Finite Group Databasebeta

← C101×#24244 #38806395

Subgroups — C101×#24244 #38806395

Order 25856.

1488 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C101C211yesmaximal, characteristic, complemented
2C2×#463×C101C211yesmaximal, characteristic, complemented
3C2×#449×C101C211yesmaximal, characteristic, complemented
4C2×#448×C101C211yesmaximal, characteristic, complemented
5C2×C4×SD16×C101C211yesmaximal, characteristic, complemented
6C101×#2535C211yesmaximal, characteristic, complemented
7C101×#2035C211yesmaximal, characteristic, complemented
8C101×#2034C211yesmaximal, characteristic, complemented
9C101×#2000C211yesmaximal, characteristic, complemented
10C101×#1999C211yesmaximal, characteristic, complemented
11C101×#1958C211yesmaximal, characteristic, complemented
12C101×#1954C211yesmaximal, characteristic, complemented
13C101×#1805C211yesmaximal, characteristic, complemented
14C101×#1788C211yesmaximal, characteristic, complemented
15C101×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×Q8×C101C2211yescharacteristic
18C22×SD16×C101C2211yescharacteristic
19C22×SD16×C101C2211yescharacteristic
20C22×D8×C101C2211yescharacteristic
21#548×C101—24no—
22#548×C101—24no—
23C2×#124×C101—21no—
24C2×#124×C101C2211yescharacteristic
25C2×C22⋊Q8×C101—21no—
26C2×C22⋊Q8×C101C2211yescharacteristic
27C2×#121×C101—21no—
28C2×#121×C101C2211yescharacteristic
29C2×#121×C101C2211yescharacteristic
30C2×#121×C101C2211yescharacteristic
31C2×C4×Q8×C101C2211yescharacteristic
32C2×C4×D4×C101—21no—
33C2×C4×D4×C101C2211yescharacteristic
34C2×C4×D4×C101C2211yescharacteristic
35#463×C101—24no—
36#449×C101—24no—
37#448×C101—24no—
38C4×SD16×C101—24no—
39C2×#106×C101C2211yescharacteristic
40C2×C4⋊C8×C101C2211yescharacteristic
41C2×#103×C101C2211yescharacteristic
42C2×#103×C101C2211yescharacteristic
43C2×#103×C101C2211yescharacteristic
44C2×#103×C101C2211yescharacteristic
45C2×#103×C101C2211yescharacteristic
46C2×#103×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
54C2×C22⋊C8×C101C2211yescharacteristic
55C2×C4×C8×C101C2211yescharacteristic
56#397×C101—21no—
57#392×C101—21no—
58#386×C101—21no—
59#386×C101—21no—
60#382×C101C2211yescharacteristic
61#380×C101C2211yescharacteristic
62#380×C101C2211yescharacteristic
63#340×C101C2211yescharacteristic
64#340×C101C2211yescharacteristic
65C2×#41×C101—22no—
66C2×#41×C101—22no—
67C2×#41×C101—22no—
68C2×#41×C101—22no—
69C2×#41×C101—41no—
70C2×#41×C101—41no—
71C22×Q8×C101—22no—
72C22×Q8×C101—22no—
73C22×Q8×C101—21no—
74C22×Q8×C101—22no—
75C22×Q8×C101—22no—
76C22×Q8×C101—41no—
77C22×Q8×C101—41no—
78C22×Q8×C101C2311yescharacteristic
79C22×Q8×C101C2311yescharacteristic
80C22×D4×C101—21no—
81C22×D4×C101—21no—
82C22×D4×C101—21no—
83C22×D4×C101—21no—
84C22×D4×C101D411yescharacteristic
85C22×D4×C101C2311yescharacteristic
86C22×D4×C101C2311yescharacteristic
87C23×C4×C101—21no—
88C23×C4×C101—21no—
89C23×C4×C101—21no—
90C23×C4×C101C2311yescharacteristic
91C23×C4×C101C2311yescharacteristic
92C2×SD16×C101—22no—
93C2×SD16×C101—22no—
94C2×SD16×C101—22no—
95C2×SD16×C101—22no—
96C2×SD16×C101—41no—
97C2×SD16×C101D414yescomplemented
98C2×D8×C101—22no—
99C2×D8×C101—22no—
100C2×D8×C101—41no—
101C22×C8×C101C2311yescharacteristic
102C22×C8×C101C2311yescharacteristic
103C22×C8×C101C2311yescharacteristic
104C22×C8×C101C2311yescharacteristic
105#124×C101—28no—
106#124×C101—22no—
107#124×C101D414yescomplemented
108C22⋊Q8×C101—28no—
109C22⋊Q8×C101—22no—
110C22⋊Q8×C101—22no—
111#121×C101—28no—
112#121×C101—22no—
113#121×C101—22no—
114#121×C101—22no—
115#121×C101—22no—
116#121×C101—41no—
117#121×C101—41no—
118C4×Q8×C101—22no—
119C4×Q8×C101D414yescomplemented
120C4×D4×C101—28no—
121C4×D4×C101—22no—
122C4×D4×C101—22no—
123C4×D4×C101—22no—
124C4×D4×C101—22no—
125C2×C4⋊C4×C101—21no—
126C2×C4⋊C4×C101—21no—
127C2×C4⋊C4×C101D411yescharacteristic
128C2×C4⋊C4×C101C2311yescharacteristic
129C2×C4⋊C4×C101C2311yescharacteristic
130C2×C4⋊C4×C101C2311yescharacteristic
131C2×C4⋊C4×C101C2311yescharacteristic
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—22no—
151#103×C101—22no—
152#103×C101—41no—
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—21no—
168C24×C101C2×D411yescharacteristic
169C24×C101C2×D411yescharacteristic
170#41×C101—44no—
171#41×C101—44no—
172#41×C101—44no—
173#41×C101—44no—
174C2×Q8×C101—24no—
175C2×Q8×C101—21no—
176C2×Q8×C101—21no—
177C2×Q8×C101—21no—
178C2×Q8×C101—21no—
179C2×Q8×C101—21no—
180C2×Q8×C101—21no—
181C2×Q8×C101—21no—
182C2×Q8×C101—21no—
183C2×Q8×C101—42no—
184C2×Q8×C101—42no—
185C2×Q8×C101—44no—
186C2×Q8×C101—44no—
187C2×Q8×C101—44no—
188C2×Q8×C101—44no—
189C2×Q8×C101C2×D412yes—
190C2×Q8×C101C2×D412yes—
191C2×Q8×C101C2×D412yes—
192C2×Q8×C101#4112yes—
193C2×D4×C101—24no—
194C2×D4×C101—24no—
195C2×D4×C101—22no—
196C2×D4×C101—22no—
197C2×D4×C101—21no—
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—21no—
207C2×D4×C101—41no—
208C2×D4×C101—42no—
209C2×D4×C101—42no—
210C2×D4×C101—42no—
211C2×D4×C101—42no—
212C2×D4×C101—42no—
213C2×D4×C101—42no—
214C2×D4×C101—42no—
215C2×D4×C101—42no—
216C2×D4×C101—81no—
217C2×D4×C101—81no—
218C2×D4×C101C2×D412yes—
219C2×D4×C101C2×D412yes—
220C22×C4×C101—21no—
221C22×C4×C101—24no—
222C22×C4×C101—24no—
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—21no—
238C22×C4×C101—21no—
239C22×C4×C101—21no—
240C22×C4×C101—42no—
241C22×C4×C101—42no—
242C22×C4×C101—42no—
243C22×C4×C101—42no—
244C22×C4×C101—42no—
245C22×C4×C101—81no—
246C22×C4×C101—81no—
247C22×C4×C101C2×D411yescharacteristic
248C22×C4×C101C2×D411yescharacteristic
249C22×C4×C101C2×D411yescharacteristic
250C22×C4×C101C2×D411yescharacteristic
251C22×C4×C101C2411yescharacteristic
252SD16×C101—28no—
253SD16×C101—44no—
254D8×C101—44no—
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—21no—
265C2×C8×C101—21no—
266C2×C8×C101C2×D412yes—
267C4⋊C4×C101—24no—
268C4⋊C4×C101—24no—
269C4⋊C4×C101—22no—
270C4⋊C4×C101—21no—
271C4⋊C4×C101—21no—
272C4⋊C4×C101—21no—
273C4⋊C4×C101—21no—
274C4⋊C4×C101—21no—
275C4⋊C4×C101—21no—
276C4⋊C4×C101—21no—
277C4⋊C4×C101C2×D412yes—
278C22⋊C4×C101—24no—
279C22⋊C4×C101—24no—
280C22⋊C4×C101—24no—
281C22⋊C4×C101—24no—
282C22⋊C4×C101—22no—
283C22⋊C4×C101—22no—
284C22⋊C4×C101—42no—
285C22⋊C4×C101—42no—
286C22⋊C4×C101—42no—
287C22⋊C4×C101—81no—
288C22⋊C4×C101—81no—
289C42×C101—24no—
290C42×C101C2×D412yes—
291C42×C101C2×D412yes—
292C23×C101—21no—
293C23×C101—21no—
294C23×C101—21no—
295C23×C101—21no—
296C23×C101—21no—
297C23×C101—21no—
298C23×C101—21no—
299C23×C101—22no—
300C23×C101—22no—
301C23×C101—21no—
302C23×C101—21no—
303C23×C101—21no—
304C23×C101—21no—
305C23×C101—21no—
306C23×C101—21no—
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#13512yes—
320C23×C101C22×D411yescharacteristic
321Q8×C101—22no—
322Q8×C101—22no—
323Q8×C101—22no—
324Q8×C101—22no—
325Q8×C101—22no—
326Q8×C101—48no—
327Q8×C101—41no—
328Q8×C101—41no—
329Q8×C101#12114yes—
330D4×C101—22no—
331D4×C101—22no—
332D4×C101—22no—
333D4×C101—22no—
334D4×C101—44no—
335D4×C101—48no—
336D4×C101—48no—
337D4×C101—41no—
338D4×C101—41no—
339D4×C101—41no—
340D4×C101—41no—
341D4×C101—84no—
342D4×C101—84no—
343C2×C4×C101—22no—
344C2×C4×C101—22no—
345C2×C4×C101—22no—
346C2×C4×C101—21no—
347C2×C4×C101—21no—
348C2×C4×C101—21no—
349C2×C4×C101—21no—
350C2×C4×C101—22no—
351C2×C4×C101—22no—
352C2×C4×C101—21no—
353C2×C4×C101—21no—
354C2×C4×C101—21no—
355C2×C4×C101—21no—
356C2×C4×C101—21no—
357C2×C4×C101—21no—
358C2×C4×C101—48no—
359C2×C4×C101—48no—
360C2×C4×C101—41no—
361C2×C4×C101—41no—
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—84no—
382C2×C4×C101#12012yes—
383C2×C4×C101#12012yes—
384C2×C4×C101C22×D411yescharacteristic
385C2×C4×C101C22×D411yescharacteristic
386C2×C4×C101C22×D411yescharacteristic
387C2×C4×C101C2×#4111yescharacteristic
388C2×C4×C101H(5,𝔽2)11yescharacteristic
389C2×C4×C101H(5,𝔽2)11yescharacteristic
390C8×C101—22no—
391C8×C101—41no—
392C8×C101—41no—
393C8×C101—41no—
394C22×C101—22no—
395C22×C101—22no—
396C22×C101—22no—
397C22×C101—41no—
398C22×C101—41no—
399C22×C101—41no—
400C22×C101—41no—
401C22×C101—42no—
402C22×C101—41no—
403C22×C101—42no—
404C22×C101—41no—
405C22×C101—42no—
406C22×C101—41no—
407C22×C101—42no—
408C22×C101—41no—
409C22×C101—42no—
410C22×C101—42no—
411C22×C101—41no—
412C22×C101—41no—
413C22×C101—41no—
414C22×C101—81no—
415C22×C101—81no—
416C22×C101—81no—
417C22×C101—81no—
418C22×C101—81no—
419C22×C101—81no—
420C22×C101—81no—
421C22×C101—81no—
422C22×C101C2×#12011yescharacteristic
423C22×C101D4211yescharacteristic
424C22×C101#54611yescharacteristic
425C22×C101C2×#13511yescharacteristic
426C22×C101#57511yescharacteristic
427C22×C101#57711yescharacteristic
428C22×C101#57711yescharacteristic
429C4×C101—24no—
430C4×C101—22no—
431C4×C101—22no—
432C4×C101—41no—
433C4×C101—41no—
434C4×C101—42no—
435C4×C101—42no—
436C4×C101—81no—
437C4×C101—81no—
438C4×C101—81no—
439C4×C101C2×#12111yescharacteristic
440C4×C101#53511yescharacteristic
441C4×C101D4211yescharacteristic
442C4×C101#54611yescharacteristic
443#24244C10111yesmaximal, characteristic, direct product factor, Sylow
444C2×C101—42no—
445C2×C101—81no—
446C2×C101—82no—
447C2×C101—82no—
448C2×C101#240811yescharacteristic
449C2×C101#300211yescharacteristic
450C2×C101#301011yescharacteristic
451C2×C101#327511yescharacteristic
452C2×C101#328211yescharacteristic
453C2×C101#330111yescharacteristic
454C2×C101#332611yescharacteristic
455C2×#548C2×C10111yescharacteristic, complemented
456C2×#463C2×C10111yescharacteristic, complemented
457C2×#449C2×C10111yescharacteristic, complemented
458C2×#448C2×C10111yescharacteristic, complemented
459C2×C4×SD16C2×C10111yescharacteristic, complemented
460#2535C2×C10111yescharacteristic, complemented
461#2035C2×C10111yescharacteristic, complemented
462#2034C2×C10111yescharacteristic, complemented
463#2000C2×C10111yescharacteristic, complemented
464#1999C2×C10111yescharacteristic, complemented
465#1958C2×C10111yescharacteristic, complemented
466#1954C2×C10111yescharacteristic, complemented
467#1805C2×C10111yescharacteristic, complemented
468#1788C2×C10111yescharacteristic, complemented
469#1787C2×C10111yescharacteristic, complemented
470C101#2424411yescharacteristic, direct product factor, Sylow
471C22×#41C22×C10111yescharacteristic
472C23×Q8C22×C10111yescharacteristic
473C22×SD16C22×C10111yescharacteristic
474C22×SD16C22×C10111yescharacteristic
475C22×D8C22×C10111yescharacteristic
476#548—24no—
477#548—24no—
478C2×#124—21no—
479C2×#124C22×C10111yescharacteristic
480C2×C22⋊Q8—21no—
481C2×C22⋊Q8C22×C10111yescharacteristic
482C2×#121—21no—
483C2×#121C22×C10111yescharacteristic
484C2×#121C22×C10111yescharacteristic
485C2×#121C22×C10111yescharacteristic
486C2×C4×Q8C22×C10111yescharacteristic
487C2×C4×D4—21no—
488C2×C4×D4C22×C10111yescharacteristic
489C2×C4×D4C22×C10111yescharacteristic
490#463—24no—
491#449—24no—
492#448—24no—
493C4×SD16—24no—
494C2×#106C22×C10111yescharacteristic
495C2×C4⋊C8C22×C10111yescharacteristic
496C2×#103C22×C10111yescharacteristic
497C2×#103C22×C10111yescharacteristic
498C2×#103C22×C10111yescharacteristic
499C2×#103C22×C10111yescharacteristic
500C2×#103C22×C10111yescharacteristic
501C2×#103C22×C10111yescharacteristic
502C2×#102C22×C10111yescharacteristic
503C2×#102C22×C10111yescharacteristic
504C2×#102C22×C10111yescharacteristic
505C2×#102C22×C10111yescharacteristic
506C2×C22⋊C8C22×C10111yescharacteristic
507C2×C22⋊C8C22×C10111yescharacteristic
508C2×C22⋊C8C22×C10111yescharacteristic
509C2×C22⋊C8C22×C10111yescharacteristic
510C2×C4×C8C22×C10111yescharacteristic
511#397—21no—
512#392—21no—
513#386—21no—
514#386—21no—
515#382C22×C10111yescharacteristic
516#380C22×C10111yescharacteristic
517#380C22×C10111yescharacteristic
518#340C22×C10111yescharacteristic
519#340C22×C10111yescharacteristic
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—41no—
525C2×#41—41no—
526C22×Q8—22no—
527C22×Q8—22no—
528C22×Q8—21no—
529C22×Q8—22no—
530C22×Q8—22no—
531C22×Q8—41no—
532C22×Q8—41no—
533C22×Q8C23×C10111yescharacteristic
534C22×Q8C23×C10111yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4D4×C10111yescharacteristic
540C22×D4C23×C10111yescharacteristic
541C22×D4C23×C10111yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4C23×C10111yescharacteristic
546C23×C4C23×C10111yescharacteristic
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—41no—
552C2×SD16D4×C10114yescomplemented
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—41no—
556C22×C8C23×C10111yescharacteristic
557C22×C8C23×C10111yescharacteristic
558C22×C8C23×C10111yescharacteristic
559C22×C8C23×C10111yescharacteristic
560#124—28no—
561#124—22no—
562#124D4×C10114yescomplemented
563C22⋊Q8—28no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566#121—28no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—41no—
572#121—41no—
573C4×Q8—22no—
574C4×Q8D4×C10114yescomplemented
575C4×D4—28no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4D4×C10111yescharacteristic
583C2×C4⋊C4C23×C10111yescharacteristic
584C2×C4⋊C4C23×C10111yescharacteristic
585C2×C4⋊C4C23×C10111yescharacteristic
586C2×C4⋊C4C23×C10111yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4D4×C10111yescharacteristic
597C2×C22⋊C4D4×C10111yescharacteristic
598C2×C42—21no—
599C2×C42C23×C10111yescharacteristic
600#106—22no—
601C4⋊C8—22no—
602#103—22no—
603#103—22no—
604#103—22no—
605#103—22no—
606#103—22no—
607#103—41no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—41no—
612C22⋊C8—22no—
613C22⋊C8—22no—
614C22⋊C8—41no—
615C22⋊C8—41no—
616C4×C8—22no—
617#95—21no—
618#95—21no—
619#95—21no—
620#95—21no—
621C24—21no—
622C24—21no—
623C24C2×D4×C10111yescharacteristic
624C24C2×D4×C10111yescharacteristic
625#41—44no—
626#41—44no—
627#41—44no—
628#41—44no—
629C2×Q8—24no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—42no—
639C2×Q8—42no—
640C2×Q8—44no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8—44no—
644C2×Q8C2×D4×C10112yes—
645C2×Q8C2×D4×C10112yes—
646C2×Q8C2×D4×C10112yes—
647C2×Q8#41×C10112yes—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—41no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4C2×D4×C10112yes—
674C2×D4C2×D4×C10112yes—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
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—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—81no—
701C22×C4—81no—
702C22×C4C2×D4×C10111yescharacteristic
703C22×C4C2×D4×C10111yescharacteristic
704C22×C4C2×D4×C10111yescharacteristic
705C22×C4C2×D4×C10111yescharacteristic
706C22×C4C24×C10111yescharacteristic
707SD16—28no—
708SD16—44no—
709D8—44no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
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×C8C2×D4×C10112yes—
722C4⋊C4—24no—
723C4⋊C4—24no—
724C4⋊C4—22no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4C2×D4×C10112yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—81no—
743C22⋊C4—81no—
744C42—24no—
745C42C2×D4×C10112yes—
746C42C2×D4×C10112yes—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—22no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23#135×C10112yes—
775C23C22×D4×C10111yescharacteristic
776Q8—22no—
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—48no—
782Q8—41no—
783Q8—41no—
784Q8#121×C10114yes—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—44no—
790D4—48no—
791D4—48no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—84no—
797D4—84no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—48no—
814C2×C4—48no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
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—84no—
837C2×C4#120×C10112yes—
838C2×C4#120×C10112yes—
839C2×C4C22×D4×C10111yescharacteristic
840C2×C4C22×D4×C10111yescharacteristic
841C2×C4C22×D4×C10111yescharacteristic
842C2×C4C2×#41×C10111yescharacteristic
843C2×C4H(5,𝔽2)×C10111yescharacteristic
844C2×C4H(5,𝔽2)×C10111yescharacteristic
845C8—22no—
846C8—41no—
847C8—41no—
848C8—41no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—42no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—42no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×#120×C10111yescharacteristic
878C22D42×C10111yescharacteristic
879C22#546×C10111yescharacteristic
880C22C2×#135×C10111yescharacteristic
881C22#575×C10111yescharacteristic
882C22#577×C10111yescharacteristic
883C22#577×C10111yescharacteristic
884C4—24no—
885C4—22no—
886C4—22no—
887C4—41no—
888C4—41no—
889C4—42no—
890C4—42no—
891C4—81no—
892C4—81no—
893C4—81no—
894C4C2×#121×C10111yescharacteristic
895C4#535×C10111yescharacteristic
896C4D42×C10111yescharacteristic
897C4#546×C10111yescharacteristic
898C2—42no—
899C2—81no—
900C2—82no—
901C2—82no—
902C2C101×#240811yescharacteristic
903C2C101×#300211yescharacteristic
904C2C101×#301011yescharacteristic
905C2C101×#327511yescharacteristic
906C2C101×#328211yescharacteristic
907C2C101×#330111yescharacteristic
908C2C101×#332611yescharacteristic
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. C2×#548×C101C2semidirect
2. C2×#463×C101C2semidirect
3. C2×#449×C101C2semidirect
4. C2×#448×C101C2semidirect
5. C2×C4×SD16×C101C2semidirect
6. C101×#2535C2semidirect
7. C101×#2035C2semidirect
8. C101×#2034C2semidirect
9. C101×#2000C2semidirect
10. C101×#1999C2semidirect
11. C101×#1958C2semidirect
12. C101×#1954C2semidirect
13. C101×#1805C2semidirect
14. C101×#1788C2semidirect
15. C101×#1787C2semidirect
97. C2×SD16×C101D4semidirect
107. #124×C101D4semidirect
119. C4×Q8×C101D4semidirect
443. #24244C101direct (N × H)
455. C2×#548C2×C101semidirect
456. C2×#463C2×C101semidirect
457. C2×#449C2×C101semidirect
458. C2×#448C2×C101semidirect
459. C2×C4×SD16C2×C101semidirect
460. #2535C2×C101semidirect
461. #2035C2×C101semidirect
462. #2034C2×C101semidirect
463. #2000C2×C101semidirect
464. #1999C2×C101semidirect
465. #1958C2×C101semidirect
466. #1954C2×C101semidirect
467. #1805C2×C101semidirect
468. #1788C2×C101semidirect
469. #1787C2×C101semidirect
470. C101#24244direct (N × H)
552. C2×SD16D4×C101semidirect
562. #124D4×C101semidirect
574. C4×Q8D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C1012
C2×#463×C1012
C2×#449×C1012
C2×#448×C1012
C2×C4×SD16×C1012
C101×#25352
C101×#20352
C101×#20342
C101×#20002
C101×#19992
C101×#19582
C101×#19542
C101×#18052
C101×#17882
C101×#17872
#24244101