Finite Group Databasebeta

← C101×#24136 #38806287

Subgroups — C101×#24136 #38806287

Order 25856.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C101C211yesmaximal, characteristic, complemented
2C2×#478×C101C211yesmaximal, characteristic, complemented
3C2×#442×C101C211yesmaximal, characteristic, complemented
4C101×#2537C211yesmaximal, characteristic, complemented
5C101×#2034C211yesmaximal, characteristic, complemented
6C101×#2033C211yesmaximal, characteristic, complemented
7C101×#1999C211yesmaximal, characteristic, complemented
8C101×#1999C211yesmaximal, characteristic, complemented
9C101×#1992C211yesmaximal, characteristic, complemented
10C101×#1955C211yesmaximal, characteristic, complemented
11C101×#1875C211yesmaximal, characteristic, complemented
12C101×#1874C211yesmaximal, characteristic, complemented
13C101×#1854C211yesmaximal, characteristic, complemented
14C101×#1853C211yesmaximal, characteristic, complemented
15C101×#1802C211yesmaximal, characteristic, complemented
16C22×D8×C101C2211yescharacteristic
17#553×C101—24no—
18#553×C101—24no—
19C2×#126×C101—21no—
20C2×#125×C101C2211yescharacteristic
21C2×#123×C101—21no—
22C2×#121×C101—21no—
23C2×#121×C101—21no—
24C2×#121×C101C2211yescharacteristic
25C2×#121×C101C2211yescharacteristic
26C2×#121×C101C2211yescharacteristic
27C2×#121×C101C2211yescharacteristic
28C2×C4×D4×C101—21no—
29C2×C4×D4×C101C2211yescharacteristic
30C2×C4×D4×C101C2211yescharacteristic
31C2×C4×D4×C101C2211yescharacteristic
32C2×#117×C101C2211yescharacteristic
33C22×C4⋊C4×C101C2211yescharacteristic
34#478×C101—24no—
35#442×C101—24no—
36C2×#107×C101C2211yescharacteristic
37C2×#106×C101C2211yescharacteristic
38C2×#106×C101C2211yescharacteristic
39C2×C4⋊C8×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×#102×C101C2211yescharacteristic
46C2×C22⋊C8×C101C2211yescharacteristic
47C2×C22⋊C8×C101C2211yescharacteristic
48C2×C22⋊C8×C101C2211yescharacteristic
49C2×C22⋊C8×C101C2211yescharacteristic
50C2×#97×C101C2211yescharacteristic
51#394×C101—21no—
52#394×C101—21no—
53#384×C101C2211yescharacteristic
54#380×C101—21no—
55#380×C101C2211yescharacteristic
56#380×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic
62#340×C101C2211yescharacteristic
63C22×D4×C101—21no—
64C22×D4×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101D411yescharacteristic
68C22×D4×C101C2311yescharacteristic
69C22×D4×C101C2311yescharacteristic
70C23×C4×C101—21no—
71C23×C4×C101—21no—
72C23×C4×C101—21no—
73C23×C4×C101C2311yescharacteristic
74C23×C4×C101C2311yescharacteristic
75C2×D8×C101—22no—
76C2×D8×C101—22no—
77C2×D8×C101—22no—
78C22×C8×C101C2311yescharacteristic
79C22×C8×C101C2311yescharacteristic
80C22×C8×C101C2311yescharacteristic
81C22×C8×C101C2311yescharacteristic
82#126×C101—28no—
83#125×C101—22no—
84#125×C101D414yescomplemented
85#123×C101—28no—
86#121×C101—28no—
87#121×C101—22no—
88#121×C101—22no—
89#121×C101—22no—
90#121×C101—22no—
91#121×C101—22no—
92#121×C101—22no—
93#121×C101—41no—
94#121×C101—41no—
95#121×C101—44no—
96C4×D4×C101—28no—
97C4×D4×C101—22no—
98C4×D4×C101—22no—
99C4×D4×C101—22no—
100C4×D4×C101—22no—
101C4×D4×C101—22no—
102C4×D4×C101D414yescomplemented
103#117×C101—22no—
104#117×C101—22no—
105C2×C4⋊C4×C101—21no—
106C2×C4⋊C4×C101—21no—
107C2×C4⋊C4×C101—21no—
108C2×C4⋊C4×C101—22no—
109C2×C4⋊C4×C101—22no—
110C2×C4⋊C4×C101—21no—
111C2×C4⋊C4×C101—21no—
112C2×C4⋊C4×C101D411yescharacteristic
113C2×C4⋊C4×C101C2311yescharacteristic
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C4⋊C4×C101C2311yescharacteristic
116C2×C4⋊C4×C101C2311yescharacteristic
117C2×C4⋊C4×C101C2311yescharacteristic
118C2×C4⋊C4×C101C2311yescharacteristic
119C2×C22⋊C4×C101—21no—
120C2×C22⋊C4×C101—21no—
121C2×C22⋊C4×C101—21no—
122C2×C22⋊C4×C101—21no—
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×C101D411yescharacteristic
129C2×C22⋊C4×C101D411yescharacteristic
130C2×C42×C101—21no—
131C2×C42×C101C2311yescharacteristic
132#107×C101—22no—
133#106×C101—22no—
134#106×C101—22no—
135C4⋊C8×C101—22no—
136#102×C101—22no—
137#102×C101—22no—
138#102×C101—22no—
139#102×C101—22no—
140#102×C101—41no—
141#102×C101—41no—
142C22⋊C8×C101—22no—
143C22⋊C8×C101—22no—
144C22⋊C8×C101—41no—
145C22⋊C8×C101—41no—
146#97×C101—22no—
147#95×C101—21no—
148#95×C101—21no—
149C24×C101—21no—
150C24×C101—21no—
151C24×C101C2×D411yescharacteristic
152C24×C101C2×D411yescharacteristic
153C2×D4×C101—24no—
154C2×D4×C101—22no—
155C2×D4×C101—24no—
156C2×D4×C101—22no—
157C2×D4×C101—21no—
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—41no—
168C2×D4×C101—42no—
169C2×D4×C101—42no—
170C2×D4×C101—42no—
171C2×D4×C101—42no—
172C2×D4×C101—42no—
173C2×D4×C101—42no—
174C2×D4×C101—81no—
175C2×D4×C101—81no—
176C2×D4×C101—81no—
177C2×D4×C101—81no—
178C2×D4×C101C2×D412yes—
179C2×D4×C101#4112yes—
180C22×C4×C101—21no—
181C22×C4×C101—21no—
182C22×C4×C101—21no—
183C22×C4×C101—24no—
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—21no—
193C22×C4×C101—21no—
194C22×C4×C101—21no—
195C22×C4×C101—21no—
196C22×C4×C101—24no—
197C22×C4×C101—21no—
198C22×C4×C101—21no—
199C22×C4×C101—21no—
200C22×C4×C101—42no—
201C22×C4×C101—42no—
202C22×C4×C101—42no—
203C22×C4×C101—81no—
204C22×C4×C101—81no—
205C22×C4×C101—81no—
206C22×C4×C101—81no—
207C22×C4×C101C2×D411yescharacteristic
208C22×C4×C101C2×D411yescharacteristic
209C22×C4×C101C2×D411yescharacteristic
210C22×C4×C101C2×D411yescharacteristic
211C22×C4×C101C2411yescharacteristic
212D8×C101—28no—
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×C101—21no—
222C2×C8×C101—21no—
223C2×C8×C101—21no—
224C2×C8×C101#4112yes—
225C4⋊C4×C101—24no—
226C4⋊C4×C101—24no—
227C4⋊C4×C101—24no—
228C4⋊C4×C101—22no—
229C4⋊C4×C101—21no—
230C4⋊C4×C101—21no—
231C4⋊C4×C101—21no—
232C4⋊C4×C101—21no—
233C4⋊C4×C101—21no—
234C4⋊C4×C101—21no—
235C4⋊C4×C101—21no—
236C4⋊C4×C101—21no—
237C4⋊C4×C101—21no—
238C4⋊C4×C101—42no—
239C4⋊C4×C101—81no—
240C4⋊C4×C101C2×D412yes—
241C4⋊C4×C101C2×D412yes—
242C4⋊C4×C101C2×D412yes—
243C22⋊C4×C101—24no—
244C22⋊C4×C101—24no—
245C22⋊C4×C101—24no—
246C22⋊C4×C101—24no—
247C22⋊C4×C101—22no—
248C22⋊C4×C101—22no—
249C22⋊C4×C101—42no—
250C22⋊C4×C101—42no—
251C22⋊C4×C101—42no—
252C22⋊C4×C101—42no—
253C22⋊C4×C101—42no—
254C42×C101—24no—
255C42×C101C2×D412yes—
256C42×C101C2×D412yes—
257C23×C101—21no—
258C23×C101—21no—
259C23×C101—21no—
260C23×C101—21no—
261C23×C101—21no—
262C23×C101—21no—
263C23×C101—21no—
264C23×C101—22no—
265C23×C101—22no—
266C23×C101—21no—
267C23×C101—21no—
268C23×C101—21no—
269C23×C101—21no—
270C23×C101—21no—
271C23×C101—21no—
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×C101AGL(1,ℤ/8)12yes—
285C23×C101C22×D411yescharacteristic
286D4×C101—22no—
287D4×C101—22no—
288D4×C101—22no—
289D4×C101—22no—
290D4×C101—44no—
291D4×C101—48no—
292D4×C101—41no—
293D4×C101—41no—
294D4×C101—41no—
295D4×C101—41no—
296D4×C101—84no—
297D4×C101—84no—
298D4×C101—84no—
299C2×C4×C101—21no—
300C2×C4×C101—21no—
301C2×C4×C101—21no—
302C2×C4×C101—21no—
303C2×C4×C101—21no—
304C2×C4×C101—22no—
305C2×C4×C101—22no—
306C2×C4×C101—21no—
307C2×C4×C101—22no—
308C2×C4×C101—21no—
309C2×C4×C101—21no—
310C2×C4×C101—21no—
311C2×C4×C101—21no—
312C2×C4×C101—41no—
313C2×C4×C101—41no—
314C2×C4×C101—41no—
315C2×C4×C101—41no—
316C2×C4×C101—41no—
317C2×C4×C101—41no—
318C2×C4×C101—41no—
319C2×C4×C101—41no—
320C2×C4×C101—41no—
321C2×C4×C101—41no—
322C2×C4×C101—41no—
323C2×C4×C101—41no—
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—84no—
336C2×C4×C101—84no—
337C2×C4×C101—84no—
338C2×C4×C101#12012yes—
339C2×C4×C101#12012yes—
340C2×C4×C101C22×D411yescharacteristic
341C2×C4×C101C22×D411yescharacteristic
342C2×C4×C101C2×#4111yescharacteristic
343C2×C4×C101C2×#4111yescharacteristic
344C2×C4×C101H(5,𝔽2)11yescharacteristic
345C2×C4×C1012−1+411yescharacteristic
346C8×C101—22no—
347C8×C101—41no—
348C8×C101—41no—
349C8×C101—41no—
350C22×C101—22no—
351C22×C101—22no—
352C22×C101—22no—
353C22×C101—41no—
354C22×C101—41no—
355C22×C101—41no—
356C22×C101—41no—
357C22×C101—41no—
358C22×C101—41no—
359C22×C101—41no—
360C22×C101—42no—
361C22×C101—42no—
362C22×C101—41no—
363C22×C101—42no—
364C22×C101—42no—
365C22×C101—41no—
366C22×C101—41no—
367C22×C101—42no—
368C22×C101—41no—
369C22×C101—42no—
370C22×C101—81no—
371C22×C101—81no—
372C22×C101—81no—
373C22×C101—81no—
374C22×C101—81no—
375C22×C101—81no—
376C22×C101—81no—
377C22×C101—81no—
378C22×C101C2×#12011yescharacteristic
379C22×C101#54611yescharacteristic
380C22×C101#54711yescharacteristic
381C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C101#57511yescharacteristic
383C22×C101#57611yescharacteristic
384C22×C101#57711yescharacteristic
385C4×C101—22no—
386C4×C101—22no—
387C4×C101—41no—
388C4×C101—41no—
389C4×C101—42no—
390C4×C101—42no—
391C4×C101—42no—
392C4×C101—81no—
393C4×C101—81no—
394C4×C101—81no—
395C4×C101#52511yescharacteristic
396C4×C101#53711yescharacteristic
397C4×C101#54811yescharacteristic
398C4×C101#55011yescharacteristic
399#24136C10111yesmaximal, characteristic, direct product factor, Sylow
400C2×C101—42no—
401C2×C101—81no—
402C2×C101—82no—
403C2×C101—82no—
404C2×C101#240711yescharacteristic
405C2×C101#300611yescharacteristic
406C2×C101#301211yescharacteristic
407C2×C101#330711yescharacteristic
408C2×C101#331811yescharacteristic
409C2×C101#334511yescharacteristic
410C2×C101#334711yescharacteristic
411C2×#553C2×C10111yescharacteristic, complemented
412C2×#478C2×C10111yescharacteristic, complemented
413C2×#442C2×C10111yescharacteristic, complemented
414#2537C2×C10111yescharacteristic, complemented
415#2034C2×C10111yescharacteristic, complemented
416#2033C2×C10111yescharacteristic, complemented
417#1999C2×C10111yescharacteristic, complemented
418#1999C2×C10111yescharacteristic, complemented
419#1992C2×C10111yescharacteristic, complemented
420#1955C2×C10111yescharacteristic, complemented
421#1875C2×C10111yescharacteristic, complemented
422#1874C2×C10111yescharacteristic, complemented
423#1854C2×C10111yescharacteristic, complemented
424#1853C2×C10111yescharacteristic, complemented
425#1802C2×C10111yescharacteristic, complemented
426C101#2413611yescharacteristic, direct product factor, Sylow
427C22×D8C22×C10111yescharacteristic
428#553—24no—
429#553—24no—
430C2×#126—21no—
431C2×#125C22×C10111yescharacteristic
432C2×#123—21no—
433C2×#121—21no—
434C2×#121—21no—
435C2×#121C22×C10111yescharacteristic
436C2×#121C22×C10111yescharacteristic
437C2×#121C22×C10111yescharacteristic
438C2×#121C22×C10111yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4C22×C10111yescharacteristic
441C2×C4×D4C22×C10111yescharacteristic
442C2×C4×D4C22×C10111yescharacteristic
443C2×#117C22×C10111yescharacteristic
444C22×C4⋊C4C22×C10111yescharacteristic
445#478—24no—
446#442—24no—
447C2×#107C22×C10111yescharacteristic
448C2×#106C22×C10111yescharacteristic
449C2×#106C22×C10111yescharacteristic
450C2×C4⋊C8C22×C10111yescharacteristic
451C2×#102C22×C10111yescharacteristic
452C2×#102C22×C10111yescharacteristic
453C2×#102C22×C10111yescharacteristic
454C2×#102C22×C10111yescharacteristic
455C2×#102C22×C10111yescharacteristic
456C2×#102C22×C10111yescharacteristic
457C2×C22⋊C8C22×C10111yescharacteristic
458C2×C22⋊C8C22×C10111yescharacteristic
459C2×C22⋊C8C22×C10111yescharacteristic
460C2×C22⋊C8C22×C10111yescharacteristic
461C2×#97C22×C10111yescharacteristic
462#394—21no—
463#394—21no—
464#384C22×C10111yescharacteristic
465#380—21no—
466#380C22×C10111yescharacteristic
467#380C22×C10111yescharacteristic
468#340C22×C10111yescharacteristic
469#340C22×C10111yescharacteristic
470#340C22×C10111yescharacteristic
471#340C22×C10111yescharacteristic
472#340C22×C10111yescharacteristic
473#340C22×C10111yescharacteristic
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4D4×C10111yescharacteristic
479C22×D4C23×C10111yescharacteristic
480C22×D4C23×C10111yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C10111yescharacteristic
485C23×C4C23×C10111yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C22×C8C23×C10111yescharacteristic
490C22×C8C23×C10111yescharacteristic
491C22×C8C23×C10111yescharacteristic
492C22×C8C23×C10111yescharacteristic
493#126—28no—
494#125—22no—
495#125D4×C10114yescomplemented
496#123—28no—
497#121—28no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—22no—
504#121—41no—
505#121—41no—
506#121—44no—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C10114yescomplemented
514#117—22no—
515#117—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C10111yescharacteristic
524C2×C4⋊C4C23×C10111yescharacteristic
525C2×C4⋊C4C23×C10111yescharacteristic
526C2×C4⋊C4C23×C10111yescharacteristic
527C2×C4⋊C4C23×C10111yescharacteristic
528C2×C4⋊C4C23×C10111yescharacteristic
529C2×C4⋊C4C23×C10111yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4D4×C10111yescharacteristic
540C2×C22⋊C4D4×C10111yescharacteristic
541C2×C42—21no—
542C2×C42C23×C10111yescharacteristic
543#107—22no—
544#106—22no—
545#106—22no—
546C4⋊C8—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—41no—
552#102—41no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—41no—
556C22⋊C8—41no—
557#97—22no—
558#95—21no—
559#95—21no—
560C24—21no—
561C24—21no—
562C24C2×D4×C10111yescharacteristic
563C24C2×D4×C10111yescharacteristic
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4C2×D4×C10112yes—
590C2×D4#41×C10112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
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—21no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4C2×D4×C10111yescharacteristic
619C22×C4C2×D4×C10111yescharacteristic
620C22×C4C2×D4×C10111yescharacteristic
621C22×C4C2×D4×C10111yescharacteristic
622C22×C4C24×C10111yescharacteristic
623D8—28no—
624C2×C8—21no—
625C2×C8—21no—
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×C8#41×C10112yes—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—81no—
651C4⋊C4C2×D4×C10112yes—
652C4⋊C4C2×D4×C10112yes—
653C4⋊C4C2×D4×C10112yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C42—24no—
666C42C2×D4×C10112yes—
667C42C2×D4×C10112yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23AGL(1,ℤ/8)×C10112yes—
696C23C22×D4×C10111yescharacteristic
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—44no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
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—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4#120×C10112yes—
750C2×C4#120×C10112yes—
751C2×C4C22×D4×C10111yescharacteristic
752C2×C4C22×D4×C10111yescharacteristic
753C2×C4C2×#41×C10111yescharacteristic
754C2×C4C2×#41×C10111yescharacteristic
755C2×C4H(5,𝔽2)×C10111yescharacteristic
756C2×C42−1+4×C10111yescharacteristic
757C8—22no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—42no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—41no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22C2×#120×C10111yescharacteristic
790C22#546×C10111yescharacteristic
791C22#547×C10111yescharacteristic
792C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
793C22#575×C10111yescharacteristic
794C22#576×C10111yescharacteristic
795C22#577×C10111yescharacteristic
796C4—22no—
797C4—22no—
798C4—41no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4#525×C10111yescharacteristic
807C4#537×C10111yescharacteristic
808C4#548×C10111yescharacteristic
809C4#550×C10111yescharacteristic
810C2—42no—
811C2—81no—
812C2—82no—
813C2—82no—
814C2C101×#240711yescharacteristic
815C2C101×#300611yescharacteristic
816C2C101×#301211yescharacteristic
817C2C101×#330711yescharacteristic
818C2C101×#331811yescharacteristic
819C2C101×#334511yescharacteristic
820C2C101×#334711yescharacteristic
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×#553×C101C2semidirect
2. C2×#478×C101C2semidirect
3. C2×#442×C101C2semidirect
4. C101×#2537C2semidirect
5. C101×#2034C2semidirect
6. C101×#2033C2semidirect
7. C101×#1999C2semidirect
8. C101×#1999C2semidirect
9. C101×#1992C2semidirect
10. C101×#1955C2semidirect
11. C101×#1875C2semidirect
12. C101×#1874C2semidirect
13. C101×#1854C2semidirect
14. C101×#1853C2semidirect
15. C101×#1802C2semidirect
84. #125×C101D4semidirect
102. C4×D4×C101D4semidirect
399. #24136C101direct (N × H)
411. C2×#553C2×C101semidirect
412. C2×#478C2×C101semidirect
413. C2×#442C2×C101semidirect
414. #2537C2×C101semidirect
415. #2034C2×C101semidirect
416. #2033C2×C101semidirect
417. #1999C2×C101semidirect
418. #1999C2×C101semidirect
419. #1992C2×C101semidirect
420. #1955C2×C101semidirect
421. #1875C2×C101semidirect
422. #1874C2×C101semidirect
423. #1854C2×C101semidirect
424. #1853C2×C101semidirect
425. #1802C2×C101semidirect
426. C101#24136direct (N × H)
495. #125D4×C101semidirect
513. C4×D4D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C1012
C2×#478×C1012
C2×#442×C1012
C101×#25372
C101×#20342
C101×#20332
C101×#19992
C101×#19922
C101×#19552
C101×#18752
C101×#18742
C101×#18542
C101×#18532
C101×#18022
#24136101