Finite Group Databasebeta

← C103×#14725 #39920000

Subgroups — C103×#14725 #39920000

Order 26368.

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×C103C211yesmaximal, characteristic
2C23×C22⋊C4×C103C211yesmaximal, characteristic, complemented
3C2×#394×C103C212yesmaximal, complemented
4C2×#386×C103C211yesmaximal, characteristic, complemented
5C2×#386×C103C211yesmaximal, characteristic, complemented
6C2×#380×C103C211yesmaximal, characteristic, complemented
7C2×#379×C103C211yesmaximal, characteristic, complemented
8C103×#1440C212yesmaximal, complemented
9C103×#1439C212yesmaximal, complemented
10C103×#1438C212yesmaximal, complemented
11C103×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C103C2211yescharacteristic
13C23×D4×C103C2211yescharacteristic
14C23×D4×C103C2212yes—
15C24×C4×C103C2211yescharacteristic
16C24×C4×C103C2211yescharacteristic
17C2×#120×C103—24no—
18C2×#120×C103—24no—
19C2×#120×C103—24no—
20C22×C4⋊C4×C103C2212yescomplemented
21C22×C22⋊C4×C103—24no—
22C22×C22⋊C4×C103—28no—
23C22×C22⋊C4×C103C2211yescharacteristic
24C22×C22⋊C4×C103C2212yes—
25C22×C22⋊C4×C103C2212yes—
26C22×C22⋊C4×C103C2212yes—
27C22×C22⋊C4×C103C2211yescharacteristic
28C22×C22⋊C4×C103C2211yescharacteristic
29C22×C22⋊C4×C103C2212yes—
30C22×C22⋊C4×C103C2212yes—
31C22×C22⋊C4×C103C2211yescharacteristic, complemented
32C22×C22⋊C4×C103C2212yescomplemented
33C22×C22⋊C4×C103C2211yescharacteristic, complemented
34#394×C103—28no—
35#386×C103—24no—
36#386×C103—24no—
37#380×C103—24no—
38#379×C103—24no—
39C2×#95×C103C2212yescomplemented
40C2×#95×C103C2212yescomplemented
41C2×#95×C103C2211yescharacteristic, complemented
42C2×#95×C103C2212yescomplemented
43C2×#95×C103C2211yescharacteristic, complemented
44C2×#95×C103C2212yescomplemented
45C25×C103—24no—
46C25×C103—22no—
47C25×C103—24no—
48C25×C103—22no—
49C25×C103—22no—
50C25×C103—22no—
51C25×C103—22no—
52C25×C103—22no—
53C25×C103—42no—
54C25×C103—42no—
55C25×C103D414yes—
56C25×C103C2311yescharacteristic
57C25×C103C2312yes—
58C25×C103C2311yescharacteristic
59C22×D4×C103—22no—
60C22×D4×C103—24no—
61C22×D4×C103—24no—
62C22×D4×C103—22no—
63C22×D4×C103—22no—
64C22×D4×C103—22no—
65C22×D4×C103—22no—
66C22×D4×C103—22no—
67C22×D4×C103—24no—
68C22×D4×C103—24no—
69C22×D4×C103—24no—
70C22×D4×C103—42no—
71C22×D4×C103—42no—
72C22×D4×C103D414yes—
73C23×C4×C103—22no—
74C23×C4×C103—22no—
75C23×C4×C103—22no—
76C23×C4×C103—24no—
77C23×C4×C103—24no—
78C23×C4×C103—22no—
79C23×C4×C103—22no—
80C23×C4×C103—42no—
81C23×C4×C103—42no—
82C23×C4×C103D414yescomplemented
83C23×C4×C103C2311yescharacteristic
84C23×C4×C103C2311yescharacteristic
85C23×C4×C103C2312yes—
86C23×C4×C103C2311yescharacteristic
87C23×C4×C103C2311yescharacteristic
88C23×C4×C103C2312yes—
89C23×C4×C103C2312yes—
90C23×C4×C103C2311yescharacteristic
91#120×C103—232no—
92C2×C4⋊C4×C103—24no—
93C2×C4⋊C4×C103—24no—
94C2×C4⋊C4×C103—42no—
95C2×C22⋊C4×C103—232no—
96C2×C22⋊C4×C103—24no—
97C2×C22⋊C4×C103—24no—
98C2×C22⋊C4×C103—22no—
99C2×C22⋊C4×C103—22no—
100C2×C22⋊C4×C103—24no—
101C2×C22⋊C4×C103—24no—
102C2×C22⋊C4×C103—24no—
103C2×C22⋊C4×C103—24no—
104C2×C22⋊C4×C103—24no—
105C2×C22⋊C4×C103—24no—
106C2×C22⋊C4×C103—24no—
107C2×C22⋊C4×C103—22no—
108C2×C22⋊C4×C103—24no—
109C2×C22⋊C4×C103—22no—
110C2×C22⋊C4×C103—22no—
111C2×C22⋊C4×C103—22no—
112C2×C22⋊C4×C103—22no—
113C2×C22⋊C4×C103—24no—
114C2×C22⋊C4×C103—24no—
115C2×C22⋊C4×C103—24no—
116C2×C22⋊C4×C103—22no—
117C2×C22⋊C4×C103—22no—
118C2×C22⋊C4×C103—22no—
119C2×C22⋊C4×C103—24no—
120C2×C22⋊C4×C103—24no—
121C2×C22⋊C4×C103—42no—
122C2×C22⋊C4×C103—42no—
123C2×C22⋊C4×C103—42no—
124C2×C22⋊C4×C103—42no—
125C2×C22⋊C4×C103D414yes—
126C2×C22⋊C4×C103D418yescomplemented
127#95×C103—24no—
128#95×C103—22no—
129#95×C103—22no—
130#95×C103—24no—
131#95×C103—24no—
132#95×C103—42no—
133C24×C103—22no—
134C24×C103—22no—
135C24×C103—22no—
136C24×C103—22no—
137C24×C103—28no—
138C24×C103—28no—
139C24×C103—216no—
140C24×C103—216no—
141C24×C103—28no—
142C24×C103—22no—
143C24×C103—22no—
144C24×C103—22no—
145C24×C103—22no—
146C24×C103—22no—
147C24×C103—22no—
148C24×C103—22no—
149C24×C103—22no—
150C24×C103—22no—
151C24×C103—22no—
152C24×C103—22no—
153C24×C103—22no—
154C24×C103—28no—
155C24×C103—28no—
156C24×C103—21no—
157C24×C103—22no—
158C24×C103—21no—
159C24×C103—21no—
160C24×C103—21no—
161C24×C103—21no—
162C24×C103—21no—
163C24×C103—22no—
164C24×C103—22no—
165C24×C103—22no—
166C24×C103—48no—
167C24×C103—48no—
168C24×C103—48no—
169C24×C103—48no—
170C24×C103—48no—
171C24×C103—48no—
172C24×C103—48no—
173C24×C103—48no—
174C24×C103—48no—
175C24×C103—44no—
176C24×C103—44no—
177C24×C103—48no—
178C24×C103—44no—
179C24×C103—44no—
180C24×C103—44no—
181C24×C103—44no—
182C24×C103C2×D412yes—
183C24×C103C2×D414yes—
184C24×C103C2×D414yes—
185C24×C103C2×D412yes—
186C24×C103C2×D412yes—
187C24×C103C2×D412yes—
188C24×C103C2×D412yes—
189C24×C103#4114yes—
190C24×C103#4112yes—
191C24×C103#4112yes—
192C24×C103#4112yes—
193C24×C103C2411yescharacteristic
194C2×D4×C103—216no—
195C2×D4×C103—28no—
196C2×D4×C103—28no—
197C2×D4×C103—28no—
198C2×D4×C103—48no—
199C2×D4×C103—48no—
200C2×D4×C103—48no—
201C2×D4×C103—48no—
202C2×D4×C103—48no—
203C2×D4×C103—48no—
204C2×D4×C103—44no—
205C2×D4×C103—44no—
206C2×D4×C103—44no—
207C2×D4×C103—44no—
208C22×C4×C103—21no—
209C22×C4×C103—21no—
210C22×C4×C103—22no—
211C22×C4×C103—28no—
212C22×C4×C103—28no—
213C22×C4×C103—21no—
214C22×C4×C103—21no—
215C22×C4×C103—22no—
216C22×C4×C103—22no—
217C22×C4×C103—22no—
218C22×C4×C103—22no—
219C22×C4×C103—22no—
220C22×C4×C103—21no—
221C22×C4×C103—21no—
222C22×C4×C103—22no—
223C22×C4×C103—22no—
224C22×C4×C103—21no—
225C22×C4×C103—22no—
226C22×C4×C103—21no—
227C22×C4×C103—21no—
228C22×C4×C103—21no—
229C22×C4×C103—22no—
230C22×C4×C103—22no—
231C22×C4×C103—22no—
232C22×C4×C103—22no—
233C22×C4×C103—22no—
234C22×C4×C103—22no—
235C22×C4×C103—28no—
236C22×C4×C103—21no—
237C22×C4×C103—22no—
238C22×C4×C103—22no—
239C22×C4×C103—21no—
240C22×C4×C103—22no—
241C22×C4×C103—22no—
242C22×C4×C103—21no—
243C22×C4×C103—21no—
244C22×C4×C103—22no—
245C22×C4×C103—21no—
246C22×C4×C103—22no—
247C22×C4×C103—21no—
248C22×C4×C103—22no—
249C22×C4×C103—22no—
250C22×C4×C103—22no—
251C22×C4×C103—22no—
252C22×C4×C103—22no—
253C22×C4×C103—44no—
254C22×C4×C103—48no—
255C22×C4×C103—48no—
256C22×C4×C103—48no—
257C22×C4×C103—48no—
258C22×C4×C103—44no—
259C22×C4×C103—44no—
260C22×C4×C103C2×D412yes—
261C22×C4×C103C2×D412yes—
262C22×C4×C103C2×D414yes—
263C22×C4×C103C2×D414yes—
264C22×C4×C103C2×D412yes—
265C22×C4×C103C2×D414yes—
266C4⋊C4×C103—48no—
267C22⋊C4×C103—216no—
268C22⋊C4×C103—216no—
269C22⋊C4×C103—28no—
270C22⋊C4×C103—216no—
271C22⋊C4×C103—48no—
272C22⋊C4×C103—44no—
273C22⋊C4×C103—48no—
274C22⋊C4×C103—44no—
275C22⋊C4×C103—48no—
276C22⋊C4×C103—44no—
277C22⋊C4×C103—44no—
278C23×C103—22no—
279C23×C103—24no—
280C23×C103—22no—
281C23×C103—24no—
282C23×C103—22no—
283C23×C103—24no—
284C23×C103—22no—
285C23×C103—24no—
286C23×C103—24no—
287C23×C103—24no—
288C23×C103—24no—
289C23×C103—24no—
290C23×C103—24no—
291C23×C103—24no—
292C23×C103—24no—
293C23×C103—24no—
294C23×C103—232no—
295C23×C103—24no—
296C23×C103—24no—
297C23×C103—24no—
298C23×C103—24no—
299C23×C103—24no—
300C23×C103—24no—
301C23×C103—24no—
302C23×C103—24no—
303C23×C103—24no—
304C23×C103—24no—
305C23×C103—24no—
306C23×C103—24no—
307C23×C103—24no—
308C23×C103—24no—
309C23×C103—24no—
310C23×C103—24no—
311C23×C103—24no—
312C23×C103—24no—
313C23×C103—22no—
314C23×C103—22no—
315C23×C103—22no—
316C23×C103—24no—
317C23×C103—24no—
318C23×C103—432no—
319C23×C103—432no—
320C23×C103—416no—
321C23×C103—416no—
322C23×C103—416no—
323C23×C103—416no—
324C23×C103—432no—
325C23×C103—432no—
326C23×C103—416no—
327C23×C103—42no—
328C23×C103—42no—
329C23×C103—42no—
330C23×C103—42no—
331C23×C103—42no—
332C23×C103—42no—
333C23×C103—42no—
334C23×C103—42no—
335C23×C103—42no—
336C23×C103—42no—
337C23×C103—42no—
338C23×C103—42no—
339C23×C103—42no—
340C23×C103—42no—
341C23×C103—42no—
342C23×C103—42no—
343C23×C103—416no—
344C23×C103—41no—
345C23×C103—41no—
346C23×C103—41no—
347C23×C103—42no—
348C23×C103—41no—
349C23×C103—42no—
350C23×C103—41no—
351C23×C103—41no—
352C23×C103—41no—
353C23×C103—42no—
354C23×C103—41no—
355C23×C103—42no—
356C23×C103—42no—
357C23×C103—42no—
358C23×C103—42no—
359C23×C103—42no—
360C23×C103—42no—
361C23×C103—42no—
362C23×C103#12014yes—
363C23×C103#12118yes—
364C23×C103#12114yes—
365C23×C103#12114yes—
366C23×C103#12114yes—
367C23×C103#12314yes—
368C23×C103#12314yes—
369C23×C103#12414yes—
370C23×C103C22×D411yescharacteristic
371C23×C103C22×D411yescharacteristic
372C23×C103C22×D411yescharacteristic
373C23×C103C22×D412yes—
374C23×C103C22×D411yescharacteristic
375C23×C103C2×#4111yescharacteristic
376C23×C103C2×#4111yescharacteristic
377C23×C103C2×#4111yescharacteristic
378C23×C103C2×#4112yes—
379C23×C103H(5,𝔽2)12yes—
380C23×C103H(5,𝔽2)12yes—
381D4×C103—432no—
382D4×C103—416no—
383C2×C4×C103—22no—
384C2×C4×C103—22no—
385C2×C4×C103—24no—
386C2×C4×C103—24no—
387C2×C4×C103—24no—
388C2×C4×C103—22no—
389C2×C4×C103—22no—
390C2×C4×C103—24no—
391C2×C4×C103—22no—
392C2×C4×C103—22no—
393C2×C4×C103—22no—
394C2×C4×C103—22no—
395C2×C4×C103—24no—
396C2×C4×C103—24no—
397C2×C4×C103—24no—
398C2×C4×C103—24no—
399C2×C4×C103—416no—
400C2×C4×C103—416no—
401C2×C4×C103—42no—
402C2×C4×C103—41no—
403C2×C4×C103—41no—
404C2×C4×C103—42no—
405C2×C4×C103—41no—
406C2×C4×C103—41no—
407C2×C4×C103—42no—
408C2×C4×C103—42no—
409C2×C4×C103—42no—
410C2×C4×C103—42no—
411C2×C4×C103—42no—
412C2×C4×C103—42no—
413C2×C4×C103—42no—
414C2×C4×C103—42no—
415C2×C4×C103—41no—
416C2×C4×C103—42no—
417C2×C4×C103—41no—
418C2×C4×C103—42no—
419C2×C4×C103—41no—
420C2×C4×C103—42no—
421C2×C4×C103—41no—
422C2×C4×C103—42no—
423C2×C4×C103—42no—
424C2×C4×C103—41no—
425C2×C4×C103—42no—
426C2×C4×C103—41no—
427C2×C4×C103—42no—
428C2×C4×C103—42no—
429C2×C4×C103—42no—
430C2×C4×C103—42no—
431C2×C4×C103—42no—
432C2×C4×C103#12014yescomplemented
433C22×C103—24no—
434C22×C103—24no—
435C22×C103—24no—
436C22×C103—24no—
437C22×C103—28no—
438C22×C103—24no—
439C22×C103—28no—
440C22×C103—28no—
441C22×C103—28no—
442C22×C103—24no—
443C22×C103—28no—
444C22×C103—28no—
445C22×C103—28no—
446C22×C103—464no—
447C22×C103—44no—
448C22×C103—44no—
449C22×C103—44no—
450C22×C103—44no—
451C22×C103—44no—
452C22×C103—44no—
453C22×C103—44no—
454C22×C103—44no—
455C22×C103—44no—
456C22×C103—44no—
457C22×C103—44no—
458C22×C103—44no—
459C22×C103—42no—
460C22×C103—42no—
461C22×C103—44no—
462C22×C103—44no—
463C22×C103—42no—
464C22×C103—81no—
465C22×C103—81no—
466C22×C103—81no—
467C22×C103—81no—
468C22×C103—82no—
469C22×C103—82no—
470C22×C103#39418yescomplemented
471C22×C103C2×#12011yescharacteristic
472C22×C103C2×#12011yescharacteristic
473C22×C103C2×#12111yescharacteristic
474C22×C103C2×#12112yes—
475C22×C103C2×#12111yescharacteristic
476C22×C103C2×#12111yescharacteristic
477C22×C103C2×#12311yescharacteristic
478C22×C103C2×#12311yescharacteristic
479C22×C103#52511yescharacteristic
480C22×C103#52512yes—
481C22×C103C2×#12411yescharacteristic
482C22×C103#53412yes—
483C22×C103#53411yescharacteristic
484C22×C103#53511yescharacteristic
485C22×C103#53812yes—
486C22×C103D4212yes—
487C22×C103D4212yes—
488C22×C103#54612yes—
489C22×C103#54612yes—
490C22×C103#54612yes—
491C22×C103#54612yes—
492C22×C103#55112yes—
493C22×C103#55112yes—
494C4×C103—24no—
495C4×C103—42no—
496C4×C103—44no—
497C4×C103—42no—
498C4×C103—44no—
499C4×C103—81no—
500C4×C103—81no—
501C4×C103—82no—
502#14725C10311yesmaximal, characteristic, direct product factor, Sylow
503C2×C103—28no—
504C2×C103—48no—
505C2×C103—82no—
506C2×C103C2×#39411yescharacteristic
507C2×C103#240811yescharacteristic
508C2×C103#241011yescharacteristic
509C2×C103#241012yes—
510C2×C103#241111yescharacteristic
511C2×C103#241212yes—
512C2×C103#241812yes—
513C2×C103#247212yes—
514C2×C103#253411yescharacteristic
515C2×C103#261711yescharacteristic
516C2×C103#284711yescharacteristic
517C22×#120C2×C10311yescharacteristic
518C23×C22⋊C4C2×C10311yescharacteristic, complemented
519C2×#394C2×C10312yescomplemented
520C2×#386C2×C10311yescharacteristic, complemented
521C2×#386C2×C10311yescharacteristic, complemented
522C2×#380C2×C10311yescharacteristic, complemented
523C2×#379C2×C10311yescharacteristic, complemented
524#1440C2×C10312yescomplemented
525#1439C2×C10312yescomplemented
526#1438C2×C10312yescomplemented
527C22⋊#95C2×C10311yescharacteristic, complemented
528C103#1472511yescharacteristic, direct product factor, Sylow
529C26C22×C10311yescharacteristic
530C23×D4C22×C10311yescharacteristic
531C23×D4C22×C10312yes—
532C24×C4C22×C10311yescharacteristic
533C24×C4C22×C10311yescharacteristic
534C2×#120—24no—
535C2×#120—24no—
536C2×#120—24no—
537C22×C4⋊C4C22×C10312yescomplemented
538C22×C22⋊C4—24no—
539C22×C22⋊C4—28no—
540C22×C22⋊C4C22×C10312yes—
541C22×C22⋊C4C22×C10312yes—
542C22×C22⋊C4C22×C10312yes—
543C22×C22⋊C4C22×C10311yescharacteristic
544C22×C22⋊C4C22×C10311yescharacteristic
545C22×C22⋊C4C22×C10311yescharacteristic
546C22×C22⋊C4C22×C10312yes—
547C22×C22⋊C4C22×C10312yes—
548C22×C22⋊C4C22×C10311yescharacteristic, complemented
549C22×C22⋊C4C22×C10312yescomplemented
550C22×C22⋊C4C22×C10311yescharacteristic, complemented
551#394—28no—
552#386—24no—
553#386—24no—
554#380—24no—
555#379—24no—
556C2×#95C22×C10312yescomplemented
557C2×#95C22×C10312yescomplemented
558C2×#95C22×C10311yescharacteristic, complemented
559C2×#95C22×C10312yescomplemented
560C2×#95C22×C10311yescharacteristic, complemented
561C2×#95C22×C10312yescomplemented
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C10314yes—
573C25C23×C10311yescharacteristic
574C25C23×C10312yes—
575C25C23×C10311yescharacteristic
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×C10314yes—
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×C10314yescomplemented
600C23×C4C23×C10312yes—
601C23×C4C23×C10311yescharacteristic
602C23×C4C23×C10311yescharacteristic
603C23×C4C23×C10311yescharacteristic
604C23×C4C23×C10312yes—
605C23×C4C23×C10312yes—
606C23×C4C23×C10311yescharacteristic
607C23×C4C23×C10311yescharacteristic
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×C10314yes—
643C2×C22⋊C4D4×C10318yescomplemented
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×C10312yes—
700C24C2×D4×C10314yes—
701C24C2×D4×C10314yes—
702C24C2×D4×C10312yes—
703C24C2×D4×C10312yes—
704C24C2×D4×C10312yes—
705C24C2×D4×C10312yes—
706C24#41×C10314yes—
707C24#41×C10312yes—
708C24#41×C10312yes—
709C24#41×C10312yes—
710C24C24×C10311yescharacteristic
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×C10312yes—
778C22×C4C2×D4×C10312yes—
779C22×C4C2×D4×C10314yes—
780C22×C4C2×D4×C10314yes—
781C22×C4C2×D4×C10312yes—
782C22×C4C2×D4×C10314yes—
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—432no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—416no—
843C23—432no—
844C23—416no—
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—42no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C10314yes—
880C23#121×C10318yes—
881C23#121×C10314yes—
882C23#121×C10314yes—
883C23#121×C10314yes—
884C23#123×C10314yes—
885C23#123×C10314yes—
886C23#124×C10314yes—
887C23C22×D4×C10311yescharacteristic
888C23C22×D4×C10311yescharacteristic
889C23C22×D4×C10311yescharacteristic
890C23C22×D4×C10312yes—
891C23C22×D4×C10311yescharacteristic
892C23C2×#41×C10311yescharacteristic
893C23C2×#41×C10311yescharacteristic
894C23C2×#41×C10311yescharacteristic
895C23C2×#41×C10312yes—
896C23H(5,𝔽2)×C10312yes—
897C23H(5,𝔽2)×C10312yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
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—41no—
920C2×C4—41no—
921C2×C4—42no—
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—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C10314yescomplemented
950C22—28no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—28no—
957C22—24no—
958C22—28no—
959C22—28no—
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—42no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—82no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22#394×C10318yescomplemented
988C22C2×#120×C10311yescharacteristic
989C22C2×#120×C10311yescharacteristic
990C22C2×#121×C10311yescharacteristic
991C22C2×#121×C10311yescharacteristic
992C22C2×#121×C10312yes—
993C22C2×#121×C10311yescharacteristic
994C22C2×#123×C10311yescharacteristic
995C22C2×#123×C10311yescharacteristic
996C22#525×C10312yes—
997C22#525×C10311yescharacteristic
998C22C2×#124×C10311yescharacteristic
999C22#534×C10311yescharacteristic
1000C22#534×C10312yes—
1001C22#535×C10311yescharacteristic
1002C22#538×C10312yes—
1003C22D42×C10312yes—
1004C22D42×C10312yes—
1005C22#546×C10312yes—
1006C22#546×C10312yes—
1007C22#546×C10312yes—
1008C22#546×C10312yes—
1009C22#551×C10312yes—
1010C22#551×C10312yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×#394×C10311yescharacteristic
1023C2C103×#240811yescharacteristic
1024C2C103×#241011yescharacteristic
1025C2C103×#241012yes—
1026C2C103×#241111yescharacteristic
1027C2C103×#241212yes—
1028C2C103×#241812yes—
1029C2C103×#247212yes—
1030C2C103×#253411yescharacteristic
1031C2C103×#261711yescharacteristic
1032C2C103×#284711yescharacteristic
subgroupG/H
center, socleC24×C103C24
commutator, Frattini, cosocleC24C24×C103
prime radicalC22×#120×C103C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C103C2semidirect
3. C2×#394×C103C2semidirect
4. C2×#386×C103C2semidirect
5. C2×#386×C103C2semidirect
6. C2×#380×C103C2semidirect
7. C2×#379×C103C2semidirect
8. C103×#1440C2semidirect
9. C103×#1439C2semidirect
10. C103×#1438C2semidirect
11. C103×C22⋊#95C2semidirect
20. C22×C4⋊C4×C103C22semidirect
31. C22×C22⋊C4×C103C22semidirect
32. C22×C22⋊C4×C103C22semidirect
33. C22×C22⋊C4×C103C22semidirect
39. C2×#95×C103C22semidirect
40. C2×#95×C103C22semidirect
41. C2×#95×C103C22semidirect
42. C2×#95×C103C22semidirect
43. C2×#95×C103C22semidirect
44. C2×#95×C103C22semidirect
82. C23×C4×C103D4semidirect
126. C2×C22⋊C4×C103D4semidirect
432. C2×C4×C103#120semidirect
470. C22×C103#394semidirect
502. #14725C103direct (N × H)
518. C23×C22⋊C4C2×C103semidirect
519. C2×#394C2×C103semidirect
520. C2×#386C2×C103semidirect
521. C2×#386C2×C103semidirect
522. C2×#380C2×C103semidirect
523. C2×#379C2×C103semidirect
524. #1440C2×C103semidirect
525. #1439C2×C103semidirect
526. #1438C2×C103semidirect
527. C22⋊#95C2×C103semidirect
528. C103#14725direct (N × H)
537. C22×C4⋊C4C22×C103semidirect
548. C22×C22⋊C4C22×C103semidirect
549. C22×C22⋊C4C22×C103semidirect
550. C22×C22⋊C4C22×C103semidirect
556. C2×#95C22×C103semidirect
557. C2×#95C22×C103semidirect
558. C2×#95C22×C103semidirect
559. C2×#95C22×C103semidirect
560. C2×#95C22×C103semidirect
561. C2×#95C22×C103semidirect
599. C23×C4D4×C103semidirect
643. C2×C22⋊C4D4×C103semidirect
949. C2×C4#120×C103semidirect
987. C22#394×C103semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1032
C23×C22⋊C4×C1032
C2×#394×C1032
C2×#386×C1032
C2×#380×C1032
C2×#379×C1032
C103×#14402
C103×#14392
C103×#14382
C103×C22⋊#952
#14725103