Finite Group Databasebeta

← C103×#33551 #39938826

Subgroups — C103×#33551 #39938826

Order 26368.

1326 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3532C211yesmaximal, characteristic, complemented
2C103×#3026C211yesmaximal, characteristic, complemented
3C2×B(4,𝔽2)×C103C211yesmaximal, characteristic, complemented
4C103×#3019C211yesmaximal, characteristic, complemented
5C103×#2200C212yesmaximal, complemented
6C103×#2199C212yesmaximal, complemented
7C103×#2197C212yesmaximal, complemented
8C103×#2196C212yesmaximal, complemented
9C103×#2127C211yesmaximal, characteristic, complemented
10C103×#2121C211yesmaximal, characteristic, complemented
11C2×AΣL(1,𝔽16)×C103C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C103C2211yescharacteristic, complemented
13#575×C103—21no—
14H(3,𝔽4)×C103C2211yescharacteristic, complemented
15#560×C103—21no—
16#560×C103C2211yescharacteristic, complemented
17#551×C103—21no—
18#551×C103C2211yescharacteristic, complemented
19#546×C103—21no—
20#546×C103—21no—
21#546×C103—21no—
22D42×C103—21no—
23D42×C103C2211yescharacteristic, complemented
24#538×C103—21no—
25#538×C103—21no—
26#538×C103—21no—
27#535×C103—21no—
28#535×C103C2211yescharacteristic
29#534×C103—21no—
30#534×C103—21no—
31#534×C103C2211yescharacteristic
32C2×#120×C103—21no—
33C2×#120×C103—21no—
34C2×#120×C103C2211yescharacteristic
35#458×C103—21no—
36#458×C103C2212yescomplemented
37B(4,𝔽2)×C103—21no—
38B(4,𝔽2)×C103—21no—
39B(4,𝔽2)×C103—21no—
40B(4,𝔽2)×C103C2212yes—
41B(4,𝔽2)×C103C2212yescomplemented
42B(4,𝔽2)×C103C2212yescomplemented
43#455×C103—21no—
44#455×C103C2212yescomplemented
45#453×C103—21no—
46#453×C103C2212yescomplemented
47#421×C103—21no—
48C2×#100×C103C2211yescharacteristic, complemented
49C2×#99×C103—21no—
50C2×#99×C103—21no—
51C2×#99×C103C2211yescharacteristic, complemented
52C2×#99×C103C2211yescharacteristic, complemented
53#354×C103C2212yescomplemented
54#353×C103C2212yescomplemented
55#352×C103C2212yescomplemented
56AΣL(1,𝔽16)×C103C2212yescomplemented
57AΣL(1,𝔽16)×C103C2212yescomplemented
58AΣL(1,𝔽16)×C103C2212yescomplemented
59C25×C103D411yescharacteristic, complemented
60H(5,𝔽2)×C103—21no—
61H(5,𝔽2)×C103—21no—
62H(5,𝔽2)×C103—21no—
63H(5,𝔽2)×C103—42no—
64H(5,𝔽2)×C103C2312yes—
65C2×#41×C103—21no—
66C2×#41×C103—21no—
67C2×#41×C103—41no—
68C2×#41×C103D411yescharacteristic, complemented
69C22×D4×C103—21no—
70C22×D4×C103—21no—
71C22×D4×C103—21no—
72C22×D4×C103—21no—
73C22×D4×C103—21no—
74C22×D4×C103—21no—
75C22×D4×C103—21no—
76C22×D4×C103—41no—
77C22×D4×C103—41no—
78C22×D4×C103D411yescharacteristic, complemented
79C22×D4×C103C2311yescharacteristic
80#137×C103—22no—
81#137×C103—41no—
82AGL(1,ℤ/8)×C103—22no—
83AGL(1,ℤ/8)×C103—41no—
84#135×C103—42no—
85C2×M16×C103—21no—
86#127×C103—21no—
87#127×C103D411yescharacteristic, complemented
88#127×C103C2311yescharacteristic
89#126×C103—21no—
90#126×C103—21no—
91#126×C103—21no—
92#126×C103—21no—
93#124×C103—21no—
94#124×C103—21no—
95#124×C103—21no—
96#124×C103—21no—
97#124×C103—21no—
98#124×C103D411yescharacteristic, complemented
99#124×C103C2311yescharacteristic
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—
108#123×C103—22no—
109#123×C103—41no—
110#123×C103D411yescharacteristic, complemented
111#123×C103C2311yescharacteristic
112C22⋊Q8×C103—21no—
113C22⋊Q8×C103—21no—
114C22⋊Q8×C103—21no—
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×C103—42no—
131#120×C103—21no—
132#120×C103—21no—
133#120×C103—21no—
134#120×C103—21no—
135#120×C103—21no—
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—21no—
145#120×C103—22no—
146#120×C103—22no—
147#120×C103—22no—
148#120×C103—42no—
149#120×C103—41no—
150#120×C103D411yescharacteristic, complemented
151#120×C103D411yescharacteristic, complemented
152#120×C103D411yescharacteristic, complemented
153#120×C103C2311yescharacteristic
154#120×C103C2311yescharacteristic
155#120×C103C2311yescharacteristic
156C4×D4×C103—21no—
157C4×D4×C103—21no—
158C4×D4×C103—21no—
159C4×D4×C103—21no—
160C4×D4×C103—21no—
161C4×D4×C103—21no—
162#117×C103—21no—
163#117×C103D411yescharacteristic, complemented
164C2×C22⋊C4×C103—21no—
165C2×C22⋊C4×C103—21no—
166C2×C22⋊C4×C103—21no—
167C2×C22⋊C4×C103—21no—
168C2×C22⋊C4×C103—21no—
169C2×C22⋊C4×C103—21no—
170C2×C22⋊C4×C103—21no—
171C2×C22⋊C4×C103—41no—
172C2×C22⋊C4×C103D411yescharacteristic, complemented
173C2×C22⋊C4×C103D411yescharacteristic, complemented
174#104×C103—22no—
175#104×C103—22no—
176#100×C103—21no—
177#100×C103C2312yes—
178#99×C103—21no—
179#99×C103—21no—
180#99×C103—22no—
181#99×C103—22no—
182#99×C103—22no—
183#99×C103—22no—
184#99×C103C2312yes—
185#99×C103C2312yes—
186C24×C103—21no—
187C24×C103—21no—
188C24×C103—21no—
189C24×C103—21no—
190C24×C103—21no—
191C24×C103—41no—
192C24×C103—41no—
193C24×C103—82no—
194C24×C103C2×D411yescharacteristic
195C24×C103C2×D411yescharacteristic
196C24×C103C2×D411yescharacteristic
197C24×C103C2×D411yescharacteristic
198C24×C103C2×D411yescharacteristic, complemented
199#41×C103—22no—
200#41×C103—22no—
201#41×C103—42no—
202#41×C103—41no—
203#41×C103—42no—
204#41×C103—42no—
205#41×C103—41no—
206#41×C103—41no—
207#41×C103—42no—
208#41×C103—41no—
209#41×C103—82no—
210C2×Q8×C103—21no—
211C2×Q8×C103—21no—
212C2×Q8×C103C2×D411yescharacteristic, complemented
213C2×D4×C103—21no—
214C2×D4×C103—21no—
215C2×D4×C103—21no—
216C2×D4×C103—22no—
217C2×D4×C103—22no—
218C2×D4×C103—21no—
219C2×D4×C103—21no—
220C2×D4×C103—21no—
221C2×D4×C103—22no—
222C2×D4×C103—22no—
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—21no—
235C2×D4×C103—21no—
236C2×D4×C103—21no—
237C2×D4×C103—21no—
238C2×D4×C103—41no—
239C2×D4×C103—41no—
240C2×D4×C103—42no—
241C2×D4×C103—42no—
242C2×D4×C103—41no—
243C2×D4×C103—41no—
244C2×D4×C103—41no—
245C2×D4×C103—41no—
246C2×D4×C103—42no—
247C2×D4×C103—42no—
248C2×D4×C103—41no—
249C2×D4×C103—41no—
250C2×D4×C103—41no—
251C2×D4×C103—41no—
252C2×D4×C103—41no—
253C2×D4×C103—42no—
254C2×D4×C103—42no—
255C2×D4×C103—42no—
256C2×D4×C103—82no—
257C2×D4×C103—82no—
258C2×D4×C103—82no—
259C2×D4×C103—82no—
260C2×D4×C103—81no—
261C2×D4×C103—81no—
262C2×D4×C103—84no—
263C2×D4×C103C2×D411yescharacteristic
264C2×D4×C103C2×D411yescharacteristic
265C2×D4×C103C2×D411yescharacteristic
266C2×D4×C103C2×D411yescharacteristic, complemented
267C2×D4×C103C2411yescharacteristic
268C22×C4×C103—21no—
269C22×C4×C103—21no—
270C22×C4×C103—21no—
271C22×C4×C103—21no—
272C22×C4×C103—21no—
273C22×C4×C103—21no—
274C22×C4×C103—21no—
275C22×C4×C103—21no—
276C22×C4×C103—21no—
277C22×C4×C103—21no—
278C22×C4×C103—41no—
279C22×C4×C103—41no—
280C22×C4×C103—41no—
281C22×C4×C103C2×D411yescharacteristic
282C22×C4×C103C2×D411yescharacteristic, complemented
283Q16×C103—42no—
284SD16×C103—42no—
285SD16×C103—42no—
286D8×C103—42no—
287M16×C103—22no—
288M16×C103—41no—
289C2×C8×C103—41no—
290C4⋊C4×C103—21no—
291C4⋊C4×C103—21no—
292C4⋊C4×C103—21no—
293C4⋊C4×C103—21no—
294C4⋊C4×C103—21no—
295C4⋊C4×C103—21no—
296C4⋊C4×C103—21no—
297C4⋊C4×C103—21no—
298C4⋊C4×C103—21no—
299C4⋊C4×C103—42no—
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—21no—
317C22⋊C4×C103—21no—
318C22⋊C4×C103—21no—
319C22⋊C4×C103—21no—
320C22⋊C4×C103—21no—
321C22⋊C4×C103—21no—
322C22⋊C4×C103—21no—
323C22⋊C4×C103—21no—
324C22⋊C4×C103—21no—
325C22⋊C4×C103—22no—
326C22⋊C4×C103—22no—
327C22⋊C4×C103—42no—
328C22⋊C4×C103—42no—
329C22⋊C4×C103—42no—
330C22⋊C4×C103—41no—
331C22⋊C4×C103—41no—
332C22⋊C4×C103—42no—
333C22⋊C4×C103C2×D411yescharacteristic
334C22⋊C4×C103C2×D411yescharacteristic
335C22⋊C4×C103C2×D411yescharacteristic, complemented
336C22⋊C4×C103C2×D411yescharacteristic, complemented
337C42×C103—21no—
338C42×C103—21no—
339C42×C103C2×D411yescharacteristic, complemented
340C42×C103C2×D411yescharacteristic, complemented
341C23×C103—21no—
342C23×C103—21no—
343C23×C103—21no—
344C23×C103—21no—
345C23×C103—21no—
346C23×C103—22no—
347C23×C103—22no—
348C23×C103—21no—
349C23×C103—21no—
350C23×C103—21no—
351C23×C103—41no—
352C23×C103—41no—
353C23×C103—42no—
354C23×C103—42no—
355C23×C103—42no—
356C23×C103—41no—
357C23×C103—41no—
358C23×C103—42no—
359C23×C103—41no—
360C23×C103—44no—
361C23×C103—41no—
362C23×C103—41no—
363C23×C103—41no—
364C23×C103—81no—
365C23×C103—81no—
366C23×C103—81no—
367C23×C103—81no—
368C23×C103—81no—
369C23×C103—81no—
370C23×C103—81no—
371C23×C103—81no—
372C23×C103—81no—
373C23×C103—82no—
374C23×C103—82no—
375C23×C103—82no—
376C23×C103—82no—
377C23×C103—161no—
378C23×C103#12011yescharacteristic
379C23×C103#12011yescharacteristic
380C23×C103#12011yescharacteristic
381C23×C103C22×D411yescharacteristic
382C23×C103C22×D411yescharacteristic
383Q8×C103—22no—
384Q8×C103—41no—
385Q8×C103—41no—
386Q8×C103—81no—
387D4×C103—22no—
388D4×C103—41no—
389D4×C103—41no—
390D4×C103—41no—
391D4×C103—41no—
392D4×C103—41no—
393D4×C103—41no—
394D4×C103—42no—
395D4×C103—42no—
396D4×C103—42no—
397D4×C103—42no—
398D4×C103—42no—
399D4×C103—42no—
400D4×C103—42no—
401D4×C103—42no—
402D4×C103—42no—
403D4×C103—42no—
404D4×C103—41no—
405D4×C103—41no—
406D4×C103—41no—
407D4×C103—41no—
408D4×C103—81no—
409D4×C103—81no—
410D4×C103—81no—
411D4×C103—81no—
412D4×C103—81no—
413D4×C103—81no—
414D4×C103—81no—
415D4×C103—81no—
416D4×C103—81no—
417D4×C103—81no—
418D4×C103—81no—
419D4×C103—81no—
420D4×C103—81no—
421D4×C103—81no—
422D4×C103—84no—
423D4×C103—84no—
424D4×C103—162no—
425C2×C4×C103—21no—
426C2×C4×C103—21no—
427C2×C4×C103—22no—
428C2×C4×C103—22no—
429C2×C4×C103—21no—
430C2×C4×C103—21no—
431C2×C4×C103—21no—
432C2×C4×C103—21no—
433C2×C4×C103—21no—
434C2×C4×C103—21no—
435C2×C4×C103—21no—
436C2×C4×C103—21no—
437C2×C4×C103—42no—
438C2×C4×C103—42no—
439C2×C4×C103—41no—
440C2×C4×C103—41no—
441C2×C4×C103—42no—
442C2×C4×C103—41no—
443C2×C4×C103—41no—
444C2×C4×C103—42no—
445C2×C4×C103—42no—
446C2×C4×C103—81no—
447C2×C4×C103—81no—
448C2×C4×C103—81no—
449C2×C4×C103—81no—
450C2×C4×C103—81no—
451C2×C4×C103—81no—
452C2×C4×C103—81no—
453C2×C4×C103—82no—
454C2×C4×C103—161no—
455C2×C4×C103#12011yescharacteristic
456C2×C4×C103C22×D411yescharacteristic
457C8×C103—42no—
458C22×C103—22no—
459C22×C103—21no—
460C22×C103—21no—
461C22×C103—21no—
462C22×C103—21no—
463C22×C103—41no—
464C22×C103—41no—
465C22×C103—41no—
466C22×C103—41no—
467C22×C103—41no—
468C22×C103—41no—
469C22×C103—42no—
470C22×C103—41no—
471C22×C103—41no—
472C22×C103—41no—
473C22×C103—41no—
474C22×C103—41no—
475C22×C103—41no—
476C22×C103—42no—
477C22×C103—41no—
478C22×C103—42no—
479C22×C103—42no—
480C22×C103—41no—
481C22×C103—41no—
482C22×C103—41no—
483C22×C103—81no—
484C22×C103—81no—
485C22×C103—81no—
486C22×C103—82no—
487C22×C103—82no—
488C22×C103—82no—
489C22×C103—81no—
490C22×C103—84no—
491C22×C103—82no—
492C22×C103—82no—
493C22×C103—82no—
494C22×C103—81no—
495C22×C103—162no—
496C22×C103—161no—
497C22×C103—161no—
498C22×C103B(4,𝔽2)11yescharacteristic
499C22×C103B(4,𝔽2)11yescharacteristic
500C22×C103C2×#12011yescharacteristic
501C4×C103—21no—
502C4×C103—21no—
503C4×C103—41no—
504C4×C103—41no—
505C4×C103—41no—
506C4×C103—41no—
507C4×C103—41no—
508C4×C103—41no—
509C4×C103—42no—
510C4×C103—41no—
511C4×C103—41no—
512C4×C103—82no—
513C4×C103—82no—
514#33551C10311yesmaximal, characteristic, direct product factor, Sylow
515C2×C103—21no—
516C2×C103—21no—
517C2×C103—21no—
518C2×C103—41no—
519C2×C103—41no—
520C2×C103—42no—
521C2×C103—41no—
522C2×C103—41no—
523C2×C103—81no—
524C2×C103—81no—
525C2×C103—81no—
526C2×C103—82no—
527C2×C103C2×B(4,𝔽2)11yescharacteristic
528#3532C2×C10311yescharacteristic, complemented
529#3026C2×C10311yescharacteristic, complemented
530C2×B(4,𝔽2)C2×C10311yescharacteristic, complemented
531#3019C2×C10311yescharacteristic, complemented
532#2200C2×C10312yescomplemented
533#2199C2×C10312yescomplemented
534#2197C2×C10312yescomplemented
535#2196C2×C10312yescomplemented
536#2127C2×C10311yescharacteristic, complemented
537#2121C2×C10311yescharacteristic, complemented
538C2×AΣL(1,𝔽16)C2×C10311yescharacteristic, complemented
539C103#3355111yescharacteristic, direct product factor, Sylow
540C2×H(5,𝔽2)C22×C10311yescharacteristic, complemented
541#575—21no—
542H(3,𝔽4)C22×C10311yescharacteristic, complemented
543#560—21no—
544#560C22×C10311yescharacteristic, complemented
545#551—21no—
546#551C22×C10311yescharacteristic, complemented
547#546—21no—
548#546—21no—
549#546—21no—
550D42—21no—
551D42C22×C10311yescharacteristic, complemented
552#538—21no—
553#538—21no—
554#538—21no—
555#535—21no—
556#535C22×C10311yescharacteristic
557#534—21no—
558#534—21no—
559#534C22×C10311yescharacteristic
560C2×#120—21no—
561C2×#120—21no—
562C2×#120C22×C10311yescharacteristic
563#458—21no—
564#458C22×C10312yescomplemented
565B(4,𝔽2)—21no—
566B(4,𝔽2)—21no—
567B(4,𝔽2)—21no—
568B(4,𝔽2)C22×C10312yes—
569B(4,𝔽2)C22×C10312yescomplemented
570B(4,𝔽2)C22×C10312yescomplemented
571#455—21no—
572#455C22×C10312yescomplemented
573#453—21no—
574#453C22×C10312yescomplemented
575#421—21no—
576C2×#100C22×C10311yescharacteristic, complemented
577C2×#99—21no—
578C2×#99—21no—
579C2×#99C22×C10311yescharacteristic, complemented
580C2×#99C22×C10311yescharacteristic, complemented
581#354C22×C10312yescomplemented
582#353C22×C10312yescomplemented
583#352C22×C10312yescomplemented
584AΣL(1,𝔽16)C22×C10312yescomplemented
585AΣL(1,𝔽16)C22×C10312yescomplemented
586AΣL(1,𝔽16)C22×C10312yescomplemented
587C25D4×C10311yescharacteristic, complemented
588H(5,𝔽2)—21no—
589H(5,𝔽2)—21no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—42no—
592H(5,𝔽2)C23×C10312yes—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—41no—
596C2×#41D4×C10311yescharacteristic, complemented
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—21no—
602C22×D4—21no—
603C22×D4—21no—
604C22×D4—41no—
605C22×D4—41no—
606C22×D4D4×C10311yescharacteristic, complemented
607C22×D4C23×C10311yescharacteristic
608#137—22no—
609#137—41no—
610AGL(1,ℤ/8)—22no—
611AGL(1,ℤ/8)—41no—
612#135—42no—
613C2×M16—21no—
614#127—21no—
615#127D4×C10311yescharacteristic, complemented
616#127C23×C10311yescharacteristic
617#126—21no—
618#126—21no—
619#126—21no—
620#126—21no—
621#124—21no—
622#124—21no—
623#124—21no—
624#124—21no—
625#124—21no—
626#124D4×C10311yescharacteristic, complemented
627#124C23×C10311yescharacteristic
628#123—21no—
629#123—21no—
630#123—21no—
631#123—21no—
632#123—21no—
633#123—21no—
634#123—21no—
635#123—21no—
636#123—22no—
637#123—41no—
638#123D4×C10311yescharacteristic, complemented
639#123C23×C10311yescharacteristic
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121—21no—
648#121—21no—
649#121—21no—
650#121—21no—
651#121—21no—
652#121—21no—
653#121—21no—
654#121—21no—
655#121—21no—
656#121—21no—
657#121—21no—
658#121—42no—
659#120—21no—
660#120—21no—
661#120—21no—
662#120—21no—
663#120—21no—
664#120—21no—
665#120—21no—
666#120—21no—
667#120—21no—
668#120—21no—
669#120—21no—
670#120—21no—
671#120—21no—
672#120—21no—
673#120—22no—
674#120—22no—
675#120—22no—
676#120—42no—
677#120—41no—
678#120D4×C10311yescharacteristic, complemented
679#120D4×C10311yescharacteristic, complemented
680#120D4×C10311yescharacteristic, complemented
681#120C23×C10311yescharacteristic
682#120C23×C10311yescharacteristic
683#120C23×C10311yescharacteristic
684C4×D4—21no—
685C4×D4—21no—
686C4×D4—21no—
687C4×D4—21no—
688C4×D4—21no—
689C4×D4—21no—
690#117—21no—
691#117D4×C10311yescharacteristic, complemented
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4D4×C10311yescharacteristic, complemented
701C2×C22⋊C4D4×C10311yescharacteristic, complemented
702#104—22no—
703#104—22no—
704#100—21no—
705#100C23×C10312yes—
706#99—21no—
707#99—21no—
708#99—22no—
709#99—22no—
710#99—22no—
711#99—22no—
712#99C23×C10312yes—
713#99C23×C10312yes—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—41no—
720C24—41no—
721C24—82no—
722C24C2×D4×C10311yescharacteristic
723C24C2×D4×C10311yescharacteristic
724C24C2×D4×C10311yescharacteristic
725C24C2×D4×C10311yescharacteristic
726C24C2×D4×C10311yescharacteristic, complemented
727#41—22no—
728#41—22no—
729#41—42no—
730#41—41no—
731#41—42no—
732#41—42no—
733#41—41no—
734#41—41no—
735#41—42no—
736#41—41no—
737#41—82no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8C2×D4×C10311yescharacteristic, complemented
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—41no—
771C2×D4—41no—
772C2×D4—41no—
773C2×D4—41no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—41no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—82no—
785C2×D4—82no—
786C2×D4—82no—
787C2×D4—82no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—84no—
791C2×D4C2×D4×C10311yescharacteristic
792C2×D4C2×D4×C10311yescharacteristic
793C2×D4C2×D4×C10311yescharacteristic
794C2×D4C2×D4×C10311yescharacteristic, complemented
795C2×D4C24×C10311yescharacteristic
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4C2×D4×C10311yescharacteristic
810C22×C4C2×D4×C10311yescharacteristic, complemented
811Q16—42no—
812SD16—42no—
813SD16—42no—
814D8—42no—
815M16—22no—
816M16—41no—
817C2×C8—41no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—42no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—41no—
859C22⋊C4—41no—
860C22⋊C4—42no—
861C22⋊C4C2×D4×C10311yescharacteristic
862C22⋊C4C2×D4×C10311yescharacteristic
863C22⋊C4C2×D4×C10311yescharacteristic, complemented
864C22⋊C4C2×D4×C10311yescharacteristic, complemented
865C42—21no—
866C42—21no—
867C42C2×D4×C10311yescharacteristic, complemented
868C42C2×D4×C10311yescharacteristic, complemented
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—22no—
875C23—22no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—41no—
880C23—41no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—41no—
885C23—41no—
886C23—42no—
887C23—41no—
888C23—44no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—81no—
893C23—81no—
894C23—81no—
895C23—81no—
896C23—81no—
897C23—81no—
898C23—81no—
899C23—81no—
900C23—81no—
901C23—82no—
902C23—82no—
903C23—82no—
904C23—82no—
905C23—161no—
906C23#120×C10311yescharacteristic
907C23#120×C10311yescharacteristic
908C23#120×C10311yescharacteristic
909C23C22×D4×C10311yescharacteristic
910C23C22×D4×C10311yescharacteristic
911Q8—22no—
912Q8—41no—
913Q8—41no—
914Q8—81no—
915D4—22no—
916D4—41no—
917D4—41no—
918D4—41no—
919D4—41no—
920D4—41no—
921D4—41no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—42no—
936D4—81no—
937D4—81no—
938D4—81no—
939D4—81no—
940D4—81no—
941D4—81no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—84no—
951D4—84no—
952D4—162no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—81no—
975C2×C4—81no—
976C2×C4—81no—
977C2×C4—81no—
978C2×C4—81no—
979C2×C4—81no—
980C2×C4—81no—
981C2×C4—82no—
982C2×C4—161no—
983C2×C4#120×C10311yescharacteristic
984C2×C4C22×D4×C10311yescharacteristic
985C8—42no—
986C22—22no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—42no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—42no—
1005C22—41no—
1006C22—42no—
1007C22—42no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—81no—
1012C22—81no—
1013C22—81no—
1014C22—82no—
1015C22—82no—
1016C22—82no—
1017C22—81no—
1018C22—84no—
1019C22—82no—
1020C22—82no—
1021C22—82no—
1022C22—81no—
1023C22—162no—
1024C22—161no—
1025C22—161no—
1026C22B(4,𝔽2)×C10311yescharacteristic
1027C22B(4,𝔽2)×C10311yescharacteristic
1028C22C2×#120×C10311yescharacteristic
1029C4—21no—
1030C4—21no—
1031C4—41no—
1032C4—41no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—41no—
1040C4—82no—
1041C4—82no—
1042C2—21no—
1043C2—21no—
1044C2—21no—
1045C2—41no—
1046C2—41no—
1047C2—42no—
1048C2—41no—
1049C2—41no—
1050C2—81no—
1051C2—81no—
1052C2—81no—
1053C2—82no—
1054C2C2×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 ◁ C23×C103 ◁ C22×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3532C2semidirect
2. C103×#3026C2semidirect
3. C2×B(4,𝔽2)×C103C2semidirect
4. C103×#3019C2semidirect
5. C103×#2200C2semidirect
6. C103×#2199C2semidirect
7. C103×#2197C2semidirect
8. C103×#2196C2semidirect
9. C103×#2127C2semidirect
10. C103×#2121C2semidirect
11. C2×AΣL(1,𝔽16)×C103C2semidirect
12. C2×H(5,𝔽2)×C103C22semidirect
14. H(3,𝔽4)×C103C22semidirect
16. #560×C103C22semidirect
18. #551×C103C22semidirect
23. D42×C103C22semidirect
36. #458×C103C22semidirect
41. B(4,𝔽2)×C103C22semidirect
42. B(4,𝔽2)×C103C22semidirect
44. #455×C103C22semidirect
46. #453×C103C22semidirect
48. C2×#100×C103C22semidirect
51. C2×#99×C103C22semidirect
52. C2×#99×C103C22semidirect
53. #354×C103C22semidirect
54. #353×C103C22semidirect
55. #352×C103C22semidirect
56. AΣL(1,𝔽16)×C103C22semidirect
57. AΣL(1,𝔽16)×C103C22semidirect
58. AΣL(1,𝔽16)×C103C22semidirect
59. C25×C103D4semidirect
68. C2×#41×C103D4semidirect
78. C22×D4×C103D4semidirect
87. #127×C103D4semidirect
98. #124×C103D4semidirect
110. #123×C103D4semidirect
150. #120×C103D4semidirect
151. #120×C103D4semidirect
152. #120×C103D4semidirect
163. #117×C103D4semidirect
172. C2×C22⋊C4×C103D4semidirect
173. C2×C22⋊C4×C103D4semidirect
198. C24×C103C2×D4semidirect
212. C2×Q8×C103C2×D4semidirect
266. C2×D4×C103C2×D4semidirect
282. C22×C4×C103C2×D4semidirect
335. C22⋊C4×C103C2×D4semidirect
336. C22⋊C4×C103C2×D4semidirect
339. C42×C103C2×D4semidirect
340. C42×C103C2×D4semidirect
514. #33551C103direct (N × H)
528. #3532C2×C103semidirect
529. #3026C2×C103semidirect
530. C2×B(4,𝔽2)C2×C103semidirect
531. #3019C2×C103semidirect
532. #2200C2×C103semidirect
533. #2199C2×C103semidirect
534. #2197C2×C103semidirect
535. #2196C2×C103semidirect
536. #2127C2×C103semidirect
537. #2121C2×C103semidirect
538. C2×AΣL(1,𝔽16)C2×C103semidirect
539. C103#33551direct (N × H)
540. C2×H(5,𝔽2)C22×C103semidirect
542. H(3,𝔽4)C22×C103semidirect
544. #560C22×C103semidirect
546. #551C22×C103semidirect
551. D42C22×C103semidirect
564. #458C22×C103semidirect
569. B(4,𝔽2)C22×C103semidirect
570. B(4,𝔽2)C22×C103semidirect
572. #455C22×C103semidirect
574. #453C22×C103semidirect
576. C2×#100C22×C103semidirect
579. C2×#99C22×C103semidirect
580. C2×#99C22×C103semidirect
581. #354C22×C103semidirect
582. #353C22×C103semidirect
583. #352C22×C103semidirect
584. AΣL(1,𝔽16)C22×C103semidirect
585. AΣL(1,𝔽16)C22×C103semidirect
586. AΣL(1,𝔽16)C22×C103semidirect
587. C25D4×C103semidirect
596. C2×#41D4×C103semidirect
606. C22×D4D4×C103semidirect
615. #127D4×C103semidirect
626. #124D4×C103semidirect
638. #123D4×C103semidirect
678. #120D4×C103semidirect
679. #120D4×C103semidirect
680. #120D4×C103semidirect
691. #117D4×C103semidirect
700. C2×C22⋊C4D4×C103semidirect
701. C2×C22⋊C4D4×C103semidirect
726. C24C2×D4×C103semidirect
740. C2×Q8C2×D4×C103semidirect
794. C2×D4C2×D4×C103semidirect
810. C22×C4C2×D4×C103semidirect
863. C22⋊C4C2×D4×C103semidirect
864. C22⋊C4C2×D4×C103semidirect
867. C42C2×D4×C103semidirect
868. C42C2×D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35322
C103×#30262
C2×B(4,𝔽2)×C1032
C103×#30192
C103×#22002
C103×#21992
C103×#21972
C103×#21962
C103×#21272
C103×#21212
C2×AΣL(1,𝔽16)×C1032
#33551103