Finite Group Databasebeta

← C101×#25554 #38807705

Subgroups — C101×#25554 #38807705

Order 25856.

1236 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C101C211yesmaximal, characteristic, complemented
2C2×#482×C101C211yesmaximal, characteristic, complemented
3C2×#469×C101C211yesmaximal, characteristic, complemented
4C101×#2416C211yesmaximal, 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×#1862C211yesmaximal, characteristic, complemented
14C101×#1854C211yesmaximal, characteristic, complemented
15C101×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C101C2211yescharacteristic
17C22×M16×C101C2211yescharacteristic
18#555×C101—24no—
19#555×C101—24no—
20C2×C4⋊Q8×C101C2211yescharacteristic
21C2×#124×C101—21no—
22C2×#124×C101—21no—
23C2×#121×C101—21no—
24C2×#121×C101—21no—
25C2×#121×C101C2211yescharacteristic
26C2×#121×C101C2211yescharacteristic
27C2×#121×C101C2211yescharacteristic
28C2×#121×C101C2211yescharacteristic
29C2×C4×D4×C101C2211yescharacteristic
30C2×C4×D4×C101C2211yescharacteristic
31C2×#117×C101—21no—
32C2×#117×C101C2211yescharacteristic
33C2×#117×C101C2211yescharacteristic
34C22×C4⋊C4×C101C2211yescharacteristic
35#482×C101—24no—
36#469×C101—24no—
37C2×#107×C101C2211yescharacteristic
38C2×#106×C101C2211yescharacteristic
39C2×#106×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
49#396×C101—21no—
50#394×C101—21no—
51#390×C101C2211yescharacteristic
52#389×C101C2211yescharacteristic
53#386×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
63C22×Q8×C101—21no—
64C22×D4×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101—21no—
68C22×D4×C101D411yescharacteristic
69C22×D4×C101C2311yescharacteristic
70C22×D4×C101C2311yescharacteristic
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—41no—
78C2×M16×C101—22no—
79C2×M16×C101—22no—
80C2×M16×C101—41no—
81C22×C8×C101C2311yescharacteristic
82C22×C8×C101C2311yescharacteristic
83C22×C8×C101C2311yescharacteristic
84C22×C8×C101C2311yescharacteristic
85C4⋊Q8×C101—22no—
86C4⋊Q8×C101—22no—
87#124×C101—28no—
88#124×C101—28no—
89#121×C101—28no—
90#121×C101—22no—
91#121×C101—22no—
92#121×C101—22no—
93#121×C101—22no—
94#121×C101—22no—
95#121×C101—22no—
96#121×C101—41no—
97#121×C101—44no—
98#121×C101D414yescomplemented
99C4×D4×C101—22no—
100C4×D4×C101—22no—
101C4×D4×C101—22no—
102C4×D4×C101—22no—
103#117×C101—28no—
104#117×C101—22no—
105#117×C101—22no—
106#117×C101—22no—
107#117×C101D414yescomplemented
108C2×C4⋊C4×C101—21no—
109C2×C4⋊C4×C101—22no—
110C2×C4⋊C4×C101—21no—
111C2×C4⋊C4×C101—21no—
112C2×C4⋊C4×C101—41no—
113C2×C4⋊C4×C101D411yescharacteristic
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C4⋊C4×C101C2311yescharacteristic
116C2×C4⋊C4×C101C2311yescharacteristic
117C2×C4⋊C4×C101C2311yescharacteristic
118C2×C4⋊C4×C101C2311yescharacteristic
119C2×C4⋊C4×C101C2311yescharacteristic
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×C101—21no—
129C2×C22⋊C4×C101—21no—
130C2×C22⋊C4×C101D411yescharacteristic
131C2×C22⋊C4×C101D411yescharacteristic
132C2×C42×C101—21no—
133C2×C42×C101—21no—
134C2×C42×C101C2311yescharacteristic
135#107×C101—22no—
136#106×C101—22no—
137#106×C101—22no—
138#102×C101—22no—
139#102×C101—22no—
140#102×C101—22no—
141#102×C101—22no—
142#102×C101—22no—
143#102×C101—41no—
144C22⋊C8×C101—22no—
145C22⋊C8×C101—22no—
146C22⋊C8×C101—41no—
147#95×C101—21no—
148#95×C101—21no—
149C24×C101—21no—
150C24×C101—21no—
151C24×C101C2×D411yescharacteristic
152C24×C101C2×D411yescharacteristic
153C2×Q8×C101—24no—
154C2×Q8×C101—81no—
155C2×Q8×C101—81no—
156C2×D4×C101—22no—
157C2×D4×C101—24no—
158C2×D4×C101—24no—
159C2×D4×C101—22no—
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—41no—
172C2×D4×C101—42no—
173C2×D4×C101—42no—
174C2×D4×C101—42no—
175C2×D4×C101—42no—
176C2×D4×C101—42no—
177C2×D4×C101—81no—
178C2×D4×C101—81no—
179C2×D4×C101—81no—
180C2×D4×C101—81no—
181C2×D4×C101—81no—
182C2×D4×C101C2×D412yes—
183C22×C4×C101—21no—
184C22×C4×C101—21no—
185C22×C4×C101—21no—
186C22×C4×C101—21no—
187C22×C4×C101—24no—
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—21no—
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—42no—
204C22×C4×C101—81no—
205C22×C4×C101C2×D411yescharacteristic
206C22×C4×C101C2×D411yescharacteristic
207C22×C4×C101C2×D411yescharacteristic
208C22×C4×C101C2×D412yes—
209C22×C4×C101C2×D412yes—
210C22×C4×C101C2×D411yescharacteristic
211C22×C4×C101C2411yescharacteristic
212D8×C101—44no—
213M16×C101—44no—
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—21no—
225C2×C8×C101#4112yes—
226C4⋊C4×C101—24no—
227C4⋊C4×C101—22no—
228C4⋊C4×C101—21no—
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—42no—
237C4⋊C4×C101—42no—
238C4⋊C4×C101C2×D412yes—
239C4⋊C4×C101C2×D412yes—
240C4⋊C4×C101C2×D412yes—
241C4⋊C4×C101#4112yes—
242C22⋊C4×C101—24no—
243C22⋊C4×C101—24no—
244C22⋊C4×C101—24no—
245C22⋊C4×C101—24no—
246C22⋊C4×C101—22no—
247C22⋊C4×C101—24no—
248C22⋊C4×C101—22no—
249C22⋊C4×C101—42no—
250C22⋊C4×C101—42no—
251C22⋊C4×C101—42no—
252C22⋊C4×C101—42no—
253C22⋊C4×C101—81no—
254C42×C101—24no—
255C42×C101—24no—
256C42×C101—21no—
257C42×C101—21no—
258C23×C101—21no—
259C23×C101—21no—
260C23×C101—21no—
261C23×C101—21no—
262C23×C101—21no—
263C23×C101—21no—
264C23×C101—21no—
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×C101—41no—
285C23×C101#12012yes—
286C23×C101C22×D411yescharacteristic
287Q8×C101—84no—
288D4×C101—22no—
289D4×C101—22no—
290D4×C101—44no—
291D4×C101—41no—
292D4×C101—41no—
293D4×C101—41no—
294D4×C101—41no—
295D4×C101—41no—
296D4×C101—41no—
297D4×C101—84no—
298D4×C101—84no—
299D4×C101—84no—
300D4×C101—84no—
301C2×C4×C101—21no—
302C2×C4×C101—21no—
303C2×C4×C101—21no—
304C2×C4×C101—21no—
305C2×C4×C101—22no—
306C2×C4×C101—22no—
307C2×C4×C101—22no—
308C2×C4×C101—22no—
309C2×C4×C101—21no—
310C2×C4×C101—22no—
311C2×C4×C101—21no—
312C2×C4×C101—22no—
313C2×C4×C101—22no—
314C2×C4×C101—21no—
315C2×C4×C101—22no—
316C2×C4×C101—21no—
317C2×C4×C101—21no—
318C2×C4×C101—21no—
319C2×C4×C101—48no—
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—41no—
336C2×C4×C101—41no—
337C2×C4×C101—41no—
338C2×C4×C101—84no—
339C2×C4×C101#12012yes—
340C2×C4×C101AGL(1,ℤ/8)12yes—
341C2×C4×C101C22×D411yescharacteristic
342C2×C4×C101C22×D411yescharacteristic
343C2×C4×C101C2×#4111yescharacteristic
344C2×C4×C101C2×#4111yescharacteristic
345C2×C4×C101H(5,𝔽2)11yescharacteristic
346C2×C4×C1012−1+411yescharacteristic
347C8×C101—22no—
348C8×C101—41no—
349C8×C101—41no—
350C8×C101—41no—
351C22×C101—22no—
352C22×C101—22no—
353C22×C101—22no—
354C22×C101—41no—
355C22×C101—41no—
356C22×C101—41no—
357C22×C101—41no—
358C22×C101—41no—
359C22×C101—41no—
360C22×C101—41no—
361C22×C101—42no—
362C22×C101—42no—
363C22×C101—41no—
364C22×C101—41no—
365C22×C101—42no—
366C22×C101—41no—
367C22×C101—41no—
368C22×C101—81no—
369C22×C101—81no—
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×C101—81no—
379C22×C101C2×#12011yescharacteristic
380C22×C101#54611yescharacteristic
381C22×C101#54711yescharacteristic
382C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C101#57511yescharacteristic
384C22×C101#57611yescharacteristic
385C22×C101#57711yescharacteristic
386C4×C101—22no—
387C4×C101—22no—
388C4×C101—41no—
389C4×C101—42no—
390C4×C101—41no—
391C4×C101—42no—
392C4×C101—42no—
393C4×C101—42no—
394C4×C101—81no—
395C4×C101—81no—
396C4×C101#53211yescharacteristic
397C4×C101#53711yescharacteristic
398C4×C101#54611yescharacteristic
399C4×C101#54711yescharacteristic
400#25554C10111yesmaximal, characteristic, direct product factor, Sylow
401C2×C101—42no—
402C2×C101—81no—
403C2×C101—82no—
404C2×C101—161no—
405C2×C101#243011yescharacteristic
406C2×C101#300611yescharacteristic
407C2×C101#301211yescharacteristic
408C2×C101#332111yescharacteristic
409C2×C101#332511yescharacteristic
410C2×C101#334711yescharacteristic
411C2×C101#335411yescharacteristic
412C2×#555C2×C10111yescharacteristic, complemented
413C2×#482C2×C10111yescharacteristic, complemented
414C2×#469C2×C10111yescharacteristic, complemented
415#2416C2×C10111yescharacteristic, complemented
416#2058C2×C10111yescharacteristic, complemented
417#2034C2×C10111yescharacteristic, complemented
418#2023C2×C10111yescharacteristic, complemented
419#1999C2×C10111yescharacteristic, complemented
420#1879C2×C10111yescharacteristic, complemented
421#1875C2×C10111yescharacteristic, complemented
422#1874C2×C10111yescharacteristic, complemented
423#1870C2×C10111yescharacteristic, complemented
424#1862C2×C10111yescharacteristic, complemented
425#1854C2×C10111yescharacteristic, complemented
426#1736C2×C10111yescharacteristic, complemented
427C101#2555411yescharacteristic, direct product factor, Sylow
428C22×D8C22×C10111yescharacteristic
429C22×M16C22×C10111yescharacteristic
430#555—24no—
431#555—24no—
432C2×C4⋊Q8C22×C10111yescharacteristic
433C2×#124—21no—
434C2×#124—21no—
435C2×#121—21no—
436C2×#121—21no—
437C2×#121C22×C10111yescharacteristic
438C2×#121C22×C10111yescharacteristic
439C2×#121C22×C10111yescharacteristic
440C2×#121C22×C10111yescharacteristic
441C2×C4×D4C22×C10111yescharacteristic
442C2×C4×D4C22×C10111yescharacteristic
443C2×#117—21no—
444C2×#117C22×C10111yescharacteristic
445C2×#117C22×C10111yescharacteristic
446C22×C4⋊C4C22×C10111yescharacteristic
447#482—24no—
448#469—24no—
449C2×#107C22×C10111yescharacteristic
450C2×#106C22×C10111yescharacteristic
451C2×#106C22×C10111yescharacteristic
452C2×#102C22×C10111yescharacteristic
453C2×#102C22×C10111yescharacteristic
454C2×#102C22×C10111yescharacteristic
455C2×#102C22×C10111yescharacteristic
456C2×#102C22×C10111yescharacteristic
457C2×#102C22×C10111yescharacteristic
458C2×C22⋊C8C22×C10111yescharacteristic
459C2×C22⋊C8C22×C10111yescharacteristic
460C2×C22⋊C8C22×C10111yescharacteristic
461#396—21no—
462#394—21no—
463#390C22×C10111yescharacteristic
464#389C22×C10111yescharacteristic
465#386—21no—
466#380C22×C10111yescharacteristic
467#340C22×C10111yescharacteristic
468#340C22×C10111yescharacteristic
469#340C22×C10111yescharacteristic
470#340C22×C10111yescharacteristic
471#340C22×C10111yescharacteristic
472#340C22×C10111yescharacteristic
473#336C22×C10111yescharacteristic
474#336C22×C10111yescharacteristic
475C22×Q8—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4D4×C10111yescharacteristic
481C22×D4C23×C10111yescharacteristic
482C22×D4C23×C10111yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C10111yescharacteristic
486C23×C4C23×C10111yescharacteristic
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—41no—
490C2×M16—22no—
491C2×M16—22no—
492C2×M16—41no—
493C22×C8C23×C10111yescharacteristic
494C22×C8C23×C10111yescharacteristic
495C22×C8C23×C10111yescharacteristic
496C22×C8C23×C10111yescharacteristic
497C4⋊Q8—22no—
498C4⋊Q8—22no—
499#124—28no—
500#124—28no—
501#121—28no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—41no—
509#121—44no—
510#121D4×C10114yescomplemented
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515#117—28no—
516#117—22no—
517#117—22no—
518#117—22no—
519#117D4×C10114yescomplemented
520C2×C4⋊C4—21no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4D4×C10111yescharacteristic
526C2×C4⋊C4C23×C10111yescharacteristic
527C2×C4⋊C4C23×C10111yescharacteristic
528C2×C4⋊C4C23×C10111yescharacteristic
529C2×C4⋊C4C23×C10111yescharacteristic
530C2×C4⋊C4C23×C10111yescharacteristic
531C2×C4⋊C4C23×C10111yescharacteristic
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⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4D4×C10111yescharacteristic
543C2×C22⋊C4D4×C10111yescharacteristic
544C2×C42—21no—
545C2×C42—21no—
546C2×C42C23×C10111yescharacteristic
547#107—22no—
548#106—22no—
549#106—22no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—22no—
555#102—41no—
556C22⋊C8—22no—
557C22⋊C8—22no—
558C22⋊C8—41no—
559#95—21no—
560#95—21no—
561C24—21no—
562C24—21no—
563C24C2×D4×C10111yescharacteristic
564C24C2×D4×C10111yescharacteristic
565C2×Q8—24no—
566C2×Q8—81no—
567C2×Q8—81no—
568C2×D4—22no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—22no—
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—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4C2×D4×C10112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4C2×D4×C10111yescharacteristic
618C22×C4C2×D4×C10111yescharacteristic
619C22×C4C2×D4×C10111yescharacteristic
620C22×C4C2×D4×C10112yes—
621C22×C4C2×D4×C10112yes—
622C22×C4C2×D4×C10111yescharacteristic
623C22×C4C24×C10111yescharacteristic
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×C8—21no—
636C2×C8—21no—
637C2×C8#41×C10112yes—
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—42no—
649C4⋊C4—42no—
650C4⋊C4C2×D4×C10112yes—
651C4⋊C4C2×D4×C10112yes—
652C4⋊C4C2×D4×C10112yes—
653C4⋊C4#41×C10112yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—24no—
660C22⋊C4—22no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—81no—
666C42—24no—
667C42—24no—
668C42—21no—
669C42—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
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#120×C10112yes—
698C23C22×D4×C10111yescharacteristic
699Q8—84no—
700D4—22no—
701D4—22no—
702D4—44no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—48no—
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—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—84no—
751C2×C4#120×C10112yes—
752C2×C4AGL(1,ℤ/8)×C10112yes—
753C2×C4C22×D4×C10111yescharacteristic
754C2×C4C22×D4×C10111yescharacteristic
755C2×C4C2×#41×C10111yescharacteristic
756C2×C4C2×#41×C10111yescharacteristic
757C2×C4H(5,𝔽2)×C10111yescharacteristic
758C2×C42−1+4×C10111yescharacteristic
759C8—22no—
760C8—41no—
761C8—41no—
762C8—41no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×#120×C10111yescharacteristic
792C22#546×C10111yescharacteristic
793C22#547×C10111yescharacteristic
794C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
795C22#575×C10111yescharacteristic
796C22#576×C10111yescharacteristic
797C22#577×C10111yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—81no—
807C4—81no—
808C4#532×C10111yescharacteristic
809C4#537×C10111yescharacteristic
810C4#546×C10111yescharacteristic
811C4#547×C10111yescharacteristic
812C2—42no—
813C2—81no—
814C2—82no—
815C2—161no—
816C2C101×#243011yescharacteristic
817C2C101×#300611yescharacteristic
818C2C101×#301211yescharacteristic
819C2C101×#332111yescharacteristic
820C2C101×#332511yescharacteristic
821C2C101×#334711yescharacteristic
822C2C101×#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×#555×C101C2semidirect
2. C2×#482×C101C2semidirect
3. C2×#469×C101C2semidirect
4. C101×#2416C2semidirect
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×#1862C2semidirect
14. C101×#1854C2semidirect
15. C101×#1736C2semidirect
98. #121×C101D4semidirect
107. #117×C101D4semidirect
400. #25554C101direct (N × H)
412. C2×#555C2×C101semidirect
413. C2×#482C2×C101semidirect
414. C2×#469C2×C101semidirect
415. #2416C2×C101semidirect
416. #2058C2×C101semidirect
417. #2034C2×C101semidirect
418. #2023C2×C101semidirect
419. #1999C2×C101semidirect
420. #1879C2×C101semidirect
421. #1875C2×C101semidirect
422. #1874C2×C101semidirect
423. #1870C2×C101semidirect
424. #1862C2×C101semidirect
425. #1854C2×C101semidirect
426. #1736C2×C101semidirect
427. C101#25554direct (N × H)
510. #121D4×C101semidirect
519. #117D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#555×C1012
C2×#482×C1012
C2×#469×C1012
C101×#24162
C101×#20582
C101×#20342
C101×#20232
C101×#19992
C101×#18792
C101×#18752
C101×#18742
C101×#18702
C101×#18622
C101×#18542
C101×#17362
#25554101