Finite Group Databasebeta

← C101×#13873 #38796024

Subgroups — C101×#13873 #38796024

Order 25856.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C101C211yesmaximal, characteristic
2C2×#388×C101C212yesmaximal, complemented
3C2×#380×C101C211yesmaximal, characteristic, complemented
4C2×#379×C101C211yesmaximal, characteristic
5C2×#379×C101C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C101C211yesmaximal, characteristic, complemented
7C101×#1440C212yesmaximal, complemented
8C101×#1439C212yesmaximal, complemented
9C101×#1437C212yesmaximal, complemented
10C101×C22⋊#95C211yesmaximal, characteristic, complemented
11C101×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C101C2211yescharacteristic
13C24×C4×C101C2211yescharacteristic
14C24×C4×C101C2211yescharacteristic
15C22×C4⋊C4×C101C2212yescomplemented
16C22×C22⋊C4×C101—28no—
17C22×C22⋊C4×C101C418yescomplemented
18C22×C22⋊C4×C101C2211yescharacteristic
19C22×C22⋊C4×C101C2211yescharacteristic
20C22×C22⋊C4×C101C2212yes—
21C22×C22⋊C4×C101C2212yes—
22C22×C22⋊C4×C101C2212yes—
23C22×C22⋊C4×C101C2212yes—
24C22×C22⋊C4×C101C2211yescharacteristic
25C22×C22⋊C4×C101C2211yescharacteristic
26C22×C22⋊C4×C101C2211yescharacteristic
27C22×C22⋊C4×C101C2211yescharacteristic
28C22×C22⋊C4×C101C2211yescharacteristic
29C22×C22⋊C4×C101C2211yescharacteristic
30C22×C42×C101C2212yescomplemented
31#388×C101—28no—
32#380×C101—24no—
33#379×C101—24no—
34#379×C101—24no—
35C4×C22⋊C4×C101—24no—
36C2×#95×C101C2212yescomplemented
37C2×#95×C101C2212yescomplemented
38C2×#95×C101C2212yescomplemented
39C2×#95×C101C2212yescomplemented
40C2×#95×C101C2212yescomplemented
41C2×#95×C101C2212yescomplemented
42C25×C101—24no—
43C25×C101—24no—
44C25×C101—22no—
45C25×C101—22no—
46C25×C101—22no—
47C25×C101—22no—
48C25×C101—22no—
49C25×C101—22no—
50C25×C101—42no—
51C25×C101—42no—
52C25×C101C2×C414yes—
53C25×C101C2311yescharacteristic
54C25×C101C2311yescharacteristic
55C25×C101C2311yescharacteristic
56C23×C4×C101—22no—
57C23×C4×C101—22no—
58C23×C4×C101—22no—
59C23×C4×C101—22no—
60C23×C4×C101—24no—
61C23×C4×C101—24no—
62C23×C4×C101—42no—
63C23×C4×C101—42no—
64C23×C4×C101C2×C414yes—
65C23×C4×C101C2×C414yes—
66C23×C4×C101C2312yes—
67C23×C4×C101C2312yes—
68C23×C4×C101C2311yescharacteristic
69C23×C4×C101C2311yescharacteristic
70C23×C4×C101C2312yes—
71C23×C4×C101C2312yes—
72C23×C4×C101C2311yescharacteristic
73C23×C4×C101C2311yescharacteristic
74C2×C4⋊C4×C101—24no—
75C2×C4⋊C4×C101—24no—
76C2×C4⋊C4×C101—42no—
77C2×C22⋊C4×C101—24no—
78C2×C22⋊C4×C101—22no—
79C2×C22⋊C4×C101—22no—
80C2×C22⋊C4×C101—22no—
81C2×C22⋊C4×C101—22no—
82C2×C22⋊C4×C101—24no—
83C2×C22⋊C4×C101—24no—
84C2×C22⋊C4×C101—232no—
85C2×C22⋊C4×C101—22no—
86C2×C22⋊C4×C101—22no—
87C2×C22⋊C4×C101—22no—
88C2×C22⋊C4×C101—24no—
89C2×C22⋊C4×C101—24no—
90C2×C22⋊C4×C101—24no—
91C2×C22⋊C4×C101—24no—
92C2×C22⋊C4×C101—22no—
93C2×C22⋊C4×C101—22no—
94C2×C22⋊C4×C101—22no—
95C2×C22⋊C4×C101—24no—
96C2×C22⋊C4×C101—24no—
97C2×C22⋊C4×C101—24no—
98C2×C22⋊C4×C101—24no—
99C2×C22⋊C4×C101—42no—
100C2×C22⋊C4×C101—42no—
101C2×C22⋊C4×C101—42no—
102C2×C22⋊C4×C101—42no—
103C2×C22⋊C4×C101C2×C414yes—
104C2×C22⋊C4×C101C2×C414yes—
105C2×C22⋊C4×C101C2×C414yes—
106C2×C22⋊C4×C101C2×C414yes—
107C2×C22⋊C4×C101D414yes—
108C2×C22⋊C4×C101D414yes—
109C2×C22⋊C4×C101D418yes—
110C2×C42×C101—24no—
111C2×C42×C101—24no—
112C2×C42×C101—42no—
113#95×C101—24no—
114#95×C101—24no—
115#95×C101—24no—
116#95×C101—24no—
117#95×C101—42no—
118#95×C101—42no—
119C24×C101—22no—
120C24×C101—22no—
121C24×C101—22no—
122C24×C101—22no—
123C24×C101—216no—
124C24×C101—216no—
125C24×C101—28no—
126C24×C101—28no—
127C24×C101—28no—
128C24×C101—22no—
129C24×C101—21no—
130C24×C101—21no—
131C24×C101—21no—
132C24×C101—21no—
133C24×C101—21no—
134C24×C101—21no—
135C24×C101—22no—
136C24×C101—21no—
137C24×C101—21no—
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—28no—
147C24×C101—28no—
148C24×C101—44no—
149C24×C101—44no—
150C24×C101—48no—
151C24×C101—48no—
152C24×C101—48no—
153C24×C101—48no—
154C24×C101—48no—
155C24×C101—48no—
156C24×C101—48no—
157C24×C101—48no—
158C24×C101—48no—
159C24×C101—48no—
160C24×C101—44no—
161C24×C101—44no—
162C24×C101—44no—
163C24×C101—44no—
164C24×C101C22×C412yes—
165C24×C101C22×C412yes—
166C24×C101C22×C412yes—
167C24×C101C2×D414yes—
168C24×C101C2×D412yes—
169C24×C101C2×D412yes—
170C24×C101#4114yes—
171C24×C101#4112yes—
172C24×C101#4112yes—
173C24×C101#4112yes—
174C24×C101#4112yes—
175C24×C101C2411yescharacteristic
176C22×C4×C101—21no—
177C22×C4×C101—21no—
178C22×C4×C101—21no—
179C22×C4×C101—21no—
180C22×C4×C101—22no—
181C22×C4×C101—22no—
182C22×C4×C101—28no—
183C22×C4×C101—28no—
184C22×C4×C101—21no—
185C22×C4×C101—21no—
186C22×C4×C101—22no—
187C22×C4×C101—22no—
188C22×C4×C101—22no—
189C22×C4×C101—22no—
190C22×C4×C101—22no—
191C22×C4×C101—22no—
192C22×C4×C101—22no—
193C22×C4×C101—22no—
194C22×C4×C101—22no—
195C22×C4×C101—22no—
196C22×C4×C101—21no—
197C22×C4×C101—21no—
198C22×C4×C101—22no—
199C22×C4×C101—22no—
200C22×C4×C101—22no—
201C22×C4×C101—22no—
202C22×C4×C101—22no—
203C22×C4×C101—22no—
204C22×C4×C101—28no—
205C22×C4×C101—28no—
206C22×C4×C101—22no—
207C22×C4×C101—22no—
208C22×C4×C101—22no—
209C22×C4×C101—22no—
210C22×C4×C101—22no—
211C22×C4×C101—22no—
212C22×C4×C101—22no—
213C22×C4×C101—22no—
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—44no—
221C22×C4×C101—44no—
222C22×C4×C101—48no—
223C22×C4×C101—48no—
224C22×C4×C101—48no—
225C22×C4×C101—48no—
226C22×C4×C101C22×C412yes—
227C22×C4×C101C22×C412yes—
228C22×C4×C101C22×C412yes—
229C22×C4×C101C22×C412yes—
230C22×C4×C101C2×D414yes—
231C22×C4×C101C2×D414yes—
232C22×C4×C101C2×D414yes—
233C22×C4×C101C2×D414yes—
234C4⋊C4×C101—48no—
235C22⋊C4×C101—28no—
236C22⋊C4×C101—28no—
237C22⋊C4×C101—28no—
238C22⋊C4×C101—28no—
239C22⋊C4×C101—28no—
240C22⋊C4×C101—48no—
241C22⋊C4×C101—48no—
242C22⋊C4×C101—48no—
243C22⋊C4×C101—48no—
244C22⋊C4×C101—44no—
245C22⋊C4×C101—44no—
246C22⋊C4×C101C22⋊C4116yescomplemented
247C42×C101—48no—
248C23×C101—22no—
249C23×C101—22no—
250C23×C101—22no—
251C23×C101—22no—
252C23×C101—24no—
253C23×C101—24no—
254C23×C101—24no—
255C23×C101—24no—
256C23×C101—24no—
257C23×C101—24no—
258C23×C101—24no—
259C23×C101—24no—
260C23×C101—24no—
261C23×C101—24no—
262C23×C101—24no—
263C23×C101—24no—
264C23×C101—232no—
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—24no—
279C23×C101—24no—
280C23×C101—24no—
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—416no—
290C23×C101—416no—
291C23×C101—416no—
292C23×C101—416no—
293C23×C101—416no—
294C23×C101—432no—
295C23×C101—432no—
296C23×C101—432no—
297C23×C101—432no—
298C23×C101—41no—
299C23×C101—41no—
300C23×C101—41no—
301C23×C101—41no—
302C23×C101—41no—
303C23×C101—41no—
304C23×C101—41no—
305C23×C101—41no—
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—416no—
319C23×C101C2×C22⋊C414yes—
320C23×C101#11714yes—
321C23×C101#11714yes—
322C23×C101C4×D414yes—
323C23×C101C4×D414yes—
324C23×C101#12114yes—
325C23×C101#12314yes—
326C23×C101#12414yes—
327C23×C101#12614yes—
328C23×C101C23×C411yescharacteristic
329C23×C101C22×D412yes—
330C23×C101C22×D411yescharacteristic
331C23×C101C22×D411yescharacteristic
332C23×C101C2×#4111yescharacteristic
333C23×C101C2×#4111yescharacteristic
334C23×C101C2×#4112yes—
335C23×C101C2×#4111yescharacteristic
336C23×C101C2×#4111yescharacteristic
337C23×C101H(5,𝔽2)12yes—
338C23×C101H(5,𝔽2)12yes—
339C2×C4×C101—22no—
340C2×C4×C101—22no—
341C2×C4×C101—22no—
342C2×C4×C101—22no—
343C2×C4×C101—24no—
344C2×C4×C101—24no—
345C2×C4×C101—24no—
346C2×C4×C101—24no—
347C2×C4×C101—22no—
348C2×C4×C101—22no—
349C2×C4×C101—22no—
350C2×C4×C101—22no—
351C2×C4×C101—22no—
352C2×C4×C101—22no—
353C2×C4×C101—24no—
354C2×C4×C101—24no—
355C2×C4×C101—24no—
356C2×C4×C101—24no—
357C2×C4×C101—24no—
358C2×C4×C101—24no—
359C2×C4×C101—416no—
360C2×C4×C101—416no—
361C2×C4×C101—42no—
362C2×C4×C101—42no—
363C2×C4×C101—42no—
364C2×C4×C101—42no—
365C2×C4×C101—42no—
366C2×C4×C101—42no—
367C2×C4×C101—42no—
368C2×C4×C101—42no—
369C2×C4×C101—42no—
370C2×C4×C101—42no—
371C2×C4×C101—42no—
372C2×C4×C101—42no—
373C2×C4×C101—42no—
374C2×C4×C101—42no—
375C2×C4×C101—42no—
376C2×C4×C101—42no—
377C2×C4×C101—42no—
378C2×C4×C101—42no—
379C2×C4×C101—42no—
380C2×C4×C101—42no—
381C2×C4×C101—42no—
382C2×C4×C101—42no—
383C2×C4×C101—42no—
384C2×C4×C101—42no—
385C2×C4×C101—42no—
386C2×C4×C101—42no—
387C2×C4×C101C2×C22⋊C414yes—
388C2×C4×C101C2×C22⋊C414yes—
389C22×C101—24no—
390C22×C101—24no—
391C22×C101—24no—
392C22×C101—24no—
393C22×C101—24no—
394C22×C101—28no—
395C22×C101—28no—
396C22×C101—28no—
397C22×C101—28no—
398C22×C101—24no—
399C22×C101—24no—
400C22×C101—24no—
401C22×C101—24no—
402C22×C101—24no—
403C22×C101—24no—
404C22×C101—24no—
405C22×C101—464no—
406C22×C101—42no—
407C22×C101—42no—
408C22×C101—42no—
409C22×C101—42no—
410C22×C101—42no—
411C22×C101—42no—
412C22×C101—44no—
413C22×C101—44no—
414C22×C101—44no—
415C22×C101—44no—
416C22×C101—44no—
417C22×C101—44no—
418C22×C101—44no—
419C22×C101—44no—
420C22×C101—42no—
421C22×C101—42no—
422C22×C101#38818yescomplemented
423C22×C101C22×C22⋊C411yescharacteristic
424C22×C101C2×#11711yescharacteristic
425C22×C101C2×#11711yescharacteristic
426C22×C101C2×C4×D411yescharacteristic
427C22×C101C2×C4×D411yescharacteristic
428C22×C101#51811yescharacteristic
429C22×C101#51811yescharacteristic
430C22×C101C2×#12111yescharacteristic
431C22×C101C2×#12311yescharacteristic
432C22×C101#52512yes—
433C22×C101#52512yes—
434C22×C101C2×#12411yescharacteristic
435C22×C101C2×#12611yescharacteristic
436C22×C101#53812yes—
437C22×C101#53812yes—
438C22×C101D4212yes—
439C22×C101D4212yes—
440C22×C101#54612yes—
441C22×C101#54612yes—
442C22×C101#54612yes—
443C22×C101#54612yes—
444C22×C101#55112yes—
445C22×C101#55112yes—
446C4×C101—24no—
447C4×C101—24no—
448C4×C101—42no—
449C4×C101—42no—
450C4×C101—44no—
451C4×C101—44no—
452C4×C101—82no—
453C4×C101—82no—
454#13873C10111yesmaximal, characteristic, direct product factor, Sylow
455C2×C101—28no—
456C2×C101—44no—
457C2×C101—44no—
458C2×C101#228011yescharacteristic
459C2×C101C2×#38811yescharacteristic
460C2×C101#231211yescharacteristic
461C2×C101D4×C22⋊C411yescharacteristic
462C2×C101D4×C22⋊C411yescharacteristic
463C2×C101#234211yescharacteristic
464C2×C101#234211yescharacteristic
465C2×C101#241812yes—
466C2×C101#242412yes—
467C2×C101#247212yes—
468C2×C101#248012yes—
469C23×C22⋊C4C2×C10111yescharacteristic
470C2×#388C2×C10112yescomplemented
471C2×#380C2×C10111yescharacteristic, complemented
472C2×#379C2×C10111yescharacteristic
473C2×#379C2×C10111yescharacteristic
474C2×C4×C22⋊C4C2×C10111yescharacteristic, complemented
475#1440C2×C10112yescomplemented
476#1439C2×C10112yescomplemented
477#1437C2×C10112yescomplemented
478C22⋊#95C2×C10111yescharacteristic, complemented
479C22⋊#95C2×C10111yescharacteristic, complemented
480C101#1387311yescharacteristic, direct product factor, Sylow
481C26C22×C10111yescharacteristic
482C24×C4C22×C10111yescharacteristic
483C24×C4C22×C10111yescharacteristic
484C22×C4⋊C4C22×C10112yescomplemented
485C22×C22⋊C4—28no—
486C22×C22⋊C4C4×C10118yescomplemented
487C22×C22⋊C4C22×C10111yescharacteristic
488C22×C22⋊C4C22×C10111yescharacteristic
489C22×C22⋊C4C22×C10112yes—
490C22×C22⋊C4C22×C10112yes—
491C22×C22⋊C4C22×C10112yes—
492C22×C22⋊C4C22×C10112yes—
493C22×C22⋊C4C22×C10111yescharacteristic
494C22×C22⋊C4C22×C10111yescharacteristic
495C22×C22⋊C4C22×C10111yescharacteristic
496C22×C22⋊C4C22×C10111yescharacteristic
497C22×C22⋊C4C22×C10111yescharacteristic
498C22×C22⋊C4C22×C10111yescharacteristic
499C22×C42C22×C10112yescomplemented
500#388—28no—
501#380—24no—
502#379—24no—
503#379—24no—
504C4×C22⋊C4—24no—
505C2×#95C22×C10112yescomplemented
506C2×#95C22×C10112yescomplemented
507C2×#95C22×C10112yescomplemented
508C2×#95C22×C10112yescomplemented
509C2×#95C22×C10112yescomplemented
510C2×#95C22×C10112yescomplemented
511C25—24no—
512C25—24no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×C4×C10114yes—
522C25C23×C10111yescharacteristic
523C25C23×C10111yescharacteristic
524C25C23×C10111yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4C2×C4×C10114yes—
534C23×C4C2×C4×C10114yes—
535C23×C4C23×C10112yes—
536C23×C4C23×C10112yes—
537C23×C4C23×C10111yescharacteristic
538C23×C4C23×C10111yescharacteristic
539C23×C4C23×C10112yes—
540C23×C4C23×C10112yes—
541C23×C4C23×C10111yescharacteristic
542C23×C4C23×C10111yescharacteristic
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—42no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—232no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4C2×C4×C10114yes—
573C2×C22⋊C4C2×C4×C10114yes—
574C2×C22⋊C4C2×C4×C10114yes—
575C2×C22⋊C4C2×C4×C10114yes—
576C2×C22⋊C4D4×C10114yes—
577C2×C22⋊C4D4×C10114yes—
578C2×C22⋊C4D4×C10118yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C22×C4×C10112yes—
634C24C22×C4×C10112yes—
635C24C22×C4×C10112yes—
636C24C2×D4×C10114yes—
637C24C2×D4×C10112yes—
638C24C2×D4×C10112yes—
639C24#41×C10114yes—
640C24#41×C10112yes—
641C24#41×C10112yes—
642C24#41×C10112yes—
643C24#41×C10112yes—
644C24C24×C10111yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×C4×C10112yes—
696C22×C4C22×C4×C10112yes—
697C22×C4C22×C4×C10112yes—
698C22×C4C22×C4×C10112yes—
699C22×C4C2×D4×C10114yes—
700C22×C4C2×D4×C10114yes—
701C22×C4C2×D4×C10114yes—
702C22×C4C2×D4×C10114yes—
703C4⋊C4—48no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4C22⋊C4×C101116yescomplemented
716C42—48no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—432no—
763C23—432no—
764C23—432no—
765C23—432no—
766C23—416no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—416no—
788C23C2×C22⋊C4×C10114yes—
789C23#117×C10114yes—
790C23#117×C10114yes—
791C23C4×D4×C10114yes—
792C23C4×D4×C10114yes—
793C23#121×C10114yes—
794C23#123×C10114yes—
795C23#124×C10114yes—
796C23#126×C10114yes—
797C23C23×C4×C10111yescharacteristic
798C23C22×D4×C10112yes—
799C23C22×D4×C10111yescharacteristic
800C23C22×D4×C10111yescharacteristic
801C23C2×#41×C10111yescharacteristic
802C23C2×#41×C10111yescharacteristic
803C23C2×#41×C10112yes—
804C23C2×#41×C10111yescharacteristic
805C23C2×#41×C10111yescharacteristic
806C23H(5,𝔽2)×C10112yes—
807C23H(5,𝔽2)×C10112yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4C2×C22⋊C4×C10114yes—
857C2×C4C2×C22⋊C4×C10114yes—
858C22—28no—
859C22—28no—
860C22—28no—
861C22—28no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—24no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22#388×C10118yescomplemented
892C22C22×C22⋊C4×C10111yescharacteristic
893C22C2×#117×C10111yescharacteristic
894C22C2×#117×C10111yescharacteristic
895C22C2×C4×D4×C10111yescharacteristic
896C22C2×C4×D4×C10111yescharacteristic
897C22#518×C10111yescharacteristic
898C22#518×C10111yescharacteristic
899C22C2×#121×C10111yescharacteristic
900C22C2×#123×C10111yescharacteristic
901C22#525×C10112yes—
902C22#525×C10112yes—
903C22C2×#124×C10111yescharacteristic
904C22C2×#126×C10111yescharacteristic
905C22#538×C10112yes—
906C22#538×C10112yes—
907C22D42×C10112yes—
908C22D42×C10112yes—
909C22#546×C10112yes—
910C22#546×C10112yes—
911C22#546×C10112yes—
912C22#546×C10112yes—
913C22#551×C10112yes—
914C22#551×C10112yes—
915C4—24no—
916C4—24no—
917C4—44no—
918C4—44no—
919C4—42no—
920C4—42no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2C101×#228011yescharacteristic
927C2C2×#388×C10111yescharacteristic
928C2C101×#231211yescharacteristic
929C2D4×C22⋊C4×C10111yescharacteristic
930C2D4×C22⋊C4×C10111yescharacteristic
931C2C101×#234211yescharacteristic
932C2C101×#234211yescharacteristic
933C2C101×#241812yes—
934C2C101×#242412yes—
935C2C101×#247212yes—
936C2C101×#248012yes—
subgroupG/H
center, socleC24×C101C24
commutatorC23C23×C4×C101
Frattini, cosocleC24C24×C101
prime radicalC26×C101C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C101C2semidirect
3. C2×#380×C101C2semidirect
6. C2×C4×C22⋊C4×C101C2semidirect
7. C101×#1440C2semidirect
8. C101×#1439C2semidirect
9. C101×#1437C2semidirect
10. C101×C22⋊#95C2semidirect
11. C101×C22⋊#95C2semidirect
15. C22×C4⋊C4×C101C22semidirect
17. C22×C22⋊C4×C101C4semidirect
30. C22×C42×C101C22semidirect
36. C2×#95×C101C22semidirect
37. C2×#95×C101C22semidirect
38. C2×#95×C101C22semidirect
39. C2×#95×C101C22semidirect
40. C2×#95×C101C22semidirect
41. C2×#95×C101C22semidirect
246. C22⋊C4×C101C22⋊C4semidirect
422. C22×C101#388semidirect
454. #13873C101direct (N × H)
470. C2×#388C2×C101semidirect
471. C2×#380C2×C101semidirect
474. C2×C4×C22⋊C4C2×C101semidirect
475. #1440C2×C101semidirect
476. #1439C2×C101semidirect
477. #1437C2×C101semidirect
478. C22⋊#95C2×C101semidirect
479. C22⋊#95C2×C101semidirect
480. C101#13873direct (N × H)
484. C22×C4⋊C4C22×C101semidirect
486. C22×C22⋊C4C4×C101semidirect
499. C22×C42C22×C101semidirect
505. C2×#95C22×C101semidirect
506. C2×#95C22×C101semidirect
507. C2×#95C22×C101semidirect
508. C2×#95C22×C101semidirect
509. C2×#95C22×C101semidirect
510. C2×#95C22×C101semidirect
715. C22⋊C4C22⋊C4×C101semidirect
891. C22#388×C101semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1012
C2×#388×C1012
C2×#380×C1012
C2×#379×C1012
C2×C4×C22⋊C4×C1012
C101×#14402
C101×#14392
C101×#14372
C101×C22⋊#952
#13873101