Finite Group Databasebeta

← C103×#24405 #39929680

Subgroups — C103×#24405 #39929680

Order 26368.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3484C211yesmaximal, characteristic
2C2×#458×C103C211yesmaximal, characteristic, complemented
3C22×#99×C103C211yesmaximal, characteristic, complemented
4C103×#2412C212yesmaximal, complemented
5C103×#2405C211yesmaximal, characteristic, complemented
6C103×#2044C212yesmaximal, complemented
7C103×#2022C212yesmaximal, complemented
8C103×#1898C212yesmaximal, complemented
9C103×#1890C211yesmaximal, characteristic, complemented
10C103×#1867C211yesmaximal, characteristic, complemented
11C103×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C103C2211yescharacteristic
13C23×D4×C103C2211yescharacteristic
14#546×C103—22no—
15#546×C103—22no—
16D42×C103—22no—
17D42×C103—22no—
18#535×C103—21no—
19#534×C103—21no—
20#534×C103C2212yes—
21#525×C103—21no—
22C2×#123×C103C2211yescharacteristic
23C2×#123×C103C2212yescomplemented
24C2×#123×C103C2211yescharacteristic, complemented
25C2×#120×C103—21no—
26C2×#120×C103C2212yes—
27#518×C103C2211yescharacteristic
28C22×C22⋊C4×C103C2211yescharacteristic, complemented
29C22×C22⋊C4×C103C2212yescomplemented
30#458×C103—24no—
31C2×#99×C103—24no—
32C2×#99×C103C2211yescharacteristic
33C2×#99×C103C2211yescharacteristic
34C2×#99×C103C2212yescomplemented
35C2×#99×C103C2212yescomplemented
36C2×#99×C103C2212yescomplemented
37#397×C103—22no—
38#394×C103—21no—
39#394×C103—21no—
40#394×C103—22no—
41#386×C103—22no—
42#386×C103C2211yescharacteristic
43#386×C103C2211yescharacteristic, complemented
44#386×C103C2212yescomplemented
45#385×C103—21no—
46#385×C103C2212yescomplemented
47#381×C103C2212yescomplemented
48#380×C103—22no—
49#379×C103—21no—
50#379×C103C2211yescharacteristic, complemented
51#342×C103C2212yescomplemented
52#342×C103C2212yescomplemented
53C25×C103D411yescharacteristic
54C25×C103C2311yescharacteristic
55H(5,𝔽2)×C103—22no—
56H(5,𝔽2)×C103—22no—
57H(5,𝔽2)×C103—42no—
58C2×#41×C103—21no—
59C2×#41×C103—22no—
60C22×D4×C103—21no—
61C22×D4×C103—22no—
62C22×D4×C103—22no—
63C22×D4×C103—22no—
64C22×D4×C103—21no—
65C22×D4×C103—21no—
66C22×D4×C103—22no—
67C22×D4×C103—22no—
68C22×D4×C103—42no—
69C22×D4×C103D411yescharacteristic
70C22×D4×C103D411yescharacteristic
71C22×D4×C103D412yes—
72C22×D4×C103D412yes—
73C22×D4×C103C2312yes—
74C22×D4×C103C2311yescharacteristic
75C22×D4×C103C2311yescharacteristic
76C23×C4×C103—22no—
77C23×C4×C103D411yescharacteristic
78C23×C4×C103C2311yescharacteristic
79C23×C4×C103C2311yescharacteristic
80#127×C103—22no—
81#124×C103—22no—
82#123×C103—22no—
83#123×C103—22no—
84#123×C103—22no—
85#123×C103—22no—
86#123×C103—22no—
87#123×C103—24no—
88#123×C103—42no—
89#123×C103—42no—
90C22⋊Q8×C103—21no—
91C22⋊Q8×C103—21no—
92#121×C103—21no—
93#121×C103—21no—
94#121×C103—22no—
95#121×C103—22no—
96#121×C103—22no—
97#121×C103—22no—
98#121×C103—22no—
99#121×C103—22no—
100#120×C103—22no—
101#120×C103—22no—
102#120×C103—22no—
103#120×C103—22no—
104#120×C103—22no—
105#120×C103—22no—
106#120×C103—22no—
107#120×C103—22no—
108#120×C103—22no—
109C4×D4×C103—22no—
110C4×D4×C103—22no—
111C4×D4×C103—22no—
112C4×D4×C103—22no—
113#117×C103—21no—
114C2×C4⋊C4×C103—22no—
115C2×C4⋊C4×C103—21no—
116C2×C4⋊C4×C103—21no—
117C2×C4⋊C4×C103—22no—
118C2×C22⋊C4×C103—21no—
119C2×C22⋊C4×C103—21no—
120C2×C22⋊C4×C103—21no—
121C2×C22⋊C4×C103—24no—
122C2×C22⋊C4×C103—21no—
123C2×C22⋊C4×C103—21no—
124C2×C22⋊C4×C103—21no—
125C2×C22⋊C4×C103—21no—
126C2×C22⋊C4×C103—22no—
127C2×C22⋊C4×C103—22no—
128C2×C22⋊C4×C103—21no—
129C2×C22⋊C4×C103—22no—
130C2×C22⋊C4×C103—22no—
131C2×C22⋊C4×C103—21no—
132C2×C22⋊C4×C103—21no—
133C2×C22⋊C4×C103—21no—
134C2×C22⋊C4×C103—22no—
135C2×C22⋊C4×C103—42no—
136C2×C22⋊C4×C103D412yes—
137C2×C22⋊C4×C103D412yes—
138C2×C22⋊C4×C103C2311yescharacteristic
139C2×C22⋊C4×C103C2311yescharacteristic
140C2×C22⋊C4×C103C2312yes—
141C2×C22⋊C4×C103C2312yes—
142C2×C22⋊C4×C103C2312yes—
143#99×C103—22no—
144#99×C103—24no—
145#99×C103—24no—
146#99×C103—42no—
147#99×C103D414yescomplemented
148#95×C103—22no—
149#95×C103—22no—
150#95×C103—22no—
151#95×C103—21no—
152#95×C103—21no—
153#95×C103—22no—
154C24×C103—21no—
155C24×C103—21no—
156C24×C103—22no—
157C24×C103—21no—
158C24×C103—21no—
159C24×C103—21no—
160C24×C103—22no—
161C24×C103—41no—
162C24×C103—42no—
163C24×C103—42no—
164C24×C103—81no—
165C24×C103—81no—
166C24×C103C2×D411yescharacteristic
167C24×C103C2×D412yes—
168C24×C103C2×D411yescharacteristic
169C24×C103C2×D412yes—
170C24×C103C2×D412yes—
171C24×C103C2×D411yescharacteristic
172C24×C103C2×D411yescharacteristic
173C24×C103C2411yescharacteristic
174#41×C103—44no—
175#41×C103—44no—
176#41×C103—42no—
177#41×C103—42no—
178C2×Q8×C103—21no—
179C2×D4×C103—22no—
180C2×D4×C103—22no—
181C2×D4×C103—22no—
182C2×D4×C103—21no—
183C2×D4×C103—22no—
184C2×D4×C103—22no—
185C2×D4×C103—22no—
186C2×D4×C103—22no—
187C2×D4×C103—22no—
188C2×D4×C103—21no—
189C2×D4×C103—22no—
190C2×D4×C103—22no—
191C2×D4×C103—22no—
192C2×D4×C103—22no—
193C2×D4×C103—21no—
194C2×D4×C103—22no—
195C2×D4×C103—22no—
196C2×D4×C103—22no—
197C2×D4×C103—22no—
198C2×D4×C103—22no—
199C2×D4×C103—22no—
200C2×D4×C103—22no—
201C2×D4×C103—22no—
202C2×D4×C103—22no—
203C2×D4×C103—41no—
204C2×D4×C103—41no—
205C2×D4×C103—44no—
206C2×D4×C103—44no—
207C2×D4×C103—44no—
208C2×D4×C103—44no—
209C2×D4×C103—44no—
210C2×D4×C103—44no—
211C2×D4×C103—42no—
212C2×D4×C103—42no—
213C2×D4×C103—44no—
214C2×D4×C103—82no—
215C2×D4×C103—82no—
216C2×D4×C103—82no—
217C2×D4×C103C2×D412yes—
218C2×D4×C103#4112yes—
219C22×C4×C103—21no—
220C22×C4×C103—22no—
221C22×C4×C103—21no—
222C22×C4×C103—21no—
223C22×C4×C103—22no—
224C22×C4×C103—21no—
225C22×C4×C103—21no—
226C22×C4×C103—22no—
227C22×C4×C103—22no—
228C22×C4×C103—21no—
229C22×C4×C103—22no—
230C22×C4×C103—22no—
231C22×C4×C103—21no—
232C22×C4×C103—21no—
233C22×C4×C103—21no—
234C22×C4×C103—21no—
235C22×C4×C103—21no—
236C22×C4×C103—22no—
237C22×C4×C103—41no—
238C22×C4×C103—44no—
239C22×C4×C103—44no—
240C22×C4×C103—81no—
241C22×C4×C103—82no—
242C22×C4×C103C2×D412yes—
243C22×C4×C103C2×D411yescharacteristic
244C22×C4×C103C2×D411yescharacteristic
245C22×C4×C103C2×D412yes—
246C22×C4×C103C2×D412yes—
247C4⋊C4×C103—21no—
248C4⋊C4×C103—21no—
249C4⋊C4×C103—22no—
250C4⋊C4×C103—22no—
251C4⋊C4×C103—44no—
252C4⋊C4×C103—42no—
253C4⋊C4×C103—42no—
254C4⋊C4×C103—82no—
255C22⋊C4×C103—22no—
256C22⋊C4×C103—22no—
257C22⋊C4×C103—22no—
258C22⋊C4×C103—22no—
259C22⋊C4×C103—22no—
260C22⋊C4×C103—22no—
261C22⋊C4×C103—22no—
262C22⋊C4×C103—22no—
263C22⋊C4×C103—22no—
264C22⋊C4×C103—22no—
265C22⋊C4×C103—22no—
266C22⋊C4×C103—22no—
267C22⋊C4×C103—22no—
268C22⋊C4×C103—21no—
269C22⋊C4×C103—21no—
270C22⋊C4×C103—22no—
271C22⋊C4×C103—22no—
272C22⋊C4×C103—44no—
273C22⋊C4×C103—44no—
274C22⋊C4×C103—42no—
275C22⋊C4×C103—42no—
276C22⋊C4×C103—41no—
277C22⋊C4×C103—42no—
278C22⋊C4×C103—41no—
279C22⋊C4×C103—42no—
280C22⋊C4×C103—81no—
281C22⋊C4×C103—81no—
282C22⋊C4×C103—81no—
283C22⋊C4×C103—82no—
284C22⋊C4×C103C2×D414yescomplemented
285C42×C103—22no—
286C23×C103—21no—
287C23×C103—21no—
288C23×C103—21no—
289C23×C103—22no—
290C23×C103—22no—
291C23×C103—22no—
292C23×C103—24no—
293C23×C103—21no—
294C23×C103—21no—
295C23×C103—21no—
296C23×C103—22no—
297C23×C103—22no—
298C23×C103—21no—
299C23×C103—22no—
300C23×C103—21no—
301C23×C103—21no—
302C23×C103—22no—
303C23×C103—22no—
304C23×C103—42no—
305C23×C103—41no—
306C23×C103—41no—
307C23×C103—41no—
308C23×C103—41no—
309C23×C103—42no—
310C23×C103—42no—
311C23×C103—41no—
312C23×C103—42no—
313C23×C103—42no—
314C23×C103—41no—
315C23×C103—41no—
316C23×C103—41no—
317C23×C103—41no—
318C23×C103—42no—
319C23×C103—42no—
320C23×C103—42no—
321C23×C103—42no—
322C23×C103—42no—
323C23×C103—81no—
324C23×C103—81no—
325C23×C103—82no—
326C23×C103—82no—
327C23×C103—84no—
328C23×C103—81no—
329C23×C103—81no—
330C23×C103—84no—
331C23×C103—84no—
332C23×C103#12011yescharacteristic
333C23×C103#12012yes—
334C23×C103#12011yescharacteristic
335C23×C103#12112yes—
336C23×C103C22×D411yescharacteristic
337C23×C103C22×D412yes—
338C23×C103C22×D411yescharacteristic
339C23×C103C2×#4111yescharacteristic
340C23×C103H(5,𝔽2)12yes—
341Q8×C103—42no—
342D4×C103—24no—
343D4×C103—24no—
344D4×C103—44no—
345D4×C103—42no—
346D4×C103—44no—
347D4×C103—44no—
348D4×C103—44no—
349D4×C103—42no—
350D4×C103—42no—
351D4×C103—42no—
352D4×C103—42no—
353D4×C103—42no—
354D4×C103—42no—
355D4×C103—44no—
356D4×C103—82no—
357D4×C103—82no—
358D4×C103—82no—
359D4×C103—82no—
360C2×C4×C103—21no—
361C2×C4×C103—21no—
362C2×C4×C103—22no—
363C2×C4×C103—22no—
364C2×C4×C103—22no—
365C2×C4×C103—21no—
366C2×C4×C103—21no—
367C2×C4×C103—21no—
368C2×C4×C103—24no—
369C2×C4×C103—22no—
370C2×C4×C103—22no—
371C2×C4×C103—42no—
372C2×C4×C103—42no—
373C2×C4×C103—44no—
374C2×C4×C103—42no—
375C2×C4×C103—42no—
376C2×C4×C103—42no—
377C2×C4×C103—42no—
378C2×C4×C103—42no—
379C2×C4×C103—41no—
380C2×C4×C103—41no—
381C2×C4×C103—41no—
382C2×C4×C103—41no—
383C2×C4×C103—42no—
384C2×C4×C103—42no—
385C2×C4×C103—41no—
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—41no—
393C2×C4×C103—41no—
394C2×C4×C103—41no—
395C2×C4×C103—42no—
396C2×C4×C103—42no—
397C2×C4×C103—42no—
398C2×C4×C103—81no—
399C2×C4×C103—81no—
400C2×C4×C103—88no—
401C2×C4×C103#12112yes—
402C22×C103—21no—
403C22×C103—22no—
404C22×C103—21no—
405C22×C103—22no—
406C22×C103—21no—
407C22×C103—21no—
408C22×C103—21no—
409C22×C103—22no—
410C22×C103—22no—
411C22×C103—22no—
412C22×C103—21no—
413C22×C103—21no—
414C22×C103—22no—
415C22×C103—41no—
416C22×C103—41no—
417C22×C103—42no—
418C22×C103—44no—
419C22×C103—44no—
420C22×C103—42no—
421C22×C103—42no—
422C22×C103—42no—
423C22×C103—42no—
424C22×C103—41no—
425C22×C103—41no—
426C22×C103—42no—
427C22×C103—41no—
428C22×C103—42no—
429C22×C103—41no—
430C22×C103—42no—
431C22×C103—41no—
432C22×C103—82no—
433C22×C103—81no—
434C22×C103—81no—
435C22×C103—81no—
436C22×C103—82no—
437C22×C103—84no—
438C22×C103—82no—
439C22×C103—82no—
440C22×C103—81no—
441C22×C103—84no—
442C22×C103—162no—
443C22×C103#45812yescomplemented
444C22×C103C2×#12011yescharacteristic
445C22×C103C2×#12111yescharacteristic
446C22×C103#53411yescharacteristic
447C22×C103D4212yes—
448C22×C103#54612yes—
449C4×C103—22no—
450C4×C103—44no—
451C4×C103—41no—
452C4×C103—42no—
453C4×C103—42no—
454C4×C103—42no—
455C4×C103—81no—
456C4×C103—81no—
457C4×C103—82no—
458C4×C103—81no—
459C4×C103—81no—
460#24405C10311yesmaximal, characteristic, direct product factor, Sylow
461C2×C103—22no—
462C2×C103—21no—
463C2×C103—21no—
464C2×C103—22no—
465C2×C103—22no—
466C2×C103—42no—
467C2×C103—41no—
468C2×C103—42no—
469C2×C103—81no—
470C2×C103—82no—
471C2×C103#241011yescharacteristic
472C2×C103C2×#45811yescharacteristic
473C2×C103#302611yescharacteristic
474#3484C2×C10311yescharacteristic
475C2×#458C2×C10311yescharacteristic, complemented
476C22×#99C2×C10311yescharacteristic, complemented
477#2412C2×C10312yescomplemented
478#2405C2×C10311yescharacteristic, complemented
479#2044C2×C10312yescomplemented
480#2022C2×C10312yescomplemented
481#1898C2×C10312yescomplemented
482#1890C2×C10311yescharacteristic, complemented
483#1867C2×C10311yescharacteristic, complemented
484#1790C2×C10311yescharacteristic, complemented
485C103#2440511yescharacteristic, direct product factor, Sylow
486C2×H(5,𝔽2)C22×C10311yescharacteristic
487C23×D4C22×C10311yescharacteristic
488#546—22no—
489#546—22no—
490D42—22no—
491D42—22no—
492#535—21no—
493#534—21no—
494#534C22×C10312yes—
495#525—21no—
496C2×#123C22×C10311yescharacteristic
497C2×#123C22×C10312yescomplemented
498C2×#123C22×C10311yescharacteristic, complemented
499C2×#120—21no—
500C2×#120C22×C10312yes—
501#518C22×C10311yescharacteristic
502C22×C22⋊C4C22×C10311yescharacteristic, complemented
503C22×C22⋊C4C22×C10312yescomplemented
504#458—24no—
505C2×#99—24no—
506C2×#99C22×C10311yescharacteristic
507C2×#99C22×C10311yescharacteristic
508C2×#99C22×C10312yescomplemented
509C2×#99C22×C10312yescomplemented
510C2×#99C22×C10312yescomplemented
511#397—22no—
512#394—21no—
513#394—21no—
514#394—22no—
515#386—22no—
516#386C22×C10311yescharacteristic
517#386C22×C10311yescharacteristic, complemented
518#386C22×C10312yescomplemented
519#385—21no—
520#385C22×C10312yescomplemented
521#381C22×C10312yescomplemented
522#380—22no—
523#379—21no—
524#379C22×C10311yescharacteristic, complemented
525#342C22×C10312yescomplemented
526#342C22×C10312yescomplemented
527C25D4×C10311yescharacteristic
528C25C23×C10311yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C10311yescharacteristic
544C22×D4D4×C10311yescharacteristic
545C22×D4D4×C10312yes—
546C22×D4D4×C10312yes—
547C22×D4C23×C10312yes—
548C22×D4C23×C10311yescharacteristic
549C22×D4C23×C10311yescharacteristic
550C23×C4—22no—
551C23×C4D4×C10311yescharacteristic
552C23×C4C23×C10311yescharacteristic
553C23×C4C23×C10311yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C10312yes—
611C2×C22⋊C4D4×C10312yes—
612C2×C22⋊C4C23×C10312yes—
613C2×C22⋊C4C23×C10311yescharacteristic
614C2×C22⋊C4C23×C10311yescharacteristic
615C2×C22⋊C4C23×C10312yes—
616C2×C22⋊C4C23×C10312yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C10314yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C10311yescharacteristic
641C24C2×D4×C10312yes—
642C24C2×D4×C10311yescharacteristic
643C24C2×D4×C10312yes—
644C24C2×D4×C10312yes—
645C24C2×D4×C10311yescharacteristic
646C24C2×D4×C10311yescharacteristic
647C24C24×C10311yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C10312yes—
692C2×D4#41×C10312yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C10312yes—
717C22×C4C2×D4×C10311yescharacteristic
718C22×C4C2×D4×C10311yescharacteristic
719C22×C4C2×D4×C10312yes—
720C22×C4C2×D4×C10312yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C10314yescomplemented
759C42—22no—
760C23—22no—
761C23—24no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C10311yescharacteristic
807C23#120×C10312yes—
808C23#120×C10311yescharacteristic
809C23#121×C10312yes—
810C23C22×D4×C10311yescharacteristic
811C23C22×D4×C10312yes—
812C23C22×D4×C10311yescharacteristic
813C23C2×#41×C10311yescharacteristic
814C23H(5,𝔽2)×C10312yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C10312yes—
876C22—22no—
877C22—21no—
878C22—22no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—21no—
884C22—21no—
885C22—22no—
886C22—21no—
887C22—22no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22#458×C10312yescomplemented
918C22C2×#120×C10311yescharacteristic
919C22C2×#121×C10311yescharacteristic
920C22#534×C10311yescharacteristic
921C22D42×C10312yes—
922C22#546×C10312yes—
923C4—22no—
924C4—44no—
925C4—42no—
926C4—42no—
927C4—41no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C103×#241011yescharacteristic
945C2C2×#458×C10311yescharacteristic
946C2C103×#302611yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC24C24×C103
prime radicalC103×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C25×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#458×C103C2semidirect
3. C22×#99×C103C2semidirect
4. C103×#2412C2semidirect
5. C103×#2405C2semidirect
6. C103×#2044C2semidirect
7. C103×#2022C2semidirect
8. C103×#1898C2semidirect
9. C103×#1890C2semidirect
10. C103×#1867C2semidirect
11. C103×#1790C2semidirect
23. C2×#123×C103C22semidirect
24. C2×#123×C103C22semidirect
28. C22×C22⋊C4×C103C22semidirect
29. C22×C22⋊C4×C103C22semidirect
34. C2×#99×C103C22semidirect
35. C2×#99×C103C22semidirect
36. C2×#99×C103C22semidirect
43. #386×C103C22semidirect
44. #386×C103C22semidirect
46. #385×C103C22semidirect
47. #381×C103C22semidirect
50. #379×C103C22semidirect
51. #342×C103C22semidirect
52. #342×C103C22semidirect
147. #99×C103D4semidirect
284. C22⋊C4×C103C2×D4semidirect
443. C22×C103#458semidirect
460. #24405C103direct (N × H)
475. C2×#458C2×C103semidirect
476. C22×#99C2×C103semidirect
477. #2412C2×C103semidirect
478. #2405C2×C103semidirect
479. #2044C2×C103semidirect
480. #2022C2×C103semidirect
481. #1898C2×C103semidirect
482. #1890C2×C103semidirect
483. #1867C2×C103semidirect
484. #1790C2×C103semidirect
485. C103#24405direct (N × H)
497. C2×#123C22×C103semidirect
498. C2×#123C22×C103semidirect
502. C22×C22⋊C4C22×C103semidirect
503. C22×C22⋊C4C22×C103semidirect
508. C2×#99C22×C103semidirect
509. C2×#99C22×C103semidirect
510. C2×#99C22×C103semidirect
517. #386C22×C103semidirect
518. #386C22×C103semidirect
520. #385C22×C103semidirect
521. #381C22×C103semidirect
524. #379C22×C103semidirect
525. #342C22×C103semidirect
526. #342C22×C103semidirect
621. #99D4×C103semidirect
758. C22⋊C4C2×D4×C103semidirect
917. C22#458×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34842
C2×#458×C1032
C22×#99×C1032
C103×#24122
C103×#24052
C103×#20442
C103×#20222
C103×#18982
C103×#18902
C103×#18672
C103×#17902
#24405103