Finite Group Databasebeta

← C103×#23894 #39929169

Subgroups — C103×#23894 #39929169

Order 26368.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3586C211yesmaximal, characteristic, complemented
2C103×#3585C211yesmaximal, characteristic, complemented
3C103×#3020C211yesmaximal, characteristic, complemented
4C103×#3019C211yesmaximal, characteristic, complemented
5C103×#3010C211yesmaximal, characteristic, complemented
6C103×#3009C211yesmaximal, characteristic, complemented
7C103×#2019C211yesmaximal, characteristic, complemented
8C103×#2017C211yesmaximal, characteristic, complemented
9C103×#2009C211yesmaximal, characteristic, complemented
10C103×#2008C211yesmaximal, characteristic, complemented
11C103×#1903C211yesmaximal, characteristic, complemented
12C103×#1902C211yesmaximal, characteristic, complemented
13C103×#1881C211yesmaximal, characteristic, complemented
14C103×#1881C211yesmaximal, characteristic, complemented
15C103×#1794C211yesmaximal, characteristic, complemented
16#585×C103C2211yescharacteristic
17C2×2−1+4×C103C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C103C2211yescharacteristic
19#578×C103—22no—
20#578×C103—22no—
21#577×C103—22no—
22#577×C103—22no—
23#577×C103—22no—
24#577×C103—22no—
25#576×C103—22no—
26#576×C103—22no—
27#575×C103—22no—
28#575×C103—22no—
29#575×C103C2211yescharacteristic
30#575×C103C2211yescharacteristic
31#575×C103C2211yescharacteristic
32#575×C103C2211yescharacteristic, complemented
33#575×C103C2211yescharacteristic, complemented
34C2×#137×C103—22no—
35C2×#137×C103C2211yescharacteristic
36C2×#137×C103C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C103—22no—
38C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
39C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
40C22×SD16×C103C2211yescharacteristic, complemented
41#568×C103C2211yescharacteristic
42#568×C103C2211yescharacteristic, complemented
43#536×C103C2211yescharacteristic, complemented
44#535×C103C2211yescharacteristic, complemented
45#456×C103—22no—
46#455×C103—22no—
47#454×C103—22no—
48#453×C103—22no—
49#452×C103—22no—
50#450×C103—22no—
51#449×C103—22no—
52#448×C103—22no—
53#421×C103C2211yescharacteristic
54#421×C103C2211yescharacteristic, complemented
55#421×C103C2211yescharacteristic, complemented
56#421×C103C2211yescharacteristic, complemented
57#419×C103C2211yescharacteristic, complemented
58#418×C103C2211yescharacteristic, complemented
59#416×C103C2211yescharacteristic
60#416×C103C2211yescharacteristic, complemented
61C2×#101×C103C2211yescharacteristic, complemented
62C2×#100×C103C2211yescharacteristic, complemented
63#410×C103C2211yescharacteristic, complemented
64#408×C103C2211yescharacteristic, complemented
65#408×C103C2211yescharacteristic, complemented
66#408×C103C2211yescharacteristic, complemented
67#344×C103C2211yescharacteristic, complemented
68#344×C103C2211yescharacteristic, complemented
69#341×C103C2211yescharacteristic, complemented
70#338×C103C2211yescharacteristic, complemented
712−1+4×C103—22no—
722−1+4×C103—21no—
732−1+4×C103—22no—
742−1+4×C103—21no—
752−1+4×C103—22no—
762−1+4×C103—41no—
772−1+4×C103D412yescomplemented
78H(5,𝔽2)×C103—22no—
79H(5,𝔽2)×C103—21no—
80H(5,𝔽2)×C103—22no—
81H(5,𝔽2)×C103—21no—
82H(5,𝔽2)×C103—22no—
83H(5,𝔽2)×C103—41no—
84H(5,𝔽2)×C103—41no—
85H(5,𝔽2)×C103D412yescomplemented
86C2×#41×C103—22no—
87C2×#41×C103—22no—
88C2×#41×C103—21no—
89C2×#41×C103—21no—
90C2×#41×C103—21no—
91C2×#41×C103—21no—
92C2×#41×C103—41no—
93C2×#41×C103—41no—
94C2×#41×C103C2311yescharacteristic
95C2×#41×C103C2311yescharacteristic
96C2×#41×C103C2311yescharacteristic
97C2×#41×C103C2311yescharacteristic
98C2×#41×C103C2311yescharacteristic
99C22×Q8×C103—21no—
100C22×Q8×C103—21no—
101C22×Q8×C103C2311yescharacteristic
102C22×D4×C103—21no—
103C22×D4×C103—21no—
104C22×D4×C103—41no—
105C22×D4×C103C2311yescharacteristic
106#137×C103—24no—
107#137×C103—24no—
108#137×C103—24no—
109#137×C103—24no—
110#137×C103—22no—
111#137×C103—22no—
112#137×C103—21no—
113#137×C103—22no—
114#137×C103—21no—
115#137×C103—21no—
116#137×C103—21no—
117#137×C103—21no—
118#137×C103—21no—
119#137×C103—21no—
120#137×C103—21no—
121#137×C103—22no—
122#137×C103D412yes—
123#137×C103D412yescomplemented
124AGL(1,ℤ/8)×C103—24no—
125AGL(1,ℤ/8)×C103—24no—
126AGL(1,ℤ/8)×C103—24no—
127AGL(1,ℤ/8)×C103—24no—
128AGL(1,ℤ/8)×C103—22no—
129AGL(1,ℤ/8)×C103—22no—
130AGL(1,ℤ/8)×C103—21no—
131AGL(1,ℤ/8)×C103—22no—
132AGL(1,ℤ/8)×C103—21no—
133AGL(1,ℤ/8)×C103—21no—
134AGL(1,ℤ/8)×C103—21no—
135AGL(1,ℤ/8)×C103—21no—
136AGL(1,ℤ/8)×C103—21no—
137AGL(1,ℤ/8)×C103—21no—
138AGL(1,ℤ/8)×C103—21no—
139AGL(1,ℤ/8)×C103—22no—
140AGL(1,ℤ/8)×C103D412yes—
141AGL(1,ℤ/8)×C103D412yescomplemented
142#135×C103—24no—
143#135×C103—24no—
144#135×C103—24no—
145#135×C103—24no—
146#135×C103—22no—
147#135×C103—22no—
148#135×C103—22no—
149#135×C103—22no—
150#135×C103—41no—
151C2×Q16×C103—24no—
152C2×Q16×C103—21no—
153C2×Q16×C103D412yescomplemented
154C2×SD16×C103—24no—
155C2×SD16×C103—24no—
156C2×SD16×C103—21no—
157C2×SD16×C103—21no—
158C2×SD16×C103—22no—
159C2×SD16×C103—22no—
160C2×SD16×C103—41no—
161C2×SD16×C103D412yes—
162C2×SD16×C103D412yescomplemented
163C2×D8×C103—24no—
164C2×D8×C103—21no—
165C2×D8×C103D412yes—
166#131×C103—22no—
167#131×C103—22no—
168#131×C103—22no—
169#131×C103—22no—
170C2×M16×C103—22no—
171C2×M16×C103—22no—
172C2×M16×C103C2311yescharacteristic
173C2×M16×C103C2311yescharacteristic
174C2×M16×C103C2311yescharacteristic
175C2×M16×C103C2311yescharacteristic
176C2×M16×C103C2311yescharacteristic
177C22×C8×C103C2311yescharacteristic
178C4⋊Q8×C103—21no—
179#127×C103—21no—
180#124×C103—21no—
181#124×C103—21no—
182#123×C103—41no—
183C22⋊Q8×C103—22no—
184#121×C103—22no—
185#120×C103—41no—
186#117×C103C2311yescharacteristic
187#117×C103C2311yescharacteristic
188#104×C103—22no—
189#104×C103—22no—
190#104×C103—22no—
191#104×C103—22no—
192#103×C103—21no—
193#103×C103—21no—
194#103×C103—22no—
195#102×C103—21no—
196#102×C103—21no—
197#102×C103—22no—
198#101×C103—22no—
199#100×C103—22no—
200#99×C103—41no—
201C22⋊C8×C103—22no—
202C22⋊C8×C103—22no—
203C22⋊C8×C103—41no—
204C24×C103—21no—
205C24×C103—41no—
206#41×C103—21no—
207#41×C103—21no—
208#41×C103—21no—
209#41×C103—21no—
210#41×C103—24no—
211#41×C103—24no—
212#41×C103—22no—
213#41×C103—22no—
214#41×C103—22no—
215#41×C103—22no—
216#41×C103—21no—
217#41×C103—21no—
218#41×C103—21no—
219#41×C103—21no—
220#41×C103—21no—
221#41×C103—21no—
222#41×C103—21no—
223#41×C103—21no—
224#41×C103—21no—
225#41×C103—21no—
226#41×C103—21no—
227#41×C103—21no—
228#41×C103—42no—
229#41×C103—42no—
230#41×C103—42no—
231#41×C103—42no—
232#41×C103—42no—
233#41×C103—44no—
234#41×C103—42no—
235#41×C103—42no—
236#41×C103—42no—
237#41×C103—41no—
238#41×C103—41no—
239#41×C103—44no—
240#41×C103—42no—
241#41×C103—42no—
242#41×C103C2×D412yes—
243#41×C103C2×D412yes—
244#41×C103C2×D412yes—
245#41×C103C2×D412yes—
246C2×Q8×C103—21no—
247C2×Q8×C103—24no—
248C2×Q8×C103—22no—
249C2×Q8×C103—22no—
250C2×Q8×C103—21no—
251C2×Q8×C103—21no—
252C2×Q8×C103—21no—
253C2×Q8×C103—21no—
254C2×Q8×C103—41no—
255C2×Q8×C103—42no—
256C2×Q8×C103—42no—
257C2×Q8×C103—41no—
258C2×Q8×C103—42no—
259C2×Q8×C103C2×D412yes—
260C2×Q8×C103C2×D411yescharacteristic
261C2×Q8×C103C2×D411yescharacteristic
262C2×Q8×C103C2×D411yescharacteristic
263C2×Q8×C103C2×D411yescharacteristic
264C2×Q8×C103C2×D411yescharacteristic
265C2×D4×C103—21no—
266C2×D4×C103—21no—
267C2×D4×C103—24no—
268C2×D4×C103—22no—
269C2×D4×C103—22no—
270C2×D4×C103—21no—
271C2×D4×C103—21no—
272C2×D4×C103—21no—
273C2×D4×C103—21no—
274C2×D4×C103—21no—
275C2×D4×C103—21no—
276C2×D4×C103—21no—
277C2×D4×C103—21no—
278C2×D4×C103—42no—
279C2×D4×C103—41no—
280C2×D4×C103—41no—
281C2×D4×C103—42no—
282C2×D4×C103—42no—
283C2×D4×C103—41no—
284C2×D4×C103—44no—
285C2×D4×C103—42no—
286C2×D4×C103—42no—
287C2×D4×C103—44no—
288C2×D4×C103—41no—
289C2×D4×C103—42no—
290C2×D4×C103—42no—
291C2×D4×C103C2×D412yes—
292C2×D4×C103C2×D411yescharacteristic
293C2×D4×C103C2×D411yescharacteristic
294C2×D4×C103C2×D411yescharacteristic
295C2×D4×C103C2×D411yescharacteristic
296C2×D4×C103C2×D411yescharacteristic
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—41no—
304C22×C4×C103—42no—
305C22×C4×C103—41no—
306C22×C4×C103—41no—
307C22×C4×C103C2411yescharacteristic
308Q16×C103—24no—
309Q16×C103—22no—
310Q16×C103—22no—
311Q16×C103—22no—
312Q16×C103—24no—
313Q16×C103—22no—
314Q16×C103—41no—
315SD16×C103—24no—
316SD16×C103—22no—
317SD16×C103—24no—
318SD16×C103—22no—
319SD16×C103—22no—
320SD16×C103—22no—
321SD16×C103—22no—
322SD16×C103—24no—
323SD16×C103—22no—
324SD16×C103—22no—
325SD16×C103—24no—
326SD16×C103—22no—
327SD16×C103—44no—
328SD16×C103—41no—
329SD16×C103—41no—
330D8×C103—24no—
331D8×C103—22no—
332D8×C103—22no—
333D8×C103—22no—
334D8×C103—24no—
335D8×C103—22no—
336D8×C103—41no—
337M16×C103—24no—
338M16×C103—24no—
339M16×C103—21no—
340M16×C103—21no—
341M16×C103—21no—
342M16×C103—21no—
343M16×C103—21no—
344M16×C103—21no—
345M16×C103—21no—
346M16×C103—21no—
347M16×C103C2×D412yes—
348M16×C103C2×D412yes—
349C2×C8×C103—24no—
350C2×C8×C103—24no—
351C2×C8×C103—21no—
352C2×C8×C103—21no—
353C2×C8×C103—21no—
354C2×C8×C103—21no—
355C2×C8×C103—21no—
356C2×C8×C103—21no—
357C2×C8×C103C2×D412yes—
358C2×C8×C103C2×D412yes—
359C4⋊C4×C103—21no—
360C4⋊C4×C103—21no—
361C4⋊C4×C103—42no—
362C22⋊C4×C103—21no—
363C22⋊C4×C103—21no—
364C22⋊C4×C103—42no—
365C22⋊C4×C103—42no—
366C42×C103—21no—
367C42×C103—21no—
368C23×C103—21no—
369C23×C103—21no—
370C23×C103—21no—
371C23×C103—21no—
372C23×C103—21no—
373C23×C103—22no—
374C23×C103—42no—
375C23×C103—44no—
376C23×C103—41no—
377C23×C103—41no—
378C23×C103—161no—
379C23×C103—162no—
380C23×C103H(5,𝔽2)11yescharacteristic
381Q8×C103—21no—
382Q8×C103—21no—
383Q8×C103—21no—
384Q8×C103—21no—
385Q8×C103—22no—
386Q8×C103—21no—
387Q8×C103—21no—
388Q8×C103—22no—
389Q8×C103—21no—
390Q8×C103—21no—
391Q8×C103—42no—
392Q8×C103—44no—
393Q8×C103—41no—
394Q8×C103—41no—
395Q8×C103#12012yes—
396Q8×C103#12012yes—
397D4×C103—22no—
398D4×C103—22no—
399D4×C103—22no—
400D4×C103—22no—
401D4×C103—21no—
402D4×C103—21no—
403D4×C103—22no—
404D4×C103—21no—
405D4×C103—21no—
406D4×C103—21no—
407D4×C103—21no—
408D4×C103—21no—
409D4×C103—21no—
410D4×C103—22no—
411D4×C103—42no—
412D4×C103—42no—
413D4×C103—44no—
414D4×C103—42no—
415D4×C103—44no—
416D4×C103—44no—
417D4×C103—41no—
418D4×C103—41no—
419D4×C103—41no—
420D4×C103—41no—
421D4×C103—41no—
422D4×C103—41no—
423D4×C103—41no—
424D4×C103—41no—
425D4×C103—162no—
426D4×C103#12012yes—
427D4×C103#12012yes—
428C2×C4×C103—21no—
429C2×C4×C103—21no—
430C2×C4×C103—22no—
431C2×C4×C103—22no—
432C2×C4×C103—22no—
433C2×C4×C103—22no—
434C2×C4×C103—21no—
435C2×C4×C103—21no—
436C2×C4×C103—22no—
437C2×C4×C103—21no—
438C2×C4×C103—42no—
439C2×C4×C103—42no—
440C2×C4×C103—42no—
441C2×C4×C103—44no—
442C2×C4×C103—44no—
443C2×C4×C103—44no—
444C2×C4×C103—41no—
445C2×C4×C103—41no—
446C2×C4×C103—41no—
447C2×C4×C103—41no—
448C2×C4×C103—41no—
449C2×C4×C103—41no—
450C2×C4×C103—41no—
451C2×C4×C103—41no—
452C2×C4×C103—41no—
453C2×C4×C103—41no—
454C2×C4×C103C22×D411yescharacteristic
455C2×C4×C103C22×D411yescharacteristic
456C2×C4×C103C22×D411yescharacteristic
457C2×C4×C103C22×D411yescharacteristic
458C2×C4×C103C22×D411yescharacteristic
459C2×C4×C103H(5,𝔽2)11yescharacteristic
460C8×C103—22no—
461C8×C103—22no—
462C8×C103—22no—
463C8×C103—22no—
464C8×C103—41no—
465C8×C103—41no—
466C22×C103—22no—
467C22×C103—22no—
468C22×C103—41no—
469C22×C103—42no—
470C22×C103—42no—
471C22×C103—41no—
472C22×C103—41no—
473C22×C103—41no—
474C22×C103—42no—
475C22×C103—81no—
476C22×C103—81no—
477C22×C103—82no—
478C22×C103—81no—
479C22×C103—82no—
480C22×C103—161no—
481C22×C103—162no—
482C22×C103—164no—
483C22×C103#53411yescharacteristic
484C22×C103D4211yescharacteristic
485C22×C103D4211yescharacteristic
486C4×C103—22no—
487C4×C103—22no—
488C4×C103—41no—
489C4×C103—41no—
490C4×C103—41no—
491C4×C103—42no—
492C4×C103—81no—
493C4×C103—81no—
494C4×C103C2×#12011yescharacteristic
495C4×C103C2×#12011yescharacteristic
496C4×C103D4211yescharacteristic
497C4×C103D4211yescharacteristic
498#23894C10311yesmaximal, characteristic, direct product factor, Sylow
499C2×C103—21no—
500C2×C103—21no—
501C2×C103—21no—
502C2×C103—42no—
503C2×C103—42no—
504C2×C103—81no—
505C2×C103—81no—
506C2×C103—82no—
507C2×C103—81no—
508C2×C103#240311yescharacteristic
509#3586C2×C10311yescharacteristic, complemented
510#3585C2×C10311yescharacteristic, complemented
511#3020C2×C10311yescharacteristic, complemented
512#3019C2×C10311yescharacteristic, complemented
513#3010C2×C10311yescharacteristic, complemented
514#3009C2×C10311yescharacteristic, complemented
515#2019C2×C10311yescharacteristic, complemented
516#2017C2×C10311yescharacteristic, complemented
517#2009C2×C10311yescharacteristic, complemented
518#2008C2×C10311yescharacteristic, complemented
519#1903C2×C10311yescharacteristic, complemented
520#1902C2×C10311yescharacteristic, complemented
521#1881C2×C10311yescharacteristic, complemented
522#1881C2×C10311yescharacteristic, complemented
523#1794C2×C10311yescharacteristic, complemented
524C103#2389411yescharacteristic, direct product factor, Sylow
525#585C22×C10311yescharacteristic
526C2×2−1+4C22×C10311yescharacteristic, complemented
527C2×H(5,𝔽2)C22×C10311yescharacteristic
528#578—22no—
529#578—22no—
530#577—22no—
531#577—22no—
532#577—22no—
533#577—22no—
534#576—22no—
535#576—22no—
536#575—22no—
537#575—22no—
538#575C22×C10311yescharacteristic
539#575C22×C10311yescharacteristic
540#575C22×C10311yescharacteristic
541#575C22×C10311yescharacteristic, complemented
542#575C22×C10311yescharacteristic, complemented
543C2×#137—22no—
544C2×#137C22×C10311yescharacteristic
545C2×#137C22×C10311yescharacteristic, complemented
546C2×AGL(1,ℤ/8)—22no—
547C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
548C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
549C22×SD16C22×C10311yescharacteristic, complemented
550#568C22×C10311yescharacteristic
551#568C22×C10311yescharacteristic, complemented
552#536C22×C10311yescharacteristic, complemented
553#535C22×C10311yescharacteristic, complemented
554#456—22no—
555#455—22no—
556#454—22no—
557#453—22no—
558#452—22no—
559#450—22no—
560#449—22no—
561#448—22no—
562#421C22×C10311yescharacteristic
563#421C22×C10311yescharacteristic, complemented
564#421C22×C10311yescharacteristic, complemented
565#421C22×C10311yescharacteristic, complemented
566#419C22×C10311yescharacteristic, complemented
567#418C22×C10311yescharacteristic, complemented
568#416C22×C10311yescharacteristic
569#416C22×C10311yescharacteristic, complemented
570C2×#101C22×C10311yescharacteristic, complemented
571C2×#100C22×C10311yescharacteristic, complemented
572#410C22×C10311yescharacteristic, complemented
573#408C22×C10311yescharacteristic, complemented
574#408C22×C10311yescharacteristic, complemented
575#408C22×C10311yescharacteristic, complemented
576#344C22×C10311yescharacteristic, complemented
577#344C22×C10311yescharacteristic, complemented
578#341C22×C10311yescharacteristic, complemented
579#338C22×C10311yescharacteristic, complemented
5802−1+4—22no—
5812−1+4—21no—
5822−1+4—22no—
5832−1+4—21no—
5842−1+4—22no—
5852−1+4—41no—
5862−1+4D4×C10312yescomplemented
587H(5,𝔽2)—22no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—22no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—41no—
593H(5,𝔽2)—41no—
594H(5,𝔽2)D4×C10312yescomplemented
595C2×#41—22no—
596C2×#41—22no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—41no—
602C2×#41—41no—
603C2×#41C23×C10311yescharacteristic
604C2×#41C23×C10311yescharacteristic
605C2×#41C23×C10311yescharacteristic
606C2×#41C23×C10311yescharacteristic
607C2×#41C23×C10311yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C10311yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—41no—
614C22×D4C23×C10311yescharacteristic
615#137—24no—
616#137—24no—
617#137—24no—
618#137—24no—
619#137—22no—
620#137—22no—
621#137—21no—
622#137—22no—
623#137—21no—
624#137—21no—
625#137—21no—
626#137—21no—
627#137—21no—
628#137—21no—
629#137—21no—
630#137—22no—
631#137D4×C10312yes—
632#137D4×C10312yescomplemented
633AGL(1,ℤ/8)—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—21no—
640AGL(1,ℤ/8)—22no—
641AGL(1,ℤ/8)—21no—
642AGL(1,ℤ/8)—21no—
643AGL(1,ℤ/8)—21no—
644AGL(1,ℤ/8)—21no—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—21no—
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)D4×C10312yes—
650AGL(1,ℤ/8)D4×C10312yescomplemented
651#135—24no—
652#135—24no—
653#135—24no—
654#135—24no—
655#135—22no—
656#135—22no—
657#135—22no—
658#135—22no—
659#135—41no—
660C2×Q16—24no—
661C2×Q16—21no—
662C2×Q16D4×C10312yescomplemented
663C2×SD16—24no—
664C2×SD16—24no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—41no—
670C2×SD16D4×C10312yes—
671C2×SD16D4×C10312yescomplemented
672C2×D8—24no—
673C2×D8—21no—
674C2×D8D4×C10312yes—
675#131—22no—
676#131—22no—
677#131—22no—
678#131—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16C23×C10311yescharacteristic
682C2×M16C23×C10311yescharacteristic
683C2×M16C23×C10311yescharacteristic
684C2×M16C23×C10311yescharacteristic
685C2×M16C23×C10311yescharacteristic
686C22×C8C23×C10311yescharacteristic
687C4⋊Q8—21no—
688#127—21no—
689#124—21no—
690#124—21no—
691#123—41no—
692C22⋊Q8—22no—
693#121—22no—
694#120—41no—
695#117C23×C10311yescharacteristic
696#117C23×C10311yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—22no—
704#102—21no—
705#102—21no—
706#102—22no—
707#101—22no—
708#100—22no—
709#99—41no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—41no—
713C24—21no—
714C24—41no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—24no—
720#41—24no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—41no—
747#41—41no—
748#41—44no—
749#41—42no—
750#41—42no—
751#41C2×D4×C10312yes—
752#41C2×D4×C10312yes—
753#41C2×D4×C10312yes—
754#41C2×D4×C10312yes—
755C2×Q8—21no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8C2×D4×C10312yes—
769C2×Q8C2×D4×C10311yescharacteristic
770C2×Q8C2×D4×C10311yescharacteristic
771C2×Q8C2×D4×C10311yescharacteristic
772C2×Q8C2×D4×C10311yescharacteristic
773C2×Q8C2×D4×C10311yescharacteristic
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
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—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C2×D4×C10312yes—
801C2×D4C2×D4×C10311yescharacteristic
802C2×D4C2×D4×C10311yescharacteristic
803C2×D4C2×D4×C10311yescharacteristic
804C2×D4C2×D4×C10311yescharacteristic
805C2×D4C2×D4×C10311yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4C24×C10311yescharacteristic
817Q16—24no—
818Q16—22no—
819Q16—22no—
820Q16—22no—
821Q16—24no—
822Q16—22no—
823Q16—41no—
824SD16—24no—
825SD16—22no—
826SD16—24no—
827SD16—22no—
828SD16—22no—
829SD16—22no—
830SD16—22no—
831SD16—24no—
832SD16—22no—
833SD16—22no—
834SD16—24no—
835SD16—22no—
836SD16—44no—
837SD16—41no—
838SD16—41no—
839D8—24no—
840D8—22no—
841D8—22no—
842D8—22no—
843D8—24no—
844D8—22no—
845D8—41no—
846M16—24no—
847M16—24no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16C2×D4×C10312yes—
857M16C2×D4×C10312yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×D4×C10312yes—
867C2×C8C2×D4×C10312yes—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—42no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C42—21no—
876C42—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—42no—
884C23—44no—
885C23—41no—
886C23—41no—
887C23—161no—
888C23—162no—
889C23H(5,𝔽2)×C10311yescharacteristic
890Q8—21no—
891Q8—21no—
892Q8—21no—
893Q8—21no—
894Q8—22no—
895Q8—21no—
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—21no—
900Q8—42no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C10312yes—
905Q8#120×C10312yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—21no—
911D4—21no—
912D4—22no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—21no—
919D4—22no—
920D4—42no—
921D4—42no—
922D4—44no—
923D4—42no—
924D4—44no—
925D4—44no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—162no—
935D4#120×C10312yes—
936D4#120×C10312yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C22×D4×C10311yescharacteristic
964C2×C4C22×D4×C10311yescharacteristic
965C2×C4C22×D4×C10311yescharacteristic
966C2×C4C22×D4×C10311yescharacteristic
967C2×C4C22×D4×C10311yescharacteristic
968C2×C4H(5,𝔽2)×C10311yescharacteristic
969C8—22no—
970C8—22no—
971C8—22no—
972C8—22no—
973C8—41no—
974C8—41no—
975C22—22no—
976C22—22no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22—81no—
988C22—82no—
989C22—161no—
990C22—162no—
991C22—164no—
992C22#534×C10311yescharacteristic
993C22D42×C10311yescharacteristic
994C22D42×C10311yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C10311yescharacteristic
1004C4C2×#120×C10311yescharacteristic
1005C4D42×C10311yescharacteristic
1006C4D42×C10311yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2C103×#240311yescharacteristic
subgroupG/H
center, socleC2×C103#2403
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3586C2semidirect
2. C103×#3585C2semidirect
3. C103×#3020C2semidirect
4. C103×#3019C2semidirect
5. C103×#3010C2semidirect
6. C103×#3009C2semidirect
7. C103×#2019C2semidirect
8. C103×#2017C2semidirect
9. C103×#2009C2semidirect
10. C103×#2008C2semidirect
11. C103×#1903C2semidirect
12. C103×#1902C2semidirect
13. C103×#1881C2semidirect
14. C103×#1881C2semidirect
15. C103×#1794C2semidirect
17. C2×2−1+4×C103C22semidirect
32. #575×C103C22semidirect
33. #575×C103C22semidirect
36. C2×#137×C103C22semidirect
40. C22×SD16×C103C22semidirect
42. #568×C103C22semidirect
43. #536×C103C22semidirect
44. #535×C103C22semidirect
54. #421×C103C22semidirect
55. #421×C103C22semidirect
56. #421×C103C22semidirect
57. #419×C103C22semidirect
58. #418×C103C22semidirect
60. #416×C103C22semidirect
61. C2×#101×C103C22semidirect
62. C2×#100×C103C22semidirect
63. #410×C103C22semidirect
64. #408×C103C22semidirect
65. #408×C103C22semidirect
66. #408×C103C22semidirect
67. #344×C103C22semidirect
68. #344×C103C22semidirect
69. #341×C103C22semidirect
70. #338×C103C22semidirect
77. 2−1+4×C103D4semidirect
85. H(5,𝔽2)×C103D4semidirect
123. #137×C103D4semidirect
141. AGL(1,ℤ/8)×C103D4semidirect
153. C2×Q16×C103D4semidirect
162. C2×SD16×C103D4semidirect
498. #23894C103direct (N × H)
509. #3586C2×C103semidirect
510. #3585C2×C103semidirect
511. #3020C2×C103semidirect
512. #3019C2×C103semidirect
513. #3010C2×C103semidirect
514. #3009C2×C103semidirect
515. #2019C2×C103semidirect
516. #2017C2×C103semidirect
517. #2009C2×C103semidirect
518. #2008C2×C103semidirect
519. #1903C2×C103semidirect
520. #1902C2×C103semidirect
521. #1881C2×C103semidirect
522. #1881C2×C103semidirect
523. #1794C2×C103semidirect
524. C103#23894direct (N × H)
526. C2×2−1+4C22×C103semidirect
541. #575C22×C103semidirect
542. #575C22×C103semidirect
545. C2×#137C22×C103semidirect
549. C22×SD16C22×C103semidirect
551. #568C22×C103semidirect
552. #536C22×C103semidirect
553. #535C22×C103semidirect
563. #421C22×C103semidirect
564. #421C22×C103semidirect
565. #421C22×C103semidirect
566. #419C22×C103semidirect
567. #418C22×C103semidirect
569. #416C22×C103semidirect
570. C2×#101C22×C103semidirect
571. C2×#100C22×C103semidirect
572. #410C22×C103semidirect
573. #408C22×C103semidirect
574. #408C22×C103semidirect
575. #408C22×C103semidirect
576. #344C22×C103semidirect
577. #344C22×C103semidirect
578. #341C22×C103semidirect
579. #338C22×C103semidirect
586. 2−1+4D4×C103semidirect
594. H(5,𝔽2)D4×C103semidirect
632. #137D4×C103semidirect
650. AGL(1,ℤ/8)D4×C103semidirect
662. C2×Q16D4×C103semidirect
671. C2×SD16D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35862
C103×#35852
C103×#30202
C103×#30192
C103×#30102
C103×#30092
C103×#20192
C103×#20172
C103×#20092
C103×#20082
C103×#19032
C103×#19022
C103×#18812
C103×#17942
#23894103