Finite Group Databasebeta

← #72317117

Subgroups — #72317117

Order 2048.

At least 6557 conjugacy classes of subgroups; only the 8072 normal subgroups are shown.

The subgroup lattice has 903 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72317116C218yesmaximal, complemented
2#72317115C218yesmaximal, complemented
3#72317105C211yesmaximal, characteristic, complemented
4#72317102C211yesmaximal, characteristic, complemented
5C2×#357435C211yesmaximal, characteristic, complemented
6#72317081C211yesmaximal, characteristic, complemented
7#72317054C212yesmaximal, complemented
8C2×#357515C212yesmaximal, complemented
9C2×#353367C212yesmaximal, complemented
10C22×#20598C211yesmaximal, characteristic, complemented
11C22×#20925C212yesmaximal, complemented
12C23×D4×C22⋊C4C211yesmaximal, characteristic, complemented
13C23×#3003C211yesmaximal, characteristic
14C26×D4C2211yescharacteristic
15C24×AGL(1,ℤ/8)C2211yescharacteristic
16C24×AGL(1,ℤ/8)C2211yescharacteristic
17C23×#525C2211yescharacteristic
18C24×C4×D4C2212yes—
19C23×#450C2214yes—
20C22×#3003C4116yescomplemented
21C23×#447C2214yes—
22C23×#407C2211yescharacteristic
23C23×#407C2211yescharacteristic
24C23×#417C2212yescomplemented
25C23×#418C2211yescharacteristic
26C23×#418C2212yes—
27C23×#418C2212yes—
28C23×#418C2211yescharacteristic
29C22×D4×C22⋊C4C2218yes—
30C22×#2297C2212yescomplemented
31C23×#390C2212yes—
32C22×#2280C2211yescharacteristic
33C23×#380C2211yescharacteristic
34C23×C4×C22⋊C4C2211yescharacteristic
35C22×#1879C2218yescomplemented
36C22×#1877C2218yescomplemented
37C22×#1786C2218yes—
38C22×#1736C2212yescomplemented
39C22×#1736C2212yescomplemented
40C22×#1736C2212yescomplemented
41C22×#1728C2212yescomplemented
42C22×#1728C2212yescomplemented
43C2×#13756C2212yescomplemented
44C2×#11023C2218yescomplemented
45C2×#11022C2218yescomplemented
46C2×#10970C2214yescomplemented
47C2×#10969C2214yescomplemented
48C2×#10788C22116yescomplemented
49#154418C2214yescomplemented
50#154384C2214yescomplemented
51#123564C22116yescomplemented
52#123511C2218yescomplemented
53#123507C2218yescomplemented
54C24×#41C2311yescharacteristic
55C25×D4C2×C418yes—
56C25×D4D418yes—
57C25×D4D418yes—
58C25×D4C2311yescharacteristic
59C25×D4C2314yes—
60C25×D4C2311yescharacteristic
61C26×C4C2311yescharacteristic
62C23×AGL(1,ℤ/8)C2×C418yes—
63C23×AGL(1,ℤ/8)C2×C418yescomplemented
64C23×AGL(1,ℤ/8)D4116yes—
65C24×SD16C2312yes—
66C24×SD16C2312yes—
67C24×D8C2312yes—
68C24×D8C2312yes—
69C24×M16C2312yes—
70C24×M16C2311yescharacteristic
71C24×M16C2311yescharacteristic
72C22×#525C2×C418yescomplemented
73C23×C22⋊Q8C2312yes—
74C23×#121C2312yes—
75C23×C4×D4D4116yescomplemented
76C23×C4×D4C2318yes—
77C23×#117C2312yes—
78C23×#117C2311yescharacteristic
79C24×C4⋊C4C2312yes—
80C24×C22⋊C4D411yescharacteristic
81C24×C22⋊C4D411yescharacteristic
82C24×C42C2312yes—
83C22×#450C2×C4132yescomplemented
84C22×#447C2×C4132yescomplemented
85C22×#418C2×C418yes—
86C22×#418C2×C418yescomplemented
87C22×#418D4116yes—
88C22×#418D4116yescomplemented
89C23×#103C2314yescomplemented
90C23×#102C2314yes—
91C23×#102C2318yes—
92C23×#102C2318yes—
93C23×#102C2314yes—
94C23×#102C2314yescomplemented
95C22×#407C2×C418yescomplemented
96C23×C22⋊C8C2314yes—
97C23×C22⋊C8C2314yes—
98C22×#391C2314yescomplemented
99C22×#390D4116yescomplemented
100C22×#390C2318yes—
101C22×#390C2314yescomplemented
102C22×#380D418yes—
103C22×#380C2314yes—
104C22×#380C2314yes—
105C22×C4×C22⋊C4D414yes—
106C22×C4×C22⋊C4C2314yes—
107C23×#95D412yes—
108C22×#340C2318yescomplemented
109C22×#340C2318yescomplemented
110C22×#340C2318yescomplemented
111C22×#336C2318yescomplemented
112C22×#336C2318yescomplemented
113C2×C4⋊#95C2318yescomplemented
114C27C2×D411yescharacteristic
115C23×#41C22×C414yes—
116C23×#41C2×D418yes—
117C24×Q8C2411yescharacteristic
118C24×D4C22⋊C4164yescomplemented
119C24×D4C22×C414yes—
120C24×D4C22×C4116yes—
121C24×D4C22×C414yes—
122C24×D4C2×D414yes—
123C24×D4C2×D414yes—
124C24×D4C2×D418yes—
125C24×D4C2×D4116yes—
126C24×D4C2×D4116yes—
127C24×D4C2×D414yes—
128C24×D4C2×D414yes—
129C24×D4C2×D418yes—
130C24×D4C2×D418yes—
131C24×D4C2×D418yes—
132C24×D4C2×D418yes—
133C24×D4#4118yes—
134C24×D4#4118yes—
135C24×D4#4118yes—
136C24×D4C2411yescharacteristic
137C24×D4C2412yes—
138C24×D4C2412yes—
139C25×C4C22×C414yes—
140C25×C4C2×D414yes—
141C25×C4C2×D414yes—
142C25×C4C2×D412yes—
143C25×C4C2×D411yescharacteristic
144C25×C4C2×D414yes—
145C25×C4C2×D412yes—
146C25×C4C2×D412yes—
147C25×C4#4114yes—
148C25×C4#4114yes—
149C25×C4C2412yes—
150C25×C4C2411yescharacteristic
151C22×AGL(1,ℤ/8)C22⋊C4164yescomplemented
152C23×SD16C22×C418yes—
153C23×SD16C22×C418yescomplemented
154C23×SD16C2×D4116yes—
155C23×D8C22×C418yes—
156C23×D8C22×C418yescomplemented
157C23×D8C2×D4116yes—
158C23×M16C22×C414yes—
159C23×M16C22×C414yes—
160C23×M16C2×D418yes—
161C23×M16C2×D418yes—
162C23×M16C2×D418yes—
163C24×C8C2414yes—
164C24×C8C2412yes—
165C24×C8C2412yes—
166C22×C22⋊Q8C22×C418yescomplemented
167C22×#121C22×C418yescomplemented
168C22×C4×D4C2×D4132yes—
169C22×#117C22×C414yes—
170C22×#117C2×D418yes—
171C22×#117C2×D418yes—
172C23×C4⋊C4C2×D418yes—
173C23×C4⋊C4C2×D418yes—
174C23×C4⋊C4C2×D418yes—
175C23×C4⋊C4C2414yes—
176C23×C4⋊C4C2412yes—
177C23×C4⋊C4C2414yes—
178C23×C22⋊C4C2×D414yes—
179C23×C22⋊C4C2×D414yes—
180C23×C42C2×D418yes—
181C23×C42C2×D418yes—
182C23×C42C2×D414yes—
183C23×C42C2414yes—
184C2×#418C22⋊C4164yescomplemented
185C22×#102C22×C4116yes—
186C22×#102C22×C4116yescomplemented
187C22×#102C2×D4132yes—
188C22×#102C2×D4132yes—
189C22×C22⋊C8C22×C4116yescomplemented
190C2×#390C2×D4132yes—
191C2×#380C2×D4116yes—
192C22×#95C2×D418yes—
193C26C4×D414yes—
194C26#12014yes—
195C26#12114yes—
196C26C22×D412yes—
197C26C22×D411yescharacteristic
198C22×#41C2×C22⋊C4116yescomplemented
199C23×Q8C23×C412yes—
200C23×Q8C22×D414yes—
201C23×D4C2×C22⋊C4116yes—
202C23×D4C2×C22⋊C4164yes—
203C23×D4C2×C22⋊C4116yes—
204C23×D4C2×C22⋊C4116yes—
205C23×D4C2×C22⋊C4116yes—
206C23×D4C4×D4132yes—
207C23×D4C4×D4132yes—
208C23×D4C4×D4132yes—
209C23×D4#120116yes—
210C23×D4#120132yes—
211C23×D4#120132yes—
212C23×D4#120116yes—
213C23×D4#120116yes—
214C23×D4#120132yes—
215C23×D4#121132yes—
216C23×D4#121132yes—
217C23×D4#121132yes—
218C23×D4#121132yes—
219C23×D4#121132yes—
220C23×D4#121132yes—
221C23×D4#121132yes—
222C23×D4#123116yes—
223C23×D4#123116yes—
224C23×D4#123116yes—
225C23×D4#123132yes—
226C23×D4#124132yes—
227C23×D4#127132yes—
228C23×D4C23×C412yes—
229C23×D4C23×C414yes—
230C23×D4C23×C414yes—
231C23×D4C22×D414yes—
232C23×D4C22×D414yes—
233C23×D4C22×D414yes—
234C23×D4C22×D418yes—
235C23×D4C22×D418yes—
236C23×D4C22×D414yes—
237C23×D4C22×D414yes—
238C23×D4C22×D418yes—
239C23×D4C22×D418yes—
240C23×D4C22×D418yes—
241C23×D4C2×#4118yes—
242C23×D4C2×#4118yes—
243C23×D4C2×#4118yes—
244C24×C4C2×C22⋊C4116yes—
245C24×C4C4×D4116yes—
246C24×C4C4×D418yes—
247C24×C4C4×D414yes—
248C24×C4#12018yes—
249C24×C4#12014yes—
250C24×C4#12018yes—
251C24×C4#12018yes—
252C24×C4#121116yes—
253C24×C4#12118yes—
254C24×C4#12114yes—
255C24×C4#123116yes—
256C24×C4C23×C414yes—
257C24×C4C23×C412yes—
258C24×C4C22×D414yes—
259C24×C4C22×D414yes—
260C24×C4C22×D414yes—
261C24×C4C22×D412yes—
262C24×C4C22×D414yes—
263C24×C4C22×D414yes—
264C24×C4C22×D412yes—
265C24×C4C22×D412yes—
266C24×C4C22×D414yes—
267C24×C4C22×D414yes—
268C24×C4C22×D414yes—
269C24×C4C22×D411yescharacteristic
270C24×C4C22×D414yes—
271C24×C4C22×D412yes—
272C24×C4C22×D414yes—
273C24×C4C2×#4114yes—
274C24×C4C2×#4114yes—
275C24×C4C2×#4114yes—
276C24×C4C2×#4114yes—
277C24×C4C2×#4114yes—
278C24×C4C2×#4112yes—
279C24×C4C2×#4112yes—
280C24×C4H(5,𝔽2)14yes—
281C24×C4H(5,𝔽2)14yes—
282C24×C4H(5,𝔽2)14yes—
283C24×C4H(5,𝔽2)14yes—
284C24×C4C2511yescharacteristic
285C22×SD16C2×C22⋊C4132yescomplemented
286C22×D8C2×C22⋊C4132yescomplemented
287C22×M16C2×C22⋊C4116yescomplemented
288C22×M16C2×C22⋊C4116yescomplemented
289C23×C8C23×C414yes—
290C23×C8C23×C414yes—
291C23×C8C22×D418yes—
292C23×C8C22×D418yes—
293C23×C8C22×D418yes—
294C2×#117C2×C22⋊C4116yescomplemented
295C22×C4⋊C4#120132yes—
296C22×C4⋊C4C23×C414yes—
297C22×C4⋊C4C22×D418yes—
298C22×C4⋊C4C22×D418yes—
299C22×C4⋊C4C22×D418yes—
300C22×C4⋊C4C22×D418yes—
301C22×C4⋊C4C22×D418yes—
302C22×C22⋊C4AGL(1,ℤ/8)116yescomplemented
303C22×C42#120116yes—
304C22×C42C22×D418yes—
305C22×C42C22×D418yes—
306C2×#102C2×C22⋊C4164yescomplemented
307C25#386116yes—
308C25C2×C4×D414yes—
309C25C2×C4×D412yes—
310C25C2×#12014yes—
311C25C2×#12014yes—
312C25C2×#12012yes—
313C25C2×#12114yes—
314C25C2×#12112yes—
315C25#52514yes—
316C25D4214yes—
317C25D4214yes—
318C25D4214yes—
319C25#54614yes—
320C25C2×AGL(1,ℤ/8)18yes—
321C25#57518yes—
322C25C23×D411yescharacteristic
323C22×Q8C22×C22⋊C414yescomplemented
324C22×D4#379164yes—
325C22×D4#386164yes—
326C22×D4#3861128yes—
327C22×D4#386164yes—
328C22×D4#386164yes—
329C22×D4#3901128yes—
330C22×D4#3921128yes—
331C22×D4#3921128yes—
332C22×D4#3941128yes—
333C22×D4#3941128yes—
334C22×D4C22×C22⋊C418yes—
335C22×D4C22×C22⋊C418yes—
336C22×D4C22×C22⋊C418yes—
337C22×D4C22×C22⋊C418yes—
338C22×D4C22×C22⋊C414yescomplemented
339C22×D4C2×C4×D4116yes—
340C22×D4C2×C4×D4116yes—
341C22×D4C2×C4×D4116yes—
342C22×D4C2×#12018yes—
343C22×D4C2×#12018yes—
344C22×D4C2×#120116yes—
345C22×D4C2×#12018yes—
346C22×D4C2×#120116yes—
347C22×D4C2×#120116yes—
348C22×D4C2×#121116yes—
349C22×D4C2×#121116yes—
350C22×D4C2×#121116yes—
351C22×D4C2×#121116yes—
352C22×D4C2×#121116yes—
353C22×D4C2×#121116yes—
354C22×D4C2×#121116yes—
355C22×D4C2×#12318yes—
356C22×D4C2×#123116yes—
357C22×D4C2×#12318yes—
358C22×D4C2×#12318yes—
359C22×D4C2×#124116yes—
360C22×D4C2×#127116yes—
361C23×C4#386132yes—
362C23×C4#386116yes—
363C23×C4C22×C22⋊C418yes—
364C23×C4C22×C22⋊C414yes—
365C23×C4C22×C22⋊C414yes—
366C23×C4C22×C22⋊C414yes—
367C23×C4C2×C4×D418yes—
368C23×C4C2×C4×D414yes—
369C23×C4C2×C4×D418yes—
370C23×C4C2×C4×D418yes—
371C23×C4C2×C4×D414yes—
372C23×C4C2×C4×D412yes—
373C23×C4C2×C4×D418yes—
374C23×C4#51818yes—
375C23×C4#51814yes—
376C23×C4#51814yes—
377C23×C4C2×#12018yes—
378C23×C4C2×#12018yes—
379C23×C4C2×#12014yes—
380C23×C4C2×#12014yes—
381C23×C4C2×#12012yes—
382C23×C4C2×#12018yes—
383C23×C4C2×#12014yes—
384C23×C4C2×#12014yes—
385C23×C4C2×#12018yes—
386C23×C4C2×#12014yes—
387C23×C4C2×#12018yes—
388C23×C4C2×#12018yes—
389C23×C4C2×#12118yes—
390C23×C4C2×#12114yes—
391C23×C4C2×#12114yes—
392C23×C4C2×#12112yes—
393C23×C4C2×#12118yes—
394C23×C4C2×#12118yes—
395C23×C4C2×#12118yes—
396C23×C4C2×#12118yes—
397C23×C4C2×#12118yes—
398C23×C4C2×#12118yes—
399C23×C4C2×#12118yes—
400C23×C4C2×#12318yes—
401C23×C4C2×#12314yes—
402C23×C4C2×#12314yes—
403C23×C4C2×#12314yes—
404C23×C4C2×#12314yes—
405C23×C4C2×#12318yes—
406C23×C4#52518yes—
407C23×C4#52518yes—
408C23×C4#52514yes—
409C23×C4#52518yes—
410C23×C4#52518yes—
411C23×C4#52518yes—
412C23×C4C2×#12418yes—
413C23×C4C2×#12718yes—
414C23×C4#53418yes—
415C23×C4#53418yes—
416C23×C4#53414yes—
417C23×C4#53414yes—
418C23×C4#53418yes—
419C23×C4#53418yes—
420C23×C4#53418yes—
421C23×C4#53518yes—
422C23×C4#53518yes—
423C23×C4#53818yes—
424C23×C4#53818yes—
425C23×C4#53818yes—
426C23×C4#53818yes—
427C23×C4D4214yes—
428C23×C4D4218yes—
429C23×C4D4218yes—
430C23×C4D4218yes—
431C23×C4D4214yes—
432C23×C4D4218yes—
433C23×C4D4218yes—
434C23×C4D4218yes—
435C23×C4D4214yes—
436C23×C4D4218yes—
437C23×C4D4218yes—
438C23×C4D4218yes—
439C23×C4#54618yes—
440C23×C4#54618yes—
441C23×C4#54618yes—
442C23×C4#54618yes—
443C23×C4#54618yes—
444C23×C4#54618yes—
445C23×C4#54618yes—
446C23×C4#54618yes—
447C23×C4#54618yes—
448C23×C4#54618yes—
449C23×C4#54618yes—
450C23×C4#54614yes—
451C23×C4#54618yes—
452C23×C4#54618yes—
453C23×C4#54618yes—
454C23×C4#54618yes—
455C23×C4#55118yes—
456C23×C4#55118yes—
457C23×C4#55118yes—
458C23×C4#55118yes—
459C23×C4C2×AGL(1,ℤ/8)116yes—
460C23×C4C24×C411yescharacteristic
461C23×C4C23×D411yescharacteristic
462C23×C4C23×D411yescharacteristic
463C23×C4C23×D412yes—
464C23×C4C23×D412yes—
465C23×C4C23×D412yes—
466C23×C4C23×D412yes—
467C23×C4C23×D412yes—
468C23×C4C23×D411yescharacteristic
469C23×C4C22×#4112yes—
470C23×C4C22×#4112yes—
471C23×C4C22×#4112yes—
472C23×C4C22×#4111yescharacteristic
473C23×C4C22×#4111yescharacteristic
474C23×C4C2×H(5,𝔽2)12yes—
475C23×C4C2×H(5,𝔽2)12yes—
476C23×C4C2×H(5,𝔽2)12yes—
477C23×C4C2×H(5,𝔽2)12yes—
478C22×C8C22×C22⋊C418yescomplemented
479C22×C8C22×C22⋊C418yescomplemented
480C2×C4⋊C4C22×C22⋊C418yescomplemented
481C2×C4⋊C4C2×#120116yes—
482C24C2×#38618yes—
483C24C2×#38614yes—
484C24C4×#12018yes—
485C24D4×C22⋊C414yes—
486C24D4×C22⋊C414yes—
487C24#235818yes—
488C24#240318yes—
489C24#240318yes—
490C24#240818yes—
491C24#241018yes—
492C24#241018yes—
493C24#241014yes—
494C24#241018yes—
495C24#241214yes—
496C24#241818yes—
497C24#242418yes—
498C24#242418yes—
499C24#243318yes—
500C24#247218yes—
501C24#284614yes—
502C24#284718yes—
503C24#284914yes—
504C24C4×AGL(1,ℤ/8)116yes—
505C24#300318yes—
506C24#300518yes—
507C24#3036116yes—
508C24C22×C4×D411yescharacteristic
509C24C22×#12012yes—
510C24C22×#12011yescharacteristic
511C24C22×#12111yescharacteristic
512C24C2×#52512yes—
513C24C2×D4212yes—
514C24C2×D4212yes—
515C24C2×D4212yes—
516C24C2×#54612yes—
517C24C22×AGL(1,ℤ/8)14yes—
518C24C2×#57514yes—
519C24#358518yes—
520C2×D4#14381256yescomplemented
521C2×D4C2×#379116yes—
522C2×D4C2×#386116yes—
523C2×D4C2×#386132yes—
524C2×D4C2×#386116yes—
525C2×D4C2×#386116yes—
526C2×D4C2×#390132yes—
527C2×D4C2×#392132yes—
528C2×D4C2×#392132yes—
529C2×D4C2×#394132yes—
530C2×D4C2×#394132yes—
531C22×C4C2×#37918yes—
532C22×C4C2×#38618yes—
533C22×C4C2×#38618yes—
534C22×C4C2×#38618yes—
535C22×C4C2×#386116yes—
536C22×C4C2×#38614yes—
537C22×C4C2×#38618yes—
538C22×C4C2×#390116yes—
539C22×C4C4×#12018yes—
540C22×C4C4×#120116yes—
541C22×C4#230818yes—
542C22×C4#230818yes—
543C22×C4#2321116yes—
544C22×C4#2321116yes—
545C22×C4D4×C22⋊C4116yes—
546C22×C4D4×C22⋊C4116yes—
547C22×C4D4×C22⋊C414yes—
548C22×C4D4×C22⋊C414yes—
549C22×C4D4×C22⋊C418yes—
550C22×C4D4×C22⋊C418yes—
551C22×C4#2358116yes—
552C22×C4#2358116yes—
553C22×C4#235818yes—
554C22×C4#2358116yes—
555C22×C4C2×#392116yes—
556C22×C4C2×#392116yes—
557C22×C4C2×#394116yes—
558C22×C4C2×#394116yes—
559C22×C4#2403116yes—
560C22×C4#240318yes—
561C22×C4#2403116yes—
562C22×C4#240318yes—
563C22×C4#2404116yes—
564C22×C4#2404116yes—
565C22×C4#2405116yes—
566C22×C4#2405116yes—
567C22×C4#2408116yes—
568C22×C4#240818yes—
569C22×C4#2410116yes—
570C22×C4#2410116yes—
571C22×C4#241018yes—
572C22×C4#2410116yes—
573C22×C4#2410116yes—
574C22×C4#2410116yes—
575C22×C4#241018yes—
576C22×C4#241014yes—
577C22×C4#241018yes—
578C22×C4#2410116yes—
579C22×C4#241018yes—
580C22×C4#2411116yes—
581C22×C4#2411116yes—
582C22×C4#2412116yes—
583C22×C4#2412116yes—
584C22×C4#241214yes—
585C22×C4#2412116yes—
586C22×C4#241218yes—
587C22×C4#2418116yes—
588C22×C4#2418116yes—
589C22×C4#2418116yes—
590C22×C4#241818yes—
591C22×C4#2424116yes—
592C22×C4#2424116yes—
593C22×C4#2424116yes—
594C22×C4#2424116yes—
595C22×C4#2424116yes—
596C22×C4#2424116yes—
597C22×C4#242418yes—
598C22×C4#242418yes—
599C22×C4#2433116yes—
600C22×C4#243318yes—
601C22×C4#2472116yes—
602C22×C4#2472116yes—
603C22×C4#2472116yes—
604C22×C4#247218yes—
605C22×C4#2534116yes—
606C22×C4#2534116yes—
607C22×C4#2539116yes—
608C22×C4#2539116yes—
609C22×C4#2613116yes—
610C22×C4#2617116yes—
611C22×C4#2617116yes—
612C22×C4#2622116yes—
613C22×C4#284614yes—
614C22×C4#2847116yes—
615C22×C4#284718yes—
616C22×C4#284918yes—
617C22×C4#284918yes—
618C22×C4#284914yes—
619C22×C4#3003116yescomplemented
620C22×C4C23×C22⋊C411yescharacteristic
621C22×C4C23×C22⋊C411yescharacteristic
622C22×C4C23×C22⋊C411yescharacteristic
623C22×C4C22×C4×D412yes—
624C22×C4C22×C4×D412yes—
625C22×C4C22×C4×D411yescharacteristic
626C22×C4C22×C4×D412yes—
627C22×C4C2×#51812yes—
628C22×C4C2×#51811yescharacteristic
629C22×C4C2×#51811yescharacteristic
630C22×C4C22×#12012yes—
631C22×C4C22×#12011yescharacteristic
632C22×C4C22×#12011yescharacteristic
633C22×C4C22×#12012yes—
634C22×C4C22×#12012yes—
635C22×C4C22×#12012yes—
636C22×C4C22×#12011yescharacteristic
637C22×C4C22×#12112yes—
638C22×C4C22×#12111yescharacteristic
639C22×C4C22×#12112yes—
640C22×C4C22×#12112yes—
641C22×C4C22×#12112yes—
642C22×C4C22×#12112yes—
643C22×C4C22×#12112yes—
644C22×C4C22×#12112yes—
645C22×C4C22×#12311yescharacteristic
646C22×C4C22×#12311yescharacteristic
647C22×C4C22×#12311yescharacteristic
648C22×C4C22×#12312yes—
649C22×C4C22×#12311yescharacteristic
650C22×C4C2×#52512yes—
651C22×C4C2×#52512yes—
652C22×C4C2×#52512yes—
653C22×C4C2×#52512yes—
654C22×C4C2×#52512yes—
655C22×C4C22×#12412yes—
656C22×C4C22×#12712yes—
657C22×C4C2×#53412yes—
658C22×C4C2×#53412yes—
659C22×C4C2×#53412yes—
660C22×C4C2×#53411yescharacteristic
661C22×C4C2×#53412yes—
662C22×C4C2×#53411yescharacteristic
663C22×C4C2×#53412yes—
664C22×C4C2×#53512yes—
665C22×C4C2×#53512yes—
666C22×C4C2×#53812yes—
667C22×C4C2×#53812yes—
668C22×C4C2×#53812yes—
669C22×C4C2×#53812yes—
670C22×C4C2×D4212yes—
671C22×C4C2×D4212yes—
672C22×C4C2×D4212yes—
673C22×C4C2×D4212yes—
674C22×C4C2×D4212yes—
675C22×C4C2×D4212yes—
676C22×C4C2×D4212yes—
677C22×C4C2×D4212yes—
678C22×C4C2×D4212yes—
679C22×C4C2×#54612yes—
680C22×C4C2×#54612yes—
681C22×C4C2×#54612yes—
682C22×C4C2×#54612yes—
683C22×C4C2×#54612yes—
684C22×C4C2×#54612yes—
685C22×C4C2×#54612yes—
686C22×C4C2×#54612yes—
687C22×C4C2×#54612yes—
688C22×C4C2×#54612yes—
689C22×C4C2×#54612yes—
690C22×C4C2×#54612yes—
691C22×C4C2×#54612yes—
692C22×C4C2×#54612yes—
693C22×C4C2×#54612yes—
694C22×C4C2×#55112yes—
695C22×C4C2×#55112yes—
696C22×C4C2×#55112yes—
697C22×C4C2×#55112yes—
698C23#1386718yes—
699C23#13967116yes—
700C23#13995116yes—
701C23#1413418yes—
702C23#1469418yes—
703C23#14715116yes—
704C23#14716116yes—
705C23#14718116yes—
706C23#14725116yes—
707C23#20925116yescomplemented
708C23C22×#38611yescharacteristic
709C23C2×C4×#12012yes—
710C23C2×D4×C22⋊C411yescharacteristic
711C23C2×D4×C22⋊C411yescharacteristic
712C23C2×#235812yes—
713C23C2×#240312yes—
714C23C2×#240312yes—
715C23C2×#241011yescharacteristic
716C23C2×#241012yes—
717C23C2×#241012yes—
718C23C2×#241012yes—
719C23C2×#241812yes—
720C23C2×#242412yes—
721C23C2×#242412yes—
722C23C2×#241211yescharacteristic
723C23C2×#247212yes—
724C23C2×#240812yes—
725C23C2×#243312yes—
726C23C2×#284611yescharacteristic
727C23C2×#284712yes—
728C23C2×#284911yescharacteristic
729C23C2×C4×AGL(1,ℤ/8)14yes—
730C23#6016814yes—
731C23C2×#300314yes—
732C23C2×#300312yes—
733C23C2×#300512yes—
734C23#6035914yes—
735C23#6036714yes—
736C23#6036714yes—
737C23#6036714yes—
738C23C2×#303614yes—
739C23#6042314yes—
740C23#6055818yes—
741C23#6056418yes—
742C23D4×AGL(1,ℤ/8)18yes—
743C23D4×AGL(1,ℤ/8)18yes—
744C23D4×AGL(1,ℤ/8)18yes—
745C23#6106618yes—
746C23#6106618yes—
747C23#6106618yes—
748C23#6115518yes—
749C23#6115618yes—
750D4C2×#1438132yes—
751C2×C4C2×#1438116yes—
752C2×C4#1386718yes—
753C2×C4#13867116yes—
754C2×C4#13967116yes—
755C2×C4#13967132yes—
756C2×C4#13995116yes—
757C2×C4#13995132yes—
758C2×C4#14134116yes—
759C2×C4#1413418yes—
760C2×C4#14255116yes—
761C2×C4#1469418yes—
762C2×C4#14715116yes—
763C2×C4#14716116yes—
764C2×C4#14716132yes—
765C2×C4#14718116yes—
766C2×C4#14718132yes—
767C2×C4#14725116yes—
768C2×C4#14725132yes—
769C2×C4#14911132yes—
770C2×C4C22×#37911yescharacteristic
771C2×C4C22×#38611yescharacteristic
772C2×C4C22×#38611yescharacteristic
773C2×C4C22×#38612yes—
774C2×C4C22×#38611yescharacteristic
775C2×C4C22×#39012yes—
776C2×C4C2×C4×#12012yes—
777C2×C4C2×#230811yescharacteristic
778C2×C4C2×#230811yescharacteristic
779C2×C4C2×#232112yes—
780C2×C4C2×#232112yes—
781C2×C4C2×D4×C22⋊C411yescharacteristic
782C2×C4C2×D4×C22⋊C412yes—
783C2×C4C2×D4×C22⋊C411yescharacteristic
784C2×C4C2×D4×C22⋊C412yes—
785C2×C4C2×#235812yes—
786C2×C4C2×#235812yes—
787C2×C4C2×#235812yes—
788C2×C4C22×#39212yes—
789C2×C4C22×#39212yes—
790C2×C4C22×#39412yes—
791C2×C4C22×#39412yes—
792C2×C4C2×#261312yes—
793C2×C4C2×#261712yes—
794C2×C4C2×#261712yes—
795C2×C4C2×#262212yes—
796C2×C4C2×#240312yes—
797C2×C4C2×#240312yes—
798C2×C4C2×#241012yes—
799C2×C4C2×#241012yes—
800C2×C4C2×#241011yescharacteristic
801C2×C4C2×#241012yes—
802C2×C4C2×#241012yes—
803C2×C4C2×#241012yes—
804C2×C4C2×#241012yes—
805C2×C4C2×#241812yes—
806C2×C4C2×#241812yes—
807C2×C4C2×#241812yes—
808C2×C4C2×#242412yes—
809C2×C4C2×#242412yes—
810C2×C4C2×#242412yes—
811C2×C4C2×#242412yes—
812C2×C4C2×#242412yes—
813C2×C4C2×#242412yes—
814C2×C4C2×#240512yes—
815C2×C4C2×#240512yes—
816C2×C4C2×#241212yes—
817C2×C4C2×#241212yes—
818C2×C4C2×#241212yes—
819C2×C4C2×#241211yescharacteristic
820C2×C4C2×#247212yes—
821C2×C4C2×#247212yes—
822C2×C4C2×#247212yes—
823C2×C4C2×#240812yes—
824C2×C4C2×#243312yes—
825C2×C4C2×#240412yes—
826C2×C4C2×#240412yes—
827C2×C4C2×#241112yes—
828C2×C4C2×#241112yes—
829C2×C4C2×#253412yes—
830C2×C4C2×#253412yes—
831C2×C4C2×#253912yes—
832C2×C4C2×#253912yes—
833C2×C4C2×#284712yes—
834C2×C4C2×#284911yescharacteristic
835C2×C4C2×#284911yescharacteristic
836C22#154195116yes—
837C22C2×#1386711yescharacteristic
838C22C2×#1396712yes—
839C22C2×#1399512yes—
840C22C2×#1413411yescharacteristic
841C22C2×#1469411yescharacteristic
842C22C2×#1471512yes—
843C22C2×#1471612yes—
844C22C2×#1471812yes—
845C22C2×#1472512yes—
846C22C2×#2092512yes—
847C22#637142012yes—
848C22C4×#300314yes—
849C22#637264414yes—
850C22C22⋊C4×AGL(1,ℤ/8)14yes—
851C22C22⋊C4×AGL(1,ℤ/8)14yes—
852C22#638141018yes—
853C22#643751014yes—
854C22#643751014yes—
855C22#643751114yes—
856C22#643751614yes—
857C22#643768018yes—
858C22#643768014yes—
859C22#643783814yes—
860C22#643783814yes—
861C22#643783914yes—
862C22#643784414yes—
863C22#643821218yes—
864C22#643866618yes—
865C22#643866618yes—
866C22#644050514yes—
867C22#644066618yes—
868C22#644265614yes—
869C22#644265814yes—
870C22#644316814yes—
871C22#644317014yes—
872C22#662884211yescharacteristic
873C22#662884411yescharacteristic
874C22#662884712yes—
875C22#662892514yes—
876C22#662893114yes—
877C22#662921712yes—
878C22#662922212yes—
879C4#154195116yes—
880C4C22×#143811yescharacteristic
881C4C2×#1386711yescharacteristic
882C4C2×#1396712yes—
883C4C2×#1399512yes—
884C4C2×#1413411yescharacteristic
885C4C2×#1425511yescharacteristic
886C4C2×#1471612yes—
887C4C2×#1471812yes—
888C4C2×#1472512yes—
889C4C2×#1491112yes—
890C2#7223179612yes—
891C2#7223562511yescharacteristic
892C2C2×#15419511yescharacteristic
893C2#7231093612yes—
894C2#7231591512yes—
895C2#7231611714yes—
896C2#7231687912yes—
897C2#7231699814yes—
898C2#7231703911yescharacteristic
899C2#7231711214yes—
900C2#7231711314yes—
901C2#7231711414yes—
subgroupG/H
center, socleC25C23×D4
commutatorC23×C4C24×C4
Frattini, cosocleC24×C4C25
prime radicalC23×#3003C2
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C25 ◁ C23×C4×C22⋊C4 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #72317116C2semidirect
2. #72317115C2semidirect
3. #72317105C2semidirect
4. #72317102C2semidirect
5. C2×#357435C2semidirect
6. #72317081C2semidirect
7. #72317054C2semidirect
8. C2×#357515C2semidirect
9. C2×#353367C2semidirect
10. C22×#20598C2semidirect
11. C22×#20925C2semidirect
12. C23×D4×C22⋊C4C2semidirect
20. C22×#3003C4semidirect
24. C23×#417C22semidirect
30. C22×#2297C22semidirect
35. C22×#1879C22semidirect
36. C22×#1877C22semidirect
38. C22×#1736C22semidirect
39. C22×#1736C22semidirect
40. C22×#1736C22semidirect
41. C22×#1728C22semidirect
42. C22×#1728C22semidirect
43. C2×#13756C22semidirect
44. C2×#11023C22semidirect
45. C2×#11022C22semidirect
46. C2×#10970C22semidirect
47. C2×#10969C22semidirect
48. C2×#10788C22semidirect
49. #154418C22semidirect
50. #154384C22semidirect
51. #123564C22semidirect
52. #123511C22semidirect
53. #123507C22semidirect
63. C23×AGL(1,ℤ/8)C2×C4semidirect
72. C22×#525C2×C4semidirect
75. C23×C4×D4D4semidirect
83. C22×#450C2×C4semidirect
84. C22×#447C2×C4semidirect
86. C22×#418C2×C4semidirect
88. C22×#418D4semidirect
89. C23×#103C23semidirect
94. C23×#102C23semidirect
95. C22×#407C2×C4semidirect
98. C22×#391C23semidirect
99. C22×#390D4semidirect
101. C22×#390C23semidirect
108. C22×#340C23semidirect
109. C22×#340C23semidirect
110. C22×#340C23semidirect
111. C22×#336C23semidirect
112. C22×#336C23semidirect
113. C2×C4⋊#95C23semidirect
118. C24×D4C22⋊C4semidirect
151. C22×AGL(1,ℤ/8)C22⋊C4semidirect
153. C23×SD16C22×C4semidirect
156. C23×D8C22×C4semidirect
166. C22×C22⋊Q8C22×C4semidirect
167. C22×#121C22×C4semidirect
184. C2×#418C22⋊C4semidirect
186. C22×#102C22×C4semidirect
189. C22×C22⋊C8C22×C4semidirect
198. C22×#41C2×C22⋊C4semidirect
285. C22×SD16C2×C22⋊C4semidirect
286. C22×D8C2×C22⋊C4semidirect
287. C22×M16C2×C22⋊C4semidirect
288. C22×M16C2×C22⋊C4semidirect
294. C2×#117C2×C22⋊C4semidirect
302. C22×C22⋊C4AGL(1,ℤ/8)semidirect
306. C2×#102C2×C22⋊C4semidirect
323. C22×Q8C22×C22⋊C4semidirect
338. C22×D4C22×C22⋊C4semidirect
478. C22×C8C22×C22⋊C4semidirect
479. C22×C8C22×C22⋊C4semidirect
480. C2×C4⋊C4C22×C22⋊C4semidirect
520. C2×D4#1438semidirect
619. C22×C4#3003semidirect
707. C23#20925semidirect

Maximal subgroups

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

subgroupindex
#723171162
#723171152
#723171052
#723171022
C2×#3574352
#723170812
#723170542
C2×#3575152
C2×#3533672
C22×#205982
C22×#209252
C23×D4×C22⋊C42
C23×#30032