Finite Group Databasebeta

← C101×#23876 #38806027

Subgroups — C101×#23876 #38806027

Order 25856.

2012 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C101C211yesmaximal, characteristic, complemented
2C101×#3488C211yesmaximal, characteristic, complemented
3C2×#453×C101C212yesmaximal, complemented
4C101×#3003C211yesmaximal, characteristic, complemented
5C101×#2433C211yesmaximal, characteristic, complemented
6C101×#2006C212yesmaximal, complemented
7C101×#2002C212yesmaximal, complemented
8C101×#1900C211yesmaximal, characteristic, complemented
9C101×#1883C212yesmaximal, complemented
10C101×#1871C211yesmaximal, characteristic, complemented
11C101×#1789C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C101C2211yescharacteristic, complemented
13C22×#41×C101C2211yescharacteristic
14C23×D4×C101C2211yescharacteristic, complemented
15C2×AGL(1,ℤ/8)×C101—21no—
16C2×AGL(1,ℤ/8)×C101—21no—
17C2×AGL(1,ℤ/8)×C101—28no—
18C2×AGL(1,ℤ/8)×C101C2212yes—
19C2×AGL(1,ℤ/8)×C101C2212yescomplemented
20C2×AGL(1,ℤ/8)×C101C2212yescomplemented
21C22×SD16×C101—21no—
22C22×D8×C101—21no—
23C22×M16×C101C2211yescharacteristic, complemented
24#550×C101—21no—
25#548×C101—21no—
26#546×C101—21no—
27#546×C101—22no—
28D42×C101—22no—
29D42×C101—21no—
30#537×C101—21no—
31#537×C101C2211yescharacteristic, complemented
32#535×C101—21no—
33#535×C101C2211yescharacteristic, complemented
34C2×#127×C101C2212yescomplemented
35#525×C101—21no—
36#525×C101C2211yescharacteristic
37C2×#121×C101—21no—
38C2×#121×C101C2211yescharacteristic
39C2×#120×C101—22no—
40#520×C101C2211yescharacteristic, complemented
41#453×C101—28no—
42#450×C101—21no—
43#450×C101—21no—
44#447×C101—21no—
45#447×C101—21no—
46C2×#104×C101C2212yescomplemented
47C2×#104×C101C2212yescomplemented
48C2×#104×C101C2212yescomplemented
49#418×C101C2212yescomplemented
50C2×#100×C101C2212yescomplemented
51#407×C101C2211yescharacteristic, complemented
52#392×C101—22no—
53#390×C101C2212yescomplemented
54C4×C22⋊C4×C101C2211yescharacteristic, complemented
55#343×C101C2212yescomplemented
56#339×C101C2212yescomplemented
57C25×C101—21no—
58H(5,𝔽2)×C101—24no—
59H(5,𝔽2)×C101—42no—
60C2×#41×C101—21no—
61C2×#41×C101—21no—
62C2×#41×C101—21no—
63C2×#41×C101—21no—
64C2×#41×C101—24no—
65C2×#41×C101—42no—
66C2×#41×C101D411yescharacteristic, complemented
67C2×#41×C101D411yescharacteristic, complemented
68C2×#41×C101C2311yescharacteristic
69C2×#41×C101C2311yescharacteristic
70C2×#41×C101C2311yescharacteristic
71C22×Q8×C101D411yescharacteristic, complemented
72C22×D4×C101—24no—
73C22×D4×C101—21no—
74C22×D4×C101—22no—
75C22×D4×C101—22no—
76C22×D4×C101—21no—
77C22×D4×C101—21no—
78C22×D4×C101—24no—
79C22×D4×C101—21no—
80C22×D4×C101—21no—
81C22×D4×C101—21no—
82C22×D4×C101—21no—
83C22×D4×C101—21no—
84C22×D4×C101—42no—
85C22×D4×C101D412yes—
86C22×D4×C101D411yescharacteristic, complemented
87C22×D4×C101C2311yescharacteristic
88C22×D4×C101C2312yes—
89C23×C4×C101—21no—
90C23×C4×C101C2311yescharacteristic
91AGL(1,ℤ/8)×C101—28no—
92AGL(1,ℤ/8)×C101—28no—
93AGL(1,ℤ/8)×C101—24no—
94AGL(1,ℤ/8)×C101—24no—
95AGL(1,ℤ/8)×C101—24no—
96AGL(1,ℤ/8)×C101—24no—
97AGL(1,ℤ/8)×C101—42no—
98AGL(1,ℤ/8)×C101D418yescomplemented
99C2×SD16×C101—28no—
100C2×SD16×C101—22no—
101C2×SD16×C101—22no—
102C2×SD16×C101—22no—
103C2×D8×C101—28no—
104C2×D8×C101—22no—
105C2×D8×C101—22no—
106C2×D8×C101—22no—
107C2×M16×C101—21no—
108C2×M16×C101—24no—
109C2×M16×C101C2312yes—
110C2×M16×C101C2312yes—
111C22×C8×C101—21no—
112#127×C101—22no—
113#127×C101—21no—
114#127×C101—24no—
115#127×C101—42no—
116#124×C101—22no—
117#124×C101—21no—
118#123×C101—22no—
119#123×C101—21no—
120C22⋊Q8×C101—22no—
121C22⋊Q8×C101—21no—
122C22⋊Q8×C101—21no—
123C22⋊Q8×C101D411yescharacteristic, complemented
124C22⋊Q8×C101D411yescharacteristic, complemented
125#121×C101—22no—
126#121×C101—22no—
127#121×C101—22no—
128#121×C101—22no—
129#121×C101—22no—
130#121×C101—21no—
131#121×C101—21no—
132#121×C101—21no—
133#121×C101—21no—
134#121×C101—21no—
135#121×C101—21no—
136#121×C101—22no—
137#121×C101—21no—
138#121×C101—21no—
139#121×C101D411yescharacteristic, complemented
140#121×C101D411yescharacteristic, complemented
141#120×C101—22no—
142#120×C101—22no—
143#120×C101—22no—
144#120×C101—21no—
145#120×C101—22no—
146#120×C101—48no—
147C4×Q8×C101—21no—
148C4×D4×C101—22no—
149C4×D4×C101—22no—
150C4×D4×C101—21no—
151C4×D4×C101—22no—
152C4×D4×C101—21no—
153C4×D4×C101—21no—
154#117×C101—21no—
155#117×C101C2311yescharacteristic
156C2×C4⋊C4×C101—21no—
157C2×C4⋊C4×C101C2311yescharacteristic
158C2×C22⋊C4×C101—22no—
159C2×C22⋊C4×C101—21no—
160C2×C22⋊C4×C101—24no—
161C2×C22⋊C4×C101D412yes—
162C2×C42×C101C2312yes—
163#104×C101—24no—
164#104×C101—24no—
165#104×C101—42no—
166#102×C101—22no—
167#102×C101—22no—
168#100×C101—24no—
169C22⋊C8×C101—21no—
170C22⋊C8×C101—21no—
171#95×C101—21no—
172C24×C101—22no—
173C24×C101—22no—
174C24×C101—21no—
175C24×C101—44no—
176C24×C101—44no—
177C24×C101—41no—
178C24×C101—41no—
179C24×C101—82no—
180C24×C101C2×D411yescharacteristic
181C24×C101C2×D412yes—
182#41×C101—22no—
183#41×C101—22no—
184#41×C101—22no—
185#41×C101—22no—
186#41×C101—22no—
187#41×C101—22no—
188#41×C101—22no—
189#41×C101—44no—
190#41×C101—41no—
191#41×C101—41no—
192#41×C101—44no—
193#41×C101—44no—
194#41×C101—42no—
195#41×C101—42no—
196#41×C101C2×D414yes—
197C2×Q8×C101—21no—
198C2×Q8×C101—22no—
199C2×Q8×C101—41no—
200C2×Q8×C101C2×D411yescharacteristic
201C2×Q8×C101C2×D411yescharacteristic
202C2×Q8×C101C2×D411yescharacteristic
203C2×D4×C101—21no—
204C2×D4×C101—24no—
205C2×D4×C101—24no—
206C2×D4×C101—22no—
207C2×D4×C101—22no—
208C2×D4×C101—22no—
209C2×D4×C101—22no—
210C2×D4×C101—21no—
211C2×D4×C101—21no—
212C2×D4×C101—21no—
213C2×D4×C101—21no—
214C2×D4×C101—21no—
215C2×D4×C101—22no—
216C2×D4×C101—22no—
217C2×D4×C101—22no—
218C2×D4×C101—21no—
219C2×D4×C101—22no—
220C2×D4×C101—21no—
221C2×D4×C101—22no—
222C2×D4×C101—22no—
223C2×D4×C101—22no—
224C2×D4×C101—22no—
225C2×D4×C101—21no—
226C2×D4×C101—21no—
227C2×D4×C101—22no—
228C2×D4×C101—22no—
229C2×D4×C101—22no—
230C2×D4×C101—41no—
231C2×D4×C101—44no—
232C2×D4×C101—44no—
233C2×D4×C101—44no—
234C2×D4×C101—44no—
235C2×D4×C101—42no—
236C2×D4×C101—42no—
237C2×D4×C101—48no—
238C2×D4×C101—44no—
239C2×D4×C101—48no—
240C2×D4×C101—42no—
241C2×D4×C101—42no—
242C2×D4×C101—44no—
243C2×D4×C101—48no—
244C2×D4×C101—41no—
245C2×D4×C101—41no—
246C2×D4×C101—84no—
247C2×D4×C101—84no—
248C2×D4×C101C2×D411yescharacteristic
249C2×D4×C101C2×D411yescharacteristic
250C2×D4×C101C2×D411yescharacteristic
251C2×D4×C101C2×D414yescomplemented
252C22×C4×C101—21no—
253C22×C4×C101—22no—
254C22×C4×C101—22no—
255C22×C4×C101—22no—
256C22×C4×C101—21no—
257C22×C4×C101—22no—
258C22×C4×C101—22no—
259C22×C4×C101—21no—
260C22×C4×C101—21no—
261C22×C4×C101—21no—
262C22×C4×C101—21no—
263C22×C4×C101—44no—
264C22×C4×C101C2×D411yescharacteristic
265C22×C4×C101C2×D411yescharacteristic
266C22×C4×C101C2×D411yescharacteristic
267C22×C4×C101C2×D411yescharacteristic
268C22×C4×C101C2×D411yescharacteristic
269C22×C4×C101C2×D412yes—
270C22×C4×C101C2411yescharacteristic
271SD16×C101—28no—
272SD16×C101—28no—
273SD16×C101—44no—
274D8×C101—28no—
275D8×C101—28no—
276D8×C101—44no—
277M16×C101—24no—
278M16×C101—22no—
279M16×C101—22no—
280M16×C101—22no—
281M16×C101C2×D414yescomplemented
282C2×C8×C101—24no—
283C2×C8×C101—22no—
284C2×C8×C101—22no—
285C4⋊C4×C101—22no—
286C4⋊C4×C101—22no—
287C4⋊C4×C101—21no—
288C4⋊C4×C101—21no—
289C4⋊C4×C101—21no—
290C4⋊C4×C101—21no—
291C4⋊C4×C101C2×D411yescharacteristic
292C4⋊C4×C101C2×D411yescharacteristic
293C22⋊C4×C101—22no—
294C22⋊C4×C101—22no—
295C22⋊C4×C101—24no—
296C22⋊C4×C101—22no—
297C22⋊C4×C101—22no—
298C22⋊C4×C101—22no—
299C22⋊C4×C101—21no—
300C22⋊C4×C101—21no—
301C22⋊C4×C101—21no—
302C22⋊C4×C101—21no—
303C22⋊C4×C101—22no—
304C22⋊C4×C101—22no—
305C22⋊C4×C101—21no—
306C22⋊C4×C101—48no—
307C42×C101—22no—
308C42×C101—21no—
309C42×C101—22no—
310C42×C101—22no—
311C23×C101—21no—
312C23×C101—22no—
313C23×C101—22no—
314C23×C101—22no—
315C23×C101—21no—
316C23×C101—21no—
317C23×C101—24no—
318C23×C101—24no—
319C23×C101—41no—
320C23×C101—42no—
321C23×C101—44no—
322C23×C101—44no—
323C23×C101—44no—
324C23×C101—44no—
325C23×C101—44no—
326C23×C101—42no—
327C23×C101—42no—
328C23×C101—42no—
329C23×C101—42no—
330C23×C101—42no—
331C23×C101—81no—
332C23×C101—82no—
333C23×C101—82no—
334C23×C101—82no—
335C23×C101—82no—
336C23×C101—82no—
337C23×C101—816no—
338C23×C101—82no—
339C23×C101#12011yescharacteristic
340C23×C101#12011yescharacteristic
341C23×C101C22×D411yescharacteristic
342Q8×C101—21no—
343Q8×C101—21no—
344Q8×C101—21no—
345Q8×C101—22no—
346Q8×C101—42no—
347Q8×C101#12012yescomplemented
348D4×C101—24no—
349D4×C101—21no—
350D4×C101—24no—
351D4×C101—21no—
352D4×C101—21no—
353D4×C101—22no—
354D4×C101—24no—
355D4×C101—42no—
356D4×C101—42no—
357D4×C101—44no—
358D4×C101—44no—
359D4×C101—44no—
360D4×C101—42no—
361D4×C101—44no—
362D4×C101—42no—
363D4×C101—42no—
364D4×C101—44no—
365D4×C101—42no—
366D4×C101—41no—
367D4×C101—42no—
368D4×C101—41no—
369D4×C101—42no—
370D4×C101—42no—
371D4×C101—81no—
372D4×C101—82no—
373D4×C101—82no—
374D4×C101—82no—
375D4×C101—82no—
376D4×C101—816no—
377D4×C101#12012yescomplemented
378C2×C4×C101—21no—
379C2×C4×C101—22no—
380C2×C4×C101—21no—
381C2×C4×C101—21no—
382C2×C4×C101—21no—
383C2×C4×C101—21no—
384C2×C4×C101—22no—
385C2×C4×C101—22no—
386C2×C4×C101—24no—
387C2×C4×C101—24no—
388C2×C4×C101—21no—
389C2×C4×C101—22no—
390C2×C4×C101—21no—
391C2×C4×C101—21no—
392C2×C4×C101—21no—
393C2×C4×C101—42no—
394C2×C4×C101—42no—
395C2×C4×C101—42no—
396C2×C4×C101—44no—
397C2×C4×C101—42no—
398C2×C4×C101—42no—
399C2×C4×C101—41no—
400C2×C4×C101—41no—
401C2×C4×C101—42no—
402C2×C4×C101—42no—
403C2×C4×C101—82no—
404C2×C4×C101#12011yescharacteristic
405C2×C4×C101#12011yescharacteristic
406C2×C4×C101C22×D411yescharacteristic
407C2×C4×C101C22×D412yes—
408C2×C4×C101C22×D411yescharacteristic
409C2×C4×C101H(5,𝔽2)12yes—
410C8×C101—24no—
411C8×C101—42no—
412C22×C101—21no—
413C22×C101—21no—
414C22×C101—21no—
415C22×C101—21no—
416C22×C101—21no—
417C22×C101—22no—
418C22×C101—21no—
419C22×C101—21no—
420C22×C101—44no—
421C22×C101—48no—
422C22×C101—41no—
423C22×C101—41no—
424C22×C101—41no—
425C22×C101—41no—
426C22×C101—42no—
427C22×C101—44no—
428C22×C101—42no—
429C22×C101—41no—
430C22×C101—41no—
431C22×C101—41no—
432C22×C101—42no—
433C22×C101—41no—
434C22×C101—84no—
435C22×C101—84no—
436C22×C101—84no—
437C22×C101—88no—
438C22×C101—88no—
439C22×C101—82no—
440C22×C101—82no—
441C22×C101—164no—
442C22×C101#45312yescomplemented
443C22×C101C2×#12011yescharacteristic
444C22×C101D4212yes—
445C4×C101—21no—
446C4×C101—21no—
447C4×C101—22no—
448C4×C101—44no—
449C4×C101—41no—
450C4×C101—41no—
451C4×C101—42no—
452C4×C101—41no—
453C4×C101—41no—
454C4×C101C2×#12011yescharacteristic
455C4×C101#53411yescharacteristic
456C4×C101D4212yes—
457#23876C10111yesmaximal, characteristic, direct product factor, Sylow
458C2×C101—22no—
459C2×C101—22no—
460C2×C101—41no—
461C2×C101—42no—
462C2×C101—81no—
463C2×C101—84no—
464C2×C101—82no—
465C2×C101—81no—
466C2×C101#240311yescharacteristic
467C2×C101C2×#45311yescharacteristic
468C2×C101#302111yescharacteristic
469C22×AGL(1,ℤ/8)C2×C10111yescharacteristic, complemented
470#3488C2×C10111yescharacteristic, complemented
471C2×#453C2×C10112yescomplemented
472#3003C2×C10111yescharacteristic, complemented
473#2433C2×C10111yescharacteristic, complemented
474#2006C2×C10112yescomplemented
475#2002C2×C10112yescomplemented
476#1900C2×C10111yescharacteristic, complemented
477#1883C2×C10112yescomplemented
478#1871C2×C10111yescharacteristic, complemented
479#1789C2×C10111yescharacteristic, complemented
480C101#2387611yescharacteristic, direct product factor, Sylow
481C2×H(5,𝔽2)C22×C10111yescharacteristic, complemented
482C22×#41C22×C10111yescharacteristic
483C23×D4C22×C10111yescharacteristic, complemented
484C2×AGL(1,ℤ/8)—21no—
485C2×AGL(1,ℤ/8)—21no—
486C2×AGL(1,ℤ/8)—28no—
487C2×AGL(1,ℤ/8)C22×C10112yes—
488C2×AGL(1,ℤ/8)C22×C10112yescomplemented
489C2×AGL(1,ℤ/8)C22×C10112yescomplemented
490C22×SD16—21no—
491C22×D8—21no—
492C22×M16C22×C10111yescharacteristic, complemented
493#550—21no—
494#548—21no—
495#546—21no—
496#546—22no—
497D42—22no—
498D42—21no—
499#537—21no—
500#537C22×C10111yescharacteristic, complemented
501#535—21no—
502#535C22×C10111yescharacteristic, complemented
503C2×#127C22×C10112yescomplemented
504#525—21no—
505#525C22×C10111yescharacteristic
506C2×#121—21no—
507C2×#121C22×C10111yescharacteristic
508C2×#120—22no—
509#520C22×C10111yescharacteristic, complemented
510#453—28no—
511#450—21no—
512#450—21no—
513#447—21no—
514#447—21no—
515C2×#104C22×C10112yescomplemented
516C2×#104C22×C10112yescomplemented
517C2×#104C22×C10112yescomplemented
518#418C22×C10112yescomplemented
519C2×#100C22×C10112yescomplemented
520#407C22×C10111yescharacteristic, complemented
521#392—22no—
522#390C22×C10112yescomplemented
523C4×C22⋊C4C22×C10111yescharacteristic, complemented
524#343C22×C10112yescomplemented
525#339C22×C10112yescomplemented
526C25—21no—
527H(5,𝔽2)—24no—
528H(5,𝔽2)—42no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—24no—
534C2×#41—42no—
535C2×#41D4×C10111yescharacteristic, complemented
536C2×#41D4×C10111yescharacteristic, complemented
537C2×#41C23×C10111yescharacteristic
538C2×#41C23×C10111yescharacteristic
539C2×#41C23×C10111yescharacteristic
540C22×Q8D4×C10111yescharacteristic, complemented
541C22×D4—24no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—24no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—42no—
554C22×D4D4×C10112yes—
555C22×D4D4×C10111yescharacteristic, complemented
556C22×D4C23×C10111yescharacteristic
557C22×D4C23×C10112yes—
558C23×C4—21no—
559C23×C4C23×C10111yescharacteristic
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—28no—
562AGL(1,ℤ/8)—24no—
563AGL(1,ℤ/8)—24no—
564AGL(1,ℤ/8)—24no—
565AGL(1,ℤ/8)—24no—
566AGL(1,ℤ/8)—42no—
567AGL(1,ℤ/8)D4×C10118yescomplemented
568C2×SD16—28no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—28no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×M16—21no—
577C2×M16—24no—
578C2×M16C23×C10112yes—
579C2×M16C23×C10112yes—
580C22×C8—21no—
581#127—22no—
582#127—21no—
583#127—24no—
584#127—42no—
585#124—22no—
586#124—21no—
587#123—22no—
588#123—21no—
589C22⋊Q8—22no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8D4×C10111yescharacteristic, complemented
593C22⋊Q8D4×C10111yescharacteristic, complemented
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—22no—
606#121—21no—
607#121—21no—
608#121D4×C10111yescharacteristic, complemented
609#121D4×C10111yescharacteristic, complemented
610#120—22no—
611#120—22no—
612#120—22no—
613#120—21no—
614#120—22no—
615#120—48no—
616C4×Q8—21no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—21no—
620C4×D4—22no—
621C4×D4—21no—
622C4×D4—21no—
623#117—21no—
624#117C23×C10111yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4C23×C10111yescharacteristic
627C2×C22⋊C4—22no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4D4×C10112yes—
631C2×C42C23×C10112yes—
632#104—24no—
633#104—24no—
634#104—42no—
635#102—22no—
636#102—22no—
637#100—24no—
638C22⋊C8—21no—
639C22⋊C8—21no—
640#95—21no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—44no—
645C24—44no—
646C24—41no—
647C24—41no—
648C24—82no—
649C24C2×D4×C10111yescharacteristic
650C24C2×D4×C10112yes—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—44no—
659#41—41no—
660#41—41no—
661#41—44no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41C2×D4×C10114yes—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C2×D4×C10111yescharacteristic
670C2×Q8C2×D4×C10111yescharacteristic
671C2×Q8C2×D4×C10111yescharacteristic
672C2×D4—21no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—84no—
716C2×D4—84no—
717C2×D4C2×D4×C10111yescharacteristic
718C2×D4C2×D4×C10111yescharacteristic
719C2×D4C2×D4×C10111yescharacteristic
720C2×D4C2×D4×C10114yescomplemented
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4C2×D4×C10111yescharacteristic
734C22×C4C2×D4×C10111yescharacteristic
735C22×C4C2×D4×C10111yescharacteristic
736C22×C4C2×D4×C10111yescharacteristic
737C22×C4C2×D4×C10111yescharacteristic
738C22×C4C2×D4×C10112yes—
739C22×C4C24×C10111yescharacteristic
740SD16—28no—
741SD16—28no—
742SD16—44no—
743D8—28no—
744D8—28no—
745D8—44no—
746M16—24no—
747M16—22no—
748M16—22no—
749M16—22no—
750M16C2×D4×C10114yescomplemented
751C2×C8—24no—
752C2×C8—22no—
753C2×C8—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4C2×D4×C10111yescharacteristic
761C4⋊C4C2×D4×C10111yescharacteristic
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—24no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—21no—
775C22⋊C4—48no—
776C42—22no—
777C42—21no—
778C42—22no—
779C42—22no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—24no—
787C23—24no—
788C23—41no—
789C23—42no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—81no—
801C23—82no—
802C23—82no—
803C23—82no—
804C23—82no—
805C23—82no—
806C23—816no—
807C23—82no—
808C23#120×C10111yescharacteristic
809C23#120×C10111yescharacteristic
810C23C22×D4×C10111yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—42no—
816Q8#120×C10112yescomplemented
817D4—24no—
818D4—21no—
819D4—24no—
820D4—21no—
821D4—21no—
822D4—22no—
823D4—24no—
824D4—42no—
825D4—42no—
826D4—44no—
827D4—44no—
828D4—44no—
829D4—42no—
830D4—44no—
831D4—44no—
832D4—42no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—42no—
837D4—41no—
838D4—42no—
839D4—42no—
840D4—82no—
841D4—81no—
842D4—82no—
843D4—82no—
844D4—82no—
845D4—816no—
846D4#120×C10112yescomplemented
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—82no—
873C2×C4#120×C10111yescharacteristic
874C2×C4#120×C10111yescharacteristic
875C2×C4C22×D4×C10111yescharacteristic
876C2×C4C22×D4×C10112yes—
877C2×C4C22×D4×C10111yescharacteristic
878C2×C4H(5,𝔽2)×C10112yes—
879C8—24no—
880C8—42no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—21no—
888C22—21no—
889C22—44no—
890C22—48no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—42no—
896C22—44no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—84no—
904C22—84no—
905C22—84no—
906C22—88no—
907C22—88no—
908C22—82no—
909C22—82no—
910C22—164no—
911C22#453×C10112yescomplemented
912C22C2×#120×C10111yescharacteristic
913C22D42×C10112yes—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—44no—
918C4—41no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—41no—
923C4C2×#120×C10111yescharacteristic
924C4#534×C10111yescharacteristic
925C4D42×C10112yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—42no—
930C2—84no—
931C2—81no—
932C2—82no—
933C2—81no—
934C2C101×#240311yescharacteristic
935C2C2×#453×C10111yescharacteristic
936C2C101×#302111yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C101C2semidirect
2. C101×#3488C2semidirect
3. C2×#453×C101C2semidirect
4. C101×#3003C2semidirect
5. C101×#2433C2semidirect
6. C101×#2006C2semidirect
7. C101×#2002C2semidirect
8. C101×#1900C2semidirect
9. C101×#1883C2semidirect
10. C101×#1871C2semidirect
11. C101×#1789C2semidirect
12. C2×H(5,𝔽2)×C101C22semidirect
14. C23×D4×C101C22semidirect
19. C2×AGL(1,ℤ/8)×C101C22semidirect
20. C2×AGL(1,ℤ/8)×C101C22semidirect
23. C22×M16×C101C22semidirect
31. #537×C101C22semidirect
33. #535×C101C22semidirect
34. C2×#127×C101C22semidirect
40. #520×C101C22semidirect
46. C2×#104×C101C22semidirect
47. C2×#104×C101C22semidirect
48. C2×#104×C101C22semidirect
49. #418×C101C22semidirect
50. C2×#100×C101C22semidirect
51. #407×C101C22semidirect
53. #390×C101C22semidirect
54. C4×C22⋊C4×C101C22semidirect
55. #343×C101C22semidirect
56. #339×C101C22semidirect
66. C2×#41×C101D4semidirect
67. C2×#41×C101D4semidirect
71. C22×Q8×C101D4semidirect
86. C22×D4×C101D4semidirect
98. AGL(1,ℤ/8)×C101D4semidirect
123. C22⋊Q8×C101D4semidirect
124. C22⋊Q8×C101D4semidirect
139. #121×C101D4semidirect
140. #121×C101D4semidirect
251. C2×D4×C101C2×D4semidirect
281. M16×C101C2×D4semidirect
347. Q8×C101#120semidirect
377. D4×C101#120semidirect
442. C22×C101#453semidirect
457. #23876C101direct (N × H)
469. C22×AGL(1,ℤ/8)C2×C101semidirect
470. #3488C2×C101semidirect
471. C2×#453C2×C101semidirect
472. #3003C2×C101semidirect
473. #2433C2×C101semidirect
474. #2006C2×C101semidirect
475. #2002C2×C101semidirect
476. #1900C2×C101semidirect
477. #1883C2×C101semidirect
478. #1871C2×C101semidirect
479. #1789C2×C101semidirect
480. C101#23876direct (N × H)
481. C2×H(5,𝔽2)C22×C101semidirect
483. C23×D4C22×C101semidirect
488. C2×AGL(1,ℤ/8)C22×C101semidirect
489. C2×AGL(1,ℤ/8)C22×C101semidirect
492. C22×M16C22×C101semidirect
500. #537C22×C101semidirect
502. #535C22×C101semidirect
503. C2×#127C22×C101semidirect
509. #520C22×C101semidirect
515. C2×#104C22×C101semidirect
516. C2×#104C22×C101semidirect
517. C2×#104C22×C101semidirect
518. #418C22×C101semidirect
519. C2×#100C22×C101semidirect
520. #407C22×C101semidirect
522. #390C22×C101semidirect
523. C4×C22⋊C4C22×C101semidirect
524. #343C22×C101semidirect
525. #339C22×C101semidirect
535. C2×#41D4×C101semidirect
536. C2×#41D4×C101semidirect
540. C22×Q8D4×C101semidirect
555. C22×D4D4×C101semidirect
567. AGL(1,ℤ/8)D4×C101semidirect
592. C22⋊Q8D4×C101semidirect
593. C22⋊Q8D4×C101semidirect
608. #121D4×C101semidirect
609. #121D4×C101semidirect
720. C2×D4C2×D4×C101semidirect
750. M16C2×D4×C101semidirect
816. Q8#120×C101semidirect
846. D4#120×C101semidirect
911. C22#453×C101semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1012
C101×#34882
C2×#453×C1012
C101×#30032
C101×#24332
C101×#20062
C101×#20022
C101×#19002
C101×#18832
C101×#18712
C101×#17892
#23876101