Finite Group Databasebeta

← C101×#24220 #38806371

Subgroups — C101×#24220 #38806371

Order 25856.

1556 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C101C211yesmaximal, characteristic
2C2×#464×C101C211yesmaximal, characteristic, complemented
3C2×#460×C101C211yesmaximal, characteristic, complemented
4C2×#452×C101C211yesmaximal, characteristic, complemented
5C2×#450×C101C211yesmaximal, characteristic, complemented
6C101×#2323C211yesmaximal, characteristic, complemented
7C101×#2042C211yesmaximal, characteristic, complemented
8C101×#2041C211yesmaximal, characteristic, complemented
9C101×#2015C211yesmaximal, characteristic, complemented
10C101×#2014C211yesmaximal, characteristic, complemented
11C101×#1983C211yesmaximal, characteristic, complemented
12C101×#1982C211yesmaximal, characteristic, complemented
13C101×#1798C211yesmaximal, characteristic, complemented
14C101×#1788C211yesmaximal, characteristic, complemented
15C101×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×D4×C101C2211yescharacteristic
18C22×Q16×C101C2211yescharacteristic, complemented
19C22×SD16×C101C2211yescharacteristic
20C22×SD16×C101C2211yescharacteristic
21C22×SD16×C101C2211yescharacteristic, complemented
22#535×C101—24no—
23#535×C101—24no—
24C2×#127×C101C2211yescharacteristic
25C2×#127×C101C2211yescharacteristic
26C2×#124×C101C2211yescharacteristic
27C2×#124×C101C2211yescharacteristic
28C2×C22⋊Q8×C101C2211yescharacteristic
29C2×#121×C101—21no—
30C2×#121×C101—21no—
31C2×#120×C101—21no—
32C2×#120×C101—21no—
33C2×C4×Q8×C101C2211yescharacteristic, complemented
34C2×#117×C101C2211yescharacteristic
35#464×C101—24no—
36#460×C101—24no—
37#452×C101—24no—
38#450×C101—24no—
39C2×C4⋊C8×C101C2211yescharacteristic, complemented
40C2×C4⋊C8×C101C2211yescharacteristic, complemented
41C2×#103×C101C2211yescharacteristic, complemented
42C2×#103×C101C2211yescharacteristic, complemented
43C2×#103×C101C2211yescharacteristic, complemented
44C2×#102×C101C2211yescharacteristic
45C2×#102×C101C2211yescharacteristic
46C2×#102×C101C2211yescharacteristic
47C2×#102×C101C2211yescharacteristic
48C2×#102×C101C2211yescharacteristic
49C2×#102×C101C2211yescharacteristic
50C2×#102×C101C2211yescharacteristic, complemented
51C2×#102×C101C2211yescharacteristic, complemented
52C2×#102×C101C2211yescharacteristic, complemented
53C2×C22⋊C8×C101C2211yescharacteristic
54C2×C22⋊C8×C101C2211yescharacteristic
55#391×C101C2211yescharacteristic, complemented
56#389×C101—21no—
57#389×C101C2211yescharacteristic, complemented
58#388×C101—21no—
59#388×C101—21no—
60#387×C101—21no—
61#380×C101C2211yescharacteristic
62C4×C4⋊C4×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—22no—
70C2×#41×C101—41no—
71C2×#41×C101—41no—
72C22×Q8×C101C2311yescharacteristic
73C22×Q8×C101C2311yescharacteristic
74C22×D4×C101—21no—
75C22×D4×C101—22no—
76C22×D4×C101—22no—
77C22×D4×C101—21no—
78C22×D4×C101—21no—
79C22×D4×C101—21no—
80C22×D4×C101—21no—
81C22×D4×C101—21no—
82C22×D4×C101—22no—
83C22×D4×C101—22no—
84C22×D4×C101—41no—
85C22×D4×C101—41no—
86C22×D4×C101C2311yescharacteristic
87C22×D4×C101C2311yescharacteristic
88C22×D4×C101C2311yescharacteristic
89C23×C4×C101—21no—
90C23×C4×C101C2311yescharacteristic
91C2×Q16×C101—22no—
92C2×Q16×C101—22no—
93C2×Q16×C101—41no—
94C2×SD16×C101—22no—
95C2×SD16×C101—22no—
96C2×SD16×C101—22no—
97C2×SD16×C101—22no—
98C2×SD16×C101—22no—
99C2×SD16×C101—22no—
100C2×SD16×C101—41no—
101C2×SD16×C101—41no—
102C2×SD16×C101—41no—
103C22×C8×C101C2311yescharacteristic
104C22×C8×C101C2311yescharacteristic
105C22×C8×C101C2311yescharacteristic
106C22×C8×C101C2311yescharacteristic
107#127×C101—22no—
108#127×C101—22no—
109#127×C101—22no—
110#127×C101D414yes—
111#124×C101—22no—
112#124×C101—22no—
113#124×C101—22no—
114#124×C101D414yes—
115C22⋊Q8×C101—22no—
116C22⋊Q8×C101D414yescomplemented
117#121×C101—28no—
118#121×C101—28no—
119#120×C101—28no—
120#120×C101—28no—
121C4×Q8×C101—22no—
122C4×Q8×C101—22no—
123#117×C101—22no—
124#117×C101—22no—
125C2×C4⋊C4×C101—21no—
126C2×C4⋊C4×C101—21no—
127C2×C4⋊C4×C101—21no—
128C2×C4⋊C4×C101D411yescharacteristic
129C2×C4⋊C4×C101D411yescharacteristic
130C2×C4⋊C4×C101C2311yescharacteristic
131C2×C4⋊C4×C101C2311yescharacteristic
132C2×C4⋊C4×C101C2311yescharacteristic
133C2×C22⋊C4×C101—21no—
134C2×C22⋊C4×C101—21no—
135C2×C22⋊C4×C101—21no—
136C2×C22⋊C4×C101—21no—
137C2×C22⋊C4×C101—21no—
138C2×C22⋊C4×C101—21no—
139C2×C22⋊C4×C101D411yescharacteristic
140C2×C22⋊C4×C101D411yescharacteristic
141C2×C42×C101—21no—
142C2×C42×C101—21no—
143C2×C42×C101C2311yescharacteristic
144C2×C42×C101C2311yescharacteristic
145C4⋊C8×C101—22no—
146C4⋊C8×C101—22no—
147#103×C101—22no—
148#103×C101—22no—
149#103×C101—41no—
150#102×C101—22no—
151#102×C101—22no—
152#102×C101—22no—
153#102×C101—22no—
154#102×C101—22no—
155#102×C101—22no—
156#102×C101—41no—
157#102×C101—41no—
158#102×C101—41no—
159C22⋊C8×C101—22no—
160C22⋊C8×C101—22no—
161#95×C101—21no—
162#95×C101—21no—
163#95×C101—21no—
164#95×C101—21no—
165#95×C101—21no—
166C24×C101—24no—
167C24×C101—21no—
168C24×C101—21no—
169C24×C101—21no—
170C24×C101—42no—
171C24×C101—42no—
172C24×C101—81no—
173C24×C101—81no—
174C24×C101—81no—
175C24×C101—81no—
176C24×C101C2×D411yescharacteristic
177#41×C101—44no—
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×C101C2×D412yes—
192C2×Q8×C101C2×D412yes—
193C2×D4×C101—24no—
194C2×D4×C101—24no—
195C2×D4×C101—24no—
196C2×D4×C101—24no—
197C2×D4×C101—24no—
198C2×D4×C101—24no—
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—21no—
207C2×D4×C101—21no—
208C2×D4×C101—21no—
209C2×D4×C101—21no—
210C2×D4×C101—21no—
211C2×D4×C101—21no—
212C2×D4×C101—21no—
213C2×D4×C101—21no—
214C2×D4×C101—44no—
215C2×D4×C101—44no—
216C2×D4×C101—44no—
217C2×D4×C101—44no—
218C2×D4×C101—42no—
219C2×D4×C101—42no—
220C2×D4×C101—42no—
221C2×D4×C101—42no—
222C2×D4×C101—81no—
223C2×D4×C101—81no—
224C2×D4×C101—81no—
225C2×D4×C101—81no—
226C2×D4×C101—81no—
227C2×D4×C101—81no—
228C2×D4×C101—81no—
229C2×D4×C101—81no—
230C2×D4×C101C2×D412yes—
231C2×D4×C101C2×D412yes—
232C2×D4×C101C2×D412yes—
233C22×C4×C101—21no—
234C22×C4×C101—21no—
235C22×C4×C101—21no—
236C22×C4×C101—21no—
237C22×C4×C101—24no—
238C22×C4×C101—21no—
239C22×C4×C101—21no—
240C22×C4×C101—21no—
241C22×C4×C101—21no—
242C22×C4×C101—21no—
243C22×C4×C101—42no—
244C22×C4×C101—42no—
245C22×C4×C101C2×D411yescharacteristic
246C22×C4×C101C2×D411yescharacteristic
247C22×C4×C101C2×D411yescharacteristic
248C22×C4×C101C2×D411yescharacteristic
249C22×C4×C101C2×D411yescharacteristic
250C22×C4×C101C2×D412yes—
251C22×C4×C101#4112yes—
252C22×C4×C101C2411yescharacteristic
253Q16×C101—44no—
254SD16×C101—44no—
255SD16×C101—44no—
256SD16×C101—44no—
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—21no—
265C2×C8×C101—21no—
266C2×C8×C101—21no—
267C2×C8×C101—21no—
268C2×C8×C101—21no—
269C4⋊C4×C101—22no—
270C4⋊C4×C101—22no—
271C4⋊C4×C101—24no—
272C4⋊C4×C101—21no—
273C4⋊C4×C101—21no—
274C4⋊C4×C101—21no—
275C4⋊C4×C101—21no—
276C4⋊C4×C101—21no—
277C4⋊C4×C101—42no—
278C4⋊C4×C101—81no—
279C4⋊C4×C101C2×D412yes—
280C22⋊C4×C101—24no—
281C22⋊C4×C101—24no—
282C22⋊C4×C101—24no—
283C22⋊C4×C101—24no—
284C22⋊C4×C101—24no—
285C22⋊C4×C101—22no—
286C22⋊C4×C101—22no—
287C22⋊C4×C101—81no—
288C42×C101—21no—
289C42×C101—21no—
290C42×C101—42no—
291C42×C101—81no—
292C42×C101C2×D412yes—
293C42×C101C2×D412yes—
294C23×C101—21no—
295C23×C101—21no—
296C23×C101—21no—
297C23×C101—21no—
298C23×C101—21no—
299C23×C101—21no—
300C23×C101—22no—
301C23×C101—22no—
302C23×C101—22no—
303C23×C101—48no—
304C23×C101—41no—
305C23×C101—41no—
306C23×C101—41no—
307C23×C101—41no—
308C23×C101—41no—
309C23×C101—41no—
310C23×C101—41no—
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—41no—
322C23×C101—84no—
323C23×C101—84no—
324C23×C101—84no—
325C23×C101—84no—
326C23×C101—84no—
327C23×C101—84no—
328C23×C101#12112yes—
329C23×C101C22×D411yescharacteristic
330Q8×C101—22no—
331Q8×C101—22no—
332Q8×C101—22no—
333Q8×C101—22no—
334Q8×C101—41no—
335Q8×C101—41no—
336Q8×C101—41no—
337Q8×C101—41no—
338D4×C101—22no—
339D4×C101—22no—
340D4×C101—22no—
341D4×C101—22no—
342D4×C101—22no—
343D4×C101—22no—
344D4×C101—48no—
345D4×C101—48no—
346D4×C101—41no—
347D4×C101—41no—
348D4×C101—41no—
349D4×C101—41no—
350D4×C101—41no—
351D4×C101—41no—
352D4×C101—84no—
353D4×C101—84no—
354D4×C101—84no—
355D4×C101—84no—
356C2×C4×C101—21no—
357C2×C4×C101—21no—
358C2×C4×C101—21no—
359C2×C4×C101—21no—
360C2×C4×C101—21no—
361C2×C4×C101—21no—
362C2×C4×C101—22no—
363C2×C4×C101—22no—
364C2×C4×C101—22no—
365C2×C4×C101—22no—
366C2×C4×C101—21no—
367C2×C4×C101—21no—
368C2×C4×C101—22no—
369C2×C4×C101—22no—
370C2×C4×C101—22no—
371C2×C4×C101—21no—
372C2×C4×C101—21no—
373C2×C4×C101—21no—
374C2×C4×C101—21no—
375C2×C4×C101—48no—
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—41no—
388C2×C4×C101#12012yes—
389C2×C4×C101#12012yes—
390C2×C4×C101#12112yes—
391C2×C4×C101C22×D411yescharacteristic
392C2×C4×C101C22×D411yescharacteristic
393C2×C4×C101C22×D411yescharacteristic
394C2×C4×C101C2×#4111yescharacteristic
395C2×C4×C101H(5,𝔽2)11yescharacteristic
396C2×C4×C101H(5,𝔽2)11yescharacteristic
397C8×C101—41no—
398C8×C101—41no—
399C8×C101—41no—
400C8×C101—41no—
401C22×C101—22no—
402C22×C101—22no—
403C22×C101—22no—
404C22×C101—41no—
405C22×C101—41no—
406C22×C101—41no—
407C22×C101—41no—
408C22×C101—42no—
409C22×C101—42no—
410C22×C101—42no—
411C22×C101—42no—
412C22×C101—42no—
413C22×C101—42no—
414C22×C101—42no—
415C22×C101—42no—
416C22×C101—42no—
417C22×C101—816no—
418C22×C101—81no—
419C22×C101—81no—
420C22×C101—81no—
421C22×C101—81no—
422C22×C101—81no—
423C22×C101—81no—
424C22×C101—81no—
425C22×C101—81no—
426C22×C101—81no—
427C22×C101—81no—
428C22×C101—81no—
429C22×C101—81no—
430C22×C101C2×#12011yescharacteristic
431C22×C101C2×#12111yescharacteristic
432C22×C101#53511yescharacteristic
433C22×C101#57611yescharacteristic
434C22×C101#57711yescharacteristic
435C22×C101#57711yescharacteristic
436C22×C101#57711yescharacteristic
437C4×C101—22no—
438C4×C101—22no—
439C4×C101—22no—
440C4×C101—42no—
441C4×C101—42no—
442C4×C101—41no—
443C4×C101—41no—
444C4×C101—42no—
445C4×C101—81no—
446C4×C101—81no—
447C4×C101D4211yescharacteristic
448C4×C101D4211yescharacteristic
449C4×C101#54611yescharacteristic
450C4×C101#54611yescharacteristic
451#24220C10111yesmaximal, characteristic, direct product factor, Sylow
452C2×C101—42no—
453C2×C101—82no—
454C2×C101—82no—
455C2×C101—82no—
456C2×C101#240811yescharacteristic
457C2×C101#300911yescharacteristic
458C2×C101#301211yescharacteristic
459C2×C101#304311yescharacteristic
460C2×C101#304511yescharacteristic
461C2×C101#322211yescharacteristic
462C2×C101#322411yescharacteristic
463C2×#535C2×C10111yescharacteristic
464C2×#464C2×C10111yescharacteristic, complemented
465C2×#460C2×C10111yescharacteristic, complemented
466C2×#452C2×C10111yescharacteristic, complemented
467C2×#450C2×C10111yescharacteristic, complemented
468#2323C2×C10111yescharacteristic, complemented
469#2042C2×C10111yescharacteristic, complemented
470#2041C2×C10111yescharacteristic, complemented
471#2015C2×C10111yescharacteristic, complemented
472#2014C2×C10111yescharacteristic, complemented
473#1983C2×C10111yescharacteristic, complemented
474#1982C2×C10111yescharacteristic, complemented
475#1798C2×C10111yescharacteristic, complemented
476#1788C2×C10111yescharacteristic, complemented
477#1786C2×C10111yescharacteristic, complemented
478C101#2422011yescharacteristic, direct product factor, Sylow
479C22×#41C22×C10111yescharacteristic
480C23×D4C22×C10111yescharacteristic
481C22×Q16C22×C10111yescharacteristic, complemented
482C22×SD16C22×C10111yescharacteristic
483C22×SD16C22×C10111yescharacteristic
484C22×SD16C22×C10111yescharacteristic, complemented
485#535—24no—
486#535—24no—
487C2×#127C22×C10111yescharacteristic
488C2×#127C22×C10111yescharacteristic
489C2×#124C22×C10111yescharacteristic
490C2×#124C22×C10111yescharacteristic
491C2×C22⋊Q8C22×C10111yescharacteristic
492C2×#121—21no—
493C2×#121—21no—
494C2×#120—21no—
495C2×#120—21no—
496C2×C4×Q8C22×C10111yescharacteristic, complemented
497C2×#117C22×C10111yescharacteristic
498#464—24no—
499#460—24no—
500#452—24no—
501#450—24no—
502C2×C4⋊C8C22×C10111yescharacteristic, complemented
503C2×C4⋊C8C22×C10111yescharacteristic, complemented
504C2×#103C22×C10111yescharacteristic, complemented
505C2×#103C22×C10111yescharacteristic, complemented
506C2×#103C22×C10111yescharacteristic, complemented
507C2×#102C22×C10111yescharacteristic
508C2×#102C22×C10111yescharacteristic
509C2×#102C22×C10111yescharacteristic
510C2×#102C22×C10111yescharacteristic
511C2×#102C22×C10111yescharacteristic
512C2×#102C22×C10111yescharacteristic
513C2×#102C22×C10111yescharacteristic, complemented
514C2×#102C22×C10111yescharacteristic, complemented
515C2×#102C22×C10111yescharacteristic, complemented
516C2×C22⋊C8C22×C10111yescharacteristic
517C2×C22⋊C8C22×C10111yescharacteristic
518#391C22×C10111yescharacteristic, complemented
519#389—21no—
520#389C22×C10111yescharacteristic, complemented
521#388—21no—
522#388—21no—
523#387—21no—
524#380C22×C10111yescharacteristic
525C4×C4⋊C4C22×C10111yescharacteristic, complemented
526#336C22×C10111yescharacteristic, complemented
527#336C22×C10111yescharacteristic, complemented
528C25—21no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—41no—
534C2×#41—41no—
535C22×Q8C23×C10111yescharacteristic
536C22×Q8C23×C10111yescharacteristic
537C22×D4—21no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—22no—
546C22×D4—22no—
547C22×D4—41no—
548C22×D4—41no—
549C22×D4C23×C10111yescharacteristic
550C22×D4C23×C10111yescharacteristic
551C22×D4C23×C10111yescharacteristic
552C23×C4—21no—
553C23×C4C23×C10111yescharacteristic
554C2×Q16—22no—
555C2×Q16—22no—
556C2×Q16—41no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C22×C8C23×C10111yescharacteristic
567C22×C8C23×C10111yescharacteristic
568C22×C8C23×C10111yescharacteristic
569C22×C8C23×C10111yescharacteristic
570#127—22no—
571#127—22no—
572#127—22no—
573#127D4×C10114yes—
574#124—22no—
575#124—22no—
576#124—22no—
577#124D4×C10114yes—
578C22⋊Q8—22no—
579C22⋊Q8D4×C10114yescomplemented
580#121—28no—
581#121—28no—
582#120—28no—
583#120—28no—
584C4×Q8—22no—
585C4×Q8—22no—
586#117—22no—
587#117—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4D4×C10111yescharacteristic
592C2×C4⋊C4D4×C10111yescharacteristic
593C2×C4⋊C4C23×C10111yescharacteristic
594C2×C4⋊C4C23×C10111yescharacteristic
595C2×C4⋊C4C23×C10111yescharacteristic
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⋊C4D4×C10111yescharacteristic
603C2×C22⋊C4D4×C10111yescharacteristic
604C2×C42—21no—
605C2×C42—21no—
606C2×C42C23×C10111yescharacteristic
607C2×C42C23×C10111yescharacteristic
608C4⋊C8—22no—
609C4⋊C8—22no—
610#103—22no—
611#103—22no—
612#103—41no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—22no—
618#102—22no—
619#102—41no—
620#102—41no—
621#102—41no—
622C22⋊C8—22no—
623C22⋊C8—22no—
624#95—21no—
625#95—21no—
626#95—21no—
627#95—21no—
628#95—21no—
629C24—24no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—42no—
634C24—42no—
635C24—81no—
636C24—81no—
637C24—81no—
638C24—81no—
639C24C2×D4×C10111yescharacteristic
640#41—44no—
641#41—44no—
642#41—44no—
643#41—44no—
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×Q8—21no—
654C2×Q8C2×D4×C10112yes—
655C2×Q8C2×D4×C10112yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—81no—
686C2×D4—81no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4—81no—
690C2×D4—81no—
691C2×D4—81no—
692C2×D4—81no—
693C2×D4C2×D4×C10112yes—
694C2×D4C2×D4×C10112yes—
695C2×D4C2×D4×C10112yes—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—24no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4C2×D4×C10111yescharacteristic
709C22×C4C2×D4×C10111yescharacteristic
710C22×C4C2×D4×C10111yescharacteristic
711C22×C4C2×D4×C10111yescharacteristic
712C22×C4C2×D4×C10111yescharacteristic
713C22×C4C2×D4×C10112yes—
714C22×C4#41×C10112yes—
715C22×C4C24×C10111yescharacteristic
716Q16—44no—
717SD16—44no—
718SD16—44no—
719SD16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C4⋊C4—22no—
733C4⋊C4—22no—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—42no—
741C4⋊C4—81no—
742C4⋊C4C2×D4×C10112yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—81no—
751C42—21no—
752C42—21no—
753C42—42no—
754C42—81no—
755C42C2×D4×C10112yes—
756C42C2×D4×C10112yes—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—48no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23#121×C10112yes—
792C23C22×D4×C10111yescharacteristic
793Q8—22no—
794Q8—22no—
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4—41no—
815D4—84no—
816D4—84no—
817D4—84no—
818D4—84no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—48no—
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—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4#120×C10112yes—
852C2×C4#120×C10112yes—
853C2×C4#121×C10112yes—
854C2×C4C22×D4×C10111yescharacteristic
855C2×C4C22×D4×C10111yescharacteristic
856C2×C4C22×D4×C10111yescharacteristic
857C2×C4C2×#41×C10111yescharacteristic
858C2×C4H(5,𝔽2)×C10111yescharacteristic
859C2×C4H(5,𝔽2)×C10111yescharacteristic
860C8—41no—
861C8—41no—
862C8—41no—
863C8—41no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—816no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22C2×#120×C10111yescharacteristic
894C22C2×#121×C10111yescharacteristic
895C22#535×C10111yescharacteristic
896C22#576×C10111yescharacteristic
897C22#577×C10111yescharacteristic
898C22#577×C10111yescharacteristic
899C22#577×C10111yescharacteristic
900C4—22no—
901C4—22no—
902C4—22no—
903C4—42no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—42no—
908C4—81no—
909C4—81no—
910C4D42×C10111yescharacteristic
911C4D42×C10111yescharacteristic
912C4#546×C10111yescharacteristic
913C4#546×C10111yescharacteristic
914C2—42no—
915C2—82no—
916C2—82no—
917C2—82no—
918C2C101×#240811yescharacteristic
919C2C101×#300911yescharacteristic
920C2C101×#301211yescharacteristic
921C2C101×#304311yescharacteristic
922C2C101×#304511yescharacteristic
923C2C101×#322211yescharacteristic
924C2C101×#322411yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#535×C101C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×#117×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#464×C101C2semidirect
3. C2×#460×C101C2semidirect
4. C2×#452×C101C2semidirect
5. C2×#450×C101C2semidirect
6. C101×#2323C2semidirect
7. C101×#2042C2semidirect
8. C101×#2041C2semidirect
9. C101×#2015C2semidirect
10. C101×#2014C2semidirect
11. C101×#1983C2semidirect
12. C101×#1982C2semidirect
13. C101×#1798C2semidirect
14. C101×#1788C2semidirect
15. C101×#1786C2semidirect
18. C22×Q16×C101C22semidirect
21. C22×SD16×C101C22semidirect
33. C2×C4×Q8×C101C22semidirect
39. C2×C4⋊C8×C101C22semidirect
40. C2×C4⋊C8×C101C22semidirect
41. C2×#103×C101C22semidirect
42. C2×#103×C101C22semidirect
43. C2×#103×C101C22semidirect
50. C2×#102×C101C22semidirect
51. C2×#102×C101C22semidirect
52. C2×#102×C101C22semidirect
55. #391×C101C22semidirect
57. #389×C101C22semidirect
62. C4×C4⋊C4×C101C22semidirect
63. #336×C101C22semidirect
64. #336×C101C22semidirect
116. C22⋊Q8×C101D4semidirect
451. #24220C101direct (N × H)
464. C2×#464C2×C101semidirect
465. C2×#460C2×C101semidirect
466. C2×#452C2×C101semidirect
467. C2×#450C2×C101semidirect
468. #2323C2×C101semidirect
469. #2042C2×C101semidirect
470. #2041C2×C101semidirect
471. #2015C2×C101semidirect
472. #2014C2×C101semidirect
473. #1983C2×C101semidirect
474. #1982C2×C101semidirect
475. #1798C2×C101semidirect
476. #1788C2×C101semidirect
477. #1786C2×C101semidirect
478. C101#24220direct (N × H)
481. C22×Q16C22×C101semidirect
484. C22×SD16C22×C101semidirect
496. C2×C4×Q8C22×C101semidirect
502. C2×C4⋊C8C22×C101semidirect
503. C2×C4⋊C8C22×C101semidirect
504. C2×#103C22×C101semidirect
505. C2×#103C22×C101semidirect
506. C2×#103C22×C101semidirect
513. C2×#102C22×C101semidirect
514. C2×#102C22×C101semidirect
515. C2×#102C22×C101semidirect
518. #391C22×C101semidirect
520. #389C22×C101semidirect
525. C4×C4⋊C4C22×C101semidirect
526. #336C22×C101semidirect
527. #336C22×C101semidirect
579. C22⋊Q8D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1012
C2×#464×C1012
C2×#460×C1012
C2×#452×C1012
C2×#450×C1012
C101×#23232
C101×#20422
C101×#20412
C101×#20152
C101×#20142
C101×#19832
C101×#19822
C101×#17982
C101×#17882
C101×#17862
#24220101