Finite Group Databasebeta

← C101×#23996 #38806147

Subgroups — C101×#23996 #38806147

Order 25856.

1396 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3490C211yesmaximal, characteristic, complemented
2C101×#3026C211yesmaximal, characteristic, complemented
3C2×B(4,𝔽2)×C101C211yesmaximal, characteristic, complemented
4C101×#2883C211yesmaximal, characteristic, complemented
5C101×#2032C212yesmaximal, complemented
6C101×#2021C212yesmaximal, complemented
7C101×#1913C212yesmaximal, complemented
8C101×#1913C211yesmaximal, characteristic, complemented
9C101×#1898C212yesmaximal, complemented
10C101×#1889C211yesmaximal, characteristic, complemented
11C101×#1828C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C101C2211yescharacteristic
13#551×C101—22no—
14#551×C101—22no—
15#546×C101—22no—
16#546×C101—22no—
17#543×C101C2211yescharacteristic, complemented
18#538×C101—22no—
19#534×C101C2212yes—
20#534×C101C2211yescharacteristic
21#525×C101—22no—
22C2×#120×C101C2212yes—
23C2×#120×C101C2211yescharacteristic
24C2×#120×C101C2211yescharacteristic, complemented
25#518×C101C2211yescharacteristic
26#518×C101C2211yescharacteristic
27#518×C101C2211yescharacteristic, complemented
28C22×C22⋊C4×C101C2211yescharacteristic, complemented
29#458×C101—22no—
30B(4,𝔽2)×C101—22no—
31B(4,𝔽2)×C101—22no—
32B(4,𝔽2)×C101—22no—
33#410×C101—22no—
34C2×#99×C101—22no—
35C2×#99×C101C2211yescharacteristic
36C2×#99×C101C2212yes—
37C2×#99×C101C2212yes—
38C2×#99×C101C2212yes—
39C2×#99×C101C2211yescharacteristic
40C2×#99×C101C2212yes—
41C2×#99×C101C2212yescomplemented
42#379×C101C2212yescomplemented
43#342×C101C2212yescomplemented
44#342×C101C2212yescomplemented
45#342×C101C2212yescomplemented
46#342×C101C2212yescomplemented
47C25×C101C2311yescharacteristic
48H(5,𝔽2)×C101—22no—
49H(5,𝔽2)×C101—22no—
50H(5,𝔽2)×C101—42no—
51C2×#41×C101—22no—
52C2×#41×C101—21no—
53C2×#41×C101—22no—
54C22×D4×C101—21no—
55C22×D4×C101—22no—
56C22×D4×C101—21no—
57C22×D4×C101—21no—
58C22×D4×C101—22no—
59C22×D4×C101C2311yescharacteristic
60C22×D4×C101C2311yescharacteristic
61C22×D4×C101C2312yes—
62C23×C4×C101—21no—
63#126×C101—22no—
64#126×C101—22no—
65#124×C101—22no—
66#124×C101—22no—
67#123×C101—22no—
68#123×C101—22no—
69#123×C101—22no—
70#123×C101—22no—
71#123×C101—21no—
72#123×C101—22no—
73#123×C101—22no—
74#123×C101D412yescomplemented
75C22⋊Q8×C101—22no—
76C22⋊Q8×C101—22no—
77C22⋊Q8×C101—22no—
78C22⋊Q8×C101—22no—
79#121×C101—22no—
80#121×C101—22no—
81#121×C101—22no—
82#121×C101—22no—
83#121×C101—42no—
84#120×C101—21no—
85#120×C101—21no—
86#120×C101—21no—
87#120×C101—22no—
88#120×C101—22no—
89#120×C101—22no—
90#120×C101—22no—
91#120×C101—22no—
92#120×C101—22no—
93#120×C101—42no—
94#120×C101D412yescomplemented
95#120×C101D412yescomplemented
96#120×C101D412yescomplemented
97C4×D4×C101—22no—
98C4×D4×C101—22no—
99C4×D4×C101—22no—
100C4×D4×C101—22no—
101C4×D4×C101—22no—
102C4×D4×C101—22no—
103C4×D4×C101—42no—
104#117×C101—22no—
105#117×C101—21no—
106#117×C101—21no—
107#117×C101D412yescomplemented
108C2×C22⋊C4×C101—21no—
109C2×C22⋊C4×C101—21no—
110C2×C22⋊C4×C101—21no—
111C2×C22⋊C4×C101—21no—
112C2×C22⋊C4×C101—22no—
113C2×C22⋊C4×C101—22no—
114C2×C22⋊C4×C101—21no—
115C2×C22⋊C4×C101—22no—
116C2×C22⋊C4×C101—42no—
117C2×C22⋊C4×C101D412yescomplemented
118C2×C22⋊C4×C101C2312yes—
119C2×C22⋊C4×C101C2312yes—
120C2×C22⋊C4×C101C2312yes—
121C2×C22⋊C4×C101C2311yescharacteristic
122C2×C22⋊C4×C101C2311yescharacteristic
123C2×C22⋊C4×C101C2311yescharacteristic
124C2×C22⋊C4×C101C2311yescharacteristic
125#99×C101—22no—
126#99×C101—22no—
127#99×C101—24no—
128#99×C101—24no—
129#99×C101—24no—
130#99×C101—24no—
131#99×C101—42no—
132C24×C101—21no—
133C24×C101—21no—
134C24×C101—21no—
135C24×C101—22no—
136C24×C101—22no—
137C24×C101—82no—
138C24×C101C2×D411yescharacteristic
139C24×C101C2×D411yescharacteristic
140C24×C101C2×D411yescharacteristic
141C24×C101C2×D411yescharacteristic
142C24×C101#4112yescomplemented
143C24×C101C2411yescharacteristic
144#41×C101—44no—
145#41×C101—44no—
146#41×C101—42no—
147#41×C101—42no—
148#41×C101—84no—
149C2×Q8×C101—21no—
150C2×Q8×C101—22no—
151C2×D4×C101—22no—
152C2×D4×C101—22no—
153C2×D4×C101—22no—
154C2×D4×C101—21no—
155C2×D4×C101—22no—
156C2×D4×C101—22no—
157C2×D4×C101—22no—
158C2×D4×C101—22no—
159C2×D4×C101—22no—
160C2×D4×C101—21no—
161C2×D4×C101—21no—
162C2×D4×C101—22no—
163C2×D4×C101—22no—
164C2×D4×C101—22no—
165C2×D4×C101—22no—
166C2×D4×C101—22no—
167C2×D4×C101—22no—
168C2×D4×C101—22no—
169C2×D4×C101—22no—
170C2×D4×C101—44no—
171C2×D4×C101—44no—
172C2×D4×C101—42no—
173C2×D4×C101—42no—
174C2×D4×C101—42no—
175C2×D4×C101—42no—
176C2×D4×C101—42no—
177C2×D4×C101—82no—
178C2×D4×C101—82no—
179C2×D4×C101—84no—
180C2×D4×C101C2×D412yes—
181C2×D4×C101C2×D412yes—
182C22×C4×C101—22no—
183C22×C4×C101—22no—
184C22×C4×C101—21no—
185C22×C4×C101—22no—
186C22×C4×C101—22no—
187C22×C4×C101—22no—
188C22×C4×C101—21no—
189C22×C4×C101—21no—
190C22×C4×C101—21no—
191C22×C4×C101—21no—
192C22×C4×C101—22no—
193C22×C4×C101—22no—
194C22×C4×C101—22no—
195C22×C4×C101—41no—
196C22×C4×C101—82no—
197C22×C4×C101C2×D411yescharacteristic
198C22×C4×C101C2×D411yescharacteristic
199C22×C4×C101#4112yescomplemented
200C4⋊C4×C101—22no—
201C4⋊C4×C101—22no—
202C4⋊C4×C101—22no—
203C4⋊C4×C101—22no—
204C4⋊C4×C101—22no—
205C4⋊C4×C101—22no—
206C4⋊C4×C101—42no—
207C4⋊C4×C101—41no—
208C22⋊C4×C101—22no—
209C22⋊C4×C101—22no—
210C22⋊C4×C101—22no—
211C22⋊C4×C101—22no—
212C22⋊C4×C101—22no—
213C22⋊C4×C101—22no—
214C22⋊C4×C101—22no—
215C22⋊C4×C101—21no—
216C22⋊C4×C101—21no—
217C22⋊C4×C101—21no—
218C22⋊C4×C101—21no—
219C22⋊C4×C101—22no—
220C22⋊C4×C101—22no—
221C22⋊C4×C101—22no—
222C22⋊C4×C101—22no—
223C22⋊C4×C101—22no—
224C22⋊C4×C101—22no—
225C22⋊C4×C101—22no—
226C22⋊C4×C101—22no—
227C22⋊C4×C101—22no—
228C22⋊C4×C101—42no—
229C22⋊C4×C101—42no—
230C22⋊C4×C101—42no—
231C22⋊C4×C101—42no—
232C22⋊C4×C101—41no—
233C22⋊C4×C101—84no—
234C22⋊C4×C101C2×D412yes—
235C22⋊C4×C101C2×D412yes—
236C22⋊C4×C101C2×D412yes—
237C22⋊C4×C101C2×D412yes—
238C42×C101—22no—
239C42×C101—22no—
240C42×C101—41no—
241C23×C101—21no—
242C23×C101—22no—
243C23×C101—21no—
244C23×C101—21no—
245C23×C101—21no—
246C23×C101—21no—
247C23×C101—22no—
248C23×C101—22no—
249C23×C101—22no—
250C23×C101—22no—
251C23×C101—22no—
252C23×C101—42no—
253C23×C101—44no—
254C23×C101—42no—
255C23×C101—42no—
256C23×C101—44no—
257C23×C101—42no—
258C23×C101—41no—
259C23×C101—41no—
260C23×C101—42no—
261C23×C101—81no—
262C23×C101—81no—
263C23×C101—81no—
264C23×C101—81no—
265C23×C101—82no—
266C23×C101—81no—
267C23×C101—81no—
268C23×C101—82no—
269C23×C101—82no—
270C23×C101—161no—
271C23×C101#12012yes—
272C23×C101C22×D411yescharacteristic
273C23×C101C22×D411yescharacteristic
274C23×C101C22×D411yescharacteristic
275C23×C101C2×#4112yes—
276C23×C101H(5,𝔽2)12yes—
277Q8×C101—42no—
278Q8×C101—82no—
279D4×C101—24no—
280D4×C101—24no—
281D4×C101—42no—
282D4×C101—44no—
283D4×C101—44no—
284D4×C101—44no—
285D4×C101—42no—
286D4×C101—41no—
287D4×C101—41no—
288D4×C101—42no—
289D4×C101—42no—
290D4×C101—42no—
291D4×C101—42no—
292D4×C101—82no—
293D4×C101—82no—
294D4×C101—82no—
295D4×C101—84no—
296D4×C101—84no—
297D4×C101—162no—
298C2×C4×C101—21no—
299C2×C4×C101—21no—
300C2×C4×C101—21no—
301C2×C4×C101—22no—
302C2×C4×C101—22no—
303C2×C4×C101—22no—
304C2×C4×C101—22no—
305C2×C4×C101—22no—
306C2×C4×C101—22no—
307C2×C4×C101—22no—
308C2×C4×C101—22no—
309C2×C4×C101—44no—
310C2×C4×C101—44no—
311C2×C4×C101—42no—
312C2×C4×C101—42no—
313C2×C4×C101—42no—
314C2×C4×C101—42no—
315C2×C4×C101—81no—
316C2×C4×C101—82no—
317C2×C4×C101—81no—
318C2×C4×C101—81no—
319C2×C4×C101—81no—
320C2×C4×C101—82no—
321C2×C4×C101—82no—
322C2×C4×C101—82no—
323C2×C4×C101—82no—
324C2×C4×C101—82no—
325C2×C4×C101—161no—
326C2×C4×C101#12012yes—
327C22×C101—22no—
328C22×C101—24no—
329C22×C101—22no—
330C22×C101—41no—
331C22×C101—42no—
332C22×C101—41no—
333C22×C101—41no—
334C22×C101—42no—
335C22×C101—42no—
336C22×C101—41no—
337C22×C101—42no—
338C22×C101—42no—
339C22×C101—41no—
340C22×C101—41no—
341C22×C101—42no—
342C22×C101—42no—
343C22×C101—41no—
344C22×C101—42no—
345C22×C101—41no—
346C22×C101—41no—
347C22×C101—81no—
348C22×C101—81no—
349C22×C101—82no—
350C22×C101—84no—
351C22×C101—82no—
352C22×C101—82no—
353C22×C101—82no—
354C22×C101—82no—
355C22×C101—82no—
356C22×C101—162no—
357C22×C101C2×#12011yescharacteristic
358C22×C101#52511yescharacteristic
359C22×C101#53511yescharacteristic
360C22×C101#54612yes—
361C22×C101#54612yes—
362C4×C101—22no—
363C4×C101—42no—
364C4×C101—42no—
365C4×C101—42no—
366C4×C101—42no—
367C4×C101—42no—
368C4×C101—41no—
369C4×C101—82no—
370C4×C101—82no—
371C4×C101—82no—
372#23996C10111yesmaximal, characteristic, direct product factor, Sylow
373C2×C101—21no—
374C2×C101—21no—
375C2×C101—22no—
376C2×C101—22no—
377C2×C101—21no—
378C2×C101—42no—
379C2×C101—42no—
380C2×C101—81no—
381C2×C101—81no—
382C2×C101—82no—
383C2×C101#240411yescharacteristic
384#3490C2×C10111yescharacteristic, complemented
385#3026C2×C10111yescharacteristic, complemented
386C2×B(4,𝔽2)C2×C10111yescharacteristic, complemented
387#2883C2×C10111yescharacteristic, complemented
388#2032C2×C10112yescomplemented
389#2021C2×C10112yescomplemented
390#1913C2×C10111yescharacteristic, complemented
391#1913C2×C10112yescomplemented
392#1898C2×C10112yescomplemented
393#1889C2×C10111yescharacteristic, complemented
394#1828C2×C10111yescharacteristic, complemented
395C101#2399611yescharacteristic, direct product factor, Sylow
396C2×H(5,𝔽2)C22×C10111yescharacteristic
397#551—22no—
398#551—22no—
399#546—22no—
400#546—22no—
401#543C22×C10111yescharacteristic, complemented
402#538—22no—
403#534C22×C10112yes—
404#534C22×C10111yescharacteristic
405#525—22no—
406C2×#120C22×C10112yes—
407C2×#120C22×C10111yescharacteristic
408C2×#120C22×C10111yescharacteristic, complemented
409#518C22×C10111yescharacteristic
410#518C22×C10111yescharacteristic
411#518C22×C10111yescharacteristic, complemented
412C22×C22⋊C4C22×C10111yescharacteristic, complemented
413#458—22no—
414B(4,𝔽2)—22no—
415B(4,𝔽2)—22no—
416B(4,𝔽2)—22no—
417#410—22no—
418C2×#99—22no—
419C2×#99C22×C10111yescharacteristic
420C2×#99C22×C10111yescharacteristic
421C2×#99C22×C10112yes—
422C2×#99C22×C10112yes—
423C2×#99C22×C10112yes—
424C2×#99C22×C10112yes—
425C2×#99C22×C10112yescomplemented
426#379C22×C10112yescomplemented
427#342C22×C10112yescomplemented
428#342C22×C10112yescomplemented
429#342C22×C10112yescomplemented
430#342C22×C10112yescomplemented
431C25C23×C10111yescharacteristic
432H(5,𝔽2)—22no—
433H(5,𝔽2)—22no—
434H(5,𝔽2)—42no—
435C2×#41—22no—
436C2×#41—21no—
437C2×#41—22no—
438C22×D4—21no—
439C22×D4—22no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—22no—
443C22×D4C23×C10111yescharacteristic
444C22×D4C23×C10111yescharacteristic
445C22×D4C23×C10112yes—
446C23×C4—21no—
447#126—22no—
448#126—22no—
449#124—22no—
450#124—22no—
451#123—22no—
452#123—22no—
453#123—22no—
454#123—22no—
455#123—21no—
456#123—22no—
457#123—22no—
458#123D4×C10112yescomplemented
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463#121—22no—
464#121—22no—
465#121—22no—
466#121—22no—
467#121—42no—
468#120—21no—
469#120—21no—
470#120—21no—
471#120—22no—
472#120—22no—
473#120—22no—
474#120—22no—
475#120—22no—
476#120—22no—
477#120—42no—
478#120D4×C10112yescomplemented
479#120D4×C10112yescomplemented
480#120D4×C10112yescomplemented
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—42no—
488#117—22no—
489#117—21no—
490#117—21no—
491#117D4×C10112yescomplemented
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4D4×C10112yescomplemented
502C2×C22⋊C4C23×C10112yes—
503C2×C22⋊C4C23×C10112yes—
504C2×C22⋊C4C23×C10112yes—
505C2×C22⋊C4C23×C10111yescharacteristic
506C2×C22⋊C4C23×C10111yescharacteristic
507C2×C22⋊C4C23×C10111yescharacteristic
508C2×C22⋊C4C23×C10111yescharacteristic
509#99—22no—
510#99—22no—
511#99—24no—
512#99—24no—
513#99—24no—
514#99—24no—
515#99—42no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—22no—
520C24—22no—
521C24—82no—
522C24C2×D4×C10111yescharacteristic
523C24C2×D4×C10111yescharacteristic
524C24C2×D4×C10111yescharacteristic
525C24C2×D4×C10111yescharacteristic
526C24#41×C10112yescomplemented
527C24C24×C10111yescharacteristic
528#41—44no—
529#41—44no—
530#41—42no—
531#41—42no—
532#41—84no—
533C2×Q8—21no—
534C2×Q8—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—82no—
562C2×D4—82no—
563C2×D4—84no—
564C2×D4C2×D4×C10112yes—
565C2×D4C2×D4×C10112yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—41no—
580C22×C4—82no—
581C22×C4C2×D4×C10111yescharacteristic
582C22×C4C2×D4×C10111yescharacteristic
583C22×C4#41×C10112yescomplemented
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—42no—
591C4⋊C4—41no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—41no—
617C22⋊C4—84no—
618C22⋊C4C2×D4×C10112yes—
619C22⋊C4C2×D4×C10112yes—
620C22⋊C4C2×D4×C10112yes—
621C22⋊C4C2×D4×C10112yes—
622C42—22no—
623C42—22no—
624C42—41no—
625C23—21no—
626C23—22no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—42no—
637C23—44no—
638C23—42no—
639C23—42no—
640C23—44no—
641C23—42no—
642C23—41no—
643C23—41no—
644C23—42no—
645C23—81no—
646C23—81no—
647C23—81no—
648C23—81no—
649C23—82no—
650C23—81no—
651C23—81no—
652C23—82no—
653C23—82no—
654C23—161no—
655C23#120×C10112yes—
656C23C22×D4×C10111yescharacteristic
657C23C22×D4×C10111yescharacteristic
658C23C22×D4×C10111yescharacteristic
659C23C2×#41×C10112yes—
660C23H(5,𝔽2)×C10112yes—
661Q8—42no—
662Q8—82no—
663D4—24no—
664D4—24no—
665D4—42no—
666D4—44no—
667D4—44no—
668D4—44no—
669D4—42no—
670D4—41no—
671D4—42no—
672D4—41no—
673D4—42no—
674D4—42no—
675D4—42no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—84no—
680D4—84no—
681D4—162no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—81no—
700C2×C4—82no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—161no—
710C2×C4#120×C10112yes—
711C22—22no—
712C22—24no—
713C22—22no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—41no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—41no—
725C22—42no—
726C22—42no—
727C22—41no—
728C22—42no—
729C22—41no—
730C22—41no—
731C22—81no—
732C22—81no—
733C22—82no—
734C22—84no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—162no—
741C22C2×#120×C10111yescharacteristic
742C22#525×C10111yescharacteristic
743C22#535×C10111yescharacteristic
744C22#546×C10112yes—
745C22#546×C10112yes—
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—41no—
753C4—82no—
754C4—82no—
755C4—82no—
756C2—21no—
757C2—21no—
758C2—22no—
759C2—22no—
760C2—21no—
761C2—42no—
762C2—42no—
763C2—81no—
764C2—81no—
765C2—82no—
766C2C101×#240411yescharacteristic
subgroupG/H
center, socleC2×C101#2404
commutator, Frattini, cosocleC24C24×C101
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C24×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3490C2semidirect
2. C101×#3026C2semidirect
3. C2×B(4,𝔽2)×C101C2semidirect
4. C101×#2883C2semidirect
5. C101×#2032C2semidirect
6. C101×#2021C2semidirect
7. C101×#1913C2semidirect
8. C101×#1913C2semidirect
9. C101×#1898C2semidirect
10. C101×#1889C2semidirect
11. C101×#1828C2semidirect
17. #543×C101C22semidirect
24. C2×#120×C101C22semidirect
27. #518×C101C22semidirect
28. C22×C22⋊C4×C101C22semidirect
41. C2×#99×C101C22semidirect
42. #379×C101C22semidirect
43. #342×C101C22semidirect
44. #342×C101C22semidirect
45. #342×C101C22semidirect
46. #342×C101C22semidirect
74. #123×C101D4semidirect
94. #120×C101D4semidirect
95. #120×C101D4semidirect
96. #120×C101D4semidirect
107. #117×C101D4semidirect
117. C2×C22⋊C4×C101D4semidirect
142. C24×C101#41semidirect
199. C22×C4×C101#41semidirect
372. #23996C101direct (N × H)
384. #3490C2×C101semidirect
385. #3026C2×C101semidirect
386. C2×B(4,𝔽2)C2×C101semidirect
387. #2883C2×C101semidirect
388. #2032C2×C101semidirect
389. #2021C2×C101semidirect
390. #1913C2×C101semidirect
391. #1913C2×C101semidirect
392. #1898C2×C101semidirect
393. #1889C2×C101semidirect
394. #1828C2×C101semidirect
395. C101#23996direct (N × H)
401. #543C22×C101semidirect
408. C2×#120C22×C101semidirect
411. #518C22×C101semidirect
412. C22×C22⋊C4C22×C101semidirect
425. C2×#99C22×C101semidirect
426. #379C22×C101semidirect
427. #342C22×C101semidirect
428. #342C22×C101semidirect
429. #342C22×C101semidirect
430. #342C22×C101semidirect
458. #123D4×C101semidirect
478. #120D4×C101semidirect
479. #120D4×C101semidirect
480. #120D4×C101semidirect
491. #117D4×C101semidirect
501. C2×C22⋊C4D4×C101semidirect
526. C24#41×C101semidirect
583. C22×C4#41×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34902
C101×#30262
C2×B(4,𝔽2)×C1012
C101×#28832
C101×#20322
C101×#20212
C101×#19132
C101×#18982
C101×#18892
C101×#18282
#23996101