Finite Group Databasebeta

← C101×#23894 #38806045

Subgroups — C101×#23894 #38806045

Order 25856.

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
1C101×#3586C211yesmaximal, characteristic, complemented
2C101×#3585C211yesmaximal, characteristic, complemented
3C101×#3020C211yesmaximal, characteristic, complemented
4C101×#3019C211yesmaximal, characteristic, complemented
5C101×#3010C211yesmaximal, characteristic, complemented
6C101×#3009C211yesmaximal, characteristic, complemented
7C101×#2019C211yesmaximal, characteristic, complemented
8C101×#2017C211yesmaximal, characteristic, complemented
9C101×#2009C211yesmaximal, characteristic, complemented
10C101×#2008C211yesmaximal, characteristic, complemented
11C101×#1903C211yesmaximal, characteristic, complemented
12C101×#1902C211yesmaximal, characteristic, complemented
13C101×#1881C211yesmaximal, characteristic, complemented
14C101×#1881C211yesmaximal, characteristic, complemented
15C101×#1794C211yesmaximal, characteristic, complemented
16#585×C101C2211yescharacteristic
17C2×2−1+4×C101C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C101C2211yescharacteristic
19#578×C101—22no—
20#578×C101—22no—
21#577×C101—22no—
22#577×C101—22no—
23#577×C101—22no—
24#577×C101—22no—
25#576×C101—22no—
26#576×C101—22no—
27#575×C101—22no—
28#575×C101—22no—
29#575×C101C2211yescharacteristic
30#575×C101C2211yescharacteristic
31#575×C101C2211yescharacteristic
32#575×C101C2211yescharacteristic, complemented
33#575×C101C2211yescharacteristic, complemented
34C2×#137×C101—22no—
35C2×#137×C101C2211yescharacteristic
36C2×#137×C101C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C101—22no—
38C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
39C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
40C22×SD16×C101C2211yescharacteristic, complemented
41#568×C101C2211yescharacteristic
42#568×C101C2211yescharacteristic, complemented
43#536×C101C2211yescharacteristic, complemented
44#535×C101C2211yescharacteristic, complemented
45#456×C101—22no—
46#455×C101—22no—
47#454×C101—22no—
48#453×C101—22no—
49#452×C101—22no—
50#450×C101—22no—
51#449×C101—22no—
52#448×C101—22no—
53#421×C101C2211yescharacteristic
54#421×C101C2211yescharacteristic, complemented
55#421×C101C2211yescharacteristic, complemented
56#421×C101C2211yescharacteristic, complemented
57#419×C101C2211yescharacteristic, complemented
58#418×C101C2211yescharacteristic, complemented
59#416×C101C2211yescharacteristic
60#416×C101C2211yescharacteristic, complemented
61C2×#101×C101C2211yescharacteristic, complemented
62C2×#100×C101C2211yescharacteristic, complemented
63#410×C101C2211yescharacteristic, complemented
64#408×C101C2211yescharacteristic, complemented
65#408×C101C2211yescharacteristic, complemented
66#408×C101C2211yescharacteristic, complemented
67#344×C101C2211yescharacteristic, complemented
68#344×C101C2211yescharacteristic, complemented
69#341×C101C2211yescharacteristic, complemented
70#338×C101C2211yescharacteristic, complemented
712−1+4×C101—22no—
722−1+4×C101—21no—
732−1+4×C101—22no—
742−1+4×C101—21no—
752−1+4×C101—22no—
762−1+4×C101—41no—
772−1+4×C101D412yescomplemented
78H(5,𝔽2)×C101—22no—
79H(5,𝔽2)×C101—21no—
80H(5,𝔽2)×C101—22no—
81H(5,𝔽2)×C101—21no—
82H(5,𝔽2)×C101—22no—
83H(5,𝔽2)×C101—41no—
84H(5,𝔽2)×C101—41no—
85H(5,𝔽2)×C101D412yescomplemented
86C2×#41×C101—22no—
87C2×#41×C101—22no—
88C2×#41×C101—21no—
89C2×#41×C101—21no—
90C2×#41×C101—21no—
91C2×#41×C101—21no—
92C2×#41×C101—41no—
93C2×#41×C101—41no—
94C2×#41×C101C2311yescharacteristic
95C2×#41×C101C2311yescharacteristic
96C2×#41×C101C2311yescharacteristic
97C2×#41×C101C2311yescharacteristic
98C2×#41×C101C2311yescharacteristic
99C22×Q8×C101—21no—
100C22×Q8×C101—21no—
101C22×Q8×C101C2311yescharacteristic
102C22×D4×C101—21no—
103C22×D4×C101—21no—
104C22×D4×C101—41no—
105C22×D4×C101C2311yescharacteristic
106#137×C101—24no—
107#137×C101—24no—
108#137×C101—24no—
109#137×C101—24no—
110#137×C101—22no—
111#137×C101—22no—
112#137×C101—21no—
113#137×C101—22no—
114#137×C101—21no—
115#137×C101—21no—
116#137×C101—21no—
117#137×C101—21no—
118#137×C101—21no—
119#137×C101—21no—
120#137×C101—21no—
121#137×C101—22no—
122#137×C101D412yes—
123#137×C101D412yescomplemented
124AGL(1,ℤ/8)×C101—24no—
125AGL(1,ℤ/8)×C101—24no—
126AGL(1,ℤ/8)×C101—24no—
127AGL(1,ℤ/8)×C101—24no—
128AGL(1,ℤ/8)×C101—22no—
129AGL(1,ℤ/8)×C101—22no—
130AGL(1,ℤ/8)×C101—21no—
131AGL(1,ℤ/8)×C101—22no—
132AGL(1,ℤ/8)×C101—21no—
133AGL(1,ℤ/8)×C101—21no—
134AGL(1,ℤ/8)×C101—21no—
135AGL(1,ℤ/8)×C101—21no—
136AGL(1,ℤ/8)×C101—21no—
137AGL(1,ℤ/8)×C101—21no—
138AGL(1,ℤ/8)×C101—21no—
139AGL(1,ℤ/8)×C101—22no—
140AGL(1,ℤ/8)×C101D412yes—
141AGL(1,ℤ/8)×C101D412yescomplemented
142#135×C101—24no—
143#135×C101—24no—
144#135×C101—24no—
145#135×C101—24no—
146#135×C101—22no—
147#135×C101—22no—
148#135×C101—22no—
149#135×C101—22no—
150#135×C101—41no—
151C2×Q16×C101—24no—
152C2×Q16×C101—21no—
153C2×Q16×C101D412yescomplemented
154C2×SD16×C101—24no—
155C2×SD16×C101—24no—
156C2×SD16×C101—21no—
157C2×SD16×C101—21no—
158C2×SD16×C101—22no—
159C2×SD16×C101—22no—
160C2×SD16×C101—41no—
161C2×SD16×C101D412yes—
162C2×SD16×C101D412yescomplemented
163C2×D8×C101—24no—
164C2×D8×C101—21no—
165C2×D8×C101D412yes—
166#131×C101—22no—
167#131×C101—22no—
168#131×C101—22no—
169#131×C101—22no—
170C2×M16×C101—22no—
171C2×M16×C101—22no—
172C2×M16×C101C2311yescharacteristic
173C2×M16×C101C2311yescharacteristic
174C2×M16×C101C2311yescharacteristic
175C2×M16×C101C2311yescharacteristic
176C2×M16×C101C2311yescharacteristic
177C22×C8×C101C2311yescharacteristic
178C4⋊Q8×C101—21no—
179#127×C101—21no—
180#124×C101—21no—
181#124×C101—21no—
182#123×C101—41no—
183C22⋊Q8×C101—22no—
184#121×C101—22no—
185#120×C101—41no—
186#117×C101C2311yescharacteristic
187#117×C101C2311yescharacteristic
188#104×C101—22no—
189#104×C101—22no—
190#104×C101—22no—
191#104×C101—22no—
192#103×C101—21no—
193#103×C101—21no—
194#103×C101—22no—
195#102×C101—21no—
196#102×C101—21no—
197#102×C101—22no—
198#101×C101—22no—
199#100×C101—22no—
200#99×C101—41no—
201C22⋊C8×C101—22no—
202C22⋊C8×C101—22no—
203C22⋊C8×C101—41no—
204C24×C101—21no—
205C24×C101—41no—
206#41×C101—21no—
207#41×C101—21no—
208#41×C101—21no—
209#41×C101—21no—
210#41×C101—24no—
211#41×C101—24no—
212#41×C101—22no—
213#41×C101—22no—
214#41×C101—22no—
215#41×C101—22no—
216#41×C101—21no—
217#41×C101—21no—
218#41×C101—21no—
219#41×C101—21no—
220#41×C101—21no—
221#41×C101—21no—
222#41×C101—21no—
223#41×C101—21no—
224#41×C101—21no—
225#41×C101—21no—
226#41×C101—21no—
227#41×C101—21no—
228#41×C101—42no—
229#41×C101—42no—
230#41×C101—42no—
231#41×C101—42no—
232#41×C101—42no—
233#41×C101—44no—
234#41×C101—42no—
235#41×C101—42no—
236#41×C101—42no—
237#41×C101—41no—
238#41×C101—41no—
239#41×C101—44no—
240#41×C101—42no—
241#41×C101—42no—
242#41×C101C2×D412yes—
243#41×C101C2×D412yes—
244#41×C101C2×D412yes—
245#41×C101C2×D412yes—
246C2×Q8×C101—21no—
247C2×Q8×C101—24no—
248C2×Q8×C101—22no—
249C2×Q8×C101—22no—
250C2×Q8×C101—21no—
251C2×Q8×C101—21no—
252C2×Q8×C101—21no—
253C2×Q8×C101—21no—
254C2×Q8×C101—41no—
255C2×Q8×C101—42no—
256C2×Q8×C101—42no—
257C2×Q8×C101—41no—
258C2×Q8×C101—42no—
259C2×Q8×C101C2×D412yes—
260C2×Q8×C101C2×D411yescharacteristic
261C2×Q8×C101C2×D411yescharacteristic
262C2×Q8×C101C2×D411yescharacteristic
263C2×Q8×C101C2×D411yescharacteristic
264C2×Q8×C101C2×D411yescharacteristic
265C2×D4×C101—21no—
266C2×D4×C101—21no—
267C2×D4×C101—24no—
268C2×D4×C101—22no—
269C2×D4×C101—22no—
270C2×D4×C101—21no—
271C2×D4×C101—21no—
272C2×D4×C101—21no—
273C2×D4×C101—21no—
274C2×D4×C101—21no—
275C2×D4×C101—21no—
276C2×D4×C101—21no—
277C2×D4×C101—21no—
278C2×D4×C101—42no—
279C2×D4×C101—41no—
280C2×D4×C101—41no—
281C2×D4×C101—42no—
282C2×D4×C101—42no—
283C2×D4×C101—41no—
284C2×D4×C101—44no—
285C2×D4×C101—42no—
286C2×D4×C101—42no—
287C2×D4×C101—44no—
288C2×D4×C101—41no—
289C2×D4×C101—42no—
290C2×D4×C101—42no—
291C2×D4×C101C2×D412yes—
292C2×D4×C101C2×D411yescharacteristic
293C2×D4×C101C2×D411yescharacteristic
294C2×D4×C101C2×D411yescharacteristic
295C2×D4×C101C2×D411yescharacteristic
296C2×D4×C101C2×D411yescharacteristic
297C22×C4×C101—21no—
298C22×C4×C101—21no—
299C22×C4×C101—21no—
300C22×C4×C101—21no—
301C22×C4×C101—21no—
302C22×C4×C101—21no—
303C22×C4×C101—41no—
304C22×C4×C101—42no—
305C22×C4×C101—41no—
306C22×C4×C101—41no—
307C22×C4×C101C2411yescharacteristic
308Q16×C101—24no—
309Q16×C101—22no—
310Q16×C101—22no—
311Q16×C101—22no—
312Q16×C101—24no—
313Q16×C101—22no—
314Q16×C101—41no—
315SD16×C101—24no—
316SD16×C101—22no—
317SD16×C101—24no—
318SD16×C101—22no—
319SD16×C101—22no—
320SD16×C101—22no—
321SD16×C101—22no—
322SD16×C101—24no—
323SD16×C101—22no—
324SD16×C101—22no—
325SD16×C101—24no—
326SD16×C101—22no—
327SD16×C101—44no—
328SD16×C101—41no—
329SD16×C101—41no—
330D8×C101—24no—
331D8×C101—22no—
332D8×C101—22no—
333D8×C101—22no—
334D8×C101—24no—
335D8×C101—22no—
336D8×C101—41no—
337M16×C101—24no—
338M16×C101—24no—
339M16×C101—21no—
340M16×C101—21no—
341M16×C101—21no—
342M16×C101—21no—
343M16×C101—21no—
344M16×C101—21no—
345M16×C101—21no—
346M16×C101—21no—
347M16×C101C2×D412yes—
348M16×C101C2×D412yes—
349C2×C8×C101—24no—
350C2×C8×C101—24no—
351C2×C8×C101—21no—
352C2×C8×C101—21no—
353C2×C8×C101—21no—
354C2×C8×C101—21no—
355C2×C8×C101—21no—
356C2×C8×C101—21no—
357C2×C8×C101C2×D412yes—
358C2×C8×C101C2×D412yes—
359C4⋊C4×C101—21no—
360C4⋊C4×C101—21no—
361C4⋊C4×C101—42no—
362C22⋊C4×C101—21no—
363C22⋊C4×C101—21no—
364C22⋊C4×C101—42no—
365C22⋊C4×C101—42no—
366C42×C101—21no—
367C42×C101—21no—
368C23×C101—21no—
369C23×C101—21no—
370C23×C101—21no—
371C23×C101—21no—
372C23×C101—21no—
373C23×C101—22no—
374C23×C101—42no—
375C23×C101—44no—
376C23×C101—41no—
377C23×C101—41no—
378C23×C101—161no—
379C23×C101—162no—
380C23×C101H(5,𝔽2)11yescharacteristic
381Q8×C101—21no—
382Q8×C101—21no—
383Q8×C101—21no—
384Q8×C101—21no—
385Q8×C101—22no—
386Q8×C101—21no—
387Q8×C101—21no—
388Q8×C101—22no—
389Q8×C101—21no—
390Q8×C101—21no—
391Q8×C101—42no—
392Q8×C101—44no—
393Q8×C101—41no—
394Q8×C101—41no—
395Q8×C101#12012yes—
396Q8×C101#12012yes—
397D4×C101—22no—
398D4×C101—22no—
399D4×C101—22no—
400D4×C101—22no—
401D4×C101—21no—
402D4×C101—21no—
403D4×C101—22no—
404D4×C101—21no—
405D4×C101—21no—
406D4×C101—21no—
407D4×C101—21no—
408D4×C101—21no—
409D4×C101—21no—
410D4×C101—22no—
411D4×C101—42no—
412D4×C101—42no—
413D4×C101—44no—
414D4×C101—42no—
415D4×C101—44no—
416D4×C101—44no—
417D4×C101—41no—
418D4×C101—41no—
419D4×C101—41no—
420D4×C101—41no—
421D4×C101—41no—
422D4×C101—41no—
423D4×C101—41no—
424D4×C101—41no—
425D4×C101—162no—
426D4×C101#12012yes—
427D4×C101#12012yes—
428C2×C4×C101—21no—
429C2×C4×C101—21no—
430C2×C4×C101—22no—
431C2×C4×C101—22no—
432C2×C4×C101—22no—
433C2×C4×C101—22no—
434C2×C4×C101—21no—
435C2×C4×C101—21no—
436C2×C4×C101—22no—
437C2×C4×C101—21no—
438C2×C4×C101—42no—
439C2×C4×C101—42no—
440C2×C4×C101—42no—
441C2×C4×C101—44no—
442C2×C4×C101—44no—
443C2×C4×C101—44no—
444C2×C4×C101—41no—
445C2×C4×C101—41no—
446C2×C4×C101—41no—
447C2×C4×C101—41no—
448C2×C4×C101—41no—
449C2×C4×C101—41no—
450C2×C4×C101—41no—
451C2×C4×C101—41no—
452C2×C4×C101—41no—
453C2×C4×C101—41no—
454C2×C4×C101C22×D411yescharacteristic
455C2×C4×C101C22×D411yescharacteristic
456C2×C4×C101C22×D411yescharacteristic
457C2×C4×C101C22×D411yescharacteristic
458C2×C4×C101C22×D411yescharacteristic
459C2×C4×C101H(5,𝔽2)11yescharacteristic
460C8×C101—22no—
461C8×C101—22no—
462C8×C101—22no—
463C8×C101—22no—
464C8×C101—41no—
465C8×C101—41no—
466C22×C101—22no—
467C22×C101—22no—
468C22×C101—41no—
469C22×C101—42no—
470C22×C101—42no—
471C22×C101—41no—
472C22×C101—41no—
473C22×C101—41no—
474C22×C101—42no—
475C22×C101—81no—
476C22×C101—81no—
477C22×C101—82no—
478C22×C101—81no—
479C22×C101—82no—
480C22×C101—161no—
481C22×C101—162no—
482C22×C101—164no—
483C22×C101#53411yescharacteristic
484C22×C101D4211yescharacteristic
485C22×C101D4211yescharacteristic
486C4×C101—22no—
487C4×C101—22no—
488C4×C101—41no—
489C4×C101—41no—
490C4×C101—41no—
491C4×C101—42no—
492C4×C101—81no—
493C4×C101—81no—
494C4×C101C2×#12011yescharacteristic
495C4×C101C2×#12011yescharacteristic
496C4×C101D4211yescharacteristic
497C4×C101D4211yescharacteristic
498#23894C10111yesmaximal, characteristic, direct product factor, Sylow
499C2×C101—21no—
500C2×C101—21no—
501C2×C101—21no—
502C2×C101—42no—
503C2×C101—42no—
504C2×C101—81no—
505C2×C101—81no—
506C2×C101—82no—
507C2×C101—81no—
508C2×C101#240311yescharacteristic
509#3586C2×C10111yescharacteristic, complemented
510#3585C2×C10111yescharacteristic, complemented
511#3020C2×C10111yescharacteristic, complemented
512#3019C2×C10111yescharacteristic, complemented
513#3010C2×C10111yescharacteristic, complemented
514#3009C2×C10111yescharacteristic, complemented
515#2019C2×C10111yescharacteristic, complemented
516#2017C2×C10111yescharacteristic, complemented
517#2009C2×C10111yescharacteristic, complemented
518#2008C2×C10111yescharacteristic, complemented
519#1903C2×C10111yescharacteristic, complemented
520#1902C2×C10111yescharacteristic, complemented
521#1881C2×C10111yescharacteristic, complemented
522#1881C2×C10111yescharacteristic, complemented
523#1794C2×C10111yescharacteristic, complemented
524C101#2389411yescharacteristic, direct product factor, Sylow
525#585C22×C10111yescharacteristic
526C2×2−1+4C22×C10111yescharacteristic, complemented
527C2×H(5,𝔽2)C22×C10111yescharacteristic
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×C10111yescharacteristic
539#575C22×C10111yescharacteristic
540#575C22×C10111yescharacteristic
541#575C22×C10111yescharacteristic, complemented
542#575C22×C10111yescharacteristic, complemented
543C2×#137—22no—
544C2×#137C22×C10111yescharacteristic
545C2×#137C22×C10111yescharacteristic, complemented
546C2×AGL(1,ℤ/8)—22no—
547C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
548C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
549C22×SD16C22×C10111yescharacteristic, complemented
550#568C22×C10111yescharacteristic
551#568C22×C10111yescharacteristic, complemented
552#536C22×C10111yescharacteristic, complemented
553#535C22×C10111yescharacteristic, 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×C10111yescharacteristic
563#421C22×C10111yescharacteristic, complemented
564#421C22×C10111yescharacteristic, complemented
565#421C22×C10111yescharacteristic, complemented
566#419C22×C10111yescharacteristic, complemented
567#418C22×C10111yescharacteristic, complemented
568#416C22×C10111yescharacteristic
569#416C22×C10111yescharacteristic, complemented
570C2×#101C22×C10111yescharacteristic, complemented
571C2×#100C22×C10111yescharacteristic, complemented
572#410C22×C10111yescharacteristic, complemented
573#408C22×C10111yescharacteristic, complemented
574#408C22×C10111yescharacteristic, complemented
575#408C22×C10111yescharacteristic, complemented
576#344C22×C10111yescharacteristic, complemented
577#344C22×C10111yescharacteristic, complemented
578#341C22×C10111yescharacteristic, complemented
579#338C22×C10111yescharacteristic, 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×C10112yescomplemented
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×C10112yescomplemented
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×C10111yescharacteristic
604C2×#41C23×C10111yescharacteristic
605C2×#41C23×C10111yescharacteristic
606C2×#41C23×C10111yescharacteristic
607C2×#41C23×C10111yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C10111yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—41no—
614C22×D4C23×C10111yescharacteristic
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×C10112yes—
632#137D4×C10112yescomplemented
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×C10112yes—
650AGL(1,ℤ/8)D4×C10112yescomplemented
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×C10112yescomplemented
663C2×SD16—24no—
664C2×SD16—24no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—41no—
670C2×SD16D4×C10112yes—
671C2×SD16D4×C10112yescomplemented
672C2×D8—24no—
673C2×D8—21no—
674C2×D8D4×C10112yes—
675#131—22no—
676#131—22no—
677#131—22no—
678#131—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16C23×C10111yescharacteristic
682C2×M16C23×C10111yescharacteristic
683C2×M16C23×C10111yescharacteristic
684C2×M16C23×C10111yescharacteristic
685C2×M16C23×C10111yescharacteristic
686C22×C8C23×C10111yescharacteristic
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×C10111yescharacteristic
696#117C23×C10111yescharacteristic
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×C10112yes—
752#41C2×D4×C10112yes—
753#41C2×D4×C10112yes—
754#41C2×D4×C10112yes—
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×C10112yes—
769C2×Q8C2×D4×C10111yescharacteristic
770C2×Q8C2×D4×C10111yescharacteristic
771C2×Q8C2×D4×C10111yescharacteristic
772C2×Q8C2×D4×C10111yescharacteristic
773C2×Q8C2×D4×C10111yescharacteristic
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×C10112yes—
801C2×D4C2×D4×C10111yescharacteristic
802C2×D4C2×D4×C10111yescharacteristic
803C2×D4C2×D4×C10111yescharacteristic
804C2×D4C2×D4×C10111yescharacteristic
805C2×D4C2×D4×C10111yescharacteristic
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×C10111yescharacteristic
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×C10112yes—
857M16C2×D4×C10112yes—
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×C10112yes—
867C2×C8C2×D4×C10112yes—
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)×C10111yescharacteristic
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×C10112yes—
905Q8#120×C10112yes—
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×C10112yes—
936D4#120×C10112yes—
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×C10111yescharacteristic
964C2×C4C22×D4×C10111yescharacteristic
965C2×C4C22×D4×C10111yescharacteristic
966C2×C4C22×D4×C10111yescharacteristic
967C2×C4C22×D4×C10111yescharacteristic
968C2×C4H(5,𝔽2)×C10111yescharacteristic
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×C10111yescharacteristic
993C22D42×C10111yescharacteristic
994C22D42×C10111yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C10111yescharacteristic
1004C4C2×#120×C10111yescharacteristic
1005C4D42×C10111yescharacteristic
1006C4D42×C10111yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2C101×#240311yescharacteristic
subgroupG/H
center, socleC2×C101#2403
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3586C2semidirect
2. C101×#3585C2semidirect
3. C101×#3020C2semidirect
4. C101×#3019C2semidirect
5. C101×#3010C2semidirect
6. C101×#3009C2semidirect
7. C101×#2019C2semidirect
8. C101×#2017C2semidirect
9. C101×#2009C2semidirect
10. C101×#2008C2semidirect
11. C101×#1903C2semidirect
12. C101×#1902C2semidirect
13. C101×#1881C2semidirect
14. C101×#1881C2semidirect
15. C101×#1794C2semidirect
17. C2×2−1+4×C101C22semidirect
32. #575×C101C22semidirect
33. #575×C101C22semidirect
36. C2×#137×C101C22semidirect
40. C22×SD16×C101C22semidirect
42. #568×C101C22semidirect
43. #536×C101C22semidirect
44. #535×C101C22semidirect
54. #421×C101C22semidirect
55. #421×C101C22semidirect
56. #421×C101C22semidirect
57. #419×C101C22semidirect
58. #418×C101C22semidirect
60. #416×C101C22semidirect
61. C2×#101×C101C22semidirect
62. C2×#100×C101C22semidirect
63. #410×C101C22semidirect
64. #408×C101C22semidirect
65. #408×C101C22semidirect
66. #408×C101C22semidirect
67. #344×C101C22semidirect
68. #344×C101C22semidirect
69. #341×C101C22semidirect
70. #338×C101C22semidirect
77. 2−1+4×C101D4semidirect
85. H(5,𝔽2)×C101D4semidirect
123. #137×C101D4semidirect
141. AGL(1,ℤ/8)×C101D4semidirect
153. C2×Q16×C101D4semidirect
162. C2×SD16×C101D4semidirect
498. #23894C101direct (N × H)
509. #3586C2×C101semidirect
510. #3585C2×C101semidirect
511. #3020C2×C101semidirect
512. #3019C2×C101semidirect
513. #3010C2×C101semidirect
514. #3009C2×C101semidirect
515. #2019C2×C101semidirect
516. #2017C2×C101semidirect
517. #2009C2×C101semidirect
518. #2008C2×C101semidirect
519. #1903C2×C101semidirect
520. #1902C2×C101semidirect
521. #1881C2×C101semidirect
522. #1881C2×C101semidirect
523. #1794C2×C101semidirect
524. C101#23894direct (N × H)
526. C2×2−1+4C22×C101semidirect
541. #575C22×C101semidirect
542. #575C22×C101semidirect
545. C2×#137C22×C101semidirect
549. C22×SD16C22×C101semidirect
551. #568C22×C101semidirect
552. #536C22×C101semidirect
553. #535C22×C101semidirect
563. #421C22×C101semidirect
564. #421C22×C101semidirect
565. #421C22×C101semidirect
566. #419C22×C101semidirect
567. #418C22×C101semidirect
569. #416C22×C101semidirect
570. C2×#101C22×C101semidirect
571. C2×#100C22×C101semidirect
572. #410C22×C101semidirect
573. #408C22×C101semidirect
574. #408C22×C101semidirect
575. #408C22×C101semidirect
576. #344C22×C101semidirect
577. #344C22×C101semidirect
578. #341C22×C101semidirect
579. #338C22×C101semidirect
586. 2−1+4D4×C101semidirect
594. H(5,𝔽2)D4×C101semidirect
632. #137D4×C101semidirect
650. AGL(1,ℤ/8)D4×C101semidirect
662. C2×Q16D4×C101semidirect
671. C2×SD16D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35862
C101×#35852
C101×#30202
C101×#30192
C101×#30102
C101×#30092
C101×#20192
C101×#20172
C101×#20092
C101×#20082
C101×#19032
C101×#19022
C101×#18812
C101×#17942
#23894101