Finite Group Databasebeta

← #72314568

Subgroups — #72314568

Order 4096.

Only the 2237 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 644 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72314516C212yesmaximal, complemented
2#72314508C214yesmaximal, complemented
3#72314498C212yesmaximal, complemented
4#72314482C212yesmaximal, complemented
5#72314476C212yesmaximal, complemented
6#72314472C2214yescomplemented
7#72314464C214yesmaximal, complemented
8#72314456C2214yescomplemented
9#72314452C2214yescomplemented
10#72314447C212yesmaximal, complemented
11#72314440C2214yescomplemented
12#72312643C212yesmaximal, complemented
13#72266926C212yesmaximal, complemented
14#72265785C211yesmaximal, characteristic, complemented
15#72265779C2212yescomplemented
16#72265766C2212yescomplemented
17#72258097C2214yescomplemented
18#72258097C2214yescomplemented
19#72258028C2214yescomplemented
20#72258028C2214yescomplemented
21#72256052C2214yescomplemented
22#72255971C2214yescomplemented
23#72255830C2214yescomplemented
24#72255764C2214yescomplemented
25#72238352C212yesmaximal, complemented
26#72238351C2214yescomplemented
27#72238350C2214yescomplemented
28#72238349C2214yescomplemented
29#72237608C2212yescomplemented
30#72234665C211yesmaximal, characteristic
31#72234663C2211yescharacteristic
32#72234662C2212yes—
33#72234661C2212yes—
34#72234659C412yescomplemented
35#72234658C412yescomplemented
36#72234619C2211yescharacteristic
37#72234619C2211yescharacteristic
38#72234591C412yescomplemented
39#72232884C2211yescharacteristic
40#72232592C412yescomplemented
41#72226366C2214yescomplemented
42#72225778C2212yescomplemented
43#72225735C2212yes—
44#72225655C412yescomplemented
45#72224136C2211yescharacteristic
46#72224136C2211yescharacteristic
47#72219445C212yesmaximal, complemented
48#72219440C212yesmaximal, complemented
49C2×#139748C2214yescomplemented
50C2×#139748C2214yescomplemented
51#72219438C2214yescomplemented
52#72219438C2214yescomplemented
53#72219418C2212yescomplemented
54#72219415C2212yescomplemented
55#72219414C2212yescomplemented
56#72219414C2212yescomplemented
57#72219397C211yesmaximal, characteristic, complemented
58#72219345C2212yescomplemented
59#72219340C2212yescomplemented
60#72219325C2212yescomplemented
61#72219314C2212yescomplemented
62#72219311C2211yescharacteristic, complemented
63#72219310C2211yescharacteristic, complemented
64#72219301C2212yescomplemented
65#72219300C2212yescomplemented
66#72219299C2212yescomplemented
67C2×#7670203C2211yescharacteristic
68#72219158C2214yescomplemented
69#72219158C2214yescomplemented
70#72218518C2211yescharacteristic, complemented
71#72218306C2212yes—
72#72218306C2212yes—
73#72218306C2212yescomplemented
74#72218306C2212yescomplemented
75#72218291C2211yescharacteristic, complemented
76C2×#139750C2214yescomplemented
77C2×#139750C2214yescomplemented
78C22×#23900C2212yes—
79#72217511C412yescomplemented
80C2×#6499867C412yescomplemented
81#72216064C412yescomplemented
82#72215179C2212yescomplemented
83#10586404D414yes—
84#10586404D414yes—
85#10586404C2311yescharacteristic
86#10586404C2311yescharacteristic
87#10586404C2312yes—
88C2×#62817C2×C412yes—
89C2×#62817C2×C412yes—
90#10586069C2×C412yes—
91#10586069D414yes—
92#10586066C2×C412yes—
93#10586066D414yes—
94C22×#3484C2×C411yescharacteristic, complemented
95C22×#3484C2312yes—
96C22×#3484C2311yescharacteristic
97C24×#120C2×C411yescharacteristic, complemented
98C24×#120C2311yescharacteristic
99#7642273C2×C414yescomplemented
100#7642244C2×C412yes—
101#7642244C2×C412yescomplemented
102#7641845C2×C414yescomplemented
103C22×#2846C2×C414yescomplemented
104C22×#2846C2×C411yescharacteristic, complemented
105#7630944C2×C414yescomplemented
106#7630939C2×C412yes—
107#7630939C2×C412yescomplemented
108C2×#35390C2311yescharacteristic
109C2×#35348C2×C411yescharacteristic, complemented
110C2×#35348C2311yescharacteristic
111C2×#35346C2×C411yescharacteristic, complemented
112C2×#34981C2×C411yescharacteristic, complemented
113C2×#34981C2311yescharacteristic
114C2×#34980C2311yescharacteristic
115C2×#34980C2311yescharacteristic
116#7626202C2×C412yescomplemented
117C2×#34198C2×C411yescharacteristic, complemented
118C2×#34198C2×C411yescharacteristic, complemented
119#6500015D4116yes—
120#6499871D414yes—
121#6499870D414yes—
122#6499869D414yes—
123#6499867D414yes—
124#6453039C2×C412yes—
125#6453039C2×C412yescomplemented
126#6451874C2×C412yes—
127#6451874C2×C412yescomplemented
128C2×#23984C2×C412yes—
129C2×#23984C2×C412yes—
130C2×#23984C2×C412yescomplemented
131C2×#23984C2×C412yescomplemented
132#6440460C2×C414yescomplemented
133#6440460C2×C414yescomplemented
134#6440460C2312yes—
135#6440460C2312yes—
136#6437621C2×C414yescomplemented
137#6437621C2×C414yescomplemented
138#6437621C2312yes—
139#6437621C2312yes—
140C2×#23900C2×C414yescomplemented
141C2×#23900C2×C414yescomplemented
142C2×#23900C2×C414yescomplemented
143C2×#23900C2×C414yescomplemented
144C2×#23900C2312yes—
145C2×#23900C2312yes—
146C2×#23900C2312yes—
147C2×#23900C2312yes—
148#6374548C2×C414yescomplemented
149#6374251C2312yes—
150#6374210C2×C412yes—
151#6374210C2×C412yescomplemented
152C2×#21778C2314yes—
153C2×#21776C2314yes—
154#6374128C2311yescharacteristic
155#6374128C2311yescharacteristic
156C2×#21746C2×C412yescomplemented
157C2×#21746C2×C414yescomplemented
158#6372488C2×C414yescomplemented
159#6371504C2×C412yes—
160#6371504C2×C412yescomplemented
161C22×#1898C2×C414yescomplemented
162#6371007C2×C412yescomplemented
163#6370693C2×C412yescomplemented
164C22×#1781C2312yes—
165#493879C2314yescomplemented
166C2×#12705C2314yes—
167C2×#12705C2314yes—
168C2×#12705C2314yes—
169C2×#12705C2314yes—
170#493357C2314yes—
171#493357C2314yes—
172#493357C2314yes—
173#493357C2314yes—
174#493357C2314yescomplemented
175C2×#12687C2314yescomplemented
176C2×#12687C2314yescomplemented
177#392113C2312yes—
178#392113C2312yes—
179#392109C2312yes—
180#392109C2312yes—
181#382436C2314yes—
182#382434C2314yes—
183#190147C2312yescomplemented
184#190116C2312yescomplemented
185#188109C2312yescomplemented
186C2×#8547C2312yescomplemented
187C2×#8547C2312yescomplemented
188#188049C2312yescomplemented
189C2×#8541C2312yescomplemented
190C2×#8541C2312yescomplemented
191C2×#7316C2314yescomplemented
192C2×#7316C2314yescomplemented
193C2×#7316C2314yescomplemented
194C2×#7316C2314yescomplemented
195C2×#7311C2314yescomplemented
196C2×#7311C2314yescomplemented
197C2×#7310C2314yescomplemented
198C2×#7310C2314yescomplemented
199C28C22×C411yescharacteristic
200C2×H(7,𝔽2)C22⋊C412yes—
201C23×H(5,𝔽2)C22×C411yescharacteristic
202C23×H(5,𝔽2)C2×D412yes—
203C25×D4C22×C411yescharacteristic
204C25×D4C2411yescharacteristic
205#62862C2×D418yes—
206#62844C22⋊C412yes—
207#62844C22⋊C414yes—
208#62844C22⋊C412yes—
209#62844C2×D414yes—
210#62844C2×D414yes—
211#62844C2×D414yes—
212#62844C2×D414yes—
213#62843C22⋊C412yes—
214#62842C22⋊C412yes—
215#62842C22⋊C414yes—
216#62842C22⋊C412yes—
217#62842C22⋊C414yes—
218#62842C22⋊C412yes—
219#62842C2×D414yes—
220#62842C2×D414yes—
221#62842C2×D414yes—
222#62842C2×D414yes—
223#62820C2×D414yes—
224#62817C2×D414yes—
225C2×#3490C22⋊C414yes—
226C2×#3490C22⋊C414yes—
227C2×#3490C22⋊C414yes—
228C2×#3490C22⋊C414yes—
229C2×#3490C22×C412yes—
230C2×#3490C22×C414yes—
231C2×#3490C22×C412yes—
232C2×#3484C22⋊C414yes—
233C2×#3484C22⋊C414yes—
234C2×#3484C22⋊C414yes—
235C2×#3484C22⋊C414yes—
236C2×#3484C22×C412yes—
237C2×#3484C22×C414yes—
238C2×#3484C22×C414yes—
239C2×#3484C22×C412yes—
240C2×#3484C2×D414yes—
241C2×#3484C2×D414yes—
242C2×#3484C2×D414yes—
243C2×#3484C2×D412yes—
244C2×#3484C2×D412yes—
245C2×#3484C2412yes—
246C2×#3484C2412yes—
247C22×#534C22×C411yescharacteristic
248C22×#534C22×C411yescharacteristic
249C22×#534C2×D414yes—
250C22×#534C2411yescharacteristic
251C22×#534C2411yescharacteristic
252C22×#534C2411yescharacteristic
253C23×#120C22×C414yes—
254C23×#120C22×C411yescharacteristic
255C23×#120C22×C411yescharacteristic
256C23×#120C22×C411yescharacteristic
257C23×#120C22×C411yescharacteristic
258C23×#120C22×C411yescharacteristic
259C23×#120C22×C411yescharacteristic
260C23×#120C22×C411yescharacteristic
261C23×#120C22×C411yescharacteristic
262C23×#120C22×C411yescharacteristic
263C23×#120C2411yescharacteristic
264C23×#120C2411yescharacteristic
265#62652C22⋊C412yes—
266#62652C22⋊C414yes—
267C22×#518C22×C411yescharacteristic
268C22×#518C22×C411yescharacteristic
269C22×#518C2×D412yes—
270C24×C22⋊C4C22×C411yescharacteristic
271C24×C22⋊C4C22×C411yescharacteristic
272#36714C22⋊C418yescomplemented
273#36702C22⋊C418yescomplemented
274#36614C22⋊C414yescomplemented
275C2×#2849C2×D412yes—
276C2×#2846C22⋊C414yescomplemented
277C2×#2846C22×C414yes—
278C2×#2846C22×C414yes—
279C2×#2846C22×C414yes—
280C2×#2846C22×C414yes—
281C2×#2846C2×D412yes—
282#35348C2×D418yes—
283#35222C22⋊C414yescomplemented
284#34992C22×C414yes—
285#34992C22×C414yes—
286#34980C22⋊C414yescomplemented
287#34980C22×C414yes—
288#34980C22×C414yes—
289C2×#2613C2×D412yes—
290C2×#2613C2×D412yes—
291#34176C22×C414yes—
292#34171C22×C412yes—
293#34171C22×C412yes—
294C2×#2315C22×C411yescharacteristic
295C2×#2315C22×C411yescharacteristic
296C2×#2308C22×C411yescharacteristic
297C2×#2308C22×C411yescharacteristic
298C2×#2308C22×C411yescharacteristic
299C2×#2308C22×C411yescharacteristic
300C2×#2308C2411yescharacteristic
301C22×#379C22×C411yescharacteristic
302C22×#379C22×C411yescharacteristic
303C22×#379C22×C411yescharacteristic
304C22×#379C22×C414yes—
305C2×#2273C22×C411yescharacteristic
306#24114C22⋊C4116yescomplemented
307#24058C2×D4116yes—
308#23985C22⋊C418yescomplemented
309#23984C22⋊C418yescomplemented
310#23984C22⋊C418yescomplemented
311#23984C22⋊C418yescomplemented
312#23984C22⋊C4116yescomplemented
313#23901C2×D418yes—
314#23900C2×D418yes—
315#23900C2×D418yes—
316#23900C2×D418yes—
317#23900C2×D4116yes—
318#21749C2×D418yes—
319#21748C22⋊C418yescomplemented
320#21747C2×D414yes—
321#21746C22⋊C418yescomplemented
322#21746C2×D414yes—
323#20985C22⋊C418yescomplemented
324#20984C22⋊C418yescomplemented
325C2×#1898C22×C414yes—
326C2×#1898C22×C414yes—
327C2×#1898C22×C414yes—
328C2×#1898C22×C414yes—
329C2×#1898C22×C414yes—
330C2×#1898C22×C414yes—
331C2×#1898C22×C414yes—
332C2×#1898C22×C414yes—
333C2×#1819C22×C412yes—
334C2×#1819C22×C412yes—
335C2×#1783C2414yes—
336C2×#1783C2414yes—
337C2×#1781C22×C414yes—
338C2×#1781C22×C414yes—
339C2×#1781C2414yes—
340C2×#1781C2414yes—
341C2×#1781C2412yes—
342C2×#1781C2412yes—
343C27C2×C22⋊C411yescharacteristic, complemented
344C27C23×C411yescharacteristic
345C27C23×C411yescharacteristic
346C27C23×C411yescharacteristic
347C27H(5,𝔽2)11yescharacteristic
348C22×H(5,𝔽2)C2×C22⋊C414yes—
349C22×H(5,𝔽2)C2×C22⋊C412yes—
350C22×H(5,𝔽2)C2×C22⋊C414yes—
351C22×H(5,𝔽2)C2×C22⋊C412yes—
352C22×H(5,𝔽2)C2×C22⋊C412yes—
353C22×H(5,𝔽2)C2×C22⋊C412yes—
354C22×H(5,𝔽2)C22×D412yes—
355C22×H(5,𝔽2)C22×D412yes—
356C24×D4C2×C22⋊C414yes—
357C24×D4C2×C22⋊C411yescharacteristic, complemented
358C24×D4C2×C22⋊C411yescharacteristic, complemented
359C24×D4C23×C411yescharacteristic
360C24×D4C23×C411yescharacteristic
361C24×D4C23×C411yescharacteristic
362C24×D4C23×C411yescharacteristic
363C24×D4C22×D412yes—
364C24×D4C22×D412yes—
365C24×D4H(5,𝔽2)11yescharacteristic
366C24×D4H(5,𝔽2)12yes—
367C24×D4H(5,𝔽2)12yes—
368C24×D4H(5,𝔽2)11yescharacteristic
369C24×D4C2511yescharacteristic
370C25×C4C2×C22⋊C411yescharacteristic, complemented
371C25×C4H(5,𝔽2)11yescharacteristic
372#3491#120116yes—
373#3490C2×C22⋊C418yes—
374#3490C2×C22⋊C418yes—
375#3490#120116yes—
376#3485#120116yes—
377#3484#120116yes—
378#3484C22×D418yes—
379#3484C22×D418yes—
380C2×#543C2×C22⋊C414yes—
381C2×#543C2×C22⋊C412yes—
382C2×#543C2×C22⋊C412yes—
383C2×#535#9918yescomplemented
384C2×#535C2×C22⋊C414yes—
385C2×#534#9918yescomplemented
386C2×#534C2×C22⋊C414yes—
387C2×#534C2×C22⋊C414yes—
388C2×#534C2×C22⋊C414yes—
389C2×#534C2×C22⋊C412yes—
390C2×#534C2×C22⋊C412yes—
391C2×#534C2×C22⋊C414yes—
392C2×#534C2×C22⋊C414yes—
393C2×#534C2×C22⋊C414yes—
394C2×#534C2×C22⋊C414yes—
395C2×#534C2×C22⋊C414yes—
396C2×#534C22×D414yes—
397C2×#534C22×D414yes—
398C2×#534C22×D414yes—
399C2×#534C22×D414yes—
400C2×#534C22×D414yes—
401C2×#534H(5,𝔽2)14yes—
402C2×#525#9918yescomplemented
403C2×#525C2×C22⋊C414yes—
404C22×#123C22×D412yes—
405C22×#123C22×D412yes—
406C22×#123H(5,𝔽2)12yes—
407C22×#120#9918yescomplemented
408C22×#120C2×C22⋊C414yes—
409C22×#120C2×C22⋊C414yes—
410C22×#120C2×C22⋊C414yes—
411C22×#120C2×C22⋊C414yes—
412C22×#120C2×C22⋊C414yes—
413C22×#120C2×C22⋊C414yescomplemented
414C22×#120C23×C414yes—
415C22×#120C23×C414yes—
416C22×#120C22×D412yes—
417C22×#120C22×D412yes—
418C22×#120C22×D412yes—
419C22×#120C22×D414yes—
420C22×#120C22×D412yes—
421C22×#120H(5,𝔽2)12yes—
422C2×#518C2×C22⋊C412yes—
423C2×#518C2×C22⋊C414yes—
424C2×#518C2×C22⋊C414yes—
425C2×#518C2×C22⋊C414yes—
426C2×#518C2×C22⋊C414yes—
427C2×#518C2×C22⋊C414yes—
428C2×#518C2×C22⋊C412yes—
429C2×#518C2×C22⋊C414yes—
430C2×#518C2×C22⋊C412yes—
431C2×#518C2×C22⋊C412yes—
432C2×#518C2×C22⋊C414yescomplemented
433C2×#518C22×D412yes—
434C2×#518C22×D412yes—
435C23×C22⋊C4C2×C22⋊C414yes—
436C23×C22⋊C4C23×C411yescharacteristic
437C23×C22⋊C4C23×C411yescharacteristic
438C23×C22⋊C4C23×C411yescharacteristic
439C23×C22⋊C4C23×C411yescharacteristic
440C23×C22⋊C4C23×C411yescharacteristic
441C23×C22⋊C4C23×C411yescharacteristic
442C23×C22⋊C4C23×C411yescharacteristic
443#2849C2×C22⋊C418yescomplemented
444#2846C2×C22⋊C418yescomplemented
445#2846C2×C22⋊C418yescomplemented
446#2846C2×C22⋊C4116yescomplemented
447#2846C2×C22⋊C418yescomplemented
448#2622C2×C22⋊C4116yescomplemented
449#2315C2×C22⋊C414yescomplemented
450#2309C2×C22⋊C414yescomplemented
451#2308C2×C22⋊C414yescomplemented
452#2308C22×D414yes—
453#2280C2×C22⋊C414yescomplemented
454C2×#381C2×C22⋊C412yescomplemented
455C2×#381C2×C22⋊C412yescomplemented
456C2×#379C2×C22⋊C412yescomplemented
457C2×#379C2×C22⋊C412yescomplemented
458C2×#379C2×C22⋊C412yescomplemented
459C2×#379C2×C22⋊C414yescomplemented
460C2×#379C2×C22⋊C412yescomplemented
461C2×#379C2×C22⋊C414yescomplemented
462C2×#379C23×C414yes—
463C2×#379C23×C414yes—
464#1898C2×C22⋊C4116yescomplemented
465#1898C2×C22⋊C4116yescomplemented
466#1898C2×C22⋊C4116yescomplemented
467#1898C2×C22⋊C4116yescomplemented
468#1819C2×C22⋊C418yescomplemented
469#1819C2×C22⋊C418yescomplemented
470#1781C22×D418yes—
471#1781C22×D418yes—
472C26C2×#9914yes—
473C26C22×C22⋊C412yes—
474C26C22×C22⋊C411yescharacteristic
475C26C22×C22⋊C411yescharacteristic
476C26C22×C22⋊C411yescharacteristic
477C26C22×C22⋊C412yes—
478C26C22×C22⋊C411yescharacteristic
479C26#51811yescharacteristic
480C26#51811yescharacteristic
481C26#51811yescharacteristic
482C26#51812yes—
483C26#51811yescharacteristic
484C26#53412yes—
485C26#53412yes—
486C26C24×C411yescharacteristic
487C26C2×H(5,𝔽2)11yescharacteristic
488C2×H(5,𝔽2)C2×#12018yes—
489C22×#41#37914yes—
490C22×#41C2×#9918yes—
491C23×D4#37914yes—
492C23×D4C2×#9914yes—
493C23×D4C2×#9914yes—
494C23×D4C2×#9918yes—
495C23×D4C22×C22⋊C411yescharacteristic
496C23×D4C22×C22⋊C411yescharacteristic
497C23×D4C22×C22⋊C412yes—
498C23×D4C22×C22⋊C414yes—
499C23×D4C22×C22⋊C414yes—
500C23×D4C22×C22⋊C412yes—
501C23×D4C22×C22⋊C412yes—
502C23×D4#51811yescharacteristic
503C23×D4#51811yescharacteristic
504C23×D4#51812yes—
505C23×D4#53412yes—
506C23×D4#53412yes—
507C23×D4#53412yes—
508C23×D4#53412yes—
509C23×D4C23×D412yes—
510C23×D4C23×D412yes—
511C23×D4C23×D412yes—
512C23×D4C2×H(5,𝔽2)12yes—
513C23×D4C2×H(5,𝔽2)12yes—
514C23×D4C2×H(5,𝔽2)12yes—
515C24×C4C2×#9914yes—
516C24×C4C22×C22⋊C411yescharacteristic
517C24×C4C22×C22⋊C411yescharacteristic
518C24×C4#51811yescharacteristic
519C24×C4#51811yescharacteristic
520C24×C4#53412yes—
521C24×C4#53412yes—
522C24×C4C2×H(5,𝔽2)11yescharacteristic
523#543#37918yes—
524#534#37918yes—
525#534C2×#120116yes—
526C2×#123#37918yes—
527C2×#123C2×#9918yes—
528C2×#123C2×#9918yes—
529C2×#123C2×#12018yes—
530C2×#123#53418yes—
531C2×#120#37918yes—
532C2×#120C2×#9918yes—
533C2×#120C2×#9918yes—
534C2×#120C2×#9918yes—
535C2×#120C2×#9918yes—
536C2×#120C2×#9918yes—
537C2×#120C2×#9918yes—
538C2×#120C22×C22⋊C418yes—
539C2×#120C22×C22⋊C418yes—
540C2×#120C2×#12018yes—
541C2×#120#53418yes—
542#518#379116yes—
543#518C2×#12018yes—
544C2×#117#37914yes—
545C2×#117C2×#9918yes—
546C22×C22⋊C4#37914yes—
547C22×C22⋊C4C2×#9918yes—
548C22×C22⋊C4C22×C22⋊C412yes—
549C22×C22⋊C4C22×C22⋊C414yes—
550C22×C22⋊C4C22×C22⋊C412yes—
551C22×C22⋊C4C22×C22⋊C412yes—
552C22×C22⋊C4C22×C22⋊C414yes—
553C22×C22⋊C4C22×C22⋊C412yes—
554C22×C22⋊C4C22×C22⋊C412yes—
555C22×C22⋊C4C22×C22⋊C412yes—
556C22×C22⋊C4C22×C22⋊C412yes—
557C22×C22⋊C4C22×C22⋊C412yes—
558C22×C22⋊C4C22×C22⋊C412yes—
559C22×C22⋊C4#51812yes—
560C22×C22⋊C4#51812yes—
561#379C22×C22⋊C418yes—
562#379C22×C22⋊C418yes—
563C25#178114yescomplemented
564C25C2×#37912yes—
565C25#230811yescharacteristic
566C25#230812yes—
567C25#230812yes—
568C25#230812yes—
569C25#230811yescharacteristic
570C25C22×#9914yes—
571C25C22×#9914yes—
572C25C22×#9914yes—
573C25C22×#9914yes—
574C25C23×C22⋊C411yescharacteristic
575C25C23×C22⋊C411yescharacteristic
576C25C23×C22⋊C411yescharacteristic
577C25C2×#51811yescharacteristic
578C25C2×#51811yescharacteristic
579C25C2×#51811yescharacteristic
580C25C2×#51811yescharacteristic
581C25C2×#53412yes—
582C25#348412yes—
583C25#348412yes—
584C22×Q8#178114yescomplemented
585C22×D4#178118yescomplemented
586C22×D4#178114yescomplemented
587C22×D4C2×#37918yes—
588C22×D4C22×#9918yes—
589C22×D4C22×#9918yes—
590C22×D4C22×#12014yes—
591C22×D4C2×#53414yes—
592C22×D4#348414yes—
593C22×D4#348414yes—
594C23×C4#178114yescomplemented
595C23×C4#178118yescomplemented
596C23×C4C2×#37912yes—
597C23×C4#230811yescharacteristic
598C23×C4#230812yes—
599C23×C4#230811yescharacteristic
600C23×C4C22×#9914yes—
601C23×C4C22×#9914yes—
602C23×C4C2×#53412yes—
603C23×C4#348412yes—
604C23×C4#348412yes—
605C2×C22⋊C4C2×#37914yes—
606C2×C22⋊C4C2×#37918yes—
607C2×C22⋊C4#230814yes—
608C2×C22⋊C4C22×#9918yes—
609C2×C22⋊C4C22×#9918yes—
610C24C2×#178114yes—
611C24C2×#178118yes—
612C24#2174612yes—
613C24#2174612yes—
614C24#2174614yes—
615C24#2177612yes—
616C24C22×#37911yescharacteristic
617C24C2×#230811yescharacteristic
618C24C2×#230811yescharacteristic
619C24#3417111yescharacteristic
620C24#3417111yescharacteristic
621C24#3417111yescharacteristic
622C24#3417111yescharacteristic
623C24#3498014yes—
624C24C23×#9914yes—
625C22×C4C2×#178118yes—
626C22×C4C2×#178114yes—
627C22×C4#2177612yes—
628C22×C4#3498014yes—
629C22⋊C4#2174618yes—
630C23#51741111yescharacteristic
631C23C22×#178112yes—
632C23C2×#2174612yes—
633C23C2×#2174612yes—
634C23C2×#2177611yescharacteristic
635C23C2×#2177611yescharacteristic
636C23#637418712yes—
637C22#7221778911yescharacteristic
638C22#7221930111yescharacteristic
639C22#7224102512yes—
640C22#7224102512yes—
641C22#7225836911yescharacteristic
642C2#7226619711yescharacteristic
subgroupG/H
center, socleC2#72266197
commutatorC26C24×C4
Frattini, cosocleC24×D4C25
prime radical#72234665C2
LCSG ▷ C26 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2 ◁ C24 ◁ C25×D4 ◁ G
LECSG ▷ C24×D4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #72314516C2semidirect
2. #72314508C2semidirect
3. #72314498C2semidirect
4. #72314482C2semidirect
5. #72314476C2semidirect
6. #72314472C22semidirect
7. #72314464C2semidirect
8. #72314456C22semidirect
9. #72314452C22semidirect
10. #72314447C2semidirect
11. #72314440C22semidirect
12. #72312643C2semidirect
13. #72266926C2semidirect
14. #72265785C2semidirect
15. #72265779C22semidirect
16. #72265766C22semidirect
17. #72258097C22semidirect
18. #72258097C22semidirect
19. #72258028C22semidirect
20. #72258028C22semidirect
21. #72256052C22semidirect
22. #72255971C22semidirect
23. #72255830C22semidirect
24. #72255764C22semidirect
25. #72238352C2semidirect
26. #72238351C22semidirect
27. #72238350C22semidirect
28. #72238349C22semidirect
29. #72237608C22semidirect
34. #72234659C4semidirect
35. #72234658C4semidirect
38. #72234591C4semidirect
40. #72232592C4semidirect
41. #72226366C22semidirect
42. #72225778C22semidirect
44. #72225655C4semidirect
47. #72219445C2semidirect
48. #72219440C2semidirect
49. C2×#139748C22semidirect
50. C2×#139748C22semidirect
51. #72219438C22semidirect
52. #72219438C22semidirect
53. #72219418C22semidirect
54. #72219415C22semidirect
55. #72219414C22semidirect
56. #72219414C22semidirect
57. #72219397C2semidirect
58. #72219345C22semidirect
59. #72219340C22semidirect
60. #72219325C22semidirect
61. #72219314C22semidirect
62. #72219311C22semidirect
63. #72219310C22semidirect
64. #72219301C22semidirect
65. #72219300C22semidirect
66. #72219299C22semidirect
68. #72219158C22semidirect
69. #72219158C22semidirect
70. #72218518C22semidirect
73. #72218306C22semidirect
74. #72218306C22semidirect
75. #72218291C22semidirect
76. C2×#139750C22semidirect
77. C2×#139750C22semidirect
79. #72217511C4semidirect
80. C2×#6499867C4semidirect
81. #72216064C4semidirect
82. #72215179C22semidirect
94. C22×#3484C2×C4semidirect
97. C24×#120C2×C4semidirect
99. #7642273C2×C4semidirect
101. #7642244C2×C4semidirect
102. #7641845C2×C4semidirect
103. C22×#2846C2×C4semidirect
104. C22×#2846C2×C4semidirect
105. #7630944C2×C4semidirect
107. #7630939C2×C4semidirect
109. C2×#35348C2×C4semidirect
111. C2×#35346C2×C4semidirect
112. C2×#34981C2×C4semidirect
116. #7626202C2×C4semidirect
117. C2×#34198C2×C4semidirect
118. C2×#34198C2×C4semidirect
125. #6453039C2×C4semidirect
127. #6451874C2×C4semidirect
130. C2×#23984C2×C4semidirect
131. C2×#23984C2×C4semidirect
132. #6440460C2×C4semidirect
133. #6440460C2×C4semidirect
136. #6437621C2×C4semidirect
137. #6437621C2×C4semidirect
140. C2×#23900C2×C4semidirect
141. C2×#23900C2×C4semidirect
142. C2×#23900C2×C4semidirect
143. C2×#23900C2×C4semidirect
148. #6374548C2×C4semidirect
151. #6374210C2×C4semidirect
156. C2×#21746C2×C4semidirect
157. C2×#21746C2×C4semidirect
158. #6372488C2×C4semidirect
160. #6371504C2×C4semidirect
161. C22×#1898C2×C4semidirect
162. #6371007C2×C4semidirect
163. #6370693C2×C4semidirect
165. #493879C23semidirect
174. #493357C23semidirect
175. C2×#12687C23semidirect
176. C2×#12687C23semidirect
183. #190147C23semidirect
184. #190116C23semidirect
185. #188109C23semidirect
186. C2×#8547C23semidirect
187. C2×#8547C23semidirect
188. #188049C23semidirect
189. C2×#8541C23semidirect
190. C2×#8541C23semidirect
191. C2×#7316C23semidirect
192. C2×#7316C23semidirect
193. C2×#7316C23semidirect
194. C2×#7316C23semidirect
195. C2×#7311C23semidirect
196. C2×#7311C23semidirect
197. C2×#7310C23semidirect
198. C2×#7310C23semidirect
272. #36714C22⋊C4semidirect
273. #36702C22⋊C4semidirect
274. #36614C22⋊C4semidirect
276. C2×#2846C22⋊C4semidirect
283. #35222C22⋊C4semidirect
286. #34980C22⋊C4semidirect
306. #24114C22⋊C4semidirect
308. #23985C22⋊C4semidirect
309. #23984C22⋊C4semidirect
310. #23984C22⋊C4semidirect
311. #23984C22⋊C4semidirect
312. #23984C22⋊C4semidirect
319. #21748C22⋊C4semidirect
321. #21746C22⋊C4semidirect
323. #20985C22⋊C4semidirect
324. #20984C22⋊C4semidirect
343. C27C2×C22⋊C4semidirect
357. C24×D4C2×C22⋊C4semidirect
358. C24×D4C2×C22⋊C4semidirect
370. C25×C4C2×C22⋊C4semidirect
383. C2×#535#99semidirect
385. C2×#534#99semidirect
402. C2×#525#99semidirect
407. C22×#120#99semidirect
413. C22×#120C2×C22⋊C4semidirect
432. C2×#518C2×C22⋊C4semidirect
443. #2849C2×C22⋊C4semidirect
444. #2846C2×C22⋊C4semidirect
445. #2846C2×C22⋊C4semidirect
446. #2846C2×C22⋊C4semidirect
447. #2846C2×C22⋊C4semidirect
448. #2622C2×C22⋊C4semidirect
449. #2315C2×C22⋊C4semidirect
450. #2309C2×C22⋊C4semidirect
451. #2308C2×C22⋊C4semidirect
453. #2280C2×C22⋊C4semidirect
454. C2×#381C2×C22⋊C4semidirect
455. C2×#381C2×C22⋊C4semidirect
456. C2×#379C2×C22⋊C4semidirect
457. C2×#379C2×C22⋊C4semidirect
458. C2×#379C2×C22⋊C4semidirect
459. C2×#379C2×C22⋊C4semidirect
460. C2×#379C2×C22⋊C4semidirect
461. C2×#379C2×C22⋊C4semidirect
464. #1898C2×C22⋊C4semidirect
465. #1898C2×C22⋊C4semidirect
466. #1898C2×C22⋊C4semidirect
467. #1898C2×C22⋊C4semidirect
468. #1819C2×C22⋊C4semidirect
469. #1819C2×C22⋊C4semidirect
563. C25#1781semidirect
584. C22×Q8#1781semidirect
585. C22×D4#1781semidirect
586. C22×D4#1781semidirect
594. C23×C4#1781semidirect
595. C23×C4#1781semidirect

Maximal subgroups

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

subgroupindex
#723145162
#723145082
#723144982
#723144822
#723144762
#723144642
#723144472
#723126432
#722669262
#722657852
#722383522
#722346652
#722194452
#722194402
#722193972