Finite Group Databasebeta

← C101×#24124 #38806275

Subgroups — C101×#24124 #38806275

Order 25856.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 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×C4×D8×C101C211yesmaximal, characteristic, complemented
4C101×#2535C211yesmaximal, characteristic, complemented
5C101×#2034C211yesmaximal, characteristic, complemented
6C101×#2033C211yesmaximal, characteristic, complemented
7C101×#1999C211yesmaximal, characteristic, complemented
8C101×#1999C211yesmaximal, characteristic, complemented
9C101×#1991C211yesmaximal, characteristic, complemented
10C101×#1954C211yesmaximal, characteristic, complemented
11C101×#1875C211yesmaximal, characteristic, complemented
12C101×#1874C211yesmaximal, characteristic, complemented
13C101×#1854C211yesmaximal, characteristic, complemented
14C101×#1852C211yesmaximal, characteristic, complemented
15C101×#1804C211yesmaximal, 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×C101C2211yescharacteristic
24C2×#121×C101C2211yescharacteristic
25C2×#121×C101C2211yescharacteristic
26C2×#121×C101C2211yescharacteristic
27C2×C4×D4×C101—21no—
28C2×C4×D4×C101C2211yescharacteristic
29C2×C4×D4×C101C2211yescharacteristic
30C2×C4×D4×C101C2211yescharacteristic
31C2×#117×C101C2211yescharacteristic
32C22×C4⋊C4×C101C2211yescharacteristic
33#478×C101—24no—
34C4×D8×C101—24no—
35C2×#107×C101C2211yescharacteristic
36C2×#107×C101C2211yescharacteristic
37C2×#106×C101C2211yescharacteristic
38C2×C4⋊C8×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
48C2×C22⋊C8×C101C2211yescharacteristic
49C2×C4×C8×C101C2211yescharacteristic
50#397×C101—21no—
51#392×C101—21no—
52#386×C101—21no—
53#386×C101—21no—
54#382×C101C2211yescharacteristic
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—
95C4×D4×C101—28no—
96C4×D4×C101—22no—
97C4×D4×C101—22no—
98C4×D4×C101—22no—
99C4×D4×C101—22no—
100C4×D4×C101—22no—
101C4×D4×C101D414yescomplemented
102#117×C101—22no—
103#117×C101—22no—
104C2×C4⋊C4×C101—21no—
105C2×C4⋊C4×C101—21no—
106C2×C4⋊C4×C101—21no—
107C2×C4⋊C4×C101—22no—
108C2×C4⋊C4×C101—22no—
109C2×C4⋊C4×C101D411yescharacteristic
110C2×C4⋊C4×C101C2311yescharacteristic
111C2×C4⋊C4×C101C2311yescharacteristic
112C2×C4⋊C4×C101C2311yescharacteristic
113C2×C4⋊C4×C101C2311yescharacteristic
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C4⋊C4×C101C2311yescharacteristic
116C2×C22⋊C4×C101—21no—
117C2×C22⋊C4×C101—21no—
118C2×C22⋊C4×C101—21no—
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×C101D411yescharacteristic
126C2×C22⋊C4×C101D411yescharacteristic
127C2×C42×C101—21no—
128C2×C42×C101C2311yescharacteristic
129#107×C101—22no—
130#107×C101—22no—
131#106×C101—22no—
132C4⋊C8×C101—22no—
133#102×C101—22no—
134#102×C101—22no—
135#102×C101—22no—
136#102×C101—22no—
137#102×C101—41no—
138#102×C101—41no—
139C22⋊C8×C101—22no—
140C22⋊C8×C101—22no—
141C22⋊C8×C101—41no—
142C22⋊C8×C101—41no—
143C4×C8×C101—22no—
144#95×C101—21no—
145#95×C101—21no—
146#95×C101—21no—
147#95×C101—21no—
148C24×C101—21no—
149C24×C101—21no—
150C24×C101C2×D411yescharacteristic
151C24×C101C2×D411yescharacteristic
152C2×D4×C101—24no—
153C2×D4×C101—22no—
154C2×D4×C101—24no—
155C2×D4×C101—22no—
156C2×D4×C101—21no—
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—41no—
167C2×D4×C101—42no—
168C2×D4×C101—42no—
169C2×D4×C101—42no—
170C2×D4×C101—42no—
171C2×D4×C101—42no—
172C2×D4×C101—42no—
173C2×D4×C101—81no—
174C2×D4×C101—81no—
175C2×D4×C101—81no—
176C2×D4×C101—81no—
177C2×D4×C101C2×D412yes—
178C2×D4×C101#4112yes—
179C22×C4×C101—21no—
180C22×C4×C101—21no—
181C22×C4×C101—21no—
182C22×C4×C101—24no—
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—21no—
193C22×C4×C101—21no—
194C22×C4×C101—21no—
195C22×C4×C101—24no—
196C22×C4×C101—21no—
197C22×C4×C101—21no—
198C22×C4×C101—21no—
199C22×C4×C101—42no—
200C22×C4×C101—81no—
201C22×C4×C101—81no—
202C22×C4×C101—81no—
203C22×C4×C101—81no—
204C22×C4×C101—81no—
205C22×C4×C101—81no—
206C22×C4×C101C2×D411yescharacteristic
207C22×C4×C101C2×D411yescharacteristic
208C22×C4×C101C2×D411yescharacteristic
209C22×C4×C101C2×D411yescharacteristic
210C22×C4×C101C2411yescharacteristic
211D8×C101—28no—
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×C101—21no—
222C2×C8×C101—21no—
223C2×C8×C101#4112yes—
224C4⋊C4×C101—24no—
225C4⋊C4×C101—24no—
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—21no—
237C4⋊C4×C101C2×D412yes—
238C4⋊C4×C101C2×D412yes—
239C4⋊C4×C101C2×D412yes—
240C22⋊C4×C101—24no—
241C22⋊C4×C101—24no—
242C22⋊C4×C101—24no—
243C22⋊C4×C101—24no—
244C22⋊C4×C101—22no—
245C22⋊C4×C101—22no—
246C22⋊C4×C101—42no—
247C22⋊C4×C101—42no—
248C22⋊C4×C101—42no—
249C22⋊C4×C101—81no—
250C22⋊C4×C101—81no—
251C42×C101—24no—
252C42×C101C2×D412yes—
253C42×C101C2×D412yes—
254C23×C101—21no—
255C23×C101—21no—
256C23×C101—21no—
257C23×C101—21no—
258C23×C101—21no—
259C23×C101—21no—
260C23×C101—21no—
261C23×C101—22no—
262C23×C101—22no—
263C23×C101—21no—
264C23×C101—21no—
265C23×C101—21no—
266C23×C101—21no—
267C23×C101—21no—
268C23×C101—21no—
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#13512yes—
282C23×C101C22×D411yescharacteristic
283D4×C101—22no—
284D4×C101—22no—
285D4×C101—22no—
286D4×C101—22no—
287D4×C101—44no—
288D4×C101—48no—
289D4×C101—41no—
290D4×C101—41no—
291D4×C101—41no—
292D4×C101—41no—
293D4×C101—84no—
294D4×C101—84no—
295D4×C101—84no—
296C2×C4×C101—21no—
297C2×C4×C101—21no—
298C2×C4×C101—21no—
299C2×C4×C101—21no—
300C2×C4×C101—21no—
301C2×C4×C101—22no—
302C2×C4×C101—22no—
303C2×C4×C101—21no—
304C2×C4×C101—22no—
305C2×C4×C101—21no—
306C2×C4×C101—21no—
307C2×C4×C101—21no—
308C2×C4×C101—21no—
309C2×C4×C101—41no—
310C2×C4×C101—41no—
311C2×C4×C101—41no—
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—84no—
333C2×C4×C101—84no—
334C2×C4×C101—84no—
335C2×C4×C101#12012yes—
336C2×C4×C101#12012yes—
337C2×C4×C101C22×D411yescharacteristic
338C2×C4×C101C22×D411yescharacteristic
339C2×C4×C101C2×#4111yescharacteristic
340C2×C4×C101C2×#4111yescharacteristic
341C2×C4×C101H(5,𝔽2)11yescharacteristic
342C2×C4×C1012−1+411yescharacteristic
343C8×C101—22no—
344C8×C101—41no—
345C8×C101—41no—
346C8×C101—41no—
347C22×C101—22no—
348C22×C101—22no—
349C22×C101—22no—
350C22×C101—41no—
351C22×C101—41no—
352C22×C101—41no—
353C22×C101—41no—
354C22×C101—41no—
355C22×C101—41no—
356C22×C101—41no—
357C22×C101—42no—
358C22×C101—42no—
359C22×C101—41no—
360C22×C101—42no—
361C22×C101—42no—
362C22×C101—41no—
363C22×C101—42no—
364C22×C101—41no—
365C22×C101—41no—
366C22×C101—42no—
367C22×C101—81no—
368C22×C101—81no—
369C22×C101—81no—
370C22×C101—81no—
371C22×C101—81no—
372C22×C101—81no—
373C22×C101—81no—
374C22×C101—81no—
375C22×C101C2×#12011yescharacteristic
376C22×C101#54611yescharacteristic
377C22×C101#54711yescharacteristic
378C22×C101C2×#13511yescharacteristic
379C22×C101#57511yescharacteristic
380C22×C101#57611yescharacteristic
381C22×C101#57611yescharacteristic
382C4×C101—22no—
383C4×C101—22no—
384C4×C101—41no—
385C4×C101—41no—
386C4×C101—42no—
387C4×C101—42no—
388C4×C101—42no—
389C4×C101—81no—
390C4×C101—81no—
391C4×C101—81no—
392C4×C101#52511yescharacteristic
393C4×C101#53711yescharacteristic
394C4×C101#54811yescharacteristic
395C4×C101#55011yescharacteristic
396#24124C10111yesmaximal, characteristic, direct product factor, Sylow
397C2×C101—42no—
398C2×C101—81no—
399C2×C101—82no—
400C2×C101—82no—
401C2×C101#240711yescharacteristic
402C2×C101#300211yescharacteristic
403C2×C101#300811yescharacteristic
404C2×C101#329711yescharacteristic
405C2×C101#332211yescharacteristic
406C2×C101#333911yescharacteristic
407C2×C101#335511yescharacteristic
408C2×#553C2×C10111yescharacteristic, complemented
409C2×#478C2×C10111yescharacteristic, complemented
410C2×C4×D8C2×C10111yescharacteristic, complemented
411#2535C2×C10111yescharacteristic, complemented
412#2034C2×C10111yescharacteristic, complemented
413#2033C2×C10111yescharacteristic, complemented
414#1999C2×C10111yescharacteristic, complemented
415#1999C2×C10111yescharacteristic, complemented
416#1991C2×C10111yescharacteristic, complemented
417#1954C2×C10111yescharacteristic, complemented
418#1875C2×C10111yescharacteristic, complemented
419#1874C2×C10111yescharacteristic, complemented
420#1854C2×C10111yescharacteristic, complemented
421#1852C2×C10111yescharacteristic, complemented
422#1804C2×C10111yescharacteristic, complemented
423C101#2412411yescharacteristic, direct product factor, Sylow
424C22×D8C22×C10111yescharacteristic
425#553—24no—
426#553—24no—
427C2×#126—21no—
428C2×#125C22×C10111yescharacteristic
429C2×#123—21no—
430C2×#121—21no—
431C2×#121C22×C10111yescharacteristic
432C2×#121C22×C10111yescharacteristic
433C2×#121C22×C10111yescharacteristic
434C2×#121C22×C10111yescharacteristic
435C2×C4×D4—21no—
436C2×C4×D4C22×C10111yescharacteristic
437C2×C4×D4C22×C10111yescharacteristic
438C2×C4×D4C22×C10111yescharacteristic
439C2×#117C22×C10111yescharacteristic
440C22×C4⋊C4C22×C10111yescharacteristic
441#478—24no—
442C4×D8—24no—
443C2×#107C22×C10111yescharacteristic
444C2×#107C22×C10111yescharacteristic
445C2×#106C22×C10111yescharacteristic
446C2×C4⋊C8C22×C10111yescharacteristic
447C2×#102C22×C10111yescharacteristic
448C2×#102C22×C10111yescharacteristic
449C2×#102C22×C10111yescharacteristic
450C2×#102C22×C10111yescharacteristic
451C2×#102C22×C10111yescharacteristic
452C2×#102C22×C10111yescharacteristic
453C2×C22⋊C8C22×C10111yescharacteristic
454C2×C22⋊C8C22×C10111yescharacteristic
455C2×C22⋊C8C22×C10111yescharacteristic
456C2×C22⋊C8C22×C10111yescharacteristic
457C2×C4×C8C22×C10111yescharacteristic
458#397—21no—
459#392—21no—
460#386—21no—
461#386—21no—
462#382C22×C10111yescharacteristic
463#380C22×C10111yescharacteristic
464#380C22×C10111yescharacteristic
465#340C22×C10111yescharacteristic
466#340C22×C10111yescharacteristic
467#340C22×C10111yescharacteristic
468#340C22×C10111yescharacteristic
469#340C22×C10111yescharacteristic
470#340C22×C10111yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C10111yescharacteristic
476C22×D4C23×C10111yescharacteristic
477C22×D4C23×C10111yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C10111yescharacteristic
482C23×C4C23×C10111yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C22×C8C23×C10111yescharacteristic
487C22×C8C23×C10111yescharacteristic
488C22×C8C23×C10111yescharacteristic
489C22×C8C23×C10111yescharacteristic
490#126—28no—
491#125—22no—
492#125D4×C10114yescomplemented
493#123—28no—
494#121—28no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—41no—
502#121—41no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4D4×C10114yescomplemented
510#117—22no—
511#117—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4D4×C10111yescharacteristic
518C2×C4⋊C4C23×C10111yescharacteristic
519C2×C4⋊C4C23×C10111yescharacteristic
520C2×C4⋊C4C23×C10111yescharacteristic
521C2×C4⋊C4C23×C10111yescharacteristic
522C2×C4⋊C4C23×C10111yescharacteristic
523C2×C4⋊C4C23×C10111yescharacteristic
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⋊C4D4×C10111yescharacteristic
534C2×C22⋊C4D4×C10111yescharacteristic
535C2×C42—21no—
536C2×C42C23×C10111yescharacteristic
537#107—22no—
538#107—22no—
539#106—22no—
540C4⋊C8—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—41no—
551C4×C8—22no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C10111yescharacteristic
559C24C2×D4×C10111yescharacteristic
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—24no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4C2×D4×C10112yes—
586C2×D4#41×C10112yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
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—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4C2×D4×C10111yescharacteristic
615C22×C4C2×D4×C10111yescharacteristic
616C22×C4C2×D4×C10111yescharacteristic
617C22×C4C2×D4×C10111yescharacteristic
618C22×C4C24×C10111yescharacteristic
619D8—28no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8#41×C10112yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4C2×D4×C10112yes—
646C4⋊C4C2×D4×C10112yes—
647C4⋊C4C2×D4×C10112yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42C2×D4×C10112yes—
661C42C2×D4×C10112yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23#135×C10112yes—
690C23C22×D4×C10111yescharacteristic
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—44no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4—84no—
703D4—84no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
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—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4#120×C10112yes—
744C2×C4#120×C10112yes—
745C2×C4C22×D4×C10111yescharacteristic
746C2×C4C22×D4×C10111yescharacteristic
747C2×C4C2×#41×C10111yescharacteristic
748C2×C4C2×#41×C10111yescharacteristic
749C2×C4H(5,𝔽2)×C10111yescharacteristic
750C2×C42−1+4×C10111yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C10111yescharacteristic
784C22#546×C10111yescharacteristic
785C22#547×C10111yescharacteristic
786C22C2×#135×C10111yescharacteristic
787C22#575×C10111yescharacteristic
788C22#576×C10111yescharacteristic
789C22#576×C10111yescharacteristic
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4#525×C10111yescharacteristic
801C4#537×C10111yescharacteristic
802C4#548×C10111yescharacteristic
803C4#550×C10111yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—82no—
808C2C101×#240711yescharacteristic
809C2C101×#300211yescharacteristic
810C2C101×#300811yescharacteristic
811C2C101×#329711yescharacteristic
812C2C101×#332211yescharacteristic
813C2C101×#333911yescharacteristic
814C2C101×#335511yescharacteristic
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×C4×D8×C101C2semidirect
4. C101×#2535C2semidirect
5. C101×#2034C2semidirect
6. C101×#2033C2semidirect
7. C101×#1999C2semidirect
8. C101×#1999C2semidirect
9. C101×#1991C2semidirect
10. C101×#1954C2semidirect
11. C101×#1875C2semidirect
12. C101×#1874C2semidirect
13. C101×#1854C2semidirect
14. C101×#1852C2semidirect
15. C101×#1804C2semidirect
84. #125×C101D4semidirect
101. C4×D4×C101D4semidirect
396. #24124C101direct (N × H)
408. C2×#553C2×C101semidirect
409. C2×#478C2×C101semidirect
410. C2×C4×D8C2×C101semidirect
411. #2535C2×C101semidirect
412. #2034C2×C101semidirect
413. #2033C2×C101semidirect
414. #1999C2×C101semidirect
415. #1999C2×C101semidirect
416. #1991C2×C101semidirect
417. #1954C2×C101semidirect
418. #1875C2×C101semidirect
419. #1874C2×C101semidirect
420. #1854C2×C101semidirect
421. #1852C2×C101semidirect
422. #1804C2×C101semidirect
423. C101#24124direct (N × H)
492. #125D4×C101semidirect
509. 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×C4×D8×C1012
C101×#25352
C101×#20342
C101×#20332
C101×#19992
C101×#19912
C101×#19542
C101×#18752
C101×#18742
C101×#18542
C101×#18522
C101×#18042
#24124101