Finite Group Databasebeta

← C103×#16392 #39921667

Subgroups — C103×#16392 #39921667

Order 26368.

1714 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C103C211yesmaximal, characteristic, complemented
2C2×#386×C103C211yesmaximal, characteristic
3C2×#381×C103C211yesmaximal, characteristic, complemented
4C2×#380×C103C211yesmaximal, characteristic, complemented
5C103×#1445C211yesmaximal, characteristic, complemented
6C103×#1442C211yesmaximal, characteristic, complemented
7C103×#1442C212yesmaximal, complemented
8C103×#1440C212yesmaximal, complemented
9C103×#1439C211yesmaximal, characteristic, complemented
10C103×#1439C212yesmaximal, complemented
11C103×#1438C212yesmaximal
12C23×D4×C103C2211yescharacteristic
13C24×C4×C103C2211yescharacteristic
14C22×C4⋊C4×C103C2211yescharacteristic
15C22×C4⋊C4×C103C2211yescharacteristic
16C22×C4⋊C4×C103C2212yes—
17C22×C22⋊C4×C103C2211yescharacteristic
18C22×C22⋊C4×C103C2212yes—
19C22×C22⋊C4×C103C2212yes—
20C22×C22⋊C4×C103C2212yes—
21C22×C22⋊C4×C103C2212yes—
22C22×C22⋊C4×C103C2211yescharacteristic
23C22×C22⋊C4×C103C2211yescharacteristic
24#399×C103—24no—
25#386×C103—24no—
26#381×C103—24no—
27#380×C103—24no—
28C2×#95×C103C2212yes—
29C2×#95×C103C2211yescharacteristic
30C2×#95×C103C2212yes—
31C2×#95×C103C2212yes—
32C2×#95×C103C2211yescharacteristic
33C2×#95×C103C2211yescharacteristic
34C2×#95×C103C2212yes—
35C2×#95×C103C2212yes—
36C2×#95×C103C2212yes—
37C2×#95×C103C2212yes—
38C2×#95×C103C2211yescharacteristic
39C25×C103C2311yescharacteristic
40C25×C103C2311yescharacteristic
41C22×D4×C103—22no—
42C22×D4×C103—22no—
43C22×D4×C103—24no—
44C22×D4×C103—22no—
45C22×D4×C103—42no—
46C23×C4×C103—24no—
47C23×C4×C103—22no—
48C23×C4×C103—22no—
49C23×C4×C103—42no—
50C23×C4×C103D414yes—
51C23×C4×C103C2312yes—
52C23×C4×C103C2311yescharacteristic
53C23×C4×C103C2312yes—
54C23×C4×C103C2311yescharacteristic
55C23×C4×C103C2312yes—
56C23×C4×C103C2311yescharacteristic
57C23×C4×C103C2312yes—
58C23×C4×C103C2311yescharacteristic
59C23×C4×C103C2311yescharacteristic
60C2×C4⋊C4×C103—22no—
61C2×C4⋊C4×C103—22no—
62C2×C4⋊C4×C103—24no—
63C2×C4⋊C4×C103—22no—
64C2×C4⋊C4×C103—22no—
65C2×C4⋊C4×C103—42no—
66C2×C4⋊C4×C103—42no—
67C2×C4⋊C4×C103—42no—
68C2×C22⋊C4×C103—24no—
69C2×C22⋊C4×C103—22no—
70C2×C22⋊C4×C103—24no—
71C2×C22⋊C4×C103—24no—
72C2×C22⋊C4×C103—24no—
73C2×C22⋊C4×C103—22no—
74C2×C22⋊C4×C103—22no—
75C2×C22⋊C4×C103—24no—
76C2×C22⋊C4×C103—22no—
77C2×C22⋊C4×C103—22no—
78C2×C22⋊C4×C103—42no—
79C2×C22⋊C4×C103—42no—
80C2×C22⋊C4×C103—42no—
81C2×C22⋊C4×C103—42no—
82C2×C22⋊C4×C103—42no—
83C2×C22⋊C4×C103—42no—
84C2×C22⋊C4×C103—42no—
85C2×C22⋊C4×C103—42no—
86C2×C22⋊C4×C103—42no—
87#95×C103—24no—
88#95×C103—24no—
89#95×C103—22no—
90#95×C103—22no—
91#95×C103—22no—
92#95×C103—24no—
93#95×C103—42no—
94#95×C103—42no—
95#95×C103—42no—
96#95×C103—42no—
97#95×C103D414yescomplemented
98C24×C103—21no—
99C24×C103—21no—
100C24×C103—21no—
101C24×C103—21no—
102C24×C103—22no—
103C24×C103—22no—
104C24×C103—22no—
105C24×C103—21no—
106C24×C103—21no—
107C24×C103—21no—
108C24×C103—21no—
109C24×C103—21no—
110C24×C103—21no—
111C24×C103—22no—
112C24×C103—22no—
113C24×C103—22no—
114C24×C103—22no—
115C24×C103—21no—
116C24×C103—21no—
117C24×C103C2×D412yes—
118C24×C103#4112yes—
119C24×C103#4114yes—
120C24×C103C2411yescharacteristic
121C2×D4×C103—28no—
122C2×D4×C103—48no—
123C2×D4×C103—48no—
124C2×D4×C103—44no—
125C2×D4×C103—44no—
126C22×C4×C103—22no—
127C22×C4×C103—22no—
128C22×C4×C103—28no—
129C22×C4×C103—21no—
130C22×C4×C103—21no—
131C22×C4×C103—22no—
132C22×C4×C103—22no—
133C22×C4×C103—21no—
134C22×C4×C103—22no—
135C22×C4×C103—21no—
136C22×C4×C103—22no—
137C22×C4×C103—22no—
138C22×C4×C103—22no—
139C22×C4×C103—22no—
140C22×C4×C103—22no—
141C22×C4×C103—22no—
142C22×C4×C103—22no—
143C22×C4×C103—28no—
144C22×C4×C103—22no—
145C22×C4×C103—21no—
146C22×C4×C103—21no—
147C22×C4×C103—22no—
148C22×C4×C103—22no—
149C22×C4×C103—21no—
150C22×C4×C103—22no—
151C22×C4×C103—22no—
152C22×C4×C103—21no—
153C22×C4×C103—22no—
154C22×C4×C103—22no—
155C22×C4×C103—22no—
156C22×C4×C103—22no—
157C22×C4×C103—22no—
158C22×C4×C103—22no—
159C22×C4×C103—22no—
160C22×C4×C103—22no—
161C22×C4×C103—22no—
162C22×C4×C103—22no—
163C22×C4×C103—22no—
164C22×C4×C103—22no—
165C22×C4×C103—22no—
166C22×C4×C103—22no—
167C22×C4×C103—22no—
168C22×C4×C103—22no—
169C22×C4×C103—22no—
170C22×C4×C103—22no—
171C22×C4×C103—22no—
172C22×C4×C103—21no—
173C22×C4×C103—21no—
174C22×C4×C103—22no—
175C22×C4×C103—44no—
176C22×C4×C103—48no—
177C22×C4×C103—48no—
178C22×C4×C103C2×D412yes—
179C22×C4×C103C2×D414yes—
180C22×C4×C103C2×D412yes—
181C22×C4×C103C2×D412yes—
182C22×C4×C103#4112yes—
183C22×C4×C103#4112yes—
184C4⋊C4×C103—44no—
185C4⋊C4×C103—48no—
186C4⋊C4×C103—44no—
187C22⋊C4×C103—48no—
188C22⋊C4×C103—44no—
189C22⋊C4×C103—48no—
190C22⋊C4×C103—48no—
191C22⋊C4×C103—44no—
192C22⋊C4×C103—48no—
193C22⋊C4×C103—44no—
194C23×C103—22no—
195C23×C103—22no—
196C23×C103—22no—
197C23×C103—22no—
198C23×C103—22no—
199C23×C103—22no—
200C23×C103—24no—
201C23×C103—24no—
202C23×C103—24no—
203C23×C103—24no—
204C23×C103—24no—
205C23×C103—24no—
206C23×C103—22no—
207C23×C103—24no—
208C23×C103—22no—
209C23×C103—24no—
210C23×C103—22no—
211C23×C103—42no—
212C23×C103—42no—
213C23×C103—42no—
214C23×C103—42no—
215C23×C103—41no—
216C23×C103—41no—
217C23×C103—41no—
218C23×C103—41no—
219C23×C103—42no—
220C23×C103—42no—
221C23×C103—41no—
222C23×C103—41no—
223C23×C103—41no—
224C23×C103—42no—
225C23×C103—41no—
226C23×C103—41no—
227C23×C103—41no—
228C23×C103—42no—
229C23×C103—42no—
230C23×C103—42no—
231C23×C103—42no—
232C23×C103—42no—
233C23×C103—41no—
234C23×C103—42no—
235C23×C103—42no—
236C23×C103—41no—
237C23×C103—42no—
238C23×C103—42no—
239C23×C103#12314yes—
240C23×C103C22×D411yescharacteristic
241C23×C103C22×D411yescharacteristic
242C23×C103C2×#4111yescharacteristic
243C23×C103C2×#4112yes—
244C23×C103C2×#4111yescharacteristic
245C23×C103C2×#4111yescharacteristic
246C23×C103H(5,𝔽2)12yes—
247C23×C103H(5,𝔽2)12yes—
248C23×C103H(5,𝔽2)12yes—
249C23×C1032−1+411yescharacteristic
250C23×C1032−1+411yescharacteristic
251D4×C103—416no—
252C2×C4×C103—22no—
253C2×C4×C103—22no—
254C2×C4×C103—24no—
255C2×C4×C103—24no—
256C2×C4×C103—22no—
257C2×C4×C103—22no—
258C2×C4×C103—22no—
259C2×C4×C103—22no—
260C2×C4×C103—24no—
261C2×C4×C103—24no—
262C2×C4×C103—24no—
263C2×C4×C103—24no—
264C2×C4×C103—416no—
265C2×C4×C103—41no—
266C2×C4×C103—41no—
267C2×C4×C103—42no—
268C2×C4×C103—42no—
269C2×C4×C103—42no—
270C2×C4×C103—42no—
271C2×C4×C103—42no—
272C2×C4×C103—42no—
273C2×C4×C103—42no—
274C2×C4×C103—41no—
275C2×C4×C103—42no—
276C2×C4×C103—42no—
277C2×C4×C103—41no—
278C2×C4×C103—42no—
279C2×C4×C103—41no—
280C2×C4×C103—41no—
281C2×C4×C103—42no—
282C2×C4×C103—42no—
283C2×C4×C103—42no—
284C2×C4×C103—42no—
285C2×C4×C103—42no—
286C2×C4×C103—42no—
287C2×C4×C103—41no—
288C2×C4×C103—42no—
289C2×C4×C103—41no—
290C2×C4×C103—42no—
291C2×C4×C103—42no—
292C2×C4×C103—42no—
293C2×C4×C103—42no—
294C2×C4×C103—42no—
295C2×C4×C103—42no—
296C2×C4×C103—42no—
297C2×C4×C103—42no—
298C2×C4×C103—42no—
299C2×C4×C103—42no—
300C2×C4×C103—42no—
301C2×C4×C103—42no—
302C2×C4×C103—42no—
303C2×C4×C103—42no—
304C2×C4×C103—42no—
305C2×C4×C103#12114yes—
306C22×C103—24no—
307C22×C103—24no—
308C22×C103—24no—
309C22×C103—42no—
310C22×C103—42no—
311C22×C103—42no—
312C22×C103—42no—
313C22×C103—44no—
314C22×C103—44no—
315C22×C103—44no—
316C22×C103—44no—
317C22×C103—42no—
318C22×C103—42no—
319C22×C103—44no—
320C22×C103—42no—
321C22×C103—44no—
322C22×C103—81no—
323C22×C103—81no—
324C22×C103—81no—
325C22×C103—81no—
326C22×C103—82no—
327C22×C103—82no—
328C22×C103C2×#12111yescharacteristic
329C22×C103C2×#12311yescharacteristic
330C22×C103#52511yescharacteristic
331C22×C103#53411yescharacteristic
332C22×C103#53511yescharacteristic
333C22×C103#53511yescharacteristic
334C22×C103#53512yes—
335C22×C103#53611yescharacteristic
336C22×C103#53812yes—
337C22×C103#53912yes—
338C22×C103#53912yes—
339C22×C103#54012yes—
340C22×C103#54012yes—
341C22×C103#54612yes—
342C22×C103#54711yescharacteristic
343C22×C103#54811yescharacteristic
344C22×C103#55112yes—
345C22×C103#55112yes—
346C22×C103#55112yes—
347C22×C103#55211yescharacteristic
348C22×C103#55611yescharacteristic
349C22×C103#56212yes—
350C22×C103#56212yes—
351C4×C103—24no—
352C4×C103—42no—
353C4×C103—44no—
354C4×C103—42no—
355C4×C103—81no—
356C4×C103—81no—
357C4×C103—82no—
358C4×C103—82no—
359C4×C103—82no—
360#16392C10311yesmaximal, characteristic, direct product factor, Sylow
361C2×C103—44no—
362C2×C103—82no—
363C2×C103#241211yescharacteristic
364C2×C103#241511yescharacteristic
365C2×C103#248211yescharacteristic
366C2×C103#261911yescharacteristic
367C2×C103#262311yescharacteristic
368C2×C103#263511yescharacteristic
369C2×C103#269612yes—
370C2×C103#270612yes—
371C2×C103#274012yes—
372C2×C103#274312yes—
373C2×C103#281611yescharacteristic
374C2×#399C2×C10311yescharacteristic, complemented
375C2×#386C2×C10311yescharacteristic
376C2×#381C2×C10311yescharacteristic, complemented
377C2×#380C2×C10311yescharacteristic, complemented
378#1445C2×C10311yescharacteristic, complemented
379#1442C2×C10312yescomplemented
380#1442C2×C10311yescharacteristic, complemented
381#1440C2×C10312yescomplemented
382#1439C2×C10311yescharacteristic, complemented
383#1439C2×C10312yescomplemented
384#1438C2×C10312yes—
385C103#1639211yescharacteristic, direct product factor, Sylow
386C23×D4C22×C10311yescharacteristic
387C24×C4C22×C10311yescharacteristic
388C22×C4⋊C4C22×C10311yescharacteristic
389C22×C4⋊C4C22×C10312yes—
390C22×C4⋊C4C22×C10311yescharacteristic
391C22×C22⋊C4C22×C10311yescharacteristic
392C22×C22⋊C4C22×C10312yes—
393C22×C22⋊C4C22×C10312yes—
394C22×C22⋊C4C22×C10312yes—
395C22×C22⋊C4C22×C10312yes—
396C22×C22⋊C4C22×C10311yescharacteristic
397C22×C22⋊C4C22×C10311yescharacteristic
398#399—24no—
399#386—24no—
400#381—24no—
401#380—24no—
402C2×#95C22×C10312yes—
403C2×#95C22×C10311yescharacteristic
404C2×#95C22×C10312yes—
405C2×#95C22×C10312yes—
406C2×#95C22×C10311yescharacteristic
407C2×#95C22×C10311yescharacteristic
408C2×#95C22×C10312yes—
409C2×#95C22×C10312yes—
410C2×#95C22×C10312yes—
411C2×#95C22×C10312yes—
412C2×#95C22×C10311yescharacteristic
413C25C23×C10311yescharacteristic
414C25C23×C10311yescharacteristic
415C22×D4—22no—
416C22×D4—22no—
417C22×D4—24no—
418C22×D4—22no—
419C22×D4—42no—
420C23×C4—24no—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—42no—
424C23×C4D4×C10314yes—
425C23×C4C23×C10311yescharacteristic
426C23×C4C23×C10312yes—
427C23×C4C23×C10312yes—
428C23×C4C23×C10312yes—
429C23×C4C23×C10311yescharacteristic
430C23×C4C23×C10312yes—
431C23×C4C23×C10311yescharacteristic
432C23×C4C23×C10311yescharacteristic
433C23×C4C23×C10311yescharacteristic
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—42no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—42no—
461#95—24no—
462#95—24no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—24no—
467#95—42no—
468#95—42no—
469#95—42no—
470#95—42no—
471#95D4×C10314yescomplemented
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—21no—
490C24—21no—
491C24C2×D4×C10312yes—
492C24#41×C10312yes—
493C24#41×C10314yes—
494C24C24×C10311yescharacteristic
495C2×D4—28no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—44no—
499C2×D4—44no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—28no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—28no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—44no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4C2×D4×C10312yes—
553C22×C4C2×D4×C10314yes—
554C22×C4C2×D4×C10312yes—
555C22×C4C2×D4×C10312yes—
556C22×C4#41×C10312yes—
557C22×C4#41×C10312yes—
558C4⋊C4—44no—
559C4⋊C4—48no—
560C4⋊C4—44no—
561C22⋊C4—48no—
562C22⋊C4—44no—
563C22⋊C4—48no—
564C22⋊C4—48no—
565C22⋊C4—44no—
566C22⋊C4—48no—
567C22⋊C4—44no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—22no—
581C23—24no—
582C23—22no—
583C23—24no—
584C23—22no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—42no—
594C23—42no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—42no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—41no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—42no—
612C23—42no—
613C23#123×C10314yes—
614C23C22×D4×C10311yescharacteristic
615C23C22×D4×C10311yescharacteristic
616C23C2×#41×C10311yescharacteristic
617C23C2×#41×C10312yes—
618C23C2×#41×C10311yescharacteristic
619C23C2×#41×C10311yescharacteristic
620C23H(5,𝔽2)×C10312yes—
621C23H(5,𝔽2)×C10312yes—
622C23H(5,𝔽2)×C10312yes—
623C232−1+4×C10311yescharacteristic
624C232−1+4×C10311yescharacteristic
625D4—416no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—416no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—41no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4#121×C10314yes—
680C22—24no—
681C22—24no—
682C22—24no—
683C22—44no—
684C22—44no—
685C22—44no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—44no—
691C22—42no—
692C22—44no—
693C22—42no—
694C22—42no—
695C22—44no—
696C22—82no—
697C22—82no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22C2×#121×C10311yescharacteristic
703C22C2×#123×C10311yescharacteristic
704C22#525×C10311yescharacteristic
705C22#534×C10311yescharacteristic
706C22#535×C10312yes—
707C22#535×C10311yescharacteristic
708C22#535×C10311yescharacteristic
709C22#536×C10311yescharacteristic
710C22#538×C10312yes—
711C22#539×C10312yes—
712C22#539×C10312yes—
713C22#540×C10312yes—
714C22#540×C10312yes—
715C22#546×C10312yes—
716C22#547×C10311yescharacteristic
717C22#548×C10311yescharacteristic
718C22#551×C10312yes—
719C22#551×C10312yes—
720C22#551×C10312yes—
721C22#552×C10311yescharacteristic
722C22#556×C10311yescharacteristic
723C22#562×C10312yes—
724C22#562×C10312yes—
725C4—24no—
726C4—44no—
727C4—42no—
728C4—42no—
729C4—81no—
730C4—81no—
731C4—82no—
732C4—82no—
733C4—82no—
734C2—44no—
735C2—82no—
736C2C103×#241211yescharacteristic
737C2C103×#241511yescharacteristic
738C2C103×#248211yescharacteristic
739C2C103×#261911yescharacteristic
740C2C103×#262311yescharacteristic
741C2C103×#263511yescharacteristic
742C2C103×#269612yes—
743C2C103×#270612yes—
744C2C103×#274012yes—
745C2C103×#274312yes—
746C2C103×#281611yescharacteristic
subgroupG/H
center, socleC24×C103C24
commutator, Frattini, cosocleC24C24×C103
prime radicalC23×D4×C103C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#399×C103C2semidirect
3. C2×#381×C103C2semidirect
4. C2×#380×C103C2semidirect
5. C103×#1445C2semidirect
6. C103×#1442C2semidirect
7. C103×#1442C2semidirect
8. C103×#1440C2semidirect
9. C103×#1439C2semidirect
10. C103×#1439C2semidirect
97. #95×C103D4semidirect
360. #16392C103direct (N × H)
374. C2×#399C2×C103semidirect
376. C2×#381C2×C103semidirect
377. C2×#380C2×C103semidirect
378. #1445C2×C103semidirect
379. #1442C2×C103semidirect
380. #1442C2×C103semidirect
381. #1440C2×C103semidirect
382. #1439C2×C103semidirect
383. #1439C2×C103semidirect
385. C103#16392direct (N × H)
471. #95D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1032
C2×#386×C1032
C2×#381×C1032
C2×#380×C1032
C103×#14452
C103×#14422
C103×#14402
C103×#14392
C103×#14382
#16392103