Finite Group Databasebeta

← C101×#24050 #38806201

Subgroups — C101×#24050 #38806201

Order 25856.

1450 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C101C211yesmaximal, characteristic
2C2×#485×C101C211yesmaximal, characteristic, complemented
3C2×#418×C101C211yesmaximal, characteristic, complemented
4C101×#2485C211yesmaximal, characteristic, complemented
5C101×#2042C211yesmaximal, characteristic, complemented
6C101×#2042C211yesmaximal, characteristic, complemented
7C101×#2034C211yesmaximal, characteristic, complemented
8C101×#2033C211yesmaximal, characteristic, complemented
9C101×#1894C211yesmaximal, characteristic, complemented
10C101×#1870C211yesmaximal, characteristic, complemented
11C101×#1864C211yesmaximal, characteristic, complemented
12C101×#1862C211yesmaximal, characteristic, complemented
13C101×#1788C211yesmaximal, characteristic, complemented
14C101×#1788C211yesmaximal, characteristic, complemented
15C101×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×D4×C101C2211yescharacteristic
18C22×M16×C101C2211yescharacteristic
19#546×C101—24no—
20#546×C101—24no—
21C2×#124×C101C2211yescharacteristic
22C2×#123×C101—21no—
23C2×C22⋊Q8×C101C2211yescharacteristic
24C2×#121×C101—21no—
25C2×#121×C101C2211yescharacteristic
26C2×#120×C101—21no—
27C2×C4×D4×C101C2211yescharacteristic
28C2×C4×D4×C101C2211yescharacteristic
29C2×#117×C101C2211yescharacteristic
30C22×C22⋊C4×C101—21no—
31#485×C101—24no—
32C2×#107×C101C2211yescharacteristic, complemented
33C2×#106×C101C2211yescharacteristic, complemented
34#418×C101—24no—
35C2×#103×C101C2211yescharacteristic, complemented
36C2×#103×C101C2211yescharacteristic, complemented
37C2×#103×C101C2211yescharacteristic, complemented
38C2×#103×C101C2211yescharacteristic, complemented
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×#102×C101C2211yescharacteristic
46C2×#102×C101C2211yescharacteristic
47C2×C22⋊C8×C101C2211yescharacteristic
48C2×C22⋊C8×C101C2211yescharacteristic, complemented
49C2×C22⋊C8×C101C2211yescharacteristic, complemented
50#397×C101—21no—
51#394×C101—21no—
52#389×C101C2211yescharacteristic, complemented
53#389×C101C2211yescharacteristic, complemented
54#388×C101—21no—
55#387×C101—21no—
56#380×C101C2211yescharacteristic
57#380×C101C2211yescharacteristic, complemented
58#380×C101C2211yescharacteristic, complemented
59#340×C101C2211yescharacteristic, complemented
60#340×C101C2211yescharacteristic, complemented
61#336×C101C2211yescharacteristic, complemented
62#336×C101C2211yescharacteristic, complemented
63C25×C101—21no—
64C2×#41×C101—22no—
65C2×#41×C101—22no—
66C2×#41×C101—22no—
67C2×#41×C101—22no—
68C2×#41×C101—41no—
69C2×#41×C101—41no—
70C22×Q8×C101C2311yescharacteristic
71C22×D4×C101—22no—
72C22×D4×C101—22no—
73C22×D4×C101—21no—
74C22×D4×C101—21no—
75C22×D4×C101—21no—
76C22×D4×C101—22no—
77C22×D4×C101—41no—
78C22×D4×C101—41no—
79C22×D4×C101D414yes—
80C22×D4×C101D411yescharacteristic
81C22×D4×C101C2311yescharacteristic
82C22×D4×C101C2311yescharacteristic
83C23×C4×C101—21no—
84C23×C4×C101—21no—
85C23×C4×C101C2311yescharacteristic
86C23×C4×C101C2311yescharacteristic
87C2×M16×C101—22no—
88C2×M16×C101—41no—
89C2×M16×C101—41no—
90C22×C8×C101C2311yescharacteristic
91C22×C8×C101C2311yescharacteristic
92C22×C8×C101C2311yescharacteristic
93C22×C8×C101C2311yescharacteristic
94#124×C101—22no—
95#124×C101—22no—
96#123×C101—28no—
97C22⋊Q8×C101—22no—
98C22⋊Q8×C101D414yes—
99#121×C101—28no—
100#121×C101—22no—
101#121×C101—22no—
102#120×C101—28no—
103C4×D4×C101—22no—
104C4×D4×C101—22no—
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×C101D411yescharacteristic
113C2×C4⋊C4×C101C2311yescharacteristic
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C4⋊C4×C101C2311yescharacteristic
116C2×C4⋊C4×C101C2311yescharacteristic
117C2×C4⋊C4×C101C2311yescharacteristic
118C2×C22⋊C4×C101—28no—
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#103×C101—22no—
135#103×C101—22no—
136#103×C101—41no—
137#103×C101—41no—
138#102×C101—22no—
139#102×C101—22no—
140#102×C101—22no—
141#102×C101—22no—
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×C101—21no—
156C24×C101—24no—
157C24×C101—42no—
158C24×C101—42no—
159C24×C101—42no—
160C24×C101—42no—
161C24×C101—81no—
162C24×C101—81no—
163C24×C101C2×D411yescharacteristic
164C24×C101C2×D411yescharacteristic
165#41×C101—44no—
166#41×C101—44no—
167#41×C101—44no—
168#41×C101—44no—
169C2×Q8×C101—21no—
170C2×Q8×C101—21no—
171C2×Q8×C101—21no—
172C2×Q8×C101—21no—
173C2×Q8×C101—21no—
174C2×Q8×C101C2×D412yes—
175C2×D4×C101—28no—
176C2×D4×C101—24no—
177C2×D4×C101—22no—
178C2×D4×C101—24no—
179C2×D4×C101—24no—
180C2×D4×C101—21no—
181C2×D4×C101—21no—
182C2×D4×C101—21no—
183C2×D4×C101—21no—
184C2×D4×C101—21no—
185C2×D4×C101—21no—
186C2×D4×C101—21no—
187C2×D4×C101—21no—
188C2×D4×C101—44no—
189C2×D4×C101—44no—
190C2×D4×C101—44no—
191C2×D4×C101—41no—
192C2×D4×C101—41no—
193C2×D4×C101—42no—
194C2×D4×C101—42no—
195C2×D4×C101—42no—
196C2×D4×C101—42no—
197C2×D4×C101—81no—
198C2×D4×C101—81no—
199C2×D4×C101C2×D412yes—
200C2×D4×C101C2×D412yes—
201C2×D4×C101#4112yes—
202C2×D4×C101#4112yes—
203C22×C4×C101—21no—
204C22×C4×C101—21no—
205C22×C4×C101—21no—
206C22×C4×C101—21no—
207C22×C4×C101—24no—
208C22×C4×C101—21no—
209C22×C4×C101—21no—
210C22×C4×C101—24no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—21no—
214C22×C4×C101—21no—
215C22×C4×C101—21no—
216C22×C4×C101—21no—
217C22×C4×C101—21no—
218C22×C4×C101—21no—
219C22×C4×C101—21no—
220C22×C4×C101—21no—
221C22×C4×C101—42no—
222C22×C4×C101—42no—
223C22×C4×C101—81no—
224C22×C4×C101—81no—
225C22×C4×C101C2×D411yescharacteristic
226C22×C4×C101C2×D411yescharacteristic
227C22×C4×C101C2×D411yescharacteristic
228C22×C4×C101C2×D411yescharacteristic
229C22×C4×C101C2×D412yes—
230C22×C4×C101C2×D412yes—
231C22×C4×C101C2411yescharacteristic
232M16×C101—44no—
233C2×C8×C101—21no—
234C2×C8×C101—21no—
235C2×C8×C101—21no—
236C2×C8×C101—21no—
237C2×C8×C101—21no—
238C2×C8×C101—21no—
239C2×C8×C101—21no—
240C2×C8×C101—21no—
241C2×C8×C101—21no—
242C2×C8×C101—21no—
243C2×C8×C101—21no—
244C2×C8×C101—21no—
245C4⋊C4×C101—24no—
246C4⋊C4×C101—22no—
247C4⋊C4×C101—21no—
248C4⋊C4×C101—21no—
249C4⋊C4×C101—21no—
250C4⋊C4×C101—21no—
251C4⋊C4×C101—21no—
252C4⋊C4×C101—21no—
253C4⋊C4×C101—21no—
254C4⋊C4×C101—21no—
255C4⋊C4×C101—21no—
256C4⋊C4×C101—42no—
257C4⋊C4×C101—81no—
258C4⋊C4×C101C2×D412yes—
259C22⋊C4×C101—24no—
260C22⋊C4×C101—24no—
261C22⋊C4×C101—24no—
262C22⋊C4×C101—24no—
263C22⋊C4×C101—22no—
264C22⋊C4×C101—24no—
265C22⋊C4×C101—22no—
266C22⋊C4×C101—42no—
267C22⋊C4×C101—42no—
268C22⋊C4×C101—81no—
269C22⋊C4×C101—81no—
270C42×C101—21no—
271C42×C101—21no—
272C42×C101—42no—
273C23×C101—22no—
274C23×C101—21no—
275C23×C101—21no—
276C23×C101—22no—
277C23×C101—22no—
278C23×C101—21no—
279C23×C101—21no—
280C23×C101—21no—
281C23×C101—21no—
282C23×C101—22no—
283C23×C101—21no—
284C23×C101—21no—
285C23×C101—21no—
286C23×C101—21no—
287C23×C101—21no—
288C23×C101—21no—
289C23×C101—21no—
290C23×C101—48no—
291C23×C101—48no—
292C23×C101—41no—
293C23×C101—41no—
294C23×C101—41no—
295C23×C101—41no—
296C23×C101—41no—
297C23×C101—41no—
298C23×C101—41no—
299C23×C101—41no—
300C23×C101—41no—
301C23×C101—41no—
302C23×C101—84no—
303C23×C101—84no—
304C23×C101—84no—
305C23×C101—84no—
306C23×C101—84no—
307C23×C101#12012yes—
308C23×C101C22×D411yescharacteristic
309Q8×C101—22no—
310Q8×C101—22no—
311Q8×C101—41no—
312Q8×C101—41no—
313D4×C101—22no—
314D4×C101—22no—
315D4×C101—22no—
316D4×C101—22no—
317D4×C101—22no—
318D4×C101—48no—
319D4×C101—44no—
320D4×C101—48no—
321D4×C101—41no—
322D4×C101—41no—
323D4×C101—84no—
324D4×C101#12314yes—
325C2×C4×C101—21no—
326C2×C4×C101—21no—
327C2×C4×C101—22no—
328C2×C4×C101—22no—
329C2×C4×C101—22no—
330C2×C4×C101—22no—
331C2×C4×C101—21no—
332C2×C4×C101—21no—
333C2×C4×C101—22no—
334C2×C4×C101—21no—
335C2×C4×C101—22no—
336C2×C4×C101—21no—
337C2×C4×C101—21no—
338C2×C4×C101—21no—
339C2×C4×C101—21no—
340C2×C4×C101—21no—
341C2×C4×C101—21no—
342C2×C4×C101—48no—
343C2×C4×C101—41no—
344C2×C4×C101—41no—
345C2×C4×C101—41no—
346C2×C4×C101—41no—
347C2×C4×C101—41no—
348C2×C4×C101—41no—
349C2×C4×C101—41no—
350C2×C4×C101—41no—
351C2×C4×C101—41no—
352C2×C4×C101—41no—
353C2×C4×C101—41no—
354C2×C4×C101—41no—
355C2×C4×C101—41no—
356C2×C4×C101—41no—
357C2×C4×C101—41no—
358C2×C4×C101—41no—
359C2×C4×C101—41no—
360C2×C4×C101—41no—
361C2×C4×C101—41no—
362C2×C4×C101—41no—
363C2×C4×C101—84no—
364C2×C4×C101#12012yes—
365C2×C4×C101C22×D411yescharacteristic
366C2×C4×C101C22×D411yescharacteristic
367C2×C4×C101C2×#4111yescharacteristic
368C2×C4×C101C2×#4111yescharacteristic
369C2×C4×C101H(5,𝔽2)11yescharacteristic
370C2×C4×C101H(5,𝔽2)11yescharacteristic
371C8×C101—41no—
372C8×C101—41no—
373C8×C101—41no—
374C8×C101—41no—
375C22×C101—22no—
376C22×C101—24no—
377C22×C101—22no—
378C22×C101—22no—
379C22×C101—42no—
380C22×C101—42no—
381C22×C101—41no—
382C22×C101—42no—
383C22×C101—41no—
384C22×C101—42no—
385C22×C101—41no—
386C22×C101—42no—
387C22×C101—41no—
388C22×C101—42no—
389C22×C101—41no—
390C22×C101—42no—
391C22×C101—41no—
392C22×C101—42no—
393C22×C101—41no—
394C22×C101—42no—
395C22×C101—41no—
396C22×C101—41no—
397C22×C101—41no—
398C22×C101—41no—
399C22×C101—816no—
400C22×C101—81no—
401C22×C101—81no—
402C22×C101—81no—
403C22×C101—81no—
404C22×C101C2×#12011yescharacteristic
405C22×C101#54611yescharacteristic
406C22×C101#54611yescharacteristic
407C22×C101#57511yescharacteristic
408C22×C101#57511yescharacteristic
409C22×C101#57611yescharacteristic
410C22×C101#57711yescharacteristic
411C4×C101—22no—
412C4×C101—41no—
413C4×C101—42no—
414C4×C101—41no—
415C4×C101—41no—
416C4×C101—42no—
417C4×C101—81no—
418C4×C101—81no—
419C4×C101—81no—
420C4×C101—81no—
421C4×C101C2×#12311yescharacteristic
422C4×C101#53411yescharacteristic
423C4×C101#54611yescharacteristic
424C4×C101#54611yescharacteristic
425#24050C10111yesmaximal, characteristic, direct product factor, Sylow
426C2×C101—42no—
427C2×C101—44no—
428C2×C101—81no—
429C2×C101—82no—
430C2×C101#240511yescharacteristic
431C2×C101#300511yescharacteristic
432C2×C101#301211yescharacteristic
433C2×C101#331111yescharacteristic
434C2×C101#331911yescharacteristic
435C2×C101#332211yescharacteristic
436C2×C101#332311yescharacteristic
437C2×#546C2×C10111yescharacteristic
438C2×#485C2×C10111yescharacteristic, complemented
439C2×#418C2×C10111yescharacteristic, complemented
440#2485C2×C10111yescharacteristic, complemented
441#2042C2×C10111yescharacteristic, complemented
442#2042C2×C10111yescharacteristic, complemented
443#2034C2×C10111yescharacteristic, complemented
444#2033C2×C10111yescharacteristic, complemented
445#1894C2×C10111yescharacteristic, complemented
446#1870C2×C10111yescharacteristic, complemented
447#1864C2×C10111yescharacteristic, complemented
448#1862C2×C10111yescharacteristic, complemented
449#1788C2×C10111yescharacteristic, complemented
450#1788C2×C10111yescharacteristic, complemented
451#1786C2×C10111yescharacteristic, complemented
452C101#2405011yescharacteristic, direct product factor, Sylow
453C22×#41C22×C10111yescharacteristic
454C23×D4C22×C10111yescharacteristic
455C22×M16C22×C10111yescharacteristic
456#546—24no—
457#546—24no—
458C2×#124C22×C10111yescharacteristic
459C2×#123—21no—
460C2×C22⋊Q8C22×C10111yescharacteristic
461C2×#121—21no—
462C2×#121C22×C10111yescharacteristic
463C2×#120—21no—
464C2×C4×D4C22×C10111yescharacteristic
465C2×C4×D4C22×C10111yescharacteristic
466C2×#117C22×C10111yescharacteristic
467C22×C22⋊C4—21no—
468#485—24no—
469C2×#107C22×C10111yescharacteristic, complemented
470C2×#106C22×C10111yescharacteristic, complemented
471#418—24no—
472C2×#103C22×C10111yescharacteristic, complemented
473C2×#103C22×C10111yescharacteristic, complemented
474C2×#103C22×C10111yescharacteristic, complemented
475C2×#103C22×C10111yescharacteristic, complemented
476C2×#102C22×C10111yescharacteristic
477C2×#102C22×C10111yescharacteristic
478C2×#102C22×C10111yescharacteristic
479C2×#102C22×C10111yescharacteristic
480C2×#102C22×C10111yescharacteristic
481C2×#102C22×C10111yescharacteristic
482C2×#102C22×C10111yescharacteristic
483C2×#102C22×C10111yescharacteristic
484C2×C22⋊C8C22×C10111yescharacteristic
485C2×C22⋊C8C22×C10111yescharacteristic, complemented
486C2×C22⋊C8C22×C10111yescharacteristic, complemented
487#397—21no—
488#394—21no—
489#389C22×C10111yescharacteristic, complemented
490#389C22×C10111yescharacteristic, complemented
491#388—21no—
492#387—21no—
493#380C22×C10111yescharacteristic
494#380C22×C10111yescharacteristic, complemented
495#380C22×C10111yescharacteristic, complemented
496#340C22×C10111yescharacteristic, complemented
497#340C22×C10111yescharacteristic, complemented
498#336C22×C10111yescharacteristic, complemented
499#336C22×C10111yescharacteristic, complemented
500C25—21no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C22×Q8C23×C10111yescharacteristic
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—22no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C10114yes—
517C22×D4D4×C10111yescharacteristic
518C22×D4C23×C10111yescharacteristic
519C22×D4C23×C10111yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C10111yescharacteristic
523C23×C4C23×C10111yescharacteristic
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—41no—
527C22×C8C23×C10111yescharacteristic
528C22×C8C23×C10111yescharacteristic
529C22×C8C23×C10111yescharacteristic
530C22×C8C23×C10111yescharacteristic
531#124—22no—
532#124—22no—
533#123—28no—
534C22⋊Q8—22no—
535C22⋊Q8D4×C10114yes—
536#121—28no—
537#121—22no—
538#121—22no—
539#120—28no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544#117—22no—
545#117—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C10111yescharacteristic
550C2×C4⋊C4C23×C10111yescharacteristic
551C2×C4⋊C4C23×C10111yescharacteristic
552C2×C4⋊C4C23×C10111yescharacteristic
553C2×C4⋊C4C23×C10111yescharacteristic
554C2×C4⋊C4C23×C10111yescharacteristic
555C2×C22⋊C4—28no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C10111yescharacteristic
566C2×C22⋊C4D4×C10111yescharacteristic
567C2×C42—21no—
568C2×C42C23×C10111yescharacteristic
569#107—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—22no—
579#102—22no—
580#102—22no—
581#102—41no—
582#102—41no—
583C22⋊C8—22no—
584C22⋊C8—41no—
585C22⋊C8—41no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590#95—21no—
591C24—21no—
592C24—21no—
593C24—24no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—42no—
598C24—81no—
599C24—81no—
600C24C2×D4×C10111yescharacteristic
601C24C2×D4×C10111yescharacteristic
602#41—44no—
603#41—44no—
604#41—44no—
605#41—44no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8C2×D4×C10112yes—
612C2×D4—28no—
613C2×D4—24no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4C2×D4×C10112yes—
637C2×D4C2×D4×C10112yes—
638C2×D4#41×C10112yes—
639C2×D4#41×C10112yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—24no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C2×D4×C10111yescharacteristic
663C22×C4C2×D4×C10111yescharacteristic
664C22×C4C2×D4×C10111yescharacteristic
665C22×C4C2×D4×C10111yescharacteristic
666C22×C4C2×D4×C10112yes—
667C22×C4C2×D4×C10112yes—
668C22×C4C24×C10111yescharacteristic
669M16—44no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C4⋊C4—24no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—42no—
694C4⋊C4—81no—
695C4⋊C4C2×D4×C10112yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—24no—
702C22⋊C4—22no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C42—21no—
708C42—21no—
709C42—42no—
710C23—22no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—48no—
728C23—48no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23—84no—
744C23#120×C10112yes—
745C23C22×D4×C10111yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—44no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4#123×C10114yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—48no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—84no—
801C2×C4#120×C10112yes—
802C2×C4C22×D4×C10111yescharacteristic
803C2×C4C22×D4×C10111yescharacteristic
804C2×C4C2×#41×C10111yescharacteristic
805C2×C4C2×#41×C10111yescharacteristic
806C2×C4H(5,𝔽2)×C10111yescharacteristic
807C2×C4H(5,𝔽2)×C10111yescharacteristic
808C8—41no—
809C8—41no—
810C8—41no—
811C8—41no—
812C22—22no—
813C22—24no—
814C22—22no—
815C22—22no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—816no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22C2×#120×C10111yescharacteristic
842C22#546×C10111yescharacteristic
843C22#546×C10111yescharacteristic
844C22#575×C10111yescharacteristic
845C22#575×C10111yescharacteristic
846C22#576×C10111yescharacteristic
847C22#577×C10111yescharacteristic
848C4—22no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—81no—
856C4—81no—
857C4—81no—
858C4C2×#123×C10111yescharacteristic
859C4#534×C10111yescharacteristic
860C4#546×C10111yescharacteristic
861C4#546×C10111yescharacteristic
862C2—42no—
863C2—44no—
864C2—81no—
865C2—82no—
866C2C101×#240511yescharacteristic
867C2C101×#300511yescharacteristic
868C2C101×#301211yescharacteristic
869C2C101×#331111yescharacteristic
870C2C101×#331911yescharacteristic
871C2C101×#332211yescharacteristic
872C2C101×#332311yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#546×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×#418×C101C2semidirect
4. C101×#2485C2semidirect
5. C101×#2042C2semidirect
6. C101×#2042C2semidirect
7. C101×#2034C2semidirect
8. C101×#2033C2semidirect
9. C101×#1894C2semidirect
10. C101×#1870C2semidirect
11. C101×#1864C2semidirect
12. C101×#1862C2semidirect
13. C101×#1788C2semidirect
14. C101×#1788C2semidirect
15. C101×#1786C2semidirect
32. C2×#107×C101C22semidirect
33. C2×#106×C101C22semidirect
35. C2×#103×C101C22semidirect
36. C2×#103×C101C22semidirect
37. C2×#103×C101C22semidirect
38. C2×#103×C101C22semidirect
48. C2×C22⋊C8×C101C22semidirect
49. C2×C22⋊C8×C101C22semidirect
52. #389×C101C22semidirect
53. #389×C101C22semidirect
57. #380×C101C22semidirect
58. #380×C101C22semidirect
59. #340×C101C22semidirect
60. #340×C101C22semidirect
61. #336×C101C22semidirect
62. #336×C101C22semidirect
425. #24050C101direct (N × H)
438. C2×#485C2×C101semidirect
439. C2×#418C2×C101semidirect
440. #2485C2×C101semidirect
441. #2042C2×C101semidirect
442. #2042C2×C101semidirect
443. #2034C2×C101semidirect
444. #2033C2×C101semidirect
445. #1894C2×C101semidirect
446. #1870C2×C101semidirect
447. #1864C2×C101semidirect
448. #1862C2×C101semidirect
449. #1788C2×C101semidirect
450. #1788C2×C101semidirect
451. #1786C2×C101semidirect
452. C101#24050direct (N × H)
469. C2×#107C22×C101semidirect
470. C2×#106C22×C101semidirect
472. C2×#103C22×C101semidirect
473. C2×#103C22×C101semidirect
474. C2×#103C22×C101semidirect
475. C2×#103C22×C101semidirect
485. C2×C22⋊C8C22×C101semidirect
486. C2×C22⋊C8C22×C101semidirect
489. #389C22×C101semidirect
490. #389C22×C101semidirect
494. #380C22×C101semidirect
495. #380C22×C101semidirect
496. #340C22×C101semidirect
497. #340C22×C101semidirect
498. #336C22×C101semidirect
499. #336C22×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1012
C2×#485×C1012
C2×#418×C1012
C101×#24852
C101×#20422
C101×#20342
C101×#20332
C101×#18942
C101×#18702
C101×#18642
C101×#18622
C101×#17882
C101×#17862
#24050101