Finite Group Databasebeta

← C101×#24441 #38806592

Subgroups — C101×#24441 #38806592

Order 25856.

1522 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C101C211yesmaximal, characteristic, complemented
2C2×#468×C101C211yesmaximal, characteristic, complemented
3C2×#449×C101C211yesmaximal, characteristic, complemented
4C2×#448×C101C211yesmaximal, characteristic, complemented
5C2×#417×C101C211yesmaximal, characteristic, complemented
6C101×#2416C211yesmaximal, characteristic, complemented
7C101×#2042C211yesmaximal, characteristic, complemented
8C101×#2033C211yesmaximal, characteristic, complemented
9C101×#2012C211yesmaximal, characteristic, complemented
10C101×#1999C211yesmaximal, characteristic, complemented
11C101×#1880C211yesmaximal, characteristic, complemented
12C101×#1872C211yesmaximal, characteristic, complemented
13C101×#1870C211yesmaximal, characteristic, complemented
14C101×#1863C211yesmaximal, characteristic, complemented
15C101×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×Q8×C101C2211yescharacteristic
18C22×SD16×C101C2211yescharacteristic
19C22×SD16×C101C2211yescharacteristic
20C22×D8×C101C2211yescharacteristic
21C22×M16×C101C2211yescharacteristic
22#548×C101—24no—
23#548×C101—24no—
24C2×#124×C101—21no—
25C2×#124×C101C2211yescharacteristic
26C2×C22⋊Q8×C101—21no—
27C2×C22⋊Q8×C101C2211yescharacteristic
28C2×#121×C101—21no—
29C2×#121×C101—21no—
30C2×#121×C101C2211yescharacteristic
31C2×#121×C101C2211yescharacteristic
32C2×#121×C101C2211yescharacteristic
33C2×C4×Q8×C101C2211yescharacteristic
34C2×C4×D4×C101—21no—
35C2×C4×D4×C101C2211yescharacteristic
36C22×C4⋊C4×C101C2211yescharacteristic
37#468×C101—24no—
38#449×C101—24no—
39#448×C101—24no—
40C2×#107×C101C2211yescharacteristic
41#417×C101—24no—
42C2×#103×C101C2211yescharacteristic
43C2×#103×C101C2211yescharacteristic
44C2×#103×C101C2211yescharacteristic
45C2×#103×C101C2211yescharacteristic
46C2×#103×C101C2211yescharacteristic
47C2×#103×C101C2211yescharacteristic
48C2×#102×C101C2211yescharacteristic
49C2×#102×C101C2211yescharacteristic
50C2×#102×C101C2211yescharacteristic
51C2×#102×C101C2211yescharacteristic
52C2×C22⋊C8×C101C2211yescharacteristic
53C2×C22⋊C8×C101C2211yescharacteristic
54C2×C22⋊C8×C101C2211yescharacteristic
55#396×C101—21no—
56#394×C101—21no—
57#390×C101C2211yescharacteristic
58#389×C101C2211yescharacteristic
59#386×C101—21no—
60#380×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic
62#340×C101C2211yescharacteristic
63#336×C101C2211yescharacteristic
64#336×C101C2211yescharacteristic
65C2×#41×C101—22no—
66C2×#41×C101—22no—
67C2×#41×C101—22no—
68C2×#41×C101—41no—
69C2×#41×C101—41no—
70C2×#41×C101D414yescomplemented
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—22no—
97C2×SD16×C101—41no—
98C2×D8×C101—22no—
99C2×D8×C101—41no—
100C2×D8×C101—41no—
101C2×M16×C101—22no—
102C2×M16×C101—22no—
103C2×M16×C101—41no—
104C22×C8×C101C2311yescharacteristic
105C22×C8×C101C2311yescharacteristic
106C22×C8×C101C2311yescharacteristic
107C22×C8×C101C2311yescharacteristic
108#124×C101—28no—
109#124×C101—22no—
110#124×C101—22no—
111C22⋊Q8×C101—28no—
112C22⋊Q8×C101—22no—
113C22⋊Q8×C101D414yescomplemented
114#121×C101—28no—
115#121×C101—22no—
116#121×C101—22no—
117#121×C101—22no—
118#121×C101—22no—
119#121×C101—22no—
120#121×C101—41no—
121#121×C101—44no—
122C4×Q8×C101—22no—
123C4×Q8×C101—22no—
124C4×D4×C101—28no—
125C4×D4×C101—22no—
126C4×D4×C101—22no—
127C2×C4⋊C4×C101—21no—
128C2×C4⋊C4×C101—21no—
129C2×C4⋊C4×C101—22no—
130C2×C4⋊C4×C101—21no—
131C2×C4⋊C4×C101—21no—
132C2×C4⋊C4×C101—41no—
133C2×C4⋊C4×C101D411yescharacteristic
134C2×C4⋊C4×C101C2311yescharacteristic
135C2×C4⋊C4×C101C2311yescharacteristic
136C2×C4⋊C4×C101C2311yescharacteristic
137C2×C4⋊C4×C101C2311yescharacteristic
138C2×C22⋊C4×C101—21no—
139C2×C22⋊C4×C101—21no—
140C2×C22⋊C4×C101—21no—
141C2×C22⋊C4×C101—21no—
142C2×C22⋊C4×C101—21no—
143C2×C22⋊C4×C101—21no—
144C2×C22⋊C4×C101—21no—
145C2×C22⋊C4×C101—21no—
146C2×C22⋊C4×C101—21no—
147C2×C22⋊C4×C101D411yescharacteristic
148C2×C22⋊C4×C101D411yescharacteristic
149C2×C42×C101—21no—
150C2×C42×C101C2311yescharacteristic
151#107×C101—22no—
152#103×C101—22no—
153#103×C101—22no—
154#103×C101—22no—
155#103×C101—22no—
156#103×C101—41no—
157#103×C101D414yescomplemented
158#102×C101—22no—
159#102×C101—22no—
160#102×C101—22no—
161#102×C101—22no—
162C22⋊C8×C101—22no—
163C22⋊C8×C101—22no—
164C22⋊C8×C101—41no—
165#95×C101—21no—
166#95×C101—21no—
167C24×C101—21no—
168C24×C101—21no—
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—24no—
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—21no—
184C2×Q8×C101—42no—
185C2×Q8×C101—42no—
186C2×Q8×C101—44no—
187C2×Q8×C101—44no—
188C2×Q8×C101—44no—
189C2×Q8×C101—44no—
190C2×Q8×C101C2×D412yes—
191C2×Q8×C101C2×D412yes—
192C2×Q8×C101C2×D412yes—
193C2×Q8×C101#4112yes—
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—21no—
207C2×D4×C101—21no—
208C2×D4×C101—21no—
209C2×D4×C101—41no—
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—42no—
217C2×D4×C101—42no—
218C2×D4×C101—42no—
219C2×D4×C101—81no—
220C2×D4×C101C2×D412yes—
221C22×C4×C101—21no—
222C22×C4×C101—21no—
223C22×C4×C101—21no—
224C22×C4×C101—21no—
225C22×C4×C101—21no—
226C22×C4×C101—24no—
227C22×C4×C101—21no—
228C22×C4×C101—21no—
229C22×C4×C101—21no—
230C22×C4×C101—24no—
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—42no—
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×C101C2×D411yescharacteristic
247C22×C4×C101C2×D411yescharacteristic
248C22×C4×C101C2×D411yescharacteristic
249C22×C4×C101C2×D411yescharacteristic
250C22×C4×C101C2×D412yes—
251C22×C4×C101C2×D412yes—
252C22×C4×C101C2411yescharacteristic
253SD16×C101—44no—
254SD16×C101—44no—
255D8×C101—44no—
256M16×C101—44no—
257C2×C8×C101—21no—
258C2×C8×C101—21no—
259C2×C8×C101—21no—
260C2×C8×C101—21no—
261C2×C8×C101—21no—
262C2×C8×C101—21no—
263C2×C8×C101—21no—
264C2×C8×C101—21no—
265C2×C8×C101—21no—
266C2×C8×C101—21no—
267C2×C8×C101—21no—
268C2×C8×C101C2×D412yes—
269C4⋊C4×C101—24no—
270C4⋊C4×C101—24no—
271C4⋊C4×C101—22no—
272C4⋊C4×C101—21no—
273C4⋊C4×C101—21no—
274C4⋊C4×C101—21no—
275C4⋊C4×C101—21no—
276C4⋊C4×C101—21no—
277C4⋊C4×C101—21no—
278C4⋊C4×C101—42no—
279C4⋊C4×C101—42no—
280C4⋊C4×C101C2×D412yes—
281C4⋊C4×C101C2×D412yes—
282C22⋊C4×C101—24no—
283C22⋊C4×C101—24no—
284C22⋊C4×C101—24no—
285C22⋊C4×C101—24no—
286C22⋊C4×C101—22no—
287C22⋊C4×C101—22no—
288C22⋊C4×C101—42no—
289C22⋊C4×C101—42no—
290C22⋊C4×C101—42no—
291C22⋊C4×C101—42no—
292C22⋊C4×C101—81no—
293C42×C101—24no—
294C42×C101—21no—
295C42×C101—21no—
296C23×C101—21no—
297C23×C101—21no—
298C23×C101—21no—
299C23×C101—21no—
300C23×C101—21no—
301C23×C101—21no—
302C23×C101—21no—
303C23×C101—21no—
304C23×C101—21no—
305C23×C101—21no—
306C23×C101—21no—
307C23×C101—21no—
308C23×C101—22no—
309C23×C101—41no—
310C23×C101—41no—
311C23×C101—41no—
312C23×C101—41no—
313C23×C101—41no—
314C23×C101—41no—
315C23×C101—41no—
316C23×C101—41no—
317C23×C101—41no—
318C23×C101—41no—
319C23×C101—41no—
320C23×C101—41no—
321C23×C101—41no—
322C23×C101#12012yes—
323C23×C101AGL(1,ℤ/8)12yes—
324C23×C101C22×D411yescharacteristic
325Q8×C101—22no—
326Q8×C101—22no—
327Q8×C101—22no—
328Q8×C101—22no—
329Q8×C101—22no—
330Q8×C101—48no—
331Q8×C101—41no—
332Q8×C101—41no—
333Q8×C101#12114yescomplemented
334D4×C101—22no—
335D4×C101—22no—
336D4×C101—48no—
337D4×C101—44no—
338D4×C101—48no—
339D4×C101—41no—
340D4×C101—41no—
341D4×C101—41no—
342D4×C101—41no—
343D4×C101—41no—
344D4×C101—41no—
345D4×C101—84no—
346D4×C101—84no—
347C2×C4×C101—22no—
348C2×C4×C101—21no—
349C2×C4×C101—22no—
350C2×C4×C101—21no—
351C2×C4×C101—22no—
352C2×C4×C101—22no—
353C2×C4×C101—22no—
354C2×C4×C101—22no—
355C2×C4×C101—22no—
356C2×C4×C101—21no—
357C2×C4×C101—21no—
358C2×C4×C101—22no—
359C2×C4×C101—22no—
360C2×C4×C101—21no—
361C2×C4×C101—21no—
362C2×C4×C101—22no—
363C2×C4×C101—21no—
364C2×C4×C101—21no—
365C2×C4×C101—21no—
366C2×C4×C101—21no—
367C2×C4×C101—21no—
368C2×C4×C101—48no—
369C2×C4×C101—48no—
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—41no—
386C2×C4×C101—84no—
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—22no—
399C22×C101—22no—
400C22×C101—22no—
401C22×C101—22no—
402C22×C101—22no—
403C22×C101—22no—
404C22×C101—41no—
405C22×C101—41no—
406C22×C101—41no—
407C22×C101—41no—
408C22×C101—41no—
409C22×C101—41no—
410C22×C101—41no—
411C22×C101—41no—
412C22×C101—42no—
413C22×C101—42no—
414C22×C101—42no—
415C22×C101—81no—
416C22×C101—81no—
417C22×C101—81no—
418C22×C101—81no—
419C22×C101—81no—
420C22×C101—81no—
421C22×C101—81no—
422C22×C101—81no—
423C22×C101—81no—
424C22×C101—81no—
425C22×C101—81no—
426C22×C101C2×#12011yescharacteristic
427C22×C101D4211yescharacteristic
428C22×C101#54611yescharacteristic
429C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
430C22×C101#57511yescharacteristic
431C22×C101#57711yescharacteristic
432C22×C101#57811yescharacteristic
433C4×C101—22no—
434C4×C101—24no—
435C4×C101—41no—
436C4×C101—42no—
437C4×C101—41no—
438C4×C101—42no—
439C4×C101—42no—
440C4×C101—41no—
441C4×C101—81no—
442C4×C101—81no—
443C4×C101C2×#12111yescharacteristic
444C4×C101#53411yescharacteristic
445C4×C101D4211yescharacteristic
446C4×C101#54611yescharacteristic
447#24441C10111yesmaximal, characteristic, direct product factor, Sylow
448C2×C101—42no—
449C2×C101—42no—
450C2×C101—82no—
451C2×C101—161no—
452C2×C101#241011yescharacteristic
453C2×C101#300611yescharacteristic
454C2×C101#301311yescharacteristic
455C2×C101#326511yescharacteristic
456C2×C101#327711yescharacteristic
457C2×C101#330811yescharacteristic
458C2×C101#332611yescharacteristic
459C2×#548C2×C10111yescharacteristic, complemented
460C2×#468C2×C10111yescharacteristic, complemented
461C2×#449C2×C10111yescharacteristic, complemented
462C2×#448C2×C10111yescharacteristic, complemented
463C2×#417C2×C10111yescharacteristic, complemented
464#2416C2×C10111yescharacteristic, complemented
465#2042C2×C10111yescharacteristic, complemented
466#2033C2×C10111yescharacteristic, complemented
467#2012C2×C10111yescharacteristic, complemented
468#1999C2×C10111yescharacteristic, complemented
469#1880C2×C10111yescharacteristic, complemented
470#1872C2×C10111yescharacteristic, complemented
471#1870C2×C10111yescharacteristic, complemented
472#1863C2×C10111yescharacteristic, complemented
473#1787C2×C10111yescharacteristic, complemented
474C101#2444111yescharacteristic, direct product factor, Sylow
475C22×#41C22×C10111yescharacteristic
476C23×Q8C22×C10111yescharacteristic
477C22×SD16C22×C10111yescharacteristic
478C22×SD16C22×C10111yescharacteristic
479C22×D8C22×C10111yescharacteristic
480C22×M16C22×C10111yescharacteristic
481#548—24no—
482#548—24no—
483C2×#124—21no—
484C2×#124C22×C10111yescharacteristic
485C2×C22⋊Q8—21no—
486C2×C22⋊Q8C22×C10111yescharacteristic
487C2×#121—21no—
488C2×#121—21no—
489C2×#121C22×C10111yescharacteristic
490C2×#121C22×C10111yescharacteristic
491C2×#121C22×C10111yescharacteristic
492C2×C4×Q8C22×C10111yescharacteristic
493C2×C4×D4—21no—
494C2×C4×D4C22×C10111yescharacteristic
495C22×C4⋊C4C22×C10111yescharacteristic
496#468—24no—
497#449—24no—
498#448—24no—
499C2×#107C22×C10111yescharacteristic
500#417—24no—
501C2×#103C22×C10111yescharacteristic
502C2×#103C22×C10111yescharacteristic
503C2×#103C22×C10111yescharacteristic
504C2×#103C22×C10111yescharacteristic
505C2×#103C22×C10111yescharacteristic
506C2×#103C22×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
514#396—21no—
515#394—21no—
516#390C22×C10111yescharacteristic
517#389C22×C10111yescharacteristic
518#386—21no—
519#380C22×C10111yescharacteristic
520#340C22×C10111yescharacteristic
521#340C22×C10111yescharacteristic
522#336C22×C10111yescharacteristic
523#336C22×C10111yescharacteristic
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C2×#41D4×C10114yescomplemented
530C22×Q8—22no—
531C22×Q8—22no—
532C22×Q8—21no—
533C22×Q8—22no—
534C22×Q8—22no—
535C22×Q8—41no—
536C22×Q8—41no—
537C22×Q8C23×C10111yescharacteristic
538C22×Q8C23×C10111yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4D4×C10111yescharacteristic
544C22×D4C23×C10111yescharacteristic
545C22×D4C23×C10111yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4C23×C10111yescharacteristic
550C23×C4C23×C10111yescharacteristic
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—41no—
557C2×D8—22no—
558C2×D8—41no—
559C2×D8—41no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—41no—
563C22×C8C23×C10111yescharacteristic
564C22×C8C23×C10111yescharacteristic
565C22×C8C23×C10111yescharacteristic
566C22×C8C23×C10111yescharacteristic
567#124—28no—
568#124—22no—
569#124—22no—
570C22⋊Q8—28no—
571C22⋊Q8—22no—
572C22⋊Q8D4×C10114yescomplemented
573#121—28no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—41no—
580#121—44no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×D4—28no—
584C4×D4—22no—
585C4×D4—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4D4×C10111yescharacteristic
593C2×C4⋊C4C23×C10111yescharacteristic
594C2×C4⋊C4C23×C10111yescharacteristic
595C2×C4⋊C4C23×C10111yescharacteristic
596C2×C4⋊C4C23×C10111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4D4×C10111yescharacteristic
607C2×C22⋊C4D4×C10111yescharacteristic
608C2×C42—21no—
609C2×C42C23×C10111yescharacteristic
610#107—22no—
611#103—22no—
612#103—22no—
613#103—22no—
614#103—22no—
615#103—41no—
616#103D4×C10114yescomplemented
617#102—22no—
618#102—22no—
619#102—22no—
620#102—22no—
621C22⋊C8—22no—
622C22⋊C8—22no—
623C22⋊C8—41no—
624#95—21no—
625#95—21no—
626C24—21no—
627C24—21no—
628C24C2×D4×C10111yescharacteristic
629C24C2×D4×C10111yescharacteristic
630#41—28no—
631#41—44no—
632#41—44no—
633#41—44no—
634C2×Q8—24no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—42no—
644C2×Q8—42no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8—44no—
649C2×Q8C2×D4×C10112yes—
650C2×Q8C2×D4×C10112yes—
651C2×Q8C2×D4×C10112yes—
652C2×Q8#41×C10112yes—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—21no—
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—21no—
667C2×D4—21no—
668C2×D4—41no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—81no—
679C2×D4C2×D4×C10112yes—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—24no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—81no—
705C22×C4C2×D4×C10111yescharacteristic
706C22×C4C2×D4×C10111yescharacteristic
707C22×C4C2×D4×C10111yescharacteristic
708C22×C4C2×D4×C10111yescharacteristic
709C22×C4C2×D4×C10112yes—
710C22×C4C2×D4×C10112yes—
711C22×C4C24×C10111yescharacteristic
712SD16—44no—
713SD16—44no—
714D8—44no—
715M16—44no—
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×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8C2×D4×C10112yes—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—22no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4C2×D4×C10112yes—
740C4⋊C4C2×D4×C10112yes—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—81no—
752C42—24no—
753C42—21no—
754C42—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—22no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23#120×C10112yes—
782C23AGL(1,ℤ/8)×C10112yes—
783C23C22×D4×C10111yescharacteristic
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—22no—
788Q8—22no—
789Q8—48no—
790Q8—41no—
791Q8—41no—
792Q8#121×C10114yescomplemented
793D4—22no—
794D4—22no—
795D4—48no—
796D4—44no—
797D4—48no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—41no—
804D4—84no—
805D4—84no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—48no—
828C2×C4—48no—
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×C4C22×D4×C10111yescharacteristic
848C2×C4C22×D4×C10111yescharacteristic
849C2×C4C22×D4×C10111yescharacteristic
850C2×C4C2×#41×C10111yescharacteristic
851C2×C4H(5,𝔽2)×C10111yescharacteristic
852C2×C4H(5,𝔽2)×C10111yescharacteristic
853C8—22no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22C2×#120×C10111yescharacteristic
886C22D42×C10111yescharacteristic
887C22#546×C10111yescharacteristic
888C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
889C22#575×C10111yescharacteristic
890C22#577×C10111yescharacteristic
891C22#578×C10111yescharacteristic
892C4—22no—
893C4—24no—
894C4—41no—
895C4—42no—
896C4—41no—
897C4—42no—
898C4—42no—
899C4—41no—
900C4—81no—
901C4—81no—
902C4C2×#121×C10111yescharacteristic
903C4#534×C10111yescharacteristic
904C4D42×C10111yescharacteristic
905C4#546×C10111yescharacteristic
906C2—42no—
907C2—42no—
908C2—82no—
909C2—161no—
910C2C101×#241011yescharacteristic
911C2C101×#300611yescharacteristic
912C2C101×#301311yescharacteristic
913C2C101×#326511yescharacteristic
914C2C101×#327711yescharacteristic
915C2C101×#330811yescharacteristic
916C2C101×#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×#468×C101C2semidirect
3. C2×#449×C101C2semidirect
4. C2×#448×C101C2semidirect
5. C2×#417×C101C2semidirect
6. C101×#2416C2semidirect
7. C101×#2042C2semidirect
8. C101×#2033C2semidirect
9. C101×#2012C2semidirect
10. C101×#1999C2semidirect
11. C101×#1880C2semidirect
12. C101×#1872C2semidirect
13. C101×#1870C2semidirect
14. C101×#1863C2semidirect
15. C101×#1787C2semidirect
70. C2×#41×C101D4semidirect
113. C22⋊Q8×C101D4semidirect
157. #103×C101D4semidirect
333. Q8×C101#121semidirect
447. #24441C101direct (N × H)
459. C2×#548C2×C101semidirect
460. C2×#468C2×C101semidirect
461. C2×#449C2×C101semidirect
462. C2×#448C2×C101semidirect
463. C2×#417C2×C101semidirect
464. #2416C2×C101semidirect
465. #2042C2×C101semidirect
466. #2033C2×C101semidirect
467. #2012C2×C101semidirect
468. #1999C2×C101semidirect
469. #1880C2×C101semidirect
470. #1872C2×C101semidirect
471. #1870C2×C101semidirect
472. #1863C2×C101semidirect
473. #1787C2×C101semidirect
474. C101#24441direct (N × H)
529. C2×#41D4×C101semidirect
572. C22⋊Q8D4×C101semidirect
616. #103D4×C101semidirect
792. Q8#121×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×#468×C1012
C2×#449×C1012
C2×#448×C1012
C2×#417×C1012
C101×#24162
C101×#20422
C101×#20332
C101×#20122
C101×#19992
C101×#18802
C101×#18722
C101×#18702
C101×#18632
C101×#17872
#24441101