Finite Group Databasebeta

← C103×#25563 #39930838

Subgroups — C103×#25563 #39930838

Order 26368.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3490C211yesmaximal, characteristic, complemented
2C103×#2410C212yesmaximal, complemented
3C103×#2405C211yesmaximal, characteristic, complemented
4C103×#2062C211yesmaximal, characteristic, complemented
5C103×#2044C211yesmaximal, characteristic, complemented
6C103×#2029C211yesmaximal, characteristic, complemented
7C103×#2021C211yesmaximal, characteristic, complemented
8C103×#1898C212yesmaximal, complemented
9C103×#1889C212yesmaximal, complemented
10C103×#1867C212yesmaximal, complemented
11C2×#342×C103C211yesmaximal, characteristic, complemented
12C23×D4×C103C2211yescharacteristic
13#551×C103—22no—
14#551×C103—22no—
15#546×C103—22no—
16#546×C103—22no—
17#543×C103C2211yescharacteristic
18#538×C103—21no—
19#538×C103—21no—
20#534×C103C2211yescharacteristic
21#525×C103—21no—
22#525×C103—21no—
23C2×#123×C103—21no—
24C2×#121×C103—22no—
25C2×#120×C103C2212yes—
26C2×#120×C103C2212yes—
27#518×C103C2212yes—
28C22×C22⋊C4×C103C2211yescharacteristic
29C22×C22⋊C4×C103C2212yes—
30C2×#99×C103C2212yes—
31C2×#99×C103C2212yes—
32#394×C103—21no—
33#394×C103—21no—
34#394×C103—22no—
35#392×C103—22no—
36#386×C103—21no—
37#386×C103—22no—
38#386×C103C2212yes—
39#385×C103C2211yescharacteristic
40#385×C103C2212yes—
41#385×C103C2211yescharacteristic
42#379×C103C2211yescharacteristic
43#379×C103C2212yes—
44#379×C103C2211yescharacteristic
45#379×C103C2211yescharacteristic
46#342×C103C2211yescharacteristic
47#342×C103C2211yescharacteristic
48#342×C103C2212yes—
49#342×C103C2212yes—
50#342×C103C2212yes—
51C25×C103C2311yescharacteristic
52C25×C103C2311yescharacteristic
53C2×#41×C103—21no—
54C2×#41×C103—21no—
55C22×D4×C103—22no—
56C22×D4×C103—21no—
57C22×D4×C103—22no—
58C22×D4×C103—21no—
59C22×D4×C103—22no—
60C22×D4×C103—44no—
61C22×D4×C103D412yescomplemented
62C22×D4×C103D412yescomplemented
63C22×D4×C103C2312yes—
64C23×C4×C103—22no—
65C23×C4×C103D411yescharacteristic, complemented
66C23×C4×C103D411yescharacteristic, complemented
67C23×C4×C103C2311yescharacteristic
68#126×C103—22no—
69#126×C103—22no—
70#124×C103—22no—
71#124×C103—22no—
72#123×C103—22no—
73#123×C103—22no—
74#123×C103—22no—
75#123×C103—22no—
76#123×C103—22no—
77#123×C103—44no—
78C22⋊Q8×C103—21no—
79C22⋊Q8×C103—21no—
80C22⋊Q8×C103—21no—
81C22⋊Q8×C103—21no—
82C22⋊Q8×C103—22no—
83C22⋊Q8×C103—22no—
84#121×C103—21no—
85#121×C103—21no—
86#121×C103—22no—
87#121×C103—22no—
88#121×C103—21no—
89#121×C103—21no—
90#121×C103—48no—
91#120×C103—22no—
92#120×C103—22no—
93#120×C103—22no—
94#120×C103—22no—
95#120×C103—22no—
96#120×C103—24no—
97#120×C103—42no—
98C4×D4×C103—22no—
99C4×D4×C103—22no—
100C4×D4×C103—22no—
101C4×D4×C103—22no—
102C4×D4×C103—22no—
103C4×D4×C103—22no—
104#117×C103—21no—
105#117×C103—21no—
106#117×C103—22no—
107C2×C4⋊C4×C103—22no—
108C2×C4⋊C4×C103—21no—
109C2×C4⋊C4×C103—21no—
110C2×C22⋊C4×C103—22no—
111C2×C22⋊C4×C103—22no—
112C2×C22⋊C4×C103—22no—
113C2×C22⋊C4×C103—24no—
114C2×C22⋊C4×C103—21no—
115C2×C22⋊C4×C103—22no—
116C2×C22⋊C4×C103—22no—
117C2×C22⋊C4×C103—22no—
118C2×C22⋊C4×C103—21no—
119C2×C22⋊C4×C103—21no—
120C2×C22⋊C4×C103—22no—
121C2×C22⋊C4×C103—21no—
122C2×C22⋊C4×C103—22no—
123C2×C22⋊C4×C103—21no—
124C2×C22⋊C4×C103—21no—
125C2×C22⋊C4×C103—42no—
126C2×C22⋊C4×C103D412yescomplemented
127C2×C22⋊C4×C103D411yescharacteristic, complemented
128C2×C22⋊C4×C103D411yescharacteristic, complemented
129C2×C22⋊C4×C103D412yescomplemented
130C2×C22⋊C4×C103C2312yes—
131C2×C22⋊C4×C103C2311yescharacteristic
132C2×C22⋊C4×C103C2311yescharacteristic
133C2×C22⋊C4×C103C2311yescharacteristic
134C2×C22⋊C4×C103C2311yescharacteristic
135C2×C22⋊C4×C103C2312yes—
136C2×C22⋊C4×C103C2312yes—
137#99×C103—24no—
138#99×C103—42no—
139#95×C103—22no—
140#95×C103—21no—
141#95×C103—21no—
142#95×C103—22no—
143C24×C103—22no—
144C24×C103—21no—
145C24×C103—21no—
146C24×C103—21no—
147C24×C103—22no—
148C24×C103—22no—
149C24×C103—21no—
150C24×C103—21no—
151C24×C103—42no—
152C24×C103—42no—
153C24×C103—81no—
154C24×C103—81no—
155C24×C103C2×D412yes—
156C24×C103C2×D411yescharacteristic
157C24×C103C2×D412yes—
158C24×C103C2×D412yes—
159C24×C103C2×D411yescharacteristic
160C24×C103C2411yescharacteristic
161#41×C103—82no—
162#41×C103—82no—
163C2×Q8×C103—21no—
164C2×Q8×C103—21no—
165C2×D4×C103—28no—
166C2×D4×C103—24no—
167C2×D4×C103—22no—
168C2×D4×C103—22no—
169C2×D4×C103—22no—
170C2×D4×C103—22no—
171C2×D4×C103—22no—
172C2×D4×C103—22no—
173C2×D4×C103—22no—
174C2×D4×C103—22no—
175C2×D4×C103—21no—
176C2×D4×C103—21no—
177C2×D4×C103—22no—
178C2×D4×C103—22no—
179C2×D4×C103—44no—
180C2×D4×C103—42no—
181C2×D4×C103—44no—
182C2×D4×C103—42no—
183C2×D4×C103—44no—
184C2×D4×C103—42no—
185C2×D4×C103—44no—
186C2×D4×C103—42no—
187C2×D4×C103—41no—
188C2×D4×C103—41no—
189C2×D4×C103—44no—
190C2×D4×C103—44no—
191C2×D4×C103—82no—
192C2×D4×C103—82no—
193C22×C4×C103—21no—
194C22×C4×C103—21no—
195C22×C4×C103—22no—
196C22×C4×C103—21no—
197C22×C4×C103—22no—
198C22×C4×C103—22no—
199C22×C4×C103—22no—
200C22×C4×C103—21no—
201C22×C4×C103—21no—
202C22×C4×C103—21no—
203C22×C4×C103—21no—
204C22×C4×C103—22no—
205C22×C4×C103—42no—
206C22×C4×C103—44no—
207C22×C4×C103—42no—
208C22×C4×C103—44no—
209C22×C4×C103—81no—
210C22×C4×C103—82no—
211C22×C4×C103C2×D412yes—
212C22×C4×C103C2×D411yescharacteristic
213C22×C4×C103C2×D412yes—
214C22×C4×C103C2×D411yescharacteristic
215C22×C4×C103C2×D411yescharacteristic
216C22×C4×C103C2×D412yes—
217C22×C4×C103C2×D411yescharacteristic
218C4⋊C4×C103—22no—
219C4⋊C4×C103—22no—
220C4⋊C4×C103—21no—
221C4⋊C4×C103—21no—
222C4⋊C4×C103—21no—
223C4⋊C4×C103—21no—
224C4⋊C4×C103—22no—
225C4⋊C4×C103—22no—
226C4⋊C4×C103—44no—
227C4⋊C4×C103—42no—
228C4⋊C4×C103—42no—
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—22no—
236C22⋊C4×C103—22no—
237C22⋊C4×C103—22no—
238C22⋊C4×C103—22no—
239C22⋊C4×C103—22no—
240C22⋊C4×C103—22no—
241C22⋊C4×C103—22no—
242C22⋊C4×C103—22no—
243C22⋊C4×C103—22no—
244C22⋊C4×C103—22no—
245C22⋊C4×C103—22no—
246C22⋊C4×C103—21no—
247C22⋊C4×C103—22no—
248C22⋊C4×C103—21no—
249C22⋊C4×C103—44no—
250C22⋊C4×C103—44no—
251C22⋊C4×C103—44no—
252C22⋊C4×C103—44no—
253C22⋊C4×C103—42no—
254C22⋊C4×C103—42no—
255C22⋊C4×C103—42no—
256C22⋊C4×C103—81no—
257C22⋊C4×C103—81no—
258C22⋊C4×C103—82no—
259C22⋊C4×C103—81no—
260C22⋊C4×C103#4114yescomplemented
261C42×C103—22no—
262C42×C103—22no—
263C23×C103—21no—
264C23×C103—21no—
265C23×C103—22no—
266C23×C103—22no—
267C23×C103—22no—
268C23×C103—24no—
269C23×C103—21no—
270C23×C103—21no—
271C23×C103—22no—
272C23×C103—22no—
273C23×C103—22no—
274C23×C103—24no—
275C23×C103—22no—
276C23×C103—22no—
277C23×C103—22no—
278C23×C103—41no—
279C23×C103—41no—
280C23×C103—42no—
281C23×C103—41no—
282C23×C103—41no—
283C23×C103—41no—
284C23×C103—42no—
285C23×C103—42no—
286C23×C103—41no—
287C23×C103—41no—
288C23×C103—42no—
289C23×C103—41no—
290C23×C103—42no—
291C23×C103—42no—
292C23×C103—42no—
293C23×C103—42no—
294C23×C103—41no—
295C23×C103—41no—
296C23×C103—41no—
297C23×C103—42no—
298C23×C103—42no—
299C23×C103—84no—
300C23×C103—84no—
301C23×C103—82no—
302C23×C103—82no—
303C23×C103—82no—
304C23×C103—82no—
305C23×C103#12012yes—
306C23×C103#12011yescharacteristic
307C23×C103#12011yescharacteristic
308C23×C103C22×D411yescharacteristic
309C23×C103C22×D412yes—
310C23×C103C2×#4112yes—
311C23×C103H(5,𝔽2)11yescharacteristic
312C23×C1032−1+411yescharacteristic
313Q8×C103—81no—
314Q8×C103—81no—
315D4×C103—44no—
316D4×C103—48no—
317D4×C103—44no—
318D4×C103—42no—
319D4×C103—42no—
320D4×C103—42no—
321D4×C103—42no—
322D4×C103—44no—
323D4×C103—44no—
324D4×C103—82no—
325D4×C103—82no—
326D4×C103—81no—
327D4×C103—81no—
328D4×C103—88no—
329C2×C4×C103—24no—
330C2×C4×C103—22no—
331C2×C4×C103—22no—
332C2×C4×C103—21no—
333C2×C4×C103—21no—
334C2×C4×C103—22no—
335C2×C4×C103—22no—
336C2×C4×C103—21no—
337C2×C4×C103—21no—
338C2×C4×C103—24no—
339C2×C4×C103—22no—
340C2×C4×C103—22no—
341C2×C4×C103—42no—
342C2×C4×C103—41no—
343C2×C4×C103—42no—
344C2×C4×C103—42no—
345C2×C4×C103—42no—
346C2×C4×C103—41no—
347C2×C4×C103—42no—
348C2×C4×C103—41no—
349C2×C4×C103—41no—
350C2×C4×C103—42no—
351C2×C4×C103—41no—
352C2×C4×C103—41no—
353C2×C4×C103—42no—
354C2×C4×C103—41no—
355C2×C4×C103—41no—
356C2×C4×C103—42no—
357C2×C4×C103—41no—
358C2×C4×C103—41no—
359C2×C4×C103—42no—
360C2×C4×C103—41no—
361C2×C4×C103—41no—
362C2×C4×C103—42no—
363C2×C4×C103—81no—
364C2×C4×C103—81no—
365C2×C4×C103—82no—
366C2×C4×C103—82no—
367C2×C4×C103—88no—
368C22×C103—21no—
369C22×C103—21no—
370C22×C103—22no—
371C22×C103—21no—
372C22×C103—22no—
373C22×C103—21no—
374C22×C103—21no—
375C22×C103—22no—
376C22×C103—21no—
377C22×C103—22no—
378C22×C103—21no—
379C22×C103—22no—
380C22×C103—42no—
381C22×C103—41no—
382C22×C103—41no—
383C22×C103—44no—
384C22×C103—42no—
385C22×C103—42no—
386C22×C103—44no—
387C22×C103—44no—
388C22×C103—42no—
389C22×C103—42no—
390C22×C103—44no—
391C22×C103—42no—
392C22×C103—42no—
393C22×C103—42no—
394C22×C103—42no—
395C22×C103—82no—
396C22×C103—81no—
397C22×C103—81no—
398C22×C103—82no—
399C22×C103—82no—
400C22×C103—82no—
401C22×C103—82no—
402C22×C103—81no—
403C22×C103—81no—
404C22×C103—82no—
405C22×C103—81no—
406C22×C103—81no—
407C22×C103B(4,𝔽2)12yes—
408C22×C103C2×#12011yescharacteristic
409C22×C103#53211yescharacteristic
410C22×C103#53711yescharacteristic
411C22×C103#54612yes—
412C22×C103#54712yes—
413C4×C103—44no—
414C4×C103—42no—
415C4×C103—42no—
416C4×C103—41no—
417C4×C103—41no—
418C4×C103—42no—
419C4×C103—41no—
420C4×C103—41no—
421C4×C103—42no—
422C4×C103—81no—
423C4×C103—81no—
424C4×C103—82no—
425#25563C10311yesmaximal, characteristic, direct product factor, Sylow
426C2×C103—22no—
427C2×C103—21no—
428C2×C103—21no—
429C2×C103—22no—
430C2×C103—22no—
431C2×C103—41no—
432C2×C103—42no—
433C2×C103—82no—
434C2×C103—82no—
435C2×C103#243011yescharacteristic
436C2×C103C2×B(4,𝔽2)11yescharacteristic
437C2×C103#302611yescharacteristic
438#3490C2×C10311yescharacteristic, complemented
439#2410C2×C10312yescomplemented
440#2405C2×C10311yescharacteristic, complemented
441#2062C2×C10311yescharacteristic, complemented
442#2044C2×C10311yescharacteristic, complemented
443#2029C2×C10311yescharacteristic, complemented
444#2021C2×C10311yescharacteristic, complemented
445#1898C2×C10312yescomplemented
446#1889C2×C10312yescomplemented
447#1867C2×C10312yescomplemented
448C2×#342C2×C10311yescharacteristic, complemented
449C103#2556311yescharacteristic, direct product factor, Sylow
450C23×D4C22×C10311yescharacteristic
451#551—22no—
452#551—22no—
453#546—22no—
454#546—22no—
455#543C22×C10311yescharacteristic
456#538—21no—
457#538—21no—
458#534C22×C10311yescharacteristic
459#525—21no—
460#525—21no—
461C2×#123—21no—
462C2×#121—22no—
463C2×#120C22×C10312yes—
464C2×#120C22×C10312yes—
465#518C22×C10312yes—
466C22×C22⋊C4C22×C10311yescharacteristic
467C22×C22⋊C4C22×C10312yes—
468C2×#99C22×C10312yes—
469C2×#99C22×C10312yes—
470#394—21no—
471#394—21no—
472#394—22no—
473#392—22no—
474#386—21no—
475#386—22no—
476#386C22×C10312yes—
477#385C22×C10312yes—
478#385C22×C10311yescharacteristic
479#385C22×C10311yescharacteristic
480#379C22×C10311yescharacteristic
481#379C22×C10312yes—
482#379C22×C10311yescharacteristic
483#379C22×C10311yescharacteristic
484#342C22×C10312yes—
485#342C22×C10311yescharacteristic
486#342C22×C10312yes—
487#342C22×C10312yes—
488#342C22×C10311yescharacteristic
489C25C23×C10311yescharacteristic
490C25C23×C10311yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C10312yescomplemented
500C22×D4D4×C10312yescomplemented
501C22×D4C23×C10312yes—
502C23×C4—22no—
503C23×C4D4×C10311yescharacteristic, complemented
504C23×C4D4×C10311yescharacteristic, complemented
505C23×C4C23×C10311yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C10311yescharacteristic, complemented
565C2×C22⋊C4D4×C10311yescharacteristic, complemented
566C2×C22⋊C4D4×C10312yescomplemented
567C2×C22⋊C4D4×C10312yescomplemented
568C2×C22⋊C4C23×C10312yes—
569C2×C22⋊C4C23×C10311yescharacteristic
570C2×C22⋊C4C23×C10311yescharacteristic
571C2×C22⋊C4C23×C10311yescharacteristic
572C2×C22⋊C4C23×C10311yescharacteristic
573C2×C22⋊C4C23×C10312yes—
574C2×C22⋊C4C23×C10312yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C10312yes—
594C24C2×D4×C10311yescharacteristic
595C24C2×D4×C10312yes—
596C24C2×D4×C10312yes—
597C24C2×D4×C10311yescharacteristic
598C24C24×C10311yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C10312yes—
650C22×C4C2×D4×C10311yescharacteristic
651C22×C4C2×D4×C10312yes—
652C22×C4C2×D4×C10311yescharacteristic
653C22×C4C2×D4×C10311yescharacteristic
654C22×C4C2×D4×C10312yes—
655C22×C4C2×D4×C10311yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C10314yescomplemented
699C42—22no—
700C42—22no—
701C23—22no—
702C23—24no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C10312yes—
744C23#120×C10311yescharacteristic
745C23#120×C10311yescharacteristic
746C23C22×D4×C10311yescharacteristic
747C23C22×D4×C10312yes—
748C23C2×#41×C10312yes—
749C23H(5,𝔽2)×C10311yescharacteristic
750C232−1+4×C10311yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—44no—
757D4—44no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—22no—
808C22—21no—
809C22—22no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22B(4,𝔽2)×C10312yes—
846C22C2×#120×C10311yescharacteristic
847C22#532×C10311yescharacteristic
848C22#537×C10311yescharacteristic
849C22#546×C10312yes—
850C22#547×C10312yes—
851C4—44no—
852C4—42no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—41no—
857C4—41no—
858C4—42no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C103×#243011yescharacteristic
873C2C2×B(4,𝔽2)×C10311yescharacteristic
874C2C103×#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×#3490C2semidirect
2. C103×#2410C2semidirect
3. C103×#2405C2semidirect
4. C103×#2062C2semidirect
5. C103×#2044C2semidirect
6. C103×#2029C2semidirect
7. C103×#2021C2semidirect
8. C103×#1898C2semidirect
9. C103×#1889C2semidirect
10. C103×#1867C2semidirect
11. C2×#342×C103C2semidirect
61. C22×D4×C103D4semidirect
62. C22×D4×C103D4semidirect
65. C23×C4×C103D4semidirect
66. C23×C4×C103D4semidirect
126. C2×C22⋊C4×C103D4semidirect
127. C2×C22⋊C4×C103D4semidirect
128. C2×C22⋊C4×C103D4semidirect
129. C2×C22⋊C4×C103D4semidirect
260. C22⋊C4×C103#41semidirect
425. #25563C103direct (N × H)
438. #3490C2×C103semidirect
439. #2410C2×C103semidirect
440. #2405C2×C103semidirect
441. #2062C2×C103semidirect
442. #2044C2×C103semidirect
443. #2029C2×C103semidirect
444. #2021C2×C103semidirect
445. #1898C2×C103semidirect
446. #1889C2×C103semidirect
447. #1867C2×C103semidirect
448. C2×#342C2×C103semidirect
449. C103#25563direct (N × H)
499. C22×D4D4×C103semidirect
500. C22×D4D4×C103semidirect
503. C23×C4D4×C103semidirect
504. C23×C4D4×C103semidirect
564. C2×C22⋊C4D4×C103semidirect
565. C2×C22⋊C4D4×C103semidirect
566. C2×C22⋊C4D4×C103semidirect
567. C2×C22⋊C4D4×C103semidirect
698. C22⋊C4#41×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34902
C103×#24102
C103×#24052
C103×#20622
C103×#20442
C103×#20292
C103×#20212
C103×#18982
C103×#18892
C103×#18672
C2×#342×C1032
#25563103