Finite Group Databasebeta

← C2×#20257179 #27124746

Subgroups — C2×#20257179 #27124746

Order 12032.

11534 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094072C211yesmaximal, characteristic, complemented
2C22×#13094070C211yesmaximal, characteristic, complemented
3#20257179C2132yesmaximal, direct product factor
4C2×#15689785C211yesmaximal, characteristic, complemented
5C2×#15689784C211yesmaximal, characteristic, complemented
6C2×#15689780C211yesmaximal, characteristic, complemented
7C2×#15689770C213yesmaximal, complemented
8C2×#15689769C213yesmaximal, complemented
9C2×#15689766C213yesmaximal, complemented
10C2×#15689764C213yesmaximal, complemented
11C2×#15689696C213yesmaximal, complemented
12C2×#15689689C213yesmaximal, complemented
13C2×#15689670C213yesmaximal, complemented
14C2×#124×D47C213yesmaximal, complemented
15C2×C4×#10625354C211yesmaximal, characteristic, complemented
16C2×C47×#548C211yesmaximal, characteristic, complemented
17C2×#13094072—216no—
18C2×#13094072C22116yescomplemented
19C2×#13094070—216no—
20C2×#13094070C22116yescomplemented
21C22×#10625354C2211yescharacteristic
22C22×#10625354C2211yescharacteristic
23C22×#10625354C2213yescomplemented
24C22×#10625350C2213yes—
25C22×#10625350C2213yescomplemented
26C22×#10625350C2213yescomplemented
27C22×Q8×D47C2211yescharacteristic, complemented
28C22×Q8×D47C2213yescomplemented
29C23×D188C2213yes—
30C22×D4×D47C2213yes—
31C22×D4×D47C2213yes—
32#15689785C22116yescomplemented
33#15689784C22116yescomplemented
34#15689780C22116yescomplemented
35#15689770C22148yescomplemented
36#15689769C22148yescomplemented
37#15689766C22148yescomplemented
38#15689764C22148yescomplemented
39#15689696C22148yescomplemented
40#15689689C22148yescomplemented
41#15689670C22148yescomplemented
42C2×#13094023C2213yescomplemented
43C2×#13094020C2213yescomplemented
44C2×#13094013C2213yescomplemented
45C2×#13094012C2213yescomplemented
46C2×#13094011C2213yescomplemented
47C2×#13094010C2213yescomplemented
48C2×#13094010C2216yescomplemented
49C2×#13094010C2211yescharacteristic, complemented
50#124×D47C22148yescomplemented
51C2×#13094009C2216yescomplemented
52C2×#13094006C2216yescomplemented
53C2×#13094004C2213yescomplemented
54C2×#13094003C2213yescomplemented
55C2×#13094000C2213yescomplemented
56C2×#13093999C2213yescomplemented
57C2×#13093999C2213yescomplemented
58C2×#13093998C2213yescomplemented
59C2×#13093997C2213yescomplemented
60C2×#13093997C2213yescomplemented
61C2×#13093995C2213yescomplemented
62C2×#13093995C2213yescomplemented
63C2×#13093994C2216yescomplemented
64C2×#13093992C2216yescomplemented
65C4×#10625354C22116yescomplemented
66C2×Q8×Dic47C2211yescharacteristic, complemented
67C2×C4×D188C2213yescomplemented
68C2×C4×D188C2213yescomplemented
69C2×#13093986C2213yescomplemented
70C2×C4×C22⋊D47C2213yescomplemented
71C2×C4×C22⋊D47C2213yescomplemented
72C2×#13093982C2213yescomplemented
73C2×C22⋊C4×D47C2216yescomplemented
74C2×C22⋊C4×D47C2216yescomplemented
75C2×C42×D47C2213yescomplemented
76C22×#41×C47C2211yescharacteristic
77C23×Q8×C47C2211yescharacteristic, complemented
78C47×#548C22116yescomplemented
79C2×#124×C47C2213yescomplemented
80C2×C22⋊Q8×C47C2213yescomplemented
81C2×#121×C47C2213yescomplemented
82C2×C4×Q8×C47C2211yescharacteristic, complemented
83C2×C4×D4×C47C2213yescomplemented
84C24×D47C2316yes—
85#13094072—2128no—
86#13094070—2128no—
87C2×#10625354—28no—
88C2×#10625354—224no—
89C2×#10625354D4116yescomplemented
90C2×#10625354C2318yes—
91C2×#10625354C2318yes—
92C2×#10625354C23124yescomplemented
93C2×#10625350—224no—
94C2×#10625350—224no—
95C2×#10625350—224no—
96C2×#10625350C23124yes—
97C2×#10625350C23124yescomplemented
98C2×#10625350C23124yescomplemented
99C22×Dic94C2313yes—
100C22×Dic94C2313yes—
101C22×Dic94C2311yescharacteristic
102C2×Q8×D47—28no—
103C2×Q8×D47—224no—
104C2×Q8×D47C2318yescomplemented
105C2×Q8×D47C23124yescomplemented
106C22×D188—224no—
107C22×D188C23124yes—
108C22×D188C2313yes—
109C22×D188C2313yes—
110C22×D188C2313yes—
111C22×D188C2313yes—
112C22×D188C2313yes—
113C22×C22⋊D47C2313yes—
114C22×C22⋊D47C2313yes—
115C22×C22⋊D47C2313yes—
116C22×C22⋊D47C2311yescharacteristic
117C22×C22⋊D47C2313yes—
118C22×C22⋊D47C2313yes—
119C2×D4×D47—224no—
120C2×D4×D47—224no—
121C2×D4×D47C23124yes—
122C2×D4×D47C23124yes—
123C22×C4×D47C2316yes—
124C22×C4×D47C2313yes—
125C22×C4×D47C2313yes—
126C22×C4×D47C2313yes—
127C22×C4×D47C2313yes—
128C22×C4×D47C2313yes—
129#13094023C23124yescomplemented
130#13094020C23124yescomplemented
131#13094013C23124yescomplemented
132#13094012C23124yescomplemented
133#13094011C23124yescomplemented
134#13094010C23124yescomplemented
135#13094010C23148yescomplemented
136#13094010C2318yescomplemented
137#13094009C23148yescomplemented
138#13094006C23148yescomplemented
139#13094004C23124yescomplemented
140#13094003C23124yescomplemented
141#13094000C23124yescomplemented
142#13093999C23124yescomplemented
143#13093999C23124yescomplemented
144#13093998C23124yescomplemented
145#13093997C23124yescomplemented
146#13093997C23124yescomplemented
147#13093995C23124yescomplemented
148#13093995C23124yescomplemented
149#13093994C23148yescomplemented
150#13093992C23148yescomplemented
151Q8×Dic47C2318yescomplemented
152C4×D188C23124yescomplemented
153C4×D188C23124yescomplemented
154#13093986C23124yescomplemented
155C4×C22⋊D47C23124yescomplemented
156C4×C22⋊D47C23124yescomplemented
157#13093982C23124yescomplemented
158C2×C4⋊Dic47C2313yes—
159C2×C4⋊Dic47C2313yes—
160C2×Dic47⋊C4C2313yes—
161C2×Dic47⋊C4C2313yes—
162C2×C22⋊Dic47C2313yes—
163C2×C22⋊Dic47C2316yes—
164C2×C22⋊Dic47C2311yescharacteristic
165C2×(C2×D47)⋊C4C2313yes—
166C2×(C2×D47)⋊C4C2313yes—
167C2×(C2×D47)⋊C4C2316yes—
168C2×(C2×D47)⋊C4C2316yes—
169C2×(C2×D47)⋊C4C2316yes—
170C2×(C2×D47)⋊C4C2311yescharacteristic
171C2×(C2×D47)⋊C4C2311yescharacteristic
172C22⋊C4×D47C23148yescomplemented
173C22⋊C4×D47C23148yescomplemented
174C2×C4×Dic47C2311yescharacteristic
175C2×C4×Dic47C2313yes—
176C2×C4×Dic47C2313yes—
177C42×D47C23124yescomplemented
178C2×#41×C47—28no—
179C2×#41×C47C2318yes—
180C22×Q8×C47—28no—
181C22×Q8×C47C2313yes—
182C22×Q8×C47C2311yescharacteristic
183C22×Q8×C47C2318yescomplemented
184C22×D4×C47C2313yes—
185C22×D4×C47C2313yes—
186C23×C4×C47C2313yes—
187C23×C4×C47C2313yes—
188#124×C47C23124yescomplemented
189C22⋊Q8×C47C23124yescomplemented
190#121×C47C23124yescomplemented
191C4×Q8×C47C2318yescomplemented
192C4×D4×C47C23124yescomplemented
193C2×C4⋊C4×C47C2313yes—
194C2×C4⋊C4×C47C2313yes—
195C2×C22⋊C4×C47C2311yescharacteristic
196C2×C22⋊C4×C47C2313yes—
197C2×C22⋊C4×C47C2316yes—
198C2×C42×C47C2313yes—
199C24×C47C2413yes—
200C24×C47C2411yescharacteristic
201C23×D47—224no—
202C23×D47—412no—
203C23×D47—412no—
204C23×D47C2413yes—
205C23×D47C2411yescharacteristic
206C23×D47C2413yes—
207C23×D47C24124yes—
208#41×C47—232no—
209C2×Q8×C47—232no—
210C2×Q8×C47—212no—
211C2×Q8×C47C2×D418yes—
212C2×Q8×C47C24112yes—
213C2×Q8×C47C2414yes—
214C2×D4×C47—212no—
215C2×D4×C47—46no—
216C2×D4×C47C24112yes—
217C2×D4×C47C24112yes—
218C22×C4×C47—212no—
219C22×C4×C47—212no—
220C22×C4×C47C2411yescharacteristic
221C22×C4×C47C2413yes—
222C22×C4×C47C2413yes—
223C22×C4×C47C2411yescharacteristic
224C22×C4×C47C24112yes—
225C22×C4×C47C24112yes—
226C22×C4×C47C2413yes—
227C2×C22⋊D47—212no—
228C2×C22⋊D47—212no—
229C2×C22⋊D47—212no—
230C2×C22⋊D47—24no—
231C2×C22⋊D47—46no—
232C2×C22⋊D47—46no—
233C2×C22⋊D47C24112yes—
234C2×C22⋊D47C24112yes—
235C2×C22⋊D47C24112yes—
236C2×C22⋊D47C2414yes—
237C2×C22⋊D47C24112yes—
238C2×C22⋊D47C24112yes—
239C22×Dic47C2411yescharacteristic
240C22×Dic47C2413yes—
241C22×Dic47C2413yes—
242C22×Dic47C2411yescharacteristic
243C22×Dic47C2411yescharacteristic
244#10625354—232no—
245#10625354—296no—
246#10625354C2×D4164yescomplemented
247Q8×D47—232no—
248Q8×D47—296no—
249D4×D47—296no—
250D4×D47—296no—
251#10625350—296no—
252#10625350—296no—
253#10625350—296no—
254C2×D188—212no—
255C2×D188—212no—
256C2×D188—212no—
257C2×D188—296no—
258C2×D188—46no—
259C2×D188C2×D4124yes—
260C2×D188C24112yes—
261C2×D188C24112yes—
262C2×D188C24112yes—
263C2×D188C24112yes—
264C2×D188C24112yes—
265C2×C4×D47—224no—
266C2×C4×D47—212no—
267C2×C4×D47—212no—
268C2×C4×D47—46no—
269C2×C4×D47—46no—
270C2×C4×D47C2×D4124yes—
271C2×C4×D47C24124yes—
272C2×C4×D47C24112yes—
273C2×C4×D47C24112yes—
274C2×C4×D47C24112yes—
275C2×C4×D47C24112yes—
276C2×C4×D47C24112yes—
277C2×Dic94—212no—
278C2×Dic94—212no—
279C2×Dic94—24no—
280C2×Dic94C24112yes—
281C2×Dic94C24112yes—
282C2×Dic94C2414yes—
283C4⋊C4×C47C24112yes—
284C4⋊C4×C47C24112yes—
285C22⋊C4×C47C2414yes—
286C22⋊C4×C47C24112yes—
287C22⋊C4×C47C24124yes—
288C42×C47C24112yes—
289C22⋊Dic47C24112yes—
290C22⋊Dic47C24124yes—
291C22⋊Dic47C2414yes—
292(C2×D47)⋊C4C24112yes—
293(C2×D47)⋊C4C24112yes—
294(C2×D47)⋊C4C24124yes—
295(C2×D47)⋊C4C24124yes—
296(C2×D47)⋊C4C24124yes—
297(C2×D47)⋊C4C2414yes—
298(C2×D47)⋊C4C2414yes—
299C4⋊Dic47C24112yes—
300C4⋊Dic47C24112yes—
301Dic47⋊C4C24112yes—
302Dic47⋊C4C24112yes—
303C4×Dic47C2414yes—
304C4×Dic47C24112yes—
305C4×Dic47C24112yes—
306C23×C47—22no—
307C23×C47—26no—
308C23×C47—22no—
309C23×C47—26no—
310C23×C47—22no—
311C23×C47—26no—
312C23×C47C2516yes—
313C23×C47C2512yes—
314C23×C47C2511yescharacteristic
315C22×D47—26no—
316C22×D47—26no—
317C22×D47—22no—
318C22×D47—26no—
319C22×D47—22no—
320C22×D47—26no—
321C22×D47—22no—
322C22×D47—26no—
323C22×D47—248no—
324C22×D47—424no—
325C22×D47—424no—
326C22×D47—848no—
327C22×D47C22×D4112yes—
328C22×D47C2516yes—
329C22×D47C2512yes—
330C22×D47C2516yes—
331Q8×C47—224no—
332Q8×C47C22×D4116yes—
333D4×C47—224no—
334D4×C47—412no—
335C2×C4×C47—26no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—26no—
339C2×C4×C47—224no—
340C2×C4×C47—224no—
341C2×C4×C47C22×D4112yes—
342C2×C4×C47C2516yes—
343C2×C4×C47C2512yes—
344C2×C4×C47C2512yes—
345C2×C4×C47C2516yes—
346C2×C4×C47C2516yes—
347C22⋊D47—224no—
348C22⋊D47—224no—
349C22⋊D47—28no—
350C22⋊D47—224no—
351C22⋊D47—412no—
352C22⋊D47—412no—
353C2×Dic47—26no—
354C2×Dic47—22no—
355C2×Dic47—22no—
356C2×Dic47—26no—
357C2×Dic47C22×D414yes—
358C2×Dic47C2512yes—
359C2×Dic47C2516yes—
360C2×Dic47C2512yes—
361C2×Dic47C2516yes—
362C2×Dic47C2512yes—
363D188—224no—
364D188—224no—
365D188—224no—
366D188—412no—
367D188C22×D4148yes—
368C4×D47—248no—
369C4×D47—224no—
370C4×D47—224no—
371C4×D47—412no—
372C4×D47—412no—
373C4×D47C22×D4148yes—
374Dic94—224no—
375Dic94—28no—
376Dic94—224no—
377C2×#3500—471nomaximal, Sylow
378C22×C47—22no—
379C22×C47—26no—
380C22×C47—22no—
381C22×C47—26no—
382C22×C47—22no—
383C22×C47—26no—
384C22×C47—412no—
385C22×C47—44no—
386C22×C47C23×D412yes—
387C22×C47#58512yes—
388C22×C47#58512yes—
389C22×C47C2611yescharacteristic
390C2×D47—26no—
391C2×D47—26no—
392C2×D47—224no—
393C2×D47—22no—
394C2×D47—26no—
395C2×D47—22no—
396C2×D47—26no—
397C2×D47—22no—
398C2×D47—26no—
399C2×D47—44no—
400C2×D47—412no—
401C2×D47—848no—
402C2×D47C23×D4112yes—
403C4×C47—26no—
404C4×C47—22no—
405C4×C47—22no—
406C4×C47—26no—
407C4×C47C23×D4112yes—
408Dic47—26no—
409Dic47—22no—
410Dic47—22no—
411Dic47—26no—
412Dic47C23×D414yes—
413C22×2−1+4—471no—
414C22×H(5,𝔽2)—471no—
415#3500—4732no—
416C2×#548—471no—
417C2×#548—471no—
418C2×#548—471no—
419C2×#548D4711yescharacteristic, complemented
420C2×#546—473no—
421C2×#546—473no—
422C2×#546—473no—
423C2×#546—473no—
424C2×#536—473no—
425C2×#535—473no—
426C2×#532—473no—
427C22×#124—473no—
428C2×C4×#41—471no—
429C2×C47—46no—
430C2×C47—42no—
431C2×C47#350014yescomplemented
432C2×C47C24×D411yescharacteristic
433C2×C47C2×#58511yescharacteristic
434C2×C47C2×#58511yescharacteristic
435D47—212no—
436D47—42no—
437D47—46no—
438C2×2−1+4—4716no—
439C2×2−1+4—9416no—
440C2×H(5,𝔽2)—4716no—
441C2×H(5,𝔽2)—9416no—
442C22×#41—471no—
443C22×#41—471no—
444C22×#41—473no—
445C22×#41—473no—
446C22×#41—473no—
447C22×#41—473no—
448C22×#41C2×D4711yescharacteristic
449C23×Q8—473no—
450C23×Q8—471no—
451C23×Q8C2×D4711yescharacteristic, complemented
452C23×D4—473no—
453C23×D4—473no—
454C23×D4—473no—
455#548—4716no—
456#548—4716no—
457#548—4716no—
458#548C2×D47116yescomplemented
459#546—4748no—
460#546—4748no—
461#546—4748no—
462#546—4748no—
463#536—4748no—
464#535—4748no—
465#532—4748no—
466C2×C4⋊Q8—473no—
467C2×#127—473no—
468C2×#124—473no—
469C2×#124—473no—
470C2×#124—4748no—
471C2×#124—473no—
472C2×#124—476no—
473C2×#124—471no—
474C2×#124—473no—
475C2×#124C2×D4713yescomplemented
476C2×#123—476no—
477C2×#123—476no—
478C2×C22⋊Q8—473no—
479C2×C22⋊Q8—473no—
480C2×C22⋊Q8—473no—
481C2×C22⋊Q8C2×D4713yescomplemented
482C2×#121—473no—
483C2×#121—473no—
484C2×#121—473no—
485C2×#121—473no—
486C2×#121—473no—
487C2×#121—473no—
488C2×#121—473no—
489C2×#121C2×D4713yescomplemented
490C2×#120—476no—
491C2×#120—476no—
492C4×#41—4716no—
493C2×C4×Q8—471no—
494C2×C4×Q8C2×D4711yescharacteristic, complemented
495C2×C4×D4—473no—
496C2×C4×D4—473no—
497C2×C4×D4—473no—
498C2×C4×D4—473no—
499C2×C4×D4—473no—
500C2×C4×D4C2×D4713yescomplemented
501C2×#117—473no—
502C22×C22⋊C4—476no—
503C22×C22⋊C4—476no—
504C22×C42—473no—
505C47C2×#350011yescharacteristic, complemented, Sylow
506C25—476no—
5072−1+4—94128no—
508H(5,𝔽2)—94128no—
509C2×#41—28no—
510C2×#41—4716no—
511C2×#41—478no—
512C2×#41—4724no—
513C2×#41—478no—
514C2×#41—4724no—
515C2×#41—4724no—
516C2×#41—4724no—
517C2×#41—9424no—
518C2×#41—9424no—
519C2×#41—9424no—
520C2×#41—9424no—
521C2×#41—948no—
522C2×#41C22×D4718yes—
523C22×Q8—28no—
524C22×Q8—4724no—
525C22×Q8—478no—
526C22×Q8—473no—
527C22×Q8—473no—
528C22×Q8—471no—
529C22×Q8—9424no—
530C22×Q8—948no—
531C22×Q8C22×D4713yes—
532C22×Q8C22×D4711yescharacteristic
533C22×Q8C22×D4718yescomplemented
534C22×D4—473no—
535C22×D4—473no—
536C22×D4—473no—
537C22×D4—471no—
538C22×D4—473no—
539C22×D4—473no—
540C22×D4—4724no—
541C22×D4—4724no—
542C22×D4—473no—
543C22×D4—473no—
544C22×D4—473no—
545C22×D4—473no—
546C22×D4—4724no—
547C22×D4—473no—
548C22×D4—9424no—
549C22×D4—9424no—
550C22×D4—9424no—
551C22×D4C22×D4713yes—
552C22×D4C22×D4713yes—
553C23×C4—473no—
554C23×C4—476no—
555C23×C4—473no—
556C23×C4—473no—
557C23×C4—473no—
558C23×C4—473no—
559C23×C4C22×D4713yes—
560C23×C4C22×D4713yes—
561C4⋊Q8—4724no—
562#127—4724no—
563#124—4724no—
564#124—4724no—
565#124—4724no—
566#124—4748no—
567#124—478no—
568#124—4724no—
569#124C22×D47124yescomplemented
570#123—4748no—
571#123—4748no—
572C22⋊Q8—4724no—
573C22⋊Q8—4724no—
574C22⋊Q8—4724no—
575C22⋊Q8C22×D47124yescomplemented
576#121—4724no—
577#121—4724no—
578#121—4724no—
579#121—4724no—
580#121—4724no—
581#121—4724no—
582#121—4724no—
583#121C22×D47124yescomplemented
584#120—4748no—
585#120—4748no—
586C4×Q8—478no—
587C4×Q8C22×D4718yescomplemented
588C4×D4—4724no—
589C4×D4—4724no—
590C4×D4—4724no—
591C4×D4—4724no—
592C4×D4—4724no—
593C4×D4C22×D47124yescomplemented
594#117—4724no—
595C2×C4⋊C4—473no—
596C2×C4⋊C4—473no—
597C2×C4⋊C4—473no—
598C2×C4⋊C4—473no—
599C2×C4⋊C4C22×D4713yes—
600C2×C4⋊C4C22×D4713yes—
601C2×C22⋊C4—473no—
602C2×C22⋊C4—476no—
603C2×C22⋊C4—471no—
604C2×C22⋊C4—473no—
605C2×C22⋊C4—473no—
606C2×C22⋊C4—476no—
607C2×C22⋊C4—476no—
608C2×C22⋊C4—476no—
609C2×C22⋊C4—471no—
610C2×C22⋊C4—471no—
611C2×C22⋊C4—4748no—
612C2×C22⋊C4—4748no—
613C2×C22⋊C4C22×D4713yes—
614C2×C22⋊C4C22×D4716yes—
615C2×C22⋊C4C22×D4711yescharacteristic
616C2×C42—473no—
617C2×C42—473no—
618C2×C42—471no—
619C2×C42—4724no—
620C2×C42C22×D4713yes—
621C24—473no—
622C24—473no—
623C24—471no—
624C24—4724no—
625C24—9424no—
626C24—18812no—
627C24—18812no—
628C24C23×D4713yes—
629C24C23×D4711yescharacteristic
630#41—232no—
631#41—4764no—
632#41—9496no—
633#41—9496no—
634#41—9496no—
635#41—9496no—
636#41—9432no—
637C2×Q8—232no—
638C2×Q8—212no—
639C2×Q8—4712no—
640C2×Q8—4712no—
641C2×Q8—474no—
642C2×Q8—9412no—
643C2×Q8—944no—
644C2×Q8—9496no—
645C2×Q8—9432no—
646C2×Q8—9412no—
647C2×Q8D4×D4718yes—
648C2×Q8C23×D47112yes—
649C2×Q8C23×D4714yes—
650C2×D4—212no—
651C2×D4—46no—
652C2×D4—4712no—
653C2×D4—4712no—
654C2×D4—4712no—
655C2×D4—474no—
656C2×D4—4712no—
657C2×D4—4712no—
658C2×D4—4724no—
659C2×D4—4712no—
660C2×D4—4712no—
661C2×D4—4712no—
662C2×D4—4712no—
663C2×D4—4712no—
664C2×D4—9496no—
665C2×D4—9412no—
666C2×D4—9412no—
667C2×D4—9496no—
668C2×D4—9412no—
669C2×D4—944no—
670C2×D4—9496no—
671C2×D4—9412no—
672C2×D4—9412no—
673C2×D4—9412no—
674C2×D4—1886no—
675C2×D4—1886no—
676C2×D4—1886no—
677C2×D4C23×D47112yes—
678C2×D4C23×D47112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—471no—
682C22×C4—4724no—
683C22×C4—4712no—
684C22×C4—471no—
685C22×C4—473no—
686C22×C4—473no—
687C22×C4—471no—
688C22×C4—4724no—
689C22×C4—4712no—
690C22×C4—4712no—
691C22×C4—4712no—
692C22×C4—4712no—
693C22×C4—9424no—
694C22×C4—9412no—
695C22×C4—9412no—
696C22×C4—1886no—
697C22×C4—1886no—
698C22×C4C23×D47112yes—
699C22×C4C23×D47112yes—
700C22×C4C23×D4711yescharacteristic
701C22×C4C23×D4713yes—
702C22×C4C23×D4713yes—
703C22×C4C23×D4711yescharacteristic
704C22×C4C23×D4713yes—
705C4⋊C4—4712no—
706C4⋊C4—4712no—
707C4⋊C4—4712no—
708C4⋊C4—4712no—
709C4⋊C4C23×D47112yes—
710C4⋊C4C23×D47112yes—
711C22⋊C4—4712no—
712C22⋊C4—4724no—
713C22⋊C4—474no—
714C22⋊C4—4712no—
715C22⋊C4—4712no—
716C22⋊C4—4724no—
717C22⋊C4—4724no—
718C22⋊C4—4724no—
719C22⋊C4—474no—
720C22⋊C4—474no—
721C22⋊C4C23×D47112yes—
722C22⋊C4C23×D47124yes—
723C22⋊C4C23×D4714yes—
724C42—474no—
725C42—4712no—
726C42—4712no—
727C42C23×D47112yes—
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—4712no—
735C23—476no—
736C23—476no—
737C23—472no—
738C23—9448no—
739C23—946no—
740C23—946no—
741C23—942no—
742C23—946no—
743C23—942no—
744C23—946no—
745C23—942no—
746C23—946no—
747C23—37648no—
748C23—18824no—
749C23—18824no—
750C23C24×D4716yes—
751C23C24×D4712yes—
752C23C24×D4711yescharacteristic
753Q8—224no—
754Q8—9424no—
755Q8—948no—
756Q8—9424no—
757Q8C2×D4×D47116yes—
758D4—224no—
759D4—412no—
760D4—4748no—
761D4—9424no—
762D4—9424no—
763D4—9424no—
764D4—948no—
765D4—9424no—
766D4—9424no—
767D4—9424no—
768D4—18812no—
769D4—18812no—
770D4—18812no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—22no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—474no—
778C2×C4—472no—
779C2×C4—4748no—
780C2×C4—472no—
781C2×C4—476no—
782C2×C4—476no—
783C2×C4—472no—
784C2×C4—9448no—
785C2×C4—942no—
786C2×C4—946no—
787C2×C4—942no—
788C2×C4—946no—
789C2×C4—9424no—
790C2×C4—9424no—
791C2×C4—18812no—
792C2×C4—18812no—
793C2×C4C2×D4×D47112yes—
794C2×C4C24×D4712yes—
795C2×C4C24×D4716yes—
796C2×C4C24×D4716yes—
797C2×C4C24×D4712yes—
798C2×C4C24×D4716yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—412no—
806C22—44no—
807C22—4712no—
808C22—946no—
809C22—946no—
810C22—9424no—
811C22—942no—
812C22—946no—
813C22—942no—
814C22—946no—
815C22—942no—
816C22—946no—
817C22—37648no—
818C22—18812no—
819C22—1884no—
820C22C22×D4×D4712yes—
821C22#1568995912yes—
822C22#1568996012yes—
823C22C25×D4711yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—474no—
829C4—942no—
830C4—946no—
831C4—942no—
832C4—946no—
833C4C22×D4×D47112yes—
834C2—46no—
835C2—42no—
836C2—9412no—
837C2—1886no—
838C2—1882no—
839C2#2025717914yesdirect product factor
840C2C23×D4×D4711yescharacteristic
841C2C2×#1568995911yescharacteristic
842C2C2×#1568996011yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#548C2
socleC23×C47C25
hypercenterC2×#548D47
hypocenterC47C2×#3500
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#13094072C2semidirect
2. C22×#13094070C2semidirect
3. #20257179C2direct (N × H)
4. C2×#15689785C2semidirect
5. C2×#15689784C2semidirect
6. C2×#15689780C2semidirect
7. C2×#15689770C2semidirect
8. C2×#15689769C2semidirect
9. C2×#15689766C2semidirect
10. C2×#15689764C2semidirect
11. C2×#15689696C2semidirect
12. C2×#15689689C2semidirect
13. C2×#15689670C2semidirect
14. C2×#124×D47C2semidirect
15. C2×C4×#10625354C2semidirect
16. C2×C47×#548C2semidirect
18. C2×#13094072C22semidirect
20. C2×#13094070C22semidirect
23. C22×#10625354C22semidirect
25. C22×#10625350C22semidirect
26. C22×#10625350C22semidirect
27. C22×Q8×D47C22semidirect
28. C22×Q8×D47C22semidirect
32. #15689785C22semidirect
33. #15689784C22semidirect
34. #15689780C22semidirect
35. #15689770C22semidirect
36. #15689769C22semidirect
37. #15689766C22semidirect
38. #15689764C22semidirect
39. #15689696C22semidirect
40. #15689689C22semidirect
41. #15689670C22semidirect
42. C2×#13094023C22semidirect
43. C2×#13094020C22semidirect
44. C2×#13094013C22semidirect
45. C2×#13094012C22semidirect
46. C2×#13094011C22semidirect
47. C2×#13094010C22semidirect
48. C2×#13094010C22semidirect
49. C2×#13094010C22semidirect
50. #124×D47C22semidirect
51. C2×#13094009C22semidirect
52. C2×#13094006C22semidirect
53. C2×#13094004C22semidirect
54. C2×#13094003C22semidirect
55. C2×#13094000C22semidirect
56. C2×#13093999C22semidirect
57. C2×#13093999C22semidirect
58. C2×#13093998C22semidirect
59. C2×#13093997C22semidirect
60. C2×#13093997C22semidirect
61. C2×#13093995C22semidirect
62. C2×#13093995C22semidirect
63. C2×#13093994C22semidirect
64. C2×#13093992C22semidirect
65. C4×#10625354C22semidirect
66. C2×Q8×Dic47C22semidirect
67. C2×C4×D188C22semidirect
68. C2×C4×D188C22semidirect
69. C2×#13093986C22semidirect
70. C2×C4×C22⋊D47C22semidirect
71. C2×C4×C22⋊D47C22semidirect
72. C2×#13093982C22semidirect
73. C2×C22⋊C4×D47C22semidirect
74. C2×C22⋊C4×D47C22semidirect
75. C2×C42×D47C22semidirect
77. C23×Q8×C47C22semidirect
78. C47×#548C22semidirect
79. C2×#124×C47C22semidirect
80. C2×C22⋊Q8×C47C22semidirect
81. C2×#121×C47C22semidirect
82. C2×C4×Q8×C47C22semidirect
83. C2×C4×D4×C47C22semidirect
89. C2×#10625354D4semidirect
92. C2×#10625354C23semidirect
97. C2×#10625350C23semidirect
98. C2×#10625350C23semidirect
104. C2×Q8×D47C23semidirect
105. C2×Q8×D47C23semidirect
129. #13094023C23semidirect
130. #13094020C23semidirect
131. #13094013C23semidirect
132. #13094012C23semidirect
133. #13094011C23semidirect
134. #13094010C23semidirect
135. #13094010C23semidirect
136. #13094010C23semidirect
137. #13094009C23semidirect
138. #13094006C23semidirect
139. #13094004C23semidirect
140. #13094003C23semidirect
141. #13094000C23semidirect
142. #13093999C23semidirect
143. #13093999C23semidirect
144. #13093998C23semidirect
145. #13093997C23semidirect
146. #13093997C23semidirect
147. #13093995C23semidirect
148. #13093995C23semidirect
149. #13093994C23semidirect
150. #13093992C23semidirect
151. Q8×Dic47C23semidirect
152. C4×D188C23semidirect
153. C4×D188C23semidirect
154. #13093986C23semidirect
155. C4×C22⋊D47C23semidirect
156. C4×C22⋊D47C23semidirect
157. #13093982C23semidirect
172. C22⋊C4×D47C23semidirect
173. C22⋊C4×D47C23semidirect
177. C42×D47C23semidirect
183. C22×Q8×C47C23semidirect
188. #124×C47C23semidirect
189. C22⋊Q8×C47C23semidirect
190. #121×C47C23semidirect
191. C4×Q8×C47C23semidirect
192. C4×D4×C47C23semidirect
246. #10625354C2×D4semidirect
419. C2×#548D47semidirect
431. C2×C47#3500semidirect
451. C23×Q8C2×D47semidirect
458. #548C2×D47semidirect
475. C2×#124C2×D47semidirect
481. C2×C22⋊Q8C2×D47semidirect
489. C2×#121C2×D47semidirect
494. C2×C4×Q8C2×D47semidirect
500. C2×C4×D4C2×D47semidirect
505. C47C2×#3500semidirect
533. C22×Q8C22×D47semidirect
569. #124C22×D47semidirect
575. C22⋊Q8C22×D47semidirect
583. #121C22×D47semidirect
587. C4×Q8C22×D47semidirect
593. C4×D4C22×D47semidirect
839. C2#20257179direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940722
C22×#130940702
#202571792
C2×#156897852
C2×#156897842
C2×#156897802
C2×#156897702
C2×#156897692
C2×#156897662
C2×#156897642
C2×#156896962
C2×#156896892
C2×#156896702
C2×#124×D472
C2×C4×#106253542
C2×C47×#5482
C2×#350047