Finite Group Databasebeta

← C101×#14722 #38796873

Subgroups — C101×#14722 #38796873

Order 25856.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C101C211yesmaximal, characteristic, complemented
2C22×C4×D4×C101C211yesmaximal, characteristic, complemented
3C2×#394×C101C211yesmaximal, characteristic, complemented
4C2×#392×C101C212yesmaximal, complemented
5C2×#392×C101C211yesmaximal, characteristic, complemented
6C2×#386×C101C212yesmaximal, complemented
7C101×#1441C211yesmaximal, characteristic, complemented
8C101×#1439C211yesmaximal, characteristic, complemented
9C101×#1438C212yesmaximal, complemented
10C101×#1437C212yesmaximal, complemented
11C101×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C101C2211yescharacteristic
13C23×D4×C101C2212yes—
14C23×D4×C101C2211yescharacteristic
15C23×D4×C101C2212yes—
16C24×C4×C101C2211yescharacteristic
17C24×C4×C101C2211yescharacteristic
18C2×#121×C101—24no—
19C2×#121×C101—28no—
20C2×C4×D4×C101—24no—
21C2×C4×D4×C101—24no—
22C2×C4×D4×C101—24no—
23C22×C4⋊C4×C101C2211yescharacteristic
24C22×C4⋊C4×C101C2211yescharacteristic
25C22×C22⋊C4×C101C2211yescharacteristic
26C22×C22⋊C4×C101C2212yes—
27C22×C22⋊C4×C101C2212yes—
28C22×C22⋊C4×C101C2212yes—
29C22×C22⋊C4×C101C2212yes—
30C22×C22⋊C4×C101C2212yes—
31C22×C22⋊C4×C101C2211yescharacteristic
32C22×C22⋊C4×C101C2212yes—
33C22×C42×C101C2211yescharacteristic
34#394×C101—24no—
35#392×C101—28no—
36#392×C101—24no—
37#386×C101—28no—
38C2×#95×C101C2212yes—
39C2×#95×C101C2211yescharacteristic
40C2×#95×C101C2211yescharacteristic
41C2×#95×C101C2212yes—
42C2×#95×C101C2212yes—
43C2×#95×C101C2212yes—
44C25×C101C2312yes—
45C25×C101C2311yescharacteristic
46C25×C101C2311yescharacteristic
47C22×D4×C101—22no—
48C22×D4×C101—22no—
49C22×D4×C101—22no—
50C22×D4×C101—22no—
51C22×D4×C101—24no—
52C22×D4×C101—24no—
53C22×D4×C101—24no—
54C22×D4×C101—24no—
55C22×D4×C101—24no—
56C22×D4×C101—24no—
57C22×D4×C101—24no—
58C22×D4×C101—24no—
59C22×D4×C101—24no—
60C22×D4×C101—22no—
61C22×D4×C101—24no—
62C22×D4×C101—22no—
63C22×D4×C101—22no—
64C22×D4×C101—22no—
65C22×D4×C101—22no—
66C22×D4×C101—24no—
67C22×D4×C101—42no—
68C22×D4×C101—42no—
69C22×D4×C101—42no—
70C22×D4×C101—42no—
71C22×D4×C101—42no—
72C22×D4×C101D414yescomplemented
73C23×C4×C101—22no—
74C23×C4×C101—22no—
75C23×C4×C101—22no—
76C23×C4×C101—22no—
77C23×C4×C101—22no—
78C23×C4×C101—24no—
79C23×C4×C101—24no—
80C23×C4×C101—42no—
81C23×C4×C101—42no—
82C23×C4×C101D414yescomplemented
83C23×C4×C101C2312yes—
84C23×C4×C101C2311yescharacteristic
85C23×C4×C101C2311yescharacteristic
86C23×C4×C101C2312yes—
87C23×C4×C101C2312yes—
88C23×C4×C101C2311yescharacteristic
89C23×C4×C101C2311yescharacteristic
90C23×C4×C101C2311yescharacteristic
91#121×C101—232no—
92C4×D4×C101—232no—
93C2×C4⋊C4×C101—22no—
94C2×C4⋊C4×C101—22no—
95C2×C4⋊C4×C101—24no—
96C2×C4⋊C4×C101—22no—
97C2×C4⋊C4×C101D414yescomplemented
98C2×C22⋊C4×C101—22no—
99C2×C22⋊C4×C101—22no—
100C2×C22⋊C4×C101—22no—
101C2×C22⋊C4×C101—22no—
102C2×C22⋊C4×C101—22no—
103C2×C22⋊C4×C101—24no—
104C2×C22⋊C4×C101—24no—
105C2×C22⋊C4×C101—24no—
106C2×C22⋊C4×C101—24no—
107C2×C22⋊C4×C101—24no—
108C2×C22⋊C4×C101—24no—
109C2×C22⋊C4×C101—24no—
110C2×C22⋊C4×C101—24no—
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—42no—
117C2×C22⋊C4×C101—42no—
118C2×C22⋊C4×C101—42no—
119C2×C22⋊C4×C101—42no—
120C2×C22⋊C4×C101D414yescomplemented
121C2×C22⋊C4×C101D418yescomplemented
122C2×C42×C101—22no—
123C2×C42×C101—22no—
124C2×C42×C101—22no—
125#95×C101—24no—
126#95×C101—24no—
127#95×C101—22no—
128#95×C101—24no—
129#95×C101—22no—
130#95×C101—42no—
131C24×C101—21no—
132C24×C101—21no—
133C24×C101—21no—
134C24×C101—21no—
135C24×C101—22no—
136C24×C101—22no—
137C24×C101—22no—
138C24×C101—21no—
139C24×C101—21no—
140C24×C101—21no—
141C24×C101—21no—
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—22no—
155C24×C101—22no—
156C24×C101—22no—
157C24×C101—22no—
158C24×C101—22no—
159C24×C101—22no—
160C24×C101—22no—
161C24×C101C2×D414yes—
162C24×C101C2×D412yes—
163C24×C101C2×D412yes—
164C24×C101C2×D412yes—
165C24×C101C2×D412yes—
166C24×C101#4112yes—
167C24×C101#4112yes—
168C24×C101C2411yescharacteristic
169C2×D4×C101—28no—
170C2×D4×C101—28no—
171C2×D4×C101—28no—
172C2×D4×C101—28no—
173C2×D4×C101—28no—
174C2×D4×C101—28no—
175C2×D4×C101—28no—
176C2×D4×C101—216no—
177C2×D4×C101—216no—
178C2×D4×C101—28no—
179C2×D4×C101—48no—
180C2×D4×C101—48no—
181C2×D4×C101—48no—
182C2×D4×C101—48no—
183C2×D4×C101—48no—
184C2×D4×C101—48no—
185C2×D4×C101—44no—
186C2×D4×C101—48no—
187C2×D4×C101—48no—
188C2×D4×C101—48no—
189C2×D4×C101—48no—
190C2×D4×C101—48no—
191C2×D4×C101—48no—
192C2×D4×C101—48no—
193C2×D4×C101—48no—
194C2×D4×C101—44no—
195C22×C4×C101—21no—
196C22×C4×C101—21no—
197C22×C4×C101—21no—
198C22×C4×C101—21no—
199C22×C4×C101—22no—
200C22×C4×C101—21no—
201C22×C4×C101—21no—
202C22×C4×C101—22no—
203C22×C4×C101—22no—
204C22×C4×C101—28no—
205C22×C4×C101—22no—
206C22×C4×C101—22no—
207C22×C4×C101—22no—
208C22×C4×C101—22no—
209C22×C4×C101—22no—
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—21no—
214C22×C4×C101—22no—
215C22×C4×C101—22no—
216C22×C4×C101—22no—
217C22×C4×C101—22no—
218C22×C4×C101—22no—
219C22×C4×C101—22no—
220C22×C4×C101—22no—
221C22×C4×C101—22no—
222C22×C4×C101—22no—
223C22×C4×C101—22no—
224C22×C4×C101—22no—
225C22×C4×C101—28no—
226C22×C4×C101—28no—
227C22×C4×C101—22no—
228C22×C4×C101—22no—
229C22×C4×C101—22no—
230C22×C4×C101—22no—
231C22×C4×C101—22no—
232C22×C4×C101—22no—
233C22×C4×C101—22no—
234C22×C4×C101—44no—
235C22×C4×C101—48no—
236C22×C4×C101—48no—
237C22×C4×C101—48no—
238C22×C4×C101—48no—
239C22×C4×C101—44no—
240C22×C4×C101—44no—
241C22×C4×C101C2×D414yes—
242C22×C4×C101C2×D412yes—
243C22×C4×C101C2×D412yes—
244C22×C4×C101C2×D414yes—
245C22×C4×C101C2×D412yes—
246C22×C4×C101C2×D412yes—
247C22×C4×C101C2×D412yes—
248C22×C4×C101C2×D412yes—
249C22×C4×C101C2×D412yes—
250C22×C4×C101C2×D412yes—
251C22×C4×C101#4114yes—
252C22×C4×C101#4112yes—
253C4⋊C4×C101—28no—
254C4⋊C4×C101—28no—
255C22⋊C4×C101—28no—
256C22⋊C4×C101—28no—
257C22⋊C4×C101—216no—
258C22⋊C4×C101—48no—
259C22⋊C4×C101—48no—
260C22⋊C4×C101—48no—
261C22⋊C4×C101—48no—
262C22⋊C4×C101—48no—
263C42×C101—28no—
264C23×C101—22no—
265C23×C101—22no—
266C23×C101—22no—
267C23×C101—22no—
268C23×C101—22no—
269C23×C101—22no—
270C23×C101—22no—
271C23×C101—22no—
272C23×C101—22no—
273C23×C101—22no—
274C23×C101—22no—
275C23×C101—22no—
276C23×C101—22no—
277C23×C101—24no—
278C23×C101—22no—
279C23×C101—22no—
280C23×C101—22no—
281C23×C101—24no—
282C23×C101—24no—
283C23×C101—24no—
284C23×C101—24no—
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—24no—
295C23×C101—24no—
296C23×C101—24no—
297C23×C101—41no—
298C23×C101—42no—
299C23×C101—42no—
300C23×C101—42no—
301C23×C101—41no—
302C23×C101—41no—
303C23×C101—41no—
304C23×C101—42no—
305C23×C101—42no—
306C23×C101—42no—
307C23×C101—42no—
308C23×C101—42no—
309C23×C101—42no—
310C23×C101—42no—
311C23×C101—42no—
312C23×C101—42no—
313C23×C101—42no—
314C23×C101—42no—
315C23×C101—42no—
316C23×C101—42no—
317C23×C101—42no—
318C23×C101—42no—
319C23×C101—42no—
320C23×C101—42no—
321C23×C101—42no—
322C23×C101—42no—
323C23×C101—42no—
324C23×C101—42no—
325C23×C101—42no—
326C23×C101—42no—
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#12114yes—
344C23×C101#12114yescomplemented
345C23×C101C22×D411yescharacteristic
346C23×C101C22×D411yescharacteristic
347C23×C101C22×D411yescharacteristic
348C23×C101C22×D412yes—
349C23×C101C22×D411yescharacteristic
350C23×C101C2×#4111yescharacteristic
351C23×C101C2×#4111yescharacteristic
352C23×C101C2×#4111yescharacteristic
353C23×C101C2×#4112yes—
354C23×C101H(5,𝔽2)12yes—
355C23×C101H(5,𝔽2)12yes—
356D4×C101—232no—
357D4×C101—416no—
358D4×C101—432no—
359D4×C101—432no—
360C2×C4×C101—22no—
361C2×C4×C101—22no—
362C2×C4×C101—22no—
363C2×C4×C101—22no—
364C2×C4×C101—22no—
365C2×C4×C101—22no—
366C2×C4×C101—22no—
367C2×C4×C101—22no—
368C2×C4×C101—22no—
369C2×C4×C101—22no—
370C2×C4×C101—24no—
371C2×C4×C101—24no—
372C2×C4×C101—24no—
373C2×C4×C101—24no—
374C2×C4×C101—22no—
375C2×C4×C101—22no—
376C2×C4×C101—24no—
377C2×C4×C101—24no—
378C2×C4×C101—24no—
379C2×C4×C101—24no—
380C2×C4×C101—24no—
381C2×C4×C101—24no—
382C2×C4×C101—24no—
383C2×C4×C101—24no—
384C2×C4×C101—416no—
385C2×C4×C101—416no—
386C2×C4×C101—41no—
387C2×C4×C101—42no—
388C2×C4×C101—42no—
389C2×C4×C101—41no—
390C2×C4×C101—41no—
391C2×C4×C101—41no—
392C2×C4×C101—42no—
393C2×C4×C101—42no—
394C2×C4×C101—42no—
395C2×C4×C101—42no—
396C2×C4×C101—42no—
397C2×C4×C101—42no—
398C2×C4×C101—42no—
399C2×C4×C101—42no—
400C2×C4×C101—42no—
401C2×C4×C101—42no—
402C2×C4×C101—42no—
403C2×C4×C101—42no—
404C2×C4×C101—42no—
405C2×C4×C101—42no—
406C2×C4×C101—42no—
407C2×C4×C101#12014yes—
408C2×C4×C101#12014yes—
409C2×C4×C101#12114yescomplemented
410C22×C101—24no—
411C22×C101—24no—
412C22×C101—24no—
413C22×C101—28no—
414C22×C101—24no—
415C22×C101—42no—
416C22×C101—42no—
417C22×C101—42no—
418C22×C101—42no—
419C22×C101—42no—
420C22×C101—42no—
421C22×C101—42no—
422C22×C101—44no—
423C22×C101—44no—
424C22×C101—44no—
425C22×C101—42no—
426C22×C101—42no—
427C22×C101—44no—
428C22×C101—44no—
429C22×C101—44no—
430C22×C101—44no—
431C22×C101—42no—
432C22×C101—44no—
433C22×C101—44no—
434C22×C101—44no—
435C22×C101—44no—
436C22×C101—44no—
437C22×C101—44no—
438C22×C101—44no—
439C22×C101—82no—
440C22×C101—82no—
441C22×C101—82no—
442C22×C101—82no—
443C22×C101—82no—
444C22×C101—82no—
445C22×C101—82no—
446C22×C101—82no—
447C22×C101C2×#12011yescharacteristic
448C22×C101C2×#12011yescharacteristic
449C22×C101C2×#12111yescharacteristic
450C22×C101C2×#12111yescharacteristic
451C22×C101C2×#12111yescharacteristic
452C22×C101#52511yescharacteristic
453C22×C101#52511yescharacteristic
454C22×C101#52511yescharacteristic
455C22×C101#52512yes—
456C22×C101#53212yes—
457C22×C101#53211yescharacteristic
458C22×C101#53411yescharacteristic
459C22×C101#53511yescharacteristic
460C22×C101#53812yes—
461C22×C101#54012yes—
462C22×C101D4212yes—
463C22×C101D4212yes—
464C22×C101D4212yes—
465C22×C101#54612yes—
466C22×C101#54612yes—
467C22×C101#54612yes—
468C22×C101#55012yes—
469C22×C101#55312yes—
470C4×C101—24no—
471C4×C101—24no—
472C4×C101—24no—
473C4×C101—42no—
474C4×C101—44no—
475C4×C101—44no—
476C4×C101—42no—
477C4×C101—82no—
478#14722C10111yesmaximal, characteristic, direct product factor, Sylow
479C2×C101—44no—
480C2×C101—44no—
481C2×C101—84no—
482C2×C101#238811yescharacteristic
483C2×C101#240311yescharacteristic
484C2×C101#240811yescharacteristic
485C2×C101#242412yes—
486C2×C101#242812yes—
487C2×C101#243111yescharacteristic
488C2×C101#245612yes—
489C2×C101#246412yes—
490C2×C101#254311yescharacteristic
491C2×C101#263511yescharacteristic
492C2×C101#284711yescharacteristic
493C22×#121C2×C10111yescharacteristic, complemented
494C22×C4×D4C2×C10111yescharacteristic, complemented
495C2×#394C2×C10111yescharacteristic, complemented
496C2×#392C2×C10112yescomplemented
497C2×#392C2×C10111yescharacteristic, complemented
498C2×#386C2×C10112yescomplemented
499#1441C2×C10111yescharacteristic, complemented
500#1439C2×C10111yescharacteristic, complemented
501#1438C2×C10112yescomplemented
502#1437C2×C10112yescomplemented
503C22⋊#95C2×C10111yescharacteristic, complemented
504C101#1472211yescharacteristic, direct product factor, Sylow
505C23×D4C22×C10111yescharacteristic
506C23×D4C22×C10112yes—
507C23×D4C22×C10111yescharacteristic
508C23×D4C22×C10112yes—
509C24×C4C22×C10111yescharacteristic
510C24×C4C22×C10111yescharacteristic
511C2×#121—24no—
512C2×#121—28no—
513C2×C4×D4—24no—
514C2×C4×D4—24no—
515C2×C4×D4—24no—
516C22×C4⋊C4C22×C10111yescharacteristic
517C22×C4⋊C4C22×C10111yescharacteristic
518C22×C22⋊C4C22×C10112yes—
519C22×C22⋊C4C22×C10111yescharacteristic
520C22×C22⋊C4C22×C10112yes—
521C22×C22⋊C4C22×C10112yes—
522C22×C22⋊C4C22×C10112yes—
523C22×C22⋊C4C22×C10112yes—
524C22×C22⋊C4C22×C10111yescharacteristic
525C22×C22⋊C4C22×C10112yes—
526C22×C42C22×C10111yescharacteristic
527#394—24no—
528#392—28no—
529#392—24no—
530#386—28no—
531C2×#95C22×C10111yescharacteristic
532C2×#95C22×C10112yes—
533C2×#95C22×C10111yescharacteristic
534C2×#95C22×C10112yes—
535C2×#95C22×C10112yes—
536C2×#95C22×C10112yes—
537C25C23×C10112yes—
538C25C23×C10111yescharacteristic
539C25C23×C10111yescharacteristic
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4—22no—
554C22×D4—24no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—42no—
564C22×D4—42no—
565C22×D4D4×C10114yescomplemented
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—24no—
572C23×C4—24no—
573C23×C4—42no—
574C23×C4—42no—
575C23×C4D4×C10114yescomplemented
576C23×C4C23×C10112yes—
577C23×C4C23×C10111yescharacteristic
578C23×C4C23×C10111yescharacteristic
579C23×C4C23×C10112yes—
580C23×C4C23×C10112yes—
581C23×C4C23×C10111yescharacteristic
582C23×C4C23×C10111yescharacteristic
583C23×C4C23×C10111yescharacteristic
584#121—232no—
585C4×D4—232no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4D4×C10114yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4D4×C10114yescomplemented
614C2×C22⋊C4D4×C10118yescomplemented
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618#95—24no—
619#95—24no—
620#95—22no—
621#95—24no—
622#95—22no—
623#95—42no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24C2×D4×C10114yes—
655C24C2×D4×C10112yes—
656C24C2×D4×C10112yes—
657C24C2×D4×C10112yes—
658C24C2×D4×C10112yes—
659C24#41×C10112yes—
660C24#41×C10112yes—
661C24C24×C10111yescharacteristic
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—28no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4C2×D4×C10114yes—
735C22×C4C2×D4×C10112yes—
736C22×C4C2×D4×C10112yes—
737C22×C4C2×D4×C10114yes—
738C22×C4C2×D4×C10112yes—
739C22×C4C2×D4×C10112yes—
740C22×C4C2×D4×C10112yes—
741C22×C4C2×D4×C10112yes—
742C22×C4C2×D4×C10112yes—
743C22×C4C2×D4×C10112yes—
744C22×C4#41×C10114yes—
745C22×C4#41×C10112yes—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—216no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—24no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—41no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23#121×C10114yes—
837C23#121×C10114yescomplemented
838C23C22×D4×C10111yescharacteristic
839C23C22×D4×C10111yescharacteristic
840C23C22×D4×C10111yescharacteristic
841C23C22×D4×C10112yes—
842C23C22×D4×C10111yescharacteristic
843C23C2×#41×C10111yescharacteristic
844C23C2×#41×C10111yescharacteristic
845C23C2×#41×C10111yescharacteristic
846C23C2×#41×C10112yes—
847C23H(5,𝔽2)×C10112yes—
848C23H(5,𝔽2)×C10112yes—
849D4—232no—
850D4—416no—
851D4—432no—
852D4—432no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4#120×C10114yes—
901C2×C4#120×C10114yes—
902C2×C4#121×C10114yescomplemented
903C22—24no—
904C22—28no—
905C22—24no—
906C22—24no—
907C22—24no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—44no—
912C22—44no—
913C22—44no—
914C22—42no—
915C22—42no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×#120×C10111yescharacteristic
941C22C2×#120×C10111yescharacteristic
942C22C2×#121×C10111yescharacteristic
943C22C2×#121×C10111yescharacteristic
944C22C2×#121×C10111yescharacteristic
945C22#525×C10112yes—
946C22#525×C10111yescharacteristic
947C22#525×C10111yescharacteristic
948C22#525×C10111yescharacteristic
949C22#532×C10112yes—
950C22#532×C10111yescharacteristic
951C22#534×C10111yescharacteristic
952C22#535×C10111yescharacteristic
953C22#538×C10112yes—
954C22#540×C10112yes—
955C22D42×C10112yes—
956C22D42×C10112yes—
957C22D42×C10112yes—
958C22#546×C10112yes—
959C22#546×C10112yes—
960C22#546×C10112yes—
961C22#550×C10112yes—
962C22#553×C10112yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—42no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C101×#238811yescharacteristic
975C2C101×#240311yescharacteristic
976C2C101×#240811yescharacteristic
977C2C101×#242412yes—
978C2C101×#242812yes—
979C2C101×#243111yescharacteristic
980C2C101×#245612yes—
981C2C101×#246412yes—
982C2C101×#254311yescharacteristic
983C2C101×#263511yescharacteristic
984C2C101×#284711yescharacteristic
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×C4×D4×C101C2semidirect
3. C2×#394×C101C2semidirect
4. C2×#392×C101C2semidirect
5. C2×#392×C101C2semidirect
6. C2×#386×C101C2semidirect
7. C101×#1441C2semidirect
8. C101×#1439C2semidirect
9. C101×#1438C2semidirect
10. C101×#1437C2semidirect
11. C101×C22⋊#95C2semidirect
72. C22×D4×C101D4semidirect
82. C23×C4×C101D4semidirect
97. C2×C4⋊C4×C101D4semidirect
120. C2×C22⋊C4×C101D4semidirect
121. C2×C22⋊C4×C101D4semidirect
344. C23×C101#121semidirect
409. C2×C4×C101#121semidirect
478. #14722C101direct (N × H)
493. C22×#121C2×C101semidirect
494. C22×C4×D4C2×C101semidirect
495. C2×#394C2×C101semidirect
496. C2×#392C2×C101semidirect
497. C2×#392C2×C101semidirect
498. C2×#386C2×C101semidirect
499. #1441C2×C101semidirect
500. #1439C2×C101semidirect
501. #1438C2×C101semidirect
502. #1437C2×C101semidirect
503. C22⋊#95C2×C101semidirect
504. C101#14722direct (N × H)
565. C22×D4D4×C101semidirect
575. C23×C4D4×C101semidirect
590. C2×C4⋊C4D4×C101semidirect
613. C2×C22⋊C4D4×C101semidirect
614. C2×C22⋊C4D4×C101semidirect
837. C23#121×C101semidirect
902. C2×C4#121×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×C4×D4×C1012
C2×#394×C1012
C2×#392×C1012
C2×#386×C1012
C101×#14412
C101×#14392
C101×#14382
C101×#14372
C101×C22⋊#952
#14722101