Finite Group Databasebeta

← C103×#18224 #39923499

Subgroups — C103×#18224 #39923499

Order 26368.

1370 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3534C211yesmaximal, characteristic, complemented
2C103×#3003C211yesmaximal, characteristic, complemented
3C2×#447×C103C211yesmaximal, characteristic, complemented
4C103×#2613C211yesmaximal, characteristic, complemented
5C103×#1600C212yesmaximal, complemented
6C103×#1598C212yesmaximal, complemented
7C103×#1597C212yesmaximal, complemented
8C103×#1595C212yesmaximal, complemented
9C103×#1516C211yesmaximal, characteristic, complemented
10C103×#1510C211yesmaximal, characteristic, complemented
11C103×#1468C211yesmaximal, characteristic, complemented
12C23×D4×C103C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C103—21no—
14C22×D8×C103—21no—
15#562×C103—21no—
16#560×C103—21no—
17#553×C103—21no—
18#551×C103—21no—
19#546×C103—21no—
20#546×C103—21no—
21#546×C103—21no—
22D42×C103—21no—
23#540×C103—21no—
24#539×C103—21no—
25#539×C103C2211yescharacteristic, complemented
26#538×C103—21no—
27#538×C103C2211yescharacteristic, complemented
28#537×C103C2211yescharacteristic, complemented
29#534×C103—21no—
30#534×C103C2211yescharacteristic, complemented
31#525×C103C2211yescharacteristic
32C2×#123×C103C2211yescharacteristic
33C2×#121×C103C2211yescharacteristic
34C2×#120×C103—21no—
35#450×C103—21no—
36#450×C103C2212yescomplemented
37#447×C103—21no—
38#447×C103—21no—
39#447×C103—21no—
40#447×C103C2212yes—
41#447×C103C2212yescomplemented
42#447×C103C2212yescomplemented
43#418×C103—21no—
44C2×#102×C103—21no—
45#407×C103C2211yescharacteristic, complemented
46C2×C22⋊C8×C103C2211yescharacteristic, complemented
47#394×C103—21no—
48#394×C103C2212yescomplemented
49#392×C103—21no—
50#392×C103C2212yescomplemented
51#381×C103C2211yescharacteristic, complemented
52#379×C103—21no—
53#328×C103C2212yescomplemented
54#327×C103C2212yescomplemented
55#327×C103C2212yescomplemented
56#327×C103C2212yescomplemented
57#324×C103C2212yescomplemented
58#323×C103C2212yescomplemented
59C25×C103—21no—
60C2×#41×C103—21no—
61C2×#41×C103D411yescharacteristic, complemented
62C22×D4×C103—21no—
63C22×D4×C103—21no—
64C22×D4×C103—21no—
65C22×D4×C103—22no—
66C22×D4×C103—21no—
67C22×D4×C103—21no—
68C22×D4×C103—21no—
69C22×D4×C103—21no—
70C22×D4×C103—21no—
71C22×D4×C103—44no—
72C22×D4×C103D411yescharacteristic
73C22×D4×C103D411yescharacteristic, complemented
74C22×D4×C103C2312yes—
75C23×C4×C103C2311yescharacteristic
76AGL(1,ℤ/8)×C103—44no—
77C2×SD16×C103—22no—
78C2×D8×C103—22no—
79C2×D8×C103—22no—
80C2×D8×C103—22no—
81C2×D8×C103—44no—
82C2×M16×C103—21no—
83C22×C8×C103—21no—
84#127×C103—21no—
85#126×C103—21no—
86#126×C103—21no—
87#126×C103—21no—
88#126×C103—21no—
89#125×C103—21no—
90#125×C103—21no—
91#124×C103—21no—
92#124×C103—21no—
93#124×C103—21no—
94#123×C103—21no—
95#123×C103—21no—
96#123×C103—21no—
97#123×C103—21no—
98#123×C103—21no—
99#123×C103—21no—
100#123×C103—21no—
101#123×C103—21no—
102#123×C103—21no—
103#123×C103—21no—
104#123×C103—21no—
105#123×C103—21no—
106#123×C103—21no—
107#123×C103—21no—
108C22⋊Q8×C103—21no—
109C22⋊Q8×C103—21no—
110C22⋊Q8×C103—21no—
111C22⋊Q8×C103—21no—
112C22⋊Q8×C103—21no—
113C22⋊Q8×C103D411yescharacteristic, complemented
114C22⋊Q8×C103C2311yescharacteristic
115#121×C103—21no—
116#121×C103—21no—
117#121×C103—21no—
118#121×C103—21no—
119#121×C103—21no—
120#121×C103—21no—
121#121×C103—21no—
122#121×C103—21no—
123#121×C103—21no—
124#121×C103—21no—
125#121×C103—21no—
126#121×C103—21no—
127#121×C103—21no—
128#121×C103—21no—
129#121×C103—21no—
130#121×C103D411yescharacteristic, complemented
131#121×C103D411yescharacteristic, complemented
132#121×C103D411yescharacteristic, complemented
133#121×C103C2311yescharacteristic
134#121×C103C2311yescharacteristic
135#121×C103C2311yescharacteristic
136#120×C103—21no—
137#120×C103—21no—
138#120×C103—21no—
139#120×C103—21no—
140#120×C103—21no—
141#120×C103—21no—
142#120×C103—21no—
143#120×C103—21no—
144#120×C103—44no—
145C4×D4×C103—21no—
146C4×D4×C103—21no—
147C4×D4×C103—21no—
148C4×D4×C103—21no—
149C4×D4×C103—21no—
150C4×D4×C103—21no—
151C4×D4×C103—21no—
152C4×D4×C103—21no—
153#117×C103—21no—
154#117×C103D411yescharacteristic, complemented
155C2×C4⋊C4×C103D411yescharacteristic
156C2×C4⋊C4×C103D411yescharacteristic, complemented
157C2×C4⋊C4×C103C2311yescharacteristic
158C2×C22⋊C4×C103—21no—
159C2×C22⋊C4×C103—21no—
160C2×C22⋊C4×C103—21no—
161C2×C22⋊C4×C103—21no—
162C2×C22⋊C4×C103—22no—
163C2×C22⋊C4×C103—22no—
164C2×C22⋊C4×C103—22no—
165C2×C22⋊C4×C103D411yescharacteristic
166C2×C22⋊C4×C103D411yescharacteristic
167C2×C22⋊C4×C103C2311yescharacteristic
168#102×C103—22no—
169#102×C103—22no—
170#102×C103—22no—
171#102×C103—22no—
172C22⋊C8×C103—21no—
173C22⋊C8×C103—21no—
174C22⋊C8×C103C2312yes—
175C22⋊C8×C103C2312yes—
176#95×C103—21no—
177#95×C103C2312yes—
178C24×C103—24no—
179C24×C103—21no—
180C24×C103—22no—
181C24×C103—21no—
182C24×C103—42no—
183C24×C103—41no—
184C24×C103—41no—
185C24×C103—82no—
186C24×C103—82no—
187C24×C103C2×D411yescharacteristic
188C24×C103C2×D411yescharacteristic
189#41×C103—42no—
190#41×C103—82no—
191C2×Q8×C103—21no—
192C2×Q8×C103C2×D411yescharacteristic
193C2×D4×C103—24no—
194C2×D4×C103—24no—
195C2×D4×C103—21no—
196C2×D4×C103—21no—
197C2×D4×C103—21no—
198C2×D4×C103—21no—
199C2×D4×C103—21no—
200C2×D4×C103—21no—
201C2×D4×C103—21no—
202C2×D4×C103—21no—
203C2×D4×C103—21no—
204C2×D4×C103—21no—
205C2×D4×C103—21no—
206C2×D4×C103—21no—
207C2×D4×C103—21no—
208C2×D4×C103—21no—
209C2×D4×C103—21no—
210C2×D4×C103—21no—
211C2×D4×C103—21no—
212C2×D4×C103—22no—
213C2×D4×C103—22no—
214C2×D4×C103—42no—
215C2×D4×C103—42no—
216C2×D4×C103—42no—
217C2×D4×C103—44no—
218C2×D4×C103—44no—
219C2×D4×C103—44no—
220C2×D4×C103—44no—
221C2×D4×C103—42no—
222C2×D4×C103—44no—
223C2×D4×C103—41no—
224C2×D4×C103—41no—
225C2×D4×C103—82no—
226C2×D4×C103—82no—
227C2×D4×C103—82no—
228C2×D4×C103—82no—
229C2×D4×C103—82no—
230C2×D4×C103C2×D411yescharacteristic
231C2×D4×C103C2×D411yescharacteristic
232C2×D4×C103C2×D411yescharacteristic
233C22×C4×C103—21no—
234C22×C4×C103—21no—
235C22×C4×C103—21no—
236C22×C4×C103—21no—
237C22×C4×C103—21no—
238C22×C4×C103—21no—
239C22×C4×C103—21no—
240C22×C4×C103—22no—
241C22×C4×C103—42no—
242C22×C4×C103C2×D411yescharacteristic
243C22×C4×C103C2×D411yescharacteristic
244C22×C4×C103C2×D411yescharacteristic
245C22×C4×C103C2×D411yescharacteristic
246C22×C4×C103C2×D411yescharacteristic
247C22×C4×C103C2×D411yescharacteristic
248C22×C4×C103C2×D411yescharacteristic
249C22×C4×C103C2×D411yescharacteristic
250C22×C4×C103C2411yescharacteristic
251SD16×C103—44no—
252D8×C103—44no—
253D8×C103—44no—
254D8×C103—44no—
255M16×C103—42no—
256C2×C8×C103—22no—
257C2×C8×C103—22no—
258C2×C8×C103—42no—
259C4⋊C4×C103—21no—
260C4⋊C4×C103—21no—
261C4⋊C4×C103—21no—
262C4⋊C4×C103—21no—
263C4⋊C4×C103—21no—
264C4⋊C4×C103—21no—
265C4⋊C4×C103—21no—
266C4⋊C4×C103—21no—
267C4⋊C4×C103—21no—
268C4⋊C4×C103—21no—
269C4⋊C4×C103—21no—
270C4⋊C4×C103—21no—
271C4⋊C4×C103—21no—
272C4⋊C4×C103C2×D411yescharacteristic
273C4⋊C4×C103C2×D411yescharacteristic
274C4⋊C4×C103C2×D411yescharacteristic
275C4⋊C4×C103C2×D411yescharacteristic
276C22⋊C4×C103—21no—
277C22⋊C4×C103—21no—
278C22⋊C4×C103—21no—
279C22⋊C4×C103—21no—
280C22⋊C4×C103—21no—
281C22⋊C4×C103—21no—
282C22⋊C4×C103—21no—
283C22⋊C4×C103—21no—
284C22⋊C4×C103—21no—
285C22⋊C4×C103—21no—
286C22⋊C4×C103—21no—
287C22⋊C4×C103—21no—
288C22⋊C4×C103—21no—
289C22⋊C4×C103—21no—
290C22⋊C4×C103—21no—
291C22⋊C4×C103—21no—
292C22⋊C4×C103—21no—
293C22⋊C4×C103—21no—
294C22⋊C4×C103—21no—
295C22⋊C4×C103—21no—
296C22⋊C4×C103—21no—
297C22⋊C4×C103—21no—
298C22⋊C4×C103—21no—
299C22⋊C4×C103—21no—
300C22⋊C4×C103—21no—
301C22⋊C4×C103—44no—
302C22⋊C4×C103—42no—
303C22⋊C4×C103—82no—
304C22⋊C4×C103—82no—
305C42×C103—21no—
306C42×C103—21no—
307C42×C103—21no—
308C23×C103—22no—
309C23×C103—22no—
310C23×C103—24no—
311C23×C103—21no—
312C23×C103—21no—
313C23×C103—21no—
314C23×C103—21no—
315C23×C103—22no—
316C23×C103—41no—
317C23×C103—42no—
318C23×C103—42no—
319C23×C103—44no—
320C23×C103—42no—
321C23×C103—41no—
322C23×C103—41no—
323C23×C103—42no—
324C23×C103—42no—
325C23×C103—42no—
326C23×C103—44no—
327C23×C103—42no—
328C23×C103—81no—
329C23×C103—81no—
330C23×C103—82no—
331C23×C103—82no—
332C23×C103—82no—
333C23×C103—82no—
334C23×C103—88no—
335C23×C103—81no—
336C23×C103—81no—
337C23×C103—81no—
338C23×C103—88no—
339C23×C103#12011yescharacteristic
340C23×C103#12011yescharacteristic
341C23×C103C22×D411yescharacteristic
342Q8×C103—41no—
343Q8×C103—81no—
344D4×C103—24no—
345D4×C103—24no—
346D4×C103—41no—
347D4×C103—41no—
348D4×C103—41no—
349D4×C103—42no—
350D4×C103—42no—
351D4×C103—44no—
352D4×C103—44no—
353D4×C103—42no—
354D4×C103—42no—
355D4×C103—42no—
356D4×C103—42no—
357D4×C103—42no—
358D4×C103—81no—
359D4×C103—81no—
360D4×C103—81no—
361D4×C103—81no—
362D4×C103—81no—
363D4×C103—81no—
364D4×C103—81no—
365D4×C103—81no—
366D4×C103—81no—
367D4×C103—81no—
368D4×C103—81no—
369D4×C103—81no—
370D4×C103—88no—
371C2×C4×C103—22no—
372C2×C4×C103—22no—
373C2×C4×C103—21no—
374C2×C4×C103—21no—
375C2×C4×C103—21no—
376C2×C4×C103—21no—
377C2×C4×C103—21no—
378C2×C4×C103—21no—
379C2×C4×C103—21no—
380C2×C4×C103—21no—
381C2×C4×C103—22no—
382C2×C4×C103—41no—
383C2×C4×C103—41no—
384C2×C4×C103—41no—
385C2×C4×C103—41no—
386C2×C4×C103—41no—
387C2×C4×C103—41no—
388C2×C4×C103—42no—
389C2×C4×C103—42no—
390C2×C4×C103—42no—
391C2×C4×C103—81no—
392C2×C4×C103—81no—
393C2×C4×C103—81no—
394C2×C4×C103—81no—
395C2×C4×C103—81no—
396C2×C4×C103—81no—
397C2×C4×C103—81no—
398C2×C4×C103#12011yescharacteristic
399C2×C4×C103#12011yescharacteristic
400C2×C4×C103C22×D411yescharacteristic
401C2×C4×C103C22×D411yescharacteristic
402C8×C103—42no—
403C8×C103—42no—
404C22×C103—21no—
405C22×C103—21no—
406C22×C103—21no—
407C22×C103—21no—
408C22×C103—21no—
409C22×C103—21no—
410C22×C103—21no—
411C22×C103—44no—
412C22×C103—44no—
413C22×C103—44no—
414C22×C103—41no—
415C22×C103—41no—
416C22×C103—41no—
417C22×C103—41no—
418C22×C103—41no—
419C22×C103—41no—
420C22×C103—41no—
421C22×C103—41no—
422C22×C103—41no—
423C22×C103—41no—
424C22×C103—44no—
425C22×C103—41no—
426C22×C103—41no—
427C22×C103—82no—
428C22×C103—82no—
429C22×C103—82no—
430C22×C103—88no—
431C22×C103—88no—
432C22×C103—82no—
433C22×C103—82no—
434C22×C103—162no—
435C22×C103—162no—
436C22×C103B(4,𝔽2)12yes—
437C22×C103C2×#12011yescharacteristic
438C22×C103#57612yes—
439C4×C103—21no—
440C4×C103—21no—
441C4×C103—21no—
442C4×C103—21no—
443C4×C103—41no—
444C4×C103—41no—
445C4×C103—41no—
446C4×C103—41no—
447C4×C103—41no—
448C4×C103—41no—
449C4×C103—41no—
450C4×C103—41no—
451C4×C103—82no—
452#18224C10311yesmaximal, characteristic, direct product factor, Sylow
453C2×C103—22no—
454C2×C103—22no—
455C2×C103—41no—
456C2×C103—84no—
457C2×C103—81no—
458C2×C103—81no—
459C2×C103—81no—
460C2×C103—81no—
461C2×C103#300811yescharacteristic
462C2×C103#302111yescharacteristic
463C2×C103C2×B(4,𝔽2)11yescharacteristic
464#3534C2×C10311yescharacteristic, complemented
465#3003C2×C10311yescharacteristic, complemented
466C2×#447C2×C10311yescharacteristic, complemented
467#2613C2×C10311yescharacteristic, complemented
468#1600C2×C10312yescomplemented
469#1598C2×C10312yescomplemented
470#1597C2×C10312yescomplemented
471#1595C2×C10312yescomplemented
472#1516C2×C10311yescharacteristic, complemented
473#1510C2×C10311yescharacteristic, complemented
474#1468C2×C10311yescharacteristic, complemented
475C103#1822411yescharacteristic, direct product factor, Sylow
476C23×D4C22×C10311yescharacteristic, complemented
477C2×AGL(1,ℤ/8)—21no—
478C22×D8—21no—
479#562—21no—
480#560—21no—
481#553—21no—
482#551—21no—
483#546—21no—
484#546—21no—
485#546—21no—
486D42—21no—
487#540—21no—
488#539—21no—
489#539C22×C10311yescharacteristic, complemented
490#538—21no—
491#538C22×C10311yescharacteristic, complemented
492#537C22×C10311yescharacteristic, complemented
493#534—21no—
494#534C22×C10311yescharacteristic, complemented
495#525C22×C10311yescharacteristic
496C2×#123C22×C10311yescharacteristic
497C2×#121C22×C10311yescharacteristic
498C2×#120—21no—
499#450—21no—
500#450C22×C10312yescomplemented
501#447—21no—
502#447—21no—
503#447—21no—
504#447C22×C10312yes—
505#447C22×C10312yescomplemented
506#447C22×C10312yescomplemented
507#418—21no—
508C2×#102—21no—
509#407C22×C10311yescharacteristic, complemented
510C2×C22⋊C8C22×C10311yescharacteristic, complemented
511#394—21no—
512#394C22×C10312yescomplemented
513#392—21no—
514#392C22×C10312yescomplemented
515#381C22×C10311yescharacteristic, complemented
516#379—21no—
517#328C22×C10312yescomplemented
518#327C22×C10312yescomplemented
519#327C22×C10312yescomplemented
520#327C22×C10312yescomplemented
521#324C22×C10312yescomplemented
522#323C22×C10312yescomplemented
523C25—21no—
524C2×#41—21no—
525C2×#41D4×C10311yescharacteristic, complemented
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—44no—
536C22×D4D4×C10311yescharacteristic
537C22×D4D4×C10311yescharacteristic, complemented
538C22×D4C23×C10312yes—
539C23×C4C23×C10311yescharacteristic
540AGL(1,ℤ/8)—44no—
541C2×SD16—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—44no—
546C2×M16—21no—
547C22×C8—21no—
548#127—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#126—21no—
553#125—21no—
554#125—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8D4×C10311yescharacteristic, complemented
578C22⋊Q8C23×C10311yescharacteristic
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121D4×C10311yescharacteristic, complemented
595#121D4×C10311yescharacteristic, complemented
596#121D4×C10311yescharacteristic, complemented
597#121C23×C10311yescharacteristic
598#121C23×C10311yescharacteristic
599#121C23×C10311yescharacteristic
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607#120—21no—
608#120—44no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617#117—21no—
618#117D4×C10311yescharacteristic, complemented
619C2×C4⋊C4D4×C10311yescharacteristic
620C2×C4⋊C4D4×C10311yescharacteristic, complemented
621C2×C4⋊C4C23×C10311yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4D4×C10311yescharacteristic
630C2×C22⋊C4D4×C10311yescharacteristic
631C2×C22⋊C4C23×C10311yescharacteristic
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8C23×C10312yes—
639C22⋊C8C23×C10312yes—
640#95—21no—
641#95C23×C10312yes—
642C24—24no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—42no—
647C24—41no—
648C24—41no—
649C24—82no—
650C24—82no—
651C24C2×D4×C10311yescharacteristic
652C24C2×D4×C10311yescharacteristic
653#41—42no—
654#41—82no—
655C2×Q8—21no—
656C2×Q8C2×D4×C10311yescharacteristic
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—82no—
693C2×D4—82no—
694C2×D4C2×D4×C10311yescharacteristic
695C2×D4C2×D4×C10311yescharacteristic
696C2×D4C2×D4×C10311yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—42no—
706C22×C4C2×D4×C10311yescharacteristic
707C22×C4C2×D4×C10311yescharacteristic
708C22×C4C2×D4×C10311yescharacteristic
709C22×C4C2×D4×C10311yescharacteristic
710C22×C4C2×D4×C10311yescharacteristic
711C22×C4C2×D4×C10311yescharacteristic
712C22×C4C2×D4×C10311yescharacteristic
713C22×C4C2×D4×C10311yescharacteristic
714C22×C4C24×C10311yescharacteristic
715SD16—44no—
716D8—44no—
717D8—44no—
718D8—44no—
719M16—42no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—42no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4C2×D4×C10311yescharacteristic
737C4⋊C4C2×D4×C10311yescharacteristic
738C4⋊C4C2×D4×C10311yescharacteristic
739C4⋊C4C2×D4×C10311yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—82no—
768C22⋊C4—82no—
769C42—21no—
770C42—21no—
771C42—21no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—42no—
785C23—41no—
786C23—41no—
787C23—44no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—81no—
793C23—81no—
794C23—82no—
795C23—82no—
796C23—82no—
797C23—82no—
798C23—88no—
799C23—81no—
800C23—81no—
801C23—81no—
802C23—88no—
803C23#120×C10311yescharacteristic
804C23#120×C10311yescharacteristic
805C23C22×D4×C10311yescharacteristic
806Q8—41no—
807Q8—81no—
808D4—24no—
809D4—24no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—44no—
817D4—42no—
818D4—42no—
819D4—42no—
820D4—42no—
821D4—42no—
822D4—81no—
823D4—81no—
824D4—81no—
825D4—81no—
826D4—81no—
827D4—81no—
828D4—81no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833D4—81no—
834D4—88no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4#120×C10311yescharacteristic
863C2×C4#120×C10311yescharacteristic
864C2×C4C22×D4×C10311yescharacteristic
865C2×C4C22×D4×C10311yescharacteristic
866C8—42no—
867C8—42no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—44no—
889C22—41no—
890C22—41no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—88no—
895C22—88no—
896C22—82no—
897C22—82no—
898C22—162no—
899C22—162no—
900C22B(4,𝔽2)×C10312yes—
901C22C2×#120×C10311yescharacteristic
902C22#576×C10312yes—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—82no—
916C2—22no—
917C2—22no—
918C2—41no—
919C2—84no—
920C2—81no—
921C2—81no—
922C2—81no—
923C2—81no—
924C2C103×#300811yescharacteristic
925C2C103×#302111yescharacteristic
926C2C2×B(4,𝔽2)×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3534C2semidirect
2. C103×#3003C2semidirect
3. C2×#447×C103C2semidirect
4. C103×#2613C2semidirect
5. C103×#1600C2semidirect
6. C103×#1598C2semidirect
7. C103×#1597C2semidirect
8. C103×#1595C2semidirect
9. C103×#1516C2semidirect
10. C103×#1510C2semidirect
11. C103×#1468C2semidirect
12. C23×D4×C103C22semidirect
25. #539×C103C22semidirect
27. #538×C103C22semidirect
28. #537×C103C22semidirect
30. #534×C103C22semidirect
36. #450×C103C22semidirect
41. #447×C103C22semidirect
42. #447×C103C22semidirect
45. #407×C103C22semidirect
46. C2×C22⋊C8×C103C22semidirect
48. #394×C103C22semidirect
50. #392×C103C22semidirect
51. #381×C103C22semidirect
53. #328×C103C22semidirect
54. #327×C103C22semidirect
55. #327×C103C22semidirect
56. #327×C103C22semidirect
57. #324×C103C22semidirect
58. #323×C103C22semidirect
61. C2×#41×C103D4semidirect
73. C22×D4×C103D4semidirect
113. C22⋊Q8×C103D4semidirect
130. #121×C103D4semidirect
131. #121×C103D4semidirect
132. #121×C103D4semidirect
154. #117×C103D4semidirect
156. C2×C4⋊C4×C103D4semidirect
452. #18224C103direct (N × H)
464. #3534C2×C103semidirect
465. #3003C2×C103semidirect
466. C2×#447C2×C103semidirect
467. #2613C2×C103semidirect
468. #1600C2×C103semidirect
469. #1598C2×C103semidirect
470. #1597C2×C103semidirect
471. #1595C2×C103semidirect
472. #1516C2×C103semidirect
473. #1510C2×C103semidirect
474. #1468C2×C103semidirect
475. C103#18224direct (N × H)
476. C23×D4C22×C103semidirect
489. #539C22×C103semidirect
491. #538C22×C103semidirect
492. #537C22×C103semidirect
494. #534C22×C103semidirect
500. #450C22×C103semidirect
505. #447C22×C103semidirect
506. #447C22×C103semidirect
509. #407C22×C103semidirect
510. C2×C22⋊C8C22×C103semidirect
512. #394C22×C103semidirect
514. #392C22×C103semidirect
515. #381C22×C103semidirect
517. #328C22×C103semidirect
518. #327C22×C103semidirect
519. #327C22×C103semidirect
520. #327C22×C103semidirect
521. #324C22×C103semidirect
522. #323C22×C103semidirect
525. C2×#41D4×C103semidirect
537. C22×D4D4×C103semidirect
577. C22⋊Q8D4×C103semidirect
594. #121D4×C103semidirect
595. #121D4×C103semidirect
596. #121D4×C103semidirect
618. #117D4×C103semidirect
620. C2×C4⋊C4D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35342
C103×#30032
C2×#447×C1032
C103×#26132
C103×#16002
C103×#15982
C103×#15972
C103×#15952
C103×#15162
C103×#15102
C103×#14682
#18224103