Finite Group Databasebeta

← C103×#23412 #39928687

Subgroups — C103×#23412 #39928687

Order 26368.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C103C211yesmaximal, characteristic, complemented
2C2×#575×C103C211yesmaximal, characteristic, complemented
3C103×#3449C211yesmaximal, characteristic, complemented
4C2×#421×C103C211yesmaximal, characteristic, complemented
5C103×#2896C211yesmaximal, characteristic, complemented
6C2×#410×C103C211yesmaximal, characteristic, complemented
7C103×#2009C214yesmaximal, complemented
8C103×#2008C214yesmaximal, complemented
9C2×#344×C103C211yesmaximal, characteristic, complemented
10C22×#41×C103C2211yescharacteristic
11C22×#41×C103C2211yescharacteristic
12C22×#41×C103C2211yescharacteristic
13#575×C103—22no—
14#575×C103—22no—
15#575×C103—22no—
16#575×C103—22no—
17#575×C103—22no—
18#575×C103—22no—
19#575×C103—22no—
20#575×C103C2214yes—
21C2×#137×C103—21no—
22C2×#137×C103—21no—
23C2×#137×C103—21no—
24C2×#137×C103C2212yescomplemented
25C2×AGL(1,ℤ/8)×C103—21no—
26C2×AGL(1,ℤ/8)×C103—21no—
27C2×AGL(1,ℤ/8)×C103—21no—
28C2×AGL(1,ℤ/8)×C103C2212yescomplemented
29C2×#135×C103—22no—
30C2×#135×C103—22no—
31C22×M16×C103C2211yescharacteristic
32C22×M16×C103C2211yescharacteristic
33#537×C103—22no—
34#536×C103—21no—
35#536×C103C2212yescomplemented
36#535×C103—21no—
37#535×C103C2212yescomplemented
38#534×C103—22no—
39#532×C103—22no—
40#525×C103—22no—
41#525×C103—22no—
42C2×#117×C103C2211yescharacteristic
43C2×#117×C103C2211yescharacteristic
44#421×C103—22no—
45#421×C103C2214yescomplemented
46C2×#104×C103—22no—
47#419×C103C2212yescomplemented
48#418×C103C2212yescomplemented
49#417×C103—22no—
50#416×C103—22no—
51#410×C103—22no—
52#410×C103C2214yescomplemented
53C2×#99×C103—22no—
54#344×C103C2214yescomplemented
55C2×#41×C103—21no—
56C2×#41×C103—21no—
57C2×#41×C103—21no—
58C2×#41×C103—21no—
59C2×#41×C103—21no—
60C2×#41×C103—21no—
61C2×#41×C103—21no—
62C2×#41×C103—21no—
63C2×#41×C103—21no—
64C2×#41×C103—21no—
65C2×#41×C103—21no—
66C2×#41×C103—21no—
67C2×#41×C103—21no—
68C2×#41×C103—21no—
69C2×#41×C103—21no—
70C2×#41×C103—21no—
71C2×#41×C103—21no—
72C2×#41×C103—21no—
73C2×#41×C103—21no—
74C2×#41×C103—21no—
75C2×#41×C103—21no—
76C2×#41×C103—21no—
77C2×#41×C103—21no—
78C2×#41×C103—21no—
79C2×#41×C103—21no—
80C2×#41×C103—21no—
81C2×#41×C103—21no—
82C2×#41×C103—21no—
83C2×#41×C103—21no—
84C2×#41×C103—21no—
85C2×#41×C103D412yes—
86C2×#41×C103D412yes—
87C2×#41×C103D412yes—
88C2×#41×C103D412yescomplemented
89C2×#41×C103C2312yes—
90C2×#41×C103C2312yes—
91C22×Q8×C103D411yescharacteristic
92C22×Q8×C103D411yescharacteristic, complemented
93C22×Q8×C103C2311yescharacteristic
94C22×D4×C103—21no—
95C22×D4×C103—21no—
96C22×D4×C103—21no—
97C22×D4×C103D411yescharacteristic
98C22×D4×C103D411yescharacteristic, complemented
99C22×D4×C103C2311yescharacteristic
100C23×C4×C103—21no—
101C23×C4×C103—21no—
102C23×C4×C103—21no—
103C23×C4×C103C2311yescharacteristic
104#137×C103—24no—
105#137×C103—24no—
106#137×C103—24no—
107#137×C103—24no—
108#137×C103—24no—
109#137×C103—24no—
110#137×C103—24no—
111#137×C103—24no—
112AGL(1,ℤ/8)×C103—24no—
113AGL(1,ℤ/8)×C103—24no—
114AGL(1,ℤ/8)×C103—24no—
115AGL(1,ℤ/8)×C103—24no—
116AGL(1,ℤ/8)×C103—24no—
117AGL(1,ℤ/8)×C103—24no—
118AGL(1,ℤ/8)×C103—24no—
119AGL(1,ℤ/8)×C103—24no—
120#135×C103—28no—
121#135×C103—28no—
122#135×C103—28no—
123#135×C103—28no—
124C2×Q16×C103—22no—
125C2×Q16×C103—22no—
126C2×SD16×C103—22no—
127C2×SD16×C103—22no—
128C2×SD16×C103—22no—
129C2×SD16×C103—22no—
130C2×D8×C103—22no—
131C2×D8×C103—22no—
132C2×M16×C103—21no—
133C2×M16×C103—21no—
134C2×M16×C103—21no—
135C2×M16×C103—21no—
136C2×M16×C103—21no—
137C2×M16×C103—21no—
138C2×M16×C103—21no—
139C2×M16×C103D412yescomplemented
140C2×M16×C103D412yescomplemented
141C2×M16×C103D412yescomplemented
142C2×M16×C103C2312yes—
143C2×M16×C103C2312yes—
144C22×C8×C103—21no—
145C22×C8×C103D412yescomplemented
146C4⋊Q8×C103—22no—
147#127×C103—22no—
148#124×C103—22no—
149#124×C103—22no—
150#123×C103—24no—
151#123×C103—24no—
152C22⋊Q8×C103—24no—
153C22⋊Q8×C103—24no—
154#121×C103—24no—
155#121×C103—28no—
156#121×C103—24no—
157#120×C103—24no—
158#120×C103—24no—
159C4×D4×C103—28no—
160#117×C103—21no—
161#117×C103—21no—
162#117×C103—21no—
163#117×C103—21no—
164#117×C103—21no—
165#117×C103D412yes—
166#117×C103C2312yes—
167#117×C103C2312yes—
168C2×C4⋊C4×C103—21no—
169C2×C4⋊C4×C103—21no—
170C2×C22⋊C4×C103—21no—
171C2×C22⋊C4×C103D412yes—
172C2×C42×C103—21no—
173C2×C42×C103—21no—
174#104×C103—28no—
175#103×C103—24no—
176#102×C103—24no—
177#99×C103—28no—
178C24×C103—21no—
179C24×C103—21no—
180C24×C103—21no—
181C24×C103C2×D411yescharacteristic
182#41×C103—22no—
183#41×C103—22no—
184#41×C103—22no—
185#41×C103—22no—
186#41×C103—22no—
187#41×C103—22no—
188#41×C103—22no—
189#41×C103—22no—
190#41×C103—22no—
191#41×C103—22no—
192#41×C103—22no—
193#41×C103—22no—
194#41×C103—22no—
195#41×C103—22no—
196#41×C103—22no—
197#41×C103—22no—
198#41×C103—22no—
199#41×C103—22no—
200#41×C103—22no—
201#41×C103—22no—
202#41×C103—22no—
203#41×C103—22no—
204#41×C103—22no—
205#41×C103—22no—
206#41×C103—41no—
207#41×C103—41no—
208#41×C103—41no—
209#41×C103—41no—
210#41×C103—41no—
211#41×C103—41no—
212#41×C103—41no—
213#41×C103—41no—
214#41×C103—41no—
215#41×C103—41no—
216#41×C103—41no—
217#41×C103—41no—
218#41×C103—41no—
219#41×C103—41no—
220#41×C103—41no—
221#41×C103—41no—
222#41×C103—41no—
223#41×C103—41no—
224#41×C103—41no—
225#41×C103—41no—
226#41×C103—41no—
227#41×C103—41no—
228#41×C103—41no—
229#41×C103—41no—
230C2×Q8×C103—21no—
231C2×Q8×C103—21no—
232C2×Q8×C103—21no—
233C2×Q8×C103—21no—
234C2×Q8×C103—21no—
235C2×Q8×C103—21no—
236C2×Q8×C103—21no—
237C2×Q8×C103—21no—
238C2×Q8×C103—21no—
239C2×Q8×C103—21no—
240C2×Q8×C103—21no—
241C2×Q8×C103—21no—
242C2×Q8×C103—21no—
243C2×Q8×C103—21no—
244C2×Q8×C103—21no—
245C2×Q8×C103C2×D412yes—
246C2×Q8×C103C2×D412yes—
247C2×Q8×C103C2×D412yes—
248C2×D4×C103—22no—
249C2×D4×C103—22no—
250C2×D4×C103—22no—
251C2×D4×C103—22no—
252C2×D4×C103—22no—
253C2×D4×C103—22no—
254C2×D4×C103—28no—
255C2×D4×C103—21no—
256C2×D4×C103—21no—
257C2×D4×C103—21no—
258C2×D4×C103—21no—
259C2×D4×C103—21no—
260C2×D4×C103—21no—
261C2×D4×C103—21no—
262C2×D4×C103—21no—
263C2×D4×C103—21no—
264C2×D4×C103—21no—
265C2×D4×C103—21no—
266C2×D4×C103—21no—
267C2×D4×C103—21no—
268C2×D4×C103—21no—
269C2×D4×C103—21no—
270C2×D4×C103—41no—
271C2×D4×C103—41no—
272C2×D4×C103—41no—
273C2×D4×C103—41no—
274C2×D4×C103—41no—
275C2×D4×C103—41no—
276C2×D4×C103—41no—
277C2×D4×C103—41no—
278C2×D4×C103—41no—
279C2×D4×C103—41no—
280C2×D4×C103—41no—
281C2×D4×C103—41no—
282C2×D4×C103C2×D412yes—
283C2×D4×C103C2×D412yes—
284C2×D4×C103C2×D412yes—
285C22×C4×C103—21no—
286C22×C4×C103—21no—
287C22×C4×C103—21no—
288C22×C4×C103—22no—
289C22×C4×C103—22no—
290C22×C4×C103—22no—
291C22×C4×C103—22no—
292C22×C4×C103—22no—
293C22×C4×C103—22no—
294C22×C4×C103—22no—
295C22×C4×C103—41no—
296C22×C4×C103—41no—
297C22×C4×C103—41no—
298C22×C4×C103—41no—
299C22×C4×C103—41no—
300C22×C4×C103—41no—
301C22×C4×C103—41no—
302C22×C4×C103—41no—
303C22×C4×C103—41no—
304C22×C4×C103—41no—
305C22×C4×C103—41no—
306C22×C4×C103—41no—
307C22×C4×C103—41no—
308C22×C4×C103C2×D411yescharacteristic
309C22×C4×C103C2×D411yescharacteristic
310C22×C4×C103C2×D411yescharacteristic
311C22×C4×C103C2×D411yescharacteristic
312C22×C4×C103C2×D411yescharacteristic
313C22×C4×C103C2×D411yescharacteristic
314C22×C4×C103C2×D411yescharacteristic
315C22×C4×C103C2×D411yescharacteristic
316C22×C4×C103C2×D411yescharacteristic
317C22×C4×C103C2×D411yescharacteristic
318C22×C4×C103C2×D411yescharacteristic
319C22×C4×C103#4111yescharacteristic
320C22×C4×C103#4111yescharacteristic
321C22×C4×C103C2411yescharacteristic
322Q16×C103—28no—
323Q16×C103—28no—
324SD16×C103—28no—
325SD16×C103—28no—
326SD16×C103—28no—
327SD16×C103—28no—
328D8×C103—28no—
329D8×C103—28no—
330M16×C103—22no—
331M16×C103—22no—
332M16×C103—22no—
333M16×C103—22no—
334M16×C103—22no—
335M16×C103—22no—
336M16×C103—22no—
337M16×C103C2×D414yes—
338C2×C8×C103—22no—
339C2×C8×C103—22no—
340C2×C8×C103—22no—
341C2×C8×C103—22no—
342C2×C8×C103—22no—
343C2×C8×C103C2×D414yes—
344C4⋊C4×C103—28no—
345C4⋊C4×C103—22no—
346C4⋊C4×C103—22no—
347C4⋊C4×C103—22no—
348C4⋊C4×C103—41no—
349C22⋊C4×C103—28no—
350C22⋊C4×C103—28no—
351C22⋊C4×C103—22no—
352C22⋊C4×C103—22no—
353C22⋊C4×C103—41no—
354C22⋊C4×C103C2×D414yes—
355C42×C103—22no—
356C42×C103—22no—
357C42×C103—22no—
358C42×C103—41no—
359C23×C103—22no—
360C23×C103—22no—
361C23×C103—22no—
362C23×C103—41no—
363C23×C103—41no—
364C23×C103—41no—
365C23×C103—41no—
366C23×C103—41no—
367C23×C103—41no—
368C23×C103—81no—
369C23×C103—82no—
370C23×C103—82no—
371C23×C103—82no—
372C23×C103#12011yescharacteristic
373C23×C103#12011yescharacteristic
374C23×C103#12111yescharacteristic
375C23×C103#12111yescharacteristic
376C23×C103#12711yescharacteristic
377C23×C103#12711yescharacteristic
378C23×C103C22×D411yescharacteristic
379Q8×C103—22no—
380Q8×C103—22no—
381Q8×C103—22no—
382Q8×C103—22no—
383Q8×C103—22no—
384Q8×C103—22no—
385Q8×C103—41no—
386Q8×C103—41no—
387Q8×C103—41no—
388Q8×C103—41no—
389Q8×C103—41no—
390Q8×C103—41no—
391D4×C103—22no—
392D4×C103—22no—
393D4×C103—22no—
394D4×C103—22no—
395D4×C103—22no—
396D4×C103—22no—
397D4×C103—42no—
398D4×C103—42no—
399D4×C103—42no—
400D4×C103—42no—
401D4×C103—42no—
402D4×C103—42no—
403D4×C103—42no—
404D4×C103—42no—
405D4×C103—42no—
406D4×C103—42no—
407D4×C103—42no—
408D4×C103—42no—
409D4×C103—41no—
410D4×C103—41no—
411D4×C103—41no—
412D4×C103—41no—
413D4×C103—41no—
414D4×C103—41no—
415D4×C103—88no—
416C2×C4×C103—24no—
417C2×C4×C103—22no—
418C2×C4×C103—22no—
419C2×C4×C103—22no—
420C2×C4×C103—41no—
421C2×C4×C103—41no—
422C2×C4×C103—41no—
423C2×C4×C103—41no—
424C2×C4×C103—41no—
425C2×C4×C103—41no—
426C2×C4×C103—42no—
427C2×C4×C103—42no—
428C2×C4×C103—42no—
429C2×C4×C103—42no—
430C2×C4×C103—42no—
431C2×C4×C103—42no—
432C2×C4×C103—42no—
433C2×C4×C103—42no—
434C2×C4×C103—42no—
435C2×C4×C103—42no—
436C2×C4×C103—42no—
437C2×C4×C103—42no—
438C2×C4×C103—42no—
439C2×C4×C103—82no—
440C2×C4×C103—82no—
441C2×C4×C103#12011yescharacteristic
442C2×C4×C103#12011yescharacteristic
443C2×C4×C103#12011yescharacteristic
444C2×C4×C103#12011yescharacteristic
445C2×C4×C103#12011yescharacteristic
446C2×C4×C103#12011yescharacteristic
447C2×C4×C103#12011yescharacteristic
448C2×C4×C103#12011yescharacteristic
449C2×C4×C103#12011yescharacteristic
450C2×C4×C103#12011yescharacteristic
451C2×C4×C103#12111yescharacteristic
452C2×C4×C103#12111yescharacteristic
453C2×C4×C103#12111yescharacteristic
454C2×C4×C103#12111yescharacteristic
455C2×C4×C103#12111yescharacteristic
456C2×C4×C103#12111yescharacteristic
457C2×C4×C103#12111yescharacteristic
458C2×C4×C103#12111yescharacteristic
459C2×C4×C103#12111yescharacteristic
460C2×C4×C103#12111yescharacteristic
461C2×C4×C103#12711yescharacteristic
462C2×C4×C103#12711yescharacteristic
463C2×C4×C103C22×D411yescharacteristic
464C2×C4×C103C22×D411yescharacteristic
465C2×C4×C103C22×D411yescharacteristic
466C2×C4×C103C22×D411yescharacteristic
467C2×C4×C103C22×D411yescharacteristic
468C2×C4×C103C2×#4111yescharacteristic
469C8×C103—24no—
470C8×C103—24no—
471C22×C103—41no—
472C22×C103—41no—
473C22×C103—41no—
474C22×C103—41no—
475C22×C103—41no—
476C22×C103—41no—
477C22×C103—41no—
478C22×C103—44no—
479C22×C103—44no—
480C22×C103—42no—
481C22×C103—42no—
482C22×C103—42no—
483C22×C103—82no—
484C22×C103—82no—
485C22×C103—82no—
486C22×C103—82no—
487C22×C103—82no—
488C22×C103—82no—
489C22×C103—82no—
490C22×C103#39211yescharacteristic
491C22×C103#39211yescharacteristic
492C22×C103#39211yescharacteristic
493C22×C103#39211yescharacteristic
494C22×C103C2×#12011yescharacteristic
495C22×C103C2×#12111yescharacteristic
496C22×C103C2×#12711yescharacteristic
497C4×C103—44no—
498C4×C103—42no—
499C4×C103—42no—
500C4×C103—42no—
501C4×C103—82no—
502C4×C103#39211yescharacteristic
503C4×C103#39211yescharacteristic
504C4×C103#39211yescharacteristic
505C4×C103#39211yescharacteristic
506C4×C103C2×#12011yescharacteristic
507C4×C103C2×#12011yescharacteristic
508C4×C103C2×#12111yescharacteristic
509C4×C103C2×#12111yescharacteristic
510#23412C10311yesmaximal, characteristic, direct product factor, Sylow
511C2×C103—21no—
512C2×C103—21no—
513C2×C103—21no—
514C2×C103—21no—
515C2×C103—21no—
516C2×C103—21no—
517C2×C103—21no—
518C2×C103—82no—
519C2×C103—82no—
520C2×C103—82no—
521C2×C103C2×#39211yescharacteristic
522C2×#575C2×C10311yescharacteristic, complemented
523C2×#575C2×C10311yescharacteristic, complemented
524#3449C2×C10311yescharacteristic, complemented
525C2×#421C2×C10311yescharacteristic, complemented
526#2896C2×C10311yescharacteristic, complemented
527C2×#410C2×C10311yescharacteristic, complemented
528#2009C2×C10314yescomplemented
529#2008C2×C10314yescomplemented
530C2×#344C2×C10311yescharacteristic, complemented
531C103#2341211yescharacteristic, direct product factor, Sylow
532C22×#41C22×C10311yescharacteristic
533C22×#41C22×C10311yescharacteristic
534C22×#41C22×C10311yescharacteristic
535#575—22no—
536#575—22no—
537#575—22no—
538#575—22no—
539#575—22no—
540#575—22no—
541#575—22no—
542#575C22×C10314yes—
543C2×#137—21no—
544C2×#137—21no—
545C2×#137—21no—
546C2×#137C22×C10312yescomplemented
547C2×AGL(1,ℤ/8)—21no—
548C2×AGL(1,ℤ/8)—21no—
549C2×AGL(1,ℤ/8)—21no—
550C2×AGL(1,ℤ/8)C22×C10312yescomplemented
551C2×#135—22no—
552C2×#135—22no—
553C22×M16C22×C10311yescharacteristic
554C22×M16C22×C10311yescharacteristic
555#537—22no—
556#536—21no—
557#536C22×C10312yescomplemented
558#535—21no—
559#535C22×C10312yescomplemented
560#534—22no—
561#532—22no—
562#525—22no—
563#525—22no—
564C2×#117C22×C10311yescharacteristic
565C2×#117C22×C10311yescharacteristic
566#421—22no—
567#421C22×C10314yescomplemented
568C2×#104—22no—
569#419C22×C10312yescomplemented
570#418C22×C10312yescomplemented
571#417—22no—
572#416—22no—
573#410—22no—
574#410C22×C10314yescomplemented
575C2×#99—22no—
576#344C22×C10314yescomplemented
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—21no—
584C2×#41—21no—
585C2×#41—21no—
586C2×#41—21no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—21no—
607C2×#41D4×C10312yes—
608C2×#41D4×C10312yes—
609C2×#41D4×C10312yes—
610C2×#41D4×C10312yescomplemented
611C2×#41C23×C10312yes—
612C2×#41C23×C10312yes—
613C22×Q8D4×C10311yescharacteristic
614C22×Q8D4×C10311yescharacteristic, complemented
615C22×Q8C23×C10311yescharacteristic
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4D4×C10311yescharacteristic
620C22×D4D4×C10311yescharacteristic, complemented
621C22×D4C23×C10311yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C10311yescharacteristic
626#137—24no—
627#137—24no—
628#137—24no—
629#137—24no—
630#137—24no—
631#137—24no—
632#137—24no—
633#137—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—24no—
638AGL(1,ℤ/8)—24no—
639AGL(1,ℤ/8)—24no—
640AGL(1,ℤ/8)—24no—
641AGL(1,ℤ/8)—24no—
642#135—28no—
643#135—28no—
644#135—28no—
645#135—28no—
646C2×Q16—22no—
647C2×Q16—22no—
648C2×SD16—22no—
649C2×SD16—22no—
650C2×SD16—22no—
651C2×SD16—22no—
652C2×D8—22no—
653C2×D8—22no—
654C2×M16—21no—
655C2×M16—21no—
656C2×M16—21no—
657C2×M16—21no—
658C2×M16—21no—
659C2×M16—21no—
660C2×M16—21no—
661C2×M16D4×C10312yescomplemented
662C2×M16D4×C10312yescomplemented
663C2×M16D4×C10312yescomplemented
664C2×M16C23×C10312yes—
665C2×M16C23×C10312yes—
666C22×C8—21no—
667C22×C8D4×C10312yescomplemented
668C4⋊Q8—22no—
669#127—22no—
670#124—22no—
671#124—22no—
672#123—24no—
673#123—24no—
674C22⋊Q8—24no—
675C22⋊Q8—24no—
676#121—24no—
677#121—28no—
678#121—24no—
679#120—24no—
680#120—24no—
681C4×D4—28no—
682#117—21no—
683#117—21no—
684#117—21no—
685#117—21no—
686#117—21no—
687#117D4×C10312yes—
688#117C23×C10312yes—
689#117C23×C10312yes—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4D4×C10312yes—
694C2×C42—21no—
695C2×C42—21no—
696#104—28no—
697#103—24no—
698#102—24no—
699#99—28no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24C2×D4×C10311yescharacteristic
704#41—22no—
705#41—22no—
706#41—22no—
707#41—22no—
708#41—22no—
709#41—22no—
710#41—22no—
711#41—22no—
712#41—22no—
713#41—22no—
714#41—22no—
715#41—22no—
716#41—22no—
717#41—22no—
718#41—22no—
719#41—22no—
720#41—22no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—22no—
726#41—22no—
727#41—22no—
728#41—41no—
729#41—41no—
730#41—41no—
731#41—41no—
732#41—41no—
733#41—41no—
734#41—41no—
735#41—41no—
736#41—41no—
737#41—41no—
738#41—41no—
739#41—41no—
740#41—41no—
741#41—41no—
742#41—41no—
743#41—41no—
744#41—41no—
745#41—41no—
746#41—41no—
747#41—41no—
748#41—41no—
749#41—41no—
750#41—41no—
751#41—41no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8C2×D4×C10312yes—
768C2×Q8C2×D4×C10312yes—
769C2×Q8C2×D4×C10312yes—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—28no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—41no—
793C2×D4—41no—
794C2×D4—41no—
795C2×D4—41no—
796C2×D4—41no—
797C2×D4—41no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C2×D4—41no—
802C2×D4—41no—
803C2×D4—41no—
804C2×D4C2×D4×C10312yes—
805C2×D4C2×D4×C10312yes—
806C2×D4C2×D4×C10312yes—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4C2×D4×C10311yescharacteristic
831C22×C4C2×D4×C10311yescharacteristic
832C22×C4C2×D4×C10311yescharacteristic
833C22×C4C2×D4×C10311yescharacteristic
834C22×C4C2×D4×C10311yescharacteristic
835C22×C4C2×D4×C10311yescharacteristic
836C22×C4C2×D4×C10311yescharacteristic
837C22×C4C2×D4×C10311yescharacteristic
838C22×C4C2×D4×C10311yescharacteristic
839C22×C4C2×D4×C10311yescharacteristic
840C22×C4C2×D4×C10311yescharacteristic
841C22×C4#41×C10311yescharacteristic
842C22×C4#41×C10311yescharacteristic
843C22×C4C24×C10311yescharacteristic
844Q16—28no—
845Q16—28no—
846SD16—28no—
847SD16—28no—
848SD16—28no—
849SD16—28no—
850D8—28no—
851D8—28no—
852M16—22no—
853M16—22no—
854M16—22no—
855M16—22no—
856M16—22no—
857M16—22no—
858M16—22no—
859M16C2×D4×C10314yes—
860C2×C8—22no—
861C2×C8—22no—
862C2×C8—22no—
863C2×C8—22no—
864C2×C8—22no—
865C2×C8C2×D4×C10314yes—
866C4⋊C4—28no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—41no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—41no—
876C22⋊C4C2×D4×C10314yes—
877C42—22no—
878C42—22no—
879C42—22no—
880C42—41no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—81no—
891C23—82no—
892C23—82no—
893C23—82no—
894C23#120×C10311yescharacteristic
895C23#120×C10311yescharacteristic
896C23#121×C10311yescharacteristic
897C23#121×C10311yescharacteristic
898C23#127×C10311yescharacteristic
899C23#127×C10311yescharacteristic
900C23C22×D4×C10311yescharacteristic
901Q8—22no—
902Q8—22no—
903Q8—22no—
904Q8—22no—
905Q8—22no—
906Q8—22no—
907Q8—41no—
908Q8—41no—
909Q8—41no—
910Q8—41no—
911Q8—41no—
912Q8—41no—
913D4—22no—
914D4—22no—
915D4—22no—
916D4—22no—
917D4—22no—
918D4—22no—
919D4—42no—
920D4—42no—
921D4—42no—
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—41no—
936D4—41no—
937D4—88no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4#120×C10311yescharacteristic
964C2×C4#120×C10311yescharacteristic
965C2×C4#120×C10311yescharacteristic
966C2×C4#120×C10311yescharacteristic
967C2×C4#120×C10311yescharacteristic
968C2×C4#120×C10311yescharacteristic
969C2×C4#120×C10311yescharacteristic
970C2×C4#120×C10311yescharacteristic
971C2×C4#120×C10311yescharacteristic
972C2×C4#120×C10311yescharacteristic
973C2×C4#121×C10311yescharacteristic
974C2×C4#121×C10311yescharacteristic
975C2×C4#121×C10311yescharacteristic
976C2×C4#121×C10311yescharacteristic
977C2×C4#121×C10311yescharacteristic
978C2×C4#121×C10311yescharacteristic
979C2×C4#121×C10311yescharacteristic
980C2×C4#121×C10311yescharacteristic
981C2×C4#121×C10311yescharacteristic
982C2×C4#121×C10311yescharacteristic
983C2×C4#127×C10311yescharacteristic
984C2×C4#127×C10311yescharacteristic
985C2×C4C22×D4×C10311yescharacteristic
986C2×C4C22×D4×C10311yescharacteristic
987C2×C4C22×D4×C10311yescharacteristic
988C2×C4C22×D4×C10311yescharacteristic
989C2×C4C22×D4×C10311yescharacteristic
990C2×C4C2×#41×C10311yescharacteristic
991C8—24no—
992C8—24no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
1010C22—82no—
1011C22—82no—
1012C22#392×C10311yescharacteristic
1013C22#392×C10311yescharacteristic
1014C22#392×C10311yescharacteristic
1015C22#392×C10311yescharacteristic
1016C22C2×#120×C10311yescharacteristic
1017C22C2×#121×C10311yescharacteristic
1018C22C2×#127×C10311yescharacteristic
1019C4—44no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—82no—
1024C4#392×C10311yescharacteristic
1025C4#392×C10311yescharacteristic
1026C4#392×C10311yescharacteristic
1027C4#392×C10311yescharacteristic
1028C4C2×#120×C10311yescharacteristic
1029C4C2×#120×C10311yescharacteristic
1030C4C2×#121×C10311yescharacteristic
1031C4C2×#121×C10311yescharacteristic
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—21no—
1037C2—21no—
1038C2—21no—
1039C2—82no—
1040C2—82no—
1041C2—82no—
1042C2C2×#392×C10311yescharacteristic
subgroupG/H
centerC4×C103#392
commutator, Frattini, cosocleC22×C4C24×C103
socleC2×C103C2×#392
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#575×C103C2semidirect
2. C2×#575×C103C2semidirect
3. C103×#3449C2semidirect
4. C2×#421×C103C2semidirect
5. C103×#2896C2semidirect
6. C2×#410×C103C2semidirect
7. C103×#2009C2semidirect
8. C103×#2008C2semidirect
9. C2×#344×C103C2semidirect
24. C2×#137×C103C22semidirect
28. C2×AGL(1,ℤ/8)×C103C22semidirect
35. #536×C103C22semidirect
37. #535×C103C22semidirect
45. #421×C103C22semidirect
47. #419×C103C22semidirect
48. #418×C103C22semidirect
52. #410×C103C22semidirect
54. #344×C103C22semidirect
88. C2×#41×C103D4semidirect
92. C22×Q8×C103D4semidirect
98. C22×D4×C103D4semidirect
139. C2×M16×C103D4semidirect
140. C2×M16×C103D4semidirect
141. C2×M16×C103D4semidirect
145. C22×C8×C103D4semidirect
510. #23412C103direct (N × H)
522. C2×#575C2×C103semidirect
523. C2×#575C2×C103semidirect
524. #3449C2×C103semidirect
525. C2×#421C2×C103semidirect
526. #2896C2×C103semidirect
527. C2×#410C2×C103semidirect
528. #2009C2×C103semidirect
529. #2008C2×C103semidirect
530. C2×#344C2×C103semidirect
531. C103#23412direct (N × H)
546. C2×#137C22×C103semidirect
550. C2×AGL(1,ℤ/8)C22×C103semidirect
557. #536C22×C103semidirect
559. #535C22×C103semidirect
567. #421C22×C103semidirect
569. #419C22×C103semidirect
570. #418C22×C103semidirect
574. #410C22×C103semidirect
576. #344C22×C103semidirect
610. C2×#41D4×C103semidirect
614. C22×Q8D4×C103semidirect
620. C22×D4D4×C103semidirect
661. C2×M16D4×C103semidirect
662. C2×M16D4×C103semidirect
663. C2×M16D4×C103semidirect
667. C22×C8D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1032
C103×#34492
C2×#421×C1032
C103×#28962
C2×#410×C1032
C103×#20092
C103×#20082
C2×#344×C1032
#23412103