Finite Group Databasebeta

← C103×#33552 #39938827

Subgroups — C103×#33552 #39938827

Order 26368.

1156 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3533C211yesmaximal, characteristic, complemented
2C103×#3026C211yesmaximal, characteristic, complemented
3C2×#458×C103C211yesmaximal, characteristic, complemented
4C103×#3019C211yesmaximal, characteristic, complemented
5C103×#2201C212yesmaximal, complemented
6C103×#2200C212yesmaximal, complemented
7C103×#2198C212yesmaximal, complemented
8C103×#2197C212yesmaximal, complemented
9C103×#2127C211yesmaximal, characteristic, complemented
10C103×#2121C211yesmaximal, characteristic, complemented
11C2×#352×C103C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C103C2211yescharacteristic
13#575×C103—21no—
14#563×C103C2211yescharacteristic, complemented
15#562×C103—21no—
16#560×C103C2211yescharacteristic, complemented
17#559×C103C2211yescharacteristic, complemented
18#553×C103—21no—
19#552×C103—21no—
20#551×C103—21no—
21#551×C103C2211yescharacteristic, complemented
22#547×C103—21no—
23#546×C103—21no—
24#542×C103—21no—
25#540×C103—21no—
26#539×C103—21no—
27#538×C103—21no—
28#538×C103—21no—
29#535×C103C2211yescharacteristic
30#534×C103—21no—
31#534×C103C2211yescharacteristic
32#525×C103—21no—
33C2×#123×C103—21no—
34C2×#123×C103C2211yescharacteristic
35#458×C103—21no—
36#458×C103—21no—
37#458×C103—21no—
38#458×C103C2212yes—
39#458×C103C2212yes—
40#458×C103C2212yes—
41B(4,𝔽2)×C103—21no—
42B(4,𝔽2)×C103C2212yes—
43#455×C103—21no—
44#455×C103C2212yes—
45#453×C103—21no—
46#453×C103C2212yes—
47#421×C103—21no—
48C2×#100×C103C2211yescharacteristic
49C2×#99×C103—21no—
50C2×#99×C103—21no—
51C2×#99×C103C2211yescharacteristic
52C2×#99×C103C2211yescharacteristic
53#354×C103C2212yescomplemented
54#353×C103C2212yescomplemented
55#352×C103C2212yescomplemented
56#352×C103C2212yescomplemented
57#352×C103C2212yescomplemented
58AΣL(1,𝔽16)×C103C2212yescomplemented
59H(5,𝔽2)×C103—21no—
60H(5,𝔽2)×C103—21no—
61H(5,𝔽2)×C103—21no—
62H(5,𝔽2)×C103—42no—
63H(5,𝔽2)×C103C2312yes—
64C2×#41×C103—21no—
65C2×#41×C103—21no—
66C2×#41×C103—41no—
67C2×#41×C103D411yescharacteristic, complemented
68C22×D4×C103—21no—
69C22×D4×C103—21no—
70C22×D4×C103—41no—
71C22×D4×C103D411yescharacteristic
72C22×D4×C103C2311yescharacteristic
73C23×C4×C103D411yescharacteristic, complemented
74#137×C103—22no—
75#137×C103—41no—
76AGL(1,ℤ/8)×C103—22no—
77AGL(1,ℤ/8)×C103—41no—
78#135×C103—42no—
79C2×M16×C103—21no—
80C4⋊Q8×C103—21no—
81#127×C103D411yescharacteristic, complemented
82#127×C103C2311yescharacteristic
83#126×C103—21no—
84#126×C103—21no—
85#126×C103—21no—
86#126×C103—21no—
87#126×C103—21no—
88#126×C103—21no—
89#125×C103—21no—
90#125×C103—21no—
91#125×C103—21no—
92#124×C103—21no—
93#124×C103—21no—
94#124×C103—21no—
95#124×C103—21no—
96#124×C103D411yescharacteristic, complemented
97#124×C103C2311yescharacteristic
98#123×C103—21no—
99#123×C103—21no—
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—21no—
109#123×C103—21no—
110#123×C103—22no—
111#123×C103—22no—
112#123×C103—22no—
113#123×C103—41no—
114#123×C103—42no—
115#123×C103D411yescharacteristic
116#123×C103D411yescharacteristic, complemented
117#123×C103D411yescharacteristic, complemented
118#123×C103C2311yescharacteristic
119#123×C103C2311yescharacteristic
120#123×C103C2311yescharacteristic
121C22⋊Q8×C103—21no—
122C22⋊Q8×C103—21no—
123C22⋊Q8×C103—21no—
124C22⋊Q8×C103—21no—
125C22⋊Q8×C103—21no—
126C22⋊Q8×C103—21no—
127C22⋊Q8×C103—21no—
128C22⋊Q8×C103—21no—
129#121×C103—21no—
130#121×C103—21no—
131#121×C103—21no—
132#121×C103—21no—
133#121×C103—21no—
134#121×C103—21no—
135#121×C103—21no—
136#121×C103—21no—
137#121×C103—21no—
138#121×C103—21no—
139#121×C103—21no—
140#121×C103—21no—
141#121×C103—42no—
142#120×C103—21no—
143#120×C103—21no—
144#120×C103—21no—
145#120×C103—21no—
146#120×C103—22no—
147#120×C103—41no—
148#120×C103D411yescharacteristic
149#120×C103C2311yescharacteristic
150C4×Q8×C103—21no—
151C4×D4×C103—21no—
152C4×D4×C103—21no—
153C4×D4×C103—21no—
154C4×D4×C103—21no—
155C4×D4×C103—21no—
156C4×D4×C103—21no—
157C4×D4×C103—21no—
158C4×D4×C103—21no—
159C4×D4×C103—21no—
160#117×C103—21no—
161#117×C103—21no—
162#117×C103—21no—
163#117×C103D411yescharacteristic, complemented
164C2×C4⋊C4×C103—21no—
165C2×C4⋊C4×C103—21no—
166C2×C4⋊C4×C103—41no—
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
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×C103C2×D411yescharacteristic
189C24×C103C2×D411yescharacteristic
190C24×C103C2×D411yescharacteristic
191#41×C103—22no—
192#41×C103—22no—
193#41×C103—42no—
194#41×C103—41no—
195#41×C103—42no—
196#41×C103—42no—
197#41×C103—41no—
198#41×C103—41no—
199#41×C103—42no—
200#41×C103—41no—
201#41×C103—81no—
202#41×C103—81no—
203C2×Q8×C103—21no—
204C2×Q8×C103—21no—
205C2×Q8×C103—21no—
206C2×Q8×C103C2×D411yescharacteristic
207C2×D4×C103—21no—
208C2×D4×C103—22no—
209C2×D4×C103—22no—
210C2×D4×C103—21no—
211C2×D4×C103—21no—
212C2×D4×C103—22no—
213C2×D4×C103—22no—
214C2×D4×C103—21no—
215C2×D4×C103—21no—
216C2×D4×C103—21no—
217C2×D4×C103—21no—
218C2×D4×C103—21no—
219C2×D4×C103—21no—
220C2×D4×C103—21no—
221C2×D4×C103—21no—
222C2×D4×C103—21no—
223C2×D4×C103—41no—
224C2×D4×C103—41no—
225C2×D4×C103—42no—
226C2×D4×C103—42no—
227C2×D4×C103—41no—
228C2×D4×C103—41no—
229C2×D4×C103—41no—
230C2×D4×C103—41no—
231C2×D4×C103—42no—
232C2×D4×C103—42no—
233C2×D4×C103—41no—
234C2×D4×C103—41no—
235C2×D4×C103—41no—
236C2×D4×C103—41no—
237C2×D4×C103—41no—
238C2×D4×C103—42no—
239C2×D4×C103C2×D411yescharacteristic
240C2×D4×C103C2×D411yescharacteristic
241C2×D4×C103C2×D411yescharacteristic
242C2×D4×C103C2×D411yescharacteristic
243C2×D4×C103C2411yescharacteristic
244C22×C4×C103—21no—
245C22×C4×C103—21no—
246C22×C4×C103—21no—
247C22×C4×C103—21no—
248C22×C4×C103—21no—
249C22×C4×C103—21no—
250C22×C4×C103—21no—
251C22×C4×C103—21no—
252C22×C4×C103—21no—
253C22×C4×C103—21no—
254C22×C4×C103—21no—
255C22×C4×C103—41no—
256C22×C4×C103—41no—
257C22×C4×C103—41no—
258C22×C4×C103—41no—
259C22×C4×C103—41no—
260C22×C4×C103C2×D411yescharacteristic
261C22×C4×C103C2×D411yescharacteristic
262C22×C4×C103C2×D411yescharacteristic
263C22×C4×C103C2×D411yescharacteristic
264Q16×C103—42no—
265SD16×C103—42no—
266SD16×C103—42no—
267D8×C103—42no—
268M16×C103—22no—
269M16×C103—41no—
270C2×C8×C103—41no—
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×C103—21no—
289C4⋊C4×C103—21no—
290C4⋊C4×C103—42no—
291C4⋊C4×C103—42no—
292C4⋊C4×C103—42no—
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—22no—
317C22⋊C4×C103—22no—
318C22⋊C4×C103—42no—
319C22⋊C4×C103—41no—
320C22⋊C4×C103—41no—
321C22⋊C4×C103—42no—
322C22⋊C4×C103—42no—
323C22⋊C4×C103—42no—
324C22⋊C4×C103C2×D411yescharacteristic
325C22⋊C4×C103C2×D411yescharacteristic
326C22⋊C4×C103C2×D411yescharacteristic
327C22⋊C4×C103C2×D411yescharacteristic
328C42×C103—21no—
329C42×C103—21no—
330C42×C103—21no—
331C42×C103—21no—
332C42×C103C2×D411yescharacteristic
333C42×C103C2×D411yescharacteristic
334C23×C103—21no—
335C23×C103—21no—
336C23×C103—21no—
337C23×C103—21no—
338C23×C103—22no—
339C23×C103—22no—
340C23×C103—21no—
341C23×C103—21no—
342C23×C103—41no—
343C23×C103—41no—
344C23×C103—41no—
345C23×C103—41no—
346C23×C103—81no—
347C23×C103—81no—
348C23×C103—81no—
349C23×C103—82no—
350C23×C103—161no—
351C23×C103#12011yescharacteristic
352C23×C103#12011yescharacteristic
353C23×C103#12011yescharacteristic
354C23×C103C22×D411yescharacteristic
355C23×C103C22×D411yescharacteristic
356Q8×C103—22no—
357Q8×C103—41no—
358Q8×C103—41no—
359Q8×C103—81no—
360Q8×C103—81no—
361D4×C103—22no—
362D4×C103—41no—
363D4×C103—41no—
364D4×C103—41no—
365D4×C103—41no—
366D4×C103—41no—
367D4×C103—41no—
368D4×C103—42no—
369D4×C103—42no—
370D4×C103—42no—
371D4×C103—42no—
372D4×C103—42no—
373D4×C103—42no—
374D4×C103—41no—
375D4×C103—41no—
376D4×C103—41no—
377D4×C103—41no—
378D4×C103—81no—
379D4×C103—81no—
380D4×C103—81no—
381D4×C103—81no—
382D4×C103—81no—
383D4×C103—81no—
384D4×C103—81no—
385D4×C103—81no—
386D4×C103—81no—
387D4×C103—162no—
388C2×C4×C103—21no—
389C2×C4×C103—21no—
390C2×C4×C103—22no—
391C2×C4×C103—22no—
392C2×C4×C103—21no—
393C2×C4×C103—21no—
394C2×C4×C103—21no—
395C2×C4×C103—21no—
396C2×C4×C103—21no—
397C2×C4×C103—21no—
398C2×C4×C103—21no—
399C2×C4×C103—21no—
400C2×C4×C103—21no—
401C2×C4×C103—21no—
402C2×C4×C103—42no—
403C2×C4×C103—42no—
404C2×C4×C103—41no—
405C2×C4×C103—41no—
406C2×C4×C103—41no—
407C2×C4×C103—41no—
408C2×C4×C103—41no—
409C2×C4×C103—41no—
410C2×C4×C103—41no—
411C2×C4×C103—41no—
412C2×C4×C103—42no—
413C2×C4×C103—42no—
414C2×C4×C103—81no—
415C2×C4×C103—81no—
416C2×C4×C103—81no—
417C2×C4×C103—81no—
418C2×C4×C103—81no—
419C2×C4×C103—81no—
420C2×C4×C103—81no—
421C2×C4×C103—81no—
422C2×C4×C103—82no—
423C2×C4×C103—161no—
424C2×C4×C103#12011yescharacteristic
425C2×C4×C103C22×D411yescharacteristic
426C8×C103—42no—
427C22×C103—21no—
428C22×C103—21no—
429C22×C103—21no—
430C22×C103—21no—
431C22×C103—41no—
432C22×C103—41no—
433C22×C103—41no—
434C22×C103—41no—
435C22×C103—41no—
436C22×C103—42no—
437C22×C103—41no—
438C22×C103—41no—
439C22×C103—41no—
440C22×C103—41no—
441C22×C103—42no—
442C22×C103—41no—
443C22×C103—41no—
444C22×C103—81no—
445C22×C103—81no—
446C22×C103—81no—
447C22×C103—82no—
448C22×C103—82no—
449C22×C103—82no—
450C22×C103—82no—
451C22×C103—161no—
452C22×C103—161no—
453C22×C103B(4,𝔽2)11yescharacteristic
454C22×C103B(4,𝔽2)11yescharacteristic
455C22×C103C2×#12011yescharacteristic
456C4×C103—21no—
457C4×C103—21no—
458C4×C103—41no—
459C4×C103—41no—
460C4×C103—41no—
461C4×C103—41no—
462C4×C103—41no—
463C4×C103—41no—
464C4×C103—42no—
465C4×C103—41no—
466C4×C103—41no—
467C4×C103—41no—
468C4×C103—41no—
469C4×C103—82no—
470C4×C103—82no—
471#33552C10311yesmaximal, characteristic, direct product factor, Sylow
472C2×C103—21no—
473C2×C103—21no—
474C2×C103—21no—
475C2×C103—41no—
476C2×C103—41no—
477C2×C103—41no—
478C2×C103—41no—
479C2×C103—81no—
480C2×C103—81no—
481C2×C103—82no—
482C2×C103C2×B(4,𝔽2)11yescharacteristic
483#3533C2×C10311yescharacteristic, complemented
484#3026C2×C10311yescharacteristic, complemented
485C2×#458C2×C10311yescharacteristic, complemented
486#3019C2×C10311yescharacteristic, complemented
487#2201C2×C10312yescomplemented
488#2200C2×C10312yescomplemented
489#2198C2×C10312yescomplemented
490#2197C2×C10312yescomplemented
491#2127C2×C10311yescharacteristic, complemented
492#2121C2×C10311yescharacteristic, complemented
493C2×#352C2×C10311yescharacteristic, complemented
494C103#3355211yescharacteristic, direct product factor, Sylow
495C2×H(5,𝔽2)C22×C10311yescharacteristic
496#575—21no—
497#563C22×C10311yescharacteristic, complemented
498#562—21no—
499#560C22×C10311yescharacteristic, complemented
500#559C22×C10311yescharacteristic, complemented
501#553—21no—
502#552—21no—
503#551—21no—
504#551C22×C10311yescharacteristic, complemented
505#547—21no—
506#546—21no—
507#542—21no—
508#540—21no—
509#539—21no—
510#538—21no—
511#538—21no—
512#535C22×C10311yescharacteristic
513#534—21no—
514#534C22×C10311yescharacteristic
515#525—21no—
516C2×#123—21no—
517C2×#123C22×C10311yescharacteristic
518#458—21no—
519#458—21no—
520#458—21no—
521#458C22×C10312yes—
522#458C22×C10312yes—
523#458C22×C10312yes—
524B(4,𝔽2)—21no—
525B(4,𝔽2)C22×C10312yes—
526#455—21no—
527#455C22×C10312yes—
528#453—21no—
529#453C22×C10312yes—
530#421—21no—
531C2×#100C22×C10311yescharacteristic
532C2×#99—21no—
533C2×#99—21no—
534C2×#99C22×C10311yescharacteristic
535C2×#99C22×C10311yescharacteristic
536#354C22×C10312yescomplemented
537#353C22×C10312yescomplemented
538#352C22×C10312yescomplemented
539#352C22×C10312yescomplemented
540#352C22×C10312yescomplemented
541AΣL(1,𝔽16)C22×C10312yescomplemented
542H(5,𝔽2)—21no—
543H(5,𝔽2)—21no—
544H(5,𝔽2)—21no—
545H(5,𝔽2)—42no—
546H(5,𝔽2)C23×C10312yes—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—41no—
550C2×#41D4×C10311yescharacteristic, complemented
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4D4×C10311yescharacteristic
555C22×D4C23×C10311yescharacteristic
556C23×C4D4×C10311yescharacteristic, complemented
557#137—22no—
558#137—41no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—41no—
561#135—42no—
562C2×M16—21no—
563C4⋊Q8—21no—
564#127D4×C10311yescharacteristic, complemented
565#127C23×C10311yescharacteristic
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124D4×C10311yescharacteristic, complemented
580#124C23×C10311yescharacteristic
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—22no—
594#123—22no—
595#123—22no—
596#123—41no—
597#123—42no—
598#123D4×C10311yescharacteristic
599#123D4×C10311yescharacteristic, complemented
600#123D4×C10311yescharacteristic, complemented
601#123C23×C10311yescharacteristic
602#123C23×C10311yescharacteristic
603#123C23×C10311yescharacteristic
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—42no—
625#120—21no—
626#120—21no—
627#120—21no—
628#120—21no—
629#120—22no—
630#120—41no—
631#120D4×C10311yescharacteristic
632#120C23×C10311yescharacteristic
633C4×Q8—21no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643#117—21no—
644#117—21no—
645#117—21no—
646#117D4×C10311yescharacteristic, complemented
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—41no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4D4×C10311yescharacteristic
656C2×C22⋊C4D4×C10311yescharacteristic, complemented
657#104—22no—
658#104—22no—
659#100—21no—
660#100C23×C10312yes—
661#99—21no—
662#99—21no—
663#99—22no—
664#99—22no—
665#99—22no—
666#99—22no—
667#99C23×C10312yes—
668#99C23×C10312yes—
669C24—21no—
670C24—21no—
671C24C2×D4×C10311yescharacteristic
672C24C2×D4×C10311yescharacteristic
673C24C2×D4×C10311yescharacteristic
674#41—22no—
675#41—22no—
676#41—42no—
677#41—41no—
678#41—42no—
679#41—42no—
680#41—41no—
681#41—41no—
682#41—42no—
683#41—41no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8C2×D4×C10311yescharacteristic
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4C2×D4×C10311yescharacteristic
723C2×D4C2×D4×C10311yescharacteristic
724C2×D4C2×D4×C10311yescharacteristic
725C2×D4C2×D4×C10311yescharacteristic
726C2×D4C24×C10311yescharacteristic
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4C2×D4×C10311yescharacteristic
744C22×C4C2×D4×C10311yescharacteristic
745C22×C4C2×D4×C10311yescharacteristic
746C22×C4C2×D4×C10311yescharacteristic
747Q16—42no—
748SD16—42no—
749SD16—42no—
750D8—42no—
751M16—22no—
752M16—41no—
753C2×C8—41no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4C2×D4×C10311yescharacteristic
808C22⋊C4C2×D4×C10311yescharacteristic
809C22⋊C4C2×D4×C10311yescharacteristic
810C22⋊C4C2×D4×C10311yescharacteristic
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C42C2×D4×C10311yescharacteristic
816C42C2×D4×C10311yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—82no—
833C23—161no—
834C23#120×C10311yescharacteristic
835C23#120×C10311yescharacteristic
836C23#120×C10311yescharacteristic
837C23C22×D4×C10311yescharacteristic
838C23C22×D4×C10311yescharacteristic
839Q8—22no—
840Q8—41no—
841Q8—41no—
842Q8—81no—
843Q8—81no—
844D4—22no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—41no—
860D4—42no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868D4—81no—
869D4—81no—
870D4—162no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—161no—
907C2×C4#120×C10311yescharacteristic
908C2×C4C22×D4×C10311yescharacteristic
909C8—42no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—161no—
935C22—161no—
936C22B(4,𝔽2)×C10311yescharacteristic
937C22B(4,𝔽2)×C10311yescharacteristic
938C22C2×#120×C10311yescharacteristic
939C4—21no—
940C4—21no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—82no—
953C4—82no—
954C2—21no—
955C2—21no—
956C2—21no—
957C2—41no—
958C2—41no—
959C2—41no—
960C2—41no—
961C2—81no—
962C2—81no—
963C2—82no—
964C2C2×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×#3533C2semidirect
2. C103×#3026C2semidirect
3. C2×#458×C103C2semidirect
4. C103×#3019C2semidirect
5. C103×#2201C2semidirect
6. C103×#2200C2semidirect
7. C103×#2198C2semidirect
8. C103×#2197C2semidirect
9. C103×#2127C2semidirect
10. C103×#2121C2semidirect
11. C2×#352×C103C2semidirect
14. #563×C103C22semidirect
16. #560×C103C22semidirect
17. #559×C103C22semidirect
21. #551×C103C22semidirect
53. #354×C103C22semidirect
54. #353×C103C22semidirect
55. #352×C103C22semidirect
56. #352×C103C22semidirect
57. #352×C103C22semidirect
58. AΣL(1,𝔽16)×C103C22semidirect
67. C2×#41×C103D4semidirect
73. C23×C4×C103D4semidirect
81. #127×C103D4semidirect
96. #124×C103D4semidirect
116. #123×C103D4semidirect
117. #123×C103D4semidirect
163. #117×C103D4semidirect
173. C2×C22⋊C4×C103D4semidirect
471. #33552C103direct (N × H)
483. #3533C2×C103semidirect
484. #3026C2×C103semidirect
485. C2×#458C2×C103semidirect
486. #3019C2×C103semidirect
487. #2201C2×C103semidirect
488. #2200C2×C103semidirect
489. #2198C2×C103semidirect
490. #2197C2×C103semidirect
491. #2127C2×C103semidirect
492. #2121C2×C103semidirect
493. C2×#352C2×C103semidirect
494. C103#33552direct (N × H)
497. #563C22×C103semidirect
499. #560C22×C103semidirect
500. #559C22×C103semidirect
504. #551C22×C103semidirect
536. #354C22×C103semidirect
537. #353C22×C103semidirect
538. #352C22×C103semidirect
539. #352C22×C103semidirect
540. #352C22×C103semidirect
541. AΣL(1,𝔽16)C22×C103semidirect
550. C2×#41D4×C103semidirect
556. C23×C4D4×C103semidirect
564. #127D4×C103semidirect
579. #124D4×C103semidirect
599. #123D4×C103semidirect
600. #123D4×C103semidirect
646. #117D4×C103semidirect
656. C2×C22⋊C4D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35332
C103×#30262
C2×#458×C1032
C103×#30192
C103×#22012
C103×#22002
C103×#21982
C103×#21972
C103×#21272
C103×#21212
C2×#352×C1032
#33552103