Finite Group Databasebeta

← C101×#25549 #38807700

Subgroups — C101×#25549 #38807700

Order 25856.

1390 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C101C211yesmaximal, characteristic, complemented
2C2×#481×C101C211yesmaximal, characteristic, complemented
3C2×#469×C101C211yesmaximal, characteristic, complemented
4C101×#2414C211yesmaximal, characteristic, complemented
5C101×#2058C211yesmaximal, characteristic, complemented
6C101×#2034C211yesmaximal, characteristic, complemented
7C101×#2023C211yesmaximal, characteristic, complemented
8C101×#1999C211yesmaximal, characteristic, complemented
9C101×#1879C211yesmaximal, characteristic, complemented
10C101×#1875C211yesmaximal, characteristic, complemented
11C101×#1874C211yesmaximal, characteristic, complemented
12C101×#1870C211yesmaximal, characteristic, complemented
13C101×#1864C211yesmaximal, characteristic, complemented
14C101×#1853C211yesmaximal, characteristic, complemented
15C101×#1736C211yesmaximal, characteristic, complemented
16C22×#41×C101—21no—
17C22×D8×C101C2211yescharacteristic
18C22×M16×C101C2211yescharacteristic
19#547×C101—24no—
20#547×C101—24no—
21C2×C4⋊Q8×C101C2211yescharacteristic
22C2×#123×C101—21no—
23C2×#123×C101—21no—
24C2×C22⋊Q8×C101—21no—
25C2×#121×C101C2211yescharacteristic
26C2×#121×C101C2211yescharacteristic
27C2×#121×C101C2211yescharacteristic
28C2×#121×C101C2211yescharacteristic
29C2×C4×D4×C101C2211yescharacteristic
30C2×C4×D4×C101C2211yescharacteristic
31C2×#117×C101C2211yescharacteristic
32C22×C4⋊C4×C101C2211yescharacteristic
33C22×C4⋊C4×C101C2211yescharacteristic
34#481×C101—24no—
35#469×C101—24no—
36C2×#106×C101C2211yescharacteristic
37C2×#106×C101C2211yescharacteristic
38C2×#106×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×C22⋊C8×C101C2211yescharacteristic
46C2×C22⋊C8×C101C2211yescharacteristic
47C2×C22⋊C8×C101C2211yescharacteristic
48#394×C101—21no—
49#392×C101—21no—
50#390×C101—21no—
51#390×C101C2211yescharacteristic
52#389×C101C2211yescharacteristic
53#388×C101—21no—
54#380×C101C2211yescharacteristic
55#340×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#336×C101C2211yescharacteristic
62#336×C101C2211yescharacteristic
63C2×#41×C101—28no—
64C2×#41×C101—44no—
65C2×#41×C101—44no—
66C22×Q8×C101—21no—
67C22×D4×C101—21no—
68C22×D4×C101—21no—
69C22×D4×C101—21no—
70C22×D4×C101—21no—
71C22×D4×C101D411yescharacteristic
72C22×D4×C101C2311yescharacteristic
73C22×D4×C101C2311yescharacteristic
74C23×C4×C101—21no—
75C23×C4×C101—21no—
76C23×C4×C101—21no—
77C23×C4×C101C2311yescharacteristic
78C23×C4×C101C2311yescharacteristic
79C2×D8×C101—22no—
80C2×D8×C101—22no—
81C2×D8×C101—41no—
82C2×M16×C101—22no—
83C2×M16×C101—22no—
84C2×M16×C101—41no—
85C22×C8×C101C2311yescharacteristic
86C22×C8×C101C2311yescharacteristic
87C22×C8×C101C2311yescharacteristic
88C22×C8×C101C2311yescharacteristic
89C4⋊Q8×C101—22no—
90C4⋊Q8×C101—22no—
91#123×C101—28no—
92#123×C101—28no—
93C22⋊Q8×C101—28no—
94#121×C101—22no—
95#121×C101—22no—
96#121×C101—22no—
97#121×C101—22no—
98#121×C101—22no—
99#121×C101—22no—
100#121×C101—41no—
101#121×C101D414yescomplemented
102C4×D4×C101—22no—
103C4×D4×C101—22no—
104C4×D4×C101—22no—
105C4×D4×C101—22no—
106#117×C101—22no—
107#117×C101—41no—
108C2×C4⋊C4×C101—21no—
109C2×C4⋊C4×C101—21no—
110C2×C4⋊C4×C101—22no—
111C2×C4⋊C4×C101—21no—
112C2×C4⋊C4×C101—22no—
113C2×C4⋊C4×C101—22no—
114C2×C4⋊C4×C101—21no—
115C2×C4⋊C4×C101D411yescharacteristic
116C2×C4⋊C4×C101D414yescomplemented
117C2×C4⋊C4×C101C2311yescharacteristic
118C2×C4⋊C4×C101C2311yescharacteristic
119C2×C4⋊C4×C101C2311yescharacteristic
120C2×C4⋊C4×C101C2311yescharacteristic
121C2×C4⋊C4×C101C2311yescharacteristic
122C2×C4⋊C4×C101C2311yescharacteristic
123C2×C22⋊C4×C101—21no—
124C2×C22⋊C4×C101—21no—
125C2×C22⋊C4×C101—21no—
126C2×C22⋊C4×C101—21no—
127C2×C22⋊C4×C101—21no—
128C2×C22⋊C4×C101—21no—
129C2×C22⋊C4×C101—21no—
130C2×C22⋊C4×C101—21no—
131C2×C22⋊C4×C101—21no—
132C2×C22⋊C4×C101D411yescharacteristic
133C2×C22⋊C4×C101D411yescharacteristic
134C2×C42×C101—21no—
135C2×C42×C101C2311yescharacteristic
136#106×C101—22no—
137#106×C101—22no—
138#106×C101—22no—
139#102×C101—22no—
140#102×C101—22no—
141#102×C101—22no—
142#102×C101—22no—
143#102×C101—22no—
144#102×C101—41no—
145C22⋊C8×C101—22no—
146C22⋊C8×C101—22no—
147C22⋊C8×C101—41no—
148#95×C101—21no—
149#95×C101—21no—
150C24×C101—21no—
151C24×C101—21no—
152C24×C101C2×D411yescharacteristic
153C24×C101C2×D411yescharacteristic
154#41×C101—432no—
155C2×Q8×C101—24no—
156C2×Q8×C101—42no—
157C2×Q8×C101—42no—
158C2×D4×C101—22no—
159C2×D4×C101—22no—
160C2×D4×C101—24no—
161C2×D4×C101—24no—
162C2×D4×C101—22no—
163C2×D4×C101—21no—
164C2×D4×C101—21no—
165C2×D4×C101—21no—
166C2×D4×C101—21no—
167C2×D4×C101—21no—
168C2×D4×C101—21no—
169C2×D4×C101—21no—
170C2×D4×C101—21no—
171C2×D4×C101—21no—
172C2×D4×C101—21no—
173C2×D4×C101—21no—
174C2×D4×C101—42no—
175C2×D4×C101—42no—
176C2×D4×C101—42no—
177C2×D4×C101—42no—
178C2×D4×C101—42no—
179C2×D4×C101—42no—
180C2×D4×C101—42no—
181C2×D4×C101—81no—
182C2×D4×C101—81no—
183C2×D4×C101—81no—
184C2×D4×C101C2×D412yes—
185C22×C4×C101—21no—
186C22×C4×C101—21no—
187C22×C4×C101—21no—
188C22×C4×C101—21no—
189C22×C4×C101—24no—
190C22×C4×C101—24no—
191C22×C4×C101—24no—
192C22×C4×C101—21no—
193C22×C4×C101—21no—
194C22×C4×C101—21no—
195C22×C4×C101—21no—
196C22×C4×C101—21no—
197C22×C4×C101—21no—
198C22×C4×C101—21no—
199C22×C4×C101—21no—
200C22×C4×C101—21no—
201C22×C4×C101—21no—
202C22×C4×C101—21no—
203C22×C4×C101—21no—
204C22×C4×C101—42no—
205C22×C4×C101—42no—
206C22×C4×C101—42no—
207C22×C4×C101—42no—
208C22×C4×C101—42no—
209C22×C4×C101—42no—
210C22×C4×C101C2×D411yescharacteristic
211C22×C4×C101C2×D411yescharacteristic
212C22×C4×C101C2×D411yescharacteristic
213C22×C4×C101C2×D412yes—
214C22×C4×C101C2×D412yes—
215C22×C4×C101C2×D411yescharacteristic
216C22×C4×C101C2411yescharacteristic
217D8×C101—44no—
218M16×C101—44no—
219C2×C8×C101—21no—
220C2×C8×C101—21no—
221C2×C8×C101—21no—
222C2×C8×C101—21no—
223C2×C8×C101—21no—
224C2×C8×C101—21no—
225C2×C8×C101—21no—
226C2×C8×C101—21no—
227C2×C8×C101—21no—
228C2×C8×C101—21no—
229C2×C8×C101—21no—
230C2×C8×C101#4112yescomplemented
231C4⋊C4×C101—24no—
232C4⋊C4×C101—24no—
233C4⋊C4×C101—24no—
234C4⋊C4×C101—22no—
235C4⋊C4×C101—21no—
236C4⋊C4×C101—21no—
237C4⋊C4×C101—21no—
238C4⋊C4×C101—21no—
239C4⋊C4×C101—21no—
240C4⋊C4×C101—21no—
241C4⋊C4×C101—21no—
242C4⋊C4×C101—21no—
243C4⋊C4×C101—81no—
244C4⋊C4×C101C2×D412yes—
245C4⋊C4×C101C2×D412yes—
246C4⋊C4×C101C2×D412yes—
247C4⋊C4×C101#4112yescomplemented
248C22⋊C4×C101—24no—
249C22⋊C4×C101—24no—
250C22⋊C4×C101—22no—
251C22⋊C4×C101—24no—
252C22⋊C4×C101—22no—
253C22⋊C4×C101—42no—
254C22⋊C4×C101—42no—
255C22⋊C4×C101—42no—
256C22⋊C4×C101—42no—
257C22⋊C4×C101—81no—
258C22⋊C4×C101—81no—
259C42×C101—21no—
260C42×C101—21no—
261C42×C101—42no—
262C23×C101—21no—
263C23×C101—21no—
264C23×C101—21no—
265C23×C101—21no—
266C23×C101—21no—
267C23×C101—21no—
268C23×C101—21no—
269C23×C101—21no—
270C23×C101—21no—
271C23×C101—21no—
272C23×C101—21no—
273C23×C101—21no—
274C23×C101—22no—
275C23×C101—41no—
276C23×C101—41no—
277C23×C101—41no—
278C23×C101—41no—
279C23×C101—41no—
280C23×C101—41no—
281C23×C101—41no—
282C23×C101—41no—
283C23×C101—41no—
284C23×C101—41no—
285C23×C101—41no—
286C23×C101—41no—
287C23×C101—41no—
288C23×C101#12012yes—
289C23×C101AGL(1,ℤ/8)12yes—
290C23×C101C22×D411yescharacteristic
291Q8×C101—48no—
292D4×C101—28no—
293D4×C101—22no—
294D4×C101—22no—
295D4×C101—48no—
296D4×C101—48no—
297D4×C101—41no—
298D4×C101—41no—
299D4×C101—41no—
300D4×C101—41no—
301D4×C101—41no—
302D4×C101—41no—
303D4×C101—84no—
304D4×C101—84no—
305C2×C4×C101—21no—
306C2×C4×C101—21no—
307C2×C4×C101—21no—
308C2×C4×C101—21no—
309C2×C4×C101—22no—
310C2×C4×C101—22no—
311C2×C4×C101—22no—
312C2×C4×C101—22no—
313C2×C4×C101—21no—
314C2×C4×C101—21no—
315C2×C4×C101—22no—
316C2×C4×C101—22no—
317C2×C4×C101—22no—
318C2×C4×C101—22no—
319C2×C4×C101—21no—
320C2×C4×C101—21no—
321C2×C4×C101—21no—
322C2×C4×C101—21no—
323C2×C4×C101—48no—
324C2×C4×C101—48no—
325C2×C4×C101—48no—
326C2×C4×C101—41no—
327C2×C4×C101—41no—
328C2×C4×C101—41no—
329C2×C4×C101—41no—
330C2×C4×C101—41no—
331C2×C4×C101—41no—
332C2×C4×C101—41no—
333C2×C4×C101—41no—
334C2×C4×C101—41no—
335C2×C4×C101—41no—
336C2×C4×C101—41no—
337C2×C4×C101—41no—
338C2×C4×C101—41no—
339C2×C4×C101—41no—
340C2×C4×C101—41no—
341C2×C4×C101—41no—
342C2×C4×C101—41no—
343C2×C4×C101—41no—
344C2×C4×C101#12012yes—
345C2×C4×C101AGL(1,ℤ/8)12yes—
346C2×C4×C101C22×D411yescharacteristic
347C2×C4×C101C22×D411yescharacteristic
348C2×C4×C101C2×#4111yescharacteristic
349C2×C4×C101C2×#4111yescharacteristic
350C2×C4×C101H(5,𝔽2)11yescharacteristic
351C2×C4×C1012−1+411yescharacteristic
352C8×C101—22no—
353C8×C101—41no—
354C8×C101—41no—
355C8×C101—41no—
356C22×C101—22no—
357C22×C101—22no—
358C22×C101—22no—
359C22×C101—22no—
360C22×C101—22no—
361C22×C101—22no—
362C22×C101—41no—
363C22×C101—41no—
364C22×C101—41no—
365C22×C101—41no—
366C22×C101—41no—
367C22×C101—41no—
368C22×C101—41no—
369C22×C101—41no—
370C22×C101—42no—
371C22×C101—42no—
372C22×C101—42no—
373C22×C101—81no—
374C22×C101—81no—
375C22×C101—81no—
376C22×C101—81no—
377C22×C101—81no—
378C22×C101—81no—
379C22×C101—81no—
380C22×C101—81no—
381C22×C101—81no—
382C22×C101—81no—
383C22×C101—81no—
384C22×C101C2×#12011yescharacteristic
385C22×C101#54611yescharacteristic
386C22×C101#54711yescharacteristic
387C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C101#57711yescharacteristic
390C22×C101#57711yescharacteristic
391C4×C101—22no—
392C4×C101—22no—
393C4×C101—41no—
394C4×C101—42no—
395C4×C101—42no—
396C4×C101—42no—
397C4×C101—41no—
398C4×C101—42no—
399C4×C101—81no—
400C4×C101—81no—
401C4×C101#53211yescharacteristic
402C4×C101#53711yescharacteristic
403C4×C101#54611yescharacteristic
404C4×C101#54711yescharacteristic
405#25549C10111yesmaximal, characteristic, direct product factor, Sylow
406C2×C101—42no—
407C2×C101—42no—
408C2×C101—82no—
409C2×C101—161no—
410C2×C101#243011yescharacteristic
411C2×C101#300311yescharacteristic
412C2×C101#301011yescharacteristic
413C2×C101#330611yescharacteristic
414C2×C101#333211yescharacteristic
415C2×C101#334511yescharacteristic
416C2×C101#335411yescharacteristic
417C2×#547C2×C10111yescharacteristic, complemented
418C2×#481C2×C10111yescharacteristic, complemented
419C2×#469C2×C10111yescharacteristic, complemented
420#2414C2×C10111yescharacteristic, complemented
421#2058C2×C10111yescharacteristic, complemented
422#2034C2×C10111yescharacteristic, complemented
423#2023C2×C10111yescharacteristic, complemented
424#1999C2×C10111yescharacteristic, complemented
425#1879C2×C10111yescharacteristic, complemented
426#1875C2×C10111yescharacteristic, complemented
427#1874C2×C10111yescharacteristic, complemented
428#1870C2×C10111yescharacteristic, complemented
429#1864C2×C10111yescharacteristic, complemented
430#1853C2×C10111yescharacteristic, complemented
431#1736C2×C10111yescharacteristic, complemented
432C101#2554911yescharacteristic, direct product factor, Sylow
433C22×#41—21no—
434C22×D8C22×C10111yescharacteristic
435C22×M16C22×C10111yescharacteristic
436#547—24no—
437#547—24no—
438C2×C4⋊Q8C22×C10111yescharacteristic
439C2×#123—21no—
440C2×#123—21no—
441C2×C22⋊Q8—21no—
442C2×#121C22×C10111yescharacteristic
443C2×#121C22×C10111yescharacteristic
444C2×#121C22×C10111yescharacteristic
445C2×#121C22×C10111yescharacteristic
446C2×C4×D4C22×C10111yescharacteristic
447C2×C4×D4C22×C10111yescharacteristic
448C2×#117C22×C10111yescharacteristic
449C22×C4⋊C4C22×C10111yescharacteristic
450C22×C4⋊C4C22×C10111yescharacteristic
451#481—24no—
452#469—24no—
453C2×#106C22×C10111yescharacteristic
454C2×#106C22×C10111yescharacteristic
455C2×#106C22×C10111yescharacteristic
456C2×#102C22×C10111yescharacteristic
457C2×#102C22×C10111yescharacteristic
458C2×#102C22×C10111yescharacteristic
459C2×#102C22×C10111yescharacteristic
460C2×#102C22×C10111yescharacteristic
461C2×#102C22×C10111yescharacteristic
462C2×C22⋊C8C22×C10111yescharacteristic
463C2×C22⋊C8C22×C10111yescharacteristic
464C2×C22⋊C8C22×C10111yescharacteristic
465#394—21no—
466#392—21no—
467#390—21no—
468#390C22×C10111yescharacteristic
469#389C22×C10111yescharacteristic
470#388—21no—
471#380C22×C10111yescharacteristic
472#340C22×C10111yescharacteristic
473#340C22×C10111yescharacteristic
474#340C22×C10111yescharacteristic
475#340C22×C10111yescharacteristic
476#340C22×C10111yescharacteristic
477#340C22×C10111yescharacteristic
478#336C22×C10111yescharacteristic
479#336C22×C10111yescharacteristic
480C2×#41—28no—
481C2×#41—44no—
482C2×#41—44no—
483C22×Q8—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C10111yescharacteristic
489C22×D4C23×C10111yescharacteristic
490C22×D4C23×C10111yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C23×C10111yescharacteristic
495C23×C4C23×C10111yescharacteristic
496C2×D8—22no—
497C2×D8—22no—
498C2×D8—41no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—41no—
502C22×C8C23×C10111yescharacteristic
503C22×C8C23×C10111yescharacteristic
504C22×C8C23×C10111yescharacteristic
505C22×C8C23×C10111yescharacteristic
506C4⋊Q8—22no—
507C4⋊Q8—22no—
508#123—28no—
509#123—28no—
510C22⋊Q8—28no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—41no—
518#121D4×C10114yescomplemented
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—22no—
523#117—22no—
524#117—41no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4D4×C10111yescharacteristic
533C2×C4⋊C4D4×C10114yescomplemented
534C2×C4⋊C4C23×C10111yescharacteristic
535C2×C4⋊C4C23×C10111yescharacteristic
536C2×C4⋊C4C23×C10111yescharacteristic
537C2×C4⋊C4C23×C10111yescharacteristic
538C2×C4⋊C4C23×C10111yescharacteristic
539C2×C4⋊C4C23×C10111yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4D4×C10111yescharacteristic
550C2×C22⋊C4D4×C10111yescharacteristic
551C2×C42—21no—
552C2×C42C23×C10111yescharacteristic
553#106—22no—
554#106—22no—
555#106—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—41no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564C22⋊C8—41no—
565#95—21no—
566#95—21no—
567C24—21no—
568C24—21no—
569C24C2×D4×C10111yescharacteristic
570C24C2×D4×C10111yescharacteristic
571#41—432no—
572C2×Q8—24no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4C2×D4×C10112yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4C2×D4×C10111yescharacteristic
628C22×C4C2×D4×C10111yescharacteristic
629C22×C4C2×D4×C10111yescharacteristic
630C22×C4C2×D4×C10112yes—
631C22×C4C2×D4×C10112yes—
632C22×C4C2×D4×C10111yescharacteristic
633C22×C4C24×C10111yescharacteristic
634D8—44no—
635M16—44no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8#41×C10112yescomplemented
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—81no—
661C4⋊C4C2×D4×C10112yes—
662C4⋊C4C2×D4×C10112yes—
663C4⋊C4C2×D4×C10112yes—
664C4⋊C4#41×C10112yescomplemented
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—22no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C42—21no—
677C42—21no—
678C42—42no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23#120×C10112yes—
706C23AGL(1,ℤ/8)×C10112yes—
707C23C22×D4×C10111yescharacteristic
708Q8—48no—
709D4—28no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—48no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—48no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4#120×C10112yes—
762C2×C4AGL(1,ℤ/8)×C10112yes—
763C2×C4C22×D4×C10111yescharacteristic
764C2×C4C22×D4×C10111yescharacteristic
765C2×C4C2×#41×C10111yescharacteristic
766C2×C4C2×#41×C10111yescharacteristic
767C2×C4H(5,𝔽2)×C10111yescharacteristic
768C2×C42−1+4×C10111yescharacteristic
769C8—22no—
770C8—41no—
771C8—41no—
772C8—41no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C2×#120×C10111yescharacteristic
802C22#546×C10111yescharacteristic
803C22#547×C10111yescharacteristic
804C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
805C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
806C22#577×C10111yescharacteristic
807C22#577×C10111yescharacteristic
808C4—22no—
809C4—22no—
810C4—41no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—41no—
815C4—42no—
816C4—81no—
817C4—81no—
818C4#532×C10111yescharacteristic
819C4#537×C10111yescharacteristic
820C4#546×C10111yescharacteristic
821C4#547×C10111yescharacteristic
822C2—42no—
823C2—42no—
824C2—82no—
825C2—161no—
826C2C101×#243011yescharacteristic
827C2C101×#300311yescharacteristic
828C2C101×#301011yescharacteristic
829C2C101×#330611yescharacteristic
830C2C101×#333211yescharacteristic
831C2C101×#334511yescharacteristic
832C2C101×#335411yescharacteristic
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×#547×C101C2semidirect
2. C2×#481×C101C2semidirect
3. C2×#469×C101C2semidirect
4. C101×#2414C2semidirect
5. C101×#2058C2semidirect
6. C101×#2034C2semidirect
7. C101×#2023C2semidirect
8. C101×#1999C2semidirect
9. C101×#1879C2semidirect
10. C101×#1875C2semidirect
11. C101×#1874C2semidirect
12. C101×#1870C2semidirect
13. C101×#1864C2semidirect
14. C101×#1853C2semidirect
15. C101×#1736C2semidirect
101. #121×C101D4semidirect
116. C2×C4⋊C4×C101D4semidirect
230. C2×C8×C101#41semidirect
247. C4⋊C4×C101#41semidirect
405. #25549C101direct (N × H)
417. C2×#547C2×C101semidirect
418. C2×#481C2×C101semidirect
419. C2×#469C2×C101semidirect
420. #2414C2×C101semidirect
421. #2058C2×C101semidirect
422. #2034C2×C101semidirect
423. #2023C2×C101semidirect
424. #1999C2×C101semidirect
425. #1879C2×C101semidirect
426. #1875C2×C101semidirect
427. #1874C2×C101semidirect
428. #1870C2×C101semidirect
429. #1864C2×C101semidirect
430. #1853C2×C101semidirect
431. #1736C2×C101semidirect
432. C101#25549direct (N × H)
518. #121D4×C101semidirect
533. C2×C4⋊C4D4×C101semidirect
647. C2×C8#41×C101semidirect
664. C4⋊C4#41×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1012
C2×#481×C1012
C2×#469×C1012
C101×#24142
C101×#20582
C101×#20342
C101×#20232
C101×#19992
C101×#18792
C101×#18752
C101×#18742
C101×#18702
C101×#18642
C101×#18532
C101×#17362
#25549101