Finite Group Databasebeta

← C103×#14722 #39919997

Subgroups — C103×#14722 #39919997

Order 26368.

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×C103C211yesmaximal, characteristic, complemented
2C22×C4×D4×C103C211yesmaximal, characteristic, complemented
3C2×#394×C103C211yesmaximal, characteristic, complemented
4C2×#392×C103C211yesmaximal, characteristic, complemented
5C2×#392×C103C212yesmaximal, complemented
6C2×#386×C103C212yesmaximal, complemented
7C103×#1441C211yesmaximal, characteristic, complemented
8C103×#1439C211yesmaximal, characteristic, complemented
9C103×#1438C212yesmaximal, complemented
10C103×#1437C212yesmaximal, complemented
11C103×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C103C2211yescharacteristic
13C23×D4×C103C2212yes—
14C23×D4×C103C2212yes—
15C23×D4×C103C2211yescharacteristic
16C24×C4×C103C2211yescharacteristic
17C24×C4×C103C2211yescharacteristic
18C2×#121×C103—24no—
19C2×#121×C103—28no—
20C2×C4×D4×C103—24no—
21C2×C4×D4×C103—24no—
22C2×C4×D4×C103—24no—
23C22×C4⋊C4×C103C2211yescharacteristic
24C22×C4⋊C4×C103C2211yescharacteristic
25C22×C22⋊C4×C103C2212yes—
26C22×C22⋊C4×C103C2211yescharacteristic
27C22×C22⋊C4×C103C2212yes—
28C22×C22⋊C4×C103C2212yes—
29C22×C22⋊C4×C103C2212yes—
30C22×C22⋊C4×C103C2212yes—
31C22×C22⋊C4×C103C2212yes—
32C22×C22⋊C4×C103C2211yescharacteristic
33C22×C42×C103C2211yescharacteristic
34#394×C103—24no—
35#392×C103—28no—
36#392×C103—24no—
37#386×C103—28no—
38C2×#95×C103C2212yes—
39C2×#95×C103C2211yescharacteristic
40C2×#95×C103C2211yescharacteristic
41C2×#95×C103C2212yes—
42C2×#95×C103C2212yes—
43C2×#95×C103C2212yes—
44C25×C103C2312yes—
45C25×C103C2311yescharacteristic
46C25×C103C2311yescharacteristic
47C22×D4×C103—22no—
48C22×D4×C103—22no—
49C22×D4×C103—22no—
50C22×D4×C103—22no—
51C22×D4×C103—24no—
52C22×D4×C103—24no—
53C22×D4×C103—24no—
54C22×D4×C103—24no—
55C22×D4×C103—24no—
56C22×D4×C103—24no—
57C22×D4×C103—24no—
58C22×D4×C103—24no—
59C22×D4×C103—24no—
60C22×D4×C103—22no—
61C22×D4×C103—24no—
62C22×D4×C103—22no—
63C22×D4×C103—22no—
64C22×D4×C103—22no—
65C22×D4×C103—22no—
66C22×D4×C103—24no—
67C22×D4×C103—42no—
68C22×D4×C103—42no—
69C22×D4×C103—42no—
70C22×D4×C103—42no—
71C22×D4×C103—42no—
72C22×D4×C103D414yescomplemented
73C23×C4×C103—22no—
74C23×C4×C103—22no—
75C23×C4×C103—22no—
76C23×C4×C103—22no—
77C23×C4×C103—22no—
78C23×C4×C103—24no—
79C23×C4×C103—24no—
80C23×C4×C103—42no—
81C23×C4×C103—42no—
82C23×C4×C103D414yescomplemented
83C23×C4×C103C2312yes—
84C23×C4×C103C2312yes—
85C23×C4×C103C2311yescharacteristic
86C23×C4×C103C2311yescharacteristic
87C23×C4×C103C2312yes—
88C23×C4×C103C2311yescharacteristic
89C23×C4×C103C2311yescharacteristic
90C23×C4×C103C2311yescharacteristic
91#121×C103—232no—
92C4×D4×C103—232no—
93C2×C4⋊C4×C103—22no—
94C2×C4⋊C4×C103—22no—
95C2×C4⋊C4×C103—24no—
96C2×C4⋊C4×C103—22no—
97C2×C4⋊C4×C103D414yescomplemented
98C2×C22⋊C4×C103—22no—
99C2×C22⋊C4×C103—22no—
100C2×C22⋊C4×C103—22no—
101C2×C22⋊C4×C103—22no—
102C2×C22⋊C4×C103—22no—
103C2×C22⋊C4×C103—24no—
104C2×C22⋊C4×C103—24no—
105C2×C22⋊C4×C103—24no—
106C2×C22⋊C4×C103—24no—
107C2×C22⋊C4×C103—24no—
108C2×C22⋊C4×C103—24no—
109C2×C22⋊C4×C103—24no—
110C2×C22⋊C4×C103—24no—
111C2×C22⋊C4×C103—24no—
112C2×C22⋊C4×C103—24no—
113C2×C22⋊C4×C103—24no—
114C2×C22⋊C4×C103—24no—
115C2×C22⋊C4×C103—24no—
116C2×C22⋊C4×C103—42no—
117C2×C22⋊C4×C103—42no—
118C2×C22⋊C4×C103—42no—
119C2×C22⋊C4×C103—42no—
120C2×C22⋊C4×C103D418yescomplemented
121C2×C22⋊C4×C103D414yescomplemented
122C2×C42×C103—22no—
123C2×C42×C103—22no—
124C2×C42×C103—22no—
125#95×C103—24no—
126#95×C103—24no—
127#95×C103—22no—
128#95×C103—24no—
129#95×C103—22no—
130#95×C103—42no—
131C24×C103—21no—
132C24×C103—21no—
133C24×C103—21no—
134C24×C103—21no—
135C24×C103—22no—
136C24×C103—22no—
137C24×C103—22no—
138C24×C103—21no—
139C24×C103—21no—
140C24×C103—21no—
141C24×C103—21no—
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—22no—
155C24×C103—22no—
156C24×C103—22no—
157C24×C103—22no—
158C24×C103—22no—
159C24×C103—22no—
160C24×C103—22no—
161C24×C103C2×D414yes—
162C24×C103C2×D412yes—
163C24×C103C2×D412yes—
164C24×C103C2×D412yes—
165C24×C103C2×D412yes—
166C24×C103#4112yes—
167C24×C103#4112yes—
168C24×C103C2411yescharacteristic
169C2×D4×C103—28no—
170C2×D4×C103—28no—
171C2×D4×C103—28no—
172C2×D4×C103—28no—
173C2×D4×C103—28no—
174C2×D4×C103—28no—
175C2×D4×C103—28no—
176C2×D4×C103—216no—
177C2×D4×C103—216no—
178C2×D4×C103—28no—
179C2×D4×C103—48no—
180C2×D4×C103—48no—
181C2×D4×C103—48no—
182C2×D4×C103—48no—
183C2×D4×C103—48no—
184C2×D4×C103—48no—
185C2×D4×C103—44no—
186C2×D4×C103—48no—
187C2×D4×C103—48no—
188C2×D4×C103—48no—
189C2×D4×C103—48no—
190C2×D4×C103—48no—
191C2×D4×C103—48no—
192C2×D4×C103—48no—
193C2×D4×C103—48no—
194C2×D4×C103—44no—
195C22×C4×C103—21no—
196C22×C4×C103—21no—
197C22×C4×C103—21no—
198C22×C4×C103—21no—
199C22×C4×C103—22no—
200C22×C4×C103—21no—
201C22×C4×C103—21no—
202C22×C4×C103—22no—
203C22×C4×C103—22no—
204C22×C4×C103—28no—
205C22×C4×C103—22no—
206C22×C4×C103—22no—
207C22×C4×C103—22no—
208C22×C4×C103—22no—
209C22×C4×C103—22no—
210C22×C4×C103—21no—
211C22×C4×C103—21no—
212C22×C4×C103—21no—
213C22×C4×C103—21no—
214C22×C4×C103—22no—
215C22×C4×C103—22no—
216C22×C4×C103—22no—
217C22×C4×C103—22no—
218C22×C4×C103—22no—
219C22×C4×C103—22no—
220C22×C4×C103—22no—
221C22×C4×C103—22no—
222C22×C4×C103—22no—
223C22×C4×C103—22no—
224C22×C4×C103—22no—
225C22×C4×C103—28no—
226C22×C4×C103—28no—
227C22×C4×C103—22no—
228C22×C4×C103—22no—
229C22×C4×C103—22no—
230C22×C4×C103—22no—
231C22×C4×C103—22no—
232C22×C4×C103—22no—
233C22×C4×C103—22no—
234C22×C4×C103—44no—
235C22×C4×C103—48no—
236C22×C4×C103—48no—
237C22×C4×C103—48no—
238C22×C4×C103—48no—
239C22×C4×C103—44no—
240C22×C4×C103—44no—
241C22×C4×C103C2×D414yes—
242C22×C4×C103C2×D412yes—
243C22×C4×C103C2×D412yes—
244C22×C4×C103C2×D414yes—
245C22×C4×C103C2×D412yes—
246C22×C4×C103C2×D412yes—
247C22×C4×C103C2×D412yes—
248C22×C4×C103C2×D412yes—
249C22×C4×C103C2×D412yes—
250C22×C4×C103C2×D412yes—
251C22×C4×C103#4114yes—
252C22×C4×C103#4112yes—
253C4⋊C4×C103—28no—
254C4⋊C4×C103—28no—
255C22⋊C4×C103—28no—
256C22⋊C4×C103—28no—
257C22⋊C4×C103—216no—
258C22⋊C4×C103—48no—
259C22⋊C4×C103—48no—
260C22⋊C4×C103—48no—
261C22⋊C4×C103—48no—
262C22⋊C4×C103—48no—
263C42×C103—28no—
264C23×C103—22no—
265C23×C103—22no—
266C23×C103—22no—
267C23×C103—22no—
268C23×C103—22no—
269C23×C103—22no—
270C23×C103—22no—
271C23×C103—22no—
272C23×C103—22no—
273C23×C103—22no—
274C23×C103—22no—
275C23×C103—22no—
276C23×C103—22no—
277C23×C103—24no—
278C23×C103—22no—
279C23×C103—22no—
280C23×C103—22no—
281C23×C103—24no—
282C23×C103—24no—
283C23×C103—24no—
284C23×C103—24no—
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—24no—
295C23×C103—24no—
296C23×C103—24no—
297C23×C103—41no—
298C23×C103—42no—
299C23×C103—42no—
300C23×C103—42no—
301C23×C103—41no—
302C23×C103—41no—
303C23×C103—41no—
304C23×C103—42no—
305C23×C103—42no—
306C23×C103—42no—
307C23×C103—42no—
308C23×C103—42no—
309C23×C103—42no—
310C23×C103—42no—
311C23×C103—42no—
312C23×C103—42no—
313C23×C103—42no—
314C23×C103—42no—
315C23×C103—42no—
316C23×C103—42no—
317C23×C103—42no—
318C23×C103—42no—
319C23×C103—42no—
320C23×C103—42no—
321C23×C103—42no—
322C23×C103—42no—
323C23×C103—42no—
324C23×C103—42no—
325C23×C103—42no—
326C23×C103—42no—
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#12114yes—
344C23×C103#12114yescomplemented
345C23×C103C22×D411yescharacteristic
346C23×C103C22×D411yescharacteristic
347C23×C103C22×D411yescharacteristic
348C23×C103C22×D412yes—
349C23×C103C22×D411yescharacteristic
350C23×C103C2×#4111yescharacteristic
351C23×C103C2×#4111yescharacteristic
352C23×C103C2×#4111yescharacteristic
353C23×C103C2×#4112yes—
354C23×C103H(5,𝔽2)12yes—
355C23×C103H(5,𝔽2)12yes—
356D4×C103—232no—
357D4×C103—416no—
358D4×C103—432no—
359D4×C103—432no—
360C2×C4×C103—22no—
361C2×C4×C103—22no—
362C2×C4×C103—22no—
363C2×C4×C103—22no—
364C2×C4×C103—22no—
365C2×C4×C103—22no—
366C2×C4×C103—22no—
367C2×C4×C103—22no—
368C2×C4×C103—22no—
369C2×C4×C103—22no—
370C2×C4×C103—24no—
371C2×C4×C103—24no—
372C2×C4×C103—24no—
373C2×C4×C103—24no—
374C2×C4×C103—22no—
375C2×C4×C103—22no—
376C2×C4×C103—24no—
377C2×C4×C103—24no—
378C2×C4×C103—24no—
379C2×C4×C103—24no—
380C2×C4×C103—24no—
381C2×C4×C103—24no—
382C2×C4×C103—24no—
383C2×C4×C103—24no—
384C2×C4×C103—416no—
385C2×C4×C103—416no—
386C2×C4×C103—41no—
387C2×C4×C103—42no—
388C2×C4×C103—42no—
389C2×C4×C103—41no—
390C2×C4×C103—41no—
391C2×C4×C103—41no—
392C2×C4×C103—42no—
393C2×C4×C103—42no—
394C2×C4×C103—42no—
395C2×C4×C103—42no—
396C2×C4×C103—42no—
397C2×C4×C103—42no—
398C2×C4×C103—42no—
399C2×C4×C103—42no—
400C2×C4×C103—42no—
401C2×C4×C103—42no—
402C2×C4×C103—42no—
403C2×C4×C103—42no—
404C2×C4×C103—42no—
405C2×C4×C103—42no—
406C2×C4×C103—42no—
407C2×C4×C103#12014yes—
408C2×C4×C103#12014yes—
409C2×C4×C103#12114yescomplemented
410C22×C103—24no—
411C22×C103—24no—
412C22×C103—24no—
413C22×C103—28no—
414C22×C103—24no—
415C22×C103—42no—
416C22×C103—42no—
417C22×C103—42no—
418C22×C103—42no—
419C22×C103—42no—
420C22×C103—42no—
421C22×C103—42no—
422C22×C103—44no—
423C22×C103—44no—
424C22×C103—44no—
425C22×C103—42no—
426C22×C103—42no—
427C22×C103—44no—
428C22×C103—44no—
429C22×C103—44no—
430C22×C103—44no—
431C22×C103—42no—
432C22×C103—44no—
433C22×C103—44no—
434C22×C103—44no—
435C22×C103—44no—
436C22×C103—44no—
437C22×C103—44no—
438C22×C103—44no—
439C22×C103—82no—
440C22×C103—82no—
441C22×C103—82no—
442C22×C103—82no—
443C22×C103—82no—
444C22×C103—82no—
445C22×C103—82no—
446C22×C103—82no—
447C22×C103C2×#12011yescharacteristic
448C22×C103C2×#12011yescharacteristic
449C22×C103C2×#12111yescharacteristic
450C22×C103C2×#12111yescharacteristic
451C22×C103C2×#12111yescharacteristic
452C22×C103#52511yescharacteristic
453C22×C103#52511yescharacteristic
454C22×C103#52511yescharacteristic
455C22×C103#52512yes—
456C22×C103#53212yes—
457C22×C103#53211yescharacteristic
458C22×C103#53411yescharacteristic
459C22×C103#53511yescharacteristic
460C22×C103#53812yes—
461C22×C103#54012yes—
462C22×C103D4212yes—
463C22×C103D4212yes—
464C22×C103D4212yes—
465C22×C103#54612yes—
466C22×C103#54612yes—
467C22×C103#54612yes—
468C22×C103#55012yes—
469C22×C103#55312yes—
470C4×C103—24no—
471C4×C103—24no—
472C4×C103—24no—
473C4×C103—42no—
474C4×C103—44no—
475C4×C103—44no—
476C4×C103—42no—
477C4×C103—82no—
478#14722C10311yesmaximal, characteristic, direct product factor, Sylow
479C2×C103—44no—
480C2×C103—44no—
481C2×C103—84no—
482C2×C103#238811yescharacteristic
483C2×C103#240311yescharacteristic
484C2×C103#240811yescharacteristic
485C2×C103#242412yes—
486C2×C103#242812yes—
487C2×C103#243111yescharacteristic
488C2×C103#245612yes—
489C2×C103#246412yes—
490C2×C103#254311yescharacteristic
491C2×C103#263511yescharacteristic
492C2×C103#284711yescharacteristic
493C22×#121C2×C10311yescharacteristic, complemented
494C22×C4×D4C2×C10311yescharacteristic, complemented
495C2×#394C2×C10311yescharacteristic, complemented
496C2×#392C2×C10312yescomplemented
497C2×#392C2×C10311yescharacteristic, complemented
498C2×#386C2×C10312yescomplemented
499#1441C2×C10311yescharacteristic, complemented
500#1439C2×C10311yescharacteristic, complemented
501#1438C2×C10312yescomplemented
502#1437C2×C10312yescomplemented
503C22⋊#95C2×C10311yescharacteristic, complemented
504C103#1472211yescharacteristic, direct product factor, Sylow
505C23×D4C22×C10311yescharacteristic
506C23×D4C22×C10312yes—
507C23×D4C22×C10311yescharacteristic
508C23×D4C22×C10312yes—
509C24×C4C22×C10311yescharacteristic
510C24×C4C22×C10311yescharacteristic
511C2×#121—24no—
512C2×#121—28no—
513C2×C4×D4—24no—
514C2×C4×D4—24no—
515C2×C4×D4—24no—
516C22×C4⋊C4C22×C10311yescharacteristic
517C22×C4⋊C4C22×C10311yescharacteristic
518C22×C22⋊C4C22×C10312yes—
519C22×C22⋊C4C22×C10311yescharacteristic
520C22×C22⋊C4C22×C10312yes—
521C22×C22⋊C4C22×C10312yes—
522C22×C22⋊C4C22×C10312yes—
523C22×C22⋊C4C22×C10312yes—
524C22×C22⋊C4C22×C10311yescharacteristic
525C22×C22⋊C4C22×C10312yes—
526C22×C42C22×C10311yescharacteristic
527#394—24no—
528#392—28no—
529#392—24no—
530#386—28no—
531C2×#95C22×C10311yescharacteristic
532C2×#95C22×C10312yes—
533C2×#95C22×C10311yescharacteristic
534C2×#95C22×C10312yes—
535C2×#95C22×C10312yes—
536C2×#95C22×C10312yes—
537C25C23×C10312yes—
538C25C23×C10311yescharacteristic
539C25C23×C10311yescharacteristic
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×C10314yescomplemented
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×C10314yescomplemented
576C23×C4C23×C10312yes—
577C23×C4C23×C10311yescharacteristic
578C23×C4C23×C10311yescharacteristic
579C23×C4C23×C10312yes—
580C23×C4C23×C10312yes—
581C23×C4C23×C10311yescharacteristic
582C23×C4C23×C10311yescharacteristic
583C23×C4C23×C10311yescharacteristic
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×C10314yescomplemented
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×C10314yescomplemented
614C2×C22⋊C4D4×C10318yescomplemented
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×C10314yes—
655C24C2×D4×C10312yes—
656C24C2×D4×C10312yes—
657C24C2×D4×C10312yes—
658C24C2×D4×C10312yes—
659C24#41×C10312yes—
660C24#41×C10312yes—
661C24C24×C10311yescharacteristic
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×C10314yes—
735C22×C4C2×D4×C10312yes—
736C22×C4C2×D4×C10312yes—
737C22×C4C2×D4×C10314yes—
738C22×C4C2×D4×C10312yes—
739C22×C4C2×D4×C10312yes—
740C22×C4C2×D4×C10312yes—
741C22×C4C2×D4×C10312yes—
742C22×C4C2×D4×C10312yes—
743C22×C4C2×D4×C10312yes—
744C22×C4#41×C10314yes—
745C22×C4#41×C10312yes—
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—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
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×C10314yes—
837C23#121×C10314yescomplemented
838C23C22×D4×C10311yescharacteristic
839C23C22×D4×C10311yescharacteristic
840C23C22×D4×C10311yescharacteristic
841C23C22×D4×C10312yes—
842C23C22×D4×C10311yescharacteristic
843C23C2×#41×C10311yescharacteristic
844C23C2×#41×C10311yescharacteristic
845C23C2×#41×C10311yescharacteristic
846C23C2×#41×C10312yes—
847C23H(5,𝔽2)×C10312yes—
848C23H(5,𝔽2)×C10312yes—
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×C10314yes—
901C2×C4#120×C10314yes—
902C2×C4#121×C10314yescomplemented
903C22—24no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—28no—
908C22—44no—
909C22—44no—
910C22—44no—
911C22—44no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—44no—
921C22—44no—
922C22—44no—
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×C10311yescharacteristic
941C22C2×#120×C10311yescharacteristic
942C22C2×#121×C10311yescharacteristic
943C22C2×#121×C10311yescharacteristic
944C22C2×#121×C10311yescharacteristic
945C22#525×C10311yescharacteristic
946C22#525×C10312yes—
947C22#525×C10311yescharacteristic
948C22#525×C10311yescharacteristic
949C22#532×C10312yes—
950C22#532×C10311yescharacteristic
951C22#534×C10311yescharacteristic
952C22#535×C10311yescharacteristic
953C22#538×C10312yes—
954C22#540×C10312yes—
955C22D42×C10312yes—
956C22D42×C10312yes—
957C22D42×C10312yes—
958C22#546×C10312yes—
959C22#546×C10312yes—
960C22#546×C10312yes—
961C22#550×C10312yes—
962C22#553×C10312yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—42no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C103×#238811yescharacteristic
975C2C103×#240311yescharacteristic
976C2C103×#240811yescharacteristic
977C2C103×#242412yes—
978C2C103×#242812yes—
979C2C103×#243111yescharacteristic
980C2C103×#245612yes—
981C2C103×#246412yes—
982C2C103×#254311yescharacteristic
983C2C103×#263511yescharacteristic
984C2C103×#284711yescharacteristic
subgroupG/H
center, socleC24×C103C24
commutator, Frattini, cosocleC24C24×C103
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C103C2semidirect
2. C22×C4×D4×C103C2semidirect
3. C2×#394×C103C2semidirect
4. C2×#392×C103C2semidirect
5. C2×#392×C103C2semidirect
6. C2×#386×C103C2semidirect
7. C103×#1441C2semidirect
8. C103×#1439C2semidirect
9. C103×#1438C2semidirect
10. C103×#1437C2semidirect
11. C103×C22⋊#95C2semidirect
72. C22×D4×C103D4semidirect
82. C23×C4×C103D4semidirect
97. C2×C4⋊C4×C103D4semidirect
120. C2×C22⋊C4×C103D4semidirect
121. C2×C22⋊C4×C103D4semidirect
344. C23×C103#121semidirect
409. C2×C4×C103#121semidirect
478. #14722C103direct (N × H)
493. C22×#121C2×C103semidirect
494. C22×C4×D4C2×C103semidirect
495. C2×#394C2×C103semidirect
496. C2×#392C2×C103semidirect
497. C2×#392C2×C103semidirect
498. C2×#386C2×C103semidirect
499. #1441C2×C103semidirect
500. #1439C2×C103semidirect
501. #1438C2×C103semidirect
502. #1437C2×C103semidirect
503. C22⋊#95C2×C103semidirect
504. C103#14722direct (N × H)
565. C22×D4D4×C103semidirect
575. C23×C4D4×C103semidirect
590. C2×C4⋊C4D4×C103semidirect
613. C2×C22⋊C4D4×C103semidirect
614. C2×C22⋊C4D4×C103semidirect
837. C23#121×C103semidirect
902. C2×C4#121×C103semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1032
C22×C4×D4×C1032
C2×#394×C1032
C2×#392×C1032
C2×#386×C1032
C103×#14412
C103×#14392
C103×#14382
C103×#14372
C103×C22⋊#952
#14722103