Finite Group Databasebeta

← C101×#25984 #38808135

Subgroups — C101×#25984 #38808135

Order 25856.

876 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3084C211yesmaximal, characteristic, complemented
2C101×#3083C211yesmaximal, characteristic, complemented
3C101×#2897C211yesmaximal, characteristic
4C101×#2897C211yesmaximal, characteristic
5C101×#2092C211yesmaximal, characteristic, complemented
6C101×#2063C211yesmaximal, characteristic, complemented
7C101×#2063C211yesmaximal, characteristic, complemented
8C101×#2027C211yesmaximal, characteristic, complemented
9C101×#1866C211yesmaximal, characteristic, complemented
10C101×#1866C211yesmaximal, characteristic, complemented
11C101×#1860C211yesmaximal, characteristic, complemented
12C101×#1860C211yesmaximal, characteristic, complemented
13C101×#1816C211yesmaximal, characteristic, complemented
14C101×#1815C211yesmaximal, characteristic, complemented
15C101×#1792C211yesmaximal, characteristic
16C2×H(5,𝔽2)×C101C2211yescharacteristic
17C2×#131×C101C2211yescharacteristic
18C2×#131×C101C2211yescharacteristic
19#544×C101C2211yescharacteristic, complemented
20#520×C101C2211yescharacteristic
21#520×C101C2211yescharacteristic
22#479×C101—21no—
23#479×C101—21no—
24#478×C101—21no—
25#478×C101—21no—
26#477×C101—21no—
27#476×C101—21no—
28#475×C101—21no—
29#474×C101—21no—
30C2×#108×C101C2211yescharacteristic, complemented
31C2×#108×C101C2211yescharacteristic, complemented
32#428×C101C2211yescharacteristic, complemented
33#428×C101C2211yescharacteristic, complemented
34C2×#107×C101C2211yescharacteristic, complemented
35C2×#106×C101C2211yescharacteristic, complemented
36#424×C101C2211yescharacteristic, complemented
37#424×C101C2211yescharacteristic, complemented
38C2×#104×C101C2211yescharacteristic
39C2×#104×C101C2211yescharacteristic
40#418×C101—21no—
41#418×C101—21no—
42#418×C101C2211yescharacteristic
43#418×C101C2211yescharacteristic
44#417×C101—21no—
45#417×C101—21no—
46#417×C101C2211yescharacteristic
47#417×C101C2211yescharacteristic
48#417×C101C2211yescharacteristic
49#417×C101C2211yescharacteristic
50#416×C101—21no—
51#416×C101—21no—
52#416×C101C2211yescharacteristic
53#416×C101C2211yescharacteristic
54C2×#102×C101—21no—
55C2×#102×C101—21no—
56C2×#102×C101C2211yescharacteristic
57C2×#102×C101C2211yescharacteristic
58C2×#100×C101C2211yescharacteristic
59#390×C101C2211yescharacteristic
60#382×C101C2211yescharacteristic, complemented
61#343×C101C2211yescharacteristic, complemented
62#343×C101C2211yescharacteristic, complemented
63#343×C101C2211yescharacteristic, complemented
64#339×C101C2211yescharacteristic, complemented
65#339×C101C2211yescharacteristic, complemented
66#336×C101C2211yescharacteristic, complemented
67H(5,𝔽2)×C101—22no—
68H(5,𝔽2)×C101—22no—
69H(5,𝔽2)×C101—41no—
70H(5,𝔽2)×C101Q814yescomplemented
71C2×#41×C101—21no—
72C2×#41×C101—21no—
73C2×#41×C101C2311yescharacteristic
74C2×#41×C101C2311yescharacteristic
75C22×D4×C101—21no—
76C22×D4×C101—21no—
77C22×D4×C101—41no—
78C22×D4×C101C2311yescharacteristic
79#131×C101—22no—
80#131×C101—22no—
81#131×C101—41no—
82#131×C101—41no—
83C2×M16×C101—21no—
84C2×M16×C101—21no—
85C2×M16×C101C2311yescharacteristic
86C2×M16×C101C2311yescharacteristic
87C2×M16×C101C2311yescharacteristic
88C2×M16×C101C2311yescharacteristic
89C22×C8×C101—21no—
90C22×C8×C101—21no—
91C22×C8×C101C2311yescharacteristic
92C22×C8×C101C2311yescharacteristic
93C4⋊Q8×C101—21no—
94C4⋊Q8×C101—21no—
95#125×C101—21no—
96#125×C101—21no—
97C22⋊Q8×C101—41no—
98C4×Q8×C101—21no—
99C4×Q8×C101—21no—
100C4×D4×C101—21no—
101C4×D4×C101—21no—
102C4×D4×C101—41no—
103C4×D4×C101—41no—
104#117×C101—21no—
105#117×C101—21no—
106#117×C101C2311yescharacteristic
107#117×C101C2311yescharacteristic
108C2×C4⋊C4×C101—21no—
109C2×C4⋊C4×C101—21no—
110C2×C4⋊C4×C101C2311yescharacteristic
111C2×C4⋊C4×C101C2311yescharacteristic
112C2×C4⋊C4×C101C2311yescharacteristic
113C2×C22⋊C4×C101—41no—
114C2×C42×C101C2311yescharacteristic
115#108×C101—41no—
116#108×C101—41no—
117#107×C101—21no—
118#107×C101—21no—
119#107×C101—21no—
120#107×C101—21no—
121#106×C101—21no—
122#106×C101—21no—
123#106×C101—21no—
124#106×C101—21no—
125C4⋊C8×C101—21no—
126C4⋊C8×C101—21no—
127C4⋊C8×C101—21no—
128C4⋊C8×C101—21no—
129#104×C101—22no—
130#104×C101—22no—
131#103×C101—21no—
132#103×C101—21no—
133#103×C101—21no—
134#103×C101—21no—
135#103×C101D411yescharacteristic
136#103×C101D411yescharacteristic
137#103×C101D411yescharacteristic
138#103×C101D411yescharacteristic
139#102×C101—21no—
140#102×C101—21no—
141#102×C101—21no—
142#102×C101—21no—
143#102×C101—21no—
144#102×C101—21no—
145#102×C101—21no—
146#102×C101—21no—
147#102×C101—21no—
148#102×C101—21no—
149#102×C101—21no—
150#102×C101—21no—
151#102×C101D411yescharacteristic
152#102×C101D411yescharacteristic
153#102×C101D411yescharacteristic
154#102×C101D411yescharacteristic
155#100×C101—41no—
156#95×C101—41no—
157C24×C101—21no—
158C24×C101—41no—
159#41×C101—21no—
160#41×C101—21no—
161#41×C101—21no—
162#41×C101—21no—
163#41×C101—24no—
164#41×C101—24no—
165#41×C101—42no—
166#41×C101—42no—
167#41×C101C2×Q812yes—
168#41×C101C2×Q812yes—
169#41×C101#4112yes—
170#41×C101#4112yes—
171C2×Q8×C101—41no—
172C2×Q8×C101C2×D411yescharacteristic
173C2×Q8×C101C2×D411yescharacteristic
174C2×D4×C101—21no—
175C2×D4×C101—21no—
176C2×D4×C101—24no—
177C2×D4×C101—24no—
178C2×D4×C101—21no—
179C2×D4×C101—21no—
180C2×D4×C101—21no—
181C2×D4×C101—21no—
182C2×D4×C101—21no—
183C2×D4×C101—42no—
184C2×D4×C101—42no—
185C2×D4×C101—41no—
186C2×D4×C101—41no—
187C2×D4×C101—44no—
188C2×D4×C101—44no—
189C2×D4×C101C2×D411yescharacteristic
190C2×D4×C101C2×D411yescharacteristic
191C2×D4×C101C2×Q812yes—
192C22×C4×C101—21no—
193C22×C4×C101—21no—
194C22×C4×C101—21no—
195C22×C4×C101—21no—
196C22×C4×C101—21no—
197C22×C4×C101—21no—
198C22×C4×C101—41no—
199C22×C4×C101—41no—
200C22×C4×C101—41no—
201C22×C4×C101C2411yescharacteristic
202M16×C101—21no—
203M16×C101—21no—
204M16×C101—21no—
205M16×C101—21no—
206M16×C101—21no—
207M16×C101—21no—
208M16×C101—21no—
209M16×C101—21no—
210M16×C101—42no—
211M16×C101—42no—
212C2×C8×C101—21no—
213C2×C8×C101—21no—
214C2×C8×C101—21no—
215C2×C8×C101—21no—
216C2×C8×C101—21no—
217C2×C8×C101—21no—
218C2×C8×C101—21no—
219C2×C8×C101—21no—
220C2×C8×C101—42no—
221C2×C8×C101—42no—
222C2×C8×C101C2×D411yescharacteristic
223C2×C8×C101C2×D411yescharacteristic
224C2×C8×C101C2×D411yescharacteristic
225C2×C8×C101C2×D411yescharacteristic
226C4⋊C4×C101—21no—
227C4⋊C4×C101—21no—
228C4⋊C4×C101—21no—
229C4⋊C4×C101—21no—
230C4⋊C4×C101—21no—
231C4⋊C4×C101—21no—
232C4⋊C4×C101—41no—
233C4⋊C4×C101—41no—
234C4⋊C4×C101—41no—
235C4⋊C4×C101—41no—
236C4⋊C4×C101—41no—
237C4⋊C4×C101C2×D411yescharacteristic
238C4⋊C4×C101C2×D411yescharacteristic
239C4⋊C4×C101C2×D411yescharacteristic
240C4⋊C4×C101C2×D411yescharacteristic
241C22⋊C4×C101—21no—
242C22⋊C4×C101—21no—
243C22⋊C4×C101—41no—
244C22⋊C4×C101—41no—
245C22⋊C4×C101—82no—
246C42×C101—21no—
247C42×C101—21no—
248C42×C101—21no—
249C42×C101—21no—
250C42×C101—41no—
251C42×C101—41no—
252C23×C101—21no—
253C23×C101—21no—
254C23×C101—22no—
255C23×C101—44no—
256C23×C101—41no—
257C23×C101—41no—
258C23×C101—81no—
259C23×C101—81no—
260C23×C101—161no—
261C23×C101—161no—
262C23×C101H(5,𝔽2)11yescharacteristic
263Q8×C101—21no—
264Q8×C101—21no—
265Q8×C101—161no—
266Q8×C101C22⋊Q812yes—
267Q8×C101C22⋊Q812yes—
268D4×C101—22no—
269D4×C101—22no—
270D4×C101—22no—
271D4×C101—22no—
272D4×C101—22no—
273D4×C101—22no—
274D4×C101—21no—
275D4×C101—21no—
276D4×C101—44no—
277D4×C101—44no—
278D4×C101—41no—
279D4×C101—41no—
280D4×C101C22⋊Q812yes—
281D4×C101C22⋊Q812yes—
282C2×C4×C101—21no—
283C2×C4×C101—21no—
284C2×C4×C101—22no—
285C2×C4×C101—22no—
286C2×C4×C101—22no—
287C2×C4×C101—22no—
288C2×C4×C101—21no—
289C2×C4×C101—21no—
290C2×C4×C101—21no—
291C2×C4×C101—21no—
292C2×C4×C101—44no—
293C2×C4×C101—41no—
294C2×C4×C101—41no—
295C2×C4×C101—41no—
296C2×C4×C101—41no—
297C2×C4×C101—41no—
298C2×C4×C101—41no—
299C2×C4×C101—81no—
300C2×C4×C101—81no—
301C2×C4×C101—81no—
302C2×C4×C101—161no—
303C2×C4×C101—161no—
304C2×C4×C101C22×D411yescharacteristic
305C2×C4×C101C22×D411yescharacteristic
306C2×C4×C101C22×Q811yescharacteristic
307C2×C4×C101C2×#4111yescharacteristic
308C2×C4×C101C2×#4111yescharacteristic
309C2×C4×C101H(5,𝔽2)11yescharacteristic
310C8×C101—21no—
311C8×C101—21no—
312C8×C101—21no—
313C8×C101—21no—
314C8×C101—41no—
315C8×C101—41no—
316C8×C101—41no—
317C8×C101—41no—
318C22×C101—21no—
319C22×C101—21no—
320C22×C101—22no—
321C22×C101—22no—
322C22×C101—41no—
323C22×C101—41no—
324C22×C101—41no—
325C22×C101—41no—
326C22×C101—42no—
327C22×C101—82no—
328C22×C101—81no—
329C22×C101—81no—
330C22×C101—161no—
331C22×C101—164no—
332C22×C101#54311yescharacteristic
333C22×C101D4211yescharacteristic
334C22×C101#55111yescharacteristic
335C4×C101—22no—
336C4×C101—22no—
337C4×C101—41no—
338C4×C101—41no—
339C4×C101—41no—
340C4×C101—41no—
341C4×C101—81no—
342C4×C101—81no—
343C4×C101—81no—
344C4×C101—81no—
345C4×C101C2×C22⋊Q811yescharacteristic
346C4×C101C2×C22⋊Q811yescharacteristic
347C4×C101#54611yescharacteristic
348C4×C101#54611yescharacteristic
349#25984C10111yesmaximal, characteristic, direct product factor, Sylow
350C2×C101—21no—
351C2×C101—21no—
352C2×C101—42no—
353C2×C101—42no—
354C2×C101—82no—
355C2×C101#243711yescharacteristic
356C2×C101#328811yescharacteristic
357C2×C101#329011yescharacteristic
358#3084C2×C10111yescharacteristic, complemented
359#3083C2×C10111yescharacteristic, complemented
360#2897C2×C10111yescharacteristic
361#2897C2×C10111yescharacteristic
362#2092C2×C10111yescharacteristic, complemented
363#2063C2×C10111yescharacteristic, complemented
364#2063C2×C10111yescharacteristic, complemented
365#2027C2×C10111yescharacteristic, complemented
366#1866C2×C10111yescharacteristic, complemented
367#1866C2×C10111yescharacteristic, complemented
368#1860C2×C10111yescharacteristic, complemented
369#1860C2×C10111yescharacteristic, complemented
370#1816C2×C10111yescharacteristic, complemented
371#1815C2×C10111yescharacteristic, complemented
372#1792C2×C10111yescharacteristic
373C101#2598411yescharacteristic, direct product factor, Sylow
374C2×H(5,𝔽2)C22×C10111yescharacteristic
375C2×#131C22×C10111yescharacteristic
376C2×#131C22×C10111yescharacteristic
377#544C22×C10111yescharacteristic, complemented
378#520C22×C10111yescharacteristic
379#520C22×C10111yescharacteristic
380#479—21no—
381#479—21no—
382#478—21no—
383#478—21no—
384#477—21no—
385#476—21no—
386#475—21no—
387#474—21no—
388C2×#108C22×C10111yescharacteristic, complemented
389C2×#108C22×C10111yescharacteristic, complemented
390#428C22×C10111yescharacteristic, complemented
391#428C22×C10111yescharacteristic, complemented
392C2×#107C22×C10111yescharacteristic, complemented
393C2×#106C22×C10111yescharacteristic, complemented
394#424C22×C10111yescharacteristic, complemented
395#424C22×C10111yescharacteristic, complemented
396C2×#104C22×C10111yescharacteristic
397C2×#104C22×C10111yescharacteristic
398#418—21no—
399#418—21no—
400#418C22×C10111yescharacteristic
401#418C22×C10111yescharacteristic
402#417—21no—
403#417—21no—
404#417C22×C10111yescharacteristic
405#417C22×C10111yescharacteristic
406#417C22×C10111yescharacteristic
407#417C22×C10111yescharacteristic
408#416—21no—
409#416—21no—
410#416C22×C10111yescharacteristic
411#416C22×C10111yescharacteristic
412C2×#102—21no—
413C2×#102—21no—
414C2×#102C22×C10111yescharacteristic
415C2×#102C22×C10111yescharacteristic
416C2×#100C22×C10111yescharacteristic
417#390C22×C10111yescharacteristic
418#382C22×C10111yescharacteristic, complemented
419#343C22×C10111yescharacteristic, complemented
420#343C22×C10111yescharacteristic, complemented
421#343C22×C10111yescharacteristic, complemented
422#339C22×C10111yescharacteristic, complemented
423#339C22×C10111yescharacteristic, complemented
424#336C22×C10111yescharacteristic, complemented
425H(5,𝔽2)—22no—
426H(5,𝔽2)—22no—
427H(5,𝔽2)—41no—
428H(5,𝔽2)Q8×C10114yescomplemented
429C2×#41—21no—
430C2×#41—21no—
431C2×#41C23×C10111yescharacteristic
432C2×#41C23×C10111yescharacteristic
433C22×D4—21no—
434C22×D4—21no—
435C22×D4—41no—
436C22×D4C23×C10111yescharacteristic
437#131—22no—
438#131—22no—
439#131—41no—
440#131—41no—
441C2×M16—21no—
442C2×M16—21no—
443C2×M16C23×C10111yescharacteristic
444C2×M16C23×C10111yescharacteristic
445C2×M16C23×C10111yescharacteristic
446C2×M16C23×C10111yescharacteristic
447C22×C8—21no—
448C22×C8—21no—
449C22×C8C23×C10111yescharacteristic
450C22×C8C23×C10111yescharacteristic
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453#125—21no—
454#125—21no—
455C22⋊Q8—41no—
456C4×Q8—21no—
457C4×Q8—21no—
458C4×D4—21no—
459C4×D4—21no—
460C4×D4—41no—
461C4×D4—41no—
462#117—21no—
463#117—21no—
464#117C23×C10111yescharacteristic
465#117C23×C10111yescharacteristic
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4C23×C10111yescharacteristic
469C2×C4⋊C4C23×C10111yescharacteristic
470C2×C4⋊C4C23×C10111yescharacteristic
471C2×C22⋊C4—41no—
472C2×C42C23×C10111yescharacteristic
473#108—41no—
474#108—41no—
475#107—21no—
476#107—21no—
477#107—21no—
478#107—21no—
479#106—21no—
480#106—21no—
481#106—21no—
482#106—21no—
483C4⋊C8—21no—
484C4⋊C8—21no—
485C4⋊C8—21no—
486C4⋊C8—21no—
487#104—22no—
488#104—22no—
489#103—21no—
490#103—21no—
491#103—21no—
492#103—21no—
493#103D4×C10111yescharacteristic
494#103D4×C10111yescharacteristic
495#103D4×C10111yescharacteristic
496#103D4×C10111yescharacteristic
497#102—21no—
498#102—21no—
499#102—21no—
500#102—21no—
501#102—21no—
502#102—21no—
503#102—21no—
504#102—21no—
505#102—21no—
506#102—21no—
507#102—21no—
508#102—21no—
509#102D4×C10111yescharacteristic
510#102D4×C10111yescharacteristic
511#102D4×C10111yescharacteristic
512#102D4×C10111yescharacteristic
513#100—41no—
514#95—41no—
515C24—21no—
516C24—41no—
517#41—21no—
518#41—21no—
519#41—21no—
520#41—21no—
521#41—24no—
522#41—24no—
523#41—42no—
524#41—42no—
525#41C2×Q8×C10112yes—
526#41C2×Q8×C10112yes—
527#41#41×C10112yes—
528#41#41×C10112yes—
529C2×Q8—41no—
530C2×Q8C2×D4×C10111yescharacteristic
531C2×Q8C2×D4×C10111yescharacteristic
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—41no—
544C2×D4—41no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4C2×D4×C10111yescharacteristic
548C2×D4C2×D4×C10111yescharacteristic
549C2×D4C2×Q8×C10112yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4C24×C10111yescharacteristic
560M16—21no—
561M16—21no—
562M16—21no—
563M16—21no—
564M16—21no—
565M16—21no—
566M16—21no—
567M16—21no—
568M16—42no—
569M16—42no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—42no—
579C2×C8—42no—
580C2×C8C2×D4×C10111yescharacteristic
581C2×C8C2×D4×C10111yescharacteristic
582C2×C8C2×D4×C10111yescharacteristic
583C2×C8C2×D4×C10111yescharacteristic
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4C2×D4×C10111yescharacteristic
596C4⋊C4C2×D4×C10111yescharacteristic
597C4⋊C4C2×D4×C10111yescharacteristic
598C4⋊C4C2×D4×C10111yescharacteristic
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C22⋊C4—82no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—41no—
609C42—41no—
610C23—21no—
611C23—21no—
612C23—22no—
613C23—44no—
614C23—41no—
615C23—41no—
616C23—81no—
617C23—81no—
618C23—161no—
619C23—161no—
620C23H(5,𝔽2)×C10111yescharacteristic
621Q8—21no—
622Q8—21no—
623Q8—161no—
624Q8C22⋊Q8×C10112yes—
625Q8C22⋊Q8×C10112yes—
626D4—22no—
627D4—22no—
628D4—22no—
629D4—22no—
630D4—22no—
631D4—22no—
632D4—21no—
633D4—21no—
634D4—44no—
635D4—44no—
636D4—41no—
637D4—41no—
638D4C22⋊Q8×C10112yes—
639D4C22⋊Q8×C10112yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—44no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—81no—
658C2×C4—81no—
659C2×C4—81no—
660C2×C4—161no—
661C2×C4—161no—
662C2×C4C22×D4×C10111yescharacteristic
663C2×C4C22×D4×C10111yescharacteristic
664C2×C4C22×Q8×C10111yescharacteristic
665C2×C4C2×#41×C10111yescharacteristic
666C2×C4C2×#41×C10111yescharacteristic
667C2×C4H(5,𝔽2)×C10111yescharacteristic
668C8—21no—
669C8—21no—
670C8—21no—
671C8—21no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C22—21no—
677C22—21no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—42no—
685C22—82no—
686C22—81no—
687C22—81no—
688C22—161no—
689C22—164no—
690C22#543×C10111yescharacteristic
691C22D42×C10111yescharacteristic
692C22#551×C10111yescharacteristic
693C4—22no—
694C4—22no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4C2×C22⋊Q8×C10111yescharacteristic
704C4C2×C22⋊Q8×C10111yescharacteristic
705C4#546×C10111yescharacteristic
706C4#546×C10111yescharacteristic
707C2—21no—
708C2—21no—
709C2—42no—
710C2—42no—
711C2—82no—
712C2C101×#243711yescharacteristic
713C2C101×#328811yescharacteristic
714C2C101×#329011yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×H(5,𝔽2)×C101C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3084C2semidirect
2. C101×#3083C2semidirect
5. C101×#2092C2semidirect
6. C101×#2063C2semidirect
7. C101×#2063C2semidirect
8. C101×#2027C2semidirect
9. C101×#1866C2semidirect
10. C101×#1866C2semidirect
11. C101×#1860C2semidirect
12. C101×#1860C2semidirect
13. C101×#1816C2semidirect
14. C101×#1815C2semidirect
19. #544×C101C22semidirect
30. C2×#108×C101C22semidirect
31. C2×#108×C101C22semidirect
32. #428×C101C22semidirect
33. #428×C101C22semidirect
34. C2×#107×C101C22semidirect
35. C2×#106×C101C22semidirect
36. #424×C101C22semidirect
37. #424×C101C22semidirect
60. #382×C101C22semidirect
61. #343×C101C22semidirect
62. #343×C101C22semidirect
63. #343×C101C22semidirect
64. #339×C101C22semidirect
65. #339×C101C22semidirect
66. #336×C101C22semidirect
70. H(5,𝔽2)×C101Q8semidirect
349. #25984C101direct (N × H)
358. #3084C2×C101semidirect
359. #3083C2×C101semidirect
362. #2092C2×C101semidirect
363. #2063C2×C101semidirect
364. #2063C2×C101semidirect
365. #2027C2×C101semidirect
366. #1866C2×C101semidirect
367. #1866C2×C101semidirect
368. #1860C2×C101semidirect
369. #1860C2×C101semidirect
370. #1816C2×C101semidirect
371. #1815C2×C101semidirect
373. C101#25984direct (N × H)
377. #544C22×C101semidirect
388. C2×#108C22×C101semidirect
389. C2×#108C22×C101semidirect
390. #428C22×C101semidirect
391. #428C22×C101semidirect
392. C2×#107C22×C101semidirect
393. C2×#106C22×C101semidirect
394. #424C22×C101semidirect
395. #424C22×C101semidirect
418. #382C22×C101semidirect
419. #343C22×C101semidirect
420. #343C22×C101semidirect
421. #343C22×C101semidirect
422. #339C22×C101semidirect
423. #339C22×C101semidirect
424. #336C22×C101semidirect
428. H(5,𝔽2)Q8×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#30842
C101×#30832
C101×#28972
C101×#20922
C101×#20632
C101×#20272
C101×#18662
C101×#18602
C101×#18162
C101×#18152
C101×#17922
#25984101