Finite Group Databasebeta

← C101×#14725 #38796876

Subgroups — C101×#14725 #38796876

Order 25856.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C101C211yesmaximal, characteristic
2C23×C22⋊C4×C101C211yesmaximal, characteristic, complemented
3C2×#394×C101C212yesmaximal, complemented
4C2×#386×C101C211yesmaximal, characteristic, complemented
5C2×#386×C101C211yesmaximal, characteristic, complemented
6C2×#380×C101C211yesmaximal, characteristic, complemented
7C2×#379×C101C211yesmaximal, characteristic, complemented
8C101×#1440C212yesmaximal, complemented
9C101×#1439C212yesmaximal, complemented
10C101×#1438C212yesmaximal, complemented
11C101×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C101C2211yescharacteristic
13C23×D4×C101C2211yescharacteristic
14C23×D4×C101C2212yes—
15C24×C4×C101C2211yescharacteristic
16C24×C4×C101C2211yescharacteristic
17C2×#120×C101—24no—
18C2×#120×C101—24no—
19C2×#120×C101—24no—
20C22×C4⋊C4×C101C2212yescomplemented
21C22×C22⋊C4×C101—24no—
22C22×C22⋊C4×C101—28no—
23C22×C22⋊C4×C101C2212yes—
24C22×C22⋊C4×C101C2212yes—
25C22×C22⋊C4×C101C2211yescharacteristic
26C22×C22⋊C4×C101C2212yes—
27C22×C22⋊C4×C101C2211yescharacteristic
28C22×C22⋊C4×C101C2211yescharacteristic
29C22×C22⋊C4×C101C2212yes—
30C22×C22⋊C4×C101C2212yes—
31C22×C22⋊C4×C101C2211yescharacteristic, complemented
32C22×C22⋊C4×C101C2212yescomplemented
33C22×C22⋊C4×C101C2211yescharacteristic, complemented
34#394×C101—28no—
35#386×C101—24no—
36#386×C101—24no—
37#380×C101—24no—
38#379×C101—24no—
39C2×#95×C101C2212yescomplemented
40C2×#95×C101C2212yescomplemented
41C2×#95×C101C2211yescharacteristic, complemented
42C2×#95×C101C2212yescomplemented
43C2×#95×C101C2211yescharacteristic, complemented
44C2×#95×C101C2212yescomplemented
45C25×C101—24no—
46C25×C101—22no—
47C25×C101—24no—
48C25×C101—22no—
49C25×C101—22no—
50C25×C101—22no—
51C25×C101—22no—
52C25×C101—22no—
53C25×C101—42no—
54C25×C101—42no—
55C25×C101D414yes—
56C25×C101C2311yescharacteristic
57C25×C101C2312yes—
58C25×C101C2311yescharacteristic
59C22×D4×C101—24no—
60C22×D4×C101—24no—
61C22×D4×C101—22no—
62C22×D4×C101—22no—
63C22×D4×C101—22no—
64C22×D4×C101—22no—
65C22×D4×C101—22no—
66C22×D4×C101—22no—
67C22×D4×C101—24no—
68C22×D4×C101—24no—
69C22×D4×C101—24no—
70C22×D4×C101—42no—
71C22×D4×C101—42no—
72C22×D4×C101D414yes—
73C23×C4×C101—22no—
74C23×C4×C101—22no—
75C23×C4×C101—22no—
76C23×C4×C101—24no—
77C23×C4×C101—24no—
78C23×C4×C101—22no—
79C23×C4×C101—22no—
80C23×C4×C101—42no—
81C23×C4×C101—42no—
82C23×C4×C101D414yescomplemented
83C23×C4×C101C2312yes—
84C23×C4×C101C2311yescharacteristic
85C23×C4×C101C2311yescharacteristic
86C23×C4×C101C2311yescharacteristic
87C23×C4×C101C2312yes—
88C23×C4×C101C2312yes—
89C23×C4×C101C2311yescharacteristic
90C23×C4×C101C2311yescharacteristic
91#120×C101—232no—
92C2×C4⋊C4×C101—24no—
93C2×C4⋊C4×C101—24no—
94C2×C4⋊C4×C101—42no—
95C2×C22⋊C4×C101—232no—
96C2×C22⋊C4×C101—24no—
97C2×C22⋊C4×C101—24no—
98C2×C22⋊C4×C101—22no—
99C2×C22⋊C4×C101—22no—
100C2×C22⋊C4×C101—24no—
101C2×C22⋊C4×C101—24no—
102C2×C22⋊C4×C101—24no—
103C2×C22⋊C4×C101—24no—
104C2×C22⋊C4×C101—24no—
105C2×C22⋊C4×C101—24no—
106C2×C22⋊C4×C101—24no—
107C2×C22⋊C4×C101—22no—
108C2×C22⋊C4×C101—24no—
109C2×C22⋊C4×C101—22no—
110C2×C22⋊C4×C101—22no—
111C2×C22⋊C4×C101—22no—
112C2×C22⋊C4×C101—22no—
113C2×C22⋊C4×C101—24no—
114C2×C22⋊C4×C101—24no—
115C2×C22⋊C4×C101—24no—
116C2×C22⋊C4×C101—22no—
117C2×C22⋊C4×C101—22no—
118C2×C22⋊C4×C101—22no—
119C2×C22⋊C4×C101—24no—
120C2×C22⋊C4×C101—24no—
121C2×C22⋊C4×C101—42no—
122C2×C22⋊C4×C101—42no—
123C2×C22⋊C4×C101—42no—
124C2×C22⋊C4×C101—42no—
125C2×C22⋊C4×C101D414yes—
126C2×C22⋊C4×C101D418yescomplemented
127#95×C101—24no—
128#95×C101—22no—
129#95×C101—22no—
130#95×C101—24no—
131#95×C101—24no—
132#95×C101—42no—
133C24×C101—22no—
134C24×C101—22no—
135C24×C101—22no—
136C24×C101—22no—
137C24×C101—28no—
138C24×C101—28no—
139C24×C101—216no—
140C24×C101—216no—
141C24×C101—28no—
142C24×C101—22no—
143C24×C101—22no—
144C24×C101—22no—
145C24×C101—22no—
146C24×C101—22no—
147C24×C101—22no—
148C24×C101—22no—
149C24×C101—22no—
150C24×C101—22no—
151C24×C101—22no—
152C24×C101—22no—
153C24×C101—22no—
154C24×C101—28no—
155C24×C101—28no—
156C24×C101—21no—
157C24×C101—22no—
158C24×C101—21no—
159C24×C101—21no—
160C24×C101—21no—
161C24×C101—21no—
162C24×C101—21no—
163C24×C101—22no—
164C24×C101—22no—
165C24×C101—22no—
166C24×C101—48no—
167C24×C101—48no—
168C24×C101—48no—
169C24×C101—48no—
170C24×C101—48no—
171C24×C101—48no—
172C24×C101—48no—
173C24×C101—48no—
174C24×C101—48no—
175C24×C101—44no—
176C24×C101—44no—
177C24×C101—48no—
178C24×C101—44no—
179C24×C101—44no—
180C24×C101—44no—
181C24×C101—44no—
182C24×C101C2×D412yes—
183C24×C101C2×D414yes—
184C24×C101C2×D414yes—
185C24×C101C2×D412yes—
186C24×C101C2×D412yes—
187C24×C101C2×D412yes—
188C24×C101C2×D412yes—
189C24×C101#4114yes—
190C24×C101#4112yes—
191C24×C101#4112yes—
192C24×C101#4112yes—
193C24×C101C2411yescharacteristic
194C2×D4×C101—216no—
195C2×D4×C101—28no—
196C2×D4×C101—28no—
197C2×D4×C101—28no—
198C2×D4×C101—48no—
199C2×D4×C101—48no—
200C2×D4×C101—48no—
201C2×D4×C101—48no—
202C2×D4×C101—48no—
203C2×D4×C101—48no—
204C2×D4×C101—44no—
205C2×D4×C101—44no—
206C2×D4×C101—44no—
207C2×D4×C101—44no—
208C22×C4×C101—21no—
209C22×C4×C101—21no—
210C22×C4×C101—22no—
211C22×C4×C101—28no—
212C22×C4×C101—28no—
213C22×C4×C101—21no—
214C22×C4×C101—21no—
215C22×C4×C101—22no—
216C22×C4×C101—22no—
217C22×C4×C101—22no—
218C22×C4×C101—22no—
219C22×C4×C101—22no—
220C22×C4×C101—21no—
221C22×C4×C101—21no—
222C22×C4×C101—22no—
223C22×C4×C101—22no—
224C22×C4×C101—21no—
225C22×C4×C101—22no—
226C22×C4×C101—21no—
227C22×C4×C101—21no—
228C22×C4×C101—21no—
229C22×C4×C101—22no—
230C22×C4×C101—22no—
231C22×C4×C101—22no—
232C22×C4×C101—22no—
233C22×C4×C101—22no—
234C22×C4×C101—22no—
235C22×C4×C101—28no—
236C22×C4×C101—21no—
237C22×C4×C101—22no—
238C22×C4×C101—22no—
239C22×C4×C101—21no—
240C22×C4×C101—22no—
241C22×C4×C101—22no—
242C22×C4×C101—21no—
243C22×C4×C101—21no—
244C22×C4×C101—22no—
245C22×C4×C101—21no—
246C22×C4×C101—22no—
247C22×C4×C101—21no—
248C22×C4×C101—22no—
249C22×C4×C101—22no—
250C22×C4×C101—22no—
251C22×C4×C101—22no—
252C22×C4×C101—22no—
253C22×C4×C101—44no—
254C22×C4×C101—48no—
255C22×C4×C101—48no—
256C22×C4×C101—48no—
257C22×C4×C101—48no—
258C22×C4×C101—44no—
259C22×C4×C101—44no—
260C22×C4×C101C2×D412yes—
261C22×C4×C101C2×D412yes—
262C22×C4×C101C2×D414yes—
263C22×C4×C101C2×D414yes—
264C22×C4×C101C2×D412yes—
265C22×C4×C101C2×D414yes—
266C4⋊C4×C101—48no—
267C22⋊C4×C101—216no—
268C22⋊C4×C101—216no—
269C22⋊C4×C101—28no—
270C22⋊C4×C101—216no—
271C22⋊C4×C101—48no—
272C22⋊C4×C101—44no—
273C22⋊C4×C101—48no—
274C22⋊C4×C101—44no—
275C22⋊C4×C101—48no—
276C22⋊C4×C101—44no—
277C22⋊C4×C101—44no—
278C23×C101—22no—
279C23×C101—24no—
280C23×C101—22no—
281C23×C101—24no—
282C23×C101—22no—
283C23×C101—24no—
284C23×C101—22no—
285C23×C101—24no—
286C23×C101—24no—
287C23×C101—24no—
288C23×C101—24no—
289C23×C101—24no—
290C23×C101—24no—
291C23×C101—24no—
292C23×C101—24no—
293C23×C101—24no—
294C23×C101—232no—
295C23×C101—24no—
296C23×C101—24no—
297C23×C101—24no—
298C23×C101—24no—
299C23×C101—24no—
300C23×C101—24no—
301C23×C101—24no—
302C23×C101—24no—
303C23×C101—24no—
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—22no—
314C23×C101—22no—
315C23×C101—22no—
316C23×C101—24no—
317C23×C101—24no—
318C23×C101—432no—
319C23×C101—432no—
320C23×C101—416no—
321C23×C101—416no—
322C23×C101—416no—
323C23×C101—416no—
324C23×C101—432no—
325C23×C101—432no—
326C23×C101—416no—
327C23×C101—42no—
328C23×C101—42no—
329C23×C101—42no—
330C23×C101—42no—
331C23×C101—42no—
332C23×C101—42no—
333C23×C101—42no—
334C23×C101—42no—
335C23×C101—42no—
336C23×C101—42no—
337C23×C101—42no—
338C23×C101—42no—
339C23×C101—42no—
340C23×C101—42no—
341C23×C101—42no—
342C23×C101—42no—
343C23×C101—416no—
344C23×C101—41no—
345C23×C101—41no—
346C23×C101—41no—
347C23×C101—42no—
348C23×C101—41no—
349C23×C101—42no—
350C23×C101—41no—
351C23×C101—41no—
352C23×C101—41no—
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#12014yes—
363C23×C101#12118yes—
364C23×C101#12114yes—
365C23×C101#12114yes—
366C23×C101#12114yes—
367C23×C101#12314yes—
368C23×C101#12314yes—
369C23×C101#12414yes—
370C23×C101C22×D411yescharacteristic
371C23×C101C22×D411yescharacteristic
372C23×C101C22×D411yescharacteristic
373C23×C101C22×D412yes—
374C23×C101C22×D411yescharacteristic
375C23×C101C2×#4111yescharacteristic
376C23×C101C2×#4111yescharacteristic
377C23×C101C2×#4111yescharacteristic
378C23×C101C2×#4112yes—
379C23×C101H(5,𝔽2)12yes—
380C23×C101H(5,𝔽2)12yes—
381D4×C101—432no—
382D4×C101—416no—
383C2×C4×C101—22no—
384C2×C4×C101—22no—
385C2×C4×C101—24no—
386C2×C4×C101—24no—
387C2×C4×C101—24no—
388C2×C4×C101—22no—
389C2×C4×C101—22no—
390C2×C4×C101—24no—
391C2×C4×C101—22no—
392C2×C4×C101—22no—
393C2×C4×C101—22no—
394C2×C4×C101—22no—
395C2×C4×C101—24no—
396C2×C4×C101—24no—
397C2×C4×C101—24no—
398C2×C4×C101—24no—
399C2×C4×C101—416no—
400C2×C4×C101—416no—
401C2×C4×C101—42no—
402C2×C4×C101—41no—
403C2×C4×C101—41no—
404C2×C4×C101—42no—
405C2×C4×C101—41no—
406C2×C4×C101—41no—
407C2×C4×C101—42no—
408C2×C4×C101—42no—
409C2×C4×C101—42no—
410C2×C4×C101—42no—
411C2×C4×C101—42no—
412C2×C4×C101—42no—
413C2×C4×C101—42no—
414C2×C4×C101—42no—
415C2×C4×C101—41no—
416C2×C4×C101—42no—
417C2×C4×C101—41no—
418C2×C4×C101—42no—
419C2×C4×C101—41no—
420C2×C4×C101—42no—
421C2×C4×C101—41no—
422C2×C4×C101—42no—
423C2×C4×C101—42no—
424C2×C4×C101—41no—
425C2×C4×C101—42no—
426C2×C4×C101—41no—
427C2×C4×C101—42no—
428C2×C4×C101—42no—
429C2×C4×C101—42no—
430C2×C4×C101—42no—
431C2×C4×C101—42no—
432C2×C4×C101#12014yescomplemented
433C22×C101—24no—
434C22×C101—24no—
435C22×C101—24no—
436C22×C101—24no—
437C22×C101—28no—
438C22×C101—24no—
439C22×C101—28no—
440C22×C101—28no—
441C22×C101—28no—
442C22×C101—24no—
443C22×C101—28no—
444C22×C101—28no—
445C22×C101—28no—
446C22×C101—464no—
447C22×C101—44no—
448C22×C101—44no—
449C22×C101—44no—
450C22×C101—44no—
451C22×C101—44no—
452C22×C101—44no—
453C22×C101—44no—
454C22×C101—44no—
455C22×C101—44no—
456C22×C101—44no—
457C22×C101—44no—
458C22×C101—44no—
459C22×C101—42no—
460C22×C101—42no—
461C22×C101—44no—
462C22×C101—44no—
463C22×C101—42no—
464C22×C101—81no—
465C22×C101—81no—
466C22×C101—81no—
467C22×C101—81no—
468C22×C101—82no—
469C22×C101—82no—
470C22×C101#39418yescomplemented
471C22×C101C2×#12011yescharacteristic
472C22×C101C2×#12011yescharacteristic
473C22×C101C2×#12111yescharacteristic
474C22×C101C2×#12112yes—
475C22×C101C2×#12111yescharacteristic
476C22×C101C2×#12111yescharacteristic
477C22×C101C2×#12311yescharacteristic
478C22×C101C2×#12311yescharacteristic
479C22×C101#52511yescharacteristic
480C22×C101#52512yes—
481C22×C101C2×#12411yescharacteristic
482C22×C101#53412yes—
483C22×C101#53411yescharacteristic
484C22×C101#53511yescharacteristic
485C22×C101#53812yes—
486C22×C101D4212yes—
487C22×C101D4212yes—
488C22×C101#54612yes—
489C22×C101#54612yes—
490C22×C101#54612yes—
491C22×C101#54612yes—
492C22×C101#55112yes—
493C22×C101#55112yes—
494C4×C101—24no—
495C4×C101—42no—
496C4×C101—44no—
497C4×C101—42no—
498C4×C101—44no—
499C4×C101—81no—
500C4×C101—81no—
501C4×C101—82no—
502#14725C10111yesmaximal, characteristic, direct product factor, Sylow
503C2×C101—28no—
504C2×C101—48no—
505C2×C101—82no—
506C2×C101C2×#39411yescharacteristic
507C2×C101#240811yescharacteristic
508C2×C101#241011yescharacteristic
509C2×C101#241012yes—
510C2×C101#241111yescharacteristic
511C2×C101#241212yes—
512C2×C101#241812yes—
513C2×C101#247212yes—
514C2×C101#253411yescharacteristic
515C2×C101#261711yescharacteristic
516C2×C101#284711yescharacteristic
517C22×#120C2×C10111yescharacteristic
518C23×C22⋊C4C2×C10111yescharacteristic, complemented
519C2×#394C2×C10112yescomplemented
520C2×#386C2×C10111yescharacteristic, complemented
521C2×#386C2×C10111yescharacteristic, complemented
522C2×#380C2×C10111yescharacteristic, complemented
523C2×#379C2×C10111yescharacteristic, complemented
524#1440C2×C10112yescomplemented
525#1439C2×C10112yescomplemented
526#1438C2×C10112yescomplemented
527C22⋊#95C2×C10111yescharacteristic, complemented
528C101#1472511yescharacteristic, direct product factor, Sylow
529C26C22×C10111yescharacteristic
530C23×D4C22×C10111yescharacteristic
531C23×D4C22×C10112yes—
532C24×C4C22×C10111yescharacteristic
533C24×C4C22×C10111yescharacteristic
534C2×#120—24no—
535C2×#120—24no—
536C2×#120—24no—
537C22×C4⋊C4C22×C10112yescomplemented
538C22×C22⋊C4—24no—
539C22×C22⋊C4—28no—
540C22×C22⋊C4C22×C10112yes—
541C22×C22⋊C4C22×C10112yes—
542C22×C22⋊C4C22×C10112yes—
543C22×C22⋊C4C22×C10111yescharacteristic
544C22×C22⋊C4C22×C10111yescharacteristic
545C22×C22⋊C4C22×C10111yescharacteristic
546C22×C22⋊C4C22×C10112yes—
547C22×C22⋊C4C22×C10112yes—
548C22×C22⋊C4C22×C10111yescharacteristic, complemented
549C22×C22⋊C4C22×C10112yescomplemented
550C22×C22⋊C4C22×C10111yescharacteristic, complemented
551#394—28no—
552#386—24no—
553#386—24no—
554#380—24no—
555#379—24no—
556C2×#95C22×C10112yescomplemented
557C2×#95C22×C10112yescomplemented
558C2×#95C22×C10111yescharacteristic, complemented
559C2×#95C22×C10112yescomplemented
560C2×#95C22×C10111yescharacteristic, complemented
561C2×#95C22×C10112yescomplemented
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C10114yes—
573C25C23×C10111yescharacteristic
574C25C23×C10112yes—
575C25C23×C10111yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C10114yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C10114yescomplemented
600C23×C4C23×C10112yes—
601C23×C4C23×C10111yescharacteristic
602C23×C4C23×C10111yescharacteristic
603C23×C4C23×C10111yescharacteristic
604C23×C4C23×C10112yes—
605C23×C4C23×C10112yes—
606C23×C4C23×C10111yescharacteristic
607C23×C4C23×C10111yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C10114yes—
643C2×C22⋊C4D4×C10118yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C10112yes—
700C24C2×D4×C10114yes—
701C24C2×D4×C10114yes—
702C24C2×D4×C10112yes—
703C24C2×D4×C10112yes—
704C24C2×D4×C10112yes—
705C24C2×D4×C10112yes—
706C24#41×C10114yes—
707C24#41×C10112yes—
708C24#41×C10112yes—
709C24#41×C10112yes—
710C24C24×C10111yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C10112yes—
778C22×C4C2×D4×C10112yes—
779C22×C4C2×D4×C10114yes—
780C22×C4C2×D4×C10114yes—
781C22×C4C2×D4×C10112yes—
782C22×C4C2×D4×C10114yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—432no—
841C23—432no—
842C23—416no—
843C23—416no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—416no—
861C23—41no—
862C23—42no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—42no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C10114yes—
880C23#121×C10118yes—
881C23#121×C10114yes—
882C23#121×C10114yes—
883C23#121×C10114yes—
884C23#123×C10114yes—
885C23#123×C10114yes—
886C23#124×C10114yes—
887C23C22×D4×C10111yescharacteristic
888C23C22×D4×C10111yescharacteristic
889C23C22×D4×C10111yescharacteristic
890C23C22×D4×C10112yes—
891C23C22×D4×C10111yescharacteristic
892C23C2×#41×C10111yescharacteristic
893C23C2×#41×C10111yescharacteristic
894C23C2×#41×C10111yescharacteristic
895C23C2×#41×C10112yes—
896C23H(5,𝔽2)×C10112yes—
897C23H(5,𝔽2)×C10112yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—24no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C10114yescomplemented
950C22—24no—
951C22—24no—
952C22—28no—
953C22—24no—
954C22—28no—
955C22—28no—
956C22—28no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—44no—
978C22—44no—
979C22—42no—
980C22—42no—
981C22—81no—
982C22—81no—
983C22—82no—
984C22—82no—
985C22—81no—
986C22—81no—
987C22#394×C10118yescomplemented
988C22C2×#120×C10111yescharacteristic
989C22C2×#120×C10111yescharacteristic
990C22C2×#121×C10111yescharacteristic
991C22C2×#121×C10111yescharacteristic
992C22C2×#121×C10112yes—
993C22C2×#121×C10111yescharacteristic
994C22C2×#123×C10111yescharacteristic
995C22C2×#123×C10111yescharacteristic
996C22#525×C10111yescharacteristic
997C22#525×C10112yes—
998C22C2×#124×C10111yescharacteristic
999C22#534×C10112yes—
1000C22#534×C10111yescharacteristic
1001C22#535×C10111yescharacteristic
1002C22#538×C10112yes—
1003C22D42×C10112yes—
1004C22D42×C10112yes—
1005C22#546×C10112yes—
1006C22#546×C10112yes—
1007C22#546×C10112yes—
1008C22#546×C10112yes—
1009C22#551×C10112yes—
1010C22#551×C10112yes—
1011C4—24no—
1012C4—44no—
1013C4—42no—
1014C4—44no—
1015C4—42no—
1016C4—82no—
1017C4—81no—
1018C4—81no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×#394×C10111yescharacteristic
1023C2C101×#240811yescharacteristic
1024C2C101×#241011yescharacteristic
1025C2C101×#241012yes—
1026C2C101×#241111yescharacteristic
1027C2C101×#241212yes—
1028C2C101×#241812yes—
1029C2C101×#247212yes—
1030C2C101×#253411yescharacteristic
1031C2C101×#261711yescharacteristic
1032C2C101×#284711yescharacteristic
subgroupG/H
center, socleC24×C101C24
commutator, Frattini, cosocleC24C24×C101
prime radicalC22×#120×C101C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C101C2semidirect
3. C2×#394×C101C2semidirect
4. C2×#386×C101C2semidirect
5. C2×#386×C101C2semidirect
6. C2×#380×C101C2semidirect
7. C2×#379×C101C2semidirect
8. C101×#1440C2semidirect
9. C101×#1439C2semidirect
10. C101×#1438C2semidirect
11. C101×C22⋊#95C2semidirect
20. C22×C4⋊C4×C101C22semidirect
31. C22×C22⋊C4×C101C22semidirect
32. C22×C22⋊C4×C101C22semidirect
33. C22×C22⋊C4×C101C22semidirect
39. C2×#95×C101C22semidirect
40. C2×#95×C101C22semidirect
41. C2×#95×C101C22semidirect
42. C2×#95×C101C22semidirect
43. C2×#95×C101C22semidirect
44. C2×#95×C101C22semidirect
82. C23×C4×C101D4semidirect
126. C2×C22⋊C4×C101D4semidirect
432. C2×C4×C101#120semidirect
470. C22×C101#394semidirect
502. #14725C101direct (N × H)
518. C23×C22⋊C4C2×C101semidirect
519. C2×#394C2×C101semidirect
520. C2×#386C2×C101semidirect
521. C2×#386C2×C101semidirect
522. C2×#380C2×C101semidirect
523. C2×#379C2×C101semidirect
524. #1440C2×C101semidirect
525. #1439C2×C101semidirect
526. #1438C2×C101semidirect
527. C22⋊#95C2×C101semidirect
528. C101#14725direct (N × H)
537. C22×C4⋊C4C22×C101semidirect
548. C22×C22⋊C4C22×C101semidirect
549. C22×C22⋊C4C22×C101semidirect
550. C22×C22⋊C4C22×C101semidirect
556. C2×#95C22×C101semidirect
557. C2×#95C22×C101semidirect
558. C2×#95C22×C101semidirect
559. C2×#95C22×C101semidirect
560. C2×#95C22×C101semidirect
561. C2×#95C22×C101semidirect
599. C23×C4D4×C101semidirect
643. C2×C22⋊C4D4×C101semidirect
949. C2×C4#120×C101semidirect
987. C22#394×C101semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1012
C23×C22⋊C4×C1012
C2×#394×C1012
C2×#386×C1012
C2×#380×C1012
C2×#379×C1012
C101×#14402
C101×#14392
C101×#14382
C101×C22⋊#952
#14725101