Finite Group Databasebeta

← C101×#24452 #38806603

Subgroups — C101×#24452 #38806603

Order 25856.

1592 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C101C211yesmaximal, characteristic
2C2×#468×C101C211yesmaximal, characteristic, complemented
3C2×#452×C101C211yesmaximal, characteristic, complemented
4C2×#450×C101C211yesmaximal, characteristic, complemented
5C2×#417×C101C211yesmaximal, characteristic, complemented
6C101×#2417C211yesmaximal, characteristic, complemented
7C101×#2042C211yesmaximal, characteristic, complemented
8C101×#2036C211yesmaximal, characteristic, complemented
9C101×#2015C211yesmaximal, characteristic, complemented
10C101×#2001C211yesmaximal, characteristic, complemented
11C101×#1877C211yesmaximal, characteristic, complemented
12C101×#1874C211yesmaximal, characteristic, complemented
13C101×#1870C211yesmaximal, characteristic, complemented
14C101×#1862C211yesmaximal, characteristic, complemented
15C101×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×D4×C101C2211yescharacteristic
18C22×Q16×C101C2211yescharacteristic, complemented
19C22×SD16×C101C2211yescharacteristic
20C22×SD16×C101C2211yescharacteristic
21C22×M16×C101C2211yescharacteristic, complemented
22#546×C101—24no—
23#546×C101—24no—
24C2×#124×C101C2211yescharacteristic
25C2×#123×C101—21no—
26C2×C22⋊Q8×C101C2211yescharacteristic
27C2×C22⋊Q8×C101C2211yescharacteristic
28C2×C22⋊Q8×C101C2211yescharacteristic, complemented
29C2×#121×C101—21no—
30C2×#121×C101C2211yescharacteristic
31C2×#120×C101—21no—
32C2×C4×D4×C101C2211yescharacteristic
33C2×C4×D4×C101C2211yescharacteristic
34C22×C4⋊C4×C101C2211yescharacteristic, complemented
35C22×C22⋊C4×C101—21no—
36#468×C101—24no—
37#452×C101—24no—
38#450×C101—24no—
39C2×#107×C101C2211yescharacteristic, complemented
40#417×C101—24no—
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
54#398×C101—21no—
55#396×C101—21no—
56#391×C101C2211yescharacteristic, complemented
57#389×C101C2211yescharacteristic, complemented
58#386×C101—21no—
59#380×C101—21no—
60#380×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic, complemented
62#340×C101C2211yescharacteristic, complemented
63#336×C101C2211yescharacteristic, complemented
64#336×C101C2211yescharacteristic, complemented
65C25×C101—21no—
66C2×#41×C101—22no—
67C2×#41×C101—22no—
68C2×#41×C101—22no—
69C2×#41×C101—41no—
70C2×#41×C101—41no—
71C2×#41×C101D414yes—
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×C101—21no—
89C23×C4×C101C2311yescharacteristic
90C23×C4×C101C2311yescharacteristic
91C2×Q16×C101—22no—
92C2×Q16×C101—41no—
93C2×Q16×C101—41no—
94C2×SD16×C101—22no—
95C2×SD16×C101—22no—
96C2×SD16×C101—22no—
97C2×SD16×C101—22no—
98C2×SD16×C101—22no—
99C2×SD16×C101—41no—
100C2×M16×C101—22no—
101C2×M16×C101—22no—
102C2×M16×C101—41no—
103C22×C8×C101C2311yescharacteristic
104C22×C8×C101C2311yescharacteristic
105C22×C8×C101C2311yescharacteristic
106C22×C8×C101C2311yescharacteristic
107#124×C101—22no—
108#124×C101—22no—
109#123×C101—28no—
110C22⋊Q8×C101—22no—
111C22⋊Q8×C101—22no—
112C22⋊Q8×C101—22no—
113C22⋊Q8×C101—22no—
114C22⋊Q8×C101—22no—
115C22⋊Q8×C101—41no—
116#121×C101—28no—
117#121×C101—22no—
118#121×C101D414yes—
119#120×C101—28no—
120C4×D4×C101—22no—
121C4×D4×C101—22no—
122C4×D4×C101—22no—
123C4×D4×C101—22no—
124C2×C4⋊C4×C101—21no—
125C2×C4⋊C4×C101—22no—
126C2×C4⋊C4×C101—21no—
127C2×C4⋊C4×C101—21no—
128C2×C4⋊C4×C101—21no—
129C2×C4⋊C4×C101—21no—
130C2×C4⋊C4×C101—41no—
131C2×C4⋊C4×C101D411yescharacteristic
132C2×C4⋊C4×C101C2311yescharacteristic
133C2×C4⋊C4×C101C2311yescharacteristic
134C2×C4⋊C4×C101C2311yescharacteristic
135C2×C4⋊C4×C101C2311yescharacteristic
136C2×C22⋊C4×C101—28no—
137C2×C22⋊C4×C101—21no—
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×C101D411yescharacteristic
146C2×C22⋊C4×C101D411yescharacteristic
147C2×C42×C101C2311yescharacteristic
148#107×C101—22no—
149#103×C101—22no—
150#103×C101—22no—
151#103×C101—22no—
152#103×C101—22no—
153#102×C101—22no—
154#102×C101—22no—
155#102×C101—22no—
156#102×C101—22no—
157#102×C101—41no—
158#102×C101D414yescomplemented
159C22⋊C8×C101—22no—
160C22⋊C8×C101—22no—
161C22⋊C8×C101—41no—
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—28no—
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×C101—21no—
192C2×Q8×C101C2×D412yes—
193C2×D4×C101—24no—
194C2×D4×C101—22no—
195C2×D4×C101—24no—
196C2×D4×C101—22no—
197C2×D4×C101—24no—
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—21no—
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—24no—
229C22×C4×C101—24no—
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—42no—
240C22×C4×C101—42no—
241C22×C4×C101—42no—
242C22×C4×C101—42no—
243C22×C4×C101—81no—
244C22×C4×C101—81no—
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
253Q16×C101—44no—
254SD16×C101—44no—
255SD16×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—22no—
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×C101—42no—
278C4⋊C4×C101—42no—
279C4⋊C4×C101—42no—
280C4⋊C4×C101—81no—
281C4⋊C4×C101C2×D412yes—
282C4⋊C4×C101C2×D412yes—
283C22⋊C4×C101—24no—
284C22⋊C4×C101—24no—
285C22⋊C4×C101—24no—
286C22⋊C4×C101—24no—
287C22⋊C4×C101—22no—
288C22⋊C4×C101—22no—
289C22⋊C4×C101—24no—
290C22⋊C4×C101—42no—
291C22⋊C4×C101—42no—
292C22⋊C4×C101—81no—
293C42×C101—21no—
294C42×C101—21no—
295C23×C101—21no—
296C23×C101—22no—
297C23×C101—21no—
298C23×C101—21no—
299C23×C101—22no—
300C23×C101—21no—
301C23×C101—21no—
302C23×C101—22no—
303C23×C101—21no—
304C23×C101—21no—
305C23×C101—21no—
306C23×C101—21no—
307C23×C101—21no—
308C23×C101—21no—
309C23×C101—21no—
310C23×C101—22no—
311C23×C101—48no—
312C23×C101—48no—
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—41no—
323C23×C101—84no—
324C23×C101—84no—
325C23×C101—84no—
326C23×C101—84no—
327C23×C101—84no—
328C23×C101#12012yes—
329C23×C101#13712yes—
330C23×C101C22×D411yescharacteristic
331Q8×C101—22no—
332Q8×C101—22no—
333Q8×C101—41no—
334Q8×C101—41no—
335Q8×C101—41no—
336Q8×C101—41no—
337Q8×C101—41no—
338Q8×C101—41no—
339D4×C101—22no—
340D4×C101—22no—
341D4×C101—22no—
342D4×C101—22no—
343D4×C101—22no—
344D4×C101—44no—
345D4×C101—48no—
346D4×C101—48no—
347D4×C101—41no—
348D4×C101—41no—
349D4×C101—84no—
350D4×C101#12114yes—
351C2×C4×C101—21no—
352C2×C4×C101—21no—
353C2×C4×C101—22no—
354C2×C4×C101—22no—
355C2×C4×C101—22no—
356C2×C4×C101—22no—
357C2×C4×C101—21no—
358C2×C4×C101—21no—
359C2×C4×C101—22no—
360C2×C4×C101—22no—
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—21no—
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—41no—
387C2×C4×C101—41no—
388C2×C4×C101—41no—
389C2×C4×C101—84no—
390C2×C4×C101—84no—
391C2×C4×C101#12012yes—
392C2×C4×C101C22×D411yescharacteristic
393C2×C4×C101C22×D411yescharacteristic
394C2×C4×C101C22×D411yescharacteristic
395C2×C4×C101C2×#4111yescharacteristic
396C2×C4×C101H(5,𝔽2)11yescharacteristic
397C2×C4×C101H(5,𝔽2)11yescharacteristic
398C8×C101—22no—
399C8×C101—41no—
400C8×C101—41no—
401C8×C101—41no—
402C22×C101—22no—
403C22×C101—24no—
404C22×C101—22no—
405C22×C101—22no—
406C22×C101—22no—
407C22×C101—22no—
408C22×C101—22no—
409C22×C101—41no—
410C22×C101—42no—
411C22×C101—41no—
412C22×C101—42no—
413C22×C101—42no—
414C22×C101—41no—
415C22×C101—41no—
416C22×C101—41no—
417C22×C101—42no—
418C22×C101—41no—
419C22×C101—42no—
420C22×C101—41no—
421C22×C101—41no—
422C22×C101—42no—
423C22×C101—42no—
424C22×C101—42no—
425C22×C101—42no—
426C22×C101—816no—
427C22×C101—81no—
428C22×C101—81no—
429C22×C101—81no—
430C22×C101—81no—
431C22×C101C2×#12011yescharacteristic
432C22×C101D4211yescharacteristic
433C22×C101#54611yescharacteristic
434C22×C101C2×#13711yescharacteristic
435C22×C101#57511yescharacteristic
436C22×C101#57611yescharacteristic
437C22×C101#57711yescharacteristic
438C4×C101—22no—
439C4×C101—41no—
440C4×C101—42no—
441C4×C101—41no—
442C4×C101—41no—
443C4×C101—42no—
444C4×C101—42no—
445C4×C101—81no—
446C4×C101—81no—
447C4×C101—81no—
448C4×C101C2×#12111yescharacteristic
449C4×C101#53411yescharacteristic
450C4×C101D4211yescharacteristic
451C4×C101#54611yescharacteristic
452#24452C10111yesmaximal, characteristic, direct product factor, Sylow
453C2×C101—42no—
454C2×C101—42no—
455C2×C101—44no—
456C2×C101—82no—
457C2×C101#241011yescharacteristic
458C2×C101#300711yescharacteristic
459C2×C101#301211yescharacteristic
460C2×C101#326611yescharacteristic
461C2×C101#327311yescharacteristic
462C2×C101#331411yescharacteristic
463C2×C101#332311yescharacteristic
464C2×#546C2×C10111yescharacteristic
465C2×#468C2×C10111yescharacteristic, complemented
466C2×#452C2×C10111yescharacteristic, complemented
467C2×#450C2×C10111yescharacteristic, complemented
468C2×#417C2×C10111yescharacteristic, complemented
469#2417C2×C10111yescharacteristic, complemented
470#2042C2×C10111yescharacteristic, complemented
471#2036C2×C10111yescharacteristic, complemented
472#2015C2×C10111yescharacteristic, complemented
473#2001C2×C10111yescharacteristic, complemented
474#1877C2×C10111yescharacteristic, complemented
475#1874C2×C10111yescharacteristic, complemented
476#1870C2×C10111yescharacteristic, complemented
477#1862C2×C10111yescharacteristic, complemented
478#1786C2×C10111yescharacteristic, complemented
479C101#2445211yescharacteristic, direct product factor, Sylow
480C22×#41C22×C10111yescharacteristic
481C23×D4C22×C10111yescharacteristic
482C22×Q16C22×C10111yescharacteristic, complemented
483C22×SD16C22×C10111yescharacteristic
484C22×SD16C22×C10111yescharacteristic
485C22×M16C22×C10111yescharacteristic, complemented
486#546—24no—
487#546—24no—
488C2×#124C22×C10111yescharacteristic
489C2×#123—21no—
490C2×C22⋊Q8C22×C10111yescharacteristic
491C2×C22⋊Q8C22×C10111yescharacteristic
492C2×C22⋊Q8C22×C10111yescharacteristic, complemented
493C2×#121—21no—
494C2×#121C22×C10111yescharacteristic
495C2×#120—21no—
496C2×C4×D4C22×C10111yescharacteristic
497C2×C4×D4C22×C10111yescharacteristic
498C22×C4⋊C4C22×C10111yescharacteristic, complemented
499C22×C22⋊C4—21no—
500#468—24no—
501#452—24no—
502#450—24no—
503C2×#107C22×C10111yescharacteristic, complemented
504#417—24no—
505C2×#103C22×C10111yescharacteristic, complemented
506C2×#103C22×C10111yescharacteristic, complemented
507C2×#103C22×C10111yescharacteristic, complemented
508C2×#103C22×C10111yescharacteristic, complemented
509C2×#102C22×C10111yescharacteristic
510C2×#102C22×C10111yescharacteristic
511C2×#102C22×C10111yescharacteristic
512C2×#102C22×C10111yescharacteristic
513C2×#102C22×C10111yescharacteristic
514C2×#102C22×C10111yescharacteristic
515C2×C22⋊C8C22×C10111yescharacteristic
516C2×C22⋊C8C22×C10111yescharacteristic
517C2×C22⋊C8C22×C10111yescharacteristic, complemented
518#398—21no—
519#396—21no—
520#391C22×C10111yescharacteristic, complemented
521#389C22×C10111yescharacteristic, complemented
522#386—21no—
523#380—21no—
524#380C22×C10111yescharacteristic
525#340C22×C10111yescharacteristic, complemented
526#340C22×C10111yescharacteristic, complemented
527#336C22×C10111yescharacteristic, complemented
528#336C22×C10111yescharacteristic, complemented
529C25—21no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41D4×C10114yes—
536C22×Q8C23×C10111yescharacteristic
537C22×Q8C23×C10111yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—21no—
545C22×D4—41no—
546C22×D4—41no—
547C22×D4D4×C10111yescharacteristic
548C22×D4C23×C10111yescharacteristic
549C22×D4C23×C10111yescharacteristic
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4C23×C10111yescharacteristic
554C23×C4C23×C10111yescharacteristic
555C2×Q16—22no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—41no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C22×C8C23×C10111yescharacteristic
568C22×C8C23×C10111yescharacteristic
569C22×C8C23×C10111yescharacteristic
570C22×C8C23×C10111yescharacteristic
571#124—22no—
572#124—22no—
573#123—28no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—41no—
580#121—28no—
581#121—22no—
582#121D4×C10114yes—
583#120—28no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4D4×C10111yescharacteristic
596C2×C4⋊C4C23×C10111yescharacteristic
597C2×C4⋊C4C23×C10111yescharacteristic
598C2×C4⋊C4C23×C10111yescharacteristic
599C2×C4⋊C4C23×C10111yescharacteristic
600C2×C22⋊C4—28no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4D4×C10111yescharacteristic
610C2×C22⋊C4D4×C10111yescharacteristic
611C2×C42C23×C10111yescharacteristic
612#107—22no—
613#103—22no—
614#103—22no—
615#103—22no—
616#103—22no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—22no—
621#102—41no—
622#102D4×C10114yescomplemented
623C22⋊C8—22no—
624C22⋊C8—22no—
625C22⋊C8—41no—
626#95—21no—
627#95—21no—
628#95—21no—
629#95—21no—
630C24—21no—
631C24—24no—
632C24—21no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—81no—
638C24—81no—
639C24C2×D4×C10111yescharacteristic
640C24C2×D4×C10111yescharacteristic
641#41—28no—
642#41—44no—
643#41—44no—
644#41—44no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8C2×D4×C10112yes—
657C2×D4—24no—
658C2×D4—22no—
659C2×D4—24no—
660C2×D4—22no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—41no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—44no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—44no—
679C2×D4—81no—
680C2×D4—81no—
681C2×D4C2×D4×C10112yes—
682C2×D4C2×D4×C10112yes—
683C2×D4C2×D4×C10112yes—
684C2×D4#41×C10112yes—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—81no—
708C22×C4—81no—
709C22×C4—81no—
710C22×C4C2×D4×C10111yescharacteristic
711C22×C4C2×D4×C10111yescharacteristic
712C22×C4C2×D4×C10111yescharacteristic
713C22×C4C2×D4×C10111yescharacteristic
714C22×C4C2×D4×C10112yes—
715C22×C4C2×D4×C10112yes—
716C22×C4C24×C10111yescharacteristic
717Q16—44no—
718SD16—44no—
719SD16—44no—
720M16—44no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8C2×D4×C10112yes—
733C4⋊C4—24no—
734C4⋊C4—22no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—81no—
745C4⋊C4C2×D4×C10112yes—
746C4⋊C4C2×D4×C10112yes—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—81no—
757C42—21no—
758C42—21no—
759C23—21no—
760C23—22no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—21no—
765C23—21no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—48no—
776C23—48no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23—84no—
792C23#120×C10112yes—
793C23#137×C10112yes—
794C23C22×D4×C10111yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—44no—
809D4—48no—
810D4—48no—
811D4—41no—
812D4—41no—
813D4—84no—
814D4#121×C10114yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—48no—
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—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—84no—
854C2×C4—84no—
855C2×C4#120×C10112yes—
856C2×C4C22×D4×C10111yescharacteristic
857C2×C4C22×D4×C10111yescharacteristic
858C2×C4C22×D4×C10111yescharacteristic
859C2×C4C2×#41×C10111yescharacteristic
860C2×C4H(5,𝔽2)×C10111yescharacteristic
861C2×C4H(5,𝔽2)×C10111yescharacteristic
862C8—22no—
863C8—41no—
864C8—41no—
865C8—41no—
866C22—22no—
867C22—24no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—41no—
874C22—42no—
875C22—41no—
876C22—42no—
877C22—42no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—42no—
882C22—41no—
883C22—42no—
884C22—41no—
885C22—41no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—816no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22—81no—
895C22C2×#120×C10111yescharacteristic
896C22D42×C10111yescharacteristic
897C22#546×C10111yescharacteristic
898C22C2×#137×C10111yescharacteristic
899C22#575×C10111yescharacteristic
900C22#576×C10111yescharacteristic
901C22#577×C10111yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—81no—
910C4—81no—
911C4—81no—
912C4C2×#121×C10111yescharacteristic
913C4#534×C10111yescharacteristic
914C4D42×C10111yescharacteristic
915C4#546×C10111yescharacteristic
916C2—42no—
917C2—42no—
918C2—44no—
919C2—82no—
920C2C101×#241011yescharacteristic
921C2C101×#300711yescharacteristic
922C2C101×#301211yescharacteristic
923C2C101×#326611yescharacteristic
924C2C101×#327311yescharacteristic
925C2C101×#331411yescharacteristic
926C2C101×#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×#468×C101C2semidirect
3. C2×#452×C101C2semidirect
4. C2×#450×C101C2semidirect
5. C2×#417×C101C2semidirect
6. C101×#2417C2semidirect
7. C101×#2042C2semidirect
8. C101×#2036C2semidirect
9. C101×#2015C2semidirect
10. C101×#2001C2semidirect
11. C101×#1877C2semidirect
12. C101×#1874C2semidirect
13. C101×#1870C2semidirect
14. C101×#1862C2semidirect
15. C101×#1786C2semidirect
18. C22×Q16×C101C22semidirect
21. C22×M16×C101C22semidirect
28. C2×C22⋊Q8×C101C22semidirect
34. C22×C4⋊C4×C101C22semidirect
39. C2×#107×C101C22semidirect
41. C2×#103×C101C22semidirect
42. C2×#103×C101C22semidirect
43. C2×#103×C101C22semidirect
44. C2×#103×C101C22semidirect
53. C2×C22⋊C8×C101C22semidirect
56. #391×C101C22semidirect
57. #389×C101C22semidirect
61. #340×C101C22semidirect
62. #340×C101C22semidirect
63. #336×C101C22semidirect
64. #336×C101C22semidirect
158. #102×C101D4semidirect
452. #24452C101direct (N × H)
465. C2×#468C2×C101semidirect
466. C2×#452C2×C101semidirect
467. C2×#450C2×C101semidirect
468. C2×#417C2×C101semidirect
469. #2417C2×C101semidirect
470. #2042C2×C101semidirect
471. #2036C2×C101semidirect
472. #2015C2×C101semidirect
473. #2001C2×C101semidirect
474. #1877C2×C101semidirect
475. #1874C2×C101semidirect
476. #1870C2×C101semidirect
477. #1862C2×C101semidirect
478. #1786C2×C101semidirect
479. C101#24452direct (N × H)
482. C22×Q16C22×C101semidirect
485. C22×M16C22×C101semidirect
492. C2×C22⋊Q8C22×C101semidirect
498. C22×C4⋊C4C22×C101semidirect
503. C2×#107C22×C101semidirect
505. C2×#103C22×C101semidirect
506. C2×#103C22×C101semidirect
507. C2×#103C22×C101semidirect
508. C2×#103C22×C101semidirect
517. C2×C22⋊C8C22×C101semidirect
520. #391C22×C101semidirect
521. #389C22×C101semidirect
525. #340C22×C101semidirect
526. #340C22×C101semidirect
527. #336C22×C101semidirect
528. #336C22×C101semidirect
622. #102D4×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×#468×C1012
C2×#452×C1012
C2×#450×C1012
C2×#417×C1012
C101×#24172
C101×#20422
C101×#20362
C101×#20152
C101×#20012
C101×#18772
C101×#18742
C101×#18702
C101×#18622
C101×#17862
#24452101