no—
530C2×#41—9416no—
531C2×#41—9416no—
532C2×#41—9416no—
533C2×#41—9416no—
534C2×#41—942no—
535C2×#41—942no—
536C2×#41—942no—
537C2×#41—942no—
538C2×#41C4×D4712yes—
539C2×#41C4×D4712yes—
540C2×#41C22×D4712yes—
541C2×#41C22×D4712yes—
542C22×Q8—474no—
543C22×Q8—474no—
544C22×Q8—471no—
545C22×Q8—474no—
546C22×Q8—471no—
547C22×Q8C22×D4711yescharacteristic
548C22×D4—472no—
549C22×D4—478no—
550C22×D4—472no—
551C22×D4—478no—
552C22×D4—474no—
553C22×D4—478no—
554C22×D4—474no—
555C22×D4—471no—
556C22×D4—474no—
557C22×D4—471no—
558C22×D4C4×D4712yes—
559C22×D4C22×D4711yescharacteristic
560C23×C4—472no—
561C23×C4—478no—
562C23×C4—472no—
563C23×C4C4×D4712yes—
564C23×C4C22×D4711yescharacteristic
565#131—9416no—
566#131—9416no—
567#131—9416no—
568#131—9416no—
569C2×M16—22no—
570C2×M16—22no—
571C2×M16—22no—
572C2×M16—474no—
573C2×M16—474no—
574C2×M16—474no—
575C2×M16—4732no—
576C2×M16—948no—
577C2×M16—9416no—
578C2×M16—942no—
579C2×M16—942no—
580C2×M16—942no—
581C2×M16C22×D4714yes—
582C2×M16C22×D4714yes—
583C2×M16C22×D4714yes—
584C22×C8—22no—
585C22×C8—948no—
586C22×C8—942no—
587#101—478no—
588#101—4716no—
589#101C22×D4718yes—
590#100—478no—
591#100—4716no—
592#100C22×D4718yes—
593C24—472no—
594C24—478no—
595C24—472no—
596C24C2×C4×D4712yes—
597C24C2×C4×D4711yescharacteristic
598#41—24no—
599#41—24no—
600#41—24no—
601#41—24no—
602#41—24no—
603#41—24no—
604#41—24no—
605#41—24no—
606#41—474no—
607#41—474no—
608#41—478no—
609#41—474no—
610#41—474no—
611#41—478no—
612#41—478no—
613#41—478no—
614#41—478no—
615#41—478no—
616#41—9416no—
617#41—9416no—
618#41—9416no—
619#41—9416no—
620#41—948no—
621#41—948no—
622#41—948no—
623#41—948no—
624#41—9432no—
625#41—9416no—
626#41—9416no—
627#41—9432no—
628#41—9416no—
629#41—9416no—
630#41—942no—
631#41—942no—
632#41—942no—
633#41—942no—
634#41—944no—
635#41—944no—
636#41—944no—
637#41—944no—
638#41—944no—
639#41—944no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8—474no—
643C2×Q8—474no—
644C2×Q8—472no—
645C2×Q8—472no—
646C2×Q8—478no—
647C2×Q8—472no—
648C2×Q8—472no—
649C2×Q8—948no—
650C2×Q8—948no—
651C2×Q8—9416no—
652C2×Q8—9416no—
653C2×Q8—942no—
654C2×Q8—942no—
655C2×Q8C2×C4×D4712yes—
656C2×Q8C23×D4712yes—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—478no—
662C2×D4—478no—
663C2×D4—474no—
664C2×D4—474no—
665C2×D4—478no—
666C2×D4—478no—
667C2×D4—474no—
668C2×D4—474no—
669C2×D4—474no—
670C2×D4—474no—
671C2×D4—472no—
672C2×D4—472no—
673C2×D4—478no—
674C2×D4—472no—
675C2×D4—472no—
676C2×D4—948no—
677C2×D4—948no—
678C2×D4—9416no—
679C2×D4—9432no—
680C2×D4—9416no—
681C2×D4—9432no—
682C2×D4—9416no—
683C2×D4—9416no—
684C2×D4—944no—
685C2×D4—944no—
686C2×D4—942no—
687C2×D4—942no—
688C2×D4C2×C4×D4714yes—
689C2×D4C2×C4×D4714yes—
690C2×D4C2×C4×D4712yes—
691C2×D4C23×D4712yes—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—472no—
697C22×C4—474no—
698C22×C4—478no—
699C22×C4—478no—
700C22×C4—474no—
701C22×C4—478no—
702C22×C4—472no—
703C22×C4—474no—
704C22×C4—478no—
705C22×C4—478no—
706C22×C4—474no—
707C22×C4—9416no—
708C22×C4—9416no—
709C22×C4—944no—
710C22×C4—944no—
711C22×C4C2×C4×D4714yes—
712C22×C4C2×C4×D4714yes—
713C22×C4C2×C4×D4712yes—
714C22×C4C2×C4×D4711yescharacteristic
715C22×C4C2×C4×D4711yescharacteristic
716C22×C4C2×C4×D4711yescharacteristic
717C22×C4D4×D4712yes—
718C22×C4D4×D4712yes—
719C22×C4D4×D4712yes—
720C22×C4D4×D4712yes—
721C22×C4C23×D4711yescharacteristic
722C22×C4C23×D4711yescharacteristic
723C22×C4C23×D4711yescharacteristic
724M16—24no—
725M16—24no—
726M16—24no—
727M16—478no—
728M16—9432no—
729M16—944no—
730M16—944no—
731M16—944no—
732M16C23×D4718yes—
733C2×C8—24no—
734C2×C8—24no—
735C2×C8—24no—
736C2×C8—9432no—
737C2×C8—944no—
738C2×C8—944no—
739C2×C8—944no—
740C23—22no—
741C23—22no—
742C23—81no—
743C23—82no—
744C23—478no—
745C23—474no—
746C23—474no—
747C23—9416no—
748C23—944no—
749C23—3762no—
750C23—3768no—
751C23—3762no—
752C23C22⋊C4×D4712yes—
753C23C22⋊C4×D4712yes—
754C23C22×C4×D4714yes—
755C23C22×C4×D4711yescharacteristic
756C23C22×C4×D4711yescharacteristic
757C23C22×C4×D4711yescharacteristic
758Q8—24no—
759Q8—24no—
760Q8—474no—
761Q8—474no—
762Q8—478no—
763Q8—9416no—
764Q8—942no—
765Q8—942no—
766Q8—944no—
767D4—28no—
768D4—28no—
769D4—24no—
770D4—24no—
771D4—478no—
772D4—478no—
773D4—4716no—
774D4—474no—
775D4—474no—
776D4—478no—
777D4—9416no—
778D4—9416no—
779D4—9416no—
780D4—944no—
781D4—944no—
782D4—948no—
783D4—942no—
784D4—942no—
785D4—944no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—478no—
793C2×C4—474no—
794C2×C4—478no—
795C2×C4—478no—
796C2×C4—4716no—
797C2×C4—474no—
798C2×C4—9416no—
799C2×C4—9416no—
800C2×C4—9416no—
801C2×C4—944no—
802C2×C4—944no—
803C2×C4—948no—
804C2×C4—944no—
805C2×C4C22⋊C4×D4711yescharacteristic
806C2×C4C22⋊C4×D4711yescharacteristic
807C2×C4C22⋊C4×D4712yes—
808C2×C4C22⋊C4×D4712yes—
809C2×C4C22⋊C4×D4712yes—
810C2×C4C22⋊C4×D4711yescharacteristic
811C2×C4C22⋊C4×D4711yescharacteristic
812C2×C4C22⋊C4×D4712yes—
813C2×C4C22×C4×D4714yes—
814C2×C4C22×C4×D4711yescharacteristic
815C2×C4C22×C4×D4711yescharacteristic
816C2×C4C22×C4×D4711yescharacteristic
817C2×C4C2×D4×D4712yes—
818C2×C4C2×D4×D4712yes—
819C2×C4C2×D4×D4712yes—
820C2×C4C2×D4×D4712yes—
821C2×C4C2×D4×D4712yes—
822C2×C4C2×D4×D4712yes—
823C2×C4C24×D4711yescharacteristic
824C8—28no—
825C8—948no—
826C22—24no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—44no—
833C22—82no—
834C22—82no—
835C22—478no—
836C22—944no—
837C22—3764no—
838C22—37616no—
839C22—1884no—
840C22—1888no—
841C22—1884no—
842C22C2×C22⋊C4×D4711yescharacteristic
843C22C2×C22⋊C4×D4711yescharacteristic
844C22C2×C22⋊C4×D4712yes—
845C22C2×C22⋊C4×D4712yes—
846C22C23×C4×D4711yescharacteristic
847C4—24no—
848C4—478no—
849C4—944no—
850C4C2×C22⋊C4×D4711yescharacteristic
851C4C2×C22⋊C4×D4711yescharacteristic
852C4C2×C22⋊C4×D4711yescharacteristic
853C4C2×C22⋊C4×D4712yes—
854C4C2×C22⋊C4×D4711yescharacteristic
855C4C22×D4×D4712yes—
856C2—21no—
857C2—21no—
858C2—21no—
859C2—22no—
860C2—22no—
861C2—44no—
862C2—948no—
863C2—1884no—
864C2C22×C22⋊C4×D4711yescharacteristic
subgroupG/H
centerC4C2×C22⋊C4×D47
commutatorC22×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#413C2
socleC2×C47C23×C22⋊C4
prime radicalC2×#15689959C2
cosocleC2×C4×C47C25
hypercenterC2×#413D47
hypocenterC47#60076
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#15689889C2semidirect
3. #20251869C2semidirect
4. #20251868C2semidirect
5. #20251865C2semidirect
6. #20251864C2semidirect
7. C2×#15689107C2semidirect
8. C2×#15689105C2semidirect
9. #413×D47C2semidirect
10. C2×C47×#413C2semidirect
29. #15689889C22semidirect
30. #15689889C22semidirect
33. C22×#10625329C22semidirect
34. C2×M16×D47C22semidirect
35. #15689107C22semidirect
36. #15689107C22semidirect
37. #15689106C22semidirect
38. #15689105C22semidirect
39. #15689105C22semidirect
40. #15689104C22semidirect
41. C2×#13093943C22semidirect
42. C2×#13093942C22semidirect
43. #101×D47C22semidirect
44. C2×#13093941C22semidirect
45. C2×#13093940C22semidirect
46. #100×D47C22semidirect
48. C22×M16×C47C22semidirect
49. C47×#413C22semidirect
50. C47×#413C22semidirect
51. C2×#101×C47C22semidirect
52. C2×#100×C47C22semidirect
433. C2×#413D47semidirect
468. C22×M16C2×D47semidirect
475. #413C2×D47semidirect
476. #413C2×D47semidirect
480. C2×#101C2×D47semidirect
484. C2×#100C2×D47semidirect
485. C47#60076semidirect

Maximal subgroups

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

subgroupindex
C2×#156899592
C2×#156898892
#202518692
#202518682
#202518652
#202518642
C2×#156891072
C2×#156891052
#413×D472
C2×C47×#4132
#6007647