Finite Group Databasebeta

← C101×#23040 #38805191

Subgroups — C101×#23040 #38805191

Order 25856.

1026 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C101C211yesmaximal, characteristic
2C2×#440×C101C211yesmaximal, characteristic, complemented
3C2×#428×C101C211yesmaximal, characteristic, complemented
4C101×#2362C211yesmaximal, characteristic, complemented
5C101×#2361C211yesmaximal, characteristic
6C101×#1968C211yesmaximal, characteristic, complemented
7C101×#1943C211yesmaximal, characteristic, complemented
8C101×#1927C211yesmaximal, characteristic, complemented
9C101×#1925C211yesmaximal, characteristic, complemented
10C101×#1875C211yesmaximal, characteristic
11C101×#1872C211yesmaximal, characteristic, complemented
12C101×#1864C211yesmaximal, characteristic, complemented
13C101×#1863C211yesmaximal, characteristic, complemented
14C4×#107×C101C211yesmaximal, characteristic, complemented
15C101×#1753C211yesmaximal, characteristic, complemented
16C22×SD16×C101C2211yescharacteristic
17C22×M16×C101C2211yescharacteristic
18C2×C22⋊Q8×C101C2211yescharacteristic
19C2×#121×C101C2211yescharacteristic
20C2×C4×Q8×C101C2211yescharacteristic
21C2×C4×D4×C101—21no—
22C2×C4×D4×C101C2211yescharacteristic
23C2×#117×C101C2211yescharacteristic
24C22×C4⋊C4×C101C2211yescharacteristic
25#468×C101C418yescomplemented
26#440×C101—24no—
27#428×C101—24no—
28C2×#107×C101C2211yescharacteristic
29C2×#107×C101C2211yescharacteristic
30C2×#107×C101C2211yescharacteristic
31C2×#106×C101C2211yescharacteristic
32C2×#106×C101C2211yescharacteristic
33C2×#103×C101C2211yescharacteristic
34C2×#103×C101C2211yescharacteristic
35C2×#103×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×C22⋊C8×C101C2211yescharacteristic
40C2×#97×C101C2211yescharacteristic
41C2×C4×C8×C101C2211yescharacteristic
42#391×C101C2211yescharacteristic
43#390×C101C2211yescharacteristic
44#389×C101C2211yescharacteristic
45#389×C101C2211yescharacteristic
46#388×C101—21no—
47#388×C101—21no—
48#388×C101—21no—
49#387×C101—21no—
50#386×C101—21no—
51#385×C101—21no—
52C4×C4⋊C4×C101—21no—
53C4×C4⋊C4×C101C2211yescharacteristic
54C4×C4⋊C4×C101C2211yescharacteristic
55C4×C22⋊C4×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#336×C101C2211yescharacteristic
61#336×C101C2211yescharacteristic
62C22×Q8×C101C2311yescharacteristic
63C22×D4×C101—21no—
64C22×D4×C101C2311yescharacteristic
65C23×C4×C101—21no—
66C23×C4×C101—21no—
67C23×C4×C101C2311yescharacteristic
68C2×SD16×C101—22no—
69C2×SD16×C101—22no—
70C2×SD16×C101C2×C414yescomplemented
71C2×M16×C101—22no—
72C2×M16×C101—22no—
73C2×M16×C101C2×C414yescomplemented
74C22×C8×C101C2311yescharacteristic
75C22×C8×C101C2311yescharacteristic
76C22×C8×C101C2311yescharacteristic
77C22×C8×C101C2311yescharacteristic
78C22⋊Q8×C101—22no—
79C22⋊Q8×C101C2×C414yescomplemented
80#121×C101—22no—
81#121×C101C2×C414yes—
82C4×Q8×C101—22no—
83C4×Q8×C101—41no—
84C4×D4×C101—22no—
85C4×D4×C101—41no—
86C4×D4×C101—44no—
87#117×C101—22no—
88#117×C101—41no—
89C2×C4⋊C4×C101—21no—
90C2×C4⋊C4×C101—22no—
91C2×C4⋊C4×C101—21no—
92C2×C4⋊C4×C101—21no—
93C2×C4⋊C4×C101—21no—
94C2×C4⋊C4×C101—21no—
95C2×C4⋊C4×C101—41no—
96C2×C4⋊C4×C101C2311yescharacteristic
97C2×C4⋊C4×C101C2311yescharacteristic
98C2×C4⋊C4×C101C2311yescharacteristic
99C2×C4⋊C4×C101C2311yescharacteristic
100C2×C4⋊C4×C101C2311yescharacteristic
101C2×C4⋊C4×C101C2311yescharacteristic
102C2×C22⋊C4×C101—21no—
103C2×C22⋊C4×C101—21no—
104C2×C22⋊C4×C101—21no—
105C2×C22⋊C4×C101—21no—
106C2×C22⋊C4×C101—21no—
107C2×C22⋊C4×C101—21no—
108C2×C22⋊C4×C101D411yescharacteristic
109C2×C22⋊C4×C101D411yescharacteristic
110C2×C42×C101—21no—
111C2×C42×C101—21no—
112C2×C42×C101—21no—
113C2×C42×C101—21no—
114C2×C42×C101C2311yescharacteristic
115C2×C42×C101C2311yescharacteristic
116#107×C101—22no—
117#107×C101C2×C414yescomplemented
118#107×C101D414yescomplemented
119#106×C101—22no—
120#106×C101—22no—
121#103×C101—22no—
122#103×C101—41no—
123#103×C101C2×C414yescomplemented
124#102×C101—22no—
125#102×C101—41no—
126#102×C101C2×C414yescomplemented
127C22⋊C8×C101—22no—
128#97×C101—22no—
129C4×C8×C101—22no—
130#95×C101—21no—
131#95×C101—21no—
132#95×C101—21no—
133#95×C101—21no—
134#95×C101—21no—
135#95×C101—21no—
136#95×C101D411yescharacteristic
137#95×C101D411yescharacteristic
138C24×C101—21no—
139C24×C101C2×D411yescharacteristic
140C2×Q8×C101—21no—
141C2×Q8×C101—21no—
142C2×Q8×C101—21no—
143C2×Q8×C101—21no—
144C2×Q8×C101—21no—
145C2×Q8×C101C22×C412yes—
146C2×D4×C101—24no—
147C2×D4×C101—21no—
148C2×D4×C101—21no—
149C2×D4×C101—21no—
150C2×D4×C101—21no—
151C2×D4×C101—21no—
152C2×D4×C101—42no—
153C2×D4×C101—42no—
154C2×D4×C101C22×C412yes—
155C22×C4×C101—21no—
156C22×C4×C101—21no—
157C22×C4×C101—21no—
158C22×C4×C101—21no—
159C22×C4×C101—21no—
160C22×C4×C101—21no—
161C22×C4×C101—21no—
162C22×C4×C101—21no—
163C22×C4×C101—21no—
164C22×C4×C101—21no—
165C22×C4×C101—21no—
166C22×C4×C101—42no—
167C22×C4×C101—42no—
168C22×C4×C101—42no—
169C22×C4×C101—42no—
170C22×C4×C101—81no—
171C22×C4×C101—81no—
172C22×C4×C101C22×C412yes—
173C22×C4×C101C2×D411yescharacteristic
174C22×C4×C101C2×D411yescharacteristic
175C22×C4×C101C2×D411yescharacteristic
176C22×C4×C101C2×D411yescharacteristic
177C22×C4×C101C2×D411yescharacteristic
178C22×C4×C101#4112yes—
179C22×C4×C101C2411yescharacteristic
180SD16×C101—28no—
181M16×C101—28no—
182C2×C8×C101—21no—
183C2×C8×C101—21no—
184C2×C8×C101—21no—
185C2×C8×C101—21no—
186C2×C8×C101—21no—
187C2×C8×C101—21no—
188C2×C8×C101—21no—
189C2×C8×C101—21no—
190C2×C8×C101C22×C412yes—
191C2×C8×C101C22×C412yes—
192C2×C8×C101C2×D412yes—
193C2×C8×C101#4112yes—
194C4⋊C4×C101—24no—
195C4⋊C4×C101—21no—
196C4⋊C4×C101—21no—
197C4⋊C4×C101—21no—
198C4⋊C4×C101—21no—
199C4⋊C4×C101—21no—
200C4⋊C4×C101—21no—
201C4⋊C4×C101—21no—
202C4⋊C4×C101—21no—
203C4⋊C4×C101—42no—
204C4⋊C4×C101—42no—
205C4⋊C4×C101—42no—
206C4⋊C4×C101—42no—
207C4⋊C4×C101C22×C412yes—
208C4⋊C4×C101C22×C412yes—
209C4⋊C4×C101C2×D412yes—
210C4⋊C4×C101C2×D412yes—
211C22⋊C4×C101—24no—
212C22⋊C4×C101—24no—
213C22⋊C4×C101—22no—
214C22⋊C4×C101—41no—
215C22⋊C4×C101—42no—
216C22⋊C4×C101—42no—
217C22⋊C4×C101—42no—
218C22⋊C4×C101—81no—
219C42×C101—21no—
220C42×C101—21no—
221C42×C101—21no—
222C42×C101—21no—
223C42×C101—42no—
224C42×C101—42no—
225C42×C101—42no—
226C42×C101—42no—
227C23×C101—21no—
228C23×C101—21no—
229C23×C101—21no—
230C23×C101—21no—
231C23×C101—21no—
232C23×C101—21no—
233C23×C101—22no—
234C23×C101—41no—
235C23×C101—41no—
236C23×C101—41no—
237C23×C101—41no—
238C23×C101—41no—
239C23×C101—41no—
240C23×C101C4×D412yes—
241C23×C101C22×D411yescharacteristic
242Q8×C101—22no—
243Q8×C101—22no—
244Q8×C101—41no—
245Q8×C101—41no—
246D4×C101—22no—
247D4×C101—22no—
248D4×C101—48no—
249D4×C101—41no—
250D4×C101—41no—
251C2×C4×C101—21no—
252C2×C4×C101—21no—
253C2×C4×C101—21no—
254C2×C4×C101—21no—
255C2×C4×C101—22no—
256C2×C4×C101—22no—
257C2×C4×C101—22no—
258C2×C4×C101—22no—
259C2×C4×C101—22no—
260C2×C4×C101—22no—
261C2×C4×C101—22no—
262C2×C4×C101—21no—
263C2×C4×C101—21no—
264C2×C4×C101—22no—
265C2×C4×C101—22no—
266C2×C4×C101—21no—
267C2×C4×C101—21no—
268C2×C4×C101—21no—
269C2×C4×C101—21no—
270C2×C4×C101—21no—
271C2×C4×C101—21no—
272C2×C4×C101—21no—
273C2×C4×C101—41no—
274C2×C4×C101—41no—
275C2×C4×C101—41no—
276C2×C4×C101—41no—
277C2×C4×C101—41no—
278C2×C4×C101—41no—
279C2×C4×C101—41no—
280C2×C4×C101—41no—
281C2×C4×C101—41no—
282C2×C4×C101—41no—
283C2×C4×C101—41no—
284C2×C4×C101—41no—
285C2×C4×C101—41no—
286C2×C4×C101—41no—
287C2×C4×C101—41no—
288C2×C4×C101—41no—
289C2×C4×C101—84no—
290C2×C4×C101—84no—
291C2×C4×C101C4×D412yes—
292C2×C4×C101AGL(1,ℤ/8)12yes—
293C2×C4×C101C23×C411yescharacteristic
294C2×C4×C101C22×D411yescharacteristic
295C2×C4×C101C2×#4111yescharacteristic
296C2×C4×C101C2×#4111yescharacteristic
297C2×C4×C101H(5,𝔽2)11yescharacteristic
298C2×C4×C1012−1+411yescharacteristic
299C8×C101—22no—
300C8×C101—41no—
301C8×C101—41no—
302C8×C101C4×D414yescomplemented
303C22×C101—22no—
304C22×C101—22no—
305C22×C101—22no—
306C22×C101—41no—
307C22×C101—41no—
308C22×C101—41no—
309C22×C101—41no—
310C22×C101—42no—
311C22×C101—42no—
312C22×C101—42no—
313C22×C101—81no—
314C22×C101—81no—
315C22×C101—81no—
316C22×C101—81no—
317C22×C101C2×C4×D411yescharacteristic
318C22×C101D4211yescharacteristic
319C22×C101#54711yescharacteristic
320C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C101#57511yescharacteristic
322C22×C101#57711yescharacteristic
323C22×C101#57811yescharacteristic
324C4×C101—22no—
325C4×C101—22no—
326C4×C101—41no—
327C4×C101—42no—
328C4×C101—42no—
329C4×C101—42no—
330C4×C101—41no—
331C4×C101—42no—
332C4×C101—42no—
333C4×C101—41no—
334C4×C101—81no—
335C4×C101—81no—
336C4×C101C2×C4×D411yescharacteristic
337C4×C101#52011yescharacteristic
338C4×C101#54811yescharacteristic
339C4×C101#55311yescharacteristic
340#23040C10111yesmaximal, characteristic, direct product factor, Sylow
341C2×C101—42no—
342C2×C101—82no—
343C2×C101#236111yescharacteristic
344C2×C101C4×AGL(1,ℤ/8)11yescharacteristic
345C2×C101#294711yescharacteristic
346C2×C101#327211yescharacteristic
347C2×C101#327711yescharacteristic
348C2×C101#334311yescharacteristic
349C2×C101#335011yescharacteristic
350C2×#468C2×C10111yescharacteristic
351C2×#440C2×C10111yescharacteristic, complemented
352C2×#428C2×C10111yescharacteristic, complemented
353#2362C2×C10111yescharacteristic, complemented
354#2361C2×C10111yescharacteristic
355#1968C2×C10111yescharacteristic, complemented
356#1943C2×C10111yescharacteristic, complemented
357#1927C2×C10111yescharacteristic, complemented
358#1925C2×C10111yescharacteristic, complemented
359#1875C2×C10111yescharacteristic
360#1872C2×C10111yescharacteristic, complemented
361#1864C2×C10111yescharacteristic, complemented
362#1863C2×C10111yescharacteristic, complemented
363C4×#107C2×C10111yescharacteristic, complemented
364#1753C2×C10111yescharacteristic, complemented
365C101#2304011yescharacteristic, direct product factor, Sylow
366C22×SD16C22×C10111yescharacteristic
367C22×M16C22×C10111yescharacteristic
368C2×C22⋊Q8C22×C10111yescharacteristic
369C2×#121C22×C10111yescharacteristic
370C2×C4×Q8C22×C10111yescharacteristic
371C2×C4×D4—21no—
372C2×C4×D4C22×C10111yescharacteristic
373C2×#117C22×C10111yescharacteristic
374C22×C4⋊C4C22×C10111yescharacteristic
375#468C4×C10118yescomplemented
376#440—24no—
377#428—24no—
378C2×#107C22×C10111yescharacteristic
379C2×#107C22×C10111yescharacteristic
380C2×#107C22×C10111yescharacteristic
381C2×#106C22×C10111yescharacteristic
382C2×#106C22×C10111yescharacteristic
383C2×#103C22×C10111yescharacteristic
384C2×#103C22×C10111yescharacteristic
385C2×#103C22×C10111yescharacteristic
386C2×#102C22×C10111yescharacteristic
387C2×#102C22×C10111yescharacteristic
388C2×#102C22×C10111yescharacteristic
389C2×C22⋊C8C22×C10111yescharacteristic
390C2×#97C22×C10111yescharacteristic
391C2×C4×C8C22×C10111yescharacteristic
392#391C22×C10111yescharacteristic
393#390C22×C10111yescharacteristic
394#389C22×C10111yescharacteristic
395#389C22×C10111yescharacteristic
396#388—21no—
397#388—21no—
398#388—21no—
399#387—21no—
400#386—21no—
401#385—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4C22×C10111yescharacteristic
404C4×C4⋊C4C22×C10111yescharacteristic
405C4×C22⋊C4C22×C10111yescharacteristic
406#340C22×C10111yescharacteristic
407#340C22×C10111yescharacteristic
408#340C22×C10111yescharacteristic
409#340C22×C10111yescharacteristic
410#336C22×C10111yescharacteristic
411#336C22×C10111yescharacteristic
412C22×Q8C23×C10111yescharacteristic
413C22×D4—21no—
414C22×D4C23×C10111yescharacteristic
415C23×C4—21no—
416C23×C4—21no—
417C23×C4C23×C10111yescharacteristic
418C2×SD16—22no—
419C2×SD16—22no—
420C2×SD16C2×C4×C10114yescomplemented
421C2×M16—22no—
422C2×M16—22no—
423C2×M16C2×C4×C10114yescomplemented
424C22×C8C23×C10111yescharacteristic
425C22×C8C23×C10111yescharacteristic
426C22×C8C23×C10111yescharacteristic
427C22×C8C23×C10111yescharacteristic
428C22⋊Q8—22no—
429C22⋊Q8C2×C4×C10114yescomplemented
430#121—22no—
431#121C2×C4×C10114yes—
432C4×Q8—22no—
433C4×Q8—41no—
434C4×D4—22no—
435C4×D4—41no—
436C4×D4—44no—
437#117—22no—
438#117—41no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4C23×C10111yescharacteristic
447C2×C4⋊C4C23×C10111yescharacteristic
448C2×C4⋊C4C23×C10111yescharacteristic
449C2×C4⋊C4C23×C10111yescharacteristic
450C2×C4⋊C4C23×C10111yescharacteristic
451C2×C4⋊C4C23×C10111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4D4×C10111yescharacteristic
459C2×C22⋊C4D4×C10111yescharacteristic
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42C23×C10111yescharacteristic
465C2×C42C23×C10111yescharacteristic
466#107—22no—
467#107C2×C4×C10114yescomplemented
468#107D4×C10114yescomplemented
469#106—22no—
470#106—22no—
471#103—22no—
472#103—41no—
473#103C2×C4×C10114yescomplemented
474#102—22no—
475#102—41no—
476#102C2×C4×C10114yescomplemented
477C22⋊C8—22no—
478#97—22no—
479C4×C8—22no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95D4×C10111yescharacteristic
487#95D4×C10111yescharacteristic
488C24—21no—
489C24C2×D4×C10111yescharacteristic
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8C22×C4×C10112yes—
496C2×D4—24no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4C22×C4×C10112yes—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4C22×C4×C10112yes—
523C22×C4C2×D4×C10111yescharacteristic
524C22×C4C2×D4×C10111yescharacteristic
525C22×C4C2×D4×C10111yescharacteristic
526C22×C4C2×D4×C10111yescharacteristic
527C22×C4C2×D4×C10111yescharacteristic
528C22×C4#41×C10112yes—
529C22×C4C24×C10111yescharacteristic
530SD16—28no—
531M16—28no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8C22×C4×C10112yes—
541C2×C8C22×C4×C10112yes—
542C2×C8C2×D4×C10112yes—
543C2×C8#41×C10112yes—
544C4⋊C4—24no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4C22×C4×C10112yes—
558C4⋊C4C22×C4×C10112yes—
559C4⋊C4C2×D4×C10112yes—
560C4⋊C4C2×D4×C10112yes—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C22⋊C4—22no—
564C22⋊C4—41no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—81no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—42no—
574C42—42no—
575C42—42no—
576C42—42no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—22no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23C4×D4×C10112yes—
591C23C22×D4×C10111yescharacteristic
592Q8—22no—
593Q8—22no—
594Q8—41no—
595Q8—41no—
596D4—22no—
597D4—22no—
598D4—48no—
599D4—41no—
600D4—41no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—84no—
640C2×C4—84no—
641C2×C4C4×D4×C10112yes—
642C2×C4AGL(1,ℤ/8)×C10112yes—
643C2×C4C23×C4×C10111yescharacteristic
644C2×C4C22×D4×C10111yescharacteristic
645C2×C4C2×#41×C10111yescharacteristic
646C2×C4C2×#41×C10111yescharacteristic
647C2×C4H(5,𝔽2)×C10111yescharacteristic
648C2×C42−1+4×C10111yescharacteristic
649C8—22no—
650C8—41no—
651C8—41no—
652C8C4×D4×C10114yescomplemented
653C22—22no—
654C22—22no—
655C22—22no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22C2×C4×D4×C10111yescharacteristic
668C22D42×C10111yescharacteristic
669C22#547×C10111yescharacteristic
670C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
671C22#575×C10111yescharacteristic
672C22#577×C10111yescharacteristic
673C22#578×C10111yescharacteristic
674C4—22no—
675C4—22no—
676C4—42no—
677C4—42no—
678C4—41no—
679C4—42no—
680C4—42no—
681C4—41no—
682C4—41no—
683C4—42no—
684C4—81no—
685C4—81no—
686C4C2×C4×D4×C10111yescharacteristic
687C4#520×C10111yescharacteristic
688C4#548×C10111yescharacteristic
689C4#553×C10111yescharacteristic
690C2—42no—
691C2—82no—
692C2C101×#236111yescharacteristic
693C2C4×AGL(1,ℤ/8)×C10111yescharacteristic
694C2C101×#294711yescharacteristic
695C2C101×#327211yescharacteristic
696C2C101×#327711yescharacteristic
697C2C101×#334311yescharacteristic
698C2C101×#335011yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC2×#121×C101C22
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×#440×C101C2semidirect
3. C2×#428×C101C2semidirect
4. C101×#2362C2semidirect
6. C101×#1968C2semidirect
7. C101×#1943C2semidirect
8. C101×#1927C2semidirect
9. C101×#1925C2semidirect
11. C101×#1872C2semidirect
12. C101×#1864C2semidirect
13. C101×#1863C2semidirect
14. C4×#107×C101C2semidirect
15. C101×#1753C2semidirect
25. #468×C101C4semidirect
70. C2×SD16×C101C2×C4semidirect
73. C2×M16×C101C2×C4semidirect
79. C22⋊Q8×C101C2×C4semidirect
117. #107×C101C2×C4semidirect
118. #107×C101D4semidirect
123. #103×C101C2×C4semidirect
126. #102×C101C2×C4semidirect
302. C8×C101C4×D4semidirect
340. #23040C101direct (N × H)
351. C2×#440C2×C101semidirect
352. C2×#428C2×C101semidirect
353. #2362C2×C101semidirect
355. #1968C2×C101semidirect
356. #1943C2×C101semidirect
357. #1927C2×C101semidirect
358. #1925C2×C101semidirect
360. #1872C2×C101semidirect
361. #1864C2×C101semidirect
362. #1863C2×C101semidirect
363. C4×#107C2×C101semidirect
364. #1753C2×C101semidirect
365. C101#23040direct (N × H)
375. #468C4×C101semidirect
420. C2×SD16C2×C4×C101semidirect
423. C2×M16C2×C4×C101semidirect
429. C22⋊Q8C2×C4×C101semidirect
467. #107C2×C4×C101semidirect
468. #107D4×C101semidirect
473. #103C2×C4×C101semidirect
476. #102C2×C4×C101semidirect
652. C8C4×D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1012
C2×#440×C1012
C2×#428×C1012
C101×#23622
C101×#23612
C101×#19682
C101×#19432
C101×#19272
C101×#19252
C101×#18752
C101×#18722
C101×#18642
C101×#18632
C4×#107×C1012
C101×#17532
#23040101