Finite Group Databasebeta

← #72313274

Subgroups — #72313274

Order 4096.

Only the 2235 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 639 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72313223C214yesmaximal, complemented
2#72313194C212yesmaximal, complemented
3#72313173C212yesmaximal, complemented
4#72313138C212yesmaximal, complemented
5#72313018C212yesmaximal, complemented
6#72312205C212yesmaximal, complemented
7#72309729C212yesmaximal, complemented
8#72309374C212yesmaximal, complemented
9#72309373C2214yescomplemented
10#72309371C214yesmaximal, complemented
11#72309370C2214yescomplemented
12#72309369C2214yescomplemented
13#72309368C2214yescomplemented
14#72309324C2214yescomplemented
15#72309324C2214yescomplemented
16#72266836C212yesmaximal, complemented
17#72266073C2212yescomplemented
18#72259092C212yesmaximal, complemented
19#72259089C2214yescomplemented
20#72259089C2214yescomplemented
21#72259089C2214yescomplemented
22#72259083C2214yescomplemented
23#72259008C2212yescomplemented
24#72259002C2214yescomplemented
25#72237628C211yesmaximal, characteristic, complemented
26#72237627C2212yescomplemented
27#72237618C2211yescharacteristic, complemented
28#72237400C2212yescomplemented
29#72236453C2214yescomplemented
30#72236453C2214yescomplemented
31#72236437C2214yescomplemented
32#72236437C2214yescomplemented
33#72234668C2211yescharacteristic, complemented
34#72234665C211yesmaximal, characteristic, complemented
35#72234663C2211yescharacteristic, complemented
36#72234661C2212yes—
37#72234661C2212yes—
38#72234661C2212yescomplemented
39#72234625C2211yescharacteristic, complemented
40#72234591C2212yescomplemented
41#72232884C2211yescharacteristic, complemented
42#72232592C2214yes—
43#72232592C2212yes—
44#72232592C2214yescomplemented
45#72232592C2214yescomplemented
46#72232592C2211yescharacteristic, complemented
47#72225664C212yesmaximal, complemented
48#72225629C211yesmaximal, characteristic, complemented
49C2×#111462C2212yescomplemented
50C2×#111462C2214yescomplemented
51C2×#115348C2212yescomplemented
52C2×#115348C2212yescomplemented
53#72219257C2212yescomplemented
54#72219230C2214yescomplemented
55#72219229C2212yescomplemented
56#72219227C2211yescharacteristic, complemented
57C2×#106076C2212yescomplemented
58C22×#8534C2212yescomplemented
59C22×#8534C2212yescomplemented
60C2×#394167C2214yescomplemented
61C2×#394058C2212yescomplemented
62C2×#359428C2212yescomplemented
63C2×#7670203C2211yescharacteristic
64#72218766C2214yescomplemented
65#72218744C2212yescomplemented
66#72218375C2211yescharacteristic, complemented
67C22×#23900C2212yescomplemented
68#72217789C2211yescharacteristic, complemented
69#72217699C2214yescomplemented
70#72217699C2212yescomplemented
71#72217511C2212yes—
72#72217511C2211yescharacteristic, complemented
73C2×#115690C2214yescomplemented
74C2×#6499867C2212yescomplemented
75C2×#62817C2312yes—
76C2×#62817C2312yes—
77C2×#62817C2311yescharacteristic, complemented
78C22×#3484D411yescharacteristic, complemented
79C22×#3484C2311yescharacteristic
80C22×#3484C2312yes—
81C24×#120C2311yescharacteristic
82C24×#120C2311yescharacteristic
83#7642273D414yescomplemented
84#7642244D414yescomplemented
85#7641845C2314yes—
86#7641845C2312yes—
87#7641845C2312yes—
88#7641845C2314yes—
89C22×#2846C2314yes—
90C22×#2846C2311yescharacteristic
91C22×#2846C2312yescomplemented
92#7630944D414yescomplemented
93#7630939D414yescomplemented
94C2×#35390D411yescharacteristic, complemented
95C2×#35348D411yescharacteristic, complemented
96C2×#35348D411yescharacteristic, complemented
97C2×#35346D411yescharacteristic, complemented
98C2×#34981D411yescharacteristic, complemented
99C2×#34981C2311yescharacteristic
100C2×#34981C2314yes—
101C2×#34980D411yescharacteristic, complemented
102C2×#34980C2311yescharacteristic
103C2×#34980C2312yes—
104#7626202C2312yes—
105#7626202C2311yescharacteristic, complemented
106C2×#34198D411yescharacteristic, complemented
107C2×#34198C2311yescharacteristic
108C23×#379C2312yescomplemented
109#6629258D414yescomplemented
110#6628892D414yescomplemented
111#6500019D4116yescomplemented
112#6453039D418yescomplemented
113#6451874D418yescomplemented
114#6440460D418yescomplemented
115#6440460D414yescomplemented
116#6440460D414yescomplemented
117#6437621D418yescomplemented
118#6437621D414yescomplemented
119#6437621D414yescomplemented
120#6432949D418yescomplemented
121C2×#21746C2314yes—
122C2×#21746C2314yes—
123C2×#21746C2314yes—
124C2×#21746C2314yes—
125C2×#21746C2312yes—
126C2×#21746C2312yes—
127C2×#21746C2312yes—
128C2×#21746C2311yescharacteristic, complemented
129C2×#21746C2314yescomplemented
130C2×#21746C2311yescharacteristic, complemented
131C2×#21746C2312yescomplemented
132C22×#1898C2314yes—
133C22×#1898C2314yes—
134C22×#1898C2314yes—
135C22×#1898C2314yes—
136C22×#1898C2314yes—
137C22×#1898C2312yescomplemented
138C22×#1898C2314yescomplemented
139C22×#1898C2314yescomplemented
140C22×#1781C2312yes—
141C22×#1781C2312yes—
142C22×#1781C2312yes—
143C2×#14679C2312yescomplemented
144C2×#14679C2312yescomplemented
145#516383C2314yes—
146C22×#1438C2312yes—
147#355913C2312yescomplemented
148#355913C2314yescomplemented
149C2×#10735C2314yescomplemented
150C2×#10735C2312yescomplemented
151C2×#10735C2314yescomplemented
152C2×#10725C2312yescomplemented
153C2×#10725C2314yescomplemented
154C2×#10725C2314yescomplemented
155C2×#8101C2314yescomplemented
156C2×#8101C2314yescomplemented
157C2×#7555C2312yescomplemented
158C28C2411yescharacteristic
159C23×H(5,𝔽2)C2×D411yescharacteristic
160C23×H(5,𝔽2)C2×D412yescomplemented
161C25×D4C2×D411yescharacteristic
162C25×D4C2×D412yes—
163C25×D4C2411yescharacteristic
164#62817C2×D418yescomplemented
165C2×#3490C2×D418yes—
166C2×#3490C2×D414yes—
167C2×#3484C2×D418yes—
168C2×#3484C2×D414yes—
169C2×#3484C2×D414yes—
170C2×#3484C2×D414yes—
171C22×#534C2×D411yescharacteristic
172C22×#534C2×D411yescharacteristic
173C22×#534C2×D411yescharacteristic
174C22×#534C2×D411yescharacteristic
175C22×#534C2×D411yescharacteristic
176C22×#534C2×D414yescomplemented
177C22×#534C2×D412yescomplemented
178C22×#534C2×D412yescomplemented
179C22×#534C2×D414yescomplemented
180C23×#120C2×D412yes—
181C23×#120C2×D411yescharacteristic
182C23×#120C2×D411yescharacteristic
183C23×#120C2×D412yes—
184C23×#120C2×D411yescharacteristic
185C23×#120C2×D411yescharacteristic
186C23×#120C2×D411yescharacteristic
187C23×#120C2×D411yescharacteristic
188C23×#120C2×D411yescharacteristic
189C23×#120C2×D411yescharacteristic
190C23×#120C2412yes—
191C23×#120C2411yescharacteristic
192C23×#120C2411yescharacteristic
193C23×#120C2414yes—
194C23×#120C2411yescharacteristic
195C22×#518C2×D411yescharacteristic
196C22×#518C2×D411yescharacteristic
197C22×#518C2×D412yescomplemented
198C24×C22⋊C4C2×D412yes—
199C24×C22⋊C4C2×D411yescharacteristic
200C24×C22⋊C4C2414yes—
201C24×C22⋊C4C2411yescharacteristic
202#37436C2×D4116yes—
203C2×#2846C2×D418yes—
204C2×#2846C2×D418yes—
205#34992C2×D414yes—
206#34992C2×D418yes—
207#34992C2×D418yes—
208#34992C2×D418yes—
209#34992C2×D414yescomplemented
210#34992C2×D418yescomplemented
211#34981C2×D418yes—
212#34980C2×D414yes—
213#34980C2×D414yes—
214#34980C2×D418yes—
215#34980C2×D414yes—
216#34980C2×D418yes—
217#34980C2×D418yes—
218#34980C2×D418yescomplemented
219#34980C2×D414yescomplemented
220#34176C2×D414yes—
221#34171C2×D414yes—
222C2×#2315C2×D411yescharacteristic
223C2×#2315C2×D411yescharacteristic
224C2×#2315C2×D414yescomplemented
225C2×#2308C2×D411yescharacteristic
226C2×#2308C2×D411yescharacteristic
227C2×#2308C2×D411yescharacteristic
228C2×#2308C2×D411yescharacteristic
229C2×#2308C2×D411yescharacteristic
230C2×#2308C2×D412yescomplemented
231C2×#2308C2×D412yescomplemented
232C2×#2308C2×D414yescomplemented
233C2×#2308C2×D414yescomplemented
234C22×#379C2×D411yescharacteristic
235C22×#379C2×D411yescharacteristic
236C22×#379C2412yes—
237C22×#379C2411yescharacteristic
238C22×#379C2412yes—
239C22×#379C2414yes—
240C22×#379C2412yes—
241C22×#379C2414yes—
242C2×#2273C2×D411yescharacteristic
243#21746C2×D418yescomplemented
244C2×#1898C2×D418yes—
245C2×#1898C2×D414yes—
246C2×#1898C2×D414yes—
247C2×#1898C2×D418yes—
248C2×#1898C2×D418yescomplemented
249C2×#1898C2×D414yescomplemented
250C2×#1898C2×D414yescomplemented
251C2×#1898C2×D418yescomplemented
252C2×#1898C2×D4116yescomplemented
253C2×#1819C2×D418yescomplemented
254C2×#1819C2×D418yescomplemented
255C2×#1781C2×D414yescomplemented
256C2×#1781C2×D414yescomplemented
257C2×#1781C2×D418yescomplemented
258C2×#1781C2×D414yescomplemented
259C2×#1781C2×D418yescomplemented
260C2×#1781C2×D414yescomplemented
261C27#12011yescharacteristic, complemented
262C27C22×D412yes—
263C27C22×D412yes—
264C27C22×D411yescharacteristic
265C27C22×D411yescharacteristic
266C27H(5,𝔽2)11yescharacteristic
267C27C2511yescharacteristic
268C22×H(5,𝔽2)#12014yes—
269C22×H(5,𝔽2)#12012yes—
270C22×H(5,𝔽2)#12012yes—
271C24×D4#12011yescharacteristic, complemented
272C24×D4#12012yescomplemented
273C24×D4#12011yescharacteristic, complemented
274C24×D4#12012yescomplemented
275C24×D4C22×D412yes—
276C24×D4C22×D411yescharacteristic
277C24×D4C22×D412yes—
278C24×D4C22×D411yescharacteristic
279C24×D4C22×D412yes—
280C24×D4C22×D414yes—
281C24×D4C22×D411yescharacteristic
282C24×D4C22×D411yescharacteristic
283C24×D4C22×D411yescharacteristic
284C24×D4C22×D412yes—
285C24×D4C22×D412yes—
286C24×D4C22×D414yes—
287C24×D4C22×D412yes—
288C24×D4C22×D412yes—
289C24×D4C22×D414yes—
290C24×D4H(5,𝔽2)11yescharacteristic
291C24×D4H(5,𝔽2)11yescharacteristic
292C24×D4H(5,𝔽2)12yes—
293C24×D4H(5,𝔽2)14yes—
294C25×C4#12011yescharacteristic, complemented
295C25×C4#12012yescomplemented
296C25×C4H(5,𝔽2)11yescharacteristic
297C2×#543#12014yes—
298C2×#534#12014yes—
299C2×#534#12018yes—
300C2×#534#12014yes—
301C2×#534#12014yes—
302C2×#534#12012yes—
303C2×#534#12014yes—
304C2×#534#12012yes—
305C2×#534#12014yescomplemented
306C22×#120C22×D414yes—
307C22×#120C22×D414yes—
308C22×#120C22×D418yes—
309C22×#120C22×D414yes—
310C22×#120C22×D418yes—
311C22×#120C22×D414yes—
312C22×#120C22×D418yes—
313C22×#120C22×D418yes—
314C22×#120C22×D414yes—
315C22×#120H(5,𝔽2)14yes—
316C22×#120H(5,𝔽2)18yes—
317C22×#120H(5,𝔽2)18yes—
318C2×#518#12012yes—
319C2×#518#12012yes—
320C2×#518#12018yes—
321C2×#518#12014yes—
322C23×C22⋊C4#12012yescomplemented
323C23×C22⋊C4#12012yescomplemented
324C23×C22⋊C4#12012yescomplemented
325C23×C22⋊C4C22×D411yescharacteristic
326C23×C22⋊C4C22×D412yes—
327C23×C22⋊C4C22×D411yescharacteristic
328C23×C22⋊C4C22×D411yescharacteristic
329C23×C22⋊C4C22×D412yes—
330C23×C22⋊C4C22×D414yes—
331C23×C22⋊C4C22×D414yes—
332C23×C22⋊C4C22×D411yescharacteristic
333C23×C22⋊C4C22×D411yescharacteristic
334C23×C22⋊C4C22×D411yescharacteristic
335C23×C22⋊C4C22×D414yes—
336C23×C22⋊C4C22×D411yescharacteristic
337C23×C22⋊C4C22×D414yes—
338C23×C22⋊C4C22×D412yes—
339C23×C22⋊C4C22×D414yes—
340C23×C22⋊C4C22×D414yes—
341C23×C22⋊C4C22×D412yes—
342C23×C22⋊C4C22×D412yes—
343C23×C22⋊C4H(5,𝔽2)14yes—
344C23×C22⋊C4H(5,𝔽2)12yes—
345#2849#120116yescomplemented
346#2849#12018yescomplemented
347#2846#12018yescomplemented
348#2483#120116yescomplemented
349#2405#120116yescomplemented
350#2405#120116yescomplemented
351#2403#120116yescomplemented
352#2315#12014yescomplemented
353#2308#12012yes—
354#2308#12014yes—
355#2308#12012yes—
356#2308#12014yescomplemented
357#2308#12014yescomplemented
358C2×#379C22×D414yes—
359C2×#379C22×D414yes—
360C2×#379C22×D418yes—
361C2×#379C22×D418yes—
362C2×#379C22×D418yes—
363C2×#379C22×D418yes—
364C2×#379C22×D414yes—
365C2×#379C22×D418yes—
366C26C2×#12011yescharacteristic
367C26C2×#12011yescharacteristic
368C26C2×#12011yescharacteristic
369C26C2×#12012yes—
370C26C2×#12011yescharacteristic
371C26C2×#12012yes—
372C26#53411yescharacteristic
373C26#53411yescharacteristic
374C26#53411yescharacteristic
375C26D4214yes—
376C26D4212yes—
377C26D4212yes—
378C26C23×D411yescharacteristic
379C26C23×D412yes—
380C26C23×D412yes—
381C26C23×D412yes—
382C26C23×D412yes—
383C26C23×D414yes—
384C26C2×H(5,𝔽2)14yes—
385C26C2×H(5,𝔽2)12yes—
386C26C2×H(5,𝔽2)11yescharacteristic
387C26C2×H(5,𝔽2)11yescharacteristic
388C26C2×H(5,𝔽2)14yes—
389C26C2×H(5,𝔽2)12yes—
390C26C2×H(5,𝔽2)14yes—
391C23×D4C2×#12012yes—
392C23×D4C2×#12018yes—
393C23×D4C2×#12012yes—
394C23×D4C2×#12012yes—
395C23×D4C2×#12014yes—
396C23×D4C2×#12011yescharacteristic
397C23×D4C2×#12011yescharacteristic
398C23×D4C2×#12012yes—
399C23×D4C2×#12012yes—
400C23×D4C2×#12011yescharacteristic
401C23×D4C2×#12011yescharacteristic
402C23×D4C2×#12012yes—
403C23×D4C2×#12012yes—
404C23×D4C2×#12018yes—
405C23×D4C2×#12018yes—
406C23×D4#53414yes—
407C23×D4#53412yes—
408C23×D4#53418yes—
409C23×D4D4218yes—
410C23×D4D4218yes—
411C23×D4D4218yes—
412C23×D4D4212yes—
413C23×D4D4212yes—
414C23×D4D4212yes—
415C23×D4D4212yes—
416C23×D4D4218yes—
417C23×D4D4218yes—
418C23×D4D4218yes—
419C23×D4D4218yes—
420C24×C4C2×#12012yes—
421C24×C4C2×#12011yescharacteristic
422C24×C4C2×#12012yes—
423C24×C4C2×#12011yescharacteristic
424C24×C4C2×#12012yes—
425C24×C4C2×#12014yes—
426C24×C4#53411yescharacteristic
427C24×C4#53411yescharacteristic
428C24×C4#53411yescharacteristic
429C24×C4#53412yes—
430C24×C4D4212yes—
431C24×C4D4212yes—
432C24×C4D4214yes—
433C24×C4D4214yes—
434C24×C4D4214yes—
435C2×#120C2×#12018yes—
436C2×#120#53418yes—
437C2×#120#534116yes—
438C2×#120D42116yes—
439C2×#120D4218yes—
440C2×#120H(3,𝔽4)18yes—
441C22×C22⋊C4C2×#12012yes—
442C22×C22⋊C4C2×#12014yes—
443C22×C22⋊C4C2×#12012yes—
444C22×C22⋊C4C2×#12012yes—
445C22×C22⋊C4C2×#12018yes—
446C22×C22⋊C4C2×#12012yes—
447C22×C22⋊C4C2×#12012yes—
448C22×C22⋊C4C2×#12018yes—
449C22×C22⋊C4C2×#12018yes—
450C22×C22⋊C4C2×#12012yes—
451C22×C22⋊C4C2×#12012yes—
452C22×C22⋊C4C2×#12012yes—
453C22×C22⋊C4C2×#12012yes—
454C22×C22⋊C4#53412yes—
455C22×C22⋊C4#53414yes—
456C22×C22⋊C4#53418yes—
457C22×C22⋊C4D4218yes—
458C22×C22⋊C4D4218yes—
459C22×C22⋊C4D4218yes—
460C22×C22⋊C4D4218yes—
461C22×C22⋊C4D4218yes—
462C22×C22⋊C4D4218yes—
463C22×C22⋊C4D4218yes—
464#379C2×#12018yes—
465#379C2×#120116yes—
466C25#240312yes—
467C25#240314yes—
468C25#240318yes—
469C25#240312yes—
470C25#240311yescharacteristic
471C25#240312yes—
472C25#240311yescharacteristic
473C25#284612yes—
474C25C22×#12011yescharacteristic
475C25C22×#12011yescharacteristic
476C25C22×#12011yescharacteristic
477C25C22×#12014yes—
478C25C22×#12012yes—
479C25C22×#12011yescharacteristic
480C25C22×#12012yes—
481C25C2×#53412yes—
482C25C2×#53414yes—
483C25C2×#53414yes—
484C25C2×#53411yescharacteristic
485C25C2×#53411yescharacteristic
486C25C2×#53411yescharacteristic
487C25C2×#53412yes—
488C25C2×D4214yes—
489C25C2×D4214yes—
490C25C2×D4214yes—
491C25C2×D4214yes—
492C25C2×D4214yes—
493C25C2×D4214yes—
494C25C2×D4214yes—
495C25C2×D4214yes—
496C25C2×D4212yes—
497C25C2×D4212yes—
498C25C2×D4214yes—
499C25C2×D4212yes—
500C25#348414yes—
501C25#348414yes—
502C25#348412yes—
503C25#348414yes—
504C25#348412yes—
505C25#348414yes—
506C25#348414yes—
507C25#348412yes—
508C25#348412yes—
509C25#348414yes—
510C25#348412yes—
511C25#348412yes—
512C25#348414yes—
513C25#348414yes—
514C25#348414yes—
515C25#348412yes—
516C25#348412yes—
517C25#348414yes—
518C25#348414yes—
519C25C2×H(3,𝔽4)12yes—
520C25#353214yes—
521C25#353214yes—
522C25#353214yes—
523C25#353212yes—
524C25#353214yes—
525C25#353214yes—
526C25#353212yes—
527C22×D4#240318yes—
528C22×D4#2403116yes—
529C22×D4#2679116yes—
530C22×D4#267918yes—
531C23×C4#240314yes—
532C23×C4#240314yes—
533C23×C4#240314yes—
534C23×C4#240312yes—
535C23×C4#240314yes—
536C23×C4#240311yescharacteristic
537C23×C4#240314yes—
538C23×C4#240318yes—
539C23×C4#240318yes—
540C23×C4#240318yes—
541C23×C4#240312yes—
542C23×C4#240311yescharacteristic
543C23×C4#240312yes—
544C23×C4#284614yes—
545C23×C4#284612yes—
546C2×C22⋊C4#240318yes—
547C2×C22⋊C4#2403116yes—
548C2×C22⋊C4#267918yes—
549C2×C22⋊C4#2679116yes—
550C24#1594714yes—
551C24#2389512yescomplemented
552C24C2×#240312yes—
553C24C2×#240311yescharacteristic
554C24C2×#240311yescharacteristic
555C24C2×#240314yes—
556C24C2×#240311yescharacteristic
557C24C2×#240312yes—
558C24C2×#240314yes—
559C24#3498011yescharacteristic
560C24#3498012yes—
561C24#3498011yescharacteristic
562C24#3498011yescharacteristic
563C24#3498014yes—
564C24#3534612yes—
565C24#3534612yes—
566C24#3534612yes—
567C24D4×#12014yes—
568C24D4×#12014yes—
569C24D4×#12014yes—
570C24D4×#12014yes—
571C24D4×#12014yes—
572C24D4×#12014yes—
573C24D4×#12012yes—
574C24D4×#12012yes—
575C24D4×#12014yes—
576C24C2×#284611yescharacteristic
577C24#3671412yes—
578C24#3671412yes—
579C24#3671412yes—
580C24#3764414yes—
581C24#3764414yes—
582C24#3764414yes—
583C24#3764414yes—
584C24#3764414yes—
585C24#3764414yes—
586C24#3764412yes—
587C24#3764412yes—
588C24#3764414yes—
589C24#3764414yes—
590C24#3764414yes—
591C24#3764414yes—
592C24#3764414yes—
593C24#4543914yes—
594C24#4543912yes—
595C24#4543912yes—
596C24C2×#267914yes—
597C24C2×#267912yes—
598C24#5899014yes—
599C24#5899014yes—
600C24#5899012yes—
601C24#5899014yes—
602C24#5899014yes—
603C24#5899012yes—
604C24#5899014yes—
605C22×C4#1594718yes—
606C22×C4#1594714yes—
607C22×C4#2389512yescomplemented
608C23C2×#1594711yescharacteristic
609C23#61242411yescharacteristic
610C23#61242412yes—
611C23#61696012yes—
612C23#61696011yescharacteristic
613C23#64765612yes—
614C23#64765614yes—
615C23#64765614yes—
616C23#64765612yes—
617C23#84529712yes—
618C23#84529714yes—
619C23#84529714yes—
620C23#84529712yes—
621C23C2×#2389511yescharacteristic
622C23C2×#2389511yescharacteristic
623C23#643762912yes—
624C23#649987412yes—
625C23#649987512yes—
626C23#649987614yes—
627C22#7221386211yescharacteristic
628C22#7221879511yescharacteristic
629C22#7223306912yes—
630C22#7223306912yes—
631C22#7223307214yes—
632C22#7223461712yes—
633C22#7223658611yescharacteristic
634C22#7224108114yes—
635C22#7225138012yes—
636C2#7225900912yes—
637C2#7225904011yescharacteristic
subgroupG/H
center, socleC22#72218795
commutator, Frattini, cosocleC27C25
LCSG ▷ C27 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C27 ◁ G
LECSG ▷ C27 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #72313223C2semidirect
2. #72313194C2semidirect
3. #72313173C2semidirect
4. #72313138C2semidirect
5. #72313018C2semidirect
6. #72312205C2semidirect
7. #72309729C2semidirect
8. #72309374C2semidirect
9. #72309373C22semidirect
10. #72309371C2semidirect
11. #72309370C22semidirect
12. #72309369C22semidirect
13. #72309368C22semidirect
14. #72309324C22semidirect
15. #72309324C22semidirect
16. #72266836C2semidirect
17. #72266073C22semidirect
18. #72259092C2semidirect
19. #72259089C22semidirect
20. #72259089C22semidirect
21. #72259089C22semidirect
22. #72259083C22semidirect
23. #72259008C22semidirect
24. #72259002C22semidirect
25. #72237628C2semidirect
26. #72237627C22semidirect
27. #72237618C22semidirect
28. #72237400C22semidirect
29. #72236453C22semidirect
30. #72236453C22semidirect
31. #72236437C22semidirect
32. #72236437C22semidirect
33. #72234668C22semidirect
34. #72234665C2semidirect
35. #72234663C22semidirect
38. #72234661C22semidirect
39. #72234625C22semidirect
40. #72234591C22semidirect
41. #72232884C22semidirect
44. #72232592C22semidirect
45. #72232592C22semidirect
46. #72232592C22semidirect
47. #72225664C2semidirect
48. #72225629C2semidirect
49. C2×#111462C22semidirect
50. C2×#111462C22semidirect
51. C2×#115348C22semidirect
52. C2×#115348C22semidirect
53. #72219257C22semidirect
54. #72219230C22semidirect
55. #72219229C22semidirect
56. #72219227C22semidirect
57. C2×#106076C22semidirect
58. C22×#8534C22semidirect
59. C22×#8534C22semidirect
60. C2×#394167C22semidirect
61. C2×#394058C22semidirect
62. C2×#359428C22semidirect
64. #72218766C22semidirect
65. #72218744C22semidirect
66. #72218375C22semidirect
67. C22×#23900C22semidirect
68. #72217789C22semidirect
69. #72217699C22semidirect
70. #72217699C22semidirect
72. #72217511C22semidirect
73. C2×#115690C22semidirect
74. C2×#6499867C22semidirect
77. C2×#62817C23semidirect
78. C22×#3484D4semidirect
83. #7642273D4semidirect
84. #7642244D4semidirect
91. C22×#2846C23semidirect
92. #7630944D4semidirect
93. #7630939D4semidirect
94. C2×#35390D4semidirect
95. C2×#35348D4semidirect
96. C2×#35348D4semidirect
97. C2×#35346D4semidirect
98. C2×#34981D4semidirect
101. C2×#34980D4semidirect
105. #7626202C23semidirect
106. C2×#34198D4semidirect
108. C23×#379C23semidirect
109. #6629258D4semidirect
110. #6628892D4semidirect
111. #6500019D4semidirect
112. #6453039D4semidirect
113. #6451874D4semidirect
114. #6440460D4semidirect
115. #6440460D4semidirect
116. #6440460D4semidirect
117. #6437621D4semidirect
118. #6437621D4semidirect
119. #6437621D4semidirect
120. #6432949D4semidirect
128. C2×#21746C23semidirect
129. C2×#21746C23semidirect
130. C2×#21746C23semidirect
131. C2×#21746C23semidirect
137. C22×#1898C23semidirect
138. C22×#1898C23semidirect
139. C22×#1898C23semidirect
143. C2×#14679C23semidirect
144. C2×#14679C23semidirect
147. #355913C23semidirect
148. #355913C23semidirect
149. C2×#10735C23semidirect
150. C2×#10735C23semidirect
151. C2×#10735C23semidirect
152. C2×#10725C23semidirect
153. C2×#10725C23semidirect
154. C2×#10725C23semidirect
155. C2×#8101C23semidirect
156. C2×#8101C23semidirect
157. C2×#7555C23semidirect
160. C23×H(5,𝔽2)C2×D4semidirect
164. #62817C2×D4semidirect
176. C22×#534C2×D4semidirect
177. C22×#534C2×D4semidirect
178. C22×#534C2×D4semidirect
179. C22×#534C2×D4semidirect
197. C22×#518C2×D4semidirect
209. #34992C2×D4semidirect
210. #34992C2×D4semidirect
218. #34980C2×D4semidirect
219. #34980C2×D4semidirect
224. C2×#2315C2×D4semidirect
230. C2×#2308C2×D4semidirect
231. C2×#2308C2×D4semidirect
232. C2×#2308C2×D4semidirect
233. C2×#2308C2×D4semidirect
243. #21746C2×D4semidirect
248. C2×#1898C2×D4semidirect
249. C2×#1898C2×D4semidirect
250. C2×#1898C2×D4semidirect
251. C2×#1898C2×D4semidirect
252. C2×#1898C2×D4semidirect
253. C2×#1819C2×D4semidirect
254. C2×#1819C2×D4semidirect
255. C2×#1781C2×D4semidirect
256. C2×#1781C2×D4semidirect
257. C2×#1781C2×D4semidirect
258. C2×#1781C2×D4semidirect
259. C2×#1781C2×D4semidirect
260. C2×#1781C2×D4semidirect
261. C27#120semidirect
271. C24×D4#120semidirect
272. C24×D4#120semidirect
273. C24×D4#120semidirect
274. C24×D4#120semidirect
294. C25×C4#120semidirect
295. C25×C4#120semidirect
305. C2×#534#120semidirect
322. C23×C22⋊C4#120semidirect
323. C23×C22⋊C4#120semidirect
324. C23×C22⋊C4#120semidirect
345. #2849#120semidirect
346. #2849#120semidirect
347. #2846#120semidirect
348. #2483#120semidirect
349. #2405#120semidirect
350. #2405#120semidirect
351. #2403#120semidirect
352. #2315#120semidirect
356. #2308#120semidirect
357. #2308#120semidirect
551. C24#23895semidirect
607. C22×C4#23895semidirect

Maximal subgroups

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

subgroupindex
#723132232
#723131942
#723131732
#723131382
#723130182
#723122052
#723097292
#723093742
#723093712
#722668362
#722590922
#722376282
#722346652
#722256642
#722256292