Finite Group Databasebeta

← #72307482

Subgroups — #72307482

Order 2048.

At least 6955 conjugacy classes of subgroups; only the 4110 normal subgroups are shown.

The subgroup lattice has 732 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72307468C214yesmaximal, complemented
2#72307452C214yesmaximal, complemented
3#72307445C214yesmaximal, complemented
4#72307392C212yesmaximal, complemented
5#72307227C212yesmaximal, complemented
6#72307199C211yesmaximal, characteristic, complemented
7#72307134C212yesmaximal, complemented
8#72307091C212yesmaximal, complemented
9#72306773C214yesmaximal, complemented
10#72281886C218yesmaximal, complemented
11#72281192C212yesmaximal, complemented
12#72250033C2116yesmaximal, complemented
13#72249762C212yesmaximal, complemented
14C2×#480440C211yesmaximal, characteristic, complemented
15C2×#6469085C211yesmaximal, characteristic, complemented
16#72231710C218yesmaximal, complemented
17#10580980C2218yescomplemented
18#10580979C2214yescomplemented
19#10580978C2214yescomplemented
20#10578435C2212yescomplemented
21#10577631C2212yes—
22#10577575C2212yes—
23#10577575C2212yescomplemented
24#10575819C2212yescomplemented
25#10575815C2212yescomplemented
26#10575319C2212yes—
27C2×#60207C2211yescharacteristic
28C2×#60184C2211yescharacteristic, complemented
29#7623149C22116yescomplemented
30#7623148C22116yescomplemented
31#7623147C2218yescomplemented
32#7623143C2218yescomplemented
33#7623062C2214yescomplemented
34#7622837C2214yescomplemented
35C2×#33426C2212yescomplemented
36#6469085C2218yescomplemented
37#6469085C2218yescomplemented
38C2×#29387C2212yescomplemented
39C2×#29384C2212yescomplemented
40C2×#27694C2211yescharacteristic, complemented
41C2×#27691C2211yescharacteristic, complemented
42C2×#24285C2211yescharacteristic, complemented
43C2×#24288C2211yescharacteristic, complemented
44C2×#23834C2212yescomplemented
45C2×#23794C2212yescomplemented
46C2×#20788C2211yescharacteristic, complemented
47#486702C22116yescomplemented
48#486701C22116yescomplemented
49#486693C2218yescomplemented
50#486692C2214yescomplemented
51#486691C2214yescomplemented
52#486690C2218yescomplemented
53#486689C2218yescomplemented
54#486346C22116yescomplemented
55#486345C22116yescomplemented
56#486337C2218yescomplemented
57#486336C2214yescomplemented
58#486335C2214yescomplemented
59#486334C2218yescomplemented
60#486333C2218yescomplemented
61#486085C22132yescomplemented
62#486084C22132yescomplemented
63#486081C22116yescomplemented
64#486080C22116yescomplemented
65#486079C22116yescomplemented
66#486078C2218yescomplemented
67#486077C2218yescomplemented
68#485591C22132yescomplemented
69#485590C22132yescomplemented
70#485587C22116yescomplemented
71#485586C2218yescomplemented
72#485585C2218yescomplemented
73#485584C22116yescomplemented
74#485583C22116yescomplemented
75#484988C2218yescomplemented
76#484982C2218yescomplemented
77#484657C2218yescomplemented
78#484651C2218yescomplemented
79#484575C2218yescomplemented
80#484569C2218yescomplemented
81#484232C2218yescomplemented
82#484226C2218yescomplemented
83#482710C22116yescomplemented
84#482709C22116yescomplemented
85#482038C2214yescomplemented
86#482032C2214yescomplemented
87#481946C2218yescomplemented
88#481728C2218yescomplemented
89#480440C2218yescomplemented
90#480440C2218yescomplemented
91C2×#11540C2212yescomplemented
92C2×#11537C2212yescomplemented
93C2×#11523C2212yescomplemented
94C2×#11521C2212yescomplemented
95C2×#11486C2212yescomplemented
96C2×#11483C2212yescomplemented
97C2×#3584C2311yescharacteristic
98C2×#3444D411yescharacteristic
99#62392C2318yescomplemented
100#62391C2318yescomplemented
101#62335C2318yes—
102#62334C2318yes—
103#62276C2314yescomplemented
104#62275C2314yes—
105#62274C2314yes—
106#62273C2314yescomplemented
107#62271C2312yes—
108#62271C2312yescomplemented
109#62270C2312yes—
110#62270C2312yescomplemented
111#62269C2314yes—
112#62269C2314yescomplemented
113#60975C2318yescomplemented
114#60974C2318yescomplemented
115#60972C2314yescomplemented
116#60971C2312yescomplemented
117#60968C2312yescomplemented
118#60967C2314yescomplemented
119#60964C2314yescomplemented
120#60915C2314yes—
121#60907C2314yes—
122#60749C2314yes—
123#60741C2314yes—
124#60699D418yescomplemented
125#60699C2318yes—
126#60698D418yescomplemented
127#60698C2318yes—
128#60693D414yescomplemented
129#60693C2314yes—
130#60682D414yescomplemented
131#60682C2314yes—
132#60660D412yescomplemented
133#60643D412yescomplemented
134#60450C2314yes—
135#60207D414yes—
136#60207D414yes—
137#60207C2314yes—
138#60207C2314yes—
139C2×#2961D411yescharacteristic
140C2×#2961C2311yescharacteristic
141#60184C2318yes—
142C2×#2956C2312yes—
143C2×#2955C2312yes—
144C2×#2943D414yescomplemented
145C2×#2932D411yescharacteristic
146C2×#2932C2311yescharacteristic
147C2×#2929D411yescharacteristic
148C2×#2929D411yescharacteristic
149C2×#2929C2311yescharacteristic
150C2×#2929C2311yescharacteristic
151C2×#2923D411yescharacteristic
152C2×#2923C2311yescharacteristic
153C2×#2920C2311yescharacteristic
154C2×#2916C2311yescharacteristic
155C2×#2875D411yescharacteristic
156C2×#2875C2311yescharacteristic
157C23×#97D411yescharacteristic
158#33693C23116yes—
159#33692C23116yes—
160#33691C23132yes—
161#33690C23132yes—
162#33689C23116yes—
163#33688C23116yes—
164#33659C23116yes—
165#33658C2318yes—
166#33657C2318yes—
167#33656C23116yes—
168#33533C23116yes—
169#33532C2318yes—
170#33531C2318yes—
171#33530C23116yes—
172#33426C23116yes—
173C2×#2166C2314yes—
174C2×#2165C2314yes—
175C2×#2115C2314yes—
176#29387C23116yes—
177#29384C2318yes—
178#29384C2318yes—
179#27694C2318yes—
180#27691C2314yes—
181#27691C2314yes—
182#24288C2318yes—
183#24285C2314yes—
184#24285C2314yes—
185#23834C23116yes—
186#23794C2318yes—
187#23794C2318yes—
188C2×#2103C2312yes—
189C2×#2102C2312yes—
190C2×#2098C2312yes—
191C2×#2091C2312yes—
192C2×#2053C2312yes—
193C2×#2050C2312yes—
194C2×#2017C2312yes—
195C2×#2010C2312yes—
196#20788C2318yes—
197C2×#1841C2312yes—
198C2×#1813C2311yescharacteristic
199C2×#1812C2311yescharacteristic
200C2×#1747C2312yes—
201#12309C23132yescomplemented
202#12308C23116yescomplemented
203#12307C23116yescomplemented
204#12306C23132yescomplemented
205#12305C23116yescomplemented
206#12304C23116yescomplemented
207#12303C23132yescomplemented
208#12302C23116yescomplemented
209#12301C23116yescomplemented
210#12300C23132yescomplemented
211#12299C23116yescomplemented
212#12298C23116yescomplemented
213#12175C23132yes—
214#12174C23116yes—
215#12173C23116yes—
216#12172C23132yes—
217#12171C23116yes—
218#12170C23116yes—
219#12119C23132yes—
220#12118C23116yes—
221#12117C23116yes—
222#12116C23132yes—
223#12115C23116yes—
224#12114C23116yes—
225#11872C23116yes—
226#11871C2318yes—
227#11870C2318yes—
228#11869C2318yes—
229#11868C2318yes—
230#11867C23116yes—
231#11838C23116yescomplemented
232#11837C23116yescomplemented
233#11836C23132yescomplemented
234#11771C23116yescomplemented
235#11770C23116yescomplemented
236#11769C23132yescomplemented
237#11688C23116yes—
238#11685C23116yes—
239#11540C23116yescomplemented
240#11537C2318yescomplemented
241#11537C2318yescomplemented
242#11523C23116yescomplemented
243#11521C2318yescomplemented
244#11521C2318yescomplemented
245#11486C23116yes—
246#11483C2314yes—
247#11483C2314yes—
248#11483C2314yes—
249#11483C2314yes—
250C2×#1328C2314yes—
251C2×#1327C2314yes—
252C2×#1321C2314yes—
253C2×#1320C2314yes—
254#3584C2414yes—
255C2×#575C2412yes—
256C22×#135C2×D414yes—
257C22×#131C2×D411yescharacteristic
258C22×#131C2×D411yescharacteristic
259C22×#131C2×D411yescharacteristic
260C22×#131C2411yescharacteristic
261C24×C8C2×D411yescharacteristic
262C24×C8C2×D411yescharacteristic
263#3444C2×D414yes—
264#3444C2×D414yes—
265C2×#533C2×D411yescharacteristic
266C2×#532C2×D411yescharacteristic
267C2×#525C2×D411yescharacteristic
268C2×#525C2×D411yescharacteristic
269C2×C4×#41C2×D411yescharacteristic
270C2×C4×#41C2×D411yescharacteristic
271C23×C42C2×D411yescharacteristic
272#3263C2418yes—
273#3261C2414yes—
274#3259C2414yes—
275#3256C2418yes—
276#3255C2414yes—
277#3253C2414yes—
278#3204C2418yes—
279#3202C2414yes—
280#3199C2414yes—
281#3197C2418yes—
282#3195C2414yes—
283#3192C2414yes—
284#3185C2×D414yes—
285#3185C2×D418yescomplemented
286#3185C2414yes—
287#3184C2×D414yes—
288#3184C2×D418yescomplemented
289#3184C2414yes—
290#3183C2×D418yes—
291#3183C2×D418yescomplemented
292#3183C2×D418yescomplemented
293#3183C2418yes—
294#3177C2×D414yes—
295#3177C2×D418yescomplemented
296#3177C2414yes—
297#3176C2×D414yes—
298#3176C2×D418yescomplemented
299#3176C2414yes—
300#3173C2×D418yes—
301#3173C2×D418yescomplemented
302#3173C2×D418yescomplemented
303#3173C2418yes—
304#3163C2×D418yescomplemented
305#3163C2×D418yescomplemented
306#3160C2×D414yes—
307#3160C2×D414yes—
308#3156C2×D418yescomplemented
309#3155C2×D418yescomplemented
310#3147C2×D414yes—
311#3147C2×D414yes—
312#3060C2×D418yes—
313#3060C2418yes—
314#3059C2×D414yes—
315#3059C2414yes—
316#3058C2×D414yes—
317#3058C2414yes—
318#3054C2×D418yes—
319#3054C2418yes—
320#2961C2×D414yes—
321#2961C2×D414yes—
322#2961C2×D414yes—
323#2961C2414yes—
324#2956C2418yes—
325#2955C2418yes—
326#2943C2×D418yes—
327#2943C2×D418yes—
328#2943C2×D418yescomplemented
329#2943C2×D418yescomplemented
330C2×#442C2×D418yescomplemented
331C2×#441C2×D418yescomplemented
332#2932C2×D414yes—
333#2932C2×D414yes—
334#2932C2×D414yes—
335#2932C2414yes—
336#2929C2×D414yes—
337#2929C2×D414yes—
338#2929C2×D412yes—
339#2929C2×D412yes—
340#2929C2×D412yes—
341#2929C2×D412yes—
342#2929C2×D414yes—
343#2929C2×D414yes—
344#2929C2412yes—
345#2929C2412yes—
346#2929C2412yes—
347#2929C2412yes—
348#2923C2×D414yes—
349#2923C2×D414yes—
350#2923C2×D414yes—
351#2923C2414yes—
352#2920C2×D412yes—
353#2920C2×D412yes—
354#2920C2412yes—
355#2920C2412yes—
356#2916C2414yes—
357C2×#430C2412yes—
358C2×#427C2×D414yes—
359C2×#424C2×D411yescharacteristic
360C2×#424C2×D411yescharacteristic
361C2×#424C2×D411yescharacteristic
362C2×#424C2411yescharacteristic
363C2×#423C2×D411yescharacteristic
364C2×#423C2411yescharacteristic
365C2×#408C2×D411yescharacteristic
366C2×#408C2×D411yescharacteristic
367C2×#408C2×D411yescharacteristic
368C2×#408C2411yescharacteristic
369C2×#407C2×D411yescharacteristic
370C2×#407C2411yescharacteristic
371#2875C2×D418yes—
372#2875C2×D414yes—
373#2875C2×D414yes—
374#2875C2×D414yes—
375#2875C2414yes—
376C2×#405C2×D412yes—
377C2×#405C2×D412yes—
378C2×#405C2×D411yescharacteristic
379C2×#405C2×D411yescharacteristic
380C2×#405C2×D411yescharacteristic
381C2×#405C2411yescharacteristic
382C2×C4×M16C2×D412yes—
383C2×C4×M16C2×D411yescharacteristic
384C2×C4×M16C2411yescharacteristic
385C22×#97C2×D412yes—
386C22×#97C2×D414yes—
387C22×#97C2×D411yescharacteristic
388C22×#97C2×D411yescharacteristic
389C22×#97C2×D414yes—
390C22×#97C2×D411yescharacteristic
391C22×#97C2×D411yescharacteristic
392#2239C24132yes—
393#2238C24132yes—
394#2191C24132yes—
395#2190C24132yes—
396#2166C24116yes—
397#2165C24116yes—
398#2115C2418yes—
399#2115C2418yes—
400C2×#349C2418yes—
401#2103C2418yes—
402#2102C2418yes—
403#2098C2418yes—
404#2091C2414yes—
405#2091C2414yes—
406#2053C2418yes—
407#2050C2418yes—
408#2017C2418yes—
409#2010C2414yes—
410#2010C2414yes—
411#1841C2418yes—
412#1813C2414yes—
413#1812C2414yes—
414#1747C2418yes—
415C2×#338C2412yes—
416C2×H(3,ℤ/4)C2412yes—
417#1342C24132yes—
418#1341C24132yes—
419#1340C24132yes—
420#1339C24132yes—
421#1328C2418yes—
422#1328C2418yes—
423#1327C24116yes—
424#1321C24116yes—
425#1320C2418yes—
426#1320C2418yes—
427C22×#41C22×D411yescharacteristic
428C22×#41C22×D411yescharacteristic
429C24×C4C22×D411yescharacteristic
430#575C2514yes—
431C2×#135C22×D418yes—
432C2×#135C22×D418yes—
433C22×Q16C22×D414yes—
434C22×D8C22×D414yes—
435C2×#131#12014yes—
436C2×#131C22×D414yes—
437C2×#131C22×D412yes—
438C2×#131C22×D412yes—
439C2×#131C22×D412yes—
440C2×#131C22×D414yes—
441C2×#131C22×D414yes—
442C2×#131C2512yes—
443C22×M16#12012yes—
444C22×M16C22×D411yescharacteristic
445C22×M16C22×D411yescharacteristic
446C22×M16C22×D411yescharacteristic
447C22×M16C22×D412yes—
448C22×M16C2511yescharacteristic
449C23×C8#12012yes—
450C23×C8C22×D411yescharacteristic
451C23×C8C22×D411yescharacteristic
452C23×C8C22×D412yes—
453C23×C8C22×D412yes—
454C23×C8C22×D412yes—
455C23×C8C22×D411yescharacteristic
456C23×C8C22×D411yescharacteristic
457C23×C8C22×D412yes—
458C23×C8C22×D412yes—
459#533C22×D414yes—
460#532AGL(1,ℤ/8)14yes—
461#532C22×D414yes—
462C2×C4⋊Q8AGL(1,ℤ/8)11yescharacteristic
463C2×#127AGL(1,ℤ/8)11yescharacteristic
464C2×#124AGL(1,ℤ/8)11yescharacteristic
465C2×#124AGL(1,ℤ/8)11yescharacteristic
466#525AGL(1,ℤ/8)12yes—
467#525AGL(1,ℤ/8)12yes—
468#525C22×D412yes—
469#525C22×D412yes—
470#525C22×D412yes—
471#525C22×D412yes—
472C2×#123AGL(1,ℤ/8)12yes—
473C2×#120AGL(1,ℤ/8)12yes—
474C4×#41#12014yes—
475C4×#41C22×D414yes—
476C4×#41C22×D414yes—
477C2×#117#12012yes—
478C2×#117C22×D411yescharacteristic
479C2×#117C22×D411yescharacteristic
480C22×C42#12012yes—
481C22×C42C22×D412yes—
482C22×C42C22×D412yes—
483C22×C42C22×D411yescharacteristic
484C22×C42C22×D411yescharacteristic
485#499C22×D414yes—
486#499C22×D414yes—
487#499C22×D418yes—
488#498C22×D418yes—
489#498C22×D414yes—
490#498C22×D414yes—
491#495C22×D418yes—
492#495C22×D418yes—
493#494C22×D414yes—
494#494C22×D414yes—
495#493C22×D414yes—
496#493C22×D414yes—
497#470C22×D418yes—
498#470C22×D418yes—
499#470C22×D418yes—
500#470C2518yes—
501#469C22×D418yes—
502#469C22×D418yes—
503#469C22×D418yes—
504#469C2518yes—
505#442C22×D418yes—
506#442C22×D418yes—
507#442C22×D418yes—
508#442C22×D418yes—
509#441C22×D418yes—
510#441C22×D418yes—
511#441C22×D418yes—
512#441C22×D418yes—
513#430C2514yes—
514#427C22×D418yes—
515#427C22×D414yes—
516#427C22×D414yes—
517C2×#106C22×D418yes—
518#424C22×D412yes—
519#424C22×D414yes—
520#424C22×D412yes—
521#424C22×D412yes—
522#424C22×D414yes—
523#424C2512yes—
524#423C22×D412yes—
525#423C22×D412yes—
526#423C22×D412yes—
527#423C2512yes—
528#408C22×D412yes—
529#408C22×D412yes—
530#408C22×D412yes—
531#408C22×D414yes—
532#408C22×D414yes—
533#408C2512yes—
534#407C22×D411yescharacteristic
535#407C22×D411yescharacteristic
536#407C22×D412yes—
537#407C22×D412yes—
538#407C2511yescharacteristic
539#407C2511yescharacteristic
540#405#12018yes—
541#405#12018yes—
542#405#12014yes—
543#405C22×D412yes—
544#405C22×D412yes—
545#405C22×D414yes—
546#405C22×D414yes—
547#405C22×D412yes—
548#405C22×D418yes—
549#405C22×D414yes—
550#405C22×D418yes—
551#405C2512yes—
552C4×M16#12018yes—
553C4×M16C22×D412yes—
554C4×M16C22×D412yes—
555C4×M16C22×D412yes—
556C4×M16C22×D418yes—
557C4×M16C22×D414yes—
558C4×M16C2512yes—
559C2×#97#12011yescharacteristic
560C2×#97#12011yescharacteristic
561C2×#97#12011yescharacteristic
562C2×#97#12011yescharacteristic
563C2×#97#12014yes—
564C2×#97#12012yes—
565C2×#97#12018yes—
566C2×#97C22×D414yes—
567C2×#97C22×D414yes—
568C2×#97C22×D414yes—
569C2×#97C22×D414yes—
570C2×#97C22×D412yes—
571C2×#97C22×D412yes—
572C2×#97C22×D418yes—
573C2×C4×C8#12012yes—
574C2×C4×C8C22×D412yes—
575C2×C4×C8C22×D412yes—
576#349C25116yes—
577#338C2514yes—
578H(3,ℤ/4)C2514yes—
579C25C2×AGL(1,ℤ/8)11yescharacteristic
580C2×#41C2×#12012yes—
581C2×#41C2×AGL(1,ℤ/8)12yes—
582C2×#41C2×AGL(1,ℤ/8)12yes—
583C2×#41C2×AGL(1,ℤ/8)12yes—
584C2×#41C23×D412yes—
585C2×#41C23×D412yes—
586C22×Q8C2×AGL(1,ℤ/8)11yescharacteristic
587C22×Q8C2×AGL(1,ℤ/8)11yescharacteristic
588C22×D4C2×AGL(1,ℤ/8)12yes—
589C22×D4C2×AGL(1,ℤ/8)11yescharacteristic
590C22×D4C2×AGL(1,ℤ/8)11yescharacteristic
591C23×C4C2×#12012yes—
592C23×C4C2×AGL(1,ℤ/8)11yescharacteristic
593C23×C4C2×AGL(1,ℤ/8)11yescharacteristic
594C23×C4C2×AGL(1,ℤ/8)11yescharacteristic
595C23×C4C23×D411yescharacteristic
596C23×C4C23×D411yescharacteristic
597C23×C4C23×D411yescharacteristic
598C2×Q16C23×D418yes—
599C2×D8C23×D418yes—
600C2×M16C2×#12018yes—
601C2×M16C2×#12012yes—
602C2×M16C2×#12014yes—
603C2×M16C23×D412yes—
604C2×M16C23×D411yescharacteristic
605C2×M16C23×D411yescharacteristic
606C2×M16C23×D414yes—
607C2×M16C23×D412yes—
608C2×M16C23×D412yes—
609C2×M16C23×D411yescharacteristic
610C2×M16C2611yescharacteristic
611C22×C8C2×#12012yes—
612C22×C8C2×#12012yes—
613C22×C8C2×#12014yes—
614C22×C8C2×#12011yescharacteristic
615C22×C8C2×#12011yescharacteristic
616C22×C8C2×#12012yes—
617C22×C8C2×#12018yes—
618C22×C8C2×#12011yescharacteristic
619C22×C8C2×#12011yescharacteristic
620C22×C8C23×D414yes—
621C22×C8C23×D412yes—
622C22×C8C23×D412yes—
623C22×C8C23×D412yes—
624C22×C8C23×D412yes—
625C22×C8C23×D412yes—
626C4⋊Q8C2×AGL(1,ℤ/8)14yes—
627#127C2×AGL(1,ℤ/8)14yes—
628#124C2×AGL(1,ℤ/8)14yes—
629#124C2×AGL(1,ℤ/8)14yes—
630#123C2×AGL(1,ℤ/8)14yes—
631#123C2×AGL(1,ℤ/8)14yes—
632#120C2×AGL(1,ℤ/8)14yes—
633#120C2×AGL(1,ℤ/8)14yes—
634#117C2×#12018yes—
635#117C2×#12012yes—
636#117C2×AGL(1,ℤ/8)12yes—
637#117C23×D412yes—
638#117C23×D412yes—
639C2×C22⋊C4C2×AGL(1,ℤ/8)12yes—
640C2×C42C2×#12018yes—
641C2×C42C2×#12012yes—
642C2×C42C2×#12011yescharacteristic
643C2×C42C2×#12012yes—
644C2×C42C2×#12011yescharacteristic
645C2×C42C2×AGL(1,ℤ/8)12yes—
646C2×C42C2×AGL(1,ℤ/8)11yescharacteristic
647C2×C42C2×AGL(1,ℤ/8)11yescharacteristic
648C2×C42C23×D412yes—
649C2×C42C23×D412yes—
650#106C23×D418yes—
651#106C23×D418yes—
652#97C2×#12014yes—
653#97C2×#12014yes—
654#97C2×#12014yes—
655#97C2×#12014yes—
656#97C2×#12014yes—
657#97C2×#12014yes—
658#97C2×#12018yes—
659#97C23×D414yes—
660#97C23×D414yes—
661C4×C8C2×#12018yes—
662C4×C8C2×#12014yes—
663C4×C8C2×#12014yes—
664C4×C8C23×D414yes—
665C4×C8C23×D414yes—
666C24#300312yes—
667C24C22×AGL(1,ℤ/8)11yescharacteristic
668C24C22×AGL(1,ℤ/8)11yescharacteristic
669C24C22×AGL(1,ℤ/8)11yescharacteristic
670C2×Q8#300312yes—
671C2×Q8C22×AGL(1,ℤ/8)12yes—
672C2×Q8C22×AGL(1,ℤ/8)12yes—
673C2×D4#300314yes—
674C2×D4#300312yes—
675C2×D4C22×AGL(1,ℤ/8)12yes—
676C2×D4C22×AGL(1,ℤ/8)12yes—
677C2×D4C22×AGL(1,ℤ/8)14yes—
678C22×C4#300314yes—
679C22×C4#300312yes—
680C22×C4C22×#12014yes—
681C22×C4C22×#12011yescharacteristic
682C22×C4C22×#12011yescharacteristic
683C22×C4C22×AGL(1,ℤ/8)11yescharacteristic
684C22×C4C22×AGL(1,ℤ/8)11yescharacteristic
685C22×C4C22×AGL(1,ℤ/8)11yescharacteristic
686C22×C4C22×AGL(1,ℤ/8)11yescharacteristic
687C22×C4C22×AGL(1,ℤ/8)11yescharacteristic
688C22×C4C24×D411yescharacteristic
689C2×C8#302112yes—
690C2×C8#302112yes—
691C2×C8#302511yescharacteristic
692C2×C8#302511yescharacteristic
693C2×C8#302512yes—
694C2×C8C22×#12012yes—
695C2×C8C22×#12012yes—
696C2×C8C22×#12012yes—
697C2×C8C22×#12014yes—
698C2×C8C22×#12012yes—
699C2×C8C22×#12012yes—
700C2×C8C24×D412yes—
701C22⋊C4C22×AGL(1,ℤ/8)14yes—
702C42C22×#12012yes—
703C42C22×#12014yes—
704C42C22×#12012yes—
705C42C22×AGL(1,ℤ/8)12yes—
706C42C22×AGL(1,ℤ/8)12yes—
707C23C2×#300314yes—
708C23C2×#300311yescharacteristic
709C23C2×#300311yescharacteristic
710C23C23×AGL(1,ℤ/8)11yescharacteristic
711C2×C4C2×#300311yescharacteristic
712C2×C4C2×#300314yes—
713C2×C4C2×#300311yescharacteristic
714C2×C4C2×#302111yescharacteristic
715C2×C4C2×#302111yescharacteristic
716C2×C4C2×#302511yescharacteristic
717C2×C4C2×#302511yescharacteristic
718C2×C4C23×#12011yescharacteristic
719C2×C4C23×AGL(1,ℤ/8)11yescharacteristic
720C8C2×#302114yes—
721C8C2×#302512yes—
722C8C2×#302512yes—
723C22#634663711yescharacteristic
724C22#634663711yescharacteristic
725C22C22×#300311yescharacteristic
726C4#634663711yescharacteristic
727C4#634663711yescharacteristic
728C4C22×#302111yescharacteristic
729C4C22×#302511yescharacteristic
730C2C2×#634663711yescharacteristic
subgroupG/H
centerC4#6346637
commutator, Frattini, cosocleC2×M16C26
socleC2C2×#6346637
LCSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#2875 ◁ G
LECSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #72307468C2semidirect
2. #72307452C2semidirect
3. #72307445C2semidirect
4. #72307392C2semidirect
5. #72307227C2semidirect
6. #72307199C2semidirect
7. #72307134C2semidirect
8. #72307091C2semidirect
9. #72306773C2semidirect
10. #72281886C2semidirect
11. #72281192C2semidirect
12. #72250033C2semidirect
13. #72249762C2semidirect
14. C2×#480440C2semidirect
15. C2×#6469085C2semidirect
16. #72231710C2semidirect
17. #10580980C22semidirect
18. #10580979C22semidirect
19. #10580978C22semidirect
20. #10578435C22semidirect
23. #10577575C22semidirect
24. #10575819C22semidirect
25. #10575815C22semidirect
28. C2×#60184C22semidirect
29. #7623149C22semidirect
30. #7623148C22semidirect
31. #7623147C22semidirect
32. #7623143C22semidirect
33. #7623062C22semidirect
34. #7622837C22semidirect
35. C2×#33426C22semidirect
36. #6469085C22semidirect
37. #6469085C22semidirect
38. C2×#29387C22semidirect
39. C2×#29384C22semidirect
40. C2×#27694C22semidirect
41. C2×#27691C22semidirect
42. C2×#24285C22semidirect
43. C2×#24288C22semidirect
44. C2×#23834C22semidirect
45. C2×#23794C22semidirect
46. C2×#20788C22semidirect
47. #486702C22semidirect
48. #486701C22semidirect
49. #486693C22semidirect
50. #486692C22semidirect
51. #486691C22semidirect
52. #486690C22semidirect
53. #486689C22semidirect
54. #486346C22semidirect
55. #486345C22semidirect
56. #486337C22semidirect
57. #486336C22semidirect
58. #486335C22semidirect
59. #486334C22semidirect
60. #486333C22semidirect
61. #486085C22semidirect
62. #486084C22semidirect
63. #486081C22semidirect
64. #486080C22semidirect
65. #486079C22semidirect
66. #486078C22semidirect
67. #486077C22semidirect
68. #485591C22semidirect
69. #485590C22semidirect
70. #485587C22semidirect
71. #485586C22semidirect
72. #485585C22semidirect
73. #485584C22semidirect
74. #485583C22semidirect
75. #484988C22semidirect
76. #484982C22semidirect
77. #484657C22semidirect
78. #484651C22semidirect
79. #484575C22semidirect
80. #484569C22semidirect
81. #484232C22semidirect
82. #484226C22semidirect
83. #482710C22semidirect
84. #482709C22semidirect
85. #482038C22semidirect
86. #482032C22semidirect
87. #481946C22semidirect
88. #481728C22semidirect
89. #480440C22semidirect
90. #480440C22semidirect
91. C2×#11540C22semidirect
92. C2×#11537C22semidirect
93. C2×#11523C22semidirect
94. C2×#11521C22semidirect
95. C2×#11486C22semidirect
96. C2×#11483C22semidirect
99. #62392C23semidirect
100. #62391C23semidirect
103. #62276C23semidirect
106. #62273C23semidirect
108. #62271C23semidirect
110. #62270C23semidirect
112. #62269C23semidirect
113. #60975C23semidirect
114. #60974C23semidirect
115. #60972C23semidirect
116. #60971C23semidirect
117. #60968C23semidirect
118. #60967C23semidirect
119. #60964C23semidirect
124. #60699D4semidirect
126. #60698D4semidirect
128. #60693D4semidirect
130. #60682D4semidirect
132. #60660D4semidirect
133. #60643D4semidirect
144. C2×#2943D4semidirect
201. #12309C23semidirect
202. #12308C23semidirect
203. #12307C23semidirect
204. #12306C23semidirect
205. #12305C23semidirect
206. #12304C23semidirect
207. #12303C23semidirect
208. #12302C23semidirect
209. #12301C23semidirect
210. #12300C23semidirect
211. #12299C23semidirect
212. #12298C23semidirect
231. #11838C23semidirect
232. #11837C23semidirect
233. #11836C23semidirect
234. #11771C23semidirect
235. #11770C23semidirect
236. #11769C23semidirect
239. #11540C23semidirect
240. #11537C23semidirect
241. #11537C23semidirect
242. #11523C23semidirect
243. #11521C23semidirect
244. #11521C23semidirect
285. #3185C2×D4semidirect
288. #3184C2×D4semidirect
291. #3183C2×D4semidirect
292. #3183C2×D4semidirect
295. #3177C2×D4semidirect
298. #3176C2×D4semidirect
301. #3173C2×D4semidirect
302. #3173C2×D4semidirect
304. #3163C2×D4semidirect
305. #3163C2×D4semidirect
308. #3156C2×D4semidirect
309. #3155C2×D4semidirect
328. #2943C2×D4semidirect
329. #2943C2×D4semidirect
330. C2×#442C2×D4semidirect
331. C2×#441C2×D4semidirect

Maximal subgroups

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

subgroupindex
#723074682
#723074522
#723074452
#723073922
#723072272
#723071992
#723071342
#723070912
#723067732
#722818862
#722811922
#722500332
#722497622
C2×#4804402
C2×#64690852
#722317102