Finite Group Databasebeta

← C101×#23863 #38806014

Subgroups — C101×#23863 #38806014

Order 25856.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C101C211yesmaximal, characteristic, complemented
2C2×#546×C101C211yesmaximal, characteristic, complemented
3C2×#452×C101C211yesmaximal, characteristic, complemented
4C2×#452×C101C211yesmaximal, characteristic, complemented
5C2×#449×C101C211yesmaximal, characteristic, complemented
6C101×#2407C211yesmaximal, characteristic, complemented
7C101×#2015C211yesmaximal, characteristic, complemented
8C101×#2012C211yesmaximal, characteristic, complemented
9C101×#2000C211yesmaximal, characteristic, complemented
10C101×#1999C211yesmaximal, characteristic, complemented
11C101×#1894C211yesmaximal, characteristic, complemented
12C101×#1879C211yesmaximal, characteristic, complemented
13C101×#1877C211yesmaximal, characteristic, complemented
14C101×#1870C211yesmaximal, characteristic, complemented
15C101×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C22×#41×C101C2211yescharacteristic
18C23×D4×C101C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C101—24no—
20C2×AGL(1,ℤ/8)×C101—24no—
21C2×AGL(1,ℤ/8)×C101—24no—
22C22×Q16×C101C2211yescharacteristic, complemented
23C22×SD16×C101C2211yescharacteristic
24C22×SD16×C101C2211yescharacteristic
25C22×SD16×C101C2211yescharacteristic, complemented
26C22×D8×C101C2211yescharacteristic
27C22×D8×C101C2211yescharacteristic
28C22×M16×C101C2211yescharacteristic
29#546×C101—24no—
30#546×C101—24no—
31C2×#124×C101C2211yescharacteristic
32C2×#123×C101—21no—
33C2×C22⋊Q8×C101C2211yescharacteristic
34C2×C22⋊Q8×C101C2211yescharacteristic, complemented
35C2×#121×C101—21no—
36C2×#121×C101C2211yescharacteristic
37C2×#121×C101C2211yescharacteristic, complemented
38C2×#120×C101—21no—
39C2×C4×D4×C101C2211yescharacteristic
40C2×C4×D4×C101C2211yescharacteristic
41C22×C22⋊C4×C101—21no—
42#452×C101—24no—
43#452×C101—24no—
44#449×C101—24no—
45C2×#103×C101C2211yescharacteristic, complemented
46C2×#103×C101C2211yescharacteristic, complemented
47C2×#103×C101C2211yescharacteristic, complemented
48C2×#102×C101C2211yescharacteristic
49C2×#102×C101C2211yescharacteristic
50C2×#102×C101C2211yescharacteristic
51C2×#102×C101C2211yescharacteristic
52C2×#102×C101C2211yescharacteristic, complemented
53C2×C22⋊C8×C101C2211yescharacteristic
54C2×C22⋊C8×C101C2211yescharacteristic, complemented
55C2×C22⋊C8×C101C2211yescharacteristic, complemented
56#394×C101—21no—
57#392×C101—21no—
58#391×C101C2211yescharacteristic, complemented
59#390×C101C2211yescharacteristic, complemented
60#386×C101—21no—
61#385×C101—21no—
62#380×C101C2211yescharacteristic
63#340×C101C2211yescharacteristic, complemented
64#340×C101C2211yescharacteristic, complemented
65#336×C101C2211yescharacteristic, complemented
66#336×C101C2211yescharacteristic, complemented
67C25×C101—21no—
68C2×#41×C101—22no—
69C2×#41×C101—22no—
70C2×#41×C101—22no—
71C2×#41×C101—22no—
72C2×#41×C101—22no—
73C2×#41×C101—22no—
74C2×#41×C101—22no—
75C2×#41×C101—22no—
76C2×#41×C101—41no—
77C2×#41×C101—41no—
78C2×#41×C101—41no—
79C2×#41×C101—41no—
80C22×Q8×C101C2311yescharacteristic
81C22×Q8×C101C2311yescharacteristic
82C22×D4×C101—22no—
83C22×D4×C101—22no—
84C22×D4×C101—21no—
85C22×D4×C101—21no—
86C22×D4×C101—21no—
87C22×D4×C101—21no—
88C22×D4×C101—21no—
89C22×D4×C101—22no—
90C22×D4×C101—41no—
91C22×D4×C101—41no—
92C22×D4×C101D411yescharacteristic
93C22×D4×C101D414yescomplemented
94C22×D4×C101C2311yescharacteristic
95C22×D4×C101C2311yescharacteristic
96C22×D4×C101C2311yescharacteristic
97C23×C4×C101—21no—
98C23×C4×C101—21no—
99C23×C4×C101—21no—
100C23×C4×C101C2311yescharacteristic
101C23×C4×C101C2311yescharacteristic
102AGL(1,ℤ/8)×C101—232no—
103C2×Q16×C101—22no—
104C2×Q16×C101—22no—
105C2×Q16×C101—41no—
106C2×SD16×C101—22no—
107C2×SD16×C101—22no—
108C2×SD16×C101—22no—
109C2×SD16×C101—22no—
110C2×SD16×C101—22no—
111C2×SD16×C101—22no—
112C2×SD16×C101—22no—
113C2×SD16×C101—41no—
114C2×SD16×C101D414yescomplemented
115C2×D8×C101—22no—
116C2×D8×C101—22no—
117C2×D8×C101—22no—
118C2×D8×C101—22no—
119C2×D8×C101—22no—
120C2×D8×C101D414yescomplemented
121C2×M16×C101—22no—
122C2×M16×C101—22no—
123C2×M16×C101—22no—
124C22×C8×C101C2311yescharacteristic
125C22×C8×C101C2311yescharacteristic
126C22×C8×C101C2311yescharacteristic
127C22×C8×C101C2311yescharacteristic
128#124×C101—22no—
129#124×C101—22no—
130#123×C101—28no—
131C22⋊Q8×C101—22no—
132C22⋊Q8×C101—22no—
133C22⋊Q8×C101—41no—
134C22⋊Q8×C101D414yescomplemented
135#121×C101—28no—
136#121×C101—22no—
137#121×C101—22no—
138#121×C101—22no—
139#121×C101—41no—
140#120×C101—28no—
141C4×D4×C101—22no—
142C4×D4×C101—22no—
143C4×D4×C101—22no—
144C4×D4×C101—22no—
145C2×C4⋊C4×C101—21no—
146C2×C4⋊C4×C101—21no—
147C2×C4⋊C4×C101D411yescharacteristic
148C2×C4⋊C4×C101C2311yescharacteristic
149C2×C4⋊C4×C101C2311yescharacteristic
150C2×C4⋊C4×C101C2311yescharacteristic
151C2×C22⋊C4×C101—28no—
152C2×C22⋊C4×C101—21no—
153C2×C22⋊C4×C101—21no—
154C2×C22⋊C4×C101—21no—
155C2×C22⋊C4×C101—21no—
156C2×C22⋊C4×C101—21no—
157C2×C22⋊C4×C101—21no—
158C2×C22⋊C4×C101—21no—
159C2×C22⋊C4×C101—21no—
160C2×C22⋊C4×C101—21no—
161C2×C22⋊C4×C101—21no—
162C2×C22⋊C4×C101D411yescharacteristic
163C2×C22⋊C4×C101D411yescharacteristic
164C2×C42×C101C2311yescharacteristic
165#103×C101—22no—
166#103×C101—22no—
167#103×C101—22no—
168#102×C101—22no—
169#102×C101—22no—
170#102×C101—22no—
171#102×C101—41no—
172#102×C101—41no—
173C22⋊C8×C101—22no—
174C22⋊C8×C101—22no—
175C22⋊C8×C101—22no—
176#95×C101—21no—
177#95×C101—21no—
178#95×C101—21no—
179C24×C101—21no—
180C24×C101—21no—
181C24×C101—21no—
182C24×C101—24no—
183C24×C101—42no—
184C24×C101—42no—
185C24×C101—42no—
186C24×C101—42no—
187C24×C101—81no—
188C24×C101—81no—
189C24×C101C2×D411yescharacteristic
190C24×C101C2×D411yescharacteristic
191#41×C101—28no—
192#41×C101—44no—
193#41×C101—44no—
194#41×C101—44no—
195#41×C101—44no—
196#41×C101—44no—
197#41×C101—44no—
198#41×C101—44no—
199C2×Q8×C101—21no—
200C2×Q8×C101—21no—
201C2×Q8×C101—21no—
202C2×Q8×C101—21no—
203C2×Q8×C101—21no—
204C2×Q8×C101—21no—
205C2×Q8×C101—21no—
206C2×Q8×C101—21no—
207C2×Q8×C101—21no—
208C2×Q8×C101—21no—
209C2×Q8×C101C2×D412yes—
210C2×Q8×C101C2×D412yes—
211C2×D4×C101—28no—
212C2×D4×C101—24no—
213C2×D4×C101—22no—
214C2×D4×C101—24no—
215C2×D4×C101—24no—
216C2×D4×C101—21no—
217C2×D4×C101—21no—
218C2×D4×C101—21no—
219C2×D4×C101—21no—
220C2×D4×C101—21no—
221C2×D4×C101—21no—
222C2×D4×C101—21no—
223C2×D4×C101—21no—
224C2×D4×C101—21no—
225C2×D4×C101—21no—
226C2×D4×C101—21no—
227C2×D4×C101—21no—
228C2×D4×C101—21no—
229C2×D4×C101—44no—
230C2×D4×C101—44no—
231C2×D4×C101—44no—
232C2×D4×C101—41no—
233C2×D4×C101—41no—
234C2×D4×C101—42no—
235C2×D4×C101—42no—
236C2×D4×C101—42no—
237C2×D4×C101—42no—
238C2×D4×C101—42no—
239C2×D4×C101—42no—
240C2×D4×C101—42no—
241C2×D4×C101—42no—
242C2×D4×C101—42no—
243C2×D4×C101—81no—
244C2×D4×C101—81no—
245C2×D4×C101—81no—
246C2×D4×C101C2×D412yes—
247C2×D4×C101C2×D412yes—
248C2×D4×C101C2×D412yes—
249C2×D4×C101C2×D412yes—
250C2×D4×C101C2×D412yes—
251C22×C4×C101—21no—
252C22×C4×C101—21no—
253C22×C4×C101—21no—
254C22×C4×C101—21no—
255C22×C4×C101—24no—
256C22×C4×C101—21no—
257C22×C4×C101—21no—
258C22×C4×C101—21no—
259C22×C4×C101—24no—
260C22×C4×C101—21no—
261C22×C4×C101—21no—
262C22×C4×C101—21no—
263C22×C4×C101—21no—
264C22×C4×C101—21no—
265C22×C4×C101—21no—
266C22×C4×C101—21no—
267C22×C4×C101—21no—
268C22×C4×C101—42no—
269C22×C4×C101—42no—
270C22×C4×C101—42no—
271C22×C4×C101—42no—
272C22×C4×C101—42no—
273C22×C4×C101—81no—
274C22×C4×C101—81no—
275C22×C4×C101C2×D411yescharacteristic
276C22×C4×C101C2×D411yescharacteristic
277C22×C4×C101C2×D411yescharacteristic
278C22×C4×C101C2×D411yescharacteristic
279C22×C4×C101C2×D412yes—
280C22×C4×C101C2×D412yes—
281C22×C4×C101C2411yescharacteristic
282Q16×C101—44no—
283SD16×C101—28no—
284SD16×C101—28no—
285SD16×C101—44no—
286D8×C101—28no—
287D8×C101—28no—
288M16×C101—28no—
289C2×C8×C101—21no—
290C2×C8×C101—21no—
291C2×C8×C101—21no—
292C2×C8×C101—21no—
293C2×C8×C101—21no—
294C2×C8×C101—21no—
295C2×C8×C101—21no—
296C2×C8×C101—21no—
297C2×C8×C101—21no—
298C2×C8×C101—21no—
299C2×C8×C101C2×D412yes—
300C2×C8×C101C2×D412yes—
301C4⋊C4×C101—24no—
302C4⋊C4×C101—22no—
303C4⋊C4×C101—21no—
304C4⋊C4×C101—21no—
305C4⋊C4×C101—21no—
306C4⋊C4×C101—21no—
307C4⋊C4×C101—21no—
308C4⋊C4×C101—42no—
309C4⋊C4×C101C2×D412yes—
310C22⋊C4×C101—24no—
311C22⋊C4×C101—24no—
312C22⋊C4×C101—24no—
313C22⋊C4×C101—24no—
314C22⋊C4×C101—22no—
315C22⋊C4×C101—24no—
316C22⋊C4×C101—22no—
317C22⋊C4×C101—42no—
318C22⋊C4×C101—42no—
319C22⋊C4×C101—42no—
320C22⋊C4×C101—81no—
321C22⋊C4×C101—81no—
322C42×C101—21no—
323C42×C101—21no—
324C23×C101—22no—
325C23×C101—21no—
326C23×C101—21no—
327C23×C101—22no—
328C23×C101—22no—
329C23×C101—21no—
330C23×C101—21no—
331C23×C101—21no—
332C23×C101—21no—
333C23×C101—22no—
334C23×C101—21no—
335C23×C101—21no—
336C23×C101—22no—
337C23×C101—21no—
338C23×C101—21no—
339C23×C101—21no—
340C23×C101—21no—
341C23×C101—21no—
342C23×C101—48no—
343C23×C101—48no—
344C23×C101—41no—
345C23×C101—41no—
346C23×C101—41no—
347C23×C101—41no—
348C23×C101—41no—
349C23×C101—41no—
350C23×C101—41no—
351C23×C101—41no—
352C23×C101—41no—
353C23×C101—41no—
354C23×C101—41no—
355C23×C101—41no—
356C23×C101—41no—
357C23×C101—41no—
358C23×C101—41no—
359C23×C101—41no—
360C23×C101—84no—
361C23×C101—84no—
362C23×C101—84no—
363C23×C101—84no—
364C23×C101—84no—
365C23×C101#12012yes—
366C23×C101C22×D411yescharacteristic
367Q8×C101—22no—
368Q8×C101—22no—
369Q8×C101—22no—
370Q8×C101—22no—
371Q8×C101—41no—
372Q8×C101—41no—
373Q8×C101—41no—
374Q8×C101—41no—
375D4×C101—22no—
376D4×C101—22no—
377D4×C101—22no—
378D4×C101—22no—
379D4×C101—22no—
380D4×C101—22no—
381D4×C101—22no—
382D4×C101—48no—
383D4×C101—44no—
384D4×C101—48no—
385D4×C101—48no—
386D4×C101—41no—
387D4×C101—41no—
388D4×C101—41no—
389D4×C101—41no—
390D4×C101—84no—
391D4×C101—84no—
392D4×C101#12014yes—
393C2×C4×C101—21no—
394C2×C4×C101—21no—
395C2×C4×C101—22no—
396C2×C4×C101—22no—
397C2×C4×C101—22no—
398C2×C4×C101—22no—
399C2×C4×C101—21no—
400C2×C4×C101—21no—
401C2×C4×C101—22no—
402C2×C4×C101—21no—
403C2×C4×C101—22no—
404C2×C4×C101—21no—
405C2×C4×C101—22no—
406C2×C4×C101—21no—
407C2×C4×C101—21no—
408C2×C4×C101—21no—
409C2×C4×C101—21no—
410C2×C4×C101—21no—
411C2×C4×C101—48no—
412C2×C4×C101—48no—
413C2×C4×C101—41no—
414C2×C4×C101—41no—
415C2×C4×C101—41no—
416C2×C4×C101—41no—
417C2×C4×C101—41no—
418C2×C4×C101—41no—
419C2×C4×C101—41no—
420C2×C4×C101—41no—
421C2×C4×C101—41no—
422C2×C4×C101—41no—
423C2×C4×C101—41no—
424C2×C4×C101—41no—
425C2×C4×C101—41no—
426C2×C4×C101—41no—
427C2×C4×C101—41no—
428C2×C4×C101—41no—
429C2×C4×C101—84no—
430C2×C4×C101#12012yes—
431C2×C4×C101C22×D411yescharacteristic
432C2×C4×C101C22×D411yescharacteristic
433C2×C4×C101C22×D411yescharacteristic
434C2×C4×C101C22×D411yescharacteristic
435C2×C4×C101H(5,𝔽2)11yescharacteristic
436C2×C4×C101H(5,𝔽2)11yescharacteristic
437C8×C101—22no—
438C8×C101—22no—
439C8×C101—41no—
440C8×C101—41no—
441C22×C101—22no—
442C22×C101—24no—
443C22×C101—22no—
444C22×C101—22no—
445C22×C101—42no—
446C22×C101—41no—
447C22×C101—42no—
448C22×C101—42no—
449C22×C101—41no—
450C22×C101—42no—
451C22×C101—41no—
452C22×C101—42no—
453C22×C101—41no—
454C22×C101—42no—
455C22×C101—42no—
456C22×C101—41no—
457C22×C101—42no—
458C22×C101—41no—
459C22×C101—42no—
460C22×C101—41no—
461C22×C101—42no—
462C22×C101—41no—
463C22×C101—42no—
464C22×C101—41no—
465C22×C101—41no—
466C22×C101—42no—
467C22×C101—41no—
468C22×C101—816no—
469C22×C101—81no—
470C22×C101—81no—
471C22×C101—81no—
472C22×C101—81no—
473C22×C101—81no—
474C22×C101—81no—
475C22×C101—81no—
476C22×C101—81no—
477C22×C101C2×#12011yescharacteristic
478C22×C101D4211yescharacteristic
479C22×C101D4211yescharacteristic
480C22×C101#57511yescharacteristic
481C22×C101#57511yescharacteristic
482C22×C101#57611yescharacteristic
483C22×C101#57711yescharacteristic
484C4×C101—22no—
485C4×C101—41no—
486C4×C101—42no—
487C4×C101—42no—
488C4×C101—41no—
489C4×C101—41no—
490C4×C101—42no—
491C4×C101—81no—
492C4×C101—81no—
493C4×C101C2×#12011yescharacteristic
494C4×C101#53411yescharacteristic
495C4×C101D4211yescharacteristic
496C4×C101D4211yescharacteristic
497#23863C10111yesmaximal, characteristic, direct product factor, Sylow
498C2×C101—42no—
499C2×C101—44no—
500C2×C101—81no—
501C2×C101—82no—
502C2×C101—82no—
503C2×C101#240311yescharacteristic
504C2×C101#300511yescharacteristic
505C2×C101#301211yescharacteristic
506C2×C101#326711yescharacteristic
507C2×C101#326811yescharacteristic
508C2×C101#327311yescharacteristic
509C2×C101#327511yescharacteristic
510C22×AGL(1,ℤ/8)C2×C10111yescharacteristic, complemented
511C2×#546C2×C10111yescharacteristic, complemented
512C2×#452C2×C10111yescharacteristic, complemented
513C2×#452C2×C10111yescharacteristic, complemented
514C2×#449C2×C10111yescharacteristic, complemented
515#2407C2×C10111yescharacteristic, complemented
516#2015C2×C10111yescharacteristic, complemented
517#2012C2×C10111yescharacteristic, complemented
518#2000C2×C10111yescharacteristic, complemented
519#1999C2×C10111yescharacteristic, complemented
520#1894C2×C10111yescharacteristic, complemented
521#1879C2×C10111yescharacteristic, complemented
522#1877C2×C10111yescharacteristic, complemented
523#1870C2×C10111yescharacteristic, complemented
524#1786C2×C10111yescharacteristic, complemented
525C101#2386311yescharacteristic, direct product factor, Sylow
526C22×#41C22×C10111yescharacteristic
527C22×#41C22×C10111yescharacteristic
528C23×D4C22×C10111yescharacteristic
529C2×AGL(1,ℤ/8)—24no—
530C2×AGL(1,ℤ/8)—24no—
531C2×AGL(1,ℤ/8)—24no—
532C22×Q16C22×C10111yescharacteristic, complemented
533C22×SD16C22×C10111yescharacteristic
534C22×SD16C22×C10111yescharacteristic
535C22×SD16C22×C10111yescharacteristic, complemented
536C22×D8C22×C10111yescharacteristic
537C22×D8C22×C10111yescharacteristic
538C22×M16C22×C10111yescharacteristic
539#546—24no—
540#546—24no—
541C2×#124C22×C10111yescharacteristic
542C2×#123—21no—
543C2×C22⋊Q8C22×C10111yescharacteristic
544C2×C22⋊Q8C22×C10111yescharacteristic, complemented
545C2×#121—21no—
546C2×#121C22×C10111yescharacteristic
547C2×#121C22×C10111yescharacteristic, complemented
548C2×#120—21no—
549C2×C4×D4C22×C10111yescharacteristic
550C2×C4×D4C22×C10111yescharacteristic
551C22×C22⋊C4—21no—
552#452—24no—
553#452—24no—
554#449—24no—
555C2×#103C22×C10111yescharacteristic, complemented
556C2×#103C22×C10111yescharacteristic, complemented
557C2×#103C22×C10111yescharacteristic, complemented
558C2×#102C22×C10111yescharacteristic
559C2×#102C22×C10111yescharacteristic
560C2×#102C22×C10111yescharacteristic
561C2×#102C22×C10111yescharacteristic
562C2×#102C22×C10111yescharacteristic, complemented
563C2×C22⋊C8C22×C10111yescharacteristic
564C2×C22⋊C8C22×C10111yescharacteristic, complemented
565C2×C22⋊C8C22×C10111yescharacteristic, complemented
566#394—21no—
567#392—21no—
568#391C22×C10111yescharacteristic, complemented
569#390C22×C10111yescharacteristic, complemented
570#386—21no—
571#385—21no—
572#380C22×C10111yescharacteristic
573#340C22×C10111yescharacteristic, complemented
574#340C22×C10111yescharacteristic, complemented
575#336C22×C10111yescharacteristic, complemented
576#336C22×C10111yescharacteristic, complemented
577C25—21no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—22no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41—41no—
590C22×Q8C23×C10111yescharacteristic
591C22×Q8C23×C10111yescharacteristic
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—22no—
600C22×D4—41no—
601C22×D4—41no—
602C22×D4D4×C10111yescharacteristic
603C22×D4D4×C10114yescomplemented
604C22×D4C23×C10111yescharacteristic
605C22×D4C23×C10111yescharacteristic
606C22×D4C23×C10111yescharacteristic
607C23×C4—21no—
608C23×C4—21no—
609C23×C4—21no—
610C23×C4C23×C10111yescharacteristic
611C23×C4C23×C10111yescharacteristic
612AGL(1,ℤ/8)—232no—
613C2×Q16—22no—
614C2×Q16—22no—
615C2×Q16—41no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—22no—
623C2×SD16—41no—
624C2×SD16D4×C10114yescomplemented
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—22no—
630C2×D8D4×C10114yescomplemented
631C2×M16—22no—
632C2×M16—22no—
633C2×M16—22no—
634C22×C8C23×C10111yescharacteristic
635C22×C8C23×C10111yescharacteristic
636C22×C8C23×C10111yescharacteristic
637C22×C8C23×C10111yescharacteristic
638#124—22no—
639#124—22no—
640#123—28no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—41no—
644C22⋊Q8D4×C10114yescomplemented
645#121—28no—
646#121—22no—
647#121—22no—
648#121—22no—
649#121—41no—
650#120—28no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4D4×C10111yescharacteristic
658C2×C4⋊C4C23×C10111yescharacteristic
659C2×C4⋊C4C23×C10111yescharacteristic
660C2×C4⋊C4C23×C10111yescharacteristic
661C2×C22⋊C4—28no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4D4×C10111yescharacteristic
673C2×C22⋊C4D4×C10111yescharacteristic
674C2×C42C23×C10111yescharacteristic
675#103—22no—
676#103—22no—
677#103—22no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—41no—
682#102—41no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—22no—
686#95—21no—
687#95—21no—
688#95—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—24no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—81no—
698C24—81no—
699C24C2×D4×C10111yescharacteristic
700C24C2×D4×C10111yescharacteristic
701#41—28no—
702#41—44no—
703#41—44no—
704#41—44no—
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8C2×D4×C10112yes—
720C2×Q8C2×D4×C10112yes—
721C2×D4—28no—
722C2×D4—24no—
723C2×D4—22no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C10112yes—
757C2×D4C2×D4×C10112yes—
758C2×D4C2×D4×C10112yes—
759C2×D4C2×D4×C10112yes—
760C2×D4C2×D4×C10112yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—24no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C2×D4×C10111yescharacteristic
786C22×C4C2×D4×C10111yescharacteristic
787C22×C4C2×D4×C10111yescharacteristic
788C22×C4C2×D4×C10111yescharacteristic
789C22×C4C2×D4×C10112yes—
790C22×C4C2×D4×C10112yes—
791C22×C4C24×C10111yescharacteristic
792Q16—44no—
793SD16—28no—
794SD16—28no—
795SD16—44no—
796D8—28no—
797D8—28no—
798M16—28no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8C2×D4×C10112yes—
810C2×C8C2×D4×C10112yes—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C10112yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—24no—
826C22⋊C4—22no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C22⋊C4—81no—
832C42—21no—
833C42—21no—
834C23—22no—
835C23—21no—
836C23—21no—
837C23—22no—
838C23—22no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—22no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—48no—
853C23—48no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23#120×C10112yes—
876C23C22×D4×C10111yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884Q8—41no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—48no—
893D4—48no—
894D4—44no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—84no—
901D4—84no—
902D4#120×C10114yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—84no—
940C2×C4#120×C10112yes—
941C2×C4C22×D4×C10111yescharacteristic
942C2×C4C22×D4×C10111yescharacteristic
943C2×C4C22×D4×C10111yescharacteristic
944C2×C4C22×D4×C10111yescharacteristic
945C2×C4H(5,𝔽2)×C10111yescharacteristic
946C2×C4H(5,𝔽2)×C10111yescharacteristic
947C8—22no—
948C8—22no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—22no—
955C22—42no—
956C22—41no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—42no—
963C22—41no—
964C22—42no—
965C22—42no—
966C22—41no—
967C22—42no—
968C22—41no—
969C22—42no—
970C22—41no—
971C22—42no—
972C22—41no—
973C22—42no—
974C22—41no—
975C22—41no—
976C22—42no—
977C22—41no—
978C22—816no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22C2×#120×C10111yescharacteristic
988C22D42×C10111yescharacteristic
989C22D42×C10111yescharacteristic
990C22#575×C10111yescharacteristic
991C22#575×C10111yescharacteristic
992C22#576×C10111yescharacteristic
993C22#577×C10111yescharacteristic
994C4—22no—
995C4—41no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C10111yescharacteristic
1004C4#534×C10111yescharacteristic
1005C4D42×C10111yescharacteristic
1006C4D42×C10111yescharacteristic
1007C2—42no—
1008C2—44no—
1009C2—81no—
1010C2—82no—
1011C2—82no—
1012C2C101×#240311yescharacteristic
1013C2C101×#300511yescharacteristic
1014C2C101×#301211yescharacteristic
1015C2C101×#326711yescharacteristic
1016C2C101×#326811yescharacteristic
1017C2C101×#327311yescharacteristic
1018C2C101×#327511yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C4×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C101C2semidirect
2. C2×#546×C101C2semidirect
3. C2×#452×C101C2semidirect
4. C2×#452×C101C2semidirect
5. C2×#449×C101C2semidirect
6. C101×#2407C2semidirect
7. C101×#2015C2semidirect
8. C101×#2012C2semidirect
9. C101×#2000C2semidirect
10. C101×#1999C2semidirect
11. C101×#1894C2semidirect
12. C101×#1879C2semidirect
13. C101×#1877C2semidirect
14. C101×#1870C2semidirect
15. C101×#1786C2semidirect
22. C22×Q16×C101C22semidirect
25. C22×SD16×C101C22semidirect
34. C2×C22⋊Q8×C101C22semidirect
37. C2×#121×C101C22semidirect
45. C2×#103×C101C22semidirect
46. C2×#103×C101C22semidirect
47. C2×#103×C101C22semidirect
52. C2×#102×C101C22semidirect
54. C2×C22⋊C8×C101C22semidirect
55. C2×C22⋊C8×C101C22semidirect
58. #391×C101C22semidirect
59. #390×C101C22semidirect
63. #340×C101C22semidirect
64. #340×C101C22semidirect
65. #336×C101C22semidirect
66. #336×C101C22semidirect
93. C22×D4×C101D4semidirect
114. C2×SD16×C101D4semidirect
120. C2×D8×C101D4semidirect
134. C22⋊Q8×C101D4semidirect
497. #23863C101direct (N × H)
510. C22×AGL(1,ℤ/8)C2×C101semidirect
511. C2×#546C2×C101semidirect
512. C2×#452C2×C101semidirect
513. C2×#452C2×C101semidirect
514. C2×#449C2×C101semidirect
515. #2407C2×C101semidirect
516. #2015C2×C101semidirect
517. #2012C2×C101semidirect
518. #2000C2×C101semidirect
519. #1999C2×C101semidirect
520. #1894C2×C101semidirect
521. #1879C2×C101semidirect
522. #1877C2×C101semidirect
523. #1870C2×C101semidirect
524. #1786C2×C101semidirect
525. C101#23863direct (N × H)
532. C22×Q16C22×C101semidirect
535. C22×SD16C22×C101semidirect
544. C2×C22⋊Q8C22×C101semidirect
547. C2×#121C22×C101semidirect
555. C2×#103C22×C101semidirect
556. C2×#103C22×C101semidirect
557. C2×#103C22×C101semidirect
562. C2×#102C22×C101semidirect
564. C2×C22⋊C8C22×C101semidirect
565. C2×C22⋊C8C22×C101semidirect
568. #391C22×C101semidirect
569. #390C22×C101semidirect
573. #340C22×C101semidirect
574. #340C22×C101semidirect
575. #336C22×C101semidirect
576. #336C22×C101semidirect
603. C22×D4D4×C101semidirect
624. C2×SD16D4×C101semidirect
630. C2×D8D4×C101semidirect
644. C22⋊Q8D4×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
C2×#546×C1012
C2×#452×C1012
C2×#449×C1012
C101×#24072
C101×#20152
C101×#20122
C101×#20002
C101×#19992
C101×#18942
C101×#18792
C101×#18772
C101×#18702
C101×#17862
#23863101