Finite Group Databasebeta

← C103×#18228 #39923503

Subgroups — C103×#18228 #39923503

Order 26368.

1300 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3537C211yesmaximal, characteristic, complemented
2C103×#3006C211yesmaximal, characteristic, complemented
3C103×#3002C211yesmaximal, characteristic, complemented
4C103×#2615C211yesmaximal, characteristic, complemented
5C103×#1606C212yesmaximal, complemented
6C103×#1601C212yesmaximal, complemented
7C103×#1600C212yesmaximal, complemented
8C103×#1595C212yesmaximal, complemented
9C103×#1519C211yesmaximal, characteristic, complemented
10C103×#1513C211yesmaximal, characteristic, complemented
11C103×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C103C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C103—21no—
14C2×#135×C103—21no—
15#560×C103—22no—
16#553×C103—21no—
17#553×C103—21no—
18D42×C103—22no—
19D42×C103—21no—
20D42×C103—21no—
21#540×C103—21no—
22#538×C103—21no—
23#538×C103C2212yes—
24#535×C103—21no—
25#534×C103—21no—
26#534×C103C2212yes—
27#525×C103C2211yescharacteristic
28C2×#121×C103—21no—
29C2×#121×C103C2211yescharacteristic
30C2×#121×C103C2211yescharacteristic
31#452×C103—21no—
32#451×C103C2211yescharacteristic, complemented
33#450×C103C2211yescharacteristic, complemented
34#449×C103—21no—
35#449×C103—22no—
36#448×C103C2211yescharacteristic, complemented
37#448×C103C2212yescomplemented
38#447×C103C2211yescharacteristic, complemented
39#447×C103C2212yescomplemented
40#417×C103—21no—
41#416×C103—21no—
42#407×C103C2211yescharacteristic, complemented
43C2×C22⋊C8×C103C2211yescharacteristic, complemented
44#393×C103C2212yescomplemented
45#392×C103—22no—
46#392×C103C2212yescomplemented
47#380×C103—21no—
48#380×C103C2211yescharacteristic, complemented
49#328×C103C2212yescomplemented
50#327×C103C2212yescomplemented
51#327×C103C2212yescomplemented
52#327×C103C2212yescomplemented
53#323×C103C2212yescomplemented
54#323×C103C2212yescomplemented
55C2×#41×C103—21no—
56C2×#41×C103—21no—
57C2×#41×C103—21no—
58C2×#41×C103—21no—
59C2×#41×C103—44no—
60C2×#41×C103D411yescharacteristic, complemented
61C22×Q8×C103C2311yescharacteristic
62C22×D4×C103—22no—
63C22×D4×C103—21no—
64C22×D4×C103—21no—
65C22×D4×C103—22no—
66C22×D4×C103—21no—
67C22×D4×C103—22no—
68C22×D4×C103D411yescharacteristic
69C22×D4×C103D412yes—
70C22×D4×C103D411yescharacteristic, complemented
71C22×D4×C103C2311yescharacteristic
72C23×C4×C103—21no—
73C23×C4×C103C2311yescharacteristic
74AGL(1,ℤ/8)×C103—44no—
75#135×C103—44no—
76C2×Q16×C103—21no—
77C2×SD16×C103—21no—
78C2×SD16×C103—21no—
79C2×SD16×C103—22no—
80C2×D8×C103—21no—
81C2×D8×C103—22no—
82C2×M16×C103—21no—
83C22×C8×C103—21no—
84#127×C103—22no—
85#127×C103—21no—
86#126×C103—22no—
87#126×C103—22no—
88#125×C103—21no—
89#124×C103—22no—
90#123×C103—22no—
91#123×C103—21no—
92#123×C103—22no—
93#123×C103—22no—
94#123×C103—22no—
95C22⋊Q8×C103D411yescharacteristic, complemented
96C22⋊Q8×C103C2311yescharacteristic
97#121×C103—22no—
98#121×C103—21no—
99#121×C103—21no—
100#121×C103—22no—
101#121×C103—22no—
102#121×C103—22no—
103#121×C103—22no—
104#121×C103—21no—
105#121×C103—21no—
106#121×C103—21no—
107#121×C103—21no—
108#121×C103—21no—
109#121×C103—21no—
110#121×C103—22no—
111#121×C103—44no—
112#121×C103D412yescomplemented
113#121×C103D411yescharacteristic, complemented
114#121×C103C2312yes—
115#121×C103C2311yescharacteristic
116#120×C103—22no—
117#120×C103—22no—
118#120×C103—22no—
119#120×C103—21no—
120#120×C103—22no—
121#120×C103—22no—
122#120×C103—22no—
123C4×D4×C103—22no—
124C4×D4×C103—21no—
125C4×D4×C103—21no—
126C4×D4×C103—21no—
127C4×D4×C103—21no—
128C4×D4×C103—22no—
129#117×C103—21no—
130#117×C103D411yescharacteristic, complemented
131C2×C4⋊C4×C103—21no—
132C2×C4⋊C4×C103D411yescharacteristic
133C2×C4⋊C4×C103D411yescharacteristic, complemented
134C2×C22⋊C4×C103—21no—
135C2×C22⋊C4×C103—22no—
136C2×C22⋊C4×C103—21no—
137C2×C22⋊C4×C103—22no—
138C2×C22⋊C4×C103C2312yes—
139#103×C103—21no—
140#103×C103—21no—
141#103×C103—22no—
142#102×C103—21no—
143#102×C103—21no—
144#102×C103—22no—
145C22⋊C8×C103—21no—
146C22⋊C8×C103—21no—
147C22⋊C8×C103C2311yescharacteristic
148C22⋊C8×C103C2311yescharacteristic
149C22⋊C8×C103C2312yes—
150#95×C103—22no—
151#95×C103C2312yes—
152C24×C103—22no—
153C24×C103—21no—
154C24×C103—21no—
155C24×C103C2×D412yes—
156C24×C103C2×D411yescharacteristic
157#41×C103—24no—
158#41×C103—24no—
159#41×C103—42no—
160#41×C103—42no—
161#41×C103—42no—
162#41×C103—42no—
163#41×C103—42no—
164#41×C103—42no—
165#41×C103—42no—
166C2×Q8×C103—21no—
167C2×Q8×C103—21no—
168C2×Q8×C103—42no—
169C2×Q8×C103C2×D411yescharacteristic
170C2×D4×C103—22no—
171C2×D4×C103—21no—
172C2×D4×C103—21no—
173C2×D4×C103—22no—
174C2×D4×C103—22no—
175C2×D4×C103—22no—
176C2×D4×C103—22no—
177C2×D4×C103—22no—
178C2×D4×C103—22no—
179C2×D4×C103—21no—
180C2×D4×C103—22no—
181C2×D4×C103—22no—
182C2×D4×C103—21no—
183C2×D4×C103—21no—
184C2×D4×C103—21no—
185C2×D4×C103—21no—
186C2×D4×C103—21no—
187C2×D4×C103—42no—
188C2×D4×C103—42no—
189C2×D4×C103—42no—
190C2×D4×C103—42no—
191C2×D4×C103—42no—
192C2×D4×C103—41no—
193C2×D4×C103—41no—
194C2×D4×C103—44no—
195C2×D4×C103—82no—
196C2×D4×C103—82no—
197C2×D4×C103—82no—
198C2×D4×C103—82no—
199C2×D4×C103—81no—
200C2×D4×C103—81no—
201C2×D4×C103—82no—
202C2×D4×C103—82no—
203C2×D4×C103—84no—
204C2×D4×C103C2×D411yescharacteristic
205C2×D4×C103C2×D412yes—
206C22×C4×C103—24no—
207C22×C4×C103—21no—
208C22×C4×C103—22no—
209C22×C4×C103—22no—
210C22×C4×C103—21no—
211C22×C4×C103—21no—
212C22×C4×C103—22no—
213C22×C4×C103—42no—
214C22×C4×C103—42no—
215C22×C4×C103—41no—
216C22×C4×C103—41no—
217C22×C4×C103C2×D411yescharacteristic
218C22×C4×C103C2×D411yescharacteristic
219C22×C4×C103C2×D411yescharacteristic
220C22×C4×C103C2×D412yes—
221C22×C4×C103C2×D411yescharacteristic
222C22×C4×C103C2×D411yescharacteristic
223C22×C4×C103C2411yescharacteristic
224Q16×C103—42no—
225SD16×C103—42no—
226SD16×C103—42no—
227SD16×C103—44no—
228D8×C103—42no—
229D8×C103—44no—
230M16×C103—42no—
231C2×C8×C103—21no—
232C2×C8×C103—21no—
233C2×C8×C103—22no—
234C2×C8×C103—42no—
235C4⋊C4×C103—22no—
236C4⋊C4×C103—22no—
237C4⋊C4×C103—21no—
238C4⋊C4×C103—21no—
239C4⋊C4×C103—21no—
240C4⋊C4×C103—21no—
241C4⋊C4×C103—21no—
242C4⋊C4×C103—42no—
243C4⋊C4×C103C2×D412yes—
244C4⋊C4×C103C2×D411yescharacteristic
245C4⋊C4×C103C2×D411yescharacteristic
246C22⋊C4×C103—22no—
247C22⋊C4×C103—22no—
248C22⋊C4×C103—22no—
249C22⋊C4×C103—22no—
250C22⋊C4×C103—22no—
251C22⋊C4×C103—21no—
252C22⋊C4×C103—21no—
253C22⋊C4×C103—21no—
254C22⋊C4×C103—22no—
255C22⋊C4×C103—21no—
256C22⋊C4×C103—22no—
257C22⋊C4×C103—22no—
258C22⋊C4×C103—22no—
259C22⋊C4×C103—21no—
260C22⋊C4×C103—44no—
261C22⋊C4×C103—81no—
262C22⋊C4×C103—82no—
263C42×C103—22no—
264C42×C103—21no—
265C23×C103—21no—
266C23×C103—21no—
267C23×C103—22no—
268C23×C103—22no—
269C23×C103—22no—
270C23×C103—21no—
271C23×C103—22no—
272C23×C103—22no—
273C23×C103—41no—
274C23×C103—41no—
275C23×C103—41no—
276C23×C103—41no—
277C23×C103—41no—
278C23×C103—42no—
279C23×C103—42no—
280C23×C103—42no—
281C23×C103—41no—
282C23×C103—41no—
283C23×C103—41no—
284C23×C103—81no—
285C23×C103—81no—
286C23×C103—82no—
287C23×C103—82no—
288C23×C103—82no—
289C23×C103#12011yescharacteristic
290C23×C103#12011yescharacteristic
291C23×C103C22×D411yescharacteristic
292Q8×C103—22no—
293Q8×C103—22no—
294Q8×C103—41no—
295Q8×C103—41no—
296Q8×C103—41no—
297D4×C103—22no—
298D4×C103—22no—
299D4×C103—42no—
300D4×C103—41no—
301D4×C103—41no—
302D4×C103—41no—
303D4×C103—44no—
304D4×C103—42no—
305D4×C103—44no—
306D4×C103—44no—
307D4×C103—42no—
308D4×C103—41no—
309D4×C103—42no—
310D4×C103—41no—
311D4×C103—42no—
312D4×C103—42no—
313D4×C103—81no—
314D4×C103—82no—
315D4×C103—82no—
316D4×C103—81no—
317D4×C103—82no—
318D4×C103—82no—
319D4×C103—82no—
320D4×C103—82no—
321D4×C103—82no—
322D4×C103—88no—
323C2×C4×C103—22no—
324C2×C4×C103—22no—
325C2×C4×C103—22no—
326C2×C4×C103—22no—
327C2×C4×C103—21no—
328C2×C4×C103—22no—
329C2×C4×C103—22no—
330C2×C4×C103—21no—
331C2×C4×C103—21no—
332C2×C4×C103—41no—
333C2×C4×C103—41no—
334C2×C4×C103—41no—
335C2×C4×C103—44no—
336C2×C4×C103—41no—
337C2×C4×C103—41no—
338C2×C4×C103—44no—
339C2×C4×C103—42no—
340C2×C4×C103—42no—
341C2×C4×C103—42no—
342C2×C4×C103—42no—
343C2×C4×C103—42no—
344C2×C4×C103—81no—
345C2×C4×C103—82no—
346C2×C4×C103—82no—
347C2×C4×C103#12011yescharacteristic
348C2×C4×C103#12011yescharacteristic
349C2×C4×C103C22×D411yescharacteristic
350C2×C4×C103C22×D411yescharacteristic
351C8×C103—41no—
352C8×C103—41no—
353C8×C103—42no—
354C22×C103—21no—
355C22×C103—21no—
356C22×C103—21no—
357C22×C103—21no—
358C22×C103—21no—
359C22×C103—21no—
360C22×C103—21no—
361C22×C103—21no—
362C22×C103—42no—
363C22×C103—42no—
364C22×C103—42no—
365C22×C103—42no—
366C22×C103—41no—
367C22×C103—42no—
368C22×C103—42no—
369C22×C103—41no—
370C22×C103—42no—
371C22×C103—41no—
372C22×C103—42no—
373C22×C103—42no—
374C22×C103—81no—
375C22×C103—81no—
376C22×C103—82no—
377C22×C103—82no—
378C22×C103—81no—
379C22×C103—81no—
380C22×C103—81no—
381C22×C103—81no—
382C22×C103—162no—
383C22×C103—164no—
384C22×C103C2×#12011yescharacteristic
385C22×C103#57611yescharacteristic
386C22×C103#57711yescharacteristic
387C4×C103—21no—
388C4×C103—21no—
389C4×C103—21no—
390C4×C103—42no—
391C4×C103—41no—
392C4×C103—42no—
393C4×C103—41no—
394C4×C103—42no—
395C4×C103—41no—
396C4×C103—82no—
397C4×C103B(4,𝔽2)12yes—
398#18228C10311yesmaximal, characteristic, direct product factor, Sylow
399C2×C103—21no—
400C2×C103—21no—
401C2×C103—41no—
402C2×C103—41no—
403C2×C103—82no—
404C2×C103—82no—
405C2×C103—82no—
406C2×C103—81no—
407C2×C103#301211yescharacteristic
408C2×C103#301911yescharacteristic
409C2×C103C2×B(4,𝔽2)11yescharacteristic
410#3537C2×C10311yescharacteristic, complemented
411#3006C2×C10311yescharacteristic, complemented
412#3002C2×C10311yescharacteristic, complemented
413#2615C2×C10311yescharacteristic, complemented
414#1606C2×C10312yescomplemented
415#1601C2×C10312yescomplemented
416#1600C2×C10312yescomplemented
417#1595C2×C10312yescomplemented
418#1519C2×C10311yescharacteristic, complemented
419#1513C2×C10311yescharacteristic, complemented
420#1471C2×C10311yescharacteristic, complemented
421C103#1822811yescharacteristic, direct product factor, Sylow
422C22×#41C22×C10311yescharacteristic, complemented
423C2×AGL(1,ℤ/8)—21no—
424C2×#135—21no—
425#560—22no—
426#553—21no—
427#553—21no—
428D42—22no—
429D42—21no—
430D42—21no—
431#540—21no—
432#538—21no—
433#538C22×C10312yes—
434#535—21no—
435#534—21no—
436#534C22×C10312yes—
437#525C22×C10311yescharacteristic
438C2×#121—21no—
439C2×#121C22×C10311yescharacteristic
440C2×#121C22×C10311yescharacteristic
441#452—21no—
442#451C22×C10311yescharacteristic, complemented
443#450C22×C10311yescharacteristic, complemented
444#449—21no—
445#449—22no—
446#448C22×C10311yescharacteristic, complemented
447#448C22×C10312yescomplemented
448#447C22×C10311yescharacteristic, complemented
449#447C22×C10312yescomplemented
450#417—21no—
451#416—21no—
452#407C22×C10311yescharacteristic, complemented
453C2×C22⋊C8C22×C10311yescharacteristic, complemented
454#393C22×C10312yescomplemented
455#392—22no—
456#392C22×C10312yescomplemented
457#380—21no—
458#380C22×C10311yescharacteristic, complemented
459#328C22×C10312yescomplemented
460#327C22×C10312yescomplemented
461#327C22×C10312yescomplemented
462#327C22×C10312yescomplemented
463#323C22×C10312yescomplemented
464#323C22×C10312yescomplemented
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—44no—
470C2×#41D4×C10311yescharacteristic, complemented
471C22×Q8C23×C10311yescharacteristic
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—22no—
478C22×D4D4×C10311yescharacteristic
479C22×D4D4×C10312yes—
480C22×D4D4×C10311yescharacteristic, complemented
481C22×D4C23×C10311yescharacteristic
482C23×C4—21no—
483C23×C4C23×C10311yescharacteristic
484AGL(1,ℤ/8)—44no—
485#135—44no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×D8—21no—
491C2×D8—22no—
492C2×M16—21no—
493C22×C8—21no—
494#127—22no—
495#127—21no—
496#126—22no—
497#126—22no—
498#125—21no—
499#124—22no—
500#123—22no—
501#123—21no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8D4×C10311yescharacteristic, complemented
506C22⋊Q8C23×C10311yescharacteristic
507#121—22no—
508#121—21no—
509#121—21no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—22no—
521#121—44no—
522#121D4×C10312yescomplemented
523#121D4×C10311yescharacteristic, complemented
524#121C23×C10312yes—
525#121C23×C10311yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529#120—21no—
530#120—22no—
531#120—22no—
532#120—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—22no—
539#117—21no—
540#117D4×C10311yescharacteristic, complemented
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C10311yescharacteristic
543C2×C4⋊C4D4×C10311yescharacteristic, complemented
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4C23×C10312yes—
549#103—21no—
550#103—21no—
551#103—22no—
552#102—21no—
553#102—21no—
554#102—22no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8C23×C10311yescharacteristic
558C22⋊C8C23×C10311yescharacteristic
559C22⋊C8C23×C10312yes—
560#95—22no—
561#95C23×C10312yes—
562C24—22no—
563C24—21no—
564C24—21no—
565C24C2×D4×C10312yes—
566C24C2×D4×C10311yescharacteristic
567#41—24no—
568#41—24no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8C2×D4×C10311yescharacteristic
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—84no—
614C2×D4C2×D4×C10311yescharacteristic
615C2×D4C2×D4×C10312yes—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×D4×C10311yescharacteristic
628C22×C4C2×D4×C10311yescharacteristic
629C22×C4C2×D4×C10311yescharacteristic
630C22×C4C2×D4×C10312yes—
631C22×C4C2×D4×C10311yescharacteristic
632C22×C4C2×D4×C10311yescharacteristic
633C22×C4C24×C10311yescharacteristic
634Q16—42no—
635SD16—42no—
636SD16—42no—
637SD16—44no—
638D8—42no—
639D8—44no—
640M16—42no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—42no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4C2×D4×C10312yes—
654C4⋊C4C2×D4×C10311yescharacteristic
655C4⋊C4C2×D4×C10311yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—81no—
672C22⋊C4—82no—
673C42—22no—
674C42—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23#120×C10311yescharacteristic
700C23#120×C10311yescharacteristic
701C23C22×D4×C10311yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—44no—
714D4—42no—
715D4—44no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4—82no—
732D4—88no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4#120×C10311yescharacteristic
758C2×C4#120×C10311yescharacteristic
759C2×C4C22×D4×C10311yescharacteristic
760C2×C4C22×D4×C10311yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—162no—
793C22—164no—
794C22C2×#120×C10311yescharacteristic
795C22#576×C10311yescharacteristic
796C22#577×C10311yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—82no—
807C4B(4,𝔽2)×C10312yes—
808C2—21no—
809C2—21no—
810C2—41no—
811C2—41no—
812C2—82no—
813C2—82no—
814C2—82no—
815C2—81no—
816C2C103×#301211yescharacteristic
817C2C103×#301911yescharacteristic
818C2C2×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×#3537C2semidirect
2. C103×#3006C2semidirect
3. C103×#3002C2semidirect
4. C103×#2615C2semidirect
5. C103×#1606C2semidirect
6. C103×#1601C2semidirect
7. C103×#1600C2semidirect
8. C103×#1595C2semidirect
9. C103×#1519C2semidirect
10. C103×#1513C2semidirect
11. C103×#1471C2semidirect
12. C22×#41×C103C22semidirect
32. #451×C103C22semidirect
33. #450×C103C22semidirect
36. #448×C103C22semidirect
37. #448×C103C22semidirect
38. #447×C103C22semidirect
39. #447×C103C22semidirect
42. #407×C103C22semidirect
43. C2×C22⋊C8×C103C22semidirect
44. #393×C103C22semidirect
46. #392×C103C22semidirect
48. #380×C103C22semidirect
49. #328×C103C22semidirect
50. #327×C103C22semidirect
51. #327×C103C22semidirect
52. #327×C103C22semidirect
53. #323×C103C22semidirect
54. #323×C103C22semidirect
60. C2×#41×C103D4semidirect
70. C22×D4×C103D4semidirect
95. C22⋊Q8×C103D4semidirect
112. #121×C103D4semidirect
113. #121×C103D4semidirect
130. #117×C103D4semidirect
133. C2×C4⋊C4×C103D4semidirect
398. #18228C103direct (N × H)
410. #3537C2×C103semidirect
411. #3006C2×C103semidirect
412. #3002C2×C103semidirect
413. #2615C2×C103semidirect
414. #1606C2×C103semidirect
415. #1601C2×C103semidirect
416. #1600C2×C103semidirect
417. #1595C2×C103semidirect
418. #1519C2×C103semidirect
419. #1513C2×C103semidirect
420. #1471C2×C103semidirect
421. C103#18228direct (N × H)
422. C22×#41C22×C103semidirect
442. #451C22×C103semidirect
443. #450C22×C103semidirect
446. #448C22×C103semidirect
447. #448C22×C103semidirect
448. #447C22×C103semidirect
449. #447C22×C103semidirect
452. #407C22×C103semidirect
453. C2×C22⋊C8C22×C103semidirect
454. #393C22×C103semidirect
456. #392C22×C103semidirect
458. #380C22×C103semidirect
459. #328C22×C103semidirect
460. #327C22×C103semidirect
461. #327C22×C103semidirect
462. #327C22×C103semidirect
463. #323C22×C103semidirect
464. #323C22×C103semidirect
470. C2×#41D4×C103semidirect
480. C22×D4D4×C103semidirect
505. C22⋊Q8D4×C103semidirect
522. #121D4×C103semidirect
523. #121D4×C103semidirect
540. #117D4×C103semidirect
543. 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×#35372
C103×#30062
C103×#30022
C103×#26152
C103×#16062
C103×#16012
C103×#16002
C103×#15952
C103×#15192
C103×#15132
C103×#14712
#18228103