Finite Group Databasebeta

← C103×#19010 #39924285

Subgroups — C103×#19010 #39924285

Order 26368.

920 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3529C211yesmaximal, characteristic, complemented
2C103×#3219C211yesmaximal, characteristic, complemented
3C103×#3214C211yesmaximal, characteristic, complemented
4C103×#3180C211yesmaximal, characteristic, complemented
5C103×#1664C211yesmaximal, characteristic, complemented
6C103×#1662C211yesmaximal, characteristic, complemented
7C103×#1661C211yesmaximal, characteristic, complemented
8C103×#1659C211yesmaximal, characteristic, complemented
9C103×#1657C211yesmaximal, characteristic, complemented
10C103×#1656C211yesmaximal, characteristic, complemented
11C103×#1656C211yesmaximal, characteristic, complemented
12C103×#1655C211yesmaximal, characteristic, complemented
13C103×#1535C211yesmaximal, characteristic, complemented
14C103×#1532C211yesmaximal, characteristic, complemented
15C103×#1530C211yesmaximal, characteristic, complemented
16#563×C103—21no—
17#563×C103C2211yescharacteristic
18#562×C103—21no—
19#562×C103—21no—
20#562×C103C2211yescharacteristic
21#562×C103C2211yescharacteristic
22H(3,𝔽4)×C103C2211yescharacteristic
23#560×C103—21no—
24#560×C103—21no—
25#560×C103—21no—
26#532×C103—21no—
27#532×C103C2211yescharacteristic
28#532×C103C2211yescharacteristic, complemented
29#529×C103—21no—
30#529×C103—21no—
31#529×C103C2211yescharacteristic
32#529×C103C2211yescharacteristic
33#525×C103—21no—
34#525×C103—21no—
35#525×C103—21no—
36#501×C103C2211yescharacteristic, complemented
37#497×C103C2211yescharacteristic
38#496×C103C2211yescharacteristic
39#496×C103C2211yescharacteristic
40#496×C103C2211yescharacteristic
41#496×C103C2211yescharacteristic, complemented
42#491×C103C2211yescharacteristic, complemented
43#490×C103C2211yescharacteristic, complemented
44#490×C103C2211yescharacteristic, complemented
45#489×C103C2211yescharacteristic
46#489×C103C2211yescharacteristic
47#489×C103C2211yescharacteristic, complemented
48#466×C103—21no—
49#465×C103—21no—
50#464×C103—21no—
51#463×C103—21no—
52#461×C103—21no—
53#459×C103—21no—
54#452×C103—21no—
55#449×C103—21no—
56#449×C103—21no—
57#449×C103—21no—
58#442×C103—21no—
59#440×C103—21no—
60#432×C103C2211yescharacteristic, complemented
61#432×C103C2211yescharacteristic, complemented
62C2×#97×C103C2211yescharacteristic, complemented
63#330×C103C2211yescharacteristic, complemented
64#330×C103C2211yescharacteristic, complemented
65#330×C103C2211yescharacteristic, complemented
66#330×C103C2211yescharacteristic, complemented
67#329×C103C2211yescharacteristic
68#329×C103C2211yescharacteristic
69#329×C103C2211yescharacteristic
70#329×C103C2211yescharacteristic
71#329×C103C2211yescharacteristic
72#329×C103C2211yescharacteristic
73#329×C103C2211yescharacteristic, complemented
74#329×C103C2211yescharacteristic, complemented
75C2×#41×C103—21no—
76C2×#41×C103—21no—
77C2×#41×C103D411yescharacteristic
78C2×#41×C103D411yescharacteristic
79C23×C4×C103—21no—
80C2×Q16×C103—21no—
81C2×SD16×C103—21no—
82C2×SD16×C103—21no—
83C2×SD16×C103—21no—
84C2×SD16×C103—21no—
85C2×SD16×C103—21no—
86C2×D8×C103—21no—
87C2×D8×C103—21no—
88C2×D8×C103—21no—
89C2×D8×C103—21no—
90C22×C8×C103—21no—
91C4⋊Q8×C103—21no—
92C4⋊Q8×C103D411yescharacteristic
93C4⋊Q8×C103C2311yescharacteristic
94#127×C103—21no—
95#127×C103D411yescharacteristic
96#127×C103C2311yescharacteristic
97#126×C103—21no—
98#126×C103—21no—
99#126×C103—21no—
100#126×C103—21no—
101#126×C103—21no—
102#126×C103—21no—
103#125×C103—21no—
104#125×C103—21no—
105#125×C103C2311yescharacteristic
106#125×C103C2311yescharacteristic
107#124×C103—21no—
108#124×C103—21no—
109#124×C103—21no—
110#124×C103—21no—
111#124×C103—21no—
112#124×C103C2311yescharacteristic
113#124×C103C2311yescharacteristic
114#124×C103C2311yescharacteristic
115#124×C103C2311yescharacteristic
116#123×C103—21no—
117#123×C103—21no—
118#123×C103—21no—
119#123×C103—21no—
120#123×C103—21no—
121#123×C103—21no—
122#123×C103—21no—
123#123×C103—21no—
124#123×C103—21no—
125#123×C103—21no—
126#123×C103—21no—
127#123×C103—21no—
128C22⋊Q8×C103—21no—
129C22⋊Q8×C103—21no—
130C22⋊Q8×C103—21no—
131C22⋊Q8×C103—21no—
132C22⋊Q8×C103—21no—
133C22⋊Q8×C103—21no—
134C22⋊Q8×C103—21no—
135C22⋊Q8×C103—21no—
136C22⋊Q8×C103D411yescharacteristic
137C22⋊Q8×C103D411yescharacteristic
138#121×C103—21no—
139#121×C103—21no—
140#121×C103—21no—
141#121×C103—21no—
142#121×C103—21no—
143#121×C103—21no—
144#121×C103—21no—
145#121×C103—21no—
146#121×C103—21no—
147#121×C103—21no—
148#121×C103—21no—
149#121×C103—21no—
150#121×C103—21no—
151#121×C103—21no—
152#121×C103—21no—
153#121×C103—21no—
154#121×C103D411yescharacteristic
155#121×C103D411yescharacteristic
156#120×C103—21no—
157#120×C103—21no—
158#120×C103—21no—
159#120×C103—21no—
160#120×C103—21no—
161#120×C103—21no—
162C4×Q8×C103D411yescharacteristic
163C4×Q8×C103D411yescharacteristic
164C4×D4×C103—21no—
165C4×D4×C103—21no—
166C4×D4×C103—21no—
167C4×D4×C103—21no—
168C4×D4×C103—21no—
169C4×D4×C103—21no—
170C4×D4×C103—21no—
171C4×D4×C103—21no—
172C4×D4×C103—21no—
173C4×D4×C103—21no—
174C4×D4×C103D411yescharacteristic
175C4×D4×C103D411yescharacteristic
176#117×C103—21no—
177#117×C103—21no—
178#117×C103—21no—
179C2×C42×C103—21no—
180C2×C42×C103C2311yescharacteristic
181#107×C103—21no—
182#106×C103—21no—
183C4⋊C8×C103—21no—
184C4⋊C8×C103—21no—
185#103×C103—21no—
186#103×C103—21no—
187#103×C103—21no—
188#103×C103—21no—
189#103×C103—21no—
190#102×C103—21no—
191#102×C103—21no—
192#102×C103—21no—
193#102×C103—21no—
194#102×C103—21no—
195#102×C103—21no—
196#102×C103—21no—
197C22⋊C8×C103—21no—
198C22⋊C8×C103—21no—
199#97×C103—21no—
200#97×C103C2311yescharacteristic
201#97×C103C2311yescharacteristic
202#97×C103C2311yescharacteristic
203#97×C103C2311yescharacteristic
204#97×C103C2311yescharacteristic
205#97×C103C2311yescharacteristic
206C24×C103—21no—
207#41×C103—81no—
208#41×C103—81no—
209#41×C103—82no—
210#41×C103—81no—
211#41×C103—81no—
212C2×Q8×C103—21no—
213C2×Q8×C103—21no—
214C2×Q8×C103C2×D411yescharacteristic
215C2×Q8×C103C2×D411yescharacteristic
216C2×Q8×C103C2×D411yescharacteristic
217C2×Q8×C103C2×D411yescharacteristic
218C2×D4×C103—21no—
219C2×D4×C103—21no—
220C2×D4×C103—21no—
221C2×D4×C103—21no—
222C2×D4×C103—21no—
223C2×D4×C103—21no—
224C2×D4×C103—21no—
225C2×D4×C103—21no—
226C2×D4×C103—21no—
227C2×D4×C103—21no—
228C2×D4×C103—21no—
229C2×D4×C103—21no—
230C2×D4×C103—21no—
231C2×D4×C103—21no—
232C2×D4×C103—21no—
233C2×D4×C103—21no—
234C2×D4×C103—41no—
235C2×D4×C103C2×D411yescharacteristic
236C2×D4×C103C2×D411yescharacteristic
237C2×D4×C103C2×D411yescharacteristic
238C2×D4×C103C2×D411yescharacteristic
239C22×C4×C103—21no—
240C22×C4×C103—21no—
241C22×C4×C103—21no—
242C22×C4×C103—21no—
243C22×C4×C103—21no—
244C22×C4×C103—21no—
245C22×C4×C103—21no—
246C22×C4×C103—21no—
247C22×C4×C103—21no—
248C22×C4×C103—41no—
249C22×C4×C103—82no—
250C22×C4×C103C2×D411yescharacteristic
251C22×C4×C103C2×D411yescharacteristic
252C22×C4×C103C2×D411yescharacteristic
253Q16×C103—81no—
254SD16×C103—42no—
255SD16×C103—81no—
256SD16×C103—81no—
257SD16×C103—81no—
258SD16×C103—81no—
259D8×C103—42no—
260D8×C103—81no—
261D8×C103—81no—
262D8×C103—81no—
263C2×C8×C103—21no—
264C2×C8×C103—21no—
265C2×C8×C103—21no—
266C2×C8×C103—21no—
267C2×C8×C103—21no—
268C2×C8×C103—21no—
269C2×C8×C103—42no—
270C4⋊C4×C103—21no—
271C4⋊C4×C103—21no—
272C4⋊C4×C103—21no—
273C4⋊C4×C103—21no—
274C4⋊C4×C103—21no—
275C4⋊C4×C103—21no—
276C4⋊C4×C103—21no—
277C4⋊C4×C103—21no—
278C4⋊C4×C103—21no—
279C4⋊C4×C103—21no—
280C4⋊C4×C103—21no—
281C4⋊C4×C103—21no—
282C4⋊C4×C103—21no—
283C4⋊C4×C103—21no—
284C4⋊C4×C103—21no—
285C4⋊C4×C103—21no—
286C4⋊C4×C103—21no—
287C4⋊C4×C103—21no—
288C4⋊C4×C103C2×D411yescharacteristic
289C4⋊C4×C103C2×D411yescharacteristic
290C4⋊C4×C103C2×D411yescharacteristic
291C4⋊C4×C103C2×D411yescharacteristic
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—21no—
302C22⋊C4×C103—21no—
303C22⋊C4×C103—21no—
304C22⋊C4×C103—21no—
305C22⋊C4×C103—21no—
306C22⋊C4×C103—21no—
307C22⋊C4×C103—21no—
308C22⋊C4×C103—21no—
309C22⋊C4×C103—21no—
310C22⋊C4×C103—21no—
311C22⋊C4×C103—21no—
312C22⋊C4×C103—21no—
313C22⋊C4×C103—21no—
314C22⋊C4×C103—21no—
315C22⋊C4×C103—21no—
316C22⋊C4×C103—41no—
317C22⋊C4×C103—41no—
318C42×C103—21no—
319C42×C103—21no—
320C42×C103—21no—
321C42×C103—21no—
322C42×C103C2×D411yescharacteristic
323C42×C103C2×D411yescharacteristic
324C42×C103C2×D411yescharacteristic
325C42×C103C2411yescharacteristic
326C23×C103—21no—
327C23×C103—21no—
328C23×C103—21no—
329C23×C103—21no—
330C23×C103—41no—
331C23×C103—81no—
332C23×C103—81no—
333C23×C103—81no—
334C23×C103#12011yescharacteristic
335Q8×C103—41no—
336Q8×C103—41no—
337Q8×C103—41no—
338Q8×C103—41no—
339Q8×C103—41no—
340Q8×C103—41no—
341Q8×C103—81no—
342D4×C103—41no—
343D4×C103—41no—
344D4×C103—41no—
345D4×C103—41no—
346D4×C103—41no—
347D4×C103—41no—
348D4×C103—41no—
349D4×C103—41no—
350D4×C103—41no—
351D4×C103—41no—
352D4×C103—81no—
353D4×C103—81no—
354D4×C103—81no—
355D4×C103—81no—
356D4×C103—81no—
357D4×C103—81no—
358D4×C103—81no—
359D4×C103—81no—
360D4×C103—81no—
361D4×C103—81no—
362D4×C103—81no—
363D4×C103—81no—
364D4×C103—81no—
365D4×C103—82no—
366C2×C4×C103—21no—
367C2×C4×C103—21no—
368C2×C4×C103—21no—
369C2×C4×C103—21no—
370C2×C4×C103—21no—
371C2×C4×C103—21no—
372C2×C4×C103—21no—
373C2×C4×C103—21no—
374C2×C4×C103—41no—
375C2×C4×C103—41no—
376C2×C4×C103—41no—
377C2×C4×C103—42no—
378C2×C4×C103—42no—
379C2×C4×C103—42no—
380C2×C4×C103—42no—
381C2×C4×C103—41no—
382C2×C4×C103—82no—
383C2×C4×C103—81no—
384C2×C4×C103—81no—
385C2×C4×C103—81no—
386C2×C4×C103—81no—
387C2×C4×C103—81no—
388C2×C4×C103#12011yescharacteristic
389C2×C4×C103#12011yescharacteristic
390C2×C4×C103#12011yescharacteristic
391C2×C4×C103C22×D411yescharacteristic
392C2×C4×C103C22×D411yescharacteristic
393C2×C4×C103C22×D411yescharacteristic
394C8×C103—22no—
395C8×C103—41no—
396C8×C103—41no—
397C8×C103—41no—
398C8×C103—41no—
399C8×C103—41no—
400C22×C103—21no—
401C22×C103—21no—
402C22×C103—21no—
403C22×C103—41no—
404C22×C103—41no—
405C22×C103—41no—
406C22×C103—41no—
407C22×C103—41no—
408C22×C103—41no—
409C22×C103—41no—
410C22×C103—41no—
411C22×C103—41no—
412C22×C103—41no—
413C22×C103—41no—
414C22×C103—41no—
415C22×C103—84no—
416C22×C103—81no—
417C22×C103—81no—
418C22×C103—81no—
419C22×C103C2×#12011yescharacteristic
420C4×C103—21no—
421C4×C103—21no—
422C4×C103—21no—
423C4×C103—21no—
424C4×C103—21no—
425C4×C103—21no—
426C4×C103—41no—
427C4×C103—41no—
428C4×C103—41no—
429C4×C103—41no—
430C4×C103—41no—
431C4×C103—41no—
432C4×C103—41no—
433C4×C103—41no—
434C4×C103—81no—
435#19010C10311yesmaximal, characteristic, direct product factor, Sylow
436C2×C103—41no—
437C2×C103—81no—
438C2×C103—81no—
439C2×C103—81no—
440C2×C103—81no—
441C2×C103—161no—
442C2×C103#301811yescharacteristic
443C2×C103#301911yescharacteristic
444C2×C103#302111yescharacteristic
445#3529C2×C10311yescharacteristic, complemented
446#3219C2×C10311yescharacteristic, complemented
447#3214C2×C10311yescharacteristic, complemented
448#3180C2×C10311yescharacteristic, complemented
449#1664C2×C10311yescharacteristic, complemented
450#1662C2×C10311yescharacteristic, complemented
451#1661C2×C10311yescharacteristic, complemented
452#1659C2×C10311yescharacteristic, complemented
453#1657C2×C10311yescharacteristic, complemented
454#1656C2×C10311yescharacteristic, complemented
455#1656C2×C10311yescharacteristic, complemented
456#1655C2×C10311yescharacteristic, complemented
457#1535C2×C10311yescharacteristic, complemented
458#1532C2×C10311yescharacteristic, complemented
459#1530C2×C10311yescharacteristic, complemented
460C103#1901011yescharacteristic, direct product factor, Sylow
461#563—21no—
462#563C22×C10311yescharacteristic
463#562—21no—
464#562—21no—
465#562C22×C10311yescharacteristic
466#562C22×C10311yescharacteristic
467H(3,𝔽4)C22×C10311yescharacteristic
468#560—21no—
469#560—21no—
470#560—21no—
471#532—21no—
472#532C22×C10311yescharacteristic
473#532C22×C10311yescharacteristic, complemented
474#529—21no—
475#529—21no—
476#529C22×C10311yescharacteristic
477#529C22×C10311yescharacteristic
478#525—21no—
479#525—21no—
480#525—21no—
481#501C22×C10311yescharacteristic, complemented
482#497C22×C10311yescharacteristic
483#496C22×C10311yescharacteristic
484#496C22×C10311yescharacteristic
485#496C22×C10311yescharacteristic
486#496C22×C10311yescharacteristic, complemented
487#491C22×C10311yescharacteristic, complemented
488#490C22×C10311yescharacteristic, complemented
489#490C22×C10311yescharacteristic, complemented
490#489C22×C10311yescharacteristic
491#489C22×C10311yescharacteristic
492#489C22×C10311yescharacteristic, complemented
493#466—21no—
494#465—21no—
495#464—21no—
496#463—21no—
497#461—21no—
498#459—21no—
499#452—21no—
500#449—21no—
501#449—21no—
502#449—21no—
503#442—21no—
504#440—21no—
505#432C22×C10311yescharacteristic, complemented
506#432C22×C10311yescharacteristic, complemented
507C2×#97C22×C10311yescharacteristic, complemented
508#330C22×C10311yescharacteristic, complemented
509#330C22×C10311yescharacteristic, complemented
510#330C22×C10311yescharacteristic, complemented
511#330C22×C10311yescharacteristic, complemented
512#329C22×C10311yescharacteristic
513#329C22×C10311yescharacteristic
514#329C22×C10311yescharacteristic
515#329C22×C10311yescharacteristic
516#329C22×C10311yescharacteristic
517#329C22×C10311yescharacteristic
518#329C22×C10311yescharacteristic, complemented
519#329C22×C10311yescharacteristic, complemented
520C2×#41—21no—
521C2×#41—21no—
522C2×#41D4×C10311yescharacteristic
523C2×#41D4×C10311yescharacteristic
524C23×C4—21no—
525C2×Q16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×D8—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8D4×C10311yescharacteristic
538C4⋊Q8C23×C10311yescharacteristic
539#127—21no—
540#127D4×C10311yescharacteristic
541#127C23×C10311yescharacteristic
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#125—21no—
549#125—21no—
550#125C23×C10311yescharacteristic
551#125C23×C10311yescharacteristic
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124C23×C10311yescharacteristic
558#124C23×C10311yescharacteristic
559#124C23×C10311yescharacteristic
560#124C23×C10311yescharacteristic
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—
572#123—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8D4×C10311yescharacteristic
582C22⋊Q8D4×C10311yescharacteristic
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#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121D4×C10311yescharacteristic
600#121D4×C10311yescharacteristic
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607C4×Q8D4×C10311yescharacteristic
608C4×Q8D4×C10311yescharacteristic
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4D4×C10311yescharacteristic
620C4×D4D4×C10311yescharacteristic
621#117—21no—
622#117—21no—
623#117—21no—
624C2×C42—21no—
625C2×C42C23×C10311yescharacteristic
626#107—21no—
627#106—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630#103—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644#97—21no—
645#97C23×C10311yescharacteristic
646#97C23×C10311yescharacteristic
647#97C23×C10311yescharacteristic
648#97C23×C10311yescharacteristic
649#97C23×C10311yescharacteristic
650#97C23×C10311yescharacteristic
651C24—21no—
652#41—81no—
653#41—81no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8C2×D4×C10311yescharacteristic
660C2×Q8C2×D4×C10311yescharacteristic
661C2×Q8C2×D4×C10311yescharacteristic
662C2×Q8C2×D4×C10311yescharacteristic
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—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—41no—
680C2×D4C2×D4×C10311yescharacteristic
681C2×D4C2×D4×C10311yescharacteristic
682C2×D4C2×D4×C10311yescharacteristic
683C2×D4C2×D4×C10311yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4—82no—
695C22×C4C2×D4×C10311yescharacteristic
696C22×C4C2×D4×C10311yescharacteristic
697C22×C4C2×D4×C10311yescharacteristic
698Q16—81no—
699SD16—42no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703SD16—81no—
704D8—42no—
705D8—81no—
706D8—81no—
707D8—81no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—42no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
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⋊C4C2×D4×C10311yescharacteristic
734C4⋊C4C2×D4×C10311yescharacteristic
735C4⋊C4C2×D4×C10311yescharacteristic
736C4⋊C4C2×D4×C10311yescharacteristic
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
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—41no—
762C22⋊C4—41no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42C2×D4×C10311yescharacteristic
768C42C2×D4×C10311yescharacteristic
769C42C2×D4×C10311yescharacteristic
770C42C24×C10311yescharacteristic
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23#120×C10311yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—81no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—82no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—82no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4#120×C10311yescharacteristic
834C2×C4#120×C10311yescharacteristic
835C2×C4#120×C10311yescharacteristic
836C2×C4C22×D4×C10311yescharacteristic
837C2×C4C22×D4×C10311yescharacteristic
838C2×C4C22×D4×C10311yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—84no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C2×#120×C10311yescharacteristic
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C2—41no—
881C2—81no—
882C2—81no—
883C2—81no—
884C2—81no—
885C2—161no—
886C2C103×#301811yescharacteristic
887C2C103×#301911yescharacteristic
888C2C103×#302111yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC42C24×C103
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3529C2semidirect
2. C103×#3219C2semidirect
3. C103×#3214C2semidirect
4. C103×#3180C2semidirect
5. C103×#1664C2semidirect
6. C103×#1662C2semidirect
7. C103×#1661C2semidirect
8. C103×#1659C2semidirect
9. C103×#1657C2semidirect
10. C103×#1656C2semidirect
11. C103×#1656C2semidirect
12. C103×#1655C2semidirect
13. C103×#1535C2semidirect
14. C103×#1532C2semidirect
15. C103×#1530C2semidirect
28. #532×C103C22semidirect
36. #501×C103C22semidirect
41. #496×C103C22semidirect
42. #491×C103C22semidirect
43. #490×C103C22semidirect
44. #490×C103C22semidirect
47. #489×C103C22semidirect
60. #432×C103C22semidirect
61. #432×C103C22semidirect
62. C2×#97×C103C22semidirect
63. #330×C103C22semidirect
64. #330×C103C22semidirect
65. #330×C103C22semidirect
66. #330×C103C22semidirect
73. #329×C103C22semidirect
74. #329×C103C22semidirect
435. #19010C103direct (N × H)
445. #3529C2×C103semidirect
446. #3219C2×C103semidirect
447. #3214C2×C103semidirect
448. #3180C2×C103semidirect
449. #1664C2×C103semidirect
450. #1662C2×C103semidirect
451. #1661C2×C103semidirect
452. #1659C2×C103semidirect
453. #1657C2×C103semidirect
454. #1656C2×C103semidirect
455. #1656C2×C103semidirect
456. #1655C2×C103semidirect
457. #1535C2×C103semidirect
458. #1532C2×C103semidirect
459. #1530C2×C103semidirect
460. C103#19010direct (N × H)
473. #532C22×C103semidirect
481. #501C22×C103semidirect
486. #496C22×C103semidirect
487. #491C22×C103semidirect
488. #490C22×C103semidirect
489. #490C22×C103semidirect
492. #489C22×C103semidirect
505. #432C22×C103semidirect
506. #432C22×C103semidirect
507. C2×#97C22×C103semidirect
508. #330C22×C103semidirect
509. #330C22×C103semidirect
510. #330C22×C103semidirect
511. #330C22×C103semidirect
518. #329C22×C103semidirect
519. #329C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35292
C103×#32192
C103×#32142
C103×#31802
C103×#16642
C103×#16622
C103×#16612
C103×#16592
C103×#16572
C103×#16562
C103×#16552
C103×#15352
C103×#15322
C103×#15302
#19010103