Finite Group Databasebeta

← C103×#25196 #39930471

Subgroups — C103×#25196 #39930471

Order 26368.

1032 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3068C211yesmaximal, characteristic, complemented
2C103×#3068C211yesmaximal, characteristic, complemented
3C103×#3019C211yesmaximal, characteristic, complemented
4C2×#453×C103C211yesmaximal, characteristic, complemented
5C103×#2956C211yesmaximal, characteristic, complemented
6C103×#2888C211yesmaximal, characteristic, complemented
7C103×#2069C211yesmaximal, characteristic, complemented
8C103×#2050C211yesmaximal, characteristic, complemented
9C103×#2048C211yesmaximal, characteristic, complemented
10C103×#2002C211yesmaximal, characteristic, complemented
11C103×#1965C211yesmaximal, characteristic, complemented
12C103×#1932C211yesmaximal, characteristic, complemented
13C103×#1914C211yesmaximal, characteristic, complemented
14C103×#1903C211yesmaximal, characteristic, complemented
15C103×#1861C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C103C2211yescharacteristic
17#575×C103C2211yescharacteristic
18#575×C103C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C103C2211yescharacteristic, complemented
22#568×C103C2211yescharacteristic
23#568×C103C2211yescharacteristic
24#568×C103C2211yescharacteristic, complemented
25#535×C103C2211yescharacteristic
26C2×#127×C103C2211yescharacteristic
27#472×C103—22no—
28#472×C103—22no—
29#471×C103—22no—
30#471×C103—22no—
31#455×C103—22no—
32#453×C103—22no—
33#453×C103—22no—
34#453×C103—22no—
35#444×C103—22no—
36#443×C103—22no—
37#430×C103C2211yescharacteristic, complemented
38#430×C103C2211yescharacteristic, complemented
39#430×C103C2211yescharacteristic, complemented
40#423×C103C2211yescharacteristic, complemented
41#421×C103C2211yescharacteristic
42#421×C103C2211yescharacteristic
43C2×#104×C103C2211yescharacteristic
44C2×#104×C103C2211yescharacteristic
45C2×#104×C103C2211yescharacteristic, complemented
46#418×C103C2211yescharacteristic, complemented
47#413×C103—22no—
48#413×C103C2211yescharacteristic
49#413×C103C2211yescharacteristic
50#413×C103C2211yescharacteristic, complemented
51C2×#100×C103—22no—
52C2×#100×C103C2211yescharacteristic
53C2×#100×C103C2211yescharacteristic
54C2×#100×C103C2211yescharacteristic
55C2×#100×C103C2211yescharacteristic
56C2×#100×C103C2211yescharacteristic, complemented
57C2×#100×C103C2211yescharacteristic, complemented
58C4×M16×C103C2211yescharacteristic, complemented
59#344×C103C2211yescharacteristic, complemented
60#344×C103C2211yescharacteristic, complemented
61#339×C103C2211yescharacteristic, complemented
62#338×C103C2211yescharacteristic, complemented
63H(5,𝔽2)×C103—22no—
64H(5,𝔽2)×C103—22no—
65H(5,𝔽2)×C103—41no—
66H(5,𝔽2)×C103—41no—
67C2×#41×C103—21no—
68C2×#41×C103—21no—
69C2×#41×C103C2311yescharacteristic
70C2×#41×C103C2311yescharacteristic
71C2×#41×C103C2311yescharacteristic
72C22×D4×C103—22no—
73C22×D4×C103—21no—
74C22×D4×C103—21no—
75C22×D4×C103—22no—
76C22×D4×C103C2311yescharacteristic
77C22×D4×C103C2311yescharacteristic
78#137×C103—21no—
79#137×C103—21no—
80#137×C103—21no—
81#137×C103D412yescomplemented
82AGL(1,ℤ/8)×C103—21no—
83AGL(1,ℤ/8)×C103—22no—
84AGL(1,ℤ/8)×C103—22no—
85AGL(1,ℤ/8)×C103—21no—
86AGL(1,ℤ/8)×C103—21no—
87AGL(1,ℤ/8)×C103—22no—
88AGL(1,ℤ/8)×C103—22no—
89AGL(1,ℤ/8)×C103—41no—
90AGL(1,ℤ/8)×C103—41no—
91AGL(1,ℤ/8)×C103D412yescomplemented
92#135×C103—22no—
93#135×C103—41no—
94C2×SD16×C103—21no—
95C2×SD16×C103—21no—
96C2×SD16×C103—21no—
97C2×D8×C103—21no—
98C2×D8×C103—21no—
99C2×D8×C103—21no—
100#131×C103—22no—
101#131×C103—22no—
102#131×C103—22no—
103#131×C103—22no—
104#131×C103—41no—
105#131×C103—41no—
106C2×M16×C103—22no—
107C2×M16×C103—22no—
108C2×M16×C103—41no—
109C2×M16×C103C2311yescharacteristic
110C2×M16×C103C2311yescharacteristic
111C2×M16×C103C2311yescharacteristic
112C2×M16×C103C2311yescharacteristic
113C2×M16×C103C2311yescharacteristic
114C2×M16×C103C2311yescharacteristic
115C2×M16×C103C2311yescharacteristic
116C2×M16×C103C2311yescharacteristic
117#127×C103—21no—
118#127×C103—21no—
119#127×C103—21no—
120#127×C103—41no—
121#124×C103—21no—
122#121×C103—41no—
123#120×C103—22no—
124#117×C103C2311yescharacteristic
125C2×C42×C103C2311yescharacteristic
126#108×C103—22no—
127#108×C103—22no—
128#108×C103—22no—
129C4⋊C8×C103—41no—
130#104×C103—22no—
131#104×C103—22no—
132#104×C103—21no—
133#104×C103—21no—
134#104×C103—21no—
135#104×C103—21no—
136#104×C103D412yescomplemented
137#104×C103D412yescomplemented
138#102×C103—41no—
139#101×C103—21no—
140#101×C103—21no—
141#101×C103D412yescomplemented
142#100×C103—21no—
143#100×C103—21no—
144#100×C103—22no—
145#100×C103—22no—
146#100×C103—22no—
147#100×C103—22no—
148#100×C103—22no—
149#100×C103—22no—
150#100×C103D412yescomplemented
151#97×C103—21no—
152C4×C8×C103—21no—
153C24×C103—22no—
154C24×C103—21no—
155C24×C103#4112yes—
156#41×C103—21no—
157#41×C103—21no—
158#41×C103—21no—
159#41×C103—21no—
160#41×C103—21no—
161#41×C103—21no—
162#41×C103—21no—
163#41×C103—21no—
164#41×C103—21no—
165#41×C103—21no—
166#41×C103—42no—
167#41×C103—42no—
168#41×C103—42no—
169#41×C103—42no—
170#41×C103C2×D412yes—
171#41×C103C2×D412yes—
172C2×Q8×C103C2×D411yescharacteristic
173C2×Q8×C103C2×D411yescharacteristic
174C2×Q8×C103#4111yescharacteristic
175C2×D4×C103—21no—
176C2×D4×C103—22no—
177C2×D4×C103—22no—
178C2×D4×C103—21no—
179C2×D4×C103—21no—
180C2×D4×C103—21no—
181C2×D4×C103—21no—
182C2×D4×C103—21no—
183C2×D4×C103—21no—
184C2×D4×C103—21no—
185C2×D4×C103—21no—
186C2×D4×C103—21no—
187C2×D4×C103—21no—
188C2×D4×C103—21no—
189C2×D4×C103—21no—
190C2×D4×C103—21no—
191C2×D4×C103—21no—
192C2×D4×C103—42no—
193C2×D4×C103—42no—
194C2×D4×C103—42no—
195C2×D4×C103—42no—
196C2×D4×C103—44no—
197C2×D4×C103—44no—
198C2×D4×C103—42no—
199C2×D4×C103—42no—
200C2×D4×C103—42no—
201C2×D4×C103—84no—
202C2×D4×C103C2×D411yescharacteristic
203C2×D4×C103C2×D411yescharacteristic
204C2×D4×C103#4111yescharacteristic
205C22×C4×C103—21no—
206C22×C4×C103—22no—
207C22×C4×C103—21no—
208C22×C4×C103—21no—
209C22×C4×C103—21no—
210C22×C4×C103C2411yescharacteristic
211Q16×C103—22no—
212Q16×C103—41no—
213SD16×C103—22no—
214SD16×C103—22no—
215SD16×C103—42no—
216SD16×C103—42no—
217SD16×C103—41no—
218SD16×C103—41no—
219SD16×C103—42no—
220D8×C103—22no—
221D8×C103—42no—
222D8×C103—42no—
223D8×C103—41no—
224D8×C103—42no—
225M16×C103—21no—
226M16×C103—21no—
227M16×C103—21no—
228M16×C103—21no—
229M16×C103—21no—
230M16×C103—21no—
231M16×C103—21no—
232M16×C103—21no—
233M16×C103—21no—
234M16×C103—21no—
235M16×C103—21no—
236M16×C103—21no—
237M16×C103—42no—
238M16×C103—42no—
239M16×C103—42no—
240M16×C103C2×D412yes—
241M16×C103C2×D412yes—
242M16×C103C2×D412yes—
243M16×C103C2×D412yes—
244C2×C8×C103—21no—
245C2×C8×C103—21no—
246C2×C8×C103—21no—
247C2×C8×C103—21no—
248C2×C8×C103—21no—
249C2×C8×C103—21no—
250C2×C8×C103—21no—
251C2×C8×C103—21no—
252C2×C8×C103—42no—
253C2×C8×C103—42no—
254C2×C8×C103—42no—
255C4⋊C4×C103—21no—
256C22⋊C4×C103—21no—
257C22⋊C4×C103—42no—
258C42×C103—21no—
259C42×C103—21no—
260C42×C103C2×D411yescharacteristic
261C42×C103C2×D411yescharacteristic
262C23×C103—21no—
263C23×C103—22no—
264C23×C103—21no—
265C23×C103—22no—
266C23×C103—21no—
267C23×C103—22no—
268C23×C103—44no—
269C23×C103—41no—
270C23×C103—41no—
271C23×C103—41no—
272C23×C103—82no—
273C23×C103—82no—
274C23×C103—162no—
275C23×C103C2×#4111yescharacteristic
276Q8×C103—21no—
277Q8×C103—21no—
278Q8×C103—21no—
279Q8×C103—21no—
280Q8×C103—21no—
281Q8×C103#12112yes—
282D4×C103—22no—
283D4×C103—22no—
284D4×C103—21no—
285D4×C103—21no—
286D4×C103—21no—
287D4×C103—21no—
288D4×C103—21no—
289D4×C103—44no—
290D4×C103—44no—
291D4×C103—41no—
292D4×C103—41no—
293D4×C103—41no—
294D4×C103—41no—
295D4×C103—41no—
296D4×C103—41no—
297D4×C103—41no—
298D4×C103—41no—
299D4×C103—41no—
300D4×C103—41no—
301D4×C103—41no—
302D4×C103—41no—
303D4×C103—84no—
304D4×C103—84no—
305D4×C103—162no—
306D4×C103#12112yes—
307C2×C4×C103—21no—
308C2×C4×C103—21no—
309C2×C4×C103—22no—
310C2×C4×C103—22no—
311C2×C4×C103—21no—
312C2×C4×C103—21no—
313C2×C4×C103—21no—
314C2×C4×C103—44no—
315C2×C4×C103—42no—
316C2×C4×C103—41no—
317C2×C4×C103—41no—
318C2×C4×C103—41no—
319C2×C4×C103—41no—
320C2×C4×C103—41no—
321C2×C4×C103C22×D411yescharacteristic
322C2×C4×C103C22×D411yescharacteristic
323C2×C4×C103C22×D411yescharacteristic
324C2×C4×C103C2×#4111yescharacteristic
325C2×C4×C103H(5,𝔽2)11yescharacteristic
326C2×C4×C103H(5,𝔽2)11yescharacteristic
327C8×C103—22no—
328C8×C103—22no—
329C8×C103—22no—
330C8×C103—22no—
331C8×C103—41no—
332C8×C103—41no—
333C8×C103—41no—
334C8×C103—41no—
335C22×C103—22no—
336C22×C103—41no—
337C22×C103—41no—
338C22×C103—41no—
339C22×C103—42no—
340C22×C103—81no—
341C22×C103—82no—
342C22×C103—81no—
343C22×C103—82no—
344C22×C103—82no—
345C22×C103—81no—
346C22×C103—82no—
347C22×C103—81no—
348C22×C103—161no—
349C22×C103—161no—
350C22×C103—164no—
351C22×C103#52511yescharacteristic
352C22×C103#54611yescharacteristic
353C22×C103#54611yescharacteristic
354C4×C103—22no—
355C4×C103—22no—
356C4×C103—41no—
357C4×C103—41no—
358C4×C103—41no—
359C4×C103—81no—
360C4×C103C2×#12111yescharacteristic
361C4×C103#53811yescharacteristic
362C4×C103D4211yescharacteristic
363C4×C103D4211yescharacteristic
364#25196C10311yesmaximal, characteristic, direct product factor, Sylow
365C2×C103—21no—
366C2×C103—21no—
367C2×C103—21no—
368C2×C103—42no—
369C2×C103—81no—
370C2×C103—82no—
371C2×C103—81no—
372C2×C103—161no—
373C2×C103#242411yescharacteristic
374#3068C2×C10311yescharacteristic, complemented
375#3068C2×C10311yescharacteristic, complemented
376#3019C2×C10311yescharacteristic, complemented
377C2×#453C2×C10311yescharacteristic, complemented
378#2956C2×C10311yescharacteristic, complemented
379#2888C2×C10311yescharacteristic, complemented
380#2069C2×C10311yescharacteristic, complemented
381#2050C2×C10311yescharacteristic, complemented
382#2048C2×C10311yescharacteristic, complemented
383#2002C2×C10311yescharacteristic, complemented
384#1965C2×C10311yescharacteristic, complemented
385#1932C2×C10311yescharacteristic, complemented
386#1914C2×C10311yescharacteristic, complemented
387#1903C2×C10311yescharacteristic, complemented
388#1861C2×C10311yescharacteristic, complemented
389C103#2519611yescharacteristic, direct product factor, Sylow
390C2×H(5,𝔽2)C22×C10311yescharacteristic
391#575C22×C10311yescharacteristic
392#575C22×C10311yescharacteristic
393C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
394C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
395C2×AGL(1,ℤ/8)C22×C10311yescharacteristic, complemented
396#568C22×C10311yescharacteristic
397#568C22×C10311yescharacteristic
398#568C22×C10311yescharacteristic, complemented
399#535C22×C10311yescharacteristic
400C2×#127C22×C10311yescharacteristic
401#472—22no—
402#472—22no—
403#471—22no—
404#471—22no—
405#455—22no—
406#453—22no—
407#453—22no—
408#453—22no—
409#444—22no—
410#443—22no—
411#430C22×C10311yescharacteristic, complemented
412#430C22×C10311yescharacteristic, complemented
413#430C22×C10311yescharacteristic, complemented
414#423C22×C10311yescharacteristic, complemented
415#421C22×C10311yescharacteristic
416#421C22×C10311yescharacteristic
417C2×#104C22×C10311yescharacteristic
418C2×#104C22×C10311yescharacteristic
419C2×#104C22×C10311yescharacteristic, complemented
420#418C22×C10311yescharacteristic, complemented
421#413—22no—
422#413C22×C10311yescharacteristic
423#413C22×C10311yescharacteristic
424#413C22×C10311yescharacteristic, complemented
425C2×#100—22no—
426C2×#100C22×C10311yescharacteristic
427C2×#100C22×C10311yescharacteristic
428C2×#100C22×C10311yescharacteristic
429C2×#100C22×C10311yescharacteristic
430C2×#100C22×C10311yescharacteristic, complemented
431C2×#100C22×C10311yescharacteristic, complemented
432C4×M16C22×C10311yescharacteristic, complemented
433#344C22×C10311yescharacteristic, complemented
434#344C22×C10311yescharacteristic, complemented
435#339C22×C10311yescharacteristic, complemented
436#338C22×C10311yescharacteristic, complemented
437H(5,𝔽2)—22no—
438H(5,𝔽2)—22no—
439H(5,𝔽2)—41no—
440H(5,𝔽2)—41no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41C23×C10311yescharacteristic
444C2×#41C23×C10311yescharacteristic
445C2×#41C23×C10311yescharacteristic
446C22×D4—22no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—22no—
450C22×D4C23×C10311yescharacteristic
451C22×D4C23×C10311yescharacteristic
452#137—21no—
453#137—21no—
454#137—21no—
455#137D4×C10312yescomplemented
456AGL(1,ℤ/8)—21no—
457AGL(1,ℤ/8)—22no—
458AGL(1,ℤ/8)—22no—
459AGL(1,ℤ/8)—21no—
460AGL(1,ℤ/8)—21no—
461AGL(1,ℤ/8)—22no—
462AGL(1,ℤ/8)—22no—
463AGL(1,ℤ/8)—41no—
464AGL(1,ℤ/8)—41no—
465AGL(1,ℤ/8)D4×C10312yescomplemented
466#135—22no—
467#135—41no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×D8—21no—
472C2×D8—21no—
473C2×D8—21no—
474#131—22no—
475#131—22no—
476#131—22no—
477#131—22no—
478#131—41no—
479#131—41no—
480C2×M16—22no—
481C2×M16—22no—
482C2×M16—41no—
483C2×M16C23×C10311yescharacteristic
484C2×M16C23×C10311yescharacteristic
485C2×M16C23×C10311yescharacteristic
486C2×M16C23×C10311yescharacteristic
487C2×M16C23×C10311yescharacteristic
488C2×M16C23×C10311yescharacteristic
489C2×M16C23×C10311yescharacteristic
490C2×M16C23×C10311yescharacteristic
491#127—21no—
492#127—21no—
493#127—21no—
494#127—41no—
495#124—21no—
496#121—41no—
497#120—22no—
498#117C23×C10311yescharacteristic
499C2×C42C23×C10311yescharacteristic
500#108—22no—
501#108—22no—
502#108—22no—
503C4⋊C8—41no—
504#104—22no—
505#104—22no—
506#104—21no—
507#104—21no—
508#104—21no—
509#104—21no—
510#104D4×C10312yescomplemented
511#104D4×C10312yescomplemented
512#102—41no—
513#101—21no—
514#101—21no—
515#101D4×C10312yescomplemented
516#100—21no—
517#100—21no—
518#100—22no—
519#100—22no—
520#100—22no—
521#100—22no—
522#100—22no—
523#100—22no—
524#100D4×C10312yescomplemented
525#97—21no—
526C4×C8—21no—
527C24—22no—
528C24—21no—
529C24#41×C10312yes—
530#41—21no—
531#41—21no—
532#41—21no—
533#41—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—21no—
539#41—21no—
540#41—42no—
541#41—42no—
542#41—42no—
543#41—42no—
544#41C2×D4×C10312yes—
545#41C2×D4×C10312yes—
546C2×Q8C2×D4×C10311yescharacteristic
547C2×Q8C2×D4×C10311yescharacteristic
548C2×Q8#41×C10311yescharacteristic
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—84no—
576C2×D4C2×D4×C10311yescharacteristic
577C2×D4C2×D4×C10311yescharacteristic
578C2×D4#41×C10311yescharacteristic
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4C24×C10311yescharacteristic
585Q16—22no—
586Q16—41no—
587SD16—22no—
588SD16—22no—
589SD16—42no—
590SD16—42no—
591SD16—41no—
592SD16—41no—
593SD16—42no—
594D8—22no—
595D8—42no—
596D8—42no—
597D8—41no—
598D8—42no—
599M16—21no—
600M16—21no—
601M16—21no—
602M16—21no—
603M16—21no—
604M16—21no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—42no—
612M16—42no—
613M16—42no—
614M16C2×D4×C10312yes—
615M16C2×D4×C10312yes—
616M16C2×D4×C10312yes—
617M16C2×D4×C10312yes—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—42no—
627C2×C8—42no—
628C2×C8—42no—
629C4⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—42no—
632C42—21no—
633C42—21no—
634C42C2×D4×C10311yescharacteristic
635C42C2×D4×C10311yescharacteristic
636C23—21no—
637C23—22no—
638C23—21no—
639C23—22no—
640C23—21no—
641C23—22no—
642C23—44no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—82no—
647C23—82no—
648C23—162no—
649C23C2×#41×C10311yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—21no—
655Q8#121×C10312yes—
656D4—22no—
657D4—22no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—21no—
663D4—44no—
664D4—44no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—84no—
678D4—84no—
679D4—162no—
680D4#121×C10312yes—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4C22×D4×C10311yescharacteristic
696C2×C4C22×D4×C10311yescharacteristic
697C2×C4C22×D4×C10311yescharacteristic
698C2×C4C2×#41×C10311yescharacteristic
699C2×C4H(5,𝔽2)×C10311yescharacteristic
700C2×C4H(5,𝔽2)×C10311yescharacteristic
701C8—22no—
702C8—22no—
703C8—22no—
704C8—22no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—81no—
715C22—82no—
716C22—81no—
717C22—82no—
718C22—82no—
719C22—81no—
720C22—82no—
721C22—81no—
722C22—161no—
723C22—161no—
724C22—164no—
725C22#525×C10311yescharacteristic
726C22#546×C10311yescharacteristic
727C22#546×C10311yescharacteristic
728C4—22no—
729C4—22no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4C2×#121×C10311yescharacteristic
735C4#538×C10311yescharacteristic
736C4D42×C10311yescharacteristic
737C4D42×C10311yescharacteristic
738C2—21no—
739C2—21no—
740C2—21no—
741C2—42no—
742C2—82no—
743C2—81no—
744C2—81no—
745C2—161no—
746C2C103×#242411yescharacteristic
subgroupG/H
center, socleC2×C103#2424
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3068C2semidirect
2. C103×#3068C2semidirect
3. C103×#3019C2semidirect
4. C2×#453×C103C2semidirect
5. C103×#2956C2semidirect
6. C103×#2888C2semidirect
7. C103×#2069C2semidirect
8. C103×#2050C2semidirect
9. C103×#2048C2semidirect
10. C103×#2002C2semidirect
11. C103×#1965C2semidirect
12. C103×#1932C2semidirect
13. C103×#1914C2semidirect
14. C103×#1903C2semidirect
15. C103×#1861C2semidirect
21. C2×AGL(1,ℤ/8)×C103C22semidirect
24. #568×C103C22semidirect
37. #430×C103C22semidirect
38. #430×C103C22semidirect
39. #430×C103C22semidirect
40. #423×C103C22semidirect
45. C2×#104×C103C22semidirect
46. #418×C103C22semidirect
50. #413×C103C22semidirect
56. C2×#100×C103C22semidirect
57. C2×#100×C103C22semidirect
58. C4×M16×C103C22semidirect
59. #344×C103C22semidirect
60. #344×C103C22semidirect
61. #339×C103C22semidirect
62. #338×C103C22semidirect
81. #137×C103D4semidirect
91. AGL(1,ℤ/8)×C103D4semidirect
136. #104×C103D4semidirect
137. #104×C103D4semidirect
141. #101×C103D4semidirect
150. #100×C103D4semidirect
364. #25196C103direct (N × H)
374. #3068C2×C103semidirect
375. #3068C2×C103semidirect
376. #3019C2×C103semidirect
377. C2×#453C2×C103semidirect
378. #2956C2×C103semidirect
379. #2888C2×C103semidirect
380. #2069C2×C103semidirect
381. #2050C2×C103semidirect
382. #2048C2×C103semidirect
383. #2002C2×C103semidirect
384. #1965C2×C103semidirect
385. #1932C2×C103semidirect
386. #1914C2×C103semidirect
387. #1903C2×C103semidirect
388. #1861C2×C103semidirect
389. C103#25196direct (N × H)
395. C2×AGL(1,ℤ/8)C22×C103semidirect
398. #568C22×C103semidirect
411. #430C22×C103semidirect
412. #430C22×C103semidirect
413. #430C22×C103semidirect
414. #423C22×C103semidirect
419. C2×#104C22×C103semidirect
420. #418C22×C103semidirect
424. #413C22×C103semidirect
430. C2×#100C22×C103semidirect
431. C2×#100C22×C103semidirect
432. C4×M16C22×C103semidirect
433. #344C22×C103semidirect
434. #344C22×C103semidirect
435. #339C22×C103semidirect
436. #338C22×C103semidirect
455. #137D4×C103semidirect
465. AGL(1,ℤ/8)D4×C103semidirect
510. #104D4×C103semidirect
511. #104D4×C103semidirect
515. #101D4×C103semidirect
524. #100D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#30682
C103×#30192
C2×#453×C1032
C103×#29562
C103×#28882
C103×#20692
C103×#20502
C103×#20482
C103×#20022
C103×#19652
C103×#19322
C103×#19142
C103×#19032
C103×#18612
#25196103