Finite Group Databasebeta

← C103×#33347 #39938622

Subgroups — C103×#33347 #39938622

Order 26368.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3449C211yesmaximal, characteristic
2C2×#413×C103C211yesmaximal, characteristic, complemented
3C2×#410×C103C211yesmaximal, characteristic, complemented
4C103×#2123C212yesmaximal, complemented
5C103×#2122C212yesmaximal, complemented
6C103×#2121C214yesmaximal, complemented
7C103×#2120C214yesmaximal, complemented
8C22×#41×C103C411yescharacteristic, complemented
9C22×#41×C103C2211yescharacteristic
10C22×M16×C103—21no—
11#537×C103—21no—
12#537×C103—21no—
13#536×C103—21no—
14#536×C103C411yescharacteristic, complemented
15#536×C103C2211yescharacteristic
16#535×C103—21no—
17#535×C103C411yescharacteristic, complemented
18#535×C103C2211yescharacteristic
19#534×C103C412yescomplemented
20#534×C103C2212yes—
21#532×C103—21no—
22#532×C103—21no—
23#525×C103—21no—
24#525×C103—21no—
25#525×C103C412yescomplemented
26#525×C103C2212yes—
27C2×#117×C103—21no—
28C2×#117×C103C411yescharacteristic, complemented
29#413×C103—21no—
30#413×C103—21no—
31#413×C103C2212yes—
32#413×C103C2212yes—
33C2×#101×C103—21no—
34C2×#100×C103C2212yes—
35#410×C103—21no—
36#410×C103—21no—
37#410×C103C2212yes—
38#410×C103C2212yes—
39C2×#99×C103—21no—
40C2×#99×C103C2212yes—
41#352×C103C2218yescomplemented
42AΣL(1,𝔽16)×C103C2218yescomplemented
43C2×#41×C103—21no—
44C2×#41×C103—21no—
45C2×#41×C103—21no—
46C2×#41×C103—21no—
47C2×#41×C103—41no—
48C2×#41×C103—41no—
49C2×#41×C103—41no—
50C2×#41×C103—41no—
51C2×#41×C103—41no—
52C2×#41×C103—41no—
53C2×#41×C103—41no—
54C2×#41×C103—41no—
55C2×#41×C103C2×C411yescharacteristic
56C2×#41×C103C2×C411yescharacteristic
57C2×#41×C103D411yescharacteristic
58C2×#41×C103D411yescharacteristic
59C2×#41×C103D411yescharacteristic
60C2×#41×C103D411yescharacteristic
61C2×#41×C103C2311yescharacteristic
62C2×#41×C103C2311yescharacteristic
63C22×Q8×C103C2×C411yescharacteristic, complemented
64C22×Q8×C103D411yescharacteristic
65C22×D4×C103C2×C411yescharacteristic
66C22×D4×C103C2×C412yes—
67C22×D4×C103C2×C411yescharacteristic, complemented
68C22×D4×C103D411yescharacteristic
69C22×D4×C103C2311yescharacteristic
70C23×C4×C103C2×C411yescharacteristic
71C23×C4×C103C2×C412yescomplemented
72C23×C4×C103D411yescharacteristic
73C23×C4×C103D411yescharacteristic
74C2×M16×C103—22no—
75C2×M16×C103—22no—
76C2×M16×C103—22no—
77C2×M16×C103—41no—
78C2×M16×C103—41no—
79C2×M16×C103—41no—
80C22×C8×C103—41no—
81C4⋊Q8×C103—21no—
82C4⋊Q8×C103—21no—
83#127×C103—21no—
84#127×C103—21no—
85#124×C103—21no—
86#124×C103—21no—
87#124×C103—21no—
88#124×C103—21no—
89#123×C103—22no—
90#123×C103—22no—
91#123×C103C2×C412yes—
92#123×C103C2×C412yescomplemented
93#123×C103C2×C412yescomplemented
94#123×C103C2312yes—
95C22⋊Q8×C103—22no—
96C22⋊Q8×C103—22no—
97C22⋊Q8×C103—21no—
98C22⋊Q8×C103—21no—
99C22⋊Q8×C103—21no—
100C22⋊Q8×C103—21no—
101#121×C103—22no—
102#121×C103—22no—
103#121×C103—22no—
104#121×C103—22no—
105#121×C103—22no—
106#121×C103—22no—
107#121×C103—21no—
108#121×C103—21no—
109#121×C103—21no—
110#121×C103—21no—
111#120×C103—22no—
112#120×C103—22no—
113#120×C103C2×C412yes—
114#120×C103C2×C412yescomplemented
115#120×C103C2×C412yescomplemented
116#120×C103C2312yes—
117C4×D4×C103—22no—
118C4×D4×C103—22no—
119C4×D4×C103—22no—
120C4×D4×C103—22no—
121#117×C103—21no—
122#117×C103—21no—
123#117×C103—22no—
124#117×C103—22no—
125#117×C103—41no—
126#117×C103—41no—
127#117×C103C2×C412yescomplemented
128#117×C103C2×C411yescharacteristic, complemented
129#117×C103C2×C411yescharacteristic, complemented
130C2×C4⋊C4×C103—21no—
131C2×C4⋊C4×C103—41no—
132C2×C22⋊C4×C103—22no—
133C2×C22⋊C4×C103C2×C412yes—
134C2×C42×C103—21no—
135C2×C42×C103—41no—
136#101×C103—22no—
137#101×C103—22no—
138#100×C103—22no—
139#100×C103C2314yes—
140#99×C103—22no—
141#99×C103—22no—
142#99×C103—22no—
143#99×C103C2314yes—
144C24×C103C22⋊C411yescharacteristic
145C24×C103C22×C411yescharacteristic
146C24×C103C22×C412yes—
147C24×C103C2×D411yescharacteristic
148#41×C103—41no—
149#41×C103—41no—
150#41×C103—41no—
151#41×C103—41no—
152#41×C103—41no—
153#41×C103—41no—
154#41×C103—41no—
155#41×C103—41no—
156#41×C103—41no—
157#41×C103—41no—
158#41×C103—41no—
159#41×C103—41no—
160#41×C103—41no—
161#41×C103—41no—
162#41×C103—41no—
163#41×C103—41no—
164#41×C103—42no—
165#41×C103—42no—
166#41×C103—42no—
167#41×C103—42no—
168#41×C103—42no—
169#41×C103—42no—
170#41×C103—41no—
171#41×C103—41no—
172#41×C103—41no—
173#41×C103—41no—
174C2×Q8×C103—21no—
175C2×Q8×C103—21no—
176C2×Q8×C103—41no—
177C2×Q8×C103—41no—
178C2×Q8×C103—41no—
179C2×Q8×C103—41no—
180C2×Q8×C103C22⋊C411yescharacteristic
181C2×Q8×C103C22⋊C411yescharacteristic
182C2×Q8×C103C2×D411yescharacteristic
183C2×Q8×C103C2×D411yescharacteristic
184C2×D4×C103—22no—
185C2×D4×C103—22no—
186C2×D4×C103—22no—
187C2×D4×C103—22no—
188C2×D4×C103—22no—
189C2×D4×C103—22no—
190C2×D4×C103—21no—
191C2×D4×C103—21no—
192C2×D4×C103—41no—
193C2×D4×C103—41no—
194C2×D4×C103—41no—
195C2×D4×C103—41no—
196C2×D4×C103—41no—
197C2×D4×C103—41no—
198C2×D4×C103—41no—
199C2×D4×C103—41no—
200C2×D4×C103—42no—
201C2×D4×C103—42no—
202C2×D4×C103C22⋊C411yescharacteristic
203C2×D4×C103C22⋊C411yescharacteristic
204C2×D4×C103C22⋊C411yescharacteristic
205C2×D4×C103C22⋊C411yescharacteristic
206C2×D4×C103C22×C411yescharacteristic
207C2×D4×C103C22×C411yescharacteristic
208C2×D4×C103C22×C411yescharacteristic
209C2×D4×C103C2×D411yescharacteristic
210C2×D4×C103C2×D411yescharacteristic
211C2×D4×C103C2×D411yescharacteristic
212C2×D4×C103C2×D411yescharacteristic
213C2×D4×C103C2411yescharacteristic
214C22×C4×C103—21no—
215C22×C4×C103—21no—
216C22×C4×C103—21no—
217C22×C4×C103—21no—
218C22×C4×C103—21no—
219C22×C4×C103—21no—
220C22×C4×C103—21no—
221C22×C4×C103—21no—
222C22×C4×C103—21no—
223C22×C4×C103—21no—
224C22×C4×C103—21no—
225C22×C4×C103—21no—
226C22×C4×C103—22no—
227C22×C4×C103—22no—
228C22×C4×C103—22no—
229C22×C4×C103—42no—
230C22×C4×C103—42no—
231C22×C4×C103—42no—
232C22×C4×C103C22⋊C411yescharacteristic
233C22×C4×C103C22⋊C411yescharacteristic
234C22×C4×C103C22⋊C411yescharacteristic
235C22×C4×C103C22⋊C411yescharacteristic
236C22×C4×C103C22⋊C411yescharacteristic
237C22×C4×C103C22⋊C411yescharacteristic
238C22×C4×C103C22⋊C411yescharacteristic
239C22×C4×C103C22⋊C411yescharacteristic
240C22×C4×C103C22⋊C411yescharacteristic
241C22×C4×C103C22×C411yescharacteristic
242C22×C4×C103C22×C411yescharacteristic
243C22×C4×C103C22×C412yes—
244C22×C4×C103C2×D411yescharacteristic
245C22×C4×C103C2×D411yescharacteristic
246C22×C4×C103C2×D411yescharacteristic
247C22×C4×C103C2×D411yescharacteristic
248C22×C4×C103C2×D411yescharacteristic
249M16×C103—24no—
250M16×C103—42no—
251M16×C103—42no—
252M16×C103—42no—
253C2×C8×C103—42no—
254C2×C8×C103—42no—
255C2×C8×C103—42no—
256C4⋊C4×C103—22no—
257C4⋊C4×C103—21no—
258C4⋊C4×C103—21no—
259C4⋊C4×C103—22no—
260C4⋊C4×C103—22no—
261C4⋊C4×C103—22no—
262C4⋊C4×C103—22no—
263C4⋊C4×C103—42no—
264C4⋊C4×C103—42no—
265C22⋊C4×C103—22no—
266C22⋊C4×C103—22no—
267C22⋊C4×C103—22no—
268C22⋊C4×C103—22no—
269C22⋊C4×C103—22no—
270C22⋊C4×C103—22no—
271C22⋊C4×C103—22no—
272C22⋊C4×C103—22no—
273C22⋊C4×C103—22no—
274C22⋊C4×C103—24no—
275C22⋊C4×C103—42no—
276C22⋊C4×C103C22×C412yes—
277C22⋊C4×C103C22×C412yes—
278C42×C103—22no—
279C42×C103—21no—
280C42×C103—21no—
281C42×C103—42no—
282C42×C103—42no—
283C23×C103—21no—
284C23×C103—21no—
285C23×C103—21no—
286C23×C103—21no—
287C23×C103—21no—
288C23×C103—21no—
289C23×C103—22no—
290C23×C103—42no—
291C23×C103—81no—
292C23×C103—81no—
293C23×C103—81no—
294C23×C103—82no—
295C23×C103C2×C22⋊C411yescharacteristic
296C23×C103C2×C22⋊C411yescharacteristic
297C23×C103C2×C22⋊C411yescharacteristic
298C23×C103C2×C22⋊C411yescharacteristic
299C23×C103C2×C22⋊C411yescharacteristic
300C23×C103C23×C411yescharacteristic
301C23×C103C22×D411yescharacteristic
302Q8×C103—41no—
303Q8×C103—41no—
304Q8×C103—41no—
305Q8×C103—41no—
306Q8×C103—42no—
307Q8×C103—41no—
308Q8×C103—41no—
309D4×C103—41no—
310D4×C103—41no—
311D4×C103—41no—
312D4×C103—41no—
313D4×C103—41no—
314D4×C103—41no—
315D4×C103—41no—
316D4×C103—41no—
317D4×C103—41no—
318D4×C103—41no—
319D4×C103—41no—
320D4×C103—41no—
321D4×C103—42no—
322D4×C103—44no—
323D4×C103—42no—
324D4×C103—42no—
325D4×C103—41no—
326D4×C103—41no—
327D4×C103—82no—
328D4×C103—82no—
329D4×C103—82no—
330D4×C103—82no—
331C2×C4×C103—21no—
332C2×C4×C103—21no—
333C2×C4×C103—21no—
334C2×C4×C103—21no—
335C2×C4×C103—21no—
336C2×C4×C103—21no—
337C2×C4×C103—21no—
338C2×C4×C103—21no—
339C2×C4×C103—21no—
340C2×C4×C103—21no—
341C2×C4×C103—21no—
342C2×C4×C103—21no—
343C2×C4×C103—21no—
344C2×C4×C103—21no—
345C2×C4×C103—21no—
346C2×C4×C103—21no—
347C2×C4×C103—21no—
348C2×C4×C103—21no—
349C2×C4×C103—21no—
350C2×C4×C103—21no—
351C2×C4×C103—21no—
352C2×C4×C103—21no—
353C2×C4×C103—21no—
354C2×C4×C103—21no—
355C2×C4×C103—21no—
356C2×C4×C103—21no—
357C2×C4×C103—21no—
358C2×C4×C103—21no—
359C2×C4×C103—21no—
360C2×C4×C103—21no—
361C2×C4×C103—22no—
362C2×C4×C103—22no—
363C2×C4×C103—22no—
364C2×C4×C103—44no—
365C2×C4×C103—42no—
366C2×C4×C103—42no—
367C2×C4×C103—42no—
368C2×C4×C103—44no—
369C2×C4×C103—82no—
370C2×C4×C103—84no—
371C2×C4×C103#9911yescharacteristic
372C2×C4×C103#9911yescharacteristic
373C2×C4×C103#9911yescharacteristic
374C2×C4×C103#9911yescharacteristic
375C2×C4×C103C2×C22⋊C411yescharacteristic
376C2×C4×C103C2×C22⋊C411yescharacteristic
377C2×C4×C103C2×C22⋊C411yescharacteristic
378C2×C4×C103C2×C22⋊C411yescharacteristic
379C2×C4×C103C2×C22⋊C411yescharacteristic
380C2×C4×C103C2×C22⋊C411yescharacteristic
381C2×C4×C103C2×C22⋊C411yescharacteristic
382C2×C4×C103C22×D411yescharacteristic
383C8×C103—44no—
384C22×C103—21no—
385C22×C103—21no—
386C22×C103—21no—
387C22×C103—21no—
388C22×C103—21no—
389C22×C103—21no—
390C22×C103—41no—
391C22×C103—41no—
392C22×C103—41no—
393C22×C103—41no—
394C22×C103—41no—
395C22×C103—41no—
396C22×C103—41no—
397C22×C103—42no—
398C22×C103—42no—
399C22×C103—42no—
400C22×C103—42no—
401C22×C103—42no—
402C22×C103—81no—
403C22×C103—81no—
404C22×C103—81no—
405C22×C103—81no—
406C22×C103—84no—
407C22×C103C2×#9911yescharacteristic
408C22×C103C2×#9911yescharacteristic
409C22×C103C22×C22⋊C411yescharacteristic
410C4×C103—21no—
411C4×C103—21no—
412C4×C103—21no—
413C4×C103—21no—
414C4×C103—21no—
415C4×C103—21no—
416C4×C103—42no—
417C4×C103—42no—
418C4×C103—42no—
419C4×C103—84no—
420C4×C103C2×#9911yescharacteristic
421C4×C103C2×#9911yescharacteristic
422C4×C103C2×#9911yescharacteristic
423C4×C103C2×#9911yescharacteristic
424#33347C10311yesmaximal, characteristic, direct product factor, Sylow
425C2×C103—21no—
426C2×C103—21no—
427C2×C103—21no—
428C2×C103—41no—
429C2×C103—41no—
430C2×C103—41no—
431C2×C103—41no—
432C2×C103—41no—
433C2×C103—41no—
434C2×C103—82no—
435C2×C103C22×#9911yescharacteristic
436#3449C2×C10311yescharacteristic
437C2×#413C2×C10311yescharacteristic, complemented
438C2×#410C2×C10311yescharacteristic, complemented
439#2123C2×C10312yescomplemented
440#2122C2×C10312yescomplemented
441#2121C2×C10314yescomplemented
442#2120C2×C10314yescomplemented
443C103#3334711yescharacteristic, direct product factor, Sylow
444C22×#41C4×C10311yescharacteristic, complemented
445C22×#41C22×C10311yescharacteristic
446C22×M16—21no—
447#537—21no—
448#537—21no—
449#536—21no—
450#536C4×C10311yescharacteristic, complemented
451#536C22×C10311yescharacteristic
452#535—21no—
453#535C4×C10311yescharacteristic, complemented
454#535C22×C10311yescharacteristic
455#534C4×C10312yescomplemented
456#534C22×C10312yes—
457#532—21no—
458#532—21no—
459#525—21no—
460#525—21no—
461#525C4×C10312yescomplemented
462#525C22×C10312yes—
463C2×#117—21no—
464C2×#117C4×C10311yescharacteristic, complemented
465#413—21no—
466#413—21no—
467#413C22×C10312yes—
468#413C22×C10312yes—
469C2×#101—21no—
470C2×#100C22×C10312yes—
471#410—21no—
472#410—21no—
473#410C22×C10312yes—
474#410C22×C10312yes—
475C2×#99—21no—
476C2×#99C22×C10312yes—
477#352C22×C10318yescomplemented
478AΣL(1,𝔽16)C22×C10318yescomplemented
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41C2×C4×C10311yescharacteristic
492C2×#41C2×C4×C10311yescharacteristic
493C2×#41D4×C10311yescharacteristic
494C2×#41D4×C10311yescharacteristic
495C2×#41D4×C10311yescharacteristic
496C2×#41D4×C10311yescharacteristic
497C2×#41C23×C10311yescharacteristic
498C2×#41C23×C10311yescharacteristic
499C22×Q8C2×C4×C10311yescharacteristic, complemented
500C22×Q8D4×C10311yescharacteristic
501C22×D4C2×C4×C10311yescharacteristic
502C22×D4C2×C4×C10312yes—
503C22×D4C2×C4×C10311yescharacteristic, complemented
504C22×D4D4×C10311yescharacteristic
505C22×D4C23×C10311yescharacteristic
506C23×C4C2×C4×C10311yescharacteristic
507C23×C4C2×C4×C10312yescomplemented
508C23×C4D4×C10311yescharacteristic
509C23×C4D4×C10311yescharacteristic
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C2×M16—41no—
516C22×C8—41no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519#127—21no—
520#127—21no—
521#124—21no—
522#124—21no—
523#124—21no—
524#124—21no—
525#123—22no—
526#123—22no—
527#123C2×C4×C10312yes—
528#123C2×C4×C10312yescomplemented
529#123C2×C4×C10312yescomplemented
530#123C23×C10312yes—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—22no—
543#121—21no—
544#121—21no—
545#121—21no—
546#121—21no—
547#120—22no—
548#120—22no—
549#120C2×C4×C10312yes—
550#120C2×C4×C10312yescomplemented
551#120C2×C4×C10312yescomplemented
552#120C23×C10312yes—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557#117—21no—
558#117—21no—
559#117—22no—
560#117—22no—
561#117—41no—
562#117—41no—
563#117C2×C4×C10312yescomplemented
564#117C2×C4×C10311yescharacteristic, complemented
565#117C2×C4×C10311yescharacteristic, complemented
566C2×C4⋊C4—21no—
567C2×C4⋊C4—41no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4C2×C4×C10312yes—
570C2×C42—21no—
571C2×C42—41no—
572#101—22no—
573#101—22no—
574#100—22no—
575#100C23×C10314yes—
576#99—22no—
577#99—22no—
578#99—22no—
579#99C23×C10314yes—
580C24C22⋊C4×C10311yescharacteristic
581C24C22×C4×C10311yescharacteristic
582C24C22×C4×C10312yes—
583C24C2×D4×C10311yescharacteristic
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—41no—
615C2×Q8—41no—
616C2×Q8C22⋊C4×C10311yescharacteristic
617C2×Q8C22⋊C4×C10311yescharacteristic
618C2×Q8C2×D4×C10311yescharacteristic
619C2×Q8C2×D4×C10311yescharacteristic
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—41no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4C22⋊C4×C10311yescharacteristic
639C2×D4C22⋊C4×C10311yescharacteristic
640C2×D4C22⋊C4×C10311yescharacteristic
641C2×D4C22⋊C4×C10311yescharacteristic
642C2×D4C22×C4×C10311yescharacteristic
643C2×D4C22×C4×C10311yescharacteristic
644C2×D4C22×C4×C10311yescharacteristic
645C2×D4C2×D4×C10311yescharacteristic
646C2×D4C2×D4×C10311yescharacteristic
647C2×D4C2×D4×C10311yescharacteristic
648C2×D4C2×D4×C10311yescharacteristic
649C2×D4C24×C10311yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22⋊C4×C10311yescharacteristic
669C22×C4C22⋊C4×C10311yescharacteristic
670C22×C4C22⋊C4×C10311yescharacteristic
671C22×C4C22⋊C4×C10311yescharacteristic
672C22×C4C22⋊C4×C10311yescharacteristic
673C22×C4C22⋊C4×C10311yescharacteristic
674C22×C4C22⋊C4×C10311yescharacteristic
675C22×C4C22⋊C4×C10311yescharacteristic
676C22×C4C22⋊C4×C10311yescharacteristic
677C22×C4C22×C4×C10311yescharacteristic
678C22×C4C22×C4×C10311yescharacteristic
679C22×C4C22×C4×C10312yes—
680C22×C4C2×D4×C10311yescharacteristic
681C22×C4C2×D4×C10311yescharacteristic
682C22×C4C2×D4×C10311yescharacteristic
683C22×C4C2×D4×C10311yescharacteristic
684C22×C4C2×D4×C10311yescharacteristic
685M16—24no—
686M16—42no—
687M16—42no—
688M16—42no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8—42no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—24no—
711C22⋊C4—42no—
712C22⋊C4C22×C4×C10312yes—
713C22⋊C4C22×C4×C10312yes—
714C42—22no—
715C42—21no—
716C42—21no—
717C42—42no—
718C42—42no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—42no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—82no—
731C23C2×C22⋊C4×C10311yescharacteristic
732C23C2×C22⋊C4×C10311yescharacteristic
733C23C2×C22⋊C4×C10311yescharacteristic
734C23C2×C22⋊C4×C10311yescharacteristic
735C23C2×C22⋊C4×C10311yescharacteristic
736C23C23×C4×C10311yescharacteristic
737C23C22×D4×C10311yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—42no—
743Q8—41no—
744Q8—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—42no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—82no—
764D4—82no—
765D4—82no—
766D4—82no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—82no—
806C2×C4—84no—
807C2×C4#99×C10311yescharacteristic
808C2×C4#99×C10311yescharacteristic
809C2×C4#99×C10311yescharacteristic
810C2×C4#99×C10311yescharacteristic
811C2×C4C2×C22⋊C4×C10311yescharacteristic
812C2×C4C2×C22⋊C4×C10311yescharacteristic
813C2×C4C2×C22⋊C4×C10311yescharacteristic
814C2×C4C2×C22⋊C4×C10311yescharacteristic
815C2×C4C2×C22⋊C4×C10311yescharacteristic
816C2×C4C2×C22⋊C4×C10311yescharacteristic
817C2×C4C2×C22⋊C4×C10311yescharacteristic
818C2×C4C22×D4×C10311yescharacteristic
819C8—44no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—84no—
843C22C2×#99×C10311yescharacteristic
844C22C2×#99×C10311yescharacteristic
845C22C22×C22⋊C4×C10311yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—84no—
856C4C2×#99×C10311yescharacteristic
857C4C2×#99×C10311yescharacteristic
858C4C2×#99×C10311yescharacteristic
859C4C2×#99×C10311yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—82no—
870C2C22×#99×C10311yescharacteristic
subgroupG/H
centerC4×C103C2×#99
commutatorC23C23×C4×C103
Frattini, cosocleC2×D4C24×C103
socleC2×C103C22×#99
prime radicalC103×#3449C2
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C103 ◁ C22×C4×C103 ◁ C22×#41×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#413×C103C2semidirect
3. C2×#410×C103C2semidirect
4. C103×#2123C2semidirect
5. C103×#2122C2semidirect
6. C103×#2121C2semidirect
7. C103×#2120C2semidirect
8. C22×#41×C103C4semidirect
14. #536×C103C4semidirect
17. #535×C103C4semidirect
19. #534×C103C4semidirect
25. #525×C103C4semidirect
28. C2×#117×C103C4semidirect
41. #352×C103C22semidirect
42. AΣL(1,𝔽16)×C103C22semidirect
63. C22×Q8×C103C2×C4semidirect
67. C22×D4×C103C2×C4semidirect
71. C23×C4×C103C2×C4semidirect
92. #123×C103C2×C4semidirect
93. #123×C103C2×C4semidirect
114. #120×C103C2×C4semidirect
115. #120×C103C2×C4semidirect
127. #117×C103C2×C4semidirect
128. #117×C103C2×C4semidirect
129. #117×C103C2×C4semidirect
424. #33347C103direct (N × H)
437. C2×#413C2×C103semidirect
438. C2×#410C2×C103semidirect
439. #2123C2×C103semidirect
440. #2122C2×C103semidirect
441. #2121C2×C103semidirect
442. #2120C2×C103semidirect
443. C103#33347direct (N × H)
444. C22×#41C4×C103semidirect
450. #536C4×C103semidirect
453. #535C4×C103semidirect
455. #534C4×C103semidirect
461. #525C4×C103semidirect
464. C2×#117C4×C103semidirect
477. #352C22×C103semidirect
478. AΣL(1,𝔽16)C22×C103semidirect
499. C22×Q8C2×C4×C103semidirect
503. C22×D4C2×C4×C103semidirect
507. C23×C4C2×C4×C103semidirect
528. #123C2×C4×C103semidirect
529. #123C2×C4×C103semidirect
550. #120C2×C4×C103semidirect
551. #120C2×C4×C103semidirect
563. #117C2×C4×C103semidirect
564. #117C2×C4×C103semidirect
565. #117C2×C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34492
C2×#413×C1032
C2×#410×C1032
C103×#21232
C103×#21222
C103×#21212
C103×#21202
#33347103