Finite Group Databasebeta

← C101×#15257 #38797408

Subgroups — C101×#15257 #38797408

Order 25856.

4462 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C101C211yesmaximal, characteristic, complemented
2C22×#120×C101C211yesmaximal, characteristic, complemented
3C22×#120×C101C211yesmaximal, characteristic, complemented
4C2×#392×C101C212yesmaximal, complemented
5C2×#386×C101C212yesmaximal, complemented
6C2×#379×C101C211yesmaximal, characteristic, complemented
7C101×#1440C211yesmaximal, characteristic, complemented
8C101×#1439C212yesmaximal, complemented
9C101×#1438C212yesmaximal, complemented
10C101×#1438C211yesmaximal, characteristic, complemented
11C101×#1438C211yesmaximal, characteristic, complemented
12C26×C101C2211yescharacteristic
13C23×D4×C101C2212yes—
14C23×D4×C101C2211yescharacteristic
15C23×D4×C101C2211yescharacteristic
16C23×D4×C101C2212yes—
17C23×D4×C101C2211yescharacteristic, complemented
18C24×C4×C101C2211yescharacteristic, complemented
19C2×#121×C101—24no—
20C2×#121×C101—24no—
21C2×#121×C101—24no—
22C2×#120×C101—24no—
23C2×#120×C101—24no—
24C2×#120×C101—28no—
25C2×#120×C101—28no—
26C22×C4⋊C4×C101C2211yescharacteristic, complemented
27C22×C22⋊C4×C101C2212yes—
28C22×C22⋊C4×C101C2211yescharacteristic
29C22×C22⋊C4×C101C2211yescharacteristic
30C22×C22⋊C4×C101C2212yes—
31C22×C22⋊C4×C101C2212yes—
32C22×C22⋊C4×C101C2212yes—
33C22×C22⋊C4×C101C2211yescharacteristic
34C22×C22⋊C4×C101C2211yescharacteristic
35C22×C22⋊C4×C101C2211yescharacteristic, complemented
36C22×C22⋊C4×C101C2212yescomplemented
37C22×C22⋊C4×C101C2212yescomplemented
38#392×C101—28no—
39#386×C101—28no—
40#379×C101—24no—
41C2×#95×C101C2212yescomplemented
42C2×#95×C101C2212yescomplemented
43C2×#95×C101C2212yescomplemented
44C2×#95×C101C2212yescomplemented
45C25×C101—22no—
46C25×C101—22no—
47C25×C101—24no—
48C25×C101—24no—
49C25×C101—22no—
50C25×C101—24no—
51C25×C101—42no—
52C25×C101—42no—
53C25×C101—42no—
54C25×C101C2311yescharacteristic
55C25×C101C2311yescharacteristic
56C25×C101C2311yescharacteristic
57C25×C101C2312yes—
58C22×D4×C101—24no—
59C22×D4×C101—24no—
60C22×D4×C101—24no—
61C22×D4×C101—24no—
62C22×D4×C101—24no—
63C22×D4×C101—22no—
64C22×D4×C101—22no—
65C22×D4×C101—22no—
66C22×D4×C101—22no—
67C22×D4×C101—22no—
68C22×D4×C101—22no—
69C22×D4×C101—24no—
70C22×D4×C101—24no—
71C22×D4×C101—24no—
72C22×D4×C101—24no—
73C22×D4×C101—24no—
74C22×D4×C101—24no—
75C22×D4×C101—24no—
76C22×D4×C101—22no—
77C22×D4×C101—42no—
78C22×D4×C101—42no—
79C22×D4×C101—42no—
80C22×D4×C101—42no—
81C22×D4×C101—42no—
82C22×D4×C101—42no—
83C22×D4×C101—42no—
84C22×D4×C101D414yescomplemented
85C22×D4×C101D414yescomplemented
86C22×D4×C101D418yescomplemented
87C23×C4×C101—22no—
88C23×C4×C101—22no—
89C23×C4×C101—22no—
90C23×C4×C101—24no—
91C23×C4×C101—42no—
92C23×C4×C101C2312yes—
93C23×C4×C101C2311yescharacteristic
94C23×C4×C101C2311yescharacteristic
95C23×C4×C101C2311yescharacteristic
96C23×C4×C101C2312yes—
97C23×C4×C101C2312yes—
98C23×C4×C101C2311yescharacteristic
99#121×C101—232no—
100#120×C101—232no—
101#120×C101—232no—
102C2×C4⋊C4×C101—22no—
103C2×C4⋊C4×C101—22no—
104C2×C4⋊C4×C101—22no—
105C2×C22⋊C4×C101—22no—
106C2×C22⋊C4×C101—22no—
107C2×C22⋊C4×C101—24no—
108C2×C22⋊C4×C101—22no—
109C2×C22⋊C4×C101—22no—
110C2×C22⋊C4×C101—22no—
111C2×C22⋊C4×C101—24no—
112C2×C22⋊C4×C101—24no—
113C2×C22⋊C4×C101—24no—
114C2×C22⋊C4×C101—24no—
115C2×C22⋊C4×C101—24no—
116C2×C22⋊C4×C101—24no—
117C2×C22⋊C4×C101—22no—
118C2×C22⋊C4×C101—22no—
119C2×C22⋊C4×C101—22no—
120C2×C22⋊C4×C101—24no—
121C2×C22⋊C4×C101—24no—
122C2×C22⋊C4×C101—24no—
123C2×C22⋊C4×C101—24no—
124C2×C22⋊C4×C101—24no—
125C2×C22⋊C4×C101—24no—
126C2×C22⋊C4×C101—24no—
127C2×C22⋊C4×C101—42no—
128C2×C22⋊C4×C101—42no—
129C2×C22⋊C4×C101—42no—
130C2×C22⋊C4×C101—42no—
131C2×C22⋊C4×C101—42no—
132C2×C22⋊C4×C101—42no—
133C2×C22⋊C4×C101D418yescomplemented
134C2×C22⋊C4×C101D414yescomplemented
135#95×C101—24no—
136#95×C101—24no—
137#95×C101—24no—
138#95×C101—42no—
139C24×C101—22no—
140C24×C101—22no—
141C24×C101—22no—
142C24×C101—22no—
143C24×C101—22no—
144C24×C101—22no—
145C24×C101—22no—
146C24×C101—22no—
147C24×C101—21no—
148C24×C101—21no—
149C24×C101—22no—
150C24×C101—22no—
151C24×C101—22no—
152C24×C101—22no—
153C24×C101—22no—
154C24×C101—22no—
155C24×C101—22no—
156C24×C101—22no—
157C24×C101—22no—
158C24×C101—22no—
159C24×C101—22no—
160C24×C101—22no—
161C24×C101—22no—
162C24×C101—22no—
163C24×C101—22no—
164C24×C101—28no—
165C24×C101—28no—
166C24×C101—28no—
167C24×C101—21no—
168C24×C101—21no—
169C24×C101—22no—
170C24×C101—22no—
171C24×C101—22no—
172C24×C101—22no—
173C24×C101—22no—
174C24×C101—22no—
175C24×C101—48no—
176C24×C101—48no—
177C24×C101—48no—
178C24×C101—48no—
179C24×C101—48no—
180C24×C101—48no—
181C24×C101—48no—
182C24×C101—48no—
183C24×C101—48no—
184C24×C101—44no—
185C24×C101—44no—
186C24×C101—48no—
187C24×C101—44no—
188C24×C101—48no—
189C24×C101—48no—
190C24×C101—48no—
191C24×C101—44no—
192C24×C101—48no—
193C24×C101C2×D412yes—
194C24×C101C2×D412yes—
195C24×C101C2×D412yes—
196C24×C101C2×D412yes—
197C24×C101C2×D414yes—
198C24×C101C2×D412yes—
199C24×C101C2×D414yes—
200C24×C101C2×D414yes—
201C24×C101#4114yes—
202C24×C101C2411yescharacteristic
203C2×D4×C101—216no—
204C2×D4×C101—28no—
205C2×D4×C101—28no—
206C2×D4×C101—28no—
207C2×D4×C101—28no—
208C2×D4×C101—216no—
209C2×D4×C101—216no—
210C2×D4×C101—28no—
211C2×D4×C101—44no—
212C2×D4×C101—48no—
213C2×D4×C101—44no—
214C2×D4×C101—48no—
215C2×D4×C101—48no—
216C2×D4×C101—48no—
217C2×D4×C101—48no—
218C2×D4×C101—48no—
219C2×D4×C101—48no—
220C2×D4×C101—48no—
221C2×D4×C101—48no—
222C2×D4×C101—48no—
223C2×D4×C101—48no—
224C2×D4×C101—48no—
225C2×D4×C101—48no—
226C2×D4×C101—48no—
227C2×D4×C101—48no—
228C2×D4×C101—44no—
229C2×D4×C101—48no—
230C2×D4×C101—44no—
231C2×D4×C101—48no—
232C22×C4×C101—21no—
233C22×C4×C101—21no—
234C22×C4×C101—22no—
235C22×C4×C101—28no—
236C22×C4×C101—22no—
237C22×C4×C101—22no—
238C22×C4×C101—22no—
239C22×C4×C101—22no—
240C22×C4×C101—21no—
241C22×C4×C101—21no—
242C22×C4×C101—22no—
243C22×C4×C101—22no—
244C22×C4×C101—22no—
245C22×C4×C101—22no—
246C22×C4×C101—22no—
247C22×C4×C101—21no—
248C22×C4×C101—21no—
249C22×C4×C101—21no—
250C22×C4×C101—21no—
251C22×C4×C101—22no—
252C22×C4×C101—22no—
253C22×C4×C101—22no—
254C22×C4×C101—22no—
255C22×C4×C101—22no—
256C22×C4×C101—22no—
257C22×C4×C101—22no—
258C22×C4×C101—22no—
259C22×C4×C101—22no—
260C22×C4×C101—22no—
261C22×C4×C101—22no—
262C22×C4×C101—22no—
263C22×C4×C101—22no—
264C22×C4×C101—22no—
265C22×C4×C101—22no—
266C22×C4×C101—22no—
267C22×C4×C101—48no—
268C22×C4×C101—48no—
269C22×C4×C101—44no—
270C22×C4×C101—44no—
271C22×C4×C101C2×D414yes—
272C22×C4×C101C2×D414yes—
273C22×C4×C101C2×D412yes—
274C22×C4×C101C2×D412yes—
275C22×C4×C101C2×D412yes—
276C22×C4×C101C2×D414yes—
277C22×C4×C101C2×D412yes—
278C4⋊C4×C101—28no—
279C22⋊C4×C101—216no—
280C22⋊C4×C101—28no—
281C22⋊C4×C101—28no—
282C22⋊C4×C101—28no—
283C22⋊C4×C101—28no—
284C22⋊C4×C101—216no—
285C22⋊C4×C101—48no—
286C22⋊C4×C101—48no—
287C22⋊C4×C101—48no—
288C22⋊C4×C101—48no—
289C22⋊C4×C101—44no—
290C23×C101—22no—
291C23×C101—22no—
292C23×C101—24no—
293C23×C101—24no—
294C23×C101—22no—
295C23×C101—24no—
296C23×C101—22no—
297C23×C101—24no—
298C23×C101—22no—
299C23×C101—22no—
300C23×C101—22no—
301C23×C101—24no—
302C23×C101—24no—
303C23×C101—22no—
304C23×C101—24no—
305C23×C101—24no—
306C23×C101—24no—
307C23×C101—24no—
308C23×C101—24no—
309C23×C101—24no—
310C23×C101—24no—
311C23×C101—24no—
312C23×C101—24no—
313C23×C101—24no—
314C23×C101—24no—
315C23×C101—24no—
316C23×C101—24no—
317C23×C101—24no—
318C23×C101—24no—
319C23×C101—24no—
320C23×C101—24no—
321C23×C101—24no—
322C23×C101—24no—
323C23×C101—24no—
324C23×C101—24no—
325C23×C101—24no—
326C23×C101—24no—
327C23×C101—24no—
328C23×C101—24no—
329C23×C101—24no—
330C23×C101—22no—
331C23×C101—22no—
332C23×C101—22no—
333C23×C101—24no—
334C23×C101—24no—
335C23×C101—416no—
336C23×C101—416no—
337C23×C101—416no—
338C23×C101—432no—
339C23×C101—432no—
340C23×C101—432no—
341C23×C101—432no—
342C23×C101—432no—
343C23×C101—432no—
344C23×C101—41no—
345C23×C101—42no—
346C23×C101—42no—
347C23×C101—42no—
348C23×C101—41no—
349C23×C101—41no—
350C23×C101—42no—
351C23×C101—42no—
352C23×C101—42no—
353C23×C101—42no—
354C23×C101—41no—
355C23×C101—42no—
356C23×C101—42no—
357C23×C101—42no—
358C23×C101—42no—
359C23×C101—42no—
360C23×C101—42no—
361C23×C101—42no—
362C23×C101—42no—
363C23×C101—42no—
364C23×C101—42no—
365C23×C101—42no—
366C23×C101—42no—
367C23×C101—42no—
368C23×C101—42no—
369C23×C101—42no—
370C23×C101—42no—
371C23×C101—42no—
372C23×C101—42no—
373C23×C101—42no—
374C23×C101—42no—
375C23×C101—42no—
376C23×C101—42no—
377C23×C101—42no—
378C23×C101—41no—
379C23×C101—42no—
380C23×C101—41no—
381C23×C101—42no—
382C23×C101—41no—
383C23×C101—42no—
384C23×C101—41no—
385C23×C101—42no—
386C23×C101—42no—
387C23×C101—42no—
388C23×C101—42no—
389C23×C101—42no—
390C23×C101—42no—
391C23×C101—42no—
392C23×C101—42no—
393C23×C101—42no—
394C23×C101#12014yes—
395C23×C101#12014yescomplemented
396C23×C101#12118yescomplemented
397C23×C101C22×D411yescharacteristic
398C23×C101C22×D411yescharacteristic
399C23×C101C22×D412yes—
400C23×C101C22×D412yes—
401C23×C101C22×D411yescharacteristic
402C23×C101C2×#4112yes—
403C23×C101H(5,𝔽2)12yes—
404C23×C101H(5,𝔽2)12yes—
405C23×C101H(5,𝔽2)12yes—
406D4×C101—416no—
407D4×C101—416no—
408D4×C101—432no—
409D4×C101—416no—
410D4×C101—432no—
411C2×C4×C101—22no—
412C2×C4×C101—22no—
413C2×C4×C101—24no—
414C2×C4×C101—24no—
415C2×C4×C101—22no—
416C2×C4×C101—22no—
417C2×C4×C101—24no—
418C2×C4×C101—24no—
419C2×C4×C101—22no—
420C2×C4×C101—22no—
421C2×C4×C101—24no—
422C2×C4×C101—24no—
423C2×C4×C101—22no—
424C2×C4×C101—24no—
425C2×C4×C101—24no—
426C2×C4×C101—24no—
427C2×C4×C101—24no—
428C2×C4×C101—416no—
429C2×C4×C101—41no—
430C2×C4×C101—41no—
431C2×C4×C101—42no—
432C2×C4×C101—41no—
433C2×C4×C101—41no—
434C2×C4×C101—42no—
435C2×C4×C101—42no—
436C2×C4×C101—42no—
437C2×C4×C101—42no—
438C2×C4×C101—42no—
439C2×C4×C101—42no—
440C2×C4×C101—42no—
441C2×C4×C101—42no—
442C2×C4×C101—42no—
443C2×C4×C101—42no—
444C2×C4×C101—42no—
445C2×C4×C101—42no—
446C2×C4×C101—42no—
447C2×C4×C101—42no—
448C2×C4×C101—42no—
449C2×C4×C101—42no—
450C2×C4×C101—42no—
451C2×C4×C101—42no—
452C2×C4×C101#12014yescomplemented
453C22×C101—24no—
454C22×C101—24no—
455C22×C101—24no—
456C22×C101—24no—
457C22×C101—28no—
458C22×C101—28no—
459C22×C101—28no—
460C22×C101—28no—
461C22×C101—464no—
462C22×C101—42no—
463C22×C101—44no—
464C22×C101—44no—
465C22×C101—42no—
466C22×C101—44no—
467C22×C101—44no—
468C22×C101—44no—
469C22×C101—44no—
470C22×C101—44no—
471C22×C101—44no—
472C22×C101—44no—
473C22×C101—44no—
474C22×C101—44no—
475C22×C101—44no—
476C22×C101—44no—
477C22×C101—44no—
478C22×C101—44no—
479C22×C101—44no—
480C22×C101—44no—
481C22×C101—44no—
482C22×C101—44no—
483C22×C101—44no—
484C22×C101—44no—
485C22×C101—44no—
486C22×C101—44no—
487C22×C101—42no—
488C22×C101—42no—
489C22×C101—42no—
490C22×C101—44no—
491C22×C101—44no—
492C22×C101—82no—
493C22×C101—82no—
494C22×C101—82no—
495C22×C101—82no—
496C22×C101C2×#12011yescharacteristic
497C22×C101C2×#12011yescharacteristic
498C22×C101C2×#12011yescharacteristic
499C22×C101C2×#12112yes—
500C22×C101#52511yescharacteristic
501C22×C101#53411yescharacteristic
502C22×C101#53411yescharacteristic
503C22×C101#53412yes—
504C22×C101#53511yescharacteristic
505C22×C101#53512yes—
506C22×C101#53812yes—
507C22×C101D4212yes—
508C22×C101D4212yes—
509C22×C101D4212yes—
510C22×C101D4212yes—
511C22×C101D4212yes—
512C22×C101#54612yes—
513C22×C101#54612yes—
514C22×C101#54612yes—
515C22×C101#54612yes—
516C22×C101#56012yes—
517C4×C101—24no—
518C4×C101—42no—
519C4×C101—42no—
520C4×C101—42no—
521C4×C101—44no—
522C4×C101—44no—
523C4×C101—82no—
524#15257C10111yesmaximal, characteristic, direct product factor, Sylow
525C2×C101—44no—
526C2×C101—44no—
527C2×C101—48no—
528C2×C101—82no—
529C2×C101#240311yescharacteristic
530C2×C101#240311yescharacteristic
531C2×C101#240411yescharacteristic
532C2×C101#240812yes—
533C2×C101#241012yes—
534C2×C101#242412yes—
535C2×C101#266812yes—
536C2×C101#266912yes—
537C2×C101#267812yes—
538C22×#121C2×C10111yescharacteristic, complemented
539C22×#120C2×C10111yescharacteristic, complemented
540C22×#120C2×C10111yescharacteristic, complemented
541C2×#392C2×C10112yescomplemented
542C2×#386C2×C10112yescomplemented
543C2×#379C2×C10111yescharacteristic, complemented
544#1440C2×C10111yescharacteristic, complemented
545#1439C2×C10112yescomplemented
546#1438C2×C10112yescomplemented
547#1438C2×C10111yescharacteristic, complemented
548#1438C2×C10111yescharacteristic, complemented
549C101#1525711yescharacteristic, direct product factor, Sylow
550C26C22×C10111yescharacteristic
551C23×D4C22×C10112yes—
552C23×D4C22×C10112yes—
553C23×D4C22×C10111yescharacteristic
554C23×D4C22×C10111yescharacteristic
555C23×D4C22×C10111yescharacteristic, complemented
556C24×C4C22×C10111yescharacteristic, complemented
557C2×#121—24no—
558C2×#121—24no—
559C2×#121—24no—
560C2×#120—24no—
561C2×#120—24no—
562C2×#120—28no—
563C2×#120—28no—
564C22×C4⋊C4C22×C10111yescharacteristic, complemented
565C22×C22⋊C4C22×C10112yes—
566C22×C22⋊C4C22×C10111yescharacteristic
567C22×C22⋊C4C22×C10111yescharacteristic
568C22×C22⋊C4C22×C10112yes—
569C22×C22⋊C4C22×C10112yes—
570C22×C22⋊C4C22×C10112yes—
571C22×C22⋊C4C22×C10111yescharacteristic
572C22×C22⋊C4C22×C10111yescharacteristic
573C22×C22⋊C4C22×C10111yescharacteristic, complemented
574C22×C22⋊C4C22×C10112yescomplemented
575C22×C22⋊C4C22×C10112yescomplemented
576#392—28no—
577#386—28no—
578#379—24no—
579C2×#95C22×C10112yescomplemented
580C2×#95C22×C10112yescomplemented
581C2×#95C22×C10112yescomplemented
582C2×#95C22×C10112yescomplemented
583C25—22no—
584C25—22no—
585C25—24no—
586C25—24no—
587C25—22no—
588C25—24no—
589C25—42no—
590C25—42no—
591C25—42no—
592C25C23×C10111yescharacteristic
593C25C23×C10111yescharacteristic
594C25C23×C10111yescharacteristic
595C25C23×C10112yes—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—24no—
600C22×D4—24no—
601C22×D4—22no—
602C22×D4—22no—
603C22×D4—22no—
604C22×D4—22no—
605C22×D4—22no—
606C22×D4—22no—
607C22×D4—24no—
608C22×D4—24no—
609C22×D4—24no—
610C22×D4—24no—
611C22×D4—24no—
612C22×D4—24no—
613C22×D4—24no—
614C22×D4—22no—
615C22×D4—42no—
616C22×D4—42no—
617C22×D4—42no—
618C22×D4—42no—
619C22×D4—42no—
620C22×D4—42no—
621C22×D4—42no—
622C22×D4D4×C10114yescomplemented
623C22×D4D4×C10114yescomplemented
624C22×D4D4×C10118yescomplemented
625C23×C4—22no—
626C23×C4—22no—
627C23×C4—22no—
628C23×C4—24no—
629C23×C4—42no—
630C23×C4C23×C10112yes—
631C23×C4C23×C10111yescharacteristic
632C23×C4C23×C10111yescharacteristic
633C23×C4C23×C10111yescharacteristic
634C23×C4C23×C10112yes—
635C23×C4C23×C10112yes—
636C23×C4C23×C10111yescharacteristic
637#121—232no—
638#120—232no—
639#120—232no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—24no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—24no—
659C2×C22⋊C4—24no—
660C2×C22⋊C4—24no—
661C2×C22⋊C4—24no—
662C2×C22⋊C4—24no—
663C2×C22⋊C4—24no—
664C2×C22⋊C4—24no—
665C2×C22⋊C4—42no—
666C2×C22⋊C4—42no—
667C2×C22⋊C4—42no—
668C2×C22⋊C4—42no—
669C2×C22⋊C4—42no—
670C2×C22⋊C4—42no—
671C2×C22⋊C4D4×C10118yescomplemented
672C2×C22⋊C4D4×C10114yescomplemented
673#95—24no—
674#95—24no—
675#95—24no—
676#95—42no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—28no—
703C24—28no—
704C24—28no—
705C24—21no—
706C24—21no—
707C24—22no—
708C24—22no—
709C24—22no—
710C24—22no—
711C24—22no—
712C24—22no—
713C24—48no—
714C24—48no—
715C24—48no—
716C24—48no—
717C24—48no—
718C24—48no—
719C24—48no—
720C24—48no—
721C24—48no—
722C24—44no—
723C24—44no—
724C24—48no—
725C24—44no—
726C24—48no—
727C24—48no—
728C24—48no—
729C24—44no—
730C24—48no—
731C24C2×D4×C10112yes—
732C24C2×D4×C10112yes—
733C24C2×D4×C10112yes—
734C24C2×D4×C10112yes—
735C24C2×D4×C10114yes—
736C24C2×D4×C10112yes—
737C24C2×D4×C10114yes—
738C24C2×D4×C10114yes—
739C24#41×C10114yes—
740C24C24×C10111yescharacteristic
741C2×D4—216no—
742C2×D4—28no—
743C2×D4—28no—
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—216no—
747C2×D4—216no—
748C2×D4—28no—
749C2×D4—44no—
750C2×D4—48no—
751C2×D4—44no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—44no—
767C2×D4—48no—
768C2×D4—44no—
769C2×D4—48no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—28no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4C2×D4×C10114yes—
810C22×C4C2×D4×C10114yes—
811C22×C4C2×D4×C10112yes—
812C22×C4C2×D4×C10112yes—
813C22×C4C2×D4×C10112yes—
814C22×C4C2×D4×C10114yes—
815C22×C4C2×D4×C10112yes—
816C4⋊C4—28no—
817C22⋊C4—216no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—216no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—44no—
828C23—22no—
829C23—22no—
830C23—24no—
831C23—24no—
832C23—22no—
833C23—24no—
834C23—22no—
835C23—24no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—24no—
840C23—24no—
841C23—22no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—24no—
872C23—24no—
873C23—416no—
874C23—416no—
875C23—416no—
876C23—432no—
877C23—432no—
878C23—432no—
879C23—432no—
880C23—432no—
881C23—432no—
882C23—41no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—41no—
887C23—41no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—42no—
905C23—42no—
906C23—42no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—42no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—42no—
915C23—42no—
916C23—41no—
917C23—42no—
918C23—41no—
919C23—42no—
920C23—41no—
921C23—42no—
922C23—41no—
923C23—42no—
924C23—42no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—42no—
930C23—42no—
931C23—42no—
932C23#120×C10114yes—
933C23#120×C10114yescomplemented
934C23#121×C10118yescomplemented
935C23C22×D4×C10111yescharacteristic
936C23C22×D4×C10111yescharacteristic
937C23C22×D4×C10112yes—
938C23C22×D4×C10112yes—
939C23C22×D4×C10111yescharacteristic
940C23C2×#41×C10112yes—
941C23H(5,𝔽2)×C10112yes—
942C23H(5,𝔽2)×C10112yes—
943C23H(5,𝔽2)×C10112yes—
944D4—416no—
945D4—416no—
946D4—432no—
947D4—416no—
948D4—432no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—416no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4#120×C10114yescomplemented
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—28no—
996C22—28no—
997C22—28no—
998C22—28no—
999C22—464no—
1000C22—42no—
1001C22—44no—
1002C22—44no—
1003C22—44no—
1004C22—42no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—44no—
1029C22—44no—
1030C22—82no—
1031C22—82no—
1032C22—82no—
1033C22—82no—
1034C22C2×#120×C10111yescharacteristic
1035C22C2×#120×C10111yescharacteristic
1036C22C2×#120×C10111yescharacteristic
1037C22C2×#121×C10112yes—
1038C22#525×C10111yescharacteristic
1039C22#534×C10111yescharacteristic
1040C22#534×C10111yescharacteristic
1041C22#534×C10112yes—
1042C22#535×C10111yescharacteristic
1043C22#535×C10112yes—
1044C22#538×C10112yes—
1045C22D42×C10112yes—
1046C22D42×C10112yes—
1047C22D42×C10112yes—
1048C22D42×C10112yes—
1049C22D42×C10112yes—
1050C22#546×C10112yes—
1051C22#546×C10112yes—
1052C22#546×C10112yes—
1053C22#546×C10112yes—
1054C22#560×C10112yes—
1055C4—24no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—44no—
1060C4—44no—
1061C4—82no—
1062C2—44no—
1063C2—48no—
1064C2—44no—
1065C2—82no—
1066C2C101×#240311yescharacteristic
1067C2C101×#240311yescharacteristic
1068C2C101×#240411yescharacteristic
1069C2C101×#240812yes—
1070C2C101×#241012yes—
1071C2C101×#242412yes—
1072C2C101×#266812yes—
1073C2C101×#266912yes—
1074C2C101×#267812yes—
subgroupG/H
center, socleC24×C101C24
commutator, Frattini, cosocleC24C24×C101
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#121×C101C2semidirect
2. C22×#120×C101C2semidirect
3. C22×#120×C101C2semidirect
4. C2×#392×C101C2semidirect
5. C2×#386×C101C2semidirect
6. C2×#379×C101C2semidirect
7. C101×#1440C2semidirect
8. C101×#1439C2semidirect
9. C101×#1438C2semidirect
10. C101×#1438C2semidirect
11. C101×#1438C2semidirect
17. C23×D4×C101C22semidirect
18. C24×C4×C101C22semidirect
26. C22×C4⋊C4×C101C22semidirect
35. C22×C22⋊C4×C101C22semidirect
36. C22×C22⋊C4×C101C22semidirect
37. C22×C22⋊C4×C101C22semidirect
41. C2×#95×C101C22semidirect
42. C2×#95×C101C22semidirect
43. C2×#95×C101C22semidirect
44. C2×#95×C101C22semidirect
84. C22×D4×C101D4semidirect
85. C22×D4×C101D4semidirect
86. C22×D4×C101D4semidirect
133. C2×C22⋊C4×C101D4semidirect
134. C2×C22⋊C4×C101D4semidirect
395. C23×C101#120semidirect
396. C23×C101#121semidirect
452. C2×C4×C101#120semidirect
524. #15257C101direct (N × H)
538. C22×#121C2×C101semidirect
539. C22×#120C2×C101semidirect
540. C22×#120C2×C101semidirect
541. C2×#392C2×C101semidirect
542. C2×#386C2×C101semidirect
543. C2×#379C2×C101semidirect
544. #1440C2×C101semidirect
545. #1439C2×C101semidirect
546. #1438C2×C101semidirect
547. #1438C2×C101semidirect
548. #1438C2×C101semidirect
549. C101#15257direct (N × H)
555. C23×D4C22×C101semidirect
556. C24×C4C22×C101semidirect
564. C22×C4⋊C4C22×C101semidirect
573. C22×C22⋊C4C22×C101semidirect
574. C22×C22⋊C4C22×C101semidirect
575. C22×C22⋊C4C22×C101semidirect
579. C2×#95C22×C101semidirect
580. C2×#95C22×C101semidirect
581. C2×#95C22×C101semidirect
582. C2×#95C22×C101semidirect
622. C22×D4D4×C101semidirect
623. C22×D4D4×C101semidirect
624. C22×D4D4×C101semidirect
671. C2×C22⋊C4D4×C101semidirect
672. C2×C22⋊C4D4×C101semidirect
933. C23#120×C101semidirect
934. C23#121×C101semidirect
990. C2×C4#120×C101semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1012
C22×#120×C1012
C2×#392×C1012
C2×#386×C1012
C2×#379×C1012
C101×#14402
C101×#14392
C101×#14382
#15257101