Finite Group Databasebeta

← C101×#24040 #38806191

Subgroups — C101×#24040 #38806191

Order 25856.

1322 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×#548×C101C211yesmaximal, characteristic
2C2×#485×C101C211yesmaximal, characteristic, complemented
3C2×#416×C101C211yesmaximal, characteristic, complemented
4C101×#2485C211yesmaximal, characteristic, complemented
5C101×#2042C211yesmaximal, characteristic, complemented
6C101×#2042C211yesmaximal, characteristic, complemented
7C101×#2034C211yesmaximal, characteristic, complemented
8C101×#2033C211yesmaximal, characteristic, complemented
9C101×#1892C211yesmaximal, characteristic, complemented
10C101×#1869C211yesmaximal, characteristic, complemented
11C101×#1865C211yesmaximal, characteristic, complemented
12C101×#1863C211yesmaximal, characteristic, complemented
13C101×#1788C211yesmaximal, characteristic, complemented
14C101×#1787C211yesmaximal, characteristic, complemented
15C101×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×Q8×C101C2211yescharacteristic
18C23×C8×C101C2211yescharacteristic
19#548×C101—24no—
20#548×C101—24no—
21C2×#124×C101—21no—
22C2×#124×C101C2211yescharacteristic
23C2×C22⋊Q8×C101—21no—
24C2×C22⋊Q8×C101C2211yescharacteristic
25C2×#121×C101—21no—
26C2×#121×C101C2211yescharacteristic
27C2×C4×Q8×C101C2211yescharacteristic
28C2×C4×D4×C101—21no—
29C2×C4×D4×C101C2211yescharacteristic
30C2×#117×C101C2211yescharacteristic
31#485×C101—24no—
32C2×#107×C101C2211yescharacteristic
33C2×#106×C101C2211yescharacteristic
34#416×C101—24no—
35C2×#103×C101C2211yescharacteristic
36C2×#103×C101C2211yescharacteristic
37C2×#103×C101C2211yescharacteristic
38C2×#103×C101C2211yescharacteristic
39C2×#103×C101C2211yescharacteristic
40C2×#103×C101C2211yescharacteristic
41C2×#103×C101C2211yescharacteristic
42C2×#103×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×#102×C101C2211yescharacteristic
46C2×#102×C101C2211yescharacteristic
47C2×C22⋊C8×C101C2211yescharacteristic
48C2×C22⋊C8×C101C2211yescharacteristic
49C2×C22⋊C8×C101C2211yescharacteristic
50#397×C101—21no—
51#394×C101—21no—
52#389×C101C2211yescharacteristic
53#389×C101C2211yescharacteristic
54#388×C101—21no—
55#387×C101—21no—
56#380×C101C2211yescharacteristic
57#380×C101C2211yescharacteristic
58#380×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#336×C101C2211yescharacteristic
62#336×C101C2211yescharacteristic
63C2×#41×C101—22no—
64C2×#41×C101—22no—
65C2×#41×C101—22no—
66C2×#41×C101—41no—
67C2×#41×C101—41no—
68C2×#41×C101D414yes—
69C22×Q8×C101—22no—
70C22×Q8×C101—22no—
71C22×Q8×C101—21no—
72C22×Q8×C101—22no—
73C22×Q8×C101—22no—
74C22×Q8×C101—41no—
75C22×Q8×C101—41no—
76C22×Q8×C101C2311yescharacteristic
77C22×Q8×C101C2311yescharacteristic
78C22×D4×C101—21no—
79C22×D4×C101—21no—
80C22×D4×C101D411yescharacteristic
81C22×D4×C101C2311yescharacteristic
82C23×C4×C101—21no—
83C23×C4×C101—21no—
84C23×C4×C101C2311yescharacteristic
85C23×C4×C101C2311yescharacteristic
86C22×C8×C101—22no—
87C22×C8×C101—41no—
88C22×C8×C101—41no—
89C22×C8×C101C2311yescharacteristic
90C22×C8×C101C2311yescharacteristic
91C22×C8×C101C2311yescharacteristic
92C22×C8×C101C2311yescharacteristic
93#124×C101—28no—
94#124×C101—22no—
95#124×C101—22no—
96C22⋊Q8×C101—28no—
97C22⋊Q8×C101—22no—
98C22⋊Q8×C101D414yes—
99#121×C101—28no—
100#121×C101—22no—
101#121×C101—22no—
102C4×Q8×C101—22no—
103C4×Q8×C101—22no—
104C4×D4×C101—28no—
105C4×D4×C101—22no—
106C4×D4×C101—22no—
107#117×C101—22no—
108#117×C101—22no—
109C2×C4⋊C4×C101—21no—
110C2×C4⋊C4×C101—21no—
111C2×C4⋊C4×C101—21no—
112C2×C4⋊C4×C101—21no—
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×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×C101D411yescharacteristic
128C2×C22⋊C4×C101D411yescharacteristic
129C2×C42×C101—21no—
130C2×C42×C101—21no—
131C2×C42×C101C2311yescharacteristic
132#107×C101—22no—
133#106×C101—22no—
134#103×C101—22no—
135#103×C101—22no—
136#103×C101—22no—
137#103×C101—22no—
138#103×C101—22no—
139#103×C101—22no—
140#103×C101—41no—
141#103×C101—41no—
142#102×C101—22no—
143#102×C101—22no—
144#102×C101—41no—
145#102×C101—41no—
146C22⋊C8×C101—22no—
147C22⋊C8×C101—41no—
148C22⋊C8×C101—41no—
149#95×C101—21no—
150#95×C101—21no—
151#95×C101—21no—
152#95×C101—21no—
153#95×C101—21no—
154C24×C101—21no—
155C24×C101C2×D411yescharacteristic
156C24×C101C2×D411yescharacteristic
157#41×C101—28no—
158#41×C101—44no—
159#41×C101—44no—
160#41×C101—44no—
161C2×Q8×C101—24no—
162C2×Q8×C101—21no—
163C2×Q8×C101—21no—
164C2×Q8×C101—21no—
165C2×Q8×C101—21no—
166C2×Q8×C101—21no—
167C2×Q8×C101—21no—
168C2×Q8×C101—21no—
169C2×Q8×C101—21no—
170C2×Q8×C101—42no—
171C2×Q8×C101—42no—
172C2×Q8×C101—44no—
173C2×Q8×C101—44no—
174C2×Q8×C101—44no—
175C2×Q8×C101—44no—
176C2×Q8×C101C2×D412yes—
177C2×Q8×C101C2×D412yes—
178C2×Q8×C101#4112yes—
179C2×Q8×C101#4112yes—
180C2×D4×C101—24no—
181C2×D4×C101—22no—
182C2×D4×C101—24no—
183C2×D4×C101—22no—
184C2×D4×C101—21no—
185C2×D4×C101—21no—
186C2×D4×C101—21no—
187C2×D4×C101—21no—
188C2×D4×C101—21no—
189C2×D4×C101—41no—
190C2×D4×C101—42no—
191C2×D4×C101—42no—
192C2×D4×C101—42no—
193C2×D4×C101—42no—
194C2×D4×C101C2×D412yes—
195C22×C4×C101—21no—
196C22×C4×C101—21no—
197C22×C4×C101—21no—
198C22×C4×C101—21no—
199C22×C4×C101—21no—
200C22×C4×C101—24no—
201C22×C4×C101—21no—
202C22×C4×C101—21no—
203C22×C4×C101—24no—
204C22×C4×C101—21no—
205C22×C4×C101—21no—
206C22×C4×C101—21no—
207C22×C4×C101—21no—
208C22×C4×C101—21no—
209C22×C4×C101—21no—
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—21no—
214C22×C4×C101—42no—
215C22×C4×C101—42no—
216C22×C4×C101—42no—
217C22×C4×C101—42no—
218C22×C4×C101C2×D411yescharacteristic
219C22×C4×C101C2×D411yescharacteristic
220C22×C4×C101C2×D411yescharacteristic
221C22×C4×C101C2×D411yescharacteristic
222C22×C4×C101C2×D412yes—
223C22×C4×C101C2×D412yes—
224C22×C4×C101C2411yescharacteristic
225C2×C8×C101—21no—
226C2×C8×C101—21no—
227C2×C8×C101—21no—
228C2×C8×C101—21no—
229C2×C8×C101—21no—
230C2×C8×C101—21no—
231C2×C8×C101—21no—
232C2×C8×C101—21no—
233C2×C8×C101—21no—
234C2×C8×C101—21no—
235C2×C8×C101—21no—
236C2×C8×C101—21no—
237C2×C8×C101—44no—
238C4⋊C4×C101—24no—
239C4⋊C4×C101—24no—
240C4⋊C4×C101—22no—
241C4⋊C4×C101—21no—
242C4⋊C4×C101—21no—
243C4⋊C4×C101—21no—
244C4⋊C4×C101—21no—
245C4⋊C4×C101—21no—
246C4⋊C4×C101—21no—
247C4⋊C4×C101—21no—
248C4⋊C4×C101—21no—
249C4⋊C4×C101—21no—
250C4⋊C4×C101—42no—
251C4⋊C4×C101—81no—
252C4⋊C4×C101C2×D412yes—
253C22⋊C4×C101—24no—
254C22⋊C4×C101—24no—
255C22⋊C4×C101—24no—
256C22⋊C4×C101—24no—
257C22⋊C4×C101—22no—
258C22⋊C4×C101—22no—
259C22⋊C4×C101—42no—
260C22⋊C4×C101—42no—
261C22⋊C4×C101—81no—
262C22⋊C4×C101—81no—
263C42×C101—24no—
264C42×C101—21no—
265C42×C101—21no—
266C42×C101—42no—
267C23×C101—21no—
268C23×C101—21no—
269C23×C101—21no—
270C23×C101—21no—
271C23×C101—21no—
272C23×C101—21no—
273C23×C101—21no—
274C23×C101—21no—
275C23×C101—21no—
276C23×C101—21no—
277C23×C101—21no—
278C23×C101—21no—
279C23×C101—22no—
280C23×C101—41no—
281C23×C101—41no—
282C23×C101—41no—
283C23×C101—41no—
284C23×C101—41no—
285C23×C101—41no—
286C23×C101#12012yes—
287C23×C101#13512yes—
288C23×C101C22×D411yescharacteristic
289Q8×C101—22no—
290Q8×C101—22no—
291Q8×C101—22no—
292Q8×C101—22no—
293Q8×C101—22no—
294Q8×C101—48no—
295Q8×C101—41no—
296Q8×C101—41no—
297Q8×C101#12314yes—
298D4×C101—22no—
299D4×C101—22no—
300D4×C101—48no—
301D4×C101—44no—
302D4×C101—48no—
303D4×C101—41no—
304D4×C101—41no—
305C2×C4×C101—22no—
306C2×C4×C101—21no—
307C2×C4×C101—21no—
308C2×C4×C101—22no—
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—22no—
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—21no—
325C2×C4×C101—48no—
326C2×C4×C101—48no—
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—41no—
339C2×C4×C101—41no—
340C2×C4×C101—41no—
341C2×C4×C101—41no—
342C2×C4×C101—41no—
343C2×C4×C101—41no—
344C2×C4×C101—41no—
345C2×C4×C101—41no—
346C2×C4×C101—41no—
347C2×C4×C101#12012yes—
348C2×C4×C101C22×D411yescharacteristic
349C2×C4×C101C22×D411yescharacteristic
350C2×C4×C101C2×#4111yescharacteristic
351C2×C4×C101C2×#4111yescharacteristic
352C2×C4×C101H(5,𝔽2)11yescharacteristic
353C2×C4×C101H(5,𝔽2)11yescharacteristic
354C8×C101—41no—
355C8×C101—41no—
356C8×C101—41no—
357C8×C101—41no—
358C22×C101—22no—
359C22×C101—22no—
360C22×C101—22no—
361C22×C101—22no—
362C22×C101—22no—
363C22×C101—22no—
364C22×C101—41no—
365C22×C101—41no—
366C22×C101—41no—
367C22×C101—41no—
368C22×C101—41no—
369C22×C101—41no—
370C22×C101—41no—
371C22×C101—41no—
372C22×C101—42no—
373C22×C101—42no—
374C22×C101—42no—
375C22×C101—81no—
376C22×C101—81no—
377C22×C101—81no—
378C22×C101—81no—
379C22×C101C2×#12011yescharacteristic
380C22×C101#54611yescharacteristic
381C22×C101#54611yescharacteristic
382C22×C101C2×#13511yescharacteristic
383C22×C101#57511yescharacteristic
384C22×C101#57711yescharacteristic
385C22×C101#57811yescharacteristic
386C4×C101—22no—
387C4×C101—24no—
388C4×C101—41no—
389C4×C101—42no—
390C4×C101—41no—
391C4×C101—42no—
392C4×C101—41no—
393C4×C101—81no—
394C4×C101—81no—
395C4×C101—81no—
396C4×C101—81no—
397C4×C101C2×#12311yescharacteristic
398C4×C101#53411yescharacteristic
399C4×C101#54611yescharacteristic
400C4×C101#54611yescharacteristic
401#24040C10111yesmaximal, characteristic, direct product factor, Sylow
402C2×C101—42no—
403C2×C101—42no—
404C2×C101—82no—
405C2×C101#240511yescharacteristic
406C2×C101#300211yescharacteristic
407C2×C101#301311yescharacteristic
408C2×C101#330011yescharacteristic
409C2×C101#330111yescharacteristic
410C2×C101#331311yescharacteristic
411C2×C101#332111yescharacteristic
412C2×#548C2×C10111yescharacteristic
413C2×#485C2×C10111yescharacteristic, complemented
414C2×#416C2×C10111yescharacteristic, complemented
415#2485C2×C10111yescharacteristic, complemented
416#2042C2×C10111yescharacteristic, complemented
417#2042C2×C10111yescharacteristic, complemented
418#2034C2×C10111yescharacteristic, complemented
419#2033C2×C10111yescharacteristic, complemented
420#1892C2×C10111yescharacteristic, complemented
421#1869C2×C10111yescharacteristic, complemented
422#1865C2×C10111yescharacteristic, complemented
423#1863C2×C10111yescharacteristic, complemented
424#1788C2×C10111yescharacteristic, complemented
425#1787C2×C10111yescharacteristic, complemented
426#1787C2×C10111yescharacteristic, complemented
427C101#2404011yescharacteristic, direct product factor, Sylow
428C22×#41C22×C10111yescharacteristic
429C23×Q8C22×C10111yescharacteristic
430C23×C8C22×C10111yescharacteristic
431#548—24no—
432#548—24no—
433C2×#124—21no—
434C2×#124C22×C10111yescharacteristic
435C2×C22⋊Q8—21no—
436C2×C22⋊Q8C22×C10111yescharacteristic
437C2×#121—21no—
438C2×#121C22×C10111yescharacteristic
439C2×C4×Q8C22×C10111yescharacteristic
440C2×C4×D4—21no—
441C2×C4×D4C22×C10111yescharacteristic
442C2×#117C22×C10111yescharacteristic
443#485—24no—
444C2×#107C22×C10111yescharacteristic
445C2×#106C22×C10111yescharacteristic
446#416—24no—
447C2×#103C22×C10111yescharacteristic
448C2×#103C22×C10111yescharacteristic
449C2×#103C22×C10111yescharacteristic
450C2×#103C22×C10111yescharacteristic
451C2×#103C22×C10111yescharacteristic
452C2×#103C22×C10111yescharacteristic
453C2×#103C22×C10111yescharacteristic
454C2×#103C22×C10111yescharacteristic
455C2×#102C22×C10111yescharacteristic
456C2×#102C22×C10111yescharacteristic
457C2×#102C22×C10111yescharacteristic
458C2×#102C22×C10111yescharacteristic
459C2×C22⋊C8C22×C10111yescharacteristic
460C2×C22⋊C8C22×C10111yescharacteristic
461C2×C22⋊C8C22×C10111yescharacteristic
462#397—21no—
463#394—21no—
464#389C22×C10111yescharacteristic
465#389C22×C10111yescharacteristic
466#388—21no—
467#387—21no—
468#380C22×C10111yescharacteristic
469#380C22×C10111yescharacteristic
470#380C22×C10111yescharacteristic
471#340C22×C10111yescharacteristic
472#340C22×C10111yescharacteristic
473#336C22×C10111yescharacteristic
474#336C22×C10111yescharacteristic
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41—41no—
479C2×#41—41no—
480C2×#41D4×C10114yes—
481C22×Q8—22no—
482C22×Q8—22no—
483C22×Q8—21no—
484C22×Q8—22no—
485C22×Q8—22no—
486C22×Q8—41no—
487C22×Q8—41no—
488C22×Q8C23×C10111yescharacteristic
489C22×Q8C23×C10111yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C10111yescharacteristic
493C22×D4C23×C10111yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C23×C10111yescharacteristic
497C23×C4C23×C10111yescharacteristic
498C22×C8—22no—
499C22×C8—41no—
500C22×C8—41no—
501C22×C8C23×C10111yescharacteristic
502C22×C8C23×C10111yescharacteristic
503C22×C8C23×C10111yescharacteristic
504C22×C8C23×C10111yescharacteristic
505#124—28no—
506#124—22no—
507#124—22no—
508C22⋊Q8—28no—
509C22⋊Q8—22no—
510C22⋊Q8D4×C10114yes—
511#121—28no—
512#121—22no—
513#121—22no—
514C4×Q8—22no—
515C4×Q8—22no—
516C4×D4—28no—
517C4×D4—22no—
518C4×D4—22no—
519#117—22no—
520#117—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
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×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×C42—21no—
543C2×C42C23×C10111yescharacteristic
544#107—22no—
545#106—22no—
546#103—22no—
547#103—22no—
548#103—22no—
549#103—22no—
550#103—22no—
551#103—22no—
552#103—41no—
553#103—41no—
554#102—22no—
555#102—22no—
556#102—41no—
557#102—41no—
558C22⋊C8—22no—
559C22⋊C8—41no—
560C22⋊C8—41no—
561#95—21no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95—21no—
566C24—21no—
567C24C2×D4×C10111yescharacteristic
568C24C2×D4×C10111yescharacteristic
569#41—28no—
570#41—44no—
571#41—44no—
572#41—44no—
573C2×Q8—24no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—42no—
583C2×Q8—42no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8—44no—
588C2×Q8C2×D4×C10112yes—
589C2×Q8C2×D4×C10112yes—
590C2×Q8#41×C10112yes—
591C2×Q8#41×C10112yes—
592C2×D4—24no—
593C2×D4—22no—
594C2×D4—24no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—41no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4C2×D4×C10112yes—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—24no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4C2×D4×C10111yescharacteristic
631C22×C4C2×D4×C10111yescharacteristic
632C22×C4C2×D4×C10111yescharacteristic
633C22×C4C2×D4×C10111yescharacteristic
634C22×C4C2×D4×C10112yes—
635C22×C4C2×D4×C10112yes—
636C22×C4C24×C10111yescharacteristic
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—44no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—42no—
663C4⋊C4—81no—
664C4⋊C4C2×D4×C10112yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C42—24no—
676C42—21no—
677C42—21no—
678C42—42no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23#120×C10112yes—
699C23#135×C10112yes—
700C23C22×D4×C10111yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—22no—
706Q8—48no—
707Q8—41no—
708Q8—41no—
709Q8#123×C10114yes—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—44no—
714D4—48no—
715D4—41no—
716D4—41no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—48no—
738C2×C4—48no—
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—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4#120×C10112yes—
760C2×C4C22×D4×C10111yescharacteristic
761C2×C4C22×D4×C10111yescharacteristic
762C2×C4C2×#41×C10111yescharacteristic
763C2×C4C2×#41×C10111yescharacteristic
764C2×C4H(5,𝔽2)×C10111yescharacteristic
765C2×C4H(5,𝔽2)×C10111yescharacteristic
766C8—41no—
767C8—41no—
768C8—41no—
769C8—41no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×#120×C10111yescharacteristic
792C22#546×C10111yescharacteristic
793C22#546×C10111yescharacteristic
794C22C2×#135×C10111yescharacteristic
795C22#575×C10111yescharacteristic
796C22#577×C10111yescharacteristic
797C22#578×C10111yescharacteristic
798C4—22no—
799C4—24no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—41no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4C2×#123×C10111yescharacteristic
810C4#534×C10111yescharacteristic
811C4#546×C10111yescharacteristic
812C4#546×C10111yescharacteristic
813C2—42no—
814C2—42no—
815C2—82no—
816C2C101×#240511yescharacteristic
817C2C101×#300211yescharacteristic
818C2C101×#301311yescharacteristic
819C2C101×#330011yescharacteristic
820C2C101×#330111yescharacteristic
821C2C101×#331311yescharacteristic
822C2C101×#332111yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#548×C101C2
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
2. C2×#485×C101C2semidirect
3. C2×#416×C101C2semidirect
4. C101×#2485C2semidirect
5. C101×#2042C2semidirect
6. C101×#2042C2semidirect
7. C101×#2034C2semidirect
8. C101×#2033C2semidirect
9. C101×#1892C2semidirect
10. C101×#1869C2semidirect
11. C101×#1865C2semidirect
12. C101×#1863C2semidirect
13. C101×#1788C2semidirect
14. C101×#1787C2semidirect
15. C101×#1787C2semidirect
401. #24040C101direct (N × H)
413. C2×#485C2×C101semidirect
414. C2×#416C2×C101semidirect
415. #2485C2×C101semidirect
416. #2042C2×C101semidirect
417. #2042C2×C101semidirect
418. #2034C2×C101semidirect
419. #2033C2×C101semidirect
420. #1892C2×C101semidirect
421. #1869C2×C101semidirect
422. #1865C2×C101semidirect
423. #1863C2×C101semidirect
424. #1788C2×C101semidirect
425. #1787C2×C101semidirect
426. #1787C2×C101semidirect
427. C101#24040direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#548×C1012
C2×#485×C1012
C2×#416×C1012
C101×#24852
C101×#20422
C101×#20342
C101×#20332
C101×#18922
C101×#18692
C101×#18652
C101×#18632
C101×#17882
C101×#17872
#24040101