Finite Group Databasebeta

← #26377321

Subgroups — #26377321

Order 12032.

5682 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094070C211yesmaximal, characteristic
2C2×#15689605C211yesmaximal, characteristic, complemented
3C2×C4×#10625354C211yesmaximal, characteristic, complemented
4#20246229C211yesmaximal, characteristic, complemented
5#20246226C211yesmaximal, characteristic, complemented
6#20246226C211yesmaximal, characteristic, complemented
7C22⋊C4×D188C213yesmaximal, complemented
8#20246209C213yesmaximal, complemented
9#20246209C213yesmaximal, complemented
10#20246208C213yesmaximal, complemented
11#20245977C213yesmaximal, complemented
12#20245967C213yesmaximal, complemented
13#20245874C213yesmaximal, complemented
14#390×D47C213yesmaximal, complemented
15C47×#2341C211yesmaximal, characteristic, complemented
16C2×#13094070—28no—
17C2×#13094070—28no—
18C2×#13094070C4116yescomplemented
19C22×#10625354C2211yescharacteristic
20C22×#10625354C2211yescharacteristic
21C22×#10625350C2213yes—
22C23×D188C2213yes—
23C22×D4×D47C2213yes—
24C22×D4×D47C2213yes—
25#15689605—28no—
26C4×#10625354—28no—
27C2×Q8×Dic47C2211yescharacteristic, complemented
28C2×Q8×Dic47C2211yescharacteristic, complemented
29C2×C4×D188C2213yescomplemented
30C2×C4×D188C2213yescomplemented
31C2×#13093986C2213yescomplemented
32C2×#13093986C2213yescomplemented
33C2×#13093982C2213yescomplemented
34C2×#13093981C2213yescomplemented
35C2×C4⋊C4×D47C2213yescomplemented
36C2×C22⋊C4×D47C2216yescomplemented
37C2×C22⋊C4×D47C2216yescomplemented
38C2×C42×D47C2213yescomplemented
39#15689027C2211yescharacteristic, complemented
40#15689027C2213yescomplemented
41#15689026C2213yescomplemented
42#15689026C2213yescomplemented
43#15689025C2213yescomplemented
44#15689025C2213yescomplemented
45#15689024C2213yescomplemented
46#15689024C2213yescomplemented
47#15689023C2213yescomplemented
48#15689023C2216yescomplemented
49#15689023C2213yescomplemented
50#15689001C2213yescomplemented
51#15689001C2213yescomplemented
52#15689001C2216yescomplemented
53#15688999C2213yescomplemented
54#15688999C2213yescomplemented
55#15688999C2216yescomplemented
56#15688983C2213yescomplemented
57#15688980C2213yescomplemented
58#15688980C2213yescomplemented
59#15688978C2216yescomplemented
60#15688978C2216yescomplemented
61C4×(C2×D47)⋊C4C2213yescomplemented
62C4×(C2×D47)⋊C4C2213yescomplemented
63C4×C22⋊Dic47C2213yescomplemented
64C22×#41×C47C2211yescharacteristic
65C2×C4×Q8×C47C2211yescharacteristic, complemented
66C2×C4×Q8×C47C2211yescharacteristic, complemented
67C47×#390C2213yescomplemented
68C47×#390C2213yescomplemented
69C47×#380C2213yescomplemented
70C4×C22⋊C4×C47C2213yescomplemented
71C24×D47C2316yes—
72#13094070—2128no—
73C2×#10625354—24no—
74C2×#10625354—24no—
75C2×#10625354C2×C418yes—
76C2×#10625354C2×C418yescomplemented
77C2×#10625354D418yes—
78C2×#10625354D418yes—
79C2×#10625350—212no—
80C2×#10625350—212no—
81C2×#10625350C2×C4124yescomplemented
82C22×Dic94C2311yescharacteristic
83C22×D188—212no—
84C22×D188—212no—
85C22×D188C2×C4124yescomplemented
86C22×D188C2313yes—
87C22×D188C2313yes—
88C22×D188C2313yes—
89C22×C22⋊D47C2313yes—
90C22×C22⋊D47C2313yes—
91C2×D4×D47—212no—
92C2×D4×D47—212no—
93C2×D4×D47—212no—
94C2×D4×D47—212no—
95C2×D4×D47C2×C4124yescomplemented
96C2×D4×D47C2×C4124yescomplemented
97C22×C4×D47C2313yes—
98C22×C4×D47C2313yes—
99C22×C4×D47C2313yes—
100C22×C4×D47C2316yes—
101C22×C4×D47C2313yes—
102Q8×Dic47—24no—
103Q8×Dic47—24no—
104C4×D188—212no—
105C4×D188—212no—
106#13093986—212no—
107#13093986—212no—
108#13093982—212no—
109#13093981—212no—
110C2×C4⋊Dic47C2313yes—
111C2×C4⋊Dic47C2313yes—
112C2×Dic47⋊C4C2313yes—
113C2×Dic47⋊C4C2311yescharacteristic
114C4⋊C4×D47—212no—
115C2×C22⋊Dic47C2313yes—
116C2×C22⋊Dic47C2313yes—
117C2×C22⋊Dic47C2316yes—
118C2×(C2×D47)⋊C4C2313yes—
119C2×(C2×D47)⋊C4C2313yes—
120C2×(C2×D47)⋊C4C2313yes—
121C2×(C2×D47)⋊C4C2313yes—
122C2×(C2×D47)⋊C4C2316yes—
123C2×(C2×D47)⋊C4C2313yes—
124C2×(C2×D47)⋊C4C2313yes—
125C2×(C2×D47)⋊C4C2316yes—
126C2×(C2×D47)⋊C4C2316yes—
127C22⋊C4×D47—412no—
128C22⋊C4×D47—412no—
129C2×C4×Dic47C2313yes—
130C2×C4×Dic47C2313yes—
131C2×C4×Dic47C2311yescharacteristic
132C2×C4×Dic47C2313yes—
133C42×D47—212no—
134C47⋊#95C2311yescharacteristic
135C47⋊#95C2313yes—
136C47⋊#95C2311yescharacteristic
137C47⋊#95C2311yescharacteristic
138C47⋊#95C2313yes—
139C47⋊#95C2313yes—
140C2×#41×C47—24no—
141C2×#41×C47—24no—
142C2×#41×C47C2×C418yescomplemented
143C22×Q8×C47C2311yescharacteristic
144C22×D4×C47C2313yes—
145C23×C4×C47C2313yes—
146C4×Q8×C47—24no—
147C4×Q8×C47—24no—
148C2×C4⋊C4×C47C2313yes—
149C2×C4⋊C4×C47C2313yes—
150C2×C22⋊C4×C47C2313yes—
151C2×C22⋊C4×C47C2313yes—
152C2×C22⋊C4×C47C2316yes—
153C2×C42×C47C2313yes—
154C2×C42×C47C2313yes—
155#95×C47C2311yescharacteristic
156#95×C47C2313yes—
157C24×C47C2413yes—
158C23×D47—212no—
159C23×D47—212no—
160C23×D47—46no—
161C23×D47—46no—
162C23×D47—46no—
163C23×D47—46no—
164C23×D47C22×C4124yes—
165C23×D47C2413yes—
166C23×D47C2413yes—
167#41×C47—232no—
168C2×Q8×C47C22×C414yes—
169C2×Q8×C47C2×D414yes—
170C2×Q8×C47C2×D414yes—
171C2×D4×C47—26no—
172C2×D4×C47—26no—
173C2×D4×C47C22×C4112yes—
174C22×C4×C47—26no—
175C22×C4×C47—26no—
176C22×C4×C47C22×C4112yes—
177C22×C4×C47C2411yescharacteristic
178C22×C4×C47C2413yes—
179C22×C4×C47C2413yes—
180C22×C4×C47C2411yescharacteristic
181C22×C4×C47C2411yescharacteristic
182C22×C4×C47C2413yes—
183C2×C22⋊D47—26no—
184C2×C22⋊D47—26no—
185C2×C22⋊D47—26no—
186C2×C22⋊D47—26no—
187C2×C22⋊D47C22×C4112yes—
188C2×C22⋊D47C22×C4112yes—
189C22×Dic47C2411yescharacteristic
190C22×Dic47C2413yes—
191C22×Dic47C2413yes—
192C22×Dic47C2411yescharacteristic
193C22×Dic47C2411yescharacteristic
194C22×Dic47C2411yescharacteristic
195#10625354—232no—
196#10625354C22⋊C4164yescomplemented
197D4×D47—296no—
198D4×D47—296no—
199#10625350—296no—
200C2×D188—26no—
201C2×D188—26no—
202C2×D188—26no—
203C2×D188—26no—
204C2×D188—296no—
205C2×D188C22×C4112yes—
206C2×D188C22×C4112yes—
207C2×D188C22×C4112yes—
208C2×D188C2×D4112yes—
209C2×D188C2×D4112yes—
210C2×C4×D47—26no—
211C2×C4×D47—26no—
212C2×C4×D47—26no—
213C2×C4×D47—26no—
214C2×C4×D47—26no—
215C2×C4×D47—26no—
216C2×C4×D47—212no—
217C2×C4×D47—43no—
218C2×C4×D47—43no—
219C2×C4×D47—46no—
220C2×C4×D47—46no—
221C2×C4×D47C22×C4112yes—
222C2×C4×D47C22×C4112yes—
223C2×C4×D47C2×D4112yes—
224C2×C4×D47C2×D4112yes—
225C2×Dic94—22no—
226C2×Dic94—22no—
227C2×Dic94C22×C414yes—
228C4⋊C4×C47—26no—
229C4⋊C4×C47—26no—
230C22⋊C4×C47—26no—
231C22⋊C4×C47—43no—
232C22⋊C4×C47—46no—
233C42×C47—26no—
234C42×C47—26no—
235C22⋊Dic47—26no—
236C22⋊Dic47—46no—
237C22⋊Dic47—43no—
238(C2×D47)⋊C4—26no—
239(C2×D47)⋊C4—26no—
240(C2×D47)⋊C4—212no—
241(C2×D47)⋊C4—26no—
242(C2×D47)⋊C4—26no—
243(C2×D47)⋊C4—46no—
244(C2×D47)⋊C4—46no—
245(C2×D47)⋊C4—43no—
246(C2×D47)⋊C4—43no—
247C4⋊Dic47—26no—
248C4⋊Dic47—26no—
249Dic47⋊C4—26no—
250Dic47⋊C4—22no—
251C4×Dic47—26no—
252C4×Dic47—26no—
253C4×Dic47—22no—
254C4×Dic47—26no—
255C23×C47—23no—
256C23×C47—23no—
257C23×C47—23no—
258C23×C47—23no—
259C23×C47—23no—
260C23×C47—23no—
261C23×C47C23×C416yes—
262C23×C47C2511yescharacteristic
263C22×D47—23no—
264C22×D47—23no—
265C22×D47—23no—
266C22×D47—23no—
267C22×D47—23no—
268C22×D47—23no—
269C22×D47—23no—
270C22×D47—23no—
271C22×D47—23no—
272C22×D47—23no—
273C22×D47—248no—
274C22×D47—424no—
275C22×D47—424no—
276C22×D47—812no—
277C22×D47—812no—
278C22×D47—812no—
279C22×D47—812no—
280C22×D47C23×C416yes—
281C22×D47C23×C416yes—
282C22×D47C22×D416yes—
283C22×D47C22×D416yes—
284Q8×C47C2×C22⋊C4116yescomplemented
285D4×C47—224no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—224no—
291C2×C4×C47—23no—
292C2×C4×C47—21no—
293C2×C4×C47—23no—
294C2×C4×C47—23no—
295C2×C4×C47—23no—
296C2×C4×C47—23no—
297C2×C4×C47—21no—
298C2×C4×C47—23no—
299C2×C4×C47—21no—
300C2×C4×C47C23×C412yes—
301C2×C4×C47C23×C416yes—
302C2×C4×C47C22×D416yes—
303C2×C4×C47C22×D416yes—
304C2×C4×C47H(5,𝔽2)12yescomplemented
305C22⋊D47—224no—
306C22⋊D47—224no—
307C2×Dic47—21no—
308C2×Dic47—21no—
309C2×Dic47—21no—
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—23no—
313C2×Dic47—23no—
314C2×Dic47—23no—
315C2×Dic47—23no—
316C2×Dic47—23no—
317C2×Dic47—21no—
318C2×Dic47—23no—
319C2×Dic47—21no—
320C2×Dic47C23×C412yes—
321C2×Dic47C23×C412yes—
322C2×Dic47C22×D412yes—
323C2×Dic47C22×D412yes—
324C2×Dic47H(5,𝔽2)12yescomplemented
325D188—224no—
326D188—224no—
327D188C2×C22⋊C4148yescomplemented
328C4×D47—224no—
329C4×D47—412no—
330C4×D47—412no—
331C4×D47—812no—
332C4×D47C2×C22⋊C4148yescomplemented
333Dic94—28no—
334#34258—471nomaximal, Sylow
335C22×C47—26no—
336C22×C47—26no—
337C22×C47—26no—
338C22×C47—43no—
339C22×C47—43no—
340C22×C47—43no—
341C22×C47—43no—
342C22×C47C24×C411yescharacteristic
343C22×C47C23×D411yescharacteristic
344C22×C47C23×D411yescharacteristic
345C22×C47C2×H(5,𝔽2)11yescharacteristic
346C22×C47C2×H(5,𝔽2)11yescharacteristic
347C22×C47#58511yescharacteristic
348C22×C47#58511yescharacteristic
349C2×D47—26no—
350C2×D47—26no—
351C2×D47—26no—
352C2×D47—26no—
353C2×D47—26no—
354C2×D47—26no—
355C2×D47—26no—
356C2×D47—26no—
357C2×D47—26no—
358C2×D47—43no—
359C2×D47—43no—
360C2×D47—43no—
361C2×D47—43no—
362C2×D47—848no—
363C2×D47C22×C22⋊C4112yes—
364C4×C47—22no—
365C4×C47—22no—
366C4×C47—43no—
367C4×C47—43no—
368C4×C47—41no—
369C4×C47C22×C22⋊C4112yes—
370Dic47—22no—
371Dic47—22no—
372Dic47—43no—
373Dic47—43no—
374Dic47—41no—
375Dic47C22×C22⋊C414yes—
376C22×H(5,𝔽2)—471no—
377C2×#520—471no—
378C2×C4×#41—471no—
379#2341—471no—
380#2341—471no—
381#2341—471no—
382#2341D4711yescharacteristic, complemented
383D4×C22⋊C4—473no—
384D4×C22⋊C4—473no—
385D4×C22⋊C4—473no—
386D4×C22⋊C4—473no—
387#2311—473no—
388#2309—473no—
389#2297—473no—
390C2×#390—473no—
391C2×C47—46no—
392C2×C47C23×C22⋊C411yescharacteristic
393C2×C47C4×H(5,𝔽2)11yescharacteristic
394C2×C47C4×H(5,𝔽2)11yescharacteristic
395C2×C47#348811yescharacteristic
396C2×C47#348811yescharacteristic
397C2×C47#349811yescharacteristic
398C2×C47#350011yescharacteristic
399D47—212no—
400D47—46no—
401C2×H(5,𝔽2)—4716no—
402C2×H(5,𝔽2)—948no—
403C2×H(5,𝔽2)—948no—
404C22×#41—471no—
405C22×#41—471no—
406C22×#41—473no—
407C22×#41C2×D4711yescharacteristic
408C23×D4—473no—
409C23×D4—473no—
410C23×D4—473no—
411#520—948no—
412C4×#41—948no—
413C2×C4×Q8—471no—
414C2×C4×Q8—471no—
415C2×C4×Q8C2×D4711yescharacteristic, complemented
416C2×C4×Q8C2×D4711yescharacteristic, complemented
417C2×C4×D4—473no—
418C2×C4×D4—473no—
419C2×C4×D4—473no—
420C2×C4×D4—473no—
421C2×#117—473no—
422C2×#117—473no—
423C22×C4⋊C4—473no—
424C22×C22⋊C4—476no—
425C22×C22⋊C4—476no—
426C22×C42—473no—
427#391—473no—
428#391—471no—
429#390—473no—
430#390—473no—
431#390—473no—
432#390—473no—
433#390—473no—
434#390—476no—
435#390—473no—
436#390—473no—
437#390—473no—
438#390C2×D4713yescomplemented
439#390C2×D4713yescomplemented
440#386—476no—
441#386—473no—
442#386—473no—
443#386—476no—
444#386—473no—
445#386—473no—
446#380—473no—
447#380—473no—
448#380—473no—
449#380C2×D4713yescomplemented
450#379—476no—
451#379—476no—
452C4×C22⋊C4—473no—
453C4×C22⋊C4—473no—
454C4×C22⋊C4—473no—
455C4×C22⋊C4C2×D4713yescomplemented
456C47#3425811yescharacteristic, complemented, Sylow
457C25—476no—
458H(5,𝔽2)—94128no—
459C2×#41—24no—
460C2×#41—24no—
461C2×#41—478no—
462C2×#41—478no—
463C2×#41—478no—
464C2×#41—478no—
465C2×#41—4724no—
466C2×#41—9412no—
467C2×#41—9412no—
468C2×#41—944no—
469C2×#41—944no—
470C2×#41C4×D4718yescomplemented
471C22×Q8—471no—
472C22×Q8C22×D4711yescharacteristic
473C22×D4—473no—
474C22×D4—473no—
475C22×D4—4724no—
476C22×D4—4724no—
477C22×D4—4724no—
478C22×D4—473no—
479C22×D4—473no—
480C22×D4—473no—
481C22×D4—9412no—
482C22×D4—9412no—
483C22×D4—9412no—
484C22×D4—9412no—
485C22×D4—9412no—
486C22×D4—9412no—
487C22×D4C22×D4713yes—
488C23×C4—473no—
489C23×C4—473no—
490C23×C4—473no—
491C23×C4—473no—
492C23×C4—476no—
493C23×C4C22×D4713yes—
494C4×Q8—24no—
495C4×Q8—24no—
496C4×Q8—944no—
497C4×Q8—944no—
498C4×D4—9412no—
499C4×D4—9412no—
500C4×D4—9412no—
501C4×D4—9412no—
502#117—9412no—
503#117—9412no—
504C2×C4⋊C4—473no—
505C2×C4⋊C4—473no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—473no—
508C2×C4⋊C4—9412no—
509C2×C4⋊C4C22×D4713yes—
510C2×C4⋊C4C22×D4713yes—
511C2×C22⋊C4—473no—
512C2×C22⋊C4—473no—
513C2×C22⋊C4—473no—
514C2×C22⋊C4—473no—
515C2×C22⋊C4—476no—
516C2×C22⋊C4—473no—
517C2×C22⋊C4—476no—
518C2×C22⋊C4—473no—
519C2×C22⋊C4—476no—
520C2×C22⋊C4—476no—
521C2×C22⋊C4—473no—
522C2×C22⋊C4—473no—
523C2×C22⋊C4—18812no—
524C2×C22⋊C4—18812no—
525C2×C22⋊C4C22×D4713yes—
526C2×C22⋊C4C22×D4716yes—
527C2×C22⋊C4C22×D4713yes—
528C2×C42—473no—
529C2×C42—473no—
530C2×C42—473no—
531C2×C42—471no—
532C2×C42—9412no—
533C2×C42C22×D4713yes—
534C2×C42C22×D4713yes—
535#95—471no—
536#95—471no—
537#95—471no—
538#95—473no—
539#95—473no—
540#95—473no—
541#95C22×D4711yescharacteristic
542#95C22×D4713yes—
543C24—473no—
544C24—473no—
545C24—4724no—
546C24—9412no—
547C24—9412no—
548C24—1886no—
549C24—1886no—
550C24—1886no—
551C24—1886no—
552C24C23×D4713yes—
553#41—232no—
554#41—4764no—
555#41—9496no—
556#41—9432no—
557C2×Q8—474no—
558C2×Q8—942no—
559C2×Q8—942no—
560C2×Q8C2×C4×D4714yes—
561C2×Q8D4×D4714yes—
562C2×Q8D4×D4714yes—
563C2×D4—26no—
564C2×D4—26no—
565C2×D4—4712no—
566C2×D4—4712no—
567C2×D4—4712no—
568C2×D4—4712no—
569C2×D4—4712no—
570C2×D4—4712no—
571C2×D4—4712no—
572C2×D4—9496no—
573C2×D4—946no—
574C2×D4—946no—
575C2×D4—9496no—
576C2×D4—946no—
577C2×D4—946no—
578C2×D4—9496no—
579C2×D4—946no—
580C2×D4—946no—
581C2×D4—946no—
582C2×D4—946no—
583C2×D4C2×C4×D47112yes—
584C22×C4—26no—
585C22×C4—26no—
586C22×C4—471no—
587C22×C4—4712no—
588C22×C4—4712no—
589C22×C4—4712no—
590C22×C4—471no—
591C22×C4—471no—
592C22×C4—4712no—
593C22×C4—471no—
594C22×C4—473no—
595C22×C4—473no—
596C22×C4—946no—
597C22×C4—9412no—
598C22×C4—946no—
599C22×C4—946no—
600C22×C4—946no—
601C22×C4—946no—
602C22×C4—946no—
603C22×C4—1886no—
604C22×C4—1886no—
605C22×C4—1883no—
606C22×C4—1883no—
607C22×C4C2×C4×D47112yes—
608C22×C4C23×D4713yes—
609C22×C4C23×D4711yescharacteristic
610C22×C4C23×D4713yes—
611C22×C4C23×D4711yescharacteristic
612C22×C4C23×D4711yescharacteristic
613C22×C4C23×D4713yes—
614C4⋊C4—26no—
615C4⋊C4—26no—
616C4⋊C4—946no—
617C4⋊C4—942no—
618C4⋊C4—946no—
619C4⋊C4—946no—
620C22⋊C4—26no—
621C22⋊C4—46no—
622C22⋊C4—43no—
623C22⋊C4—946no—
624C22⋊C4—946no—
625C22⋊C4—9412no—
626C22⋊C4—946no—
627C22⋊C4—946no—
628C22⋊C4—946no—
629C22⋊C4—1883no—
630C22⋊C4—1883no—
631C22⋊C4—1886no—
632C22⋊C4—1886no—
633C22⋊C4—1883no—
634C22⋊C4—1886no—
635C42—26no—
636C42—26no—
637C42—942no—
638C42—946no—
639C42—946no—
640C42—946no—
641C23—23no—
642C23—23no—
643C23—23no—
644C23—23no—
645C23—23no—
646C23—23no—
647C23—476no—
648C23—476no—
649C23—476no—
650C23—476no—
651C23—9448no—
652C23—943no—
653C23—943no—
654C23—943no—
655C23—943no—
656C23—943no—
657C23—943no—
658C23—943no—
659C23—943no—
660C23—943no—
661C23—943no—
662C23—37612no—
663C23—37612no—
664C23—37612no—
665C23—37612no—
666C23—18824no—
667C23—18824no—
668C23C22×C4×D4716yes—
669C23C24×D4711yescharacteristic
670Q8—948no—
671Q8C22⋊C4×D47116yescomplemented
672D4—224no—
673D4—4748no—
674D4—9424no—
675D4—9424no—
676D4—9424no—
677D4—9424no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—224no—
683C2×C4—21no—
684C2×C4—23no—
685C2×C4—23no—
686C2×C4—23no—
687C2×C4—23no—
688C2×C4—23no—
689C2×C4—21no—
690C2×C4—23no—
691C2×C4—21no—
692C2×C4—472no—
693C2×C4—472no—
694C2×C4—472no—
695C2×C4—4748no—
696C2×C4—472no—
697C2×C4—472no—
698C2×C4—941no—
699C2×C4—941no—
700C2×C4—941no—
701C2×C4—941no—
702C2×C4—9424no—
703C2×C4—941no—
704C2×C4—943no—
705C2×C4—943no—
706C2×C4—943no—
707C2×C4—943no—
708C2×C4—943no—
709C2×C4—941no—
710C2×C4—941no—
711C2×C4—943no—
712C2×C4—37612no—
713C2×C4—18812no—
714C2×C4—18812no—
715C2×C4C22×C4×D4712yes—
716C2×C4C22×C4×D4716yes—
717C2×C4C2×D4×D4716yes—
718C2×C4C2×D4×D4716yes—
719C2×C4#1309407012yescomplemented
720C22—26no—
721C22—26no—
722C22—26no—
723C22—43no—
724C22—43no—
725C22—43no—
726C22—43no—
727C22—4712no—
728C22—946no—
729C22—946no—
730C22—946no—
731C22—946no—
732C22—946no—
733C22—946no—
734C22—946no—
735C22—946no—
736C22—946no—
737C22—37648no—
738C22—1883no—
739C22—1883no—
740C22—1883no—
741C22—1883no—
742C22C23×C4×D4711yescharacteristic
743C22C22×D4×D4711yescharacteristic
744C22C22×D4×D4711yescharacteristic
745C22H(5,𝔽2)×D4711yescharacteristic
746C22C2×#1309407011yescharacteristic
747C22#1568995911yescharacteristic
748C22#1568996011yescharacteristic
749C4—22no—
750C4—22no—
751C4—43no—
752C4—43no—
753C4—41no—
754C4—474no—
755C4—942no—
756C4—942no—
757C4—1883no—
758C4—1883no—
759C4—1881no—
760C4C2×C22⋊C4×D47112yes—
761C2—46no—
762C2—9412no—
763C2—1886no—
764C2C22×C22⋊C4×D4711yescharacteristic
765C2#2025659411yescharacteristic
766C2C4×#1309407011yescharacteristic
767C2#2025705411yescharacteristic
768C2#2025705611yescharacteristic
769C2#2025716511yescharacteristic
770C2#2025717911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2341C2
socle, cosocleC23×C47C25
prime radicalC22×#13094070C2
hypercenter#2341D47
hypocenterC47#34258
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#15689605C2semidirect
3. C2×C4×#10625354C2semidirect
4. #20246229C2semidirect
5. #20246226C2semidirect
6. #20246226C2semidirect
7. C22⋊C4×D188C2semidirect
8. #20246209C2semidirect
9. #20246209C2semidirect
10. #20246208C2semidirect
11. #20245977C2semidirect
12. #20245967C2semidirect
13. #20245874C2semidirect
14. #390×D47C2semidirect
15. C47×#2341C2semidirect
18. C2×#13094070C4semidirect
27. C2×Q8×Dic47C22semidirect
28. C2×Q8×Dic47C22semidirect
29. C2×C4×D188C22semidirect
30. C2×C4×D188C22semidirect
31. C2×#13093986C22semidirect
32. C2×#13093986C22semidirect
33. C2×#13093982C22semidirect
34. C2×#13093981C22semidirect
35. C2×C4⋊C4×D47C22semidirect
36. C2×C22⋊C4×D47C22semidirect
37. C2×C22⋊C4×D47C22semidirect
38. C2×C42×D47C22semidirect
39. #15689027C22semidirect
40. #15689027C22semidirect
41. #15689026C22semidirect
42. #15689026C22semidirect
43. #15689025C22semidirect
44. #15689025C22semidirect
45. #15689024C22semidirect
46. #15689024C22semidirect
47. #15689023C22semidirect
48. #15689023C22semidirect
49. #15689023C22semidirect
50. #15689001C22semidirect
51. #15689001C22semidirect
52. #15689001C22semidirect
53. #15688999C22semidirect
54. #15688999C22semidirect
55. #15688999C22semidirect
56. #15688983C22semidirect
57. #15688980C22semidirect
58. #15688980C22semidirect
59. #15688978C22semidirect
60. #15688978C22semidirect
61. C4×(C2×D47)⋊C4C22semidirect
62. C4×(C2×D47)⋊C4C22semidirect
63. C4×C22⋊Dic47C22semidirect
65. C2×C4×Q8×C47C22semidirect
66. C2×C4×Q8×C47C22semidirect
67. C47×#390C22semidirect
68. C47×#390C22semidirect
69. C47×#380C22semidirect
70. C4×C22⋊C4×C47C22semidirect
76. C2×#10625354C2×C4semidirect
81. C2×#10625350C2×C4semidirect
85. C22×D188C2×C4semidirect
95. C2×D4×D47C2×C4semidirect
96. C2×D4×D47C2×C4semidirect
142. C2×#41×C47C2×C4semidirect
196. #10625354C22⋊C4semidirect
284. Q8×C47C2×C22⋊C4semidirect
304. C2×C4×C47H(5,𝔽2)semidirect
324. C2×Dic47H(5,𝔽2)semidirect
327. D188C2×C22⋊C4semidirect
332. C4×D47C2×C22⋊C4semidirect
382. #2341D47semidirect
415. C2×C4×Q8C2×D47semidirect
416. C2×C4×Q8C2×D47semidirect
438. #390C2×D47semidirect
439. #390C2×D47semidirect
449. #380C2×D47semidirect
455. C4×C22⋊C4C2×D47semidirect
456. C47#34258semidirect
470. C2×#41C4×D47semidirect
671. Q8C22⋊C4×D47semidirect
719. C2×C4#13094070semidirect

Maximal subgroups

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

subgroupindex
C22×#130940702
C2×#156896052
C2×C4×#106253542
#202462292
#202462262
C22⋊C4×D1882
#202462092
#202462082
#202459772
#202459672
#202458742
#390×D472
C47×#23412
#3425847