Finite Group Databasebeta

← C101×#24436 #38806587

Subgroups — C101×#24436 #38806587

Order 25856.

1582 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C101C211yesmaximal, characteristic
2C2×#465×C101C211yesmaximal, characteristic, complemented
3C2×#452×C101C211yesmaximal, characteristic, complemented
4C2×#450×C101C211yesmaximal, characteristic, complemented
5C2×#416×C101C211yesmaximal, characteristic, complemented
6C101×#2415C211yesmaximal, characteristic, complemented
7C101×#2042C211yesmaximal, characteristic, complemented
8C101×#2035C211yesmaximal, characteristic, complemented
9C101×#2015C211yesmaximal, characteristic, complemented
10C101×#2001C211yesmaximal, characteristic, complemented
11C101×#1877C211yesmaximal, characteristic, complemented
12C101×#1875C211yesmaximal, characteristic, complemented
13C101×#1869C211yesmaximal, characteristic, complemented
14C101×#1864C211yesmaximal, characteristic, complemented
15C101×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×D4×C101C2211yescharacteristic
18C22×Q16×C101C2211yescharacteristic, complemented
19C22×SD16×C101C2211yescharacteristic
20C22×SD16×C101C2211yescharacteristic
21C23×C8×C101C2211yescharacteristic, complemented
22#546×C101—24no—
23#546×C101—24no—
24C2×#124×C101C2211yescharacteristic
25C2×#123×C101—21no—
26C2×C22⋊Q8×C101C2211yescharacteristic
27C2×C22⋊Q8×C101C2211yescharacteristic
28C2×C22⋊Q8×C101C2211yescharacteristic, complemented
29C2×#121×C101—21no—
30C2×#121×C101C2211yescharacteristic
31C2×#120×C101—21no—
32C2×C4×D4×C101C2211yescharacteristic
33C2×C4×D4×C101C2211yescharacteristic
34C2×#117×C101C2211yescharacteristic, complemented
35C22×C22⋊C4×C101—21no—
36#465×C101—24no—
37#452×C101—24no—
38#450×C101—24no—
39C2×#106×C101C2211yescharacteristic, complemented
40#416×C101—24no—
41C2×#103×C101C2211yescharacteristic, complemented
42C2×#103×C101C2211yescharacteristic, complemented
43C2×#103×C101C2211yescharacteristic, complemented
44C2×#103×C101C2211yescharacteristic, complemented
45C2×#102×C101C2211yescharacteristic
46C2×#102×C101C2211yescharacteristic
47C2×#102×C101C2211yescharacteristic
48C2×#102×C101C2211yescharacteristic
49C2×#102×C101C2211yescharacteristic
50C2×#102×C101C2211yescharacteristic
51C2×C22⋊C8×C101C2211yescharacteristic
52C2×C22⋊C8×C101C2211yescharacteristic
53C2×C22⋊C8×C101C2211yescharacteristic, complemented
54#397×C101—21no—
55#394×C101—21no—
56#391×C101C2211yescharacteristic, complemented
57#389×C101—21no—
58#389×C101C2211yescharacteristic, complemented
59#388×C101—21no—
60#380×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic, complemented
62#340×C101C2211yescharacteristic, complemented
63#336×C101C2211yescharacteristic, complemented
64#336×C101C2211yescharacteristic, complemented
65C25×C101—21no—
66C2×#41×C101—22no—
67C2×#41×C101—22no—
68C2×#41×C101—22no—
69C2×#41×C101—41no—
70C2×#41×C101—41no—
71C2×#41×C101D414yes—
72C22×Q8×C101C2311yescharacteristic
73C22×Q8×C101C2311yescharacteristic
74C22×D4×C101—21no—
75C22×D4×C101—21no—
76C22×D4×C101—22no—
77C22×D4×C101—22no—
78C22×D4×C101—22no—
79C22×D4×C101—22no—
80C22×D4×C101—21no—
81C22×D4×C101—41no—
82C22×D4×C101—41no—
83C22×D4×C101D411yescharacteristic
84C22×D4×C101C2311yescharacteristic
85C22×D4×C101C2311yescharacteristic
86C23×C4×C101—21no—
87C23×C4×C101—21no—
88C23×C4×C101C2311yescharacteristic
89C23×C4×C101C2311yescharacteristic
90C2×Q16×C101—22no—
91C2×Q16×C101—41no—
92C2×Q16×C101—41no—
93C2×SD16×C101—22no—
94C2×SD16×C101—22no—
95C2×SD16×C101—22no—
96C2×SD16×C101—22no—
97C2×SD16×C101—22no—
98C2×SD16×C101—41no—
99C22×C8×C101—22no—
100C22×C8×C101—22no—
101C22×C8×C101—41no—
102C22×C8×C101C2311yescharacteristic
103C22×C8×C101C2311yescharacteristic
104C22×C8×C101C2311yescharacteristic
105C22×C8×C101C2311yescharacteristic
106#124×C101—22no—
107#124×C101—22no—
108#123×C101—28no—
109C22⋊Q8×C101—22no—
110C22⋊Q8×C101—22no—
111C22⋊Q8×C101—22no—
112C22⋊Q8×C101—22no—
113C22⋊Q8×C101—22no—
114C22⋊Q8×C101—41no—
115#121×C101—28no—
116#121×C101—22no—
117#121×C101D414yes—
118#120×C101—28no—
119C4×D4×C101—22no—
120C4×D4×C101—22no—
121C4×D4×C101—22no—
122C4×D4×C101—22no—
123#117×C101—22no—
124#117×C101—41no—
125C2×C4⋊C4×C101—21no—
126C2×C4⋊C4×C101—21no—
127C2×C4⋊C4×C101—21no—
128C2×C4⋊C4×C101—21no—
129C2×C4⋊C4×C101D411yescharacteristic
130C2×C4⋊C4×C101C2311yescharacteristic
131C2×C4⋊C4×C101C2311yescharacteristic
132C2×C4⋊C4×C101C2311yescharacteristic
133C2×C4⋊C4×C101C2311yescharacteristic
134C2×C22⋊C4×C101—28no—
135C2×C22⋊C4×C101—21no—
136C2×C22⋊C4×C101—21no—
137C2×C22⋊C4×C101—21no—
138C2×C22⋊C4×C101—21no—
139C2×C22⋊C4×C101—21no—
140C2×C22⋊C4×C101—21no—
141C2×C22⋊C4×C101—21no—
142C2×C22⋊C4×C101—21no—
143C2×C22⋊C4×C101—21no—
144C2×C22⋊C4×C101D411yescharacteristic
145C2×C22⋊C4×C101D411yescharacteristic
146C2×C42×C101—21no—
147C2×C42×C101C2311yescharacteristic
148#106×C101—22no—
149#103×C101—22no—
150#103×C101—22no—
151#103×C101—22no—
152#103×C101—22no—
153#102×C101—22no—
154#102×C101—22no—
155#102×C101—22no—
156#102×C101—22no—
157#102×C101—41no—
158#102×C101D414yescomplemented
159C22⋊C8×C101—22no—
160C22⋊C8×C101—22no—
161C22⋊C8×C101—41no—
162#95×C101—21no—
163#95×C101—21no—
164#95×C101—21no—
165#95×C101—21no—
166C24×C101—21no—
167C24×C101—24no—
168C24×C101—21no—
169C24×C101—42no—
170C24×C101—42no—
171C24×C101—42no—
172C24×C101—42no—
173C24×C101—81no—
174C24×C101—81no—
175C24×C101C2×D411yescharacteristic
176C24×C101C2×D411yescharacteristic
177#41×C101—28no—
178#41×C101—44no—
179#41×C101—44no—
180#41×C101—44no—
181C2×Q8×C101—21no—
182C2×Q8×C101—21no—
183C2×Q8×C101—21no—
184C2×Q8×C101—21no—
185C2×Q8×C101—21no—
186C2×Q8×C101—21no—
187C2×Q8×C101—21no—
188C2×Q8×C101—21no—
189C2×Q8×C101—21no—
190C2×Q8×C101—21no—
191C2×Q8×C101—21no—
192C2×Q8×C101C2×D412yes—
193C2×D4×C101—24no—
194C2×D4×C101—22no—
195C2×D4×C101—24no—
196C2×D4×C101—22no—
197C2×D4×C101—24no—
198C2×D4×C101—21no—
199C2×D4×C101—21no—
200C2×D4×C101—21no—
201C2×D4×C101—21no—
202C2×D4×C101—21no—
203C2×D4×C101—21no—
204C2×D4×C101—21no—
205C2×D4×C101—21no—
206C2×D4×C101—41no—
207C2×D4×C101—42no—
208C2×D4×C101—42no—
209C2×D4×C101—44no—
210C2×D4×C101—44no—
211C2×D4×C101—44no—
212C2×D4×C101—42no—
213C2×D4×C101—42no—
214C2×D4×C101—44no—
215C2×D4×C101—81no—
216C2×D4×C101—81no—
217C2×D4×C101C2×D412yes—
218C2×D4×C101C2×D412yes—
219C2×D4×C101C2×D412yes—
220C2×D4×C101#4112yes—
221C22×C4×C101—21no—
222C22×C4×C101—21no—
223C22×C4×C101—21no—
224C22×C4×C101—21no—
225C22×C4×C101—21no—
226C22×C4×C101—21no—
227C22×C4×C101—21no—
228C22×C4×C101—24no—
229C22×C4×C101—24no—
230C22×C4×C101—21no—
231C22×C4×C101—21no—
232C22×C4×C101—21no—
233C22×C4×C101—21no—
234C22×C4×C101—21no—
235C22×C4×C101—21no—
236C22×C4×C101—21no—
237C22×C4×C101—21no—
238C22×C4×C101—21no—
239C22×C4×C101—42no—
240C22×C4×C101—42no—
241C22×C4×C101—81no—
242C22×C4×C101—81no—
243C22×C4×C101C2×D411yescharacteristic
244C22×C4×C101C2×D411yescharacteristic
245C22×C4×C101C2×D411yescharacteristic
246C22×C4×C101C2×D411yescharacteristic
247C22×C4×C101C2×D412yes—
248C22×C4×C101C2×D412yes—
249C22×C4×C101C2411yescharacteristic
250Q16×C101—44no—
251SD16×C101—44no—
252SD16×C101—44no—
253C2×C8×C101—21no—
254C2×C8×C101—21no—
255C2×C8×C101—21no—
256C2×C8×C101—21no—
257C2×C8×C101—21no—
258C2×C8×C101—21no—
259C2×C8×C101—21no—
260C2×C8×C101—21no—
261C2×C8×C101—21no—
262C2×C8×C101—21no—
263C2×C8×C101—21no—
264C2×C8×C101—44no—
265C2×C8×C101C2×D412yes—
266C4⋊C4×C101—24no—
267C4⋊C4×C101—22no—
268C4⋊C4×C101—21no—
269C4⋊C4×C101—21no—
270C4⋊C4×C101—21no—
271C4⋊C4×C101—21no—
272C4⋊C4×C101—21no—
273C4⋊C4×C101—21no—
274C4⋊C4×C101—42no—
275C4⋊C4×C101—42no—
276C4⋊C4×C101—42no—
277C4⋊C4×C101C2×D412yes—
278C4⋊C4×C101C2×D412yes—
279C22⋊C4×C101—24no—
280C22⋊C4×C101—24no—
281C22⋊C4×C101—24no—
282C22⋊C4×C101—24no—
283C22⋊C4×C101—22no—
284C22⋊C4×C101—22no—
285C22⋊C4×C101—24no—
286C22⋊C4×C101—42no—
287C22⋊C4×C101—42no—
288C22⋊C4×C101—42no—
289C22⋊C4×C101—42no—
290C42×C101—21no—
291C42×C101—21no—
292C42×C101—42no—
293C23×C101—21no—
294C23×C101—22no—
295C23×C101—21no—
296C23×C101—21no—
297C23×C101—22no—
298C23×C101—21no—
299C23×C101—21no—
300C23×C101—22no—
301C23×C101—21no—
302C23×C101—21no—
303C23×C101—21no—
304C23×C101—21no—
305C23×C101—21no—
306C23×C101—21no—
307C23×C101—21no—
308C23×C101—22no—
309C23×C101—48no—
310C23×C101—48no—
311C23×C101—41no—
312C23×C101—41no—
313C23×C101—41no—
314C23×C101—41no—
315C23×C101—41no—
316C23×C101—41no—
317C23×C101—41no—
318C23×C101—41no—
319C23×C101—41no—
320C23×C101—41no—
321C23×C101—84no—
322C23×C101—84no—
323C23×C101—84no—
324C23×C101—84no—
325C23×C101—84no—
326C23×C101#12012yes—
327C23×C101#13512yes—
328C23×C101C22×D411yescharacteristic
329Q8×C101—22no—
330Q8×C101—22no—
331Q8×C101—41no—
332Q8×C101—41no—
333Q8×C101—41no—
334Q8×C101—41no—
335Q8×C101—41no—
336Q8×C101—41no—
337D4×C101—22no—
338D4×C101—22no—
339D4×C101—22no—
340D4×C101—22no—
341D4×C101—22no—
342D4×C101—44no—
343D4×C101—48no—
344D4×C101—48no—
345D4×C101—41no—
346D4×C101—41no—
347D4×C101—84no—
348D4×C101#12114yes—
349C2×C4×C101—21no—
350C2×C4×C101—21no—
351C2×C4×C101—22no—
352C2×C4×C101—22no—
353C2×C4×C101—22no—
354C2×C4×C101—22no—
355C2×C4×C101—21no—
356C2×C4×C101—21no—
357C2×C4×C101—22no—
358C2×C4×C101—22no—
359C2×C4×C101—21no—
360C2×C4×C101—22no—
361C2×C4×C101—21no—
362C2×C4×C101—21no—
363C2×C4×C101—21no—
364C2×C4×C101—21no—
365C2×C4×C101—21no—
366C2×C4×C101—21no—
367C2×C4×C101—48no—
368C2×C4×C101—41no—
369C2×C4×C101—41no—
370C2×C4×C101—41no—
371C2×C4×C101—41no—
372C2×C4×C101—41no—
373C2×C4×C101—41no—
374C2×C4×C101—41no—
375C2×C4×C101—41no—
376C2×C4×C101—41no—
377C2×C4×C101—41no—
378C2×C4×C101—41no—
379C2×C4×C101—41no—
380C2×C4×C101—41no—
381C2×C4×C101—41no—
382C2×C4×C101—41no—
383C2×C4×C101—41no—
384C2×C4×C101—41no—
385C2×C4×C101—41no—
386C2×C4×C101—41no—
387C2×C4×C101—84no—
388C2×C4×C101#12012yes—
389C2×C4×C101C22×D411yescharacteristic
390C2×C4×C101C22×D411yescharacteristic
391C2×C4×C101C22×D411yescharacteristic
392C2×C4×C101C2×#4111yescharacteristic
393C2×C4×C101H(5,𝔽2)11yescharacteristic
394C2×C4×C101H(5,𝔽2)11yescharacteristic
395C8×C101—22no—
396C8×C101—41no—
397C8×C101—41no—
398C8×C101—41no—
399C22×C101—22no—
400C22×C101—24no—
401C22×C101—22no—
402C22×C101—22no—
403C22×C101—22no—
404C22×C101—22no—
405C22×C101—22no—
406C22×C101—41no—
407C22×C101—42no—
408C22×C101—42no—
409C22×C101—41no—
410C22×C101—41no—
411C22×C101—41no—
412C22×C101—42no—
413C22×C101—41no—
414C22×C101—42no—
415C22×C101—41no—
416C22×C101—42no—
417C22×C101—41no—
418C22×C101—41no—
419C22×C101—42no—
420C22×C101—42no—
421C22×C101—42no—
422C22×C101—42no—
423C22×C101—816no—
424C22×C101—81no—
425C22×C101—81no—
426C22×C101—81no—
427C22×C101—81no—
428C22×C101C2×#12011yescharacteristic
429C22×C101D4211yescharacteristic
430C22×C101#54611yescharacteristic
431C22×C101C2×#13511yescharacteristic
432C22×C101#57511yescharacteristic
433C22×C101#57711yescharacteristic
434C22×C101#57711yescharacteristic
435C4×C101—22no—
436C4×C101—41no—
437C4×C101—42no—
438C4×C101—41no—
439C4×C101—41no—
440C4×C101—42no—
441C4×C101—42no—
442C4×C101—81no—
443C4×C101—81no—
444C4×C101—81no—
445C4×C101C2×#12111yescharacteristic
446C4×C101#53411yescharacteristic
447C4×C101D4211yescharacteristic
448C4×C101#54611yescharacteristic
449#24436C10111yesmaximal, characteristic, direct product factor, Sylow
450C2×C101—42no—
451C2×C101—42no—
452C2×C101—44no—
453C2×C101—82no—
454C2×C101#241011yescharacteristic
455C2×C101#300211yescharacteristic
456C2×C101#300911yescharacteristic
457C2×C101#326711yescharacteristic
458C2×C101#328211yescharacteristic
459C2×C101#329611yescharacteristic
460C2×C101#331111yescharacteristic
461C2×#546C2×C10111yescharacteristic
462C2×#465C2×C10111yescharacteristic, complemented
463C2×#452C2×C10111yescharacteristic, complemented
464C2×#450C2×C10111yescharacteristic, complemented
465C2×#416C2×C10111yescharacteristic, complemented
466#2415C2×C10111yescharacteristic, complemented
467#2042C2×C10111yescharacteristic, complemented
468#2035C2×C10111yescharacteristic, complemented
469#2015C2×C10111yescharacteristic, complemented
470#2001C2×C10111yescharacteristic, complemented
471#1877C2×C10111yescharacteristic, complemented
472#1875C2×C10111yescharacteristic, complemented
473#1869C2×C10111yescharacteristic, complemented
474#1864C2×C10111yescharacteristic, complemented
475#1786C2×C10111yescharacteristic, complemented
476C101#2443611yescharacteristic, direct product factor, Sylow
477C22×#41C22×C10111yescharacteristic
478C23×D4C22×C10111yescharacteristic
479C22×Q16C22×C10111yescharacteristic, complemented
480C22×SD16C22×C10111yescharacteristic
481C22×SD16C22×C10111yescharacteristic
482C23×C8C22×C10111yescharacteristic, complemented
483#546—24no—
484#546—24no—
485C2×#124C22×C10111yescharacteristic
486C2×#123—21no—
487C2×C22⋊Q8C22×C10111yescharacteristic
488C2×C22⋊Q8C22×C10111yescharacteristic
489C2×C22⋊Q8C22×C10111yescharacteristic, complemented
490C2×#121—21no—
491C2×#121C22×C10111yescharacteristic
492C2×#120—21no—
493C2×C4×D4C22×C10111yescharacteristic
494C2×C4×D4C22×C10111yescharacteristic
495C2×#117C22×C10111yescharacteristic, complemented
496C22×C22⋊C4—21no—
497#465—24no—
498#452—24no—
499#450—24no—
500C2×#106C22×C10111yescharacteristic, complemented
501#416—24no—
502C2×#103C22×C10111yescharacteristic, complemented
503C2×#103C22×C10111yescharacteristic, complemented
504C2×#103C22×C10111yescharacteristic, complemented
505C2×#103C22×C10111yescharacteristic, complemented
506C2×#102C22×C10111yescharacteristic
507C2×#102C22×C10111yescharacteristic
508C2×#102C22×C10111yescharacteristic
509C2×#102C22×C10111yescharacteristic
510C2×#102C22×C10111yescharacteristic
511C2×#102C22×C10111yescharacteristic
512C2×C22⋊C8C22×C10111yescharacteristic
513C2×C22⋊C8C22×C10111yescharacteristic
514C2×C22⋊C8C22×C10111yescharacteristic, complemented
515#397—21no—
516#394—21no—
517#391C22×C10111yescharacteristic, complemented
518#389—21no—
519#389C22×C10111yescharacteristic, complemented
520#388—21no—
521#380C22×C10111yescharacteristic
522#340C22×C10111yescharacteristic, complemented
523#340C22×C10111yescharacteristic, complemented
524#336C22×C10111yescharacteristic, complemented
525#336C22×C10111yescharacteristic, complemented
526C25—21no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41D4×C10114yes—
533C22×Q8C23×C10111yescharacteristic
534C22×Q8C23×C10111yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—21no—
542C22×D4—41no—
543C22×D4—41no—
544C22×D4D4×C10111yescharacteristic
545C22×D4C23×C10111yescharacteristic
546C22×D4C23×C10111yescharacteristic
547C23×C4—21no—
548C23×C4—21no—
549C23×C4C23×C10111yescharacteristic
550C23×C4C23×C10111yescharacteristic
551C2×Q16—22no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—41no—
560C22×C8—22no—
561C22×C8—22no—
562C22×C8—41no—
563C22×C8C23×C10111yescharacteristic
564C22×C8C23×C10111yescharacteristic
565C22×C8C23×C10111yescharacteristic
566C22×C8C23×C10111yescharacteristic
567#124—22no—
568#124—22no—
569#123—28no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—41no—
576#121—28no—
577#121—22no—
578#121D4×C10114yes—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—41no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4D4×C10111yescharacteristic
591C2×C4⋊C4C23×C10111yescharacteristic
592C2×C4⋊C4C23×C10111yescharacteristic
593C2×C4⋊C4C23×C10111yescharacteristic
594C2×C4⋊C4C23×C10111yescharacteristic
595C2×C22⋊C4—28no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4D4×C10111yescharacteristic
606C2×C22⋊C4D4×C10111yescharacteristic
607C2×C42—21no—
608C2×C42C23×C10111yescharacteristic
609#106—22no—
610#103—22no—
611#103—22no—
612#103—22no—
613#103—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—22no—
618#102—41no—
619#102D4×C10114yescomplemented
620C22⋊C8—22no—
621C22⋊C8—22no—
622C22⋊C8—41no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—81no—
635C24—81no—
636C24C2×D4×C10111yescharacteristic
637C24C2×D4×C10111yescharacteristic
638#41—28no—
639#41—44no—
640#41—44no—
641#41—44no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8C2×D4×C10112yes—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—44no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4C2×D4×C10112yes—
679C2×D4C2×D4×C10112yes—
680C2×D4C2×D4×C10112yes—
681C2×D4#41×C10112yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—81no—
703C22×C4—81no—
704C22×C4C2×D4×C10111yescharacteristic
705C22×C4C2×D4×C10111yescharacteristic
706C22×C4C2×D4×C10111yescharacteristic
707C22×C4C2×D4×C10111yescharacteristic
708C22×C4C2×D4×C10112yes—
709C22×C4C2×D4×C10112yes—
710C22×C4C24×C10111yescharacteristic
711Q16—44no—
712SD16—44no—
713SD16—44no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—44no—
726C2×C8C2×D4×C10112yes—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4C2×D4×C10112yes—
739C4⋊C4C2×D4×C10112yes—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—24no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C42—21no—
752C42—21no—
753C42—42no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—48no—
771C23—48no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23—84no—
787C23#120×C10112yes—
788C23#135×C10112yes—
789C23C22×D4×C10111yescharacteristic
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796Q8—41no—
797Q8—41no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—44no—
804D4—48no—
805D4—48no—
806D4—41no—
807D4—41no—
808D4—84no—
809D4#121×C10114yes—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—48no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—84no—
849C2×C4#120×C10112yes—
850C2×C4C22×D4×C10111yescharacteristic
851C2×C4C22×D4×C10111yescharacteristic
852C2×C4C22×D4×C10111yescharacteristic
853C2×C4C2×#41×C10111yescharacteristic
854C2×C4H(5,𝔽2)×C10111yescharacteristic
855C2×C4H(5,𝔽2)×C10111yescharacteristic
856C8—22no—
857C8—41no—
858C8—41no—
859C8—41no—
860C22—22no—
861C22—24no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—41no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—42no—
874C22—41no—
875C22—42no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—41no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—816no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22C2×#120×C10111yescharacteristic
890C22D42×C10111yescharacteristic
891C22#546×C10111yescharacteristic
892C22C2×#135×C10111yescharacteristic
893C22#575×C10111yescharacteristic
894C22#577×C10111yescharacteristic
895C22#577×C10111yescharacteristic
896C4—22no—
897C4—41no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—42no—
902C4—42no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4C2×#121×C10111yescharacteristic
907C4#534×C10111yescharacteristic
908C4D42×C10111yescharacteristic
909C4#546×C10111yescharacteristic
910C2—42no—
911C2—42no—
912C2—44no—
913C2—82no—
914C2C101×#241011yescharacteristic
915C2C101×#300211yescharacteristic
916C2C101×#300911yescharacteristic
917C2C101×#326711yescharacteristic
918C2C101×#328211yescharacteristic
919C2C101×#329611yescharacteristic
920C2C101×#331111yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#546×C101C2
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
2. C2×#465×C101C2semidirect
3. C2×#452×C101C2semidirect
4. C2×#450×C101C2semidirect
5. C2×#416×C101C2semidirect
6. C101×#2415C2semidirect
7. C101×#2042C2semidirect
8. C101×#2035C2semidirect
9. C101×#2015C2semidirect
10. C101×#2001C2semidirect
11. C101×#1877C2semidirect
12. C101×#1875C2semidirect
13. C101×#1869C2semidirect
14. C101×#1864C2semidirect
15. C101×#1786C2semidirect
18. C22×Q16×C101C22semidirect
21. C23×C8×C101C22semidirect
28. C2×C22⋊Q8×C101C22semidirect
34. C2×#117×C101C22semidirect
39. C2×#106×C101C22semidirect
41. C2×#103×C101C22semidirect
42. C2×#103×C101C22semidirect
43. C2×#103×C101C22semidirect
44. C2×#103×C101C22semidirect
53. C2×C22⋊C8×C101C22semidirect
56. #391×C101C22semidirect
58. #389×C101C22semidirect
61. #340×C101C22semidirect
62. #340×C101C22semidirect
63. #336×C101C22semidirect
64. #336×C101C22semidirect
158. #102×C101D4semidirect
449. #24436C101direct (N × H)
462. C2×#465C2×C101semidirect
463. C2×#452C2×C101semidirect
464. C2×#450C2×C101semidirect
465. C2×#416C2×C101semidirect
466. #2415C2×C101semidirect
467. #2042C2×C101semidirect
468. #2035C2×C101semidirect
469. #2015C2×C101semidirect
470. #2001C2×C101semidirect
471. #1877C2×C101semidirect
472. #1875C2×C101semidirect
473. #1869C2×C101semidirect
474. #1864C2×C101semidirect
475. #1786C2×C101semidirect
476. C101#24436direct (N × H)
479. C22×Q16C22×C101semidirect
482. C23×C8C22×C101semidirect
489. C2×C22⋊Q8C22×C101semidirect
495. C2×#117C22×C101semidirect
500. C2×#106C22×C101semidirect
502. C2×#103C22×C101semidirect
503. C2×#103C22×C101semidirect
504. C2×#103C22×C101semidirect
505. C2×#103C22×C101semidirect
514. C2×C22⋊C8C22×C101semidirect
517. #391C22×C101semidirect
519. #389C22×C101semidirect
522. #340C22×C101semidirect
523. #340C22×C101semidirect
524. #336C22×C101semidirect
525. #336C22×C101semidirect
619. #102D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1012
C2×#465×C1012
C2×#452×C1012
C2×#450×C1012
C2×#416×C1012
C101×#24152
C101×#20422
C101×#20352
C101×#20152
C101×#20012
C101×#18772
C101×#18752
C101×#18692
C101×#18642
C101×#17862
#24436101