Finite Group Databasebeta

← C103×#33553 #39938828

Subgroups — C103×#33553 #39938828

Order 26368.

1252 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3537C211yesmaximal, characteristic, complemented
2C103×#3027C211yesmaximal, characteristic, complemented
3C103×#3025C211yesmaximal, characteristic, complemented
4C103×#3021C211yesmaximal, characteristic, complemented
5C103×#2200C214yesmaximal, complemented
6C103×#2196C214yesmaximal, complemented
7C103×#2128C211yesmaximal, characteristic, complemented
8C103×#2122C211yesmaximal, characteristic, complemented
9C103×#2120C211yesmaximal, characteristic, complemented
10#585×C103C2211yescharacteristic, complemented
11C2×AGL(1,ℤ/8)×C103—21no—
12#560×C103—21no—
13#560×C103C2212yescomplemented
14#553×C103—21no—
15#553×C103—21no—
16D42×C103—21no—
17D42×C103—21no—
18D42×C103—21no—
19D42×C103C2212yescomplemented
20#540×C103—21no—
21#538×C103—22no—
22#535×C103—21no—
23#535×C103C2211yescharacteristic
24#535×C103C2211yescharacteristic
25#534×C103—22no—
26#525×C103—21no—
27#525×C103C2211yescharacteristic
28C2×#121×C103—21no—
29#458×C103—21no—
30#458×C103C2212yescomplemented
31B(4,𝔽2)×C103—21no—
32B(4,𝔽2)×C103—22no—
33B(4,𝔽2)×C103C2212yescomplemented
34B(4,𝔽2)×C103C2214yescomplemented
35#454×C103—22no—
36#453×C103C2214yescomplemented
37#421×C103—21no—
38#413×C103C2211yescharacteristic, complemented
39#410×C103—21no—
40#410×C103—21no—
41#410×C103C2211yescharacteristic, complemented
42#410×C103C2211yescharacteristic, complemented
43#353×C103C2214yescomplemented
44#352×C103C2212yescomplemented
45AΣL(1,𝔽16)×C103C2212yescomplemented
46AΣL(1,𝔽16)×C103C2214yescomplemented
472−1+4×C103—21no—
482−1+4×C103—41no—
49H(5,𝔽2)×C103—21no—
50H(5,𝔽2)×C103—21no—
51H(5,𝔽2)×C103—41no—
52H(5,𝔽2)×C103C2312yes—
53C2×#41×C103—21no—
54C2×#41×C103—21no—
55C2×#41×C103—21no—
56C2×#41×C103—42no—
57C2×#41×C103C2311yescharacteristic
58C22×D4×C103—21no—
59C22×D4×C103—22no—
60C22×D4×C103—22no—
61C22×D4×C103—22no—
62C22×D4×C103D411yescharacteristic, complemented
63C22×D4×C103D411yescharacteristic, complemented
64C23×C4×C103D411yescharacteristic, complemented
65AGL(1,ℤ/8)×C103—24no—
66AGL(1,ℤ/8)×C103—42no—
67C2×SD16×C103—41no—
68C2×D8×C103—41no—
69C2×M16×C103—21no—
70#127×C103—21no—
71#127×C103—21no—
72#127×C103—41no—
73#127×C103C2312yes—
74#126×C103—22no—
75#126×C103—22no—
76#125×C103—21no—
77#124×C103—21no—
78#124×C103—41no—
79#124×C103D412yescomplemented
80#123×C103—22no—
81#123×C103—22no—
82#123×C103—22no—
83#123×C103—22no—
84#123×C103—22no—
85#123×C103D411yescharacteristic, complemented
86#123×C103C2311yescharacteristic
87C22⋊Q8×C103—21no—
88C22⋊Q8×C103—41no—
89#121×C103—22no—
90#121×C103—21no—
91#121×C103—21no—
92#121×C103—22no—
93#121×C103—22no—
94#121×C103—21no—
95#121×C103—22no—
96#121×C103—21no—
97#121×C103—21no—
98#121×C103—22no—
99#121×C103—21no—
100#121×C103—21no—
101#121×C103—22no—
102#121×C103—22no—
103#121×C103—22no—
104#121×C103—42no—
105#121×C103—41no—
106#120×C103—22no—
107#120×C103—22no—
108#120×C103—22no—
109#120×C103—21no—
110#120×C103—21no—
111#120×C103—22no—
112#120×C103—22no—
113#120×C103—24no—
114#120×C103D411yescharacteristic, complemented
115#120×C103D412yescomplemented
116#120×C103C2311yescharacteristic
117#120×C103C2312yes—
118C4×D4×C103—22no—
119C4×D4×C103—21no—
120C4×D4×C103—21no—
121C4×D4×C103—21no—
122C4×D4×C103—21no—
123C4×D4×C103—22no—
124C4×D4×C103—42no—
125#117×C103—21no—
126#117×C103—21no—
127#117×C103D411yescharacteristic, complemented
128#117×C103D411yescharacteristic, complemented
129#117×C103D411yescharacteristic, complemented
130C2×C4⋊C4×C103—21no—
131C2×C22⋊C4×C103—22no—
132#104×C103—24no—
133#101×C103—21no—
134#100×C103C2312yes—
135#99×C103—21no—
136#99×C103—21no—
137#99×C103—24no—
138#99×C103—22no—
139#99×C103—22no—
140#99×C103C2312yes—
141#99×C103C2312yes—
142C24×C103—22no—
143C24×C103—21no—
144C24×C103C2×D411yescharacteristic
145C24×C103C2×D412yes—
146#41×C103—22no—
147#41×C103—22no—
148#41×C103—41no—
149#41×C103—41no—
150#41×C103—42no—
151#41×C103—41no—
152#41×C103—41no—
153#41×C103—41no—
154#41×C103—41no—
155#41×C103—41no—
156#41×C103—42no—
157#41×C103—42no—
158#41×C103—42no—
159#41×C103—41no—
160#41×C103—41no—
161#41×C103—41no—
162C2×Q8×C103—21no—
163C2×Q8×C103—21no—
164C2×Q8×C103—21no—
165C2×Q8×C103—42no—
166C2×Q8×C103C2×D411yescharacteristic
167C2×D4×C103—21no—
168C2×D4×C103—22no—
169C2×D4×C103—22no—
170C2×D4×C103—21no—
171C2×D4×C103—21no—
172C2×D4×C103—21no—
173C2×D4×C103—22no—
174C2×D4×C103—22no—
175C2×D4×C103—21no—
176C2×D4×C103—22no—
177C2×D4×C103—22no—
178C2×D4×C103—22no—
179C2×D4×C103—22no—
180C2×D4×C103—22no—
181C2×D4×C103—22no—
182C2×D4×C103—22no—
183C2×D4×C103—21no—
184C2×D4×C103—21no—
185C2×D4×C103—21no—
186C2×D4×C103—41no—
187C2×D4×C103—41no—
188C2×D4×C103—41no—
189C2×D4×C103—41no—
190C2×D4×C103—42no—
191C2×D4×C103—42no—
192C2×D4×C103—42no—
193C2×D4×C103—41no—
194C2×D4×C103—42no—
195C2×D4×C103—44no—
196C2×D4×C103—81no—
197C2×D4×C103—81no—
198C2×D4×C103—84no—
199C2×D4×C103—84no—
200C2×D4×C103—84no—
201C2×D4×C103C2×D411yescharacteristic
202C2×D4×C103C2×D411yescharacteristic
203C2×D4×C103C2×D412yes—
204C2×D4×C103C2411yescharacteristic
205C22×C4×C103—22no—
206C22×C4×C103—22no—
207C22×C4×C103—22no—
208C22×C4×C103—22no—
209C22×C4×C103—22no—
210C22×C4×C103—21no—
211C22×C4×C103—21no—
212C22×C4×C103—41no—
213C22×C4×C103—41no—
214C22×C4×C103—41no—
215C22×C4×C103C2×D411yescharacteristic
216C22×C4×C103C2×D411yescharacteristic
217C22×C4×C103C2×D411yescharacteristic
218C22×C4×C103C2×D411yescharacteristic
219SD16×C103—44no—
220D8×C103—44no—
221M16×C103—22no—
222M16×C103—41no—
223C2×C8×C103—41no—
224C4⋊C4×C103—22no—
225C4⋊C4×C103—22no—
226C4⋊C4×C103—22no—
227C4⋊C4×C103—21no—
228C4⋊C4×C103—21no—
229C4⋊C4×C103—21no—
230C4⋊C4×C103—21no—
231C4⋊C4×C103—21no—
232C4⋊C4×C103—41no—
233C4⋊C4×C103—41no—
234C4⋊C4×C103—42no—
235C22⋊C4×C103—22no—
236C22⋊C4×C103—22no—
237C22⋊C4×C103—22no—
238C22⋊C4×C103—22no—
239C22⋊C4×C103—21no—
240C22⋊C4×C103—21no—
241C22⋊C4×C103—21no—
242C22⋊C4×C103—22no—
243C22⋊C4×C103—22no—
244C22⋊C4×C103—21no—
245C22⋊C4×C103—22no—
246C22⋊C4×C103—21no—
247C22⋊C4×C103—22no—
248C22⋊C4×C103—22no—
249C22⋊C4×C103—22no—
250C22⋊C4×C103—42no—
251C22⋊C4×C103—44no—
252C22⋊C4×C103—42no—
253C22⋊C4×C103C2×D412yes—
254C22⋊C4×C103C2×D411yescharacteristic
255C22⋊C4×C103C2×D411yescharacteristic
256C42×C103—21no—
257C42×C103—21no—
258C42×C103—41no—
259C42×C103—41no—
260C42×C103C2×D412yes—
261C23×C103—21no—
262C23×C103—22no—
263C23×C103—22no—
264C23×C103—22no—
265C23×C103—22no—
266C23×C103—41no—
267C23×C103—42no—
268C23×C103—41no—
269C23×C103—44no—
270C23×C103—42no—
271C23×C103—81no—
272C23×C103—82no—
273C23×C103—82no—
274C23×C103—82no—
275C23×C103—82no—
276C23×C103#12011yescharacteristic
277C23×C103C22×D411yescharacteristic
278C23×C103C22×D411yescharacteristic
279Q8×C103—22no—
280Q8×C103—41no—
281Q8×C103—41no—
282Q8×C103—41no—
283Q8×C103—41no—
284D4×C103—22no—
285D4×C103—41no—
286D4×C103—41no—
287D4×C103—41no—
288D4×C103—42no—
289D4×C103—41no—
290D4×C103—41no—
291D4×C103—42no—
292D4×C103—42no—
293D4×C103—42no—
294D4×C103—42no—
295D4×C103—44no—
296D4×C103—44no—
297D4×C103—42no—
298D4×C103—42no—
299D4×C103—41no—
300D4×C103—41no—
301D4×C103—41no—
302D4×C103—41no—
303D4×C103—41no—
304D4×C103—81no—
305D4×C103—82no—
306D4×C103—82no—
307D4×C103—82no—
308D4×C103—82no—
309D4×C103—82no—
310D4×C103—82no—
311D4×C103—82no—
312D4×C103—84no—
313D4×C103—164no—
314C2×C4×C103—21no—
315C2×C4×C103—21no—
316C2×C4×C103—21no—
317C2×C4×C103—21no—
318C2×C4×C103—21no—
319C2×C4×C103—21no—
320C2×C4×C103—22no—
321C2×C4×C103—22no—
322C2×C4×C103—22no—
323C2×C4×C103—21no—
324C2×C4×C103—21no—
325C2×C4×C103—22no—
326C2×C4×C103—21no—
327C2×C4×C103—42no—
328C2×C4×C103—42no—
329C2×C4×C103—42no—
330C2×C4×C103—41no—
331C2×C4×C103—42no—
332C2×C4×C103—41no—
333C2×C4×C103—41no—
334C2×C4×C103—41no—
335C2×C4×C103—42no—
336C2×C4×C103—42no—
337C2×C4×C103—81no—
338C2×C4×C103—82no—
339C2×C4×C103—82no—
340C2×C4×C103—82no—
341C2×C4×C103#12011yescharacteristic
342C2×C4×C103#12011yescharacteristic
343C2×C4×C103#12011yescharacteristic
344C2×C4×C103C22×D411yescharacteristic
345C8×C103—42no—
346C22×C103—22no—
347C22×C103—21no—
348C22×C103—21no—
349C22×C103—21no—
350C22×C103—41no—
351C22×C103—41no—
352C22×C103—41no—
353C22×C103—41no—
354C22×C103—42no—
355C22×C103—42no—
356C22×C103—42no—
357C22×C103—42no—
358C22×C103—42no—
359C22×C103—41no—
360C22×C103—42no—
361C22×C103—42no—
362C22×C103—42no—
363C22×C103—81no—
364C22×C103—82no—
365C22×C103—82no—
366C22×C103—84no—
367C22×C103—161no—
368C22×C103—164no—
369C22×C103—162no—
370C22×C103C2×#12011yescharacteristic
371C4×C103—21no—
372C4×C103—21no—
373C4×C103—21no—
374C4×C103—42no—
375C4×C103—41no—
376C4×C103—41no—
377C4×C103—42no—
378C4×C103—42no—
379C4×C103—41no—
380C4×C103—82no—
381C4×C103—82no—
382C4×C103B(4,𝔽2)11yescharacteristic
383C4×C103B(4,𝔽2)11yescharacteristic
384#33553C10311yesmaximal, characteristic, direct product factor, Sylow
385C2×C103—21no—
386C2×C103—41no—
387C2×C103—41no—
388C2×C103—42no—
389C2×C103—41no—
390C2×C103—82no—
391C2×C103—82no—
392C2×C103—82no—
393C2×C103C2×B(4,𝔽2)11yescharacteristic
394#3537C2×C10311yescharacteristic, complemented
395#3027C2×C10311yescharacteristic, complemented
396#3025C2×C10311yescharacteristic, complemented
397#3021C2×C10311yescharacteristic, complemented
398#2200C2×C10314yescomplemented
399#2196C2×C10314yescomplemented
400#2128C2×C10311yescharacteristic, complemented
401#2122C2×C10311yescharacteristic, complemented
402#2120C2×C10311yescharacteristic, complemented
403C103#3355311yescharacteristic, direct product factor, Sylow
404#585C22×C10311yescharacteristic, complemented
405C2×AGL(1,ℤ/8)—21no—
406#560—21no—
407#560C22×C10312yescomplemented
408#553—21no—
409#553—21no—
410D42—21no—
411D42—21no—
412D42—21no—
413D42C22×C10312yescomplemented
414#540—21no—
415#538—22no—
416#535—21no—
417#535C22×C10311yescharacteristic
418#535C22×C10311yescharacteristic
419#534—22no—
420#525—21no—
421#525C22×C10311yescharacteristic
422C2×#121—21no—
423#458—21no—
424#458C22×C10312yescomplemented
425B(4,𝔽2)—21no—
426B(4,𝔽2)—22no—
427B(4,𝔽2)C22×C10312yescomplemented
428B(4,𝔽2)C22×C10314yescomplemented
429#454—22no—
430#453C22×C10314yescomplemented
431#421—21no—
432#413C22×C10311yescharacteristic, complemented
433#410—21no—
434#410—21no—
435#410C22×C10311yescharacteristic, complemented
436#410C22×C10311yescharacteristic, complemented
437#353C22×C10314yescomplemented
438#352C22×C10312yescomplemented
439AΣL(1,𝔽16)C22×C10312yescomplemented
440AΣL(1,𝔽16)C22×C10314yescomplemented
4412−1+4—21no—
4422−1+4—41no—
443H(5,𝔽2)—21no—
444H(5,𝔽2)—21no—
445H(5,𝔽2)—41no—
446H(5,𝔽2)C23×C10312yes—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—42no—
451C2×#41C23×C10311yescharacteristic
452C22×D4—21no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4D4×C10311yescharacteristic, complemented
457C22×D4D4×C10311yescharacteristic, complemented
458C23×C4D4×C10311yescharacteristic, complemented
459AGL(1,ℤ/8)—24no—
460AGL(1,ℤ/8)—42no—
461C2×SD16—41no—
462C2×D8—41no—
463C2×M16—21no—
464#127—21no—
465#127—21no—
466#127—41no—
467#127C23×C10312yes—
468#126—22no—
469#126—22no—
470#125—21no—
471#124—21no—
472#124—41no—
473#124D4×C10312yescomplemented
474#123—22no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123—22no—
479#123D4×C10311yescharacteristic, complemented
480#123C23×C10311yescharacteristic
481C22⋊Q8—21no—
482C22⋊Q8—41no—
483#121—22no—
484#121—21no—
485#121—21no—
486#121—22no—
487#121—22no—
488#121—21no—
489#121—22no—
490#121—21no—
491#121—21no—
492#121—22no—
493#121—21no—
494#121—21no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—42no—
499#121—41no—
500#120—22no—
501#120—22no—
502#120—22no—
503#120—21no—
504#120—21no—
505#120—22no—
506#120—22no—
507#120—24no—
508#120D4×C10311yescharacteristic, complemented
509#120D4×C10312yescomplemented
510#120C23×C10311yescharacteristic
511#120C23×C10312yes—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—22no—
518C4×D4—42no—
519#117—21no—
520#117—21no—
521#117D4×C10311yescharacteristic, complemented
522#117D4×C10311yescharacteristic, complemented
523#117D4×C10311yescharacteristic, complemented
524C2×C4⋊C4—21no—
525C2×C22⋊C4—22no—
526#104—24no—
527#101—21no—
528#100C23×C10312yes—
529#99—21no—
530#99—21no—
531#99—24no—
532#99—22no—
533#99—22no—
534#99C23×C10312yes—
535#99C23×C10312yes—
536C24—22no—
537C24—21no—
538C24C2×D4×C10311yescharacteristic
539C24C2×D4×C10312yes—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—42no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—41no—
554#41—41no—
555#41—41no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—42no—
560C2×Q8C2×D4×C10311yescharacteristic
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—44no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4—84no—
594C2×D4—84no—
595C2×D4C2×D4×C10311yescharacteristic
596C2×D4C2×D4×C10311yescharacteristic
597C2×D4C2×D4×C10312yes—
598C2×D4C24×C10311yescharacteristic
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4C2×D4×C10311yescharacteristic
610C22×C4C2×D4×C10311yescharacteristic
611C22×C4C2×D4×C10311yescharacteristic
612C22×C4C2×D4×C10311yescharacteristic
613SD16—44no—
614D8—44no—
615M16—22no—
616M16—41no—
617C2×C8—41no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—42no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—42no—
645C22⋊C4—44no—
646C22⋊C4—42no—
647C22⋊C4C2×D4×C10312yes—
648C22⋊C4C2×D4×C10311yescharacteristic
649C22⋊C4C2×D4×C10311yescharacteristic
650C42—21no—
651C42—21no—
652C42—41no—
653C42—41no—
654C42C2×D4×C10312yes—
655C23—21no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—44no—
664C23—42no—
665C23—81no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23#120×C10311yescharacteristic
671C23C22×D4×C10311yescharacteristic
672C23C22×D4×C10311yescharacteristic
673Q8—22no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—42no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—82no—
705D4—82no—
706D4—84no—
707D4—164no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4#120×C10311yescharacteristic
736C2×C4#120×C10311yescharacteristic
737C2×C4#120×C10311yescharacteristic
738C2×C4C22×D4×C10311yescharacteristic
739C8—42no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—82no—
759C22—82no—
760C22—84no—
761C22—164no—
762C22—161no—
763C22—162no—
764C22C2×#120×C10311yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—82no—
775C4—82no—
776C4B(4,𝔽2)×C10311yescharacteristic
777C4B(4,𝔽2)×C10311yescharacteristic
778C2—21no—
779C2—41no—
780C2—41no—
781C2—42no—
782C2—41no—
783C2—82no—
784C2—82no—
785C2—82no—
786C2C2×B(4,𝔽2)×C10311yescharacteristic
subgroupG/H
center, socleC2×C103C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C103
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C2×C4×C103 ◁ C2×#41×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3537C2semidirect
2. C103×#3027C2semidirect
3. C103×#3025C2semidirect
4. C103×#3021C2semidirect
5. C103×#2200C2semidirect
6. C103×#2196C2semidirect
7. C103×#2128C2semidirect
8. C103×#2122C2semidirect
9. C103×#2120C2semidirect
10. #585×C103C22semidirect
13. #560×C103C22semidirect
19. D42×C103C22semidirect
30. #458×C103C22semidirect
33. B(4,𝔽2)×C103C22semidirect
34. B(4,𝔽2)×C103C22semidirect
36. #453×C103C22semidirect
38. #413×C103C22semidirect
41. #410×C103C22semidirect
42. #410×C103C22semidirect
43. #353×C103C22semidirect
44. #352×C103C22semidirect
45. AΣL(1,𝔽16)×C103C22semidirect
46. AΣL(1,𝔽16)×C103C22semidirect
62. C22×D4×C103D4semidirect
63. C22×D4×C103D4semidirect
64. C23×C4×C103D4semidirect
79. #124×C103D4semidirect
85. #123×C103D4semidirect
114. #120×C103D4semidirect
115. #120×C103D4semidirect
127. #117×C103D4semidirect
128. #117×C103D4semidirect
129. #117×C103D4semidirect
384. #33553C103direct (N × H)
394. #3537C2×C103semidirect
395. #3027C2×C103semidirect
396. #3025C2×C103semidirect
397. #3021C2×C103semidirect
398. #2200C2×C103semidirect
399. #2196C2×C103semidirect
400. #2128C2×C103semidirect
401. #2122C2×C103semidirect
402. #2120C2×C103semidirect
403. C103#33553direct (N × H)
404. #585C22×C103semidirect
407. #560C22×C103semidirect
413. D42C22×C103semidirect
424. #458C22×C103semidirect
427. B(4,𝔽2)C22×C103semidirect
428. B(4,𝔽2)C22×C103semidirect
430. #453C22×C103semidirect
432. #413C22×C103semidirect
435. #410C22×C103semidirect
436. #410C22×C103semidirect
437. #353C22×C103semidirect
438. #352C22×C103semidirect
439. AΣL(1,𝔽16)C22×C103semidirect
440. AΣL(1,𝔽16)C22×C103semidirect
456. C22×D4D4×C103semidirect
457. C22×D4D4×C103semidirect
458. C23×C4D4×C103semidirect
473. #124D4×C103semidirect
479. #123D4×C103semidirect
508. #120D4×C103semidirect
509. #120D4×C103semidirect
521. #117D4×C103semidirect
522. #117D4×C103semidirect
523. #117D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35372
C103×#30272
C103×#30252
C103×#30212
C103×#22002
C103×#21962
C103×#21282
C103×#21222
C103×#21202
#33553103