Finite Group Databasebeta

← C101×#22868 #38805019

Subgroups — C101×#22868 #38805019

Order 25856.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C101C211yesmaximal, characteristic
2C2×#442×C101C211yesmaximal, characteristic, complemented
3C2×#418×C101C211yesmaximal, characteristic, complemented
4C101×#2363C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C101C211yesmaximal, characteristic, complemented
6C101×#1970C211yesmaximal, characteristic, complemented
7C101×#1936C211yesmaximal, characteristic, complemented
8C101×#1926C211yesmaximal, characteristic, complemented
9C101×#1895C211yesmaximal, characteristic, complemented
10C101×#1879C211yesmaximal, characteristic, complemented
11C101×#1879C211yesmaximal, characteristic, complemented
12C101×#1862C211yesmaximal, characteristic, complemented
13C101×#1854C211yesmaximal, characteristic, complemented
14C4×#102×C101C211yesmaximal, characteristic, complemented
15C101×#1753C211yesmaximal, characteristic, complemented
16C23×D4×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C22×D8×C101C2211yescharacteristic
19C22×M16×C101C2211yescharacteristic
20C2×#121×C101C2211yescharacteristic
21C2×C4×D4×C101C2211yescharacteristic
22C2×C4×D4×C101C2211yescharacteristic
23C2×C4×D4×C101C2211yescharacteristic, complemented
24C2×#117×C101C2211yescharacteristic
25C22×C22⋊C4×C101—21no—
26#447×C101C418yescomplemented
27#442×C101—24no—
28C2×#107×C101C2211yescharacteristic, complemented
29C2×#106×C101C2211yescharacteristic, complemented
30#418×C101—24no—
31C2×#102×C101C2211yescharacteristic
32C2×#102×C101C2211yescharacteristic
33C2×#102×C101C2211yescharacteristic
34C2×#102×C101C2211yescharacteristic
35C2×#102×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic, complemented
38C2×#102×C101C2211yescharacteristic, complemented
39C2×C22⋊C8×C101C2211yescharacteristic
40C2×#97×C101C2211yescharacteristic, complemented
41C2×C4×C8×C101C2211yescharacteristic, complemented
42#390×C101—21no—
43#390×C101C2211yescharacteristic
44#390×C101C2211yescharacteristic
45#390×C101C2211yescharacteristic, complemented
46#389×C101C2211yescharacteristic, complemented
47#388×C101—21no—
48#386×C101—21no—
49#386×C101—21no—
50#386×C101—21no—
51#380×C101C2211yescharacteristic
52#379×C101—21no—
53C4×C4⋊C4×C101C2211yescharacteristic, complemented
54C4×C22⋊C4×C101—21no—
55C4×C22⋊C4×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic, complemented
57#340×C101C2211yescharacteristic, complemented
58#340×C101C2211yescharacteristic, complemented
59#340×C101C2211yescharacteristic, complemented
60#336×C101C2211yescharacteristic, complemented
61#336×C101C2211yescharacteristic, complemented
62C25×C101—21no—
63C22×D4×C101—22no—
64C22×D4×C101—22no—
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101—22no—
68C22×D4×C101—41no—
69C22×D4×C101—41no—
70C22×D4×C101C2×C414yescomplemented
71C22×D4×C101C2311yescharacteristic
72C22×D4×C101C2311yescharacteristic
73C22×D4×C101C2311yescharacteristic
74C23×C4×C101—21no—
75C23×C4×C101—21no—
76C23×C4×C101—21no—
77C23×C4×C101C2311yescharacteristic
78C2×D8×C101—22no—
79C2×D8×C101—22no—
80C2×D8×C101—41no—
81C2×D8×C101—41no—
82C2×D8×C101C2×C414yes—
83C2×D8×C101C2×C414yescomplemented
84C2×M16×C101—22no—
85C2×M16×C101—22no—
86C2×M16×C101—41no—
87C22×C8×C101C2311yescharacteristic
88C22×C8×C101C2311yescharacteristic
89C22×C8×C101C2311yescharacteristic
90C22×C8×C101C2311yescharacteristic
91#121×C101—22no—
92#121×C101C2×C414yescomplemented
93C4×D4×C101—22no—
94C4×D4×C101—22no—
95C4×D4×C101—22no—
96C4×D4×C101—41no—
97C4×D4×C101—41no—
98C4×D4×C101—41no—
99#117×C101—22no—
100#117×C101—41no—
101C2×C4⋊C4×C101—21no—
102C2×C4⋊C4×C101C2311yescharacteristic
103C2×C4⋊C4×C101C2311yescharacteristic
104C2×C4⋊C4×C101C2311yescharacteristic
105C2×C4⋊C4×C101C2311yescharacteristic
106C2×C4⋊C4×C101C2311yescharacteristic
107C2×C22⋊C4×C101—21no—
108C2×C22⋊C4×C101—21no—
109C2×C22⋊C4×C101—21no—
110C2×C22⋊C4×C101—21no—
111C2×C22⋊C4×C101—21no—
112C2×C22⋊C4×C101—21no—
113C2×C22⋊C4×C101—21no—
114C2×C22⋊C4×C101—21no—
115C2×C22⋊C4×C101—21no—
116C2×C22⋊C4×C101—21no—
117C2×C22⋊C4×C101—21no—
118C2×C22⋊C4×C101—21no—
119C2×C22⋊C4×C101—44no—
120C2×C22⋊C4×C101D411yescharacteristic
121C2×C22⋊C4×C101D411yescharacteristic
122C2×C42×C101—21no—
123C2×C42×C101—21no—
124C2×C42×C101C2311yescharacteristic
125C2×C42×C101C2311yescharacteristic
126#107×C101—41no—
127#106×C101—22no—
128#102×C101—22no—
129#102×C101—22no—
130#102×C101—22no—
131#102×C101—22no—
132#102×C101—41no—
133#102×C101C2×C414yescomplemented
134#102×C101C2×C414yescomplemented
135#102×C101D414yescomplemented
136C22⋊C8×C101C2×C414yescomplemented
137#97×C101—22no—
138C4×C8×C101—41no—
139#95×C101—21no—
140#95×C101—21no—
141#95×C101—21no—
142#95×C101D411yescharacteristic
143#95×C101D411yescharacteristic
144C24×C101—21no—
145C24×C101—21no—
146C24×C101—21no—
147C24×C101—24no—
148C24×C101—42no—
149C24×C101—42no—
150C24×C101—42no—
151C24×C101—42no—
152C24×C101—81no—
153C24×C101—81no—
154C24×C101C2×D411yescharacteristic
155C2×D4×C101—28no—
156C2×D4×C101—24no—
157C2×D4×C101—24no—
158C2×D4×C101—21no—
159C2×D4×C101—21no—
160C2×D4×C101—21no—
161C2×D4×C101—21no—
162C2×D4×C101—21no—
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—44no—
172C2×D4×C101—44no—
173C2×D4×C101—44no—
174C2×D4×C101—42no—
175C2×D4×C101—42no—
176C2×D4×C101—81no—
177C2×D4×C101—81no—
178C2×D4×C101C22×C412yes—
179C2×D4×C101C22×C412yes—
180C2×D4×C101C22×C412yes—
181C2×D4×C101C2×D412yes—
182C2×D4×C101#4112yes—
183C22×C4×C101—21no—
184C22×C4×C101—21no—
185C22×C4×C101—21no—
186C22×C4×C101—21no—
187C22×C4×C101—21no—
188C22×C4×C101—21no—
189C22×C4×C101—21no—
190C22×C4×C101—21no—
191C22×C4×C101—21no—
192C22×C4×C101—42no—
193C22×C4×C101—42no—
194C22×C4×C101—42no—
195C22×C4×C101—42no—
196C22×C4×C101—42no—
197C22×C4×C101—42no—
198C22×C4×C101—81no—
199C22×C4×C101—81no—
200C22×C4×C101—81no—
201C22×C4×C101C22×C412yes—
202C22×C4×C101C2×D411yescharacteristic
203C22×C4×C101C2×D411yescharacteristic
204C22×C4×C101C2×D411yescharacteristic
205C22×C4×C101C2×D411yescharacteristic
206C22×C4×C101C2×D411yescharacteristic
207C22×C4×C101#4112yes—
208C22×C4×C101C2411yescharacteristic
209D8×C101—28no—
210D8×C101—44no—
211M16×C101—44no—
212C2×C8×C101—21no—
213C2×C8×C101—21no—
214C2×C8×C101—21no—
215C2×C8×C101—21no—
216C2×C8×C101—21no—
217C2×C8×C101—21no—
218C2×C8×C101—21no—
219C2×C8×C101—21no—
220C2×C8×C101—21no—
221C2×C8×C101C22×C412yes—
222C2×C8×C101C22×C412yes—
223C2×C8×C101C2×D412yes—
224C4⋊C4×C101—21no—
225C4⋊C4×C101—21no—
226C4⋊C4×C101—21no—
227C4⋊C4×C101—21no—
228C4⋊C4×C101—21no—
229C4⋊C4×C101—21no—
230C4⋊C4×C101—21no—
231C4⋊C4×C101—21no—
232C4⋊C4×C101—81no—
233C4⋊C4×C101C22×C412yes—
234C4⋊C4×C101C2×D412yes—
235C22⋊C4×C101—24no—
236C22⋊C4×C101—22no—
237C22⋊C4×C101—41no—
238C22⋊C4×C101—42no—
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—42no—
246C22⋊C4×C101—81no—
247C22⋊C4×C101—81no—
248C22⋊C4×C101—81no—
249C42×C101—21no—
250C42×C101—21no—
251C42×C101—21no—
252C42×C101—21no—
253C42×C101—42no—
254C42×C101—81no—
255C23×C101—22no—
256C23×C101—21no—
257C23×C101—22no—
258C23×C101—22no—
259C23×C101—21no—
260C23×C101—21no—
261C23×C101—21no—
262C23×C101—21no—
263C23×C101—21no—
264C23×C101—22no—
265C23×C101—22no—
266C23×C101—48no—
267C23×C101—48no—
268C23×C101—41no—
269C23×C101—41no—
270C23×C101—41no—
271C23×C101—41no—
272C23×C101—41no—
273C23×C101—41no—
274C23×C101—41no—
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—84no—
285C23×C101—84no—
286C23×C101—84no—
287C23×C101—84no—
288C23×C101—84no—
289C23×C101C4×D412yes—
290C23×C101C22×D411yescharacteristic
291D4×C101—22no—
292D4×C101—22no—
293D4×C101—22no—
294D4×C101—22no—
295D4×C101—22no—
296D4×C101—22no—
297D4×C101—22no—
298D4×C101—48no—
299D4×C101—41no—
300D4×C101—41no—
301D4×C101—41no—
302D4×C101—41no—
303D4×C101—84no—
304D4×C101C4×D414yes—
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—22no—
314C2×C4×C101—21no—
315C2×C4×C101—21no—
316C2×C4×C101—22no—
317C2×C4×C101—21no—
318C2×C4×C101—21no—
319C2×C4×C101—21no—
320C2×C4×C101—21no—
321C2×C4×C101—21no—
322C2×C4×C101—21no—
323C2×C4×C101—21no—
324C2×C4×C101—41no—
325C2×C4×C101—41no—
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—84no—
338C2×C4×C101—84no—
339C2×C4×C101—84no—
340C2×C4×C101C4×D412yes—
341C2×C4×C101AGL(1,ℤ/8)12yes—
342C2×C4×C101C23×C411yescharacteristic
343C2×C4×C101C22×D411yescharacteristic
344C2×C4×C101C2×#4111yescharacteristic
345C2×C4×C101C2×#4111yescharacteristic
346C2×C4×C101H(5,𝔽2)11yescharacteristic
347C2×C4×C101H(5,𝔽2)11yescharacteristic
348C8×C101—22no—
349C8×C101—22no—
350C8×C101—22no—
351C8×C101—41no—
352C22×C101—22no—
353C22×C101—24no—
354C22×C101—22no—
355C22×C101—22no—
356C22×C101—42no—
357C22×C101—42no—
358C22×C101—41no—
359C22×C101—42no—
360C22×C101—42no—
361C22×C101—41no—
362C22×C101—42no—
363C22×C101—41no—
364C22×C101—41no—
365C22×C101—42no—
366C22×C101—42no—
367C22×C101—42no—
368C22×C101—42no—
369C22×C101—42no—
370C22×C101—42no—
371C22×C101—42no—
372C22×C101—816no—
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×C101C2×C4×D411yescharacteristic
382C22×C101D4211yescharacteristic
383C22×C101#54611yescharacteristic
384C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
385C22×C101#57511yescharacteristic
386C22×C101#57611yescharacteristic
387C22×C101#57611yescharacteristic
388C4×C101—22no—
389C4×C101—22no—
390C4×C101—42no—
391C4×C101—41no—
392C4×C101—42no—
393C4×C101—41no—
394C4×C101—41no—
395C4×C101—81no—
396C4×C101—81no—
397C4×C101—81no—
398C4×C101C2×C4×D411yescharacteristic
399C4×C101#51811yescharacteristic
400C4×C101#54611yescharacteristic
401C4×C101#55111yescharacteristic
402#22868C10111yesmaximal, characteristic, direct product factor, Sylow
403C2×C101—42no—
404C2×C101—44no—
405C2×C101—82no—
406C2×C101—82no—
407C2×C101#235811yescharacteristic
408C2×C101C4×AGL(1,ℤ/8)11yescharacteristic
409C2×C101#294811yescharacteristic
410C2×C101#327311yescharacteristic
411C2×C101#327411yescharacteristic
412C2×C101#331811yescharacteristic
413C2×C101#331911yescharacteristic
414C2×#447C2×C10111yescharacteristic
415C2×#442C2×C10111yescharacteristic, complemented
416C2×#418C2×C10111yescharacteristic, complemented
417#2363C2×C10111yescharacteristic, complemented
418D4×C22⋊C4C2×C10111yescharacteristic, complemented
419#1970C2×C10111yescharacteristic, complemented
420#1936C2×C10111yescharacteristic, complemented
421#1926C2×C10111yescharacteristic, complemented
422#1895C2×C10111yescharacteristic, complemented
423#1879C2×C10111yescharacteristic, complemented
424#1879C2×C10111yescharacteristic, complemented
425#1862C2×C10111yescharacteristic, complemented
426#1854C2×C10111yescharacteristic, complemented
427C4×#102C2×C10111yescharacteristic, complemented
428#1753C2×C10111yescharacteristic, complemented
429C101#2286811yescharacteristic, direct product factor, Sylow
430C23×D4C22×C10111yescharacteristic
431C22×D8C22×C10111yescharacteristic
432C22×D8C22×C10111yescharacteristic
433C22×M16C22×C10111yescharacteristic
434C2×#121C22×C10111yescharacteristic
435C2×C4×D4C22×C10111yescharacteristic
436C2×C4×D4C22×C10111yescharacteristic
437C2×C4×D4C22×C10111yescharacteristic, complemented
438C2×#117C22×C10111yescharacteristic
439C22×C22⋊C4—21no—
440#447C4×C10118yescomplemented
441#442—24no—
442C2×#107C22×C10111yescharacteristic, complemented
443C2×#106C22×C10111yescharacteristic, complemented
444#418—24no—
445C2×#102C22×C10111yescharacteristic
446C2×#102C22×C10111yescharacteristic
447C2×#102C22×C10111yescharacteristic
448C2×#102C22×C10111yescharacteristic
449C2×#102C22×C10111yescharacteristic
450C2×#102C22×C10111yescharacteristic
451C2×#102C22×C10111yescharacteristic, complemented
452C2×#102C22×C10111yescharacteristic, complemented
453C2×C22⋊C8C22×C10111yescharacteristic
454C2×#97C22×C10111yescharacteristic, complemented
455C2×C4×C8C22×C10111yescharacteristic, complemented
456#390—21no—
457#390C22×C10111yescharacteristic
458#390C22×C10111yescharacteristic
459#390C22×C10111yescharacteristic, complemented
460#389C22×C10111yescharacteristic, complemented
461#388—21no—
462#386—21no—
463#386—21no—
464#386—21no—
465#380C22×C10111yescharacteristic
466#379—21no—
467C4×C4⋊C4C22×C10111yescharacteristic, complemented
468C4×C22⋊C4—21no—
469C4×C22⋊C4C22×C10111yescharacteristic
470#340C22×C10111yescharacteristic, complemented
471#340C22×C10111yescharacteristic, complemented
472#340C22×C10111yescharacteristic, complemented
473#340C22×C10111yescharacteristic, complemented
474#336C22×C10111yescharacteristic, complemented
475#336C22×C10111yescharacteristic, complemented
476C25—21no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—22no—
482C22×D4—41no—
483C22×D4—41no—
484C22×D4C2×C4×C10114yescomplemented
485C22×D4C23×C10111yescharacteristic
486C22×D4C23×C10111yescharacteristic
487C22×D4C23×C10111yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4C23×C10111yescharacteristic
492C2×D8—22no—
493C2×D8—22no—
494C2×D8—41no—
495C2×D8—41no—
496C2×D8C2×C4×C10114yes—
497C2×D8C2×C4×C10114yescomplemented
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—41no—
501C22×C8C23×C10111yescharacteristic
502C22×C8C23×C10111yescharacteristic
503C22×C8C23×C10111yescharacteristic
504C22×C8C23×C10111yescharacteristic
505#121—22no—
506#121C2×C4×C10114yescomplemented
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—41no—
511C4×D4—41no—
512C4×D4—41no—
513#117—22no—
514#117—41no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4C23×C10111yescharacteristic
517C2×C4⋊C4C23×C10111yescharacteristic
518C2×C4⋊C4C23×C10111yescharacteristic
519C2×C4⋊C4C23×C10111yescharacteristic
520C2×C4⋊C4C23×C10111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—44no—
534C2×C22⋊C4D4×C10111yescharacteristic
535C2×C22⋊C4D4×C10111yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42C23×C10111yescharacteristic
539C2×C42C23×C10111yescharacteristic
540#107—41no—
541#106—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—41no—
547#102C2×C4×C10114yescomplemented
548#102C2×C4×C10114yescomplemented
549#102D4×C10114yescomplemented
550C22⋊C8C2×C4×C10114yescomplemented
551#97—22no—
552C4×C8—41no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95D4×C10111yescharacteristic
557#95D4×C10111yescharacteristic
558C24—21no—
559C24—21no—
560C24—21no—
561C24—24no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—42no—
566C24—81no—
567C24—81no—
568C24C2×D4×C10111yescharacteristic
569C2×D4—28no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C22×C4×C10112yes—
593C2×D4C22×C4×C10112yes—
594C2×D4C22×C4×C10112yes—
595C2×D4C2×D4×C10112yes—
596C2×D4#41×C10112yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C22×C4×C10112yes—
616C22×C4C2×D4×C10111yescharacteristic
617C22×C4C2×D4×C10111yescharacteristic
618C22×C4C2×D4×C10111yescharacteristic
619C22×C4C2×D4×C10111yescharacteristic
620C22×C4C2×D4×C10111yescharacteristic
621C22×C4#41×C10112yes—
622C22×C4C24×C10111yescharacteristic
623D8—28no—
624D8—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8C22×C4×C10112yes—
636C2×C8C22×C4×C10112yes—
637C2×C8C2×D4×C10112yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C22×C4×C10112yes—
648C4⋊C4C2×D4×C10112yes—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—81no—
661C22⋊C4—81no—
662C22⋊C4—81no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—42no—
668C42—81no—
669C23—22no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—48no—
681C23—48no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23C4×D4×C10112yes—
704C23C22×D4×C10111yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—84no—
718D4C4×D4×C10114yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
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—84no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4C4×D4×C10112yes—
755C2×C4AGL(1,ℤ/8)×C10112yes—
756C2×C4C23×C4×C10111yescharacteristic
757C2×C4C22×D4×C10111yescharacteristic
758C2×C4C2×#41×C10111yescharacteristic
759C2×C4C2×#41×C10111yescharacteristic
760C2×C4H(5,𝔽2)×C10111yescharacteristic
761C2×C4H(5,𝔽2)×C10111yescharacteristic
762C8—22no—
763C8—22no—
764C8—22no—
765C8—41no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—24no—
770C22—42no—
771C22—42no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×C4×D4×C10111yescharacteristic
796C22D42×C10111yescharacteristic
797C22#546×C10111yescharacteristic
798C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
799C22#575×C10111yescharacteristic
800C22#576×C10111yescharacteristic
801C22#576×C10111yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—41no—
806C4—42no—
807C4—41no—
808C4—41no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4C2×C4×D4×C10111yescharacteristic
813C4#518×C10111yescharacteristic
814C4#546×C10111yescharacteristic
815C4#551×C10111yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—82no—
820C2C101×#235811yescharacteristic
821C2C4×AGL(1,ℤ/8)×C10111yescharacteristic
822C2C101×#294811yescharacteristic
823C2C101×#327311yescharacteristic
824C2C101×#327411yescharacteristic
825C2C101×#331811yescharacteristic
826C2C101×#331911yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC2×#447×C101C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C4×C22⋊C4×C101 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#442×C101C2semidirect
3. C2×#418×C101C2semidirect
4. C101×#2363C2semidirect
5. D4×C22⋊C4×C101C2semidirect
6. C101×#1970C2semidirect
7. C101×#1936C2semidirect
8. C101×#1926C2semidirect
9. C101×#1895C2semidirect
10. C101×#1879C2semidirect
11. C101×#1879C2semidirect
12. C101×#1862C2semidirect
13. C101×#1854C2semidirect
14. C4×#102×C101C2semidirect
15. C101×#1753C2semidirect
23. C2×C4×D4×C101C22semidirect
26. #447×C101C4semidirect
28. C2×#107×C101C22semidirect
29. C2×#106×C101C22semidirect
37. C2×#102×C101C22semidirect
38. C2×#102×C101C22semidirect
40. C2×#97×C101C22semidirect
41. C2×C4×C8×C101C22semidirect
45. #390×C101C22semidirect
46. #389×C101C22semidirect
53. C4×C4⋊C4×C101C22semidirect
56. #340×C101C22semidirect
57. #340×C101C22semidirect
58. #340×C101C22semidirect
59. #340×C101C22semidirect
60. #336×C101C22semidirect
61. #336×C101C22semidirect
70. C22×D4×C101C2×C4semidirect
83. C2×D8×C101C2×C4semidirect
92. #121×C101C2×C4semidirect
133. #102×C101C2×C4semidirect
134. #102×C101C2×C4semidirect
135. #102×C101D4semidirect
136. C22⋊C8×C101C2×C4semidirect
402. #22868C101direct (N × H)
415. C2×#442C2×C101semidirect
416. C2×#418C2×C101semidirect
417. #2363C2×C101semidirect
418. D4×C22⋊C4C2×C101semidirect
419. #1970C2×C101semidirect
420. #1936C2×C101semidirect
421. #1926C2×C101semidirect
422. #1895C2×C101semidirect
423. #1879C2×C101semidirect
424. #1879C2×C101semidirect
425. #1862C2×C101semidirect
426. #1854C2×C101semidirect
427. C4×#102C2×C101semidirect
428. #1753C2×C101semidirect
429. C101#22868direct (N × H)
437. C2×C4×D4C22×C101semidirect
440. #447C4×C101semidirect
442. C2×#107C22×C101semidirect
443. C2×#106C22×C101semidirect
451. C2×#102C22×C101semidirect
452. C2×#102C22×C101semidirect
454. C2×#97C22×C101semidirect
455. C2×C4×C8C22×C101semidirect
459. #390C22×C101semidirect
460. #389C22×C101semidirect
467. C4×C4⋊C4C22×C101semidirect
470. #340C22×C101semidirect
471. #340C22×C101semidirect
472. #340C22×C101semidirect
473. #340C22×C101semidirect
474. #336C22×C101semidirect
475. #336C22×C101semidirect
484. C22×D4C2×C4×C101semidirect
497. C2×D8C2×C4×C101semidirect
506. #121C2×C4×C101semidirect
547. #102C2×C4×C101semidirect
548. #102C2×C4×C101semidirect
549. #102D4×C101semidirect
550. C22⋊C8C2×C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1012
C2×#442×C1012
C2×#418×C1012
C101×#23632
D4×C22⋊C4×C1012
C101×#19702
C101×#19362
C101×#19262
C101×#18952
C101×#18792
C101×#18622
C101×#18542
C4×#102×C1012
C101×#17532
#22868101