Finite Group Databasebeta

← C103×#23876 #39929151

Subgroups — C103×#23876 #39929151

Order 26368.

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)×C103C211yesmaximal, characteristic, complemented
2C103×#3488C211yesmaximal, characteristic, complemented
3C2×#453×C103C212yesmaximal, complemented
4C103×#3003C211yesmaximal, characteristic, complemented
5C103×#2433C211yesmaximal, characteristic, complemented
6C103×#2006C212yesmaximal, complemented
7C103×#2002C212yesmaximal, complemented
8C103×#1900C211yesmaximal, characteristic, complemented
9C103×#1883C212yesmaximal, complemented
10C103×#1871C211yesmaximal, characteristic, complemented
11C103×#1789C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C103C2211yescharacteristic, complemented
13C22×#41×C103C2211yescharacteristic
14C23×D4×C103C2211yescharacteristic, complemented
15C2×AGL(1,ℤ/8)×C103—21no—
16C2×AGL(1,ℤ/8)×C103—21no—
17C2×AGL(1,ℤ/8)×C103—28no—
18C2×AGL(1,ℤ/8)×C103C2212yes—
19C2×AGL(1,ℤ/8)×C103C2212yescomplemented
20C2×AGL(1,ℤ/8)×C103C2212yescomplemented
21C22×SD16×C103—21no—
22C22×D8×C103—21no—
23C22×M16×C103C2211yescharacteristic, complemented
24#550×C103—21no—
25#548×C103—21no—
26#546×C103—21no—
27#546×C103—22no—
28D42×C103—22no—
29D42×C103—21no—
30#537×C103—21no—
31#537×C103C2211yescharacteristic, complemented
32#535×C103—21no—
33#535×C103C2211yescharacteristic, complemented
34C2×#127×C103C2212yescomplemented
35#525×C103—21no—
36#525×C103C2211yescharacteristic
37C2×#121×C103—21no—
38C2×#121×C103C2211yescharacteristic
39C2×#120×C103—22no—
40#520×C103C2211yescharacteristic, complemented
41#453×C103—28no—
42#450×C103—21no—
43#450×C103—21no—
44#447×C103—21no—
45#447×C103—21no—
46C2×#104×C103C2212yescomplemented
47C2×#104×C103C2212yescomplemented
48C2×#104×C103C2212yescomplemented
49#418×C103C2212yescomplemented
50C2×#100×C103C2212yescomplemented
51#407×C103C2211yescharacteristic, complemented
52#392×C103—22no—
53#390×C103C2212yescomplemented
54C4×C22⋊C4×C103C2211yescharacteristic, complemented
55#343×C103C2212yescomplemented
56#339×C103C2212yescomplemented
57C25×C103—21no—
58H(5,𝔽2)×C103—24no—
59H(5,𝔽2)×C103—42no—
60C2×#41×C103—21no—
61C2×#41×C103—21no—
62C2×#41×C103—21no—
63C2×#41×C103—21no—
64C2×#41×C103—24no—
65C2×#41×C103—42no—
66C2×#41×C103D411yescharacteristic, complemented
67C2×#41×C103D411yescharacteristic, complemented
68C2×#41×C103C2311yescharacteristic
69C2×#41×C103C2311yescharacteristic
70C2×#41×C103C2311yescharacteristic
71C22×Q8×C103D411yescharacteristic, complemented
72C22×D4×C103—24no—
73C22×D4×C103—21no—
74C22×D4×C103—22no—
75C22×D4×C103—22no—
76C22×D4×C103—21no—
77C22×D4×C103—21no—
78C22×D4×C103—24no—
79C22×D4×C103—21no—
80C22×D4×C103—21no—
81C22×D4×C103—21no—
82C22×D4×C103—21no—
83C22×D4×C103—21no—
84C22×D4×C103—42no—
85C22×D4×C103D412yes—
86C22×D4×C103D411yescharacteristic, complemented
87C22×D4×C103C2311yescharacteristic
88C22×D4×C103C2312yes—
89C23×C4×C103—21no—
90C23×C4×C103C2311yescharacteristic
91AGL(1,ℤ/8)×C103—28no—
92AGL(1,ℤ/8)×C103—28no—
93AGL(1,ℤ/8)×C103—24no—
94AGL(1,ℤ/8)×C103—24no—
95AGL(1,ℤ/8)×C103—24no—
96AGL(1,ℤ/8)×C103—24no—
97AGL(1,ℤ/8)×C103—42no—
98AGL(1,ℤ/8)×C103D418yescomplemented
99C2×SD16×C103—28no—
100C2×SD16×C103—22no—
101C2×SD16×C103—22no—
102C2×SD16×C103—22no—
103C2×D8×C103—28no—
104C2×D8×C103—22no—
105C2×D8×C103—22no—
106C2×D8×C103—22no—
107C2×M16×C103—21no—
108C2×M16×C103—24no—
109C2×M16×C103C2312yes—
110C2×M16×C103C2312yes—
111C22×C8×C103—21no—
112#127×C103—22no—
113#127×C103—21no—
114#127×C103—24no—
115#127×C103—42no—
116#124×C103—22no—
117#124×C103—21no—
118#123×C103—22no—
119#123×C103—21no—
120C22⋊Q8×C103—22no—
121C22⋊Q8×C103—21no—
122C22⋊Q8×C103—21no—
123C22⋊Q8×C103D411yescharacteristic, complemented
124C22⋊Q8×C103D411yescharacteristic, complemented
125#121×C103—22no—
126#121×C103—22no—
127#121×C103—22no—
128#121×C103—22no—
129#121×C103—22no—
130#121×C103—21no—
131#121×C103—21no—
132#121×C103—21no—
133#121×C103—21no—
134#121×C103—21no—
135#121×C103—21no—
136#121×C103—22no—
137#121×C103—21no—
138#121×C103—21no—
139#121×C103D411yescharacteristic, complemented
140#121×C103D411yescharacteristic, complemented
141#120×C103—22no—
142#120×C103—22no—
143#120×C103—22no—
144#120×C103—21no—
145#120×C103—22no—
146#120×C103—48no—
147C4×Q8×C103—21no—
148C4×D4×C103—22no—
149C4×D4×C103—22no—
150C4×D4×C103—21no—
151C4×D4×C103—22no—
152C4×D4×C103—21no—
153C4×D4×C103—21no—
154#117×C103—21no—
155#117×C103C2311yescharacteristic
156C2×C4⋊C4×C103—21no—
157C2×C4⋊C4×C103C2311yescharacteristic
158C2×C22⋊C4×C103—22no—
159C2×C22⋊C4×C103—21no—
160C2×C22⋊C4×C103—24no—
161C2×C22⋊C4×C103D412yes—
162C2×C42×C103C2312yes—
163#104×C103—24no—
164#104×C103—24no—
165#104×C103—42no—
166#102×C103—22no—
167#102×C103—22no—
168#100×C103—24no—
169C22⋊C8×C103—21no—
170C22⋊C8×C103—21no—
171#95×C103—21no—
172C24×C103—22no—
173C24×C103—22no—
174C24×C103—21no—
175C24×C103—44no—
176C24×C103—44no—
177C24×C103—41no—
178C24×C103—41no—
179C24×C103—82no—
180C24×C103C2×D411yescharacteristic
181C24×C103C2×D412yes—
182#41×C103—22no—
183#41×C103—22no—
184#41×C103—22no—
185#41×C103—22no—
186#41×C103—22no—
187#41×C103—22no—
188#41×C103—22no—
189#41×C103—44no—
190#41×C103—41no—
191#41×C103—41no—
192#41×C103—44no—
193#41×C103—44no—
194#41×C103—42no—
195#41×C103—42no—
196#41×C103C2×D414yes—
197C2×Q8×C103—21no—
198C2×Q8×C103—22no—
199C2×Q8×C103—41no—
200C2×Q8×C103C2×D411yescharacteristic
201C2×Q8×C103C2×D411yescharacteristic
202C2×Q8×C103C2×D411yescharacteristic
203C2×D4×C103—21no—
204C2×D4×C103—24no—
205C2×D4×C103—24no—
206C2×D4×C103—22no—
207C2×D4×C103—22no—
208C2×D4×C103—22no—
209C2×D4×C103—22no—
210C2×D4×C103—21no—
211C2×D4×C103—21no—
212C2×D4×C103—21no—
213C2×D4×C103—21no—
214C2×D4×C103—21no—
215C2×D4×C103—22no—
216C2×D4×C103—22no—
217C2×D4×C103—22no—
218C2×D4×C103—21no—
219C2×D4×C103—22no—
220C2×D4×C103—21no—
221C2×D4×C103—22no—
222C2×D4×C103—22no—
223C2×D4×C103—22no—
224C2×D4×C103—22no—
225C2×D4×C103—21no—
226C2×D4×C103—21no—
227C2×D4×C103—22no—
228C2×D4×C103—22no—
229C2×D4×C103—22no—
230C2×D4×C103—41no—
231C2×D4×C103—44no—
232C2×D4×C103—44no—
233C2×D4×C103—44no—
234C2×D4×C103—44no—
235C2×D4×C103—42no—
236C2×D4×C103—42no—
237C2×D4×C103—48no—
238C2×D4×C103—44no—
239C2×D4×C103—48no—
240C2×D4×C103—42no—
241C2×D4×C103—42no—
242C2×D4×C103—44no—
243C2×D4×C103—48no—
244C2×D4×C103—41no—
245C2×D4×C103—41no—
246C2×D4×C103—84no—
247C2×D4×C103—84no—
248C2×D4×C103C2×D411yescharacteristic
249C2×D4×C103C2×D411yescharacteristic
250C2×D4×C103C2×D411yescharacteristic
251C2×D4×C103C2×D414yescomplemented
252C22×C4×C103—21no—
253C22×C4×C103—22no—
254C22×C4×C103—22no—
255C22×C4×C103—22no—
256C22×C4×C103—21no—
257C22×C4×C103—22no—
258C22×C4×C103—22no—
259C22×C4×C103—21no—
260C22×C4×C103—21no—
261C22×C4×C103—21no—
262C22×C4×C103—21no—
263C22×C4×C103—44no—
264C22×C4×C103C2×D411yescharacteristic
265C22×C4×C103C2×D411yescharacteristic
266C22×C4×C103C2×D411yescharacteristic
267C22×C4×C103C2×D411yescharacteristic
268C22×C4×C103C2×D411yescharacteristic
269C22×C4×C103C2×D412yes—
270C22×C4×C103C2411yescharacteristic
271SD16×C103—28no—
272SD16×C103—28no—
273SD16×C103—44no—
274D8×C103—28no—
275D8×C103—28no—
276D8×C103—44no—
277M16×C103—24no—
278M16×C103—22no—
279M16×C103—22no—
280M16×C103—22no—
281M16×C103C2×D414yescomplemented
282C2×C8×C103—24no—
283C2×C8×C103—22no—
284C2×C8×C103—22no—
285C4⋊C4×C103—22no—
286C4⋊C4×C103—22no—
287C4⋊C4×C103—21no—
288C4⋊C4×C103—21no—
289C4⋊C4×C103—21no—
290C4⋊C4×C103—21no—
291C4⋊C4×C103C2×D411yescharacteristic
292C4⋊C4×C103C2×D411yescharacteristic
293C22⋊C4×C103—22no—
294C22⋊C4×C103—22no—
295C22⋊C4×C103—24no—
296C22⋊C4×C103—22no—
297C22⋊C4×C103—22no—
298C22⋊C4×C103—22no—
299C22⋊C4×C103—21no—
300C22⋊C4×C103—21no—
301C22⋊C4×C103—21no—
302C22⋊C4×C103—21no—
303C22⋊C4×C103—22no—
304C22⋊C4×C103—22no—
305C22⋊C4×C103—21no—
306C22⋊C4×C103—48no—
307C42×C103—22no—
308C42×C103—21no—
309C42×C103—22no—
310C42×C103—22no—
311C23×C103—21no—
312C23×C103—22no—
313C23×C103—22no—
314C23×C103—22no—
315C23×C103—21no—
316C23×C103—21no—
317C23×C103—24no—
318C23×C103—24no—
319C23×C103—41no—
320C23×C103—42no—
321C23×C103—44no—
322C23×C103—44no—
323C23×C103—44no—
324C23×C103—44no—
325C23×C103—44no—
326C23×C103—42no—
327C23×C103—42no—
328C23×C103—42no—
329C23×C103—42no—
330C23×C103—42no—
331C23×C103—81no—
332C23×C103—82no—
333C23×C103—82no—
334C23×C103—82no—
335C23×C103—82no—
336C23×C103—82no—
337C23×C103—816no—
338C23×C103—82no—
339C23×C103#12011yescharacteristic
340C23×C103#12011yescharacteristic
341C23×C103C22×D411yescharacteristic
342Q8×C103—21no—
343Q8×C103—21no—
344Q8×C103—21no—
345Q8×C103—22no—
346Q8×C103—42no—
347Q8×C103#12012yescomplemented
348D4×C103—24no—
349D4×C103—21no—
350D4×C103—24no—
351D4×C103—21no—
352D4×C103—21no—
353D4×C103—22no—
354D4×C103—24no—
355D4×C103—42no—
356D4×C103—42no—
357D4×C103—44no—
358D4×C103—44no—
359D4×C103—44no—
360D4×C103—42no—
361D4×C103—44no—
362D4×C103—42no—
363D4×C103—42no—
364D4×C103—44no—
365D4×C103—42no—
366D4×C103—41no—
367D4×C103—42no—
368D4×C103—41no—
369D4×C103—42no—
370D4×C103—42no—
371D4×C103—81no—
372D4×C103—82no—
373D4×C103—82no—
374D4×C103—82no—
375D4×C103—82no—
376D4×C103—816no—
377D4×C103#12012yescomplemented
378C2×C4×C103—21no—
379C2×C4×C103—22no—
380C2×C4×C103—21no—
381C2×C4×C103—21no—
382C2×C4×C103—21no—
383C2×C4×C103—21no—
384C2×C4×C103—22no—
385C2×C4×C103—22no—
386C2×C4×C103—24no—
387C2×C4×C103—24no—
388C2×C4×C103—21no—
389C2×C4×C103—22no—
390C2×C4×C103—21no—
391C2×C4×C103—21no—
392C2×C4×C103—21no—
393C2×C4×C103—42no—
394C2×C4×C103—42no—
395C2×C4×C103—42no—
396C2×C4×C103—44no—
397C2×C4×C103—42no—
398C2×C4×C103—42no—
399C2×C4×C103—41no—
400C2×C4×C103—41no—
401C2×C4×C103—42no—
402C2×C4×C103—42no—
403C2×C4×C103—82no—
404C2×C4×C103#12011yescharacteristic
405C2×C4×C103#12011yescharacteristic
406C2×C4×C103C22×D411yescharacteristic
407C2×C4×C103C22×D412yes—
408C2×C4×C103C22×D411yescharacteristic
409C2×C4×C103H(5,𝔽2)12yes—
410C8×C103—24no—
411C8×C103—42no—
412C22×C103—21no—
413C22×C103—21no—
414C22×C103—21no—
415C22×C103—21no—
416C22×C103—21no—
417C22×C103—22no—
418C22×C103—21no—
419C22×C103—21no—
420C22×C103—44no—
421C22×C103—48no—
422C22×C103—41no—
423C22×C103—41no—
424C22×C103—41no—
425C22×C103—41no—
426C22×C103—42no—
427C22×C103—44no—
428C22×C103—42no—
429C22×C103—41no—
430C22×C103—41no—
431C22×C103—41no—
432C22×C103—42no—
433C22×C103—41no—
434C22×C103—84no—
435C22×C103—84no—
436C22×C103—84no—
437C22×C103—88no—
438C22×C103—88no—
439C22×C103—82no—
440C22×C103—82no—
441C22×C103—164no—
442C22×C103#45312yescomplemented
443C22×C103C2×#12011yescharacteristic
444C22×C103D4212yes—
445C4×C103—21no—
446C4×C103—21no—
447C4×C103—22no—
448C4×C103—44no—
449C4×C103—41no—
450C4×C103—41no—
451C4×C103—42no—
452C4×C103—41no—
453C4×C103—41no—
454C4×C103C2×#12011yescharacteristic
455C4×C103#53411yescharacteristic
456C4×C103D4212yes—
457#23876C10311yesmaximal, characteristic, direct product factor, Sylow
458C2×C103—22no—
459C2×C103—22no—
460C2×C103—41no—
461C2×C103—42no—
462C2×C103—81no—
463C2×C103—84no—
464C2×C103—82no—
465C2×C103—81no—
466C2×C103#240311yescharacteristic
467C2×C103C2×#45311yescharacteristic
468C2×C103#302111yescharacteristic
469C22×AGL(1,ℤ/8)C2×C10311yescharacteristic, complemented
470#3488C2×C10311yescharacteristic, complemented
471C2×#453C2×C10312yescomplemented
472#3003C2×C10311yescharacteristic, complemented
473#2433C2×C10311yescharacteristic, complemented
474#2006C2×C10312yescomplemented
475#2002C2×C10312yescomplemented
476#1900C2×C10311yescharacteristic, complemented
477#1883C2×C10312yescomplemented
478#1871C2×C10311yescharacteristic, complemented
479#1789C2×C10311yescharacteristic, complemented
480C103#2387611yescharacteristic, direct product factor, Sylow
481C2×H(5,𝔽2)C22×C10311yescharacteristic, complemented
482C22×#41C22×C10311yescharacteristic
483C23×D4C22×C10311yescharacteristic, 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×C10312yes—
488C2×AGL(1,ℤ/8)C22×C10312yescomplemented
489C2×AGL(1,ℤ/8)C22×C10312yescomplemented
490C22×SD16—21no—
491C22×D8—21no—
492C22×M16C22×C10311yescharacteristic, complemented
493#550—21no—
494#548—21no—
495#546—21no—
496#546—22no—
497D42—22no—
498D42—21no—
499#537—21no—
500#537C22×C10311yescharacteristic, complemented
501#535—21no—
502#535C22×C10311yescharacteristic, complemented
503C2×#127C22×C10312yescomplemented
504#525—21no—
505#525C22×C10311yescharacteristic
506C2×#121—21no—
507C2×#121C22×C10311yescharacteristic
508C2×#120—22no—
509#520C22×C10311yescharacteristic, complemented
510#453—28no—
511#450—21no—
512#450—21no—
513#447—21no—
514#447—21no—
515C2×#104C22×C10312yescomplemented
516C2×#104C22×C10312yescomplemented
517C2×#104C22×C10312yescomplemented
518#418C22×C10312yescomplemented
519C2×#100C22×C10312yescomplemented
520#407C22×C10311yescharacteristic, complemented
521#392—22no—
522#390C22×C10312yescomplemented
523C4×C22⋊C4C22×C10311yescharacteristic, complemented
524#343C22×C10312yescomplemented
525#339C22×C10312yescomplemented
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×C10311yescharacteristic, complemented
536C2×#41D4×C10311yescharacteristic, complemented
537C2×#41C23×C10311yescharacteristic
538C2×#41C23×C10311yescharacteristic
539C2×#41C23×C10311yescharacteristic
540C22×Q8D4×C10311yescharacteristic, 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×C10312yes—
555C22×D4D4×C10311yescharacteristic, complemented
556C22×D4C23×C10311yescharacteristic
557C22×D4C23×C10312yes—
558C23×C4—21no—
559C23×C4C23×C10311yescharacteristic
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×C10318yescomplemented
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×C10312yes—
579C2×M16C23×C10312yes—
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×C10311yescharacteristic, complemented
593C22⋊Q8D4×C10311yescharacteristic, 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×C10311yescharacteristic, complemented
609#121D4×C10311yescharacteristic, 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×C10311yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4C23×C10311yescharacteristic
627C2×C22⋊C4—22no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4D4×C10312yes—
631C2×C42C23×C10312yes—
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×C10311yescharacteristic
650C24C2×D4×C10312yes—
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×C10314yes—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C2×D4×C10311yescharacteristic
670C2×Q8C2×D4×C10311yescharacteristic
671C2×Q8C2×D4×C10311yescharacteristic
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×C10311yescharacteristic
718C2×D4C2×D4×C10311yescharacteristic
719C2×D4C2×D4×C10311yescharacteristic
720C2×D4C2×D4×C10314yescomplemented
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×C10311yescharacteristic
734C22×C4C2×D4×C10311yescharacteristic
735C22×C4C2×D4×C10311yescharacteristic
736C22×C4C2×D4×C10311yescharacteristic
737C22×C4C2×D4×C10311yescharacteristic
738C22×C4C2×D4×C10312yes—
739C22×C4C24×C10311yescharacteristic
740SD16—28no—
741SD16—28no—
742SD16—44no—
743D8—28no—
744D8—28no—
745D8—44no—
746M16—24no—
747M16—22no—
748M16—22no—
749M16—22no—
750M16C2×D4×C10314yescomplemented
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×C10311yescharacteristic
761C4⋊C4C2×D4×C10311yescharacteristic
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×C10311yescharacteristic
809C23#120×C10311yescharacteristic
810C23C22×D4×C10311yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—42no—
816Q8#120×C10312yescomplemented
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×C10312yescomplemented
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×C10311yescharacteristic
874C2×C4#120×C10311yescharacteristic
875C2×C4C22×D4×C10311yescharacteristic
876C2×C4C22×D4×C10312yes—
877C2×C4C22×D4×C10311yescharacteristic
878C2×C4H(5,𝔽2)×C10312yes—
879C8—24no—
880C8—42no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—44no—
890C22—48no—
891C22—41no—
892C22—41no—
893C22—42no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—44no—
903C22—84no—
904C22—84no—
905C22—84no—
906C22—88no—
907C22—88no—
908C22—82no—
909C22—82no—
910C22—164no—
911C22#453×C10312yescomplemented
912C22C2×#120×C10311yescharacteristic
913C22D42×C10312yes—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—44no—
918C4—42no—
919C4—41no—
920C4—41no—
921C4—41no—
922C4—41no—
923C4C2×#120×C10311yescharacteristic
924C4#534×C10311yescharacteristic
925C4D42×C10312yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—42no—
930C2—84no—
931C2—81no—
932C2—82no—
933C2—81no—
934C2C103×#240311yescharacteristic
935C2C2×#453×C10311yescharacteristic
936C2C103×#302111yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C103C2semidirect
2. C103×#3488C2semidirect
3. C2×#453×C103C2semidirect
4. C103×#3003C2semidirect
5. C103×#2433C2semidirect
6. C103×#2006C2semidirect
7. C103×#2002C2semidirect
8. C103×#1900C2semidirect
9. C103×#1883C2semidirect
10. C103×#1871C2semidirect
11. C103×#1789C2semidirect
12. C2×H(5,𝔽2)×C103C22semidirect
14. C23×D4×C103C22semidirect
19. C2×AGL(1,ℤ/8)×C103C22semidirect
20. C2×AGL(1,ℤ/8)×C103C22semidirect
23. C22×M16×C103C22semidirect
31. #537×C103C22semidirect
33. #535×C103C22semidirect
34. C2×#127×C103C22semidirect
40. #520×C103C22semidirect
46. C2×#104×C103C22semidirect
47. C2×#104×C103C22semidirect
48. C2×#104×C103C22semidirect
49. #418×C103C22semidirect
50. C2×#100×C103C22semidirect
51. #407×C103C22semidirect
53. #390×C103C22semidirect
54. C4×C22⋊C4×C103C22semidirect
55. #343×C103C22semidirect
56. #339×C103C22semidirect
66. C2×#41×C103D4semidirect
67. C2×#41×C103D4semidirect
71. C22×Q8×C103D4semidirect
86. C22×D4×C103D4semidirect
98. AGL(1,ℤ/8)×C103D4semidirect
123. C22⋊Q8×C103D4semidirect
124. C22⋊Q8×C103D4semidirect
139. #121×C103D4semidirect
140. #121×C103D4semidirect
251. C2×D4×C103C2×D4semidirect
281. M16×C103C2×D4semidirect
347. Q8×C103#120semidirect
377. D4×C103#120semidirect
442. C22×C103#453semidirect
457. #23876C103direct (N × H)
469. C22×AGL(1,ℤ/8)C2×C103semidirect
470. #3488C2×C103semidirect
471. C2×#453C2×C103semidirect
472. #3003C2×C103semidirect
473. #2433C2×C103semidirect
474. #2006C2×C103semidirect
475. #2002C2×C103semidirect
476. #1900C2×C103semidirect
477. #1883C2×C103semidirect
478. #1871C2×C103semidirect
479. #1789C2×C103semidirect
480. C103#23876direct (N × H)
481. C2×H(5,𝔽2)C22×C103semidirect
483. C23×D4C22×C103semidirect
488. C2×AGL(1,ℤ/8)C22×C103semidirect
489. C2×AGL(1,ℤ/8)C22×C103semidirect
492. C22×M16C22×C103semidirect
500. #537C22×C103semidirect
502. #535C22×C103semidirect
503. C2×#127C22×C103semidirect
509. #520C22×C103semidirect
515. C2×#104C22×C103semidirect
516. C2×#104C22×C103semidirect
517. C2×#104C22×C103semidirect
518. #418C22×C103semidirect
519. C2×#100C22×C103semidirect
520. #407C22×C103semidirect
522. #390C22×C103semidirect
523. C4×C22⋊C4C22×C103semidirect
524. #343C22×C103semidirect
525. #339C22×C103semidirect
535. C2×#41D4×C103semidirect
536. C2×#41D4×C103semidirect
540. C22×Q8D4×C103semidirect
555. C22×D4D4×C103semidirect
567. AGL(1,ℤ/8)D4×C103semidirect
592. C22⋊Q8D4×C103semidirect
593. C22⋊Q8D4×C103semidirect
608. #121D4×C103semidirect
609. #121D4×C103semidirect
720. C2×D4C2×D4×C103semidirect
750. M16C2×D4×C103semidirect
816. Q8#120×C103semidirect
846. D4#120×C103semidirect
911. C22#453×C103semidirect

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)×C1032
C103×#34882
C2×#453×C1032
C103×#30032
C103×#24332
C103×#20062
C103×#20022
C103×#19002
C103×#18832
C103×#18712
C103×#17892
#23876103