Finite Group Databasebeta

← C103×#24404 #39929679

Subgroups — C103×#24404 #39929679

Order 26368.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3484C211yesmaximal, characteristic, complemented
2C2×B(4,𝔽2)×C103C211yesmaximal, characteristic, complemented
3C22×#99×C103C211yesmaximal, characteristic, complemented
4C103×#2410C212yesmaximal, complemented
5C103×#2403C211yesmaximal, characteristic, complemented
6C103×#2044C212yesmaximal, complemented
7C103×#2021C212yesmaximal, complemented
8C103×#1898C212yesmaximal, complemented
9C103×#1889C211yesmaximal, characteristic, complemented
10C103×#1867C211yesmaximal, characteristic, complemented
11C103×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C103C2211yescharacteristic
13C23×D4×C103C2211yescharacteristic
14C23×D4×C103C2211yescharacteristic, complemented
15#546×C103—22no—
16#546×C103—22no—
17D42×C103—22no—
18D42×C103—22no—
19#535×C103—21no—
20#534×C103—21no—
21#534×C103C2212yes—
22#525×C103—21no—
23C2×#121×C103—22no—
24C2×#120×C103—21no—
25C2×#120×C103—21no—
26C2×#120×C103C2211yescharacteristic
27C2×#120×C103C2212yes—
28C2×#120×C103C2212yescomplemented
29C2×#120×C103C2211yescharacteristic, complemented
30#518×C103C2211yescharacteristic
31C22×C22⋊C4×C103C2212yescomplemented
32B(4,𝔽2)×C103—24no—
33C2×#99×C103—24no—
34C2×#99×C103C2211yescharacteristic
35C2×#99×C103C2211yescharacteristic
36C2×#99×C103C2212yescomplemented
37C2×#99×C103C2212yescomplemented
38C2×#99×C103C2212yescomplemented
39#394×C103—22no—
40#392×C103—21no—
41#392×C103—21no—
42#392×C103—22no—
43#386×C103—21no—
44#386×C103—22no—
45#386×C103C2211yescharacteristic
46#386×C103C2211yescharacteristic, complemented
47#386×C103C2212yescomplemented
48#385×C103C2212yescomplemented
49#379×C103C2212yescomplemented
50#379×C103C2211yescharacteristic, complemented
51#342×C103C2212yescomplemented
52#342×C103C2212yescomplemented
53C25×C103D411yescharacteristic, complemented
54C25×C103C2311yescharacteristic
55C25×C103C2311yescharacteristic
56H(5,𝔽2)×C103—22no—
57H(5,𝔽2)×C103—22no—
58H(5,𝔽2)×C103—42no—
59C2×#41×C103—21no—
60C2×#41×C103—22no—
61C22×D4×C103—21no—
62C22×D4×C103—22no—
63C22×D4×C103—21no—
64C22×D4×C103—22no—
65C22×D4×C103—22no—
66C22×D4×C103—22no—
67C22×D4×C103—21no—
68C22×D4×C103—21no—
69C22×D4×C103—22no—
70C22×D4×C103—22no—
71C22×D4×C103—21no—
72C22×D4×C103—22no—
73C22×D4×C103—21no—
74C22×D4×C103—21no—
75C22×D4×C103—22no—
76C22×D4×C103—44no—
77C22×D4×C103—42no—
78C22×D4×C103D411yescharacteristic, complemented
79C22×D4×C103D411yescharacteristic, complemented
80C22×D4×C103D412yescomplemented
81C22×D4×C103D412yescomplemented
82C22×D4×C103C2312yes—
83C22×D4×C103C2311yescharacteristic
84C22×D4×C103C2311yescharacteristic
85C23×C4×C103—22no—
86C23×C4×C103D411yescharacteristic, complemented
87C23×C4×C103C2311yescharacteristic
88#127×C103—22no—
89#124×C103—22no—
90#123×C103—22no—
91#123×C103—22no—
92#123×C103—22no—
93C22⋊Q8×C103—21no—
94C22⋊Q8×C103—21no—
95#121×C103—21no—
96#121×C103—21no—
97#121×C103—22no—
98#121×C103—22no—
99#121×C103—22no—
100#121×C103—22no—
101#121×C103—22no—
102#121×C103—22no—
103#121×C103—48no—
104#120×C103—22no—
105#120×C103—22no—
106#120×C103—22no—
107#120×C103—22no—
108#120×C103—22no—
109#120×C103—22no—
110#120×C103—22no—
111#120×C103—22no—
112#120×C103—22no—
113#120×C103—22no—
114#120×C103—22no—
115#120×C103—24no—
116#120×C103—42no—
117#120×C103—42no—
118#120×C103—44no—
119C4×D4×C103—22no—
120C4×D4×C103—22no—
121C4×D4×C103—22no—
122C4×D4×C103—22no—
123#117×C103—21no—
124C2×C4⋊C4×C103—22no—
125C2×C22⋊C4×C103—21no—
126C2×C22⋊C4×C103—21no—
127C2×C22⋊C4×C103—21no—
128C2×C22⋊C4×C103—24no—
129C2×C22⋊C4×C103—21no—
130C2×C22⋊C4×C103—21no—
131C2×C22⋊C4×C103—21no—
132C2×C22⋊C4×C103—22no—
133C2×C22⋊C4×C103—22no—
134C2×C22⋊C4×C103—22no—
135C2×C22⋊C4×C103—21no—
136C2×C22⋊C4×C103—21no—
137C2×C22⋊C4×C103—22no—
138C2×C22⋊C4×C103—21no—
139C2×C22⋊C4×C103—22no—
140C2×C22⋊C4×C103—42no—
141C2×C22⋊C4×C103D412yescomplemented
142C2×C22⋊C4×C103D412yescomplemented
143C2×C22⋊C4×C103C2311yescharacteristic
144C2×C22⋊C4×C103C2311yescharacteristic
145C2×C22⋊C4×C103C2312yes—
146C2×C22⋊C4×C103C2312yes—
147C2×C22⋊C4×C103C2312yes—
148#99×C103—22no—
149#99×C103—24no—
150#99×C103—24no—
151#99×C103—42no—
152#99×C103D414yescomplemented
153#95×C103—22no—
154#95×C103—21no—
155#95×C103—21no—
156#95×C103—22no—
157C24×C103—21no—
158C24×C103—21no—
159C24×C103—22no—
160C24×C103—21no—
161C24×C103—22no—
162C24×C103—21no—
163C24×C103—21no—
164C24×C103—21no—
165C24×C103—22no—
166C24×C103—21no—
167C24×C103—21no—
168C24×C103—22no—
169C24×C103—41no—
170C24×C103—42no—
171C24×C103—42no—
172C24×C103—42no—
173C24×C103—81no—
174C24×C103—81no—
175C24×C103—81no—
176C24×C103C2×D411yescharacteristic
177C24×C103C2×D412yes—
178C24×C103C2×D411yescharacteristic
179C24×C103C2×D412yes—
180C24×C103C2×D412yes—
181C24×C103C2×D411yescharacteristic
182C24×C103C2×D411yescharacteristic
183C24×C103C2411yescharacteristic
184#41×C103—44no—
185#41×C103—44no—
186#41×C103—42no—
187#41×C103—42no—
188C2×Q8×C103—21no—
189C2×D4×C103—22no—
190C2×D4×C103—22no—
191C2×D4×C103—22no—
192C2×D4×C103—24no—
193C2×D4×C103—21no—
194C2×D4×C103—28no—
195C2×D4×C103—22no—
196C2×D4×C103—22no—
197C2×D4×C103—22no—
198C2×D4×C103—22no—
199C2×D4×C103—22no—
200C2×D4×C103—21no—
201C2×D4×C103—22no—
202C2×D4×C103—22no—
203C2×D4×C103—22no—
204C2×D4×C103—22no—
205C2×D4×C103—21no—
206C2×D4×C103—22no—
207C2×D4×C103—22no—
208C2×D4×C103—22no—
209C2×D4×C103—22no—
210C2×D4×C103—22no—
211C2×D4×C103—22no—
212C2×D4×C103—22no—
213C2×D4×C103—22no—
214C2×D4×C103—22no—
215C2×D4×C103—41no—
216C2×D4×C103—41no—
217C2×D4×C103—42no—
218C2×D4×C103—44no—
219C2×D4×C103—44no—
220C2×D4×C103—44no—
221C2×D4×C103—44no—
222C2×D4×C103—44no—
223C2×D4×C103—44no—
224C2×D4×C103—44no—
225C2×D4×C103—44no—
226C2×D4×C103—44no—
227C2×D4×C103—42no—
228C2×D4×C103—42no—
229C2×D4×C103—44no—
230C2×D4×C103—42no—
231C2×D4×C103—41no—
232C2×D4×C103—42no—
233C2×D4×C103—41no—
234C2×D4×C103—42no—
235C2×D4×C103—44no—
236C2×D4×C103—42no—
237C2×D4×C103—42no—
238C2×D4×C103—42no—
239C2×D4×C103—44no—
240C2×D4×C103—42no—
241C2×D4×C103—82no—
242C2×D4×C103—82no—
243C2×D4×C103—81no—
244C2×D4×C103—81no—
245C2×D4×C103—82no—
246C2×D4×C103—82no—
247C2×D4×C103C2×D412yes—
248C2×D4×C103#4112yes—
249C22×C4×C103—21no—
250C22×C4×C103—22no—
251C22×C4×C103—21no—
252C22×C4×C103—21no—
253C22×C4×C103—21no—
254C22×C4×C103—22no—
255C22×C4×C103—22no—
256C22×C4×C103—21no—
257C22×C4×C103—21no—
258C22×C4×C103—22no—
259C22×C4×C103—22no—
260C22×C4×C103—21no—
261C22×C4×C103—21no—
262C22×C4×C103—42no—
263C22×C4×C103—41no—
264C22×C4×C103—44no—
265C22×C4×C103—44no—
266C22×C4×C103—82no—
267C22×C4×C103C2×D412yes—
268C22×C4×C103C2×D411yescharacteristic
269C22×C4×C103C2×D411yescharacteristic
270C22×C4×C103C2×D412yes—
271C22×C4×C103C2×D412yes—
272C4⋊C4×C103—21no—
273C4⋊C4×C103—21no—
274C4⋊C4×C103—22no—
275C4⋊C4×C103—22no—
276C4⋊C4×C103—44no—
277C22⋊C4×C103—22no—
278C22⋊C4×C103—22no—
279C22⋊C4×C103—22no—
280C22⋊C4×C103—22no—
281C22⋊C4×C103—22no—
282C22⋊C4×C103—22no—
283C22⋊C4×C103—22no—
284C22⋊C4×C103—22no—
285C22⋊C4×C103—22no—
286C22⋊C4×C103—22no—
287C22⋊C4×C103—22no—
288C22⋊C4×C103—22no—
289C22⋊C4×C103—22no—
290C22⋊C4×C103—21no—
291C22⋊C4×C103—21no—
292C22⋊C4×C103—22no—
293C22⋊C4×C103—22no—
294C22⋊C4×C103—44no—
295C22⋊C4×C103—44no—
296C22⋊C4×C103—42no—
297C22⋊C4×C103—42no—
298C22⋊C4×C103—42no—
299C22⋊C4×C103—44no—
300C22⋊C4×C103—42no—
301C22⋊C4×C103—44no—
302C22⋊C4×C103—42no—
303C22⋊C4×C103—82no—
304C22⋊C4×C103—81no—
305C22⋊C4×C103C2×D414yescomplemented
306C42×C103—22no—
307C23×C103—21no—
308C23×C103—21no—
309C23×C103—21no—
310C23×C103—22no—
311C23×C103—22no—
312C23×C103—22no—
313C23×C103—24no—
314C23×C103—21no—
315C23×C103—21no—
316C23×C103—21no—
317C23×C103—22no—
318C23×C103—22no—
319C23×C103—24no—
320C23×C103—22no—
321C23×C103—21no—
322C23×C103—22no—
323C23×C103—21no—
324C23×C103—21no—
325C23×C103—22no—
326C23×C103—22no—
327C23×C103—41no—
328C23×C103—42no—
329C23×C103—41no—
330C23×C103—41no—
331C23×C103—41no—
332C23×C103—42no—
333C23×C103—41no—
334C23×C103—42no—
335C23×C103—42no—
336C23×C103—42no—
337C23×C103—41no—
338C23×C103—41no—
339C23×C103—41no—
340C23×C103—41no—
341C23×C103—42no—
342C23×C103—42no—
343C23×C103—41no—
344C23×C103—42no—
345C23×C103—41no—
346C23×C103—41no—
347C23×C103—42no—
348C23×C103—42no—
349C23×C103—42no—
350C23×C103—42no—
351C23×C103—41no—
352C23×C103—41no—
353C23×C103—41no—
354C23×C103—42no—
355C23×C103—42no—
356C23×C103—42no—
357C23×C103—81no—
358C23×C103—81no—
359C23×C103—82no—
360C23×C103—82no—
361C23×C103—82no—
362C23×C103—82no—
363C23×C103—84no—
364C23×C103—84no—
365C23×C103—81no—
366C23×C103—81no—
367C23×C103—84no—
368C23×C103—84no—
369C23×C103#12011yescharacteristic
370C23×C103#12012yes—
371C23×C103#12011yescharacteristic
372C23×C103#12112yescomplemented
373C23×C103C22×D411yescharacteristic
374C23×C103C22×D412yes—
375C23×C103C22×D411yescharacteristic
376C23×C103C2×#4111yescharacteristic
377C23×C103H(5,𝔽2)12yes—
378Q8×C103—42no—
379D4×C103—24no—
380D4×C103—24no—
381D4×C103—44no—
382D4×C103—42no—
383D4×C103—44no—
384D4×C103—48no—
385D4×C103—44no—
386D4×C103—44no—
387D4×C103—44no—
388D4×C103—42no—
389D4×C103—42no—
390D4×C103—42no—
391D4×C103—42no—
392D4×C103—42no—
393D4×C103—42no—
394D4×C103—44no—
395D4×C103—44no—
396D4×C103—82no—
397D4×C103—82no—
398D4×C103—82no—
399D4×C103—82no—
400D4×C103—88no—
401D4×C103—84no—
402D4×C103—84no—
403C2×C4×C103—21no—
404C2×C4×C103—21no—
405C2×C4×C103—22no—
406C2×C4×C103—24no—
407C2×C4×C103—22no—
408C2×C4×C103—22no—
409C2×C4×C103—22no—
410C2×C4×C103—21no—
411C2×C4×C103—21no—
412C2×C4×C103—21no—
413C2×C4×C103—24no—
414C2×C4×C103—22no—
415C2×C4×C103—22no—
416C2×C4×C103—42no—
417C2×C4×C103—42no—
418C2×C4×C103—44no—
419C2×C4×C103—42no—
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—42no—
427C2×C4×C103—42no—
428C2×C4×C103—41no—
429C2×C4×C103—41no—
430C2×C4×C103—42no—
431C2×C4×C103—41no—
432C2×C4×C103—41no—
433C2×C4×C103—41no—
434C2×C4×C103—41no—
435C2×C4×C103—42no—
436C2×C4×C103—81no—
437C2×C4×C103—81no—
438C2×C4×C103—88no—
439C2×C4×C103#12112yescomplemented
440C22×C103—21no—
441C22×C103—22no—
442C22×C103—21no—
443C22×C103—22no—
444C22×C103—21no—
445C22×C103—21no—
446C22×C103—21no—
447C22×C103—22no—
448C22×C103—22no—
449C22×C103—22no—
450C22×C103—21no—
451C22×C103—21no—
452C22×C103—22no—
453C22×C103—41no—
454C22×C103—41no—
455C22×C103—42no—
456C22×C103—44no—
457C22×C103—44no—
458C22×C103—42no—
459C22×C103—42no—
460C22×C103—42no—
461C22×C103—44no—
462C22×C103—42no—
463C22×C103—42no—
464C22×C103—42no—
465C22×C103—44no—
466C22×C103—41no—
467C22×C103—41no—
468C22×C103—42no—
469C22×C103—41no—
470C22×C103—42no—
471C22×C103—42no—
472C22×C103—41no—
473C22×C103—42no—
474C22×C103—41no—
475C22×C103—82no—
476C22×C103—81no—
477C22×C103—81no—
478C22×C103—81no—
479C22×C103—82no—
480C22×C103—84no—
481C22×C103—82no—
482C22×C103—82no—
483C22×C103—81no—
484C22×C103—82no—
485C22×C103—81no—
486C22×C103—81no—
487C22×C103—82no—
488C22×C103—84no—
489C22×C103—81no—
490C22×C103—81no—
491C22×C103—162no—
492C22×C103B(4,𝔽2)12yescomplemented
493C22×C103C2×#12011yescharacteristic
494C22×C103C2×#12111yescharacteristic
495C22×C103#53411yescharacteristic
496C22×C103D4212yes—
497C22×C103#54612yes—
498C4×C103—22no—
499C4×C103—44no—
500C4×C103—41no—
501C4×C103—42no—
502C4×C103—42no—
503C4×C103—42no—
504C4×C103—42no—
505C4×C103—82no—
506C4×C103—81no—
507C4×C103—81no—
508#24404C10311yesmaximal, characteristic, direct product factor, Sylow
509C2×C103—22no—
510C2×C103—21no—
511C2×C103—21no—
512C2×C103—22no—
513C2×C103—22no—
514C2×C103—42no—
515C2×C103—41no—
516C2×C103—42no—
517C2×C103—82no—
518C2×C103—81no—
519C2×C103—82no—
520C2×C103#241011yescharacteristic
521C2×C103C2×B(4,𝔽2)11yescharacteristic
522C2×C103#302611yescharacteristic
523#3484C2×C10311yescharacteristic, complemented
524C2×B(4,𝔽2)C2×C10311yescharacteristic, complemented
525C22×#99C2×C10311yescharacteristic, complemented
526#2410C2×C10312yescomplemented
527#2403C2×C10311yescharacteristic, complemented
528#2044C2×C10312yescomplemented
529#2021C2×C10312yescomplemented
530#1898C2×C10312yescomplemented
531#1889C2×C10311yescharacteristic, complemented
532#1867C2×C10311yescharacteristic, complemented
533#1790C2×C10311yescharacteristic, complemented
534C103#2440411yescharacteristic, direct product factor, Sylow
535C2×H(5,𝔽2)C22×C10311yescharacteristic
536C23×D4C22×C10311yescharacteristic
537C23×D4C22×C10311yescharacteristic, complemented
538#546—22no—
539#546—22no—
540D42—22no—
541D42—22no—
542#535—21no—
543#534—21no—
544#534C22×C10312yes—
545#525—21no—
546C2×#121—22no—
547C2×#120—21no—
548C2×#120—21no—
549C2×#120C22×C10311yescharacteristic
550C2×#120C22×C10312yes—
551C2×#120C22×C10312yescomplemented
552C2×#120C22×C10311yescharacteristic, complemented
553#518C22×C10311yescharacteristic
554C22×C22⋊C4C22×C10312yescomplemented
555B(4,𝔽2)—24no—
556C2×#99—24no—
557C2×#99C22×C10311yescharacteristic
558C2×#99C22×C10311yescharacteristic
559C2×#99C22×C10312yescomplemented
560C2×#99C22×C10312yescomplemented
561C2×#99C22×C10312yescomplemented
562#394—22no—
563#392—21no—
564#392—21no—
565#392—22no—
566#386—21no—
567#386—22no—
568#386C22×C10311yescharacteristic
569#386C22×C10311yescharacteristic, complemented
570#386C22×C10312yescomplemented
571#385C22×C10312yescomplemented
572#379C22×C10312yescomplemented
573#379C22×C10311yescharacteristic, complemented
574#342C22×C10312yescomplemented
575#342C22×C10312yescomplemented
576C25D4×C10311yescharacteristic, complemented
577C25C23×C10311yescharacteristic
578C25C23×C10311yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C10311yescharacteristic, complemented
602C22×D4D4×C10311yescharacteristic, complemented
603C22×D4D4×C10312yescomplemented
604C22×D4D4×C10312yescomplemented
605C22×D4C23×C10312yes—
606C22×D4C23×C10311yescharacteristic
607C22×D4C23×C10311yescharacteristic
608C23×C4—22no—
609C23×C4D4×C10311yescharacteristic, complemented
610C23×C4C23×C10311yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C10312yescomplemented
665C2×C22⋊C4D4×C10312yescomplemented
666C2×C22⋊C4C23×C10312yes—
667C2×C22⋊C4C23×C10311yescharacteristic
668C2×C22⋊C4C23×C10311yescharacteristic
669C2×C22⋊C4C23×C10312yes—
670C2×C22⋊C4C23×C10312yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C10314yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C10311yescharacteristic
700C24C2×D4×C10312yes—
701C24C2×D4×C10311yescharacteristic
702C24C2×D4×C10312yes—
703C24C2×D4×C10312yes—
704C24C2×D4×C10311yescharacteristic
705C24C2×D4×C10311yescharacteristic
706C24C24×C10311yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C10312yes—
771C2×D4#41×C10312yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C10312yes—
791C22×C4C2×D4×C10311yescharacteristic
792C22×C4C2×D4×C10311yescharacteristic
793C22×C4C2×D4×C10312yes—
794C22×C4C2×D4×C10312yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C10314yescomplemented
829C42—22no—
830C23—22no—
831C23—24no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—22no—
836C23—22no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C10311yescharacteristic
893C23#120×C10312yes—
894C23#120×C10311yescharacteristic
895C23#121×C10312yescomplemented
896C23C22×D4×C10311yescharacteristic
897C23C22×D4×C10312yes—
898C23C22×D4×C10311yescharacteristic
899C23C2×#41×C10311yescharacteristic
900C23H(5,𝔽2)×C10312yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—44no—
912D4—44no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—42no—
918D4—42no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C10312yescomplemented
963C22—22no—
964C22—21no—
965C22—22no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—22no—
970C22—21no—
971C22—21no—
972C22—22no—
973C22—21no—
974C22—22no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—42no—
993C22—41no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22B(4,𝔽2)×C10312yescomplemented
1016C22C2×#120×C10311yescharacteristic
1017C22C2×#121×C10311yescharacteristic
1018C22#534×C10311yescharacteristic
1019C22D42×C10312yes—
1020C22#546×C10312yes—
1021C4—22no—
1022C4—44no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4—41no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C103×#241011yescharacteristic
1043C2C2×B(4,𝔽2)×C10311yescharacteristic
1044C2C103×#302611yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC24C24×C103
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C25×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3484C2semidirect
2. C2×B(4,𝔽2)×C103C2semidirect
3. C22×#99×C103C2semidirect
4. C103×#2410C2semidirect
5. C103×#2403C2semidirect
6. C103×#2044C2semidirect
7. C103×#2021C2semidirect
8. C103×#1898C2semidirect
9. C103×#1889C2semidirect
10. C103×#1867C2semidirect
11. C103×#1790C2semidirect
14. C23×D4×C103C22semidirect
28. C2×#120×C103C22semidirect
29. C2×#120×C103C22semidirect
31. C22×C22⋊C4×C103C22semidirect
36. C2×#99×C103C22semidirect
37. C2×#99×C103C22semidirect
38. C2×#99×C103C22semidirect
46. #386×C103C22semidirect
47. #386×C103C22semidirect
48. #385×C103C22semidirect
49. #379×C103C22semidirect
50. #379×C103C22semidirect
51. #342×C103C22semidirect
52. #342×C103C22semidirect
53. C25×C103D4semidirect
78. C22×D4×C103D4semidirect
79. C22×D4×C103D4semidirect
80. C22×D4×C103D4semidirect
81. C22×D4×C103D4semidirect
86. C23×C4×C103D4semidirect
141. C2×C22⋊C4×C103D4semidirect
142. C2×C22⋊C4×C103D4semidirect
152. #99×C103D4semidirect
305. C22⋊C4×C103C2×D4semidirect
372. C23×C103#121semidirect
439. C2×C4×C103#121semidirect
492. C22×C103B(4,𝔽2)semidirect
508. #24404C103direct (N × H)
523. #3484C2×C103semidirect
524. C2×B(4,𝔽2)C2×C103semidirect
525. C22×#99C2×C103semidirect
526. #2410C2×C103semidirect
527. #2403C2×C103semidirect
528. #2044C2×C103semidirect
529. #2021C2×C103semidirect
530. #1898C2×C103semidirect
531. #1889C2×C103semidirect
532. #1867C2×C103semidirect
533. #1790C2×C103semidirect
534. C103#24404direct (N × H)
537. C23×D4C22×C103semidirect
551. C2×#120C22×C103semidirect
552. C2×#120C22×C103semidirect
554. C22×C22⋊C4C22×C103semidirect
559. C2×#99C22×C103semidirect
560. C2×#99C22×C103semidirect
561. C2×#99C22×C103semidirect
569. #386C22×C103semidirect
570. #386C22×C103semidirect
571. #385C22×C103semidirect
572. #379C22×C103semidirect
573. #379C22×C103semidirect
574. #342C22×C103semidirect
575. #342C22×C103semidirect
576. C25D4×C103semidirect
601. C22×D4D4×C103semidirect
602. C22×D4D4×C103semidirect
603. C22×D4D4×C103semidirect
604. C22×D4D4×C103semidirect
609. C23×C4D4×C103semidirect
664. C2×C22⋊C4D4×C103semidirect
665. C2×C22⋊C4D4×C103semidirect
675. #99D4×C103semidirect
828. C22⋊C4C2×D4×C103semidirect
895. C23#121×C103semidirect
962. C2×C4#121×C103semidirect
1015. C22B(4,𝔽2)×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34842
C2×B(4,𝔽2)×C1032
C22×#99×C1032
C103×#24102
C103×#24032
C103×#20442
C103×#20212
C103×#18982
C103×#18892
C103×#18672
C103×#17902
#24404103