Finite Group Databasebeta

← C101×#22419 #38804570

Subgroups — C101×#22419 #38804570

Order 25856.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C101C211yesmaximal, characteristic
2C2×#435×C101C211yesmaximal, characteristic, complemented
3C2×#417×C101C211yesmaximal, characteristic, complemented
4C22×#102×C101C211yesmaximal, characteristic, complemented
5D4×C4⋊C4×C101C211yesmaximal, characteristic, complemented
6C101×#1983C211yesmaximal, characteristic, complemented
7C101×#1959C211yesmaximal, characteristic, complemented
8C101×#1895C211yesmaximal, characteristic, complemented
9C101×#1892C211yesmaximal, characteristic, complemented
10C101×#1874C211yesmaximal, characteristic, complemented
11C101×#1872C211yesmaximal, characteristic, complemented
12C101×#1802C211yesmaximal, characteristic, complemented
13C101×#1788C211yesmaximal, characteristic, complemented
14C101×#1786C211yesmaximal, characteristic, complemented
15C101×#1762C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×D4×C101C2211yescharacteristic
18C22×M16×C101C2211yescharacteristic, complemented
19C23×C8×C101C2211yescharacteristic
20#546×C101—24no—
21#546×C101C418yescomplemented
22C2×#124×C101C2211yescharacteristic
23C2×#123×C101—21no—
24C2×C22⋊Q8×C101C2211yescharacteristic
25C2×#121×C101—21no—
26C2×#121×C101C2211yescharacteristic
27C2×#120×C101—21no—
28C2×C4×D4×C101—21no—
29C2×C4×D4×C101C2211yescharacteristic
30C2×C4×D4×C101C2211yescharacteristic
31C22×C4⋊C4×C101C2211yescharacteristic
32C22×C4⋊C4×C101C2211yescharacteristic, complemented
33C22×C22⋊C4×C101—21no—
34#435×C101—24no—
35C2×C4⋊C8×C101C2211yescharacteristic, complemented
36#417×C101—24no—
37C2×#103×C101C2211yescharacteristic, complemented
38C2×#103×C101C2211yescharacteristic, complemented
39C2×#103×C101C2211yescharacteristic, complemented
40C2×#103×C101C2211yescharacteristic, complemented
41C2×#102×C101—24no—
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×#102×C101C2211yescharacteristic
46C2×#102×C101C2211yescharacteristic
47C2×#102×C101C2211yescharacteristic
48C2×#102×C101C2211yescharacteristic
49C2×#102×C101C2211yescharacteristic
50C2×C22⋊C8×C101C2211yescharacteristic
51C2×C22⋊C8×C101C2211yescharacteristic, complemented
52C2×#97×C101C2211yescharacteristic, complemented
53#389×C101—21no—
54#385×C101—21no—
55#385×C101—21no—
56#384×C101C2211yescharacteristic, complemented
57#380×C101C2211yescharacteristic
58#380×C101C2211yescharacteristic, complemented
59C4×C4⋊C4×C101C2211yescharacteristic, complemented
60#340×C101C2211yescharacteristic, complemented
61#340×C101C2211yescharacteristic, complemented
62#340×C101C2211yescharacteristic, complemented
63#340×C101C2211yescharacteristic, complemented
64C25×C101—21no—
65C2×#41×C101—22no—
66C2×#41×C101—22no—
67C2×#41×C101—22no—
68C2×#41×C101—41no—
69C2×#41×C101—41no—
70C2×#41×C101C2×C414yescomplemented
71C22×Q8×C101C2311yescharacteristic
72C22×D4×C101—22no—
73C22×D4×C101—22no—
74C22×D4×C101—21no—
75C22×D4×C101—21no—
76C22×D4×C101—21no—
77C22×D4×C101—22no—
78C22×D4×C101—41no—
79C22×D4×C101—41no—
80C22×D4×C101C2×C414yescomplemented
81C22×D4×C101D411yescharacteristic
82C22×D4×C101C2311yescharacteristic
83C22×D4×C101C2311yescharacteristic
84C23×C4×C101—21no—
85C23×C4×C101—21no—
86C23×C4×C101—21no—
87C23×C4×C101—21no—
88C23×C4×C101C2311yescharacteristic
89C23×C4×C101C2311yescharacteristic
90C2×M16×C101—22no—
91C2×M16×C101—22no—
92C2×M16×C101—41no—
93C22×C8×C101—22no—
94C22×C8×C101—22no—
95C22×C8×C101—41no—
96C22×C8×C101C2311yescharacteristic
97C22×C8×C101C2311yescharacteristic
98C22×C8×C101C2311yescharacteristic
99C22×C8×C101C2311yescharacteristic
100#124×C101—22no—
101#124×C101C2×C414yescomplemented
102#123×C101—28no—
103C22⋊Q8×C101—22no—
104C22⋊Q8×C101C2×C414yescomplemented
105#121×C101—22no—
106#121×C101—28no—
107#121×C101C2×C414yescomplemented
108#120×C101—28no—
109C4×D4×C101—22no—
110C4×D4×C101—44no—
111C4×D4×C101C2×C414yes—
112C4×D4×C101C2×C414yescomplemented
113C4×D4×C101D414yes—
114C2×C4⋊C4×C101—21no—
115C2×C4⋊C4×C101—22no—
116C2×C4⋊C4×C101—22no—
117C2×C4⋊C4×C101—21no—
118C2×C4⋊C4×C101—21no—
119C2×C4⋊C4×C101—21no—
120C2×C4⋊C4×C101—21no—
121C2×C4⋊C4×C101—41no—
122C2×C4⋊C4×C101—41no—
123C2×C4⋊C4×C101D411yescharacteristic
124C2×C4⋊C4×C101C2311yescharacteristic
125C2×C4⋊C4×C101C2311yescharacteristic
126C2×C4⋊C4×C101C2311yescharacteristic
127C2×C4⋊C4×C101C2311yescharacteristic
128C2×C4⋊C4×C101C2311yescharacteristic
129C2×C22⋊C4×C101—21no—
130C2×C22⋊C4×C101—21no—
131C2×C22⋊C4×C101—21no—
132C2×C22⋊C4×C101—21no—
133C2×C22⋊C4×C101—21no—
134C2×C22⋊C4×C101—28no—
135C2×C22⋊C4×C101—21no—
136C2×C22⋊C4×C101—21no—
137C2×C22⋊C4×C101D411yescharacteristic
138C2×C22⋊C4×C101D411yescharacteristic
139C2×C42×C101—21no—
140C2×C42×C101C2311yescharacteristic
141C4⋊C8×C101—22no—
142#103×C101—22no—
143#103×C101—22no—
144#103×C101—41no—
145#103×C101—41no—
146#102×C101—22no—
147#102×C101—22no—
148#102×C101—22no—
149#102×C101—22no—
150#102×C101—22no—
151#102×C101—41no—
152#102×C101—41no—
153#102×C101D414yescomplemented
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×C101—21no—
162C24×C101—24no—
163C24×C101—42no—
164C24×C101—42no—
165C24×C101—42no—
166C24×C101—42no—
167C24×C101—81no—
168C24×C101—81no—
169C24×C101C2×D411yescharacteristic
170C24×C101C2×D411yescharacteristic
171#41×C101—28no—
172#41×C101—44no—
173#41×C101—44no—
174#41×C101—44no—
175C2×Q8×C101—21no—
176C2×Q8×C101—21no—
177C2×Q8×C101—21no—
178C2×Q8×C101—21no—
179C2×Q8×C101—21no—
180C2×Q8×C101C22×C412yes—
181C2×D4×C101—22no—
182C2×D4×C101—22no—
183C2×D4×C101—28no—
184C2×D4×C101—24no—
185C2×D4×C101—24no—
186C2×D4×C101—24no—
187C2×D4×C101—21no—
188C2×D4×C101—21no—
189C2×D4×C101—21no—
190C2×D4×C101—21no—
191C2×D4×C101—21no—
192C2×D4×C101—21no—
193C2×D4×C101—21no—
194C2×D4×C101—21no—
195C2×D4×C101—44no—
196C2×D4×C101—44no—
197C2×D4×C101—44no—
198C2×D4×C101—42no—
199C2×D4×C101—42no—
200C2×D4×C101—42no—
201C2×D4×C101—42no—
202C2×D4×C101—81no—
203C2×D4×C101—81no—
204C2×D4×C101C22⋊C414yes—
205C2×D4×C101C22×C412yes—
206C2×D4×C101C22×C412yes—
207C2×D4×C101C2×D412yes—
208C2×D4×C101#4112yes—
209C22×C4×C101—21no—
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—21no—
214C22×C4×C101—21no—
215C22×C4×C101—21no—
216C22×C4×C101—21no—
217C22×C4×C101—21no—
218C22×C4×C101—21no—
219C22×C4×C101—21no—
220C22×C4×C101—24no—
221C22×C4×C101—24no—
222C22×C4×C101—21no—
223C22×C4×C101—21no—
224C22×C4×C101—21no—
225C22×C4×C101—42no—
226C22×C4×C101—42no—
227C22×C4×C101—42no—
228C22×C4×C101—42no—
229C22×C4×C101—42no—
230C22×C4×C101—42no—
231C22×C4×C101—81no—
232C22×C4×C101—81no—
233C22×C4×C101—81no—
234C22×C4×C101—81no—
235C22×C4×C101C22×C412yes—
236C22×C4×C101C22×C412yes—
237C22×C4×C101C2×D411yescharacteristic
238C22×C4×C101C2×D411yescharacteristic
239C22×C4×C101C2×D411yescharacteristic
240C22×C4×C101C2×D411yescharacteristic
241C22×C4×C101C2×D412yes—
242C22×C4×C101C2×D412yes—
243C22×C4×C101C2411yescharacteristic
244M16×C101—44no—
245C2×C8×C101—21no—
246C2×C8×C101—21no—
247C2×C8×C101—21no—
248C2×C8×C101—21no—
249C2×C8×C101—21no—
250C2×C8×C101—21no—
251C2×C8×C101—21no—
252C2×C8×C101—21no—
253C2×C8×C101—21no—
254C2×C8×C101—21no—
255C2×C8×C101—21no—
256C2×C8×C101—44no—
257C2×C8×C101C2×D412yes—
258C4⋊C4×C101—24no—
259C4⋊C4×C101—21no—
260C4⋊C4×C101—21no—
261C4⋊C4×C101—21no—
262C4⋊C4×C101—21no—
263C4⋊C4×C101—21no—
264C4⋊C4×C101—21no—
265C4⋊C4×C101—21no—
266C4⋊C4×C101—21no—
267C4⋊C4×C101—42no—
268C4⋊C4×C101—42no—
269C4⋊C4×C101—42no—
270C4⋊C4×C101—81no—
271C4⋊C4×C101C22⋊C414yes—
272C4⋊C4×C101C22×C412yes—
273C4⋊C4×C101C2×D412yes—
274C22⋊C4×C101—24no—
275C22⋊C4×C101—24no—
276C22⋊C4×C101—24no—
277C22⋊C4×C101—24no—
278C22⋊C4×C101—24no—
279C22⋊C4×C101—42no—
280C22⋊C4×C101—42no—
281C22⋊C4×C101C22⋊C414yes—
282C22⋊C4×C101C22⋊C414yes—
283C42×C101—42no—
284C42×C101C22×C412yes—
285C42×C101C2×D412yes—
286C23×C101—21no—
287C23×C101—21no—
288C23×C101—21no—
289C23×C101—21no—
290C23×C101—22no—
291C23×C101—21no—
292C23×C101—22no—
293C23×C101—21no—
294C23×C101—22no—
295C23×C101—21no—
296C23×C101—21no—
297C23×C101—21no—
298C23×C101—21no—
299C23×C101—22no—
300C23×C101—48no—
301C23×C101—41no—
302C23×C101—41no—
303C23×C101—41no—
304C23×C101—41no—
305C23×C101—41no—
306C23×C101—41no—
307C23×C101—41no—
308C23×C101—41no—
309C23×C101—41no—
310C23×C101—41no—
311C23×C101—48no—
312C23×C101—84no—
313C23×C101—84no—
314C23×C101—84no—
315C23×C101—84no—
316C23×C101—84no—
317C23×C101C2×C22⋊C412yes—
318C23×C101C2×C22⋊C412yes—
319C23×C101AGL(1,ℤ/8)12yes—
320C23×C101#13712yes—
321C23×C101C22×D411yescharacteristic
322Q8×C101—22no—
323Q8×C101—22no—
324Q8×C101—41no—
325Q8×C101—41no—
326D4×C101—28no—
327D4×C101—22no—
328D4×C101—22no—
329D4×C101—22no—
330D4×C101—22no—
331D4×C101—22no—
332D4×C101—48no—
333D4×C101—48no—
334D4×C101—41no—
335D4×C101—41no—
336D4×C101—84no—
337D4×C101C4×D414yescomplemented
338C2×C4×C101—21no—
339C2×C4×C101—21no—
340C2×C4×C101—21no—
341C2×C4×C101—21no—
342C2×C4×C101—21no—
343C2×C4×C101—21no—
344C2×C4×C101—21no—
345C2×C4×C101—21no—
346C2×C4×C101—22no—
347C2×C4×C101—22no—
348C2×C4×C101—22no—
349C2×C4×C101—22no—
350C2×C4×C101—22no—
351C2×C4×C101—22no—
352C2×C4×C101—22no—
353C2×C4×C101—22no—
354C2×C4×C101—22no—
355C2×C4×C101—22no—
356C2×C4×C101—22no—
357C2×C4×C101—48no—
358C2×C4×C101—41no—
359C2×C4×C101—41no—
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—84no—
374C2×C4×C101—84no—
375C2×C4×C101—84no—
376C2×C4×C101C2×C22⋊C412yes—
377C2×C4×C101C2×C22⋊C412yes—
378C2×C4×C101C2×C22⋊C412yes—
379C2×C4×C101C2×C22⋊C412yes—
380C2×C4×C101C23×C411yescharacteristic
381C2×C4×C101C22×D411yescharacteristic
382C2×C4×C101C22×D411yescharacteristic
383C2×C4×C101C2×#4111yescharacteristic
384C2×C4×C101H(5,𝔽2)11yescharacteristic
385C2×C4×C101H(5,𝔽2)11yescharacteristic
386C8×C101—22no—
387C8×C101—41no—
388C8×C101—41no—
389C8×C101—41no—
390C22×C101—22no—
391C22×C101—22no—
392C22×C101—22no—
393C22×C101—22no—
394C22×C101—22no—
395C22×C101—22no—
396C22×C101—22no—
397C22×C101—24no—
398C22×C101—22no—
399C22×C101—22no—
400C22×C101—42no—
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—42no—
412C22×C101—42no—
413C22×C101—816no—
414C22×C101—81no—
415C22×C101—81no—
416C22×C101—81no—
417C22×C101—81no—
418C22×C101#41714yescomplemented
419C22×C101C22×C22⋊C411yescharacteristic
420C22×C101D4211yescharacteristic
421C22×C101#54611yescharacteristic
422C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C101C2×#13711yescharacteristic
424C22×C101#57611yescharacteristic
425C22×C101#57711yescharacteristic
426C4×C101—22no—
427C4×C101—22no—
428C4×C101—22no—
429C4×C101—22no—
430C4×C101—42no—
431C4×C101—42no—
432C4×C101—42no—
433C4×C101—81no—
434C4×C101—81no—
435C4×C101—81no—
436C4×C101C2×C4×D411yescharacteristic
437C4×C101#51811yescharacteristic
438C4×C101D4211yescharacteristic
439C4×C101#54611yescharacteristic
440#22419C10111yesmaximal, characteristic, direct product factor, Sylow
441C2×C101—24no—
442C2×C101—42no—
443C2×C101—44no—
444C2×C101—82no—
445C2×C101D4×C22⋊C411yescharacteristic
446C2×C101C2×#41711yescharacteristic
447C2×C101#289711yescharacteristic
448C2×C101#326411yescharacteristic
449C2×C101#326611yescharacteristic
450C2×C101#330611yescharacteristic
451C2×C101#331411yescharacteristic
452C2×#546C2×C10111yescharacteristic
453C2×#435C2×C10111yescharacteristic, complemented
454C2×#417C2×C10111yescharacteristic, complemented
455C22×#102C2×C10111yescharacteristic, complemented
456D4×C4⋊C4C2×C10111yescharacteristic, complemented
457#1983C2×C10111yescharacteristic, complemented
458#1959C2×C10111yescharacteristic, complemented
459#1895C2×C10111yescharacteristic, complemented
460#1892C2×C10111yescharacteristic, complemented
461#1874C2×C10111yescharacteristic, complemented
462#1872C2×C10111yescharacteristic, complemented
463#1802C2×C10111yescharacteristic, complemented
464#1788C2×C10111yescharacteristic, complemented
465#1786C2×C10111yescharacteristic, complemented
466#1762C2×C10111yescharacteristic, complemented
467C101#2241911yescharacteristic, direct product factor, Sylow
468C22×#41C22×C10111yescharacteristic
469C23×D4C22×C10111yescharacteristic
470C22×M16C22×C10111yescharacteristic, complemented
471C23×C8C22×C10111yescharacteristic
472#546—24no—
473#546C4×C10118yescomplemented
474C2×#124C22×C10111yescharacteristic
475C2×#123—21no—
476C2×C22⋊Q8C22×C10111yescharacteristic
477C2×#121—21no—
478C2×#121C22×C10111yescharacteristic
479C2×#120—21no—
480C2×C4×D4—21no—
481C2×C4×D4C22×C10111yescharacteristic
482C2×C4×D4C22×C10111yescharacteristic
483C22×C4⋊C4C22×C10111yescharacteristic
484C22×C4⋊C4C22×C10111yescharacteristic, complemented
485C22×C22⋊C4—21no—
486#435—24no—
487C2×C4⋊C8C22×C10111yescharacteristic, complemented
488#417—24no—
489C2×#103C22×C10111yescharacteristic, complemented
490C2×#103C22×C10111yescharacteristic, complemented
491C2×#103C22×C10111yescharacteristic, complemented
492C2×#103C22×C10111yescharacteristic, complemented
493C2×#102—24no—
494C2×#102C22×C10111yescharacteristic
495C2×#102C22×C10111yescharacteristic
496C2×#102C22×C10111yescharacteristic
497C2×#102C22×C10111yescharacteristic
498C2×#102C22×C10111yescharacteristic
499C2×#102C22×C10111yescharacteristic
500C2×#102C22×C10111yescharacteristic
501C2×#102C22×C10111yescharacteristic
502C2×C22⋊C8C22×C10111yescharacteristic
503C2×C22⋊C8C22×C10111yescharacteristic, complemented
504C2×#97C22×C10111yescharacteristic, complemented
505#389—21no—
506#385—21no—
507#385—21no—
508#384C22×C10111yescharacteristic, complemented
509#380C22×C10111yescharacteristic
510#380C22×C10111yescharacteristic, complemented
511C4×C4⋊C4C22×C10111yescharacteristic, complemented
512#340C22×C10111yescharacteristic, complemented
513#340C22×C10111yescharacteristic, complemented
514#340C22×C10111yescharacteristic, complemented
515#340C22×C10111yescharacteristic, complemented
516C25—21no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C2×C4×C10114yescomplemented
523C22×Q8C23×C10111yescharacteristic
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×C4×C10114yescomplemented
533C22×D4D4×C10111yescharacteristic
534C22×D4C23×C10111yescharacteristic
535C22×D4C23×C10111yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C23×C10111yescharacteristic
541C23×C4C23×C10111yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8C23×C10111yescharacteristic
549C22×C8C23×C10111yescharacteristic
550C22×C8C23×C10111yescharacteristic
551C22×C8C23×C10111yescharacteristic
552#124—22no—
553#124C2×C4×C10114yescomplemented
554#123—28no—
555C22⋊Q8—22no—
556C22⋊Q8C2×C4×C10114yescomplemented
557#121—22no—
558#121—28no—
559#121C2×C4×C10114yescomplemented
560#120—28no—
561C4×D4—22no—
562C4×D4—44no—
563C4×D4C2×C4×C10114yes—
564C4×D4C2×C4×C10114yescomplemented
565C4×D4D4×C10114yes—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4D4×C10111yescharacteristic
576C2×C4⋊C4C23×C10111yescharacteristic
577C2×C4⋊C4C23×C10111yescharacteristic
578C2×C4⋊C4C23×C10111yescharacteristic
579C2×C4⋊C4C23×C10111yescharacteristic
580C2×C4⋊C4C23×C10111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—28no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4D4×C10111yescharacteristic
590C2×C22⋊C4D4×C10111yescharacteristic
591C2×C42—21no—
592C2×C42C23×C10111yescharacteristic
593C4⋊C8—22no—
594#103—22no—
595#103—22no—
596#103—41no—
597#103—41no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—41no—
604#102—41no—
605#102D4×C10114yescomplemented
606C22⋊C8—22no—
607C22⋊C8—22no—
608#97—22no—
609#95—21no—
610#95—21no—
611#95—21no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×D4×C10111yescharacteristic
622C24C2×D4×C10111yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C22×C4×C10112yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊C4×C10114yes—
657C2×D4C22×C4×C10112yes—
658C2×D4C22×C4×C10112yes—
659C2×D4C2×D4×C10112yes—
660C2×D4#41×C10112yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—81no—
684C22×C4—81no—
685C22×C4—81no—
686C22×C4—81no—
687C22×C4C22×C4×C10112yes—
688C22×C4C22×C4×C10112yes—
689C22×C4C2×D4×C10111yescharacteristic
690C22×C4C2×D4×C10111yescharacteristic
691C22×C4C2×D4×C10111yescharacteristic
692C22×C4C2×D4×C10111yescharacteristic
693C22×C4C2×D4×C10112yes—
694C22×C4C2×D4×C10112yes—
695C22×C4C24×C10111yescharacteristic
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—44no—
709C2×C8C2×D4×C10112yes—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—42no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—81no—
723C4⋊C4C22⋊C4×C10114yes—
724C4⋊C4C22×C4×C10112yes—
725C4⋊C4C2×D4×C10112yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4C22⋊C4×C10114yes—
734C22⋊C4C22⋊C4×C10114yes—
735C42—42no—
736C42C22×C4×C10112yes—
737C42C2×D4×C10112yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—22no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—48no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23C2×C22⋊C4×C10112yes—
770C23C2×C22⋊C4×C10112yes—
771C23AGL(1,ℤ/8)×C10112yes—
772C23#137×C10112yes—
773C23C22×D4×C10111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4C4×D4×C10114yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—48no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
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—84no—
826C2×C4—84no—
827C2×C4—84no—
828C2×C4C2×C22⋊C4×C10112yes—
829C2×C4C2×C22⋊C4×C10112yes—
830C2×C4C2×C22⋊C4×C10112yes—
831C2×C4C2×C22⋊C4×C10112yes—
832C2×C4C23×C4×C10111yescharacteristic
833C2×C4C22×D4×C10111yescharacteristic
834C2×C4C22×D4×C10111yescharacteristic
835C2×C4C2×#41×C10111yescharacteristic
836C2×C4H(5,𝔽2)×C10111yescharacteristic
837C2×C4H(5,𝔽2)×C10111yescharacteristic
838C8—22no—
839C8—41no—
840C8—41no—
841C8—41no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#417×C10114yescomplemented
871C22C22×C22⋊C4×C10111yescharacteristic
872C22D42×C10111yescharacteristic
873C22#546×C10111yescharacteristic
874C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
875C22C2×#137×C10111yescharacteristic
876C22#576×C10111yescharacteristic
877C22#577×C10111yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4C2×C4×D4×C10111yescharacteristic
889C4#518×C10111yescharacteristic
890C4D42×C10111yescharacteristic
891C4#546×C10111yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊C4×C10111yescharacteristic
897C2C2×#417×C10111yescharacteristic
898C2C101×#289711yescharacteristic
899C2C101×#326411yescharacteristic
900C2C101×#326611yescharacteristic
901C2C101×#330611yescharacteristic
902C2C101×#331411yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC2×#546×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×#102×C101C2semidirect
5. D4×C4⋊C4×C101C2semidirect
6. C101×#1983C2semidirect
7. C101×#1959C2semidirect
8. C101×#1895C2semidirect
9. C101×#1892C2semidirect
10. C101×#1874C2semidirect
11. C101×#1872C2semidirect
12. C101×#1802C2semidirect
13. C101×#1788C2semidirect
14. C101×#1786C2semidirect
15. C101×#1762C2semidirect
18. C22×M16×C101C22semidirect
21. #546×C101C4semidirect
32. C22×C4⋊C4×C101C22semidirect
35. C2×C4⋊C8×C101C22semidirect
37. C2×#103×C101C22semidirect
38. C2×#103×C101C22semidirect
39. C2×#103×C101C22semidirect
40. C2×#103×C101C22semidirect
51. C2×C22⋊C8×C101C22semidirect
52. C2×#97×C101C22semidirect
56. #384×C101C22semidirect
58. #380×C101C22semidirect
59. C4×C4⋊C4×C101C22semidirect
60. #340×C101C22semidirect
61. #340×C101C22semidirect
62. #340×C101C22semidirect
63. #340×C101C22semidirect
70. C2×#41×C101C2×C4semidirect
80. C22×D4×C101C2×C4semidirect
101. #124×C101C2×C4semidirect
104. C22⋊Q8×C101C2×C4semidirect
107. #121×C101C2×C4semidirect
112. C4×D4×C101C2×C4semidirect
153. #102×C101D4semidirect
337. D4×C101C4×D4semidirect
418. C22×C101#417semidirect
440. #22419C101direct (N × H)
453. C2×#435C2×C101semidirect
454. C2×#417C2×C101semidirect
455. C22×#102C2×C101semidirect
456. D4×C4⋊C4C2×C101semidirect
457. #1983C2×C101semidirect
458. #1959C2×C101semidirect
459. #1895C2×C101semidirect
460. #1892C2×C101semidirect
461. #1874C2×C101semidirect
462. #1872C2×C101semidirect
463. #1802C2×C101semidirect
464. #1788C2×C101semidirect
465. #1786C2×C101semidirect
466. #1762C2×C101semidirect
467. C101#22419direct (N × H)
470. C22×M16C22×C101semidirect
473. #546C4×C101semidirect
484. C22×C4⋊C4C22×C101semidirect
487. C2×C4⋊C8C22×C101semidirect
489. C2×#103C22×C101semidirect
490. C2×#103C22×C101semidirect
491. C2×#103C22×C101semidirect
492. C2×#103C22×C101semidirect
503. C2×C22⋊C8C22×C101semidirect
504. C2×#97C22×C101semidirect
508. #384C22×C101semidirect
510. #380C22×C101semidirect
511. C4×C4⋊C4C22×C101semidirect
512. #340C22×C101semidirect
513. #340C22×C101semidirect
514. #340C22×C101semidirect
515. #340C22×C101semidirect
522. C2×#41C2×C4×C101semidirect
532. C22×D4C2×C4×C101semidirect
553. #124C2×C4×C101semidirect
556. C22⋊Q8C2×C4×C101semidirect
559. #121C2×C4×C101semidirect
564. C4×D4C2×C4×C101semidirect
605. #102D4×C101semidirect
789. D4C4×D4×C101semidirect
870. C22#417×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×#435×C1012
C2×#417×C1012
C22×#102×C1012
D4×C4⋊C4×C1012
C101×#19832
C101×#19592
C101×#18952
C101×#18922
C101×#18742
C101×#18722
C101×#18022
C101×#17882
C101×#17862
C101×#17622
#22419101