Finite Group Databasebeta

← C101×#24247 #38806398

Subgroups — C101×#24247 #38806398

Order 25856.

1564 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C101C211yesmaximal, characteristic
2C2×#464×C101C211yesmaximal, characteristic, complemented
3C2×#452×C101C211yesmaximal, characteristic, complemented
4C2×#450×C101C211yesmaximal, characteristic, complemented
5C2×C4×SD16×C101C211yesmaximal, characteristic, complemented
6C101×#2536C211yesmaximal, characteristic, complemented
7C101×#2035C211yesmaximal, characteristic, complemented
8C101×#2034C211yesmaximal, characteristic, complemented
9C101×#2001C211yesmaximal, characteristic, complemented
10C101×#2000C211yesmaximal, characteristic, complemented
11C101×#1958C211yesmaximal, characteristic, complemented
12C101×#1954C211yesmaximal, characteristic, complemented
13C101×#1804C211yesmaximal, 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
21#546×C101—24no—
22#546×C101—24no—
23C2×#124×C101C2211yescharacteristic
24C2×#123×C101—21no—
25C2×C22⋊Q8×C101C2211yescharacteristic
26C2×C22⋊Q8×C101C2211yescharacteristic
27C2×C22⋊Q8×C101C2211yescharacteristic, complemented
28C2×#121×C101—21no—
29C2×#121×C101C2211yescharacteristic
30C2×#120×C101—21no—
31C2×C4×Q8×C101C2211yescharacteristic, complemented
32C2×C4×D4×C101C2211yescharacteristic
33C2×C4×D4×C101C2211yescharacteristic
34C22×C22⋊C4×C101—21no—
35#464×C101—24no—
36#452×C101—24no—
37#450×C101—24no—
38C4×SD16×C101—24no—
39C2×#106×C101C2211yescharacteristic, complemented
40C2×C4⋊C8×C101C2211yescharacteristic, complemented
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
54C2×C22⋊C8×C101C2211yescharacteristic, complemented
55C2×C4×C8×C101C2211yescharacteristic, complemented
56#398×C101—21no—
57#394×C101—21no—
58#388×C101—21no—
59#388×C101—21no—
60#382×C101C2211yescharacteristic, complemented
61#380×C101C2211yescharacteristic
62#380×C101C2211yescharacteristic, complemented
63#340×C101C2211yescharacteristic, complemented
64#340×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—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—22no—
92C2×Q16×C101—41no—
93C2×SD16×C101—22no—
94C2×SD16×C101—22no—
95C2×SD16×C101—22no—
96C2×SD16×C101—22no—
97C2×SD16×C101—41no—
98C2×SD16×C101D414yescomplemented
99C22×C8×C101C2311yescharacteristic
100C22×C8×C101C2311yescharacteristic
101C22×C8×C101C2311yescharacteristic
102C22×C8×C101C2311yescharacteristic
103#124×C101—22no—
104#124×C101D414yes—
105#123×C101—28no—
106C22⋊Q8×C101—22no—
107C22⋊Q8×C101—22no—
108C22⋊Q8×C101—22no—
109C22⋊Q8×C101—22no—
110C22⋊Q8×C101—41no—
111C22⋊Q8×C101—41no—
112#121×C101—28no—
113#121×C101—22no—
114#121×C101—22no—
115#120×C101—28no—
116C4×Q8×C101—22no—
117C4×Q8×C101—22no—
118C4×D4×C101—22no—
119C4×D4×C101—22no—
120C4×D4×C101—22no—
121C4×D4×C101D414yes—
122C2×C4⋊C4×C101—21no—
123C2×C4⋊C4×C101—21no—
124C2×C4⋊C4×C101—21no—
125C2×C4⋊C4×C101—21no—
126C2×C4⋊C4×C101D411yescharacteristic
127C2×C4⋊C4×C101C2311yescharacteristic
128C2×C4⋊C4×C101C2311yescharacteristic
129C2×C4⋊C4×C101C2311yescharacteristic
130C2×C4⋊C4×C101C2311yescharacteristic
131C2×C22⋊C4×C101—28no—
132C2×C22⋊C4×C101—21no—
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×C101—21no—
140C2×C22⋊C4×C101—21no—
141C2×C22⋊C4×C101D411yescharacteristic
142C2×C22⋊C4×C101D411yescharacteristic
143C2×C42×C101—21no—
144C2×C42×C101C2311yescharacteristic
145#106×C101—22no—
146C4⋊C8×C101—22no—
147#103×C101—22no—
148#103×C101—22no—
149#103×C101—22no—
150#103×C101—41no—
151#102×C101—22no—
152#102×C101—22no—
153#102×C101—22no—
154#102×C101—22no—
155#102×C101—22no—
156#102×C101—41no—
157C22⋊C8×C101—22no—
158C22⋊C8×C101—22no—
159C22⋊C8×C101—41no—
160C22⋊C8×C101—41no—
161C4×C8×C101—22no—
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—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—22no—
196C2×D4×C101—24no—
197C2×D4×C101—22no—
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—24no—
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—21no—
229C22×C4×C101—21no—
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—24no—
238C22×C4×C101—21no—
239C22×C4×C101—21no—
240C22×C4×C101—21no—
241C22×C4×C101—42no—
242C22×C4×C101—42no—
243C22×C4×C101—81no—
244C22×C4×C101—81no—
245C22×C4×C101C2×D411yescharacteristic
246C22×C4×C101C2×D411yescharacteristic
247C22×C4×C101C2×D411yescharacteristic
248C22×C4×C101C2×D411yescharacteristic
249C22×C4×C101C2411yescharacteristic
250Q16×C101—44no—
251SD16×C101—28no—
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×C101C2×D412yes—
265C4⋊C4×C101—24no—
266C4⋊C4×C101—22no—
267C4⋊C4×C101—21no—
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—
278C22⋊C4×C101—24no—
279C22⋊C4×C101—24no—
280C22⋊C4×C101—22no—
281C22⋊C4×C101—24no—
282C22⋊C4×C101—24no—
283C22⋊C4×C101—24no—
284C22⋊C4×C101—22no—
285C22⋊C4×C101—42no—
286C22⋊C4×C101—42no—
287C22⋊C4×C101—42no—
288C22⋊C4×C101—42no—
289C42×C101—42no—
290C42×C101C2×D412yes—
291C42×C101C2×D412yes—
292C23×C101—21no—
293C23×C101—22no—
294C23×C101—21no—
295C23×C101—22no—
296C23×C101—21no—
297C23×C101—22no—
298C23×C101—21no—
299C23×C101—21no—
300C23×C101—21no—
301C23×C101—22no—
302C23×C101—21no—
303C23×C101—21no—
304C23×C101—21no—
305C23×C101—21no—
306C23×C101—21no—
307C23×C101—21no—
308C23×C101—21no—
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#13512yes—
327C23×C101C22×D411yescharacteristic
328Q8×C101—22no—
329Q8×C101—22no—
330Q8×C101—22no—
331Q8×C101—22no—
332Q8×C101—41no—
333Q8×C101—41no—
334Q8×C101—41no—
335Q8×C101—41no—
336D4×C101—22no—
337D4×C101—22no—
338D4×C101—22no—
339D4×C101—22no—
340D4×C101—22no—
341D4×C101—44no—
342D4×C101—48no—
343D4×C101—48no—
344D4×C101—41no—
345D4×C101—41no—
346D4×C101—84no—
347D4×C101#12114yes—
348C2×C4×C101—21no—
349C2×C4×C101—21no—
350C2×C4×C101—21no—
351C2×C4×C101—21no—
352C2×C4×C101—22no—
353C2×C4×C101—21no—
354C2×C4×C101—22no—
355C2×C4×C101—21no—
356C2×C4×C101—22no—
357C2×C4×C101—21no—
358C2×C4×C101—21no—
359C2×C4×C101—21no—
360C2×C4×C101—21no—
361C2×C4×C101—48no—
362C2×C4×C101—41no—
363C2×C4×C101—41no—
364C2×C4×C101—41no—
365C2×C4×C101—41no—
366C2×C4×C101—41no—
367C2×C4×C101—41no—
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—84no—
386C2×C4×C101#12012yes—
387C2×C4×C101#12012yes—
388C2×C4×C101C22×D411yescharacteristic
389C2×C4×C101C22×D411yescharacteristic
390C2×C4×C101C22×D411yescharacteristic
391C2×C4×C101C2×#4111yescharacteristic
392C2×C4×C101H(5,𝔽2)11yescharacteristic
393C2×C4×C101H(5,𝔽2)11yescharacteristic
394C8×C101—22no—
395C8×C101—41no—
396C8×C101—41no—
397C8×C101—41no—
398C22×C101—24no—
399C22×C101—22no—
400C22×C101—22no—
401C22×C101—22no—
402C22×C101—41no—
403C22×C101—42no—
404C22×C101—42no—
405C22×C101—41no—
406C22×C101—41no—
407C22×C101—42no—
408C22×C101—42no—
409C22×C101—42no—
410C22×C101—41no—
411C22×C101—42no—
412C22×C101—41no—
413C22×C101—42no—
414C22×C101—41no—
415C22×C101—42no—
416C22×C101—41no—
417C22×C101—42no—
418C22×C101—41no—
419C22×C101—41no—
420C22×C101—41no—
421C22×C101—41no—
422C22×C101—816no—
423C22×C101—81no—
424C22×C101—81no—
425C22×C101—81no—
426C22×C101—81no—
427C22×C101C2×#12011yescharacteristic
428C22×C101D4211yescharacteristic
429C22×C101#54611yescharacteristic
430C22×C101C2×#13511yescharacteristic
431C22×C101#57511yescharacteristic
432C22×C101#57711yescharacteristic
433C22×C101#57711yescharacteristic
434C4×C101—22no—
435C4×C101—22no—
436C4×C101—41no—
437C4×C101—41no—
438C4×C101—42no—
439C4×C101—42no—
440C4×C101—42no—
441C4×C101—81no—
442C4×C101—81no—
443C4×C101—81no—
444C4×C101C2×#12111yescharacteristic
445C4×C101#53511yescharacteristic
446C4×C101D4211yescharacteristic
447C4×C101#54611yescharacteristic
448#24247C10111yesmaximal, characteristic, direct product factor, Sylow
449C2×C101—42no—
450C2×C101—44no—
451C2×C101—81no—
452C2×C101—82no—
453C2×C101#240811yescharacteristic
454C2×C101#300211yescharacteristic
455C2×C101#300911yescharacteristic
456C2×C101#327511yescharacteristic
457C2×C101#328211yescharacteristic
458C2×C101#329611yescharacteristic
459C2×C101#332311yescharacteristic
460C2×#546C2×C10111yescharacteristic
461C2×#464C2×C10111yescharacteristic, complemented
462C2×#452C2×C10111yescharacteristic, complemented
463C2×#450C2×C10111yescharacteristic, complemented
464C2×C4×SD16C2×C10111yescharacteristic, complemented
465#2536C2×C10111yescharacteristic, complemented
466#2035C2×C10111yescharacteristic, complemented
467#2034C2×C10111yescharacteristic, complemented
468#2001C2×C10111yescharacteristic, complemented
469#2000C2×C10111yescharacteristic, complemented
470#1958C2×C10111yescharacteristic, complemented
471#1954C2×C10111yescharacteristic, complemented
472#1804C2×C10111yescharacteristic, complemented
473#1788C2×C10111yescharacteristic, complemented
474#1786C2×C10111yescharacteristic, complemented
475C101#2424711yescharacteristic, direct product factor, Sylow
476C22×#41C22×C10111yescharacteristic
477C23×D4C22×C10111yescharacteristic
478C22×Q16C22×C10111yescharacteristic, complemented
479C22×SD16C22×C10111yescharacteristic
480C22×SD16C22×C10111yescharacteristic
481#546—24no—
482#546—24no—
483C2×#124C22×C10111yescharacteristic
484C2×#123—21no—
485C2×C22⋊Q8C22×C10111yescharacteristic
486C2×C22⋊Q8C22×C10111yescharacteristic
487C2×C22⋊Q8C22×C10111yescharacteristic, complemented
488C2×#121—21no—
489C2×#121C22×C10111yescharacteristic
490C2×#120—21no—
491C2×C4×Q8C22×C10111yescharacteristic, complemented
492C2×C4×D4C22×C10111yescharacteristic
493C2×C4×D4C22×C10111yescharacteristic
494C22×C22⋊C4—21no—
495#464—24no—
496#452—24no—
497#450—24no—
498C4×SD16—24no—
499C2×#106C22×C10111yescharacteristic, complemented
500C2×C4⋊C8C22×C10111yescharacteristic, complemented
501C2×#103C22×C10111yescharacteristic, complemented
502C2×#103C22×C10111yescharacteristic, complemented
503C2×#103C22×C10111yescharacteristic, complemented
504C2×#103C22×C10111yescharacteristic, complemented
505C2×#102C22×C10111yescharacteristic
506C2×#102C22×C10111yescharacteristic
507C2×#102C22×C10111yescharacteristic
508C2×#102C22×C10111yescharacteristic
509C2×#102C22×C10111yescharacteristic
510C2×#102C22×C10111yescharacteristic
511C2×C22⋊C8C22×C10111yescharacteristic
512C2×C22⋊C8C22×C10111yescharacteristic
513C2×C22⋊C8C22×C10111yescharacteristic, complemented
514C2×C22⋊C8C22×C10111yescharacteristic, complemented
515C2×C4×C8C22×C10111yescharacteristic, complemented
516#398—21no—
517#394—21no—
518#388—21no—
519#388—21no—
520#382C22×C10111yescharacteristic, complemented
521#380C22×C10111yescharacteristic
522#380C22×C10111yescharacteristic, complemented
523#340C22×C10111yescharacteristic, complemented
524#340C22×C10111yescharacteristic, complemented
525C25—21no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C22×Q8C23×C10111yescharacteristic
533C22×Q8C23×C10111yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—41no—
542C22×D4—41no—
543C22×D4D4×C10111yescharacteristic
544C22×D4C23×C10111yescharacteristic
545C22×D4C23×C10111yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C23×C10111yescharacteristic
549C23×C4C23×C10111yescharacteristic
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—41no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16D4×C10114yescomplemented
559C22×C8C23×C10111yescharacteristic
560C22×C8C23×C10111yescharacteristic
561C22×C8C23×C10111yescharacteristic
562C22×C8C23×C10111yescharacteristic
563#124—22no—
564#124D4×C10114yes—
565#123—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572#121—28no—
573#121—22no—
574#121—22no—
575#120—28no—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4D4×C10114yes—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4D4×C10111yescharacteristic
587C2×C4⋊C4C23×C10111yescharacteristic
588C2×C4⋊C4C23×C10111yescharacteristic
589C2×C4⋊C4C23×C10111yescharacteristic
590C2×C4⋊C4C23×C10111yescharacteristic
591C2×C22⋊C4—28no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C10111yescharacteristic
602C2×C22⋊C4D4×C10111yescharacteristic
603C2×C42—21no—
604C2×C42C23×C10111yescharacteristic
605#106—22no—
606C4⋊C8—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—41no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—41no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8—41no—
620C22⋊C8—41no—
621C4×C8—22no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626C24—21no—
627C24—24no—
628C24—21no—
629C24—42no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—81no—
634C24—81no—
635C24C2×D4×C10111yescharacteristic
636C24C2×D4×C10111yescharacteristic
637#41—44no—
638#41—44no—
639#41—44no—
640#41—44no—
641C2×Q8—21no—
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×Q8C2×D4×C10112yes—
652C2×Q8C2×D4×C10112yes—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—44no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C10112yes—
678C2×D4C2×D4×C10112yes—
679C2×D4C2×D4×C10112yes—
680C2×D4#41×C10112yes—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—24no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—81no—
704C22×C4—81no—
705C22×C4C2×D4×C10111yescharacteristic
706C22×C4C2×D4×C10111yescharacteristic
707C22×C4C2×D4×C10111yescharacteristic
708C22×C4C2×D4×C10111yescharacteristic
709C22×C4C24×C10111yescharacteristic
710Q16—44no—
711SD16—28no—
712SD16—44no—
713C2×C8—21no—
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×C8C2×D4×C10112yes—
725C4⋊C4—24no—
726C4⋊C4—22no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4C2×D4×C10112yes—
738C22⋊C4—24no—
739C22⋊C4—24no—
740C22⋊C4—22no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C42—42no—
750C42C2×D4×C10112yes—
751C42C2×D4×C10112yes—
752C23—21no—
753C23—22no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—48no—
770C23—48no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—84no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23#135×C10112yes—
787C23C22×D4×C10111yescharacteristic
788Q8—22no—
789Q8—22no—
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—44no—
802D4—48no—
803D4—48no—
804D4—41no—
805D4—41no—
806D4—84no—
807D4#121×C10114yes—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—48no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
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—84no—
846C2×C4#120×C10112yes—
847C2×C4#120×C10112yes—
848C2×C4C22×D4×C10111yescharacteristic
849C2×C4C22×D4×C10111yescharacteristic
850C2×C4C22×D4×C10111yescharacteristic
851C2×C4C2×#41×C10111yescharacteristic
852C2×C4H(5,𝔽2)×C10111yescharacteristic
853C2×C4H(5,𝔽2)×C10111yescharacteristic
854C8—22no—
855C8—41no—
856C8—41no—
857C8—41no—
858C22—24no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—41no—
863C22—42no—
864C22—42no—
865C22—41no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—42no—
874C22—41no—
875C22—42no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—816no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22C2×#120×C10111yescharacteristic
888C22D42×C10111yescharacteristic
889C22#546×C10111yescharacteristic
890C22C2×#135×C10111yescharacteristic
891C22#575×C10111yescharacteristic
892C22#577×C10111yescharacteristic
893C22#577×C10111yescharacteristic
894C4—22no—
895C4—22no—
896C4—41no—
897C4—41no—
898C4—42no—
899C4—42no—
900C4—42no—
901C4—81no—
902C4—81no—
903C4—81no—
904C4C2×#121×C10111yescharacteristic
905C4#535×C10111yescharacteristic
906C4D42×C10111yescharacteristic
907C4#546×C10111yescharacteristic
908C2—42no—
909C2—44no—
910C2—81no—
911C2—82no—
912C2C101×#240811yescharacteristic
913C2C101×#300211yescharacteristic
914C2C101×#300911yescharacteristic
915C2C101×#327511yescharacteristic
916C2C101×#328211yescharacteristic
917C2C101×#329611yescharacteristic
918C2C101×#332311yescharacteristic
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×#464×C101C2semidirect
3. C2×#452×C101C2semidirect
4. C2×#450×C101C2semidirect
5. C2×C4×SD16×C101C2semidirect
6. C101×#2536C2semidirect
7. C101×#2035C2semidirect
8. C101×#2034C2semidirect
9. C101×#2001C2semidirect
10. C101×#2000C2semidirect
11. C101×#1958C2semidirect
12. C101×#1954C2semidirect
13. C101×#1804C2semidirect
14. C101×#1788C2semidirect
15. C101×#1786C2semidirect
18. C22×Q16×C101C22semidirect
27. C2×C22⋊Q8×C101C22semidirect
31. C2×C4×Q8×C101C22semidirect
39. C2×#106×C101C22semidirect
40. C2×C4⋊C8×C101C22semidirect
41. C2×#103×C101C22semidirect
42. C2×#103×C101C22semidirect
43. C2×#103×C101C22semidirect
44. C2×#103×C101C22semidirect
53. C2×C22⋊C8×C101C22semidirect
54. C2×C22⋊C8×C101C22semidirect
55. C2×C4×C8×C101C22semidirect
60. #382×C101C22semidirect
62. #380×C101C22semidirect
63. #340×C101C22semidirect
64. #340×C101C22semidirect
98. C2×SD16×C101D4semidirect
448. #24247C101direct (N × H)
461. C2×#464C2×C101semidirect
462. C2×#452C2×C101semidirect
463. C2×#450C2×C101semidirect
464. C2×C4×SD16C2×C101semidirect
465. #2536C2×C101semidirect
466. #2035C2×C101semidirect
467. #2034C2×C101semidirect
468. #2001C2×C101semidirect
469. #2000C2×C101semidirect
470. #1958C2×C101semidirect
471. #1954C2×C101semidirect
472. #1804C2×C101semidirect
473. #1788C2×C101semidirect
474. #1786C2×C101semidirect
475. C101#24247direct (N × H)
478. C22×Q16C22×C101semidirect
487. C2×C22⋊Q8C22×C101semidirect
491. C2×C4×Q8C22×C101semidirect
499. C2×#106C22×C101semidirect
500. C2×C4⋊C8C22×C101semidirect
501. C2×#103C22×C101semidirect
502. C2×#103C22×C101semidirect
503. C2×#103C22×C101semidirect
504. C2×#103C22×C101semidirect
513. C2×C22⋊C8C22×C101semidirect
514. C2×C22⋊C8C22×C101semidirect
515. C2×C4×C8C22×C101semidirect
520. #382C22×C101semidirect
522. #380C22×C101semidirect
523. #340C22×C101semidirect
524. #340C22×C101semidirect
558. C2×SD16D4×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×#464×C1012
C2×#452×C1012
C2×#450×C1012
C2×C4×SD16×C1012
C101×#25362
C101×#20352
C101×#20342
C101×#20012
C101×#20002
C101×#19582
C101×#19542
C101×#18042
C101×#17882
C101×#17862
#24247101