Finite Group Databasebeta

← C101×#22421 #38804572

Subgroups — C101×#22421 #38804572

Order 25856.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C101C211yesmaximal, characteristic
2C2×#435×C101C211yesmaximal, characteristic, complemented
3C2×#417×C101C211yesmaximal, characteristic, complemented
4C22×#103×C101C211yesmaximal, characteristic, complemented
5D4×C4⋊C4×C101C211yesmaximal, characteristic, complemented
6C101×#1983C211yesmaximal, characteristic, complemented
7C101×#1959C211yesmaximal, characteristic, complemented
8C101×#1894C211yesmaximal, characteristic, complemented
9C101×#1893C211yesmaximal, characteristic, complemented
10C101×#1874C211yesmaximal, characteristic, complemented
11C101×#1872C211yesmaximal, characteristic, complemented
12C101×#1803C211yesmaximal, characteristic, complemented
13C101×#1788C211yesmaximal, characteristic, complemented
14C101×#1787C211yesmaximal, characteristic, complemented
15C101×#1763C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×Q8×C101C2211yescharacteristic
18C22×M16×C101C2211yescharacteristic
19C23×C8×C101C2211yescharacteristic
20#548×C101—24no—
21#548×C101C418yescomplemented
22C2×#124×C101—21no—
23C2×#124×C101C2211yescharacteristic
24C2×C22⋊Q8×C101—21no—
25C2×C22⋊Q8×C101C2211yescharacteristic
26C2×#121×C101—21no—
27C2×#121×C101C2211yescharacteristic
28C2×C4×Q8×C101C2211yescharacteristic
29C2×C4×D4×C101—21no—
30C2×C4×D4×C101—21no—
31C2×C4×D4×C101C2211yescharacteristic
32C22×C4⋊C4×C101C2211yescharacteristic
33C22×C4⋊C4×C101C2211yescharacteristic
34#435×C101—24no—
35C2×C4⋊C8×C101C2211yescharacteristic
36#417×C101—24no—
37C2×#103×C101—24no—
38C2×#103×C101C2211yescharacteristic
39C2×#103×C101C2211yescharacteristic
40C2×#103×C101C2211yescharacteristic
41C2×#103×C101C2211yescharacteristic
42C2×#103×C101C2211yescharacteristic
43C2×#103×C101C2211yescharacteristic
44C2×#103×C101C2211yescharacteristic
45C2×#103×C101C2211yescharacteristic
46C2×#102×C101C2211yescharacteristic
47C2×#102×C101C2211yescharacteristic
48C2×#102×C101C2211yescharacteristic
49C2×#102×C101C2211yescharacteristic
50C2×C22⋊C8×C101C2211yescharacteristic
51C2×C22⋊C8×C101C2211yescharacteristic
52C2×#97×C101C2211yescharacteristic
53#389×C101—21no—
54#385×C101—21no—
55#385×C101—21no—
56#384×C101C2211yescharacteristic
57#380×C101C2211yescharacteristic
58#380×C101C2211yescharacteristic
59C4×C4⋊C4×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic
62#340×C101C2211yescharacteristic
63#340×C101C2211yescharacteristic
64C2×#41×C101—22no—
65C2×#41×C101—22no—
66C2×#41×C101—22no—
67C2×#41×C101—41no—
68C2×#41×C101—41no—
69C2×#41×C101C2×C414yescomplemented
70C22×Q8×C101—21no—
71C22×Q8×C101—22no—
72C22×Q8×C101—22no—
73C22×Q8×C101—22no—
74C22×Q8×C101—41no—
75C22×Q8×C101—41no—
76C22×Q8×C101C2×C414yescomplemented
77C22×Q8×C101C2311yescharacteristic
78C22×Q8×C101C2311yescharacteristic
79C22×D4×C101—21no—
80C22×D4×C101—21no—
81C22×D4×C101D411yescharacteristic
82C22×D4×C101C2311yescharacteristic
83C23×C4×C101—21no—
84C23×C4×C101—21no—
85C23×C4×C101—21no—
86C23×C4×C101—21no—
87C23×C4×C101C2311yescharacteristic
88C23×C4×C101C2311yescharacteristic
89C2×M16×C101—22no—
90C2×M16×C101—22no—
91C2×M16×C101—41no—
92C22×C8×C101—22no—
93C22×C8×C101—22no—
94C22×C8×C101—41no—
95C22×C8×C101C2311yescharacteristic
96C22×C8×C101C2311yescharacteristic
97C22×C8×C101C2311yescharacteristic
98C22×C8×C101C2311yescharacteristic
99#124×C101—28no—
100#124×C101—22no—
101#124×C101C2×C414yescomplemented
102C22⋊Q8×C101—22no—
103C22⋊Q8×C101—28no—
104C22⋊Q8×C101C2×C414yescomplemented
105#121×C101—28no—
106#121×C101—22no—
107#121×C101C2×C414yescomplemented
108C4×Q8×C101—22no—
109C4×Q8×C101C2×C414yescomplemented
110C4×D4×C101—28no—
111C4×D4×C101—44no—
112C4×D4×C101C2×C414yes—
113C4×D4×C101D414yes—
114C2×C4⋊C4×C101—21no—
115C2×C4⋊C4×C101—21no—
116C2×C4⋊C4×C101—22no—
117C2×C4⋊C4×C101—22no—
118C2×C4⋊C4×C101—21no—
119C2×C4⋊C4×C101—21no—
120C2×C4⋊C4×C101—21no—
121C2×C4⋊C4×C101—21no—
122C2×C4⋊C4×C101—41no—
123C2×C4⋊C4×C101—41no—
124C2×C4⋊C4×C101D411yescharacteristic
125C2×C4⋊C4×C101C2311yescharacteristic
126C2×C4⋊C4×C101C2311yescharacteristic
127C2×C4⋊C4×C101C2311yescharacteristic
128C2×C4⋊C4×C101C2311yescharacteristic
129C2×C4⋊C4×C101C2311yescharacteristic
130C2×C22⋊C4×C101—21no—
131C2×C22⋊C4×C101—21no—
132C2×C22⋊C4×C101—21no—
133C2×C22⋊C4×C101—21no—
134C2×C22⋊C4×C101—21no—
135C2×C22⋊C4×C101—21no—
136C2×C22⋊C4×C101D411yescharacteristic
137C2×C22⋊C4×C101D411yescharacteristic
138C2×C42×C101—21no—
139C2×C42×C101—21no—
140C2×C42×C101C2311yescharacteristic
141C4⋊C8×C101—22no—
142#103×C101—22no—
143#103×C101—22no—
144#103×C101—22no—
145#103×C101—22no—
146#103×C101—22no—
147#103×C101—41no—
148#103×C101—41no—
149#103×C101D414yescomplemented
150#102×C101—22no—
151#102×C101—22no—
152#102×C101—41no—
153#102×C101—41no—
154C22⋊C8×C101—22no—
155C22⋊C8×C101—22no—
156#97×C101—22no—
157#95×C101—21no—
158#95×C101—21no—
159#95×C101—21no—
160C24×C101—21no—
161C24×C101C2×D411yescharacteristic
162C24×C101C2×D411yescharacteristic
163#41×C101—28no—
164#41×C101—44no—
165#41×C101—44no—
166#41×C101—44no—
167C2×Q8×C101—24no—
168C2×Q8×C101—21no—
169C2×Q8×C101—21no—
170C2×Q8×C101—21no—
171C2×Q8×C101—21no—
172C2×Q8×C101—28no—
173C2×Q8×C101—21no—
174C2×Q8×C101—21no—
175C2×Q8×C101—21no—
176C2×Q8×C101—21no—
177C2×Q8×C101—42no—
178C2×Q8×C101—42no—
179C2×Q8×C101—44no—
180C2×Q8×C101—44no—
181C2×Q8×C101—44no—
182C2×Q8×C101C22×C412yes—
183C2×Q8×C101C22×C412yes—
184C2×Q8×C101C2×D412yes—
185C2×Q8×C101#4112yes—
186C2×D4×C101—22no—
187C2×D4×C101—22no—
188C2×D4×C101—24no—
189C2×D4×C101—24no—
190C2×D4×C101—21no—
191C2×D4×C101—21no—
192C2×D4×C101—21no—
193C2×D4×C101—21no—
194C2×D4×C101—21no—
195C2×D4×C101—42no—
196C2×D4×C101—42no—
197C2×D4×C101—42no—
198C2×D4×C101—42no—
199C2×D4×C101C22⋊C414yes—
200C2×D4×C101C22×C412yes—
201C22×C4×C101—21no—
202C22×C4×C101—21no—
203C22×C4×C101—21no—
204C22×C4×C101—21no—
205C22×C4×C101—21no—
206C22×C4×C101—21no—
207C22×C4×C101—21no—
208C22×C4×C101—21no—
209C22×C4×C101—21no—
210C22×C4×C101—24no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—21no—
214C22×C4×C101—24no—
215C22×C4×C101—21no—
216C22×C4×C101—21no—
217C22×C4×C101—21no—
218C22×C4×C101—42no—
219C22×C4×C101—42no—
220C22×C4×C101—42no—
221C22×C4×C101—42no—
222C22×C4×C101—42no—
223C22×C4×C101—42no—
224C22×C4×C101—42no—
225C22×C4×C101—42no—
226C22×C4×C101—81no—
227C22×C4×C101—81no—
228C22×C4×C101C22×C412yes—
229C22×C4×C101C22×C412yes—
230C22×C4×C101C2×D411yescharacteristic
231C22×C4×C101C2×D411yescharacteristic
232C22×C4×C101C2×D411yescharacteristic
233C22×C4×C101C2×D411yescharacteristic
234C22×C4×C101C2×D412yes—
235C22×C4×C101C2×D412yes—
236C22×C4×C101C2411yescharacteristic
237M16×C101—44no—
238C2×C8×C101—21no—
239C2×C8×C101—21no—
240C2×C8×C101—21no—
241C2×C8×C101—21no—
242C2×C8×C101—21no—
243C2×C8×C101—21no—
244C2×C8×C101—21no—
245C2×C8×C101—21no—
246C2×C8×C101—21no—
247C2×C8×C101—21no—
248C2×C8×C101—21no—
249C2×C8×C101—44no—
250C2×C8×C101C2×D412yes—
251C4⋊C4×C101—24no—
252C4⋊C4×C101—24no—
253C4⋊C4×C101—21no—
254C4⋊C4×C101—21no—
255C4⋊C4×C101—21no—
256C4⋊C4×C101—21no—
257C4⋊C4×C101—21no—
258C4⋊C4×C101—21no—
259C4⋊C4×C101—21no—
260C4⋊C4×C101—21no—
261C4⋊C4×C101—42no—
262C4⋊C4×C101—42no—
263C4⋊C4×C101—42no—
264C4⋊C4×C101—81no—
265C4⋊C4×C101C22⋊C414yes—
266C4⋊C4×C101C22×C412yes—
267C4⋊C4×C101C2×D412yes—
268C22⋊C4×C101—24no—
269C22⋊C4×C101—24no—
270C22⋊C4×C101—24no—
271C22⋊C4×C101—24no—
272C22⋊C4×C101—42no—
273C22⋊C4×C101—42no—
274C22⋊C4×C101C22⋊C414yes—
275C22⋊C4×C101C22⋊C414yes—
276C42×C101—24no—
277C42×C101—42no—
278C42×C101C22×C412yes—
279C42×C101C2×D412yes—
280C23×C101—21no—
281C23×C101—21no—
282C23×C101—21no—
283C23×C101—21no—
284C23×C101—21no—
285C23×C101—21no—
286C23×C101—21no—
287C23×C101—21no—
288C23×C101—21no—
289C23×C101—21no—
290C23×C101—22no—
291C23×C101—41no—
292C23×C101—41no—
293C23×C101—41no—
294C23×C101—41no—
295C23×C101—41no—
296C23×C101—41no—
297C23×C101C2×C22⋊C412yes—
298C23×C101C2×C22⋊C412yes—
299C23×C101AGL(1,ℤ/8)12yes—
300C23×C101#13712yes—
301C23×C101C22×D411yescharacteristic
302Q8×C101—22no—
303Q8×C101—22no—
304Q8×C101—22no—
305Q8×C101—22no—
306Q8×C101—22no—
307Q8×C101—48no—
308Q8×C101—41no—
309Q8×C101—41no—
310Q8×C101C4×D414yescomplemented
311D4×C101—28no—
312D4×C101—22no—
313D4×C101—22no—
314D4×C101—48no—
315D4×C101—48no—
316D4×C101—41no—
317D4×C101—41no—
318C2×C4×C101—22no—
319C2×C4×C101—21no—
320C2×C4×C101—21no—
321C2×C4×C101—22no—
322C2×C4×C101—21no—
323C2×C4×C101—21no—
324C2×C4×C101—22no—
325C2×C4×C101—21no—
326C2×C4×C101—21no—
327C2×C4×C101—21no—
328C2×C4×C101—21no—
329C2×C4×C101—22no—
330C2×C4×C101—22no—
331C2×C4×C101—22no—
332C2×C4×C101—22no—
333C2×C4×C101—22no—
334C2×C4×C101—22no—
335C2×C4×C101—22no—
336C2×C4×C101—22no—
337C2×C4×C101—22no—
338C2×C4×C101—22no—
339C2×C4×C101—22no—
340C2×C4×C101—48no—
341C2×C4×C101—48no—
342C2×C4×C101—41no—
343C2×C4×C101—41no—
344C2×C4×C101—41no—
345C2×C4×C101—41no—
346C2×C4×C101—41no—
347C2×C4×C101—41no—
348C2×C4×C101—41no—
349C2×C4×C101—41no—
350C2×C4×C101—41no—
351C2×C4×C101—41no—
352C2×C4×C101—41no—
353C2×C4×C101—41no—
354C2×C4×C101—41no—
355C2×C4×C101—41no—
356C2×C4×C101—41no—
357C2×C4×C101—84no—
358C2×C4×C101—84no—
359C2×C4×C101C2×C22⋊C412yes—
360C2×C4×C101C2×C22⋊C412yes—
361C2×C4×C101C2×C22⋊C412yes—
362C2×C4×C101C2×C22⋊C412yes—
363C2×C4×C101C23×C411yescharacteristic
364C2×C4×C101C22×D411yescharacteristic
365C2×C4×C101C22×D411yescharacteristic
366C2×C4×C101C2×#4111yescharacteristic
367C2×C4×C101H(5,𝔽2)11yescharacteristic
368C2×C4×C101H(5,𝔽2)11yescharacteristic
369C8×C101—22no—
370C8×C101—41no—
371C8×C101—41no—
372C8×C101—41no—
373C22×C101—22no—
374C22×C101—22no—
375C22×C101—22no—
376C22×C101—22no—
377C22×C101—22no—
378C22×C101—22no—
379C22×C101—22no—
380C22×C101—22no—
381C22×C101—22no—
382C22×C101—41no—
383C22×C101—41no—
384C22×C101—41no—
385C22×C101—41no—
386C22×C101—42no—
387C22×C101—42no—
388C22×C101—42no—
389C22×C101—81no—
390C22×C101—81no—
391C22×C101—81no—
392C22×C101—81no—
393C22×C101#41714yescomplemented
394C22×C101C22×C22⋊C411yescharacteristic
395C22×C101D4211yescharacteristic
396C22×C101#54611yescharacteristic
397C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
398C22×C101C2×#13711yescharacteristic
399C22×C101#57711yescharacteristic
400C22×C101#57811yescharacteristic
401C4×C101—22no—
402C4×C101—22no—
403C4×C101—24no—
404C4×C101—22no—
405C4×C101—22no—
406C4×C101—42no—
407C4×C101—42no—
408C4×C101—42no—
409C4×C101—81no—
410C4×C101—81no—
411C4×C101—81no—
412C4×C101C2×C4×D411yescharacteristic
413C4×C101#51811yescharacteristic
414C4×C101D4211yescharacteristic
415C4×C101#54611yescharacteristic
416#22421C10111yesmaximal, characteristic, direct product factor, Sylow
417C2×C101—24no—
418C2×C101—42no—
419C2×C101—82no—
420C2×C101D4×C22⋊C411yescharacteristic
421C2×C101C2×#41711yescharacteristic
422C2×C101#289811yescharacteristic
423C2×C101#326511yescharacteristic
424C2×C101#327011yescharacteristic
425C2×C101#330811yescharacteristic
426C2×C101#331611yescharacteristic
427C2×#548C2×C10111yescharacteristic
428C2×#435C2×C10111yescharacteristic, complemented
429C2×#417C2×C10111yescharacteristic, complemented
430C22×#103C2×C10111yescharacteristic, complemented
431D4×C4⋊C4C2×C10111yescharacteristic, complemented
432#1983C2×C10111yescharacteristic, complemented
433#1959C2×C10111yescharacteristic, complemented
434#1894C2×C10111yescharacteristic, complemented
435#1893C2×C10111yescharacteristic, complemented
436#1874C2×C10111yescharacteristic, complemented
437#1872C2×C10111yescharacteristic, complemented
438#1803C2×C10111yescharacteristic, complemented
439#1788C2×C10111yescharacteristic, complemented
440#1787C2×C10111yescharacteristic, complemented
441#1763C2×C10111yescharacteristic, complemented
442C101#2242111yescharacteristic, direct product factor, Sylow
443C22×#41C22×C10111yescharacteristic
444C23×Q8C22×C10111yescharacteristic
445C22×M16C22×C10111yescharacteristic
446C23×C8C22×C10111yescharacteristic
447#548—24no—
448#548C4×C10118yescomplemented
449C2×#124—21no—
450C2×#124C22×C10111yescharacteristic
451C2×C22⋊Q8—21no—
452C2×C22⋊Q8C22×C10111yescharacteristic
453C2×#121—21no—
454C2×#121C22×C10111yescharacteristic
455C2×C4×Q8C22×C10111yescharacteristic
456C2×C4×D4—21no—
457C2×C4×D4—21no—
458C2×C4×D4C22×C10111yescharacteristic
459C22×C4⋊C4C22×C10111yescharacteristic
460C22×C4⋊C4C22×C10111yescharacteristic
461#435—24no—
462C2×C4⋊C8C22×C10111yescharacteristic
463#417—24no—
464C2×#103—24no—
465C2×#103C22×C10111yescharacteristic
466C2×#103C22×C10111yescharacteristic
467C2×#103C22×C10111yescharacteristic
468C2×#103C22×C10111yescharacteristic
469C2×#103C22×C10111yescharacteristic
470C2×#103C22×C10111yescharacteristic
471C2×#103C22×C10111yescharacteristic
472C2×#103C22×C10111yescharacteristic
473C2×#102C22×C10111yescharacteristic
474C2×#102C22×C10111yescharacteristic
475C2×#102C22×C10111yescharacteristic
476C2×#102C22×C10111yescharacteristic
477C2×C22⋊C8C22×C10111yescharacteristic
478C2×C22⋊C8C22×C10111yescharacteristic
479C2×#97C22×C10111yescharacteristic
480#389—21no—
481#385—21no—
482#385—21no—
483#384C22×C10111yescharacteristic
484#380C22×C10111yescharacteristic
485#380C22×C10111yescharacteristic
486C4×C4⋊C4C22×C10111yescharacteristic
487#340C22×C10111yescharacteristic
488#340C22×C10111yescharacteristic
489#340C22×C10111yescharacteristic
490#340C22×C10111yescharacteristic
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41C2×C4×C10114yescomplemented
497C22×Q8—21no—
498C22×Q8—22no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8C2×C4×C10114yescomplemented
504C22×Q8C23×C10111yescharacteristic
505C22×Q8C23×C10111yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4D4×C10111yescharacteristic
509C22×D4C23×C10111yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4C23×C10111yescharacteristic
515C23×C4C23×C10111yescharacteristic
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—41no—
519C22×C8—22no—
520C22×C8—22no—
521C22×C8—41no—
522C22×C8C23×C10111yescharacteristic
523C22×C8C23×C10111yescharacteristic
524C22×C8C23×C10111yescharacteristic
525C22×C8C23×C10111yescharacteristic
526#124—28no—
527#124—22no—
528#124C2×C4×C10114yescomplemented
529C22⋊Q8—22no—
530C22⋊Q8—28no—
531C22⋊Q8C2×C4×C10114yescomplemented
532#121—28no—
533#121—22no—
534#121C2×C4×C10114yescomplemented
535C4×Q8—22no—
536C4×Q8C2×C4×C10114yescomplemented
537C4×D4—28no—
538C4×D4—44no—
539C4×D4C2×C4×C10114yes—
540C4×D4D4×C10114yes—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4D4×C10111yescharacteristic
552C2×C4⋊C4C23×C10111yescharacteristic
553C2×C4⋊C4C23×C10111yescharacteristic
554C2×C4⋊C4C23×C10111yescharacteristic
555C2×C4⋊C4C23×C10111yescharacteristic
556C2×C4⋊C4C23×C10111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4D4×C10111yescharacteristic
564C2×C22⋊C4D4×C10111yescharacteristic
565C2×C42—21no—
566C2×C42—21no—
567C2×C42C23×C10111yescharacteristic
568C4⋊C8—22no—
569#103—22no—
570#103—22no—
571#103—22no—
572#103—22no—
573#103—22no—
574#103—41no—
575#103—41no—
576#103D4×C10114yescomplemented
577#102—22no—
578#102—22no—
579#102—41no—
580#102—41no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583#97—22no—
584#95—21no—
585#95—21no—
586#95—21no—
587C24—21no—
588C24C2×D4×C10111yescharacteristic
589C24C2×D4×C10111yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594C2×Q8—24no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—28no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—42no—
605C2×Q8—42no—
606C2×Q8—44no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8C22×C4×C10112yes—
610C2×Q8C22×C4×C10112yes—
611C2×Q8C2×D4×C10112yes—
612C2×Q8#41×C10112yes—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4C22⋊C4×C10114yes—
627C2×D4C22×C4×C10112yes—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—24no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—81no—
654C22×C4—81no—
655C22×C4C22×C4×C10112yes—
656C22×C4C22×C4×C10112yes—
657C22×C4C2×D4×C10111yescharacteristic
658C22×C4C2×D4×C10111yescharacteristic
659C22×C4C2×D4×C10111yescharacteristic
660C22×C4C2×D4×C10111yescharacteristic
661C22×C4C2×D4×C10112yes—
662C22×C4C2×D4×C10112yes—
663C22×C4C24×C10111yescharacteristic
664M16—44no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—44no—
677C2×C8C2×D4×C10112yes—
678C4⋊C4—24no—
679C4⋊C4—24no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—81no—
692C4⋊C4C22⋊C4×C10114yes—
693C4⋊C4C22×C4×C10112yes—
694C4⋊C4C2×D4×C10112yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4C22⋊C4×C10114yes—
702C22⋊C4C22⋊C4×C10114yes—
703C42—24no—
704C42—42no—
705C42C22×C4×C10112yes—
706C42C2×D4×C10112yes—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23C2×C22⋊C4×C10112yes—
725C23C2×C22⋊C4×C10112yes—
726C23AGL(1,ℤ/8)×C10112yes—
727C23#137×C10112yes—
728C23C22×D4×C10111yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—48no—
735Q8—41no—
736Q8—41no—
737Q8C4×D4×C10114yescomplemented
738D4—28no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—48no—
743D4—41no—
744D4—41no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4C2×C22⋊C4×C10112yes—
787C2×C4C2×C22⋊C4×C10112yes—
788C2×C4C2×C22⋊C4×C10112yes—
789C2×C4C2×C22⋊C4×C10112yes—
790C2×C4C23×C4×C10111yescharacteristic
791C2×C4C22×D4×C10111yescharacteristic
792C2×C4C22×D4×C10111yescharacteristic
793C2×C4C2×#41×C10111yescharacteristic
794C2×C4H(5,𝔽2)×C10111yescharacteristic
795C2×C4H(5,𝔽2)×C10111yescharacteristic
796C8—22no—
797C8—41no—
798C8—41no—
799C8—41no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22#417×C10114yescomplemented
821C22C22×C22⋊C4×C10111yescharacteristic
822C22D42×C10111yescharacteristic
823C22#546×C10111yescharacteristic
824C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
825C22C2×#137×C10111yescharacteristic
826C22#577×C10111yescharacteristic
827C22#578×C10111yescharacteristic
828C4—22no—
829C4—22no—
830C4—24no—
831C4—22no—
832C4—22no—
833C4—42no—
834C4—42no—
835C4—42no—
836C4—81no—
837C4—81no—
838C4—81no—
839C4C2×C4×D4×C10111yescharacteristic
840C4#518×C10111yescharacteristic
841C4D42×C10111yescharacteristic
842C4#546×C10111yescharacteristic
843C2—24no—
844C2—42no—
845C2—82no—
846C2D4×C22⋊C4×C10111yescharacteristic
847C2C2×#417×C10111yescharacteristic
848C2C101×#289811yescharacteristic
849C2C101×#326511yescharacteristic
850C2C101×#327011yescharacteristic
851C2C101×#330811yescharacteristic
852C2C101×#331611yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC2×#548×C101C2
LCSG ▷ C2×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×#435×C101C2semidirect
3. C2×#417×C101C2semidirect
4. C22×#103×C101C2semidirect
5. D4×C4⋊C4×C101C2semidirect
6. C101×#1983C2semidirect
7. C101×#1959C2semidirect
8. C101×#1894C2semidirect
9. C101×#1893C2semidirect
10. C101×#1874C2semidirect
11. C101×#1872C2semidirect
12. C101×#1803C2semidirect
13. C101×#1788C2semidirect
14. C101×#1787C2semidirect
15. C101×#1763C2semidirect
21. #548×C101C4semidirect
69. C2×#41×C101C2×C4semidirect
76. C22×Q8×C101C2×C4semidirect
101. #124×C101C2×C4semidirect
104. C22⋊Q8×C101C2×C4semidirect
107. #121×C101C2×C4semidirect
109. C4×Q8×C101C2×C4semidirect
149. #103×C101D4semidirect
310. Q8×C101C4×D4semidirect
393. C22×C101#417semidirect
416. #22421C101direct (N × H)
428. C2×#435C2×C101semidirect
429. C2×#417C2×C101semidirect
430. C22×#103C2×C101semidirect
431. D4×C4⋊C4C2×C101semidirect
432. #1983C2×C101semidirect
433. #1959C2×C101semidirect
434. #1894C2×C101semidirect
435. #1893C2×C101semidirect
436. #1874C2×C101semidirect
437. #1872C2×C101semidirect
438. #1803C2×C101semidirect
439. #1788C2×C101semidirect
440. #1787C2×C101semidirect
441. #1763C2×C101semidirect
442. C101#22421direct (N × H)
448. #548C4×C101semidirect
496. C2×#41C2×C4×C101semidirect
503. C22×Q8C2×C4×C101semidirect
528. #124C2×C4×C101semidirect
531. C22⋊Q8C2×C4×C101semidirect
534. #121C2×C4×C101semidirect
536. C4×Q8C2×C4×C101semidirect
576. #103D4×C101semidirect
737. Q8C4×D4×C101semidirect
820. C22#417×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×#435×C1012
C2×#417×C1012
C22×#103×C1012
D4×C4⋊C4×C1012
C101×#19832
C101×#19592
C101×#18942
C101×#18932
C101×#18742
C101×#18722
C101×#18032
C101×#17882
C101×#17872
C101×#17632
#22421101