Finite Group Databasebeta

← C101×#25196 #38807347

Subgroups — C101×#25196 #38807347

Order 25856.

1032 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3068C211yesmaximal, characteristic, complemented
2C101×#3068C211yesmaximal, characteristic, complemented
3C101×#3019C211yesmaximal, characteristic, complemented
4C2×#453×C101C211yesmaximal, characteristic, complemented
5C101×#2956C211yesmaximal, characteristic, complemented
6C101×#2888C211yesmaximal, characteristic, complemented
7C101×#2069C211yesmaximal, characteristic, complemented
8C101×#2050C211yesmaximal, characteristic, complemented
9C101×#2048C211yesmaximal, characteristic, complemented
10C101×#2002C211yesmaximal, characteristic, complemented
11C101×#1965C211yesmaximal, characteristic, complemented
12C101×#1932C211yesmaximal, characteristic, complemented
13C101×#1914C211yesmaximal, characteristic, complemented
14C101×#1903C211yesmaximal, characteristic, complemented
15C101×#1861C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C101C2211yescharacteristic
17#575×C101C2211yescharacteristic
18#575×C101C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C101C2211yescharacteristic, complemented
22#568×C101C2211yescharacteristic
23#568×C101C2211yescharacteristic
24#568×C101C2211yescharacteristic, complemented
25#535×C101C2211yescharacteristic
26C2×#127×C101C2211yescharacteristic
27#472×C101—22no—
28#472×C101—22no—
29#471×C101—22no—
30#471×C101—22no—
31#455×C101—22no—
32#453×C101—22no—
33#453×C101—22no—
34#453×C101—22no—
35#444×C101—22no—
36#443×C101—22no—
37#430×C101C2211yescharacteristic, complemented
38#430×C101C2211yescharacteristic, complemented
39#430×C101C2211yescharacteristic, complemented
40#423×C101C2211yescharacteristic, complemented
41#421×C101C2211yescharacteristic
42#421×C101C2211yescharacteristic
43C2×#104×C101C2211yescharacteristic
44C2×#104×C101C2211yescharacteristic
45C2×#104×C101C2211yescharacteristic, complemented
46#418×C101C2211yescharacteristic, complemented
47#413×C101—22no—
48#413×C101C2211yescharacteristic
49#413×C101C2211yescharacteristic
50#413×C101C2211yescharacteristic, complemented
51C2×#100×C101—22no—
52C2×#100×C101C2211yescharacteristic
53C2×#100×C101C2211yescharacteristic
54C2×#100×C101C2211yescharacteristic
55C2×#100×C101C2211yescharacteristic
56C2×#100×C101C2211yescharacteristic, complemented
57C2×#100×C101C2211yescharacteristic, complemented
58C4×M16×C101C2211yescharacteristic, complemented
59#344×C101C2211yescharacteristic, complemented
60#344×C101C2211yescharacteristic, complemented
61#339×C101C2211yescharacteristic, complemented
62#338×C101C2211yescharacteristic, complemented
63H(5,𝔽2)×C101—22no—
64H(5,𝔽2)×C101—22no—
65H(5,𝔽2)×C101—41no—
66H(5,𝔽2)×C101—41no—
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69C2×#41×C101C2311yescharacteristic
70C2×#41×C101C2311yescharacteristic
71C2×#41×C101C2311yescharacteristic
72C22×D4×C101—22no—
73C22×D4×C101—21no—
74C22×D4×C101—21no—
75C22×D4×C101—22no—
76C22×D4×C101C2311yescharacteristic
77C22×D4×C101C2311yescharacteristic
78#137×C101—21no—
79#137×C101—21no—
80#137×C101—21no—
81#137×C101D412yescomplemented
82AGL(1,ℤ/8)×C101—21no—
83AGL(1,ℤ/8)×C101—22no—
84AGL(1,ℤ/8)×C101—22no—
85AGL(1,ℤ/8)×C101—21no—
86AGL(1,ℤ/8)×C101—21no—
87AGL(1,ℤ/8)×C101—22no—
88AGL(1,ℤ/8)×C101—22no—
89AGL(1,ℤ/8)×C101—41no—
90AGL(1,ℤ/8)×C101—41no—
91AGL(1,ℤ/8)×C101D412yescomplemented
92#135×C101—22no—
93#135×C101—41no—
94C2×SD16×C101—21no—
95C2×SD16×C101—21no—
96C2×SD16×C101—21no—
97C2×D8×C101—21no—
98C2×D8×C101—21no—
99C2×D8×C101—21no—
100#131×C101—22no—
101#131×C101—22no—
102#131×C101—22no—
103#131×C101—22no—
104#131×C101—41no—
105#131×C101—41no—
106C2×M16×C101—22no—
107C2×M16×C101—22no—
108C2×M16×C101—41no—
109C2×M16×C101C2311yescharacteristic
110C2×M16×C101C2311yescharacteristic
111C2×M16×C101C2311yescharacteristic
112C2×M16×C101C2311yescharacteristic
113C2×M16×C101C2311yescharacteristic
114C2×M16×C101C2311yescharacteristic
115C2×M16×C101C2311yescharacteristic
116C2×M16×C101C2311yescharacteristic
117#127×C101—21no—
118#127×C101—21no—
119#127×C101—21no—
120#127×C101—41no—
121#124×C101—21no—
122#121×C101—41no—
123#120×C101—22no—
124#117×C101C2311yescharacteristic
125C2×C42×C101C2311yescharacteristic
126#108×C101—22no—
127#108×C101—22no—
128#108×C101—22no—
129C4⋊C8×C101—41no—
130#104×C101—22no—
131#104×C101—22no—
132#104×C101—21no—
133#104×C101—21no—
134#104×C101—21no—
135#104×C101—21no—
136#104×C101D412yescomplemented
137#104×C101D412yescomplemented
138#102×C101—41no—
139#101×C101—21no—
140#101×C101—21no—
141#101×C101D412yescomplemented
142#100×C101—21no—
143#100×C101—21no—
144#100×C101—22no—
145#100×C101—22no—
146#100×C101—22no—
147#100×C101—22no—
148#100×C101—22no—
149#100×C101—22no—
150#100×C101D412yescomplemented
151#97×C101—21no—
152C4×C8×C101—21no—
153C24×C101—22no—
154C24×C101—21no—
155C24×C101#4112yes—
156#41×C101—21no—
157#41×C101—21no—
158#41×C101—21no—
159#41×C101—21no—
160#41×C101—21no—
161#41×C101—21no—
162#41×C101—21no—
163#41×C101—21no—
164#41×C101—21no—
165#41×C101—21no—
166#41×C101—42no—
167#41×C101—42no—
168#41×C101—42no—
169#41×C101—42no—
170#41×C101C2×D412yes—
171#41×C101C2×D412yes—
172C2×Q8×C101C2×D411yescharacteristic
173C2×Q8×C101C2×D411yescharacteristic
174C2×Q8×C101#4111yescharacteristic
175C2×D4×C101—21no—
176C2×D4×C101—22no—
177C2×D4×C101—22no—
178C2×D4×C101—21no—
179C2×D4×C101—21no—
180C2×D4×C101—21no—
181C2×D4×C101—21no—
182C2×D4×C101—21no—
183C2×D4×C101—21no—
184C2×D4×C101—21no—
185C2×D4×C101—21no—
186C2×D4×C101—21no—
187C2×D4×C101—21no—
188C2×D4×C101—21no—
189C2×D4×C101—21no—
190C2×D4×C101—21no—
191C2×D4×C101—21no—
192C2×D4×C101—42no—
193C2×D4×C101—42no—
194C2×D4×C101—42no—
195C2×D4×C101—42no—
196C2×D4×C101—44no—
197C2×D4×C101—44no—
198C2×D4×C101—42no—
199C2×D4×C101—42no—
200C2×D4×C101—42no—
201C2×D4×C101—84no—
202C2×D4×C101C2×D411yescharacteristic
203C2×D4×C101C2×D411yescharacteristic
204C2×D4×C101#4111yescharacteristic
205C22×C4×C101—21no—
206C22×C4×C101—22no—
207C22×C4×C101—21no—
208C22×C4×C101—21no—
209C22×C4×C101—21no—
210C22×C4×C101C2411yescharacteristic
211Q16×C101—22no—
212Q16×C101—41no—
213SD16×C101—22no—
214SD16×C101—22no—
215SD16×C101—42no—
216SD16×C101—42no—
217SD16×C101—41no—
218SD16×C101—41no—
219SD16×C101—42no—
220D8×C101—22no—
221D8×C101—42no—
222D8×C101—42no—
223D8×C101—41no—
224D8×C101—42no—
225M16×C101—21no—
226M16×C101—21no—
227M16×C101—21no—
228M16×C101—21no—
229M16×C101—21no—
230M16×C101—21no—
231M16×C101—21no—
232M16×C101—21no—
233M16×C101—21no—
234M16×C101—21no—
235M16×C101—21no—
236M16×C101—21no—
237M16×C101—42no—
238M16×C101—42no—
239M16×C101—42no—
240M16×C101C2×D412yes—
241M16×C101C2×D412yes—
242M16×C101C2×D412yes—
243M16×C101C2×D412yes—
244C2×C8×C101—21no—
245C2×C8×C101—21no—
246C2×C8×C101—21no—
247C2×C8×C101—21no—
248C2×C8×C101—21no—
249C2×C8×C101—21no—
250C2×C8×C101—21no—
251C2×C8×C101—21no—
252C2×C8×C101—42no—
253C2×C8×C101—42no—
254C2×C8×C101—42no—
255C4⋊C4×C101—21no—
256C22⋊C4×C101—21no—
257C22⋊C4×C101—42no—
258C42×C101—21no—
259C42×C101—21no—
260C42×C101C2×D411yescharacteristic
261C42×C101C2×D411yescharacteristic
262C23×C101—21no—
263C23×C101—22no—
264C23×C101—21no—
265C23×C101—22no—
266C23×C101—21no—
267C23×C101—22no—
268C23×C101—44no—
269C23×C101—41no—
270C23×C101—41no—
271C23×C101—41no—
272C23×C101—82no—
273C23×C101—82no—
274C23×C101—162no—
275C23×C101C2×#4111yescharacteristic
276Q8×C101—21no—
277Q8×C101—21no—
278Q8×C101—21no—
279Q8×C101—21no—
280Q8×C101—21no—
281Q8×C101#12112yes—
282D4×C101—22no—
283D4×C101—22no—
284D4×C101—21no—
285D4×C101—21no—
286D4×C101—21no—
287D4×C101—21no—
288D4×C101—21no—
289D4×C101—44no—
290D4×C101—44no—
291D4×C101—41no—
292D4×C101—41no—
293D4×C101—41no—
294D4×C101—41no—
295D4×C101—41no—
296D4×C101—41no—
297D4×C101—41no—
298D4×C101—41no—
299D4×C101—41no—
300D4×C101—41no—
301D4×C101—41no—
302D4×C101—41no—
303D4×C101—84no—
304D4×C101—84no—
305D4×C101—162no—
306D4×C101#12112yes—
307C2×C4×C101—21no—
308C2×C4×C101—21no—
309C2×C4×C101—22no—
310C2×C4×C101—22no—
311C2×C4×C101—21no—
312C2×C4×C101—21no—
313C2×C4×C101—21no—
314C2×C4×C101—44no—
315C2×C4×C101—42no—
316C2×C4×C101—41no—
317C2×C4×C101—41no—
318C2×C4×C101—41no—
319C2×C4×C101—41no—
320C2×C4×C101—41no—
321C2×C4×C101C22×D411yescharacteristic
322C2×C4×C101C22×D411yescharacteristic
323C2×C4×C101C22×D411yescharacteristic
324C2×C4×C101C2×#4111yescharacteristic
325C2×C4×C101H(5,𝔽2)11yescharacteristic
326C2×C4×C101H(5,𝔽2)11yescharacteristic
327C8×C101—22no—
328C8×C101—22no—
329C8×C101—22no—
330C8×C101—22no—
331C8×C101—41no—
332C8×C101—41no—
333C8×C101—41no—
334C8×C101—41no—
335C22×C101—22no—
336C22×C101—41no—
337C22×C101—41no—
338C22×C101—41no—
339C22×C101—42no—
340C22×C101—81no—
341C22×C101—82no—
342C22×C101—81no—
343C22×C101—82no—
344C22×C101—82no—
345C22×C101—81no—
346C22×C101—82no—
347C22×C101—81no—
348C22×C101—161no—
349C22×C101—161no—
350C22×C101—164no—
351C22×C101#52511yescharacteristic
352C22×C101#54611yescharacteristic
353C22×C101#54611yescharacteristic
354C4×C101—22no—
355C4×C101—22no—
356C4×C101—41no—
357C4×C101—41no—
358C4×C101—41no—
359C4×C101—81no—
360C4×C101C2×#12111yescharacteristic
361C4×C101#53811yescharacteristic
362C4×C101D4211yescharacteristic
363C4×C101D4211yescharacteristic
364#25196C10111yesmaximal, characteristic, direct product factor, Sylow
365C2×C101—21no—
366C2×C101—21no—
367C2×C101—21no—
368C2×C101—42no—
369C2×C101—81no—
370C2×C101—82no—
371C2×C101—81no—
372C2×C101—161no—
373C2×C101#242411yescharacteristic
374#3068C2×C10111yescharacteristic, complemented
375#3068C2×C10111yescharacteristic, complemented
376#3019C2×C10111yescharacteristic, complemented
377C2×#453C2×C10111yescharacteristic, complemented
378#2956C2×C10111yescharacteristic, complemented
379#2888C2×C10111yescharacteristic, complemented
380#2069C2×C10111yescharacteristic, complemented
381#2050C2×C10111yescharacteristic, complemented
382#2048C2×C10111yescharacteristic, complemented
383#2002C2×C10111yescharacteristic, complemented
384#1965C2×C10111yescharacteristic, complemented
385#1932C2×C10111yescharacteristic, complemented
386#1914C2×C10111yescharacteristic, complemented
387#1903C2×C10111yescharacteristic, complemented
388#1861C2×C10111yescharacteristic, complemented
389C101#2519611yescharacteristic, direct product factor, Sylow
390C2×H(5,𝔽2)C22×C10111yescharacteristic
391#575C22×C10111yescharacteristic
392#575C22×C10111yescharacteristic
393C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
394C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
395C2×AGL(1,ℤ/8)C22×C10111yescharacteristic, complemented
396#568C22×C10111yescharacteristic
397#568C22×C10111yescharacteristic
398#568C22×C10111yescharacteristic, complemented
399#535C22×C10111yescharacteristic
400C2×#127C22×C10111yescharacteristic
401#472—22no—
402#472—22no—
403#471—22no—
404#471—22no—
405#455—22no—
406#453—22no—
407#453—22no—
408#453—22no—
409#444—22no—
410#443—22no—
411#430C22×C10111yescharacteristic, complemented
412#430C22×C10111yescharacteristic, complemented
413#430C22×C10111yescharacteristic, complemented
414#423C22×C10111yescharacteristic, complemented
415#421C22×C10111yescharacteristic
416#421C22×C10111yescharacteristic
417C2×#104C22×C10111yescharacteristic
418C2×#104C22×C10111yescharacteristic
419C2×#104C22×C10111yescharacteristic, complemented
420#418C22×C10111yescharacteristic, complemented
421#413—22no—
422#413C22×C10111yescharacteristic
423#413C22×C10111yescharacteristic
424#413C22×C10111yescharacteristic, complemented
425C2×#100—22no—
426C2×#100C22×C10111yescharacteristic
427C2×#100C22×C10111yescharacteristic
428C2×#100C22×C10111yescharacteristic
429C2×#100C22×C10111yescharacteristic
430C2×#100C22×C10111yescharacteristic, complemented
431C2×#100C22×C10111yescharacteristic, complemented
432C4×M16C22×C10111yescharacteristic, complemented
433#344C22×C10111yescharacteristic, complemented
434#344C22×C10111yescharacteristic, complemented
435#339C22×C10111yescharacteristic, complemented
436#338C22×C10111yescharacteristic, complemented
437H(5,𝔽2)—22no—
438H(5,𝔽2)—22no—
439H(5,𝔽2)—41no—
440H(5,𝔽2)—41no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41C23×C10111yescharacteristic
444C2×#41C23×C10111yescharacteristic
445C2×#41C23×C10111yescharacteristic
446C22×D4—22no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—22no—
450C22×D4C23×C10111yescharacteristic
451C22×D4C23×C10111yescharacteristic
452#137—21no—
453#137—21no—
454#137—21no—
455#137D4×C10112yescomplemented
456AGL(1,ℤ/8)—21no—
457AGL(1,ℤ/8)—22no—
458AGL(1,ℤ/8)—22no—
459AGL(1,ℤ/8)—21no—
460AGL(1,ℤ/8)—21no—
461AGL(1,ℤ/8)—22no—
462AGL(1,ℤ/8)—22no—
463AGL(1,ℤ/8)—41no—
464AGL(1,ℤ/8)—41no—
465AGL(1,ℤ/8)D4×C10112yescomplemented
466#135—22no—
467#135—41no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×D8—21no—
472C2×D8—21no—
473C2×D8—21no—
474#131—22no—
475#131—22no—
476#131—22no—
477#131—22no—
478#131—41no—
479#131—41no—
480C2×M16—22no—
481C2×M16—22no—
482C2×M16—41no—
483C2×M16C23×C10111yescharacteristic
484C2×M16C23×C10111yescharacteristic
485C2×M16C23×C10111yescharacteristic
486C2×M16C23×C10111yescharacteristic
487C2×M16C23×C10111yescharacteristic
488C2×M16C23×C10111yescharacteristic
489C2×M16C23×C10111yescharacteristic
490C2×M16C23×C10111yescharacteristic
491#127—21no—
492#127—21no—
493#127—21no—
494#127—41no—
495#124—21no—
496#121—41no—
497#120—22no—
498#117C23×C10111yescharacteristic
499C2×C42C23×C10111yescharacteristic
500#108—22no—
501#108—22no—
502#108—22no—
503C4⋊C8—41no—
504#104—22no—
505#104—22no—
506#104—21no—
507#104—21no—
508#104—21no—
509#104—21no—
510#104D4×C10112yescomplemented
511#104D4×C10112yescomplemented
512#102—41no—
513#101—21no—
514#101—21no—
515#101D4×C10112yescomplemented
516#100—21no—
517#100—21no—
518#100—22no—
519#100—22no—
520#100—22no—
521#100—22no—
522#100—22no—
523#100—22no—
524#100D4×C10112yescomplemented
525#97—21no—
526C4×C8—21no—
527C24—22no—
528C24—21no—
529C24#41×C10112yes—
530#41—21no—
531#41—21no—
532#41—21no—
533#41—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—21no—
539#41—21no—
540#41—42no—
541#41—42no—
542#41—42no—
543#41—42no—
544#41C2×D4×C10112yes—
545#41C2×D4×C10112yes—
546C2×Q8C2×D4×C10111yescharacteristic
547C2×Q8C2×D4×C10111yescharacteristic
548C2×Q8#41×C10111yescharacteristic
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—84no—
576C2×D4C2×D4×C10111yescharacteristic
577C2×D4C2×D4×C10111yescharacteristic
578C2×D4#41×C10111yescharacteristic
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4C24×C10111yescharacteristic
585Q16—22no—
586Q16—41no—
587SD16—22no—
588SD16—22no—
589SD16—42no—
590SD16—42no—
591SD16—41no—
592SD16—41no—
593SD16—42no—
594D8—22no—
595D8—42no—
596D8—42no—
597D8—41no—
598D8—42no—
599M16—21no—
600M16—21no—
601M16—21no—
602M16—21no—
603M16—21no—
604M16—21no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—42no—
612M16—42no—
613M16—42no—
614M16C2×D4×C10112yes—
615M16C2×D4×C10112yes—
616M16C2×D4×C10112yes—
617M16C2×D4×C10112yes—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—42no—
627C2×C8—42no—
628C2×C8—42no—
629C4⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—42no—
632C42—21no—
633C42—21no—
634C42C2×D4×C10111yescharacteristic
635C42C2×D4×C10111yescharacteristic
636C23—21no—
637C23—22no—
638C23—21no—
639C23—22no—
640C23—21no—
641C23—22no—
642C23—44no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—82no—
647C23—82no—
648C23—162no—
649C23C2×#41×C10111yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—21no—
655Q8#121×C10112yes—
656D4—22no—
657D4—22no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—21no—
663D4—44no—
664D4—44no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—84no—
678D4—84no—
679D4—162no—
680D4#121×C10112yes—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4C22×D4×C10111yescharacteristic
696C2×C4C22×D4×C10111yescharacteristic
697C2×C4C22×D4×C10111yescharacteristic
698C2×C4C2×#41×C10111yescharacteristic
699C2×C4H(5,𝔽2)×C10111yescharacteristic
700C2×C4H(5,𝔽2)×C10111yescharacteristic
701C8—22no—
702C8—22no—
703C8—22no—
704C8—22no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—81no—
715C22—82no—
716C22—81no—
717C22—82no—
718C22—82no—
719C22—81no—
720C22—82no—
721C22—81no—
722C22—161no—
723C22—161no—
724C22—164no—
725C22#525×C10111yescharacteristic
726C22#546×C10111yescharacteristic
727C22#546×C10111yescharacteristic
728C4—22no—
729C4—22no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4C2×#121×C10111yescharacteristic
735C4#538×C10111yescharacteristic
736C4D42×C10111yescharacteristic
737C4D42×C10111yescharacteristic
738C2—21no—
739C2—21no—
740C2—21no—
741C2—42no—
742C2—82no—
743C2—81no—
744C2—81no—
745C2—161no—
746C2C101×#242411yescharacteristic
subgroupG/H
center, socleC2×C101#2424
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×#3068C2semidirect
2. C101×#3068C2semidirect
3. C101×#3019C2semidirect
4. C2×#453×C101C2semidirect
5. C101×#2956C2semidirect
6. C101×#2888C2semidirect
7. C101×#2069C2semidirect
8. C101×#2050C2semidirect
9. C101×#2048C2semidirect
10. C101×#2002C2semidirect
11. C101×#1965C2semidirect
12. C101×#1932C2semidirect
13. C101×#1914C2semidirect
14. C101×#1903C2semidirect
15. C101×#1861C2semidirect
21. C2×AGL(1,ℤ/8)×C101C22semidirect
24. #568×C101C22semidirect
37. #430×C101C22semidirect
38. #430×C101C22semidirect
39. #430×C101C22semidirect
40. #423×C101C22semidirect
45. C2×#104×C101C22semidirect
46. #418×C101C22semidirect
50. #413×C101C22semidirect
56. C2×#100×C101C22semidirect
57. C2×#100×C101C22semidirect
58. C4×M16×C101C22semidirect
59. #344×C101C22semidirect
60. #344×C101C22semidirect
61. #339×C101C22semidirect
62. #338×C101C22semidirect
81. #137×C101D4semidirect
91. AGL(1,ℤ/8)×C101D4semidirect
136. #104×C101D4semidirect
137. #104×C101D4semidirect
141. #101×C101D4semidirect
150. #100×C101D4semidirect
364. #25196C101direct (N × H)
374. #3068C2×C101semidirect
375. #3068C2×C101semidirect
376. #3019C2×C101semidirect
377. C2×#453C2×C101semidirect
378. #2956C2×C101semidirect
379. #2888C2×C101semidirect
380. #2069C2×C101semidirect
381. #2050C2×C101semidirect
382. #2048C2×C101semidirect
383. #2002C2×C101semidirect
384. #1965C2×C101semidirect
385. #1932C2×C101semidirect
386. #1914C2×C101semidirect
387. #1903C2×C101semidirect
388. #1861C2×C101semidirect
389. C101#25196direct (N × H)
395. C2×AGL(1,ℤ/8)C22×C101semidirect
398. #568C22×C101semidirect
411. #430C22×C101semidirect
412. #430C22×C101semidirect
413. #430C22×C101semidirect
414. #423C22×C101semidirect
419. C2×#104C22×C101semidirect
420. #418C22×C101semidirect
424. #413C22×C101semidirect
430. C2×#100C22×C101semidirect
431. C2×#100C22×C101semidirect
432. C4×M16C22×C101semidirect
433. #344C22×C101semidirect
434. #344C22×C101semidirect
435. #339C22×C101semidirect
436. #338C22×C101semidirect
455. #137D4×C101semidirect
465. AGL(1,ℤ/8)D4×C101semidirect
510. #104D4×C101semidirect
511. #104D4×C101semidirect
515. #101D4×C101semidirect
524. #100D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#30682
C101×#30192
C2×#453×C1012
C101×#29562
C101×#28882
C101×#20692
C101×#20502
C101×#20482
C101×#20022
C101×#19652
C101×#19322
C101×#19142
C101×#19032
C101×#18612
#25196101