Finite Group Databasebeta

← C101×#18462 #38800613

Subgroups — C101×#18462 #38800613

Order 25856.

1030 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3560C211yesmaximal, characteristic, complemented
2C101×#3217C211yesmaximal, characteristic, complemented
3C101×#3205C211yesmaximal, characteristic, complemented
4C101×#2818C211yesmaximal, characteristic, complemented
5C101×#1600C212yesmaximal, complemented
6C101×#1598C212yesmaximal, complemented
7C101×#1597C212yesmaximal, complemented
8C101×#1595C212yesmaximal, complemented
9C101×#1521C211yesmaximal, characteristic, complemented
10C101×#1514C211yesmaximal, characteristic, complemented
11C101×#1473C211yesmaximal, characteristic, complemented
12#563×C101—21no—
13#560×C101—21no—
14#553×C101—21no—
15#553×C101—21no—
16#551×C101—21no—
17#547×C101—21no—
18#546×C101—21no—
19#546×C101—21no—
20#542×C101—21no—
21#539×C101—21no—
22#539×C101C2211yescharacteristic
23#538×C101—21no—
24#538×C101—21no—
25#538×C101C2211yescharacteristic
26#537×C101C2211yescharacteristic
27#534×C101C2211yescharacteristic
28#532×C101C2211yescharacteristic
29C2×#127×C101C2211yescharacteristic, complemented
30#529×C101C2211yescharacteristic
31C2×#126×C101C2211yescharacteristic
32#496×C101—21no—
33#493×C101—21no—
34#490×C101—21no—
35#486×C101—21no—
36#460×C101—21no—
37#459×C101—21no—
38#459×C101—21no—
39#459×C101—21no—
40#450×C101C2212yescomplemented
41#447×C101C2212yes—
42#447×C101C2212yes—
43#447×C101C2212yescomplemented
44#432×C101C2211yescharacteristic, complemented
45#431×C101C2211yescharacteristic, complemented
46#394×C101—21no—
47#394×C101—21no—
48#394×C101C2212yescomplemented
49#392×C101—21no—
50#392×C101—21no—
51#392×C101C2212yes—
52#383×C101C2211yescharacteristic, complemented
53#328×C101C2212yescomplemented
54#327×C101C2212yes—
55#327×C101C2212yes—
56#327×C101C2212yescomplemented
57#324×C101C2212yescomplemented
58#323×C101C2212yes—
59C2×#41×C101—21no—
60C2×#41×C101—21no—
61C22×D4×C101—21no—
62C22×D4×C101—22no—
63C22×D4×C101—21no—
64C22×D4×C101—21no—
65C22×D4×C101C2312yes—
66C2×SD16×C101—22no—
67C2×D8×C101—22no—
68C2×D8×C101—22no—
69C2×D8×C101—22no—
70C4⋊Q8×C101—21no—
71C4⋊Q8×C101D411yescharacteristic, complemented
72#127×C101—21no—
73#127×C101—21no—
74#127×C101—21no—
75#127×C101—21no—
76#127×C101D411yescharacteristic, complemented
77#126×C101—21no—
78#126×C101—21no—
79#126×C101—21no—
80#126×C101—21no—
81#126×C101—21no—
82#126×C101—21no—
83#126×C101—21no—
84#126×C101—21no—
85#126×C101—21no—
86#125×C101—21no—
87#125×C101—21no—
88#125×C101D411yescharacteristic, complemented
89#124×C101—21no—
90#124×C101—21no—
91#124×C101—21no—
92#124×C101—21no—
93#124×C101D411yescharacteristic, complemented
94#123×C101—21no—
95#123×C101—21no—
96#123×C101—21no—
97#123×C101—21no—
98#123×C101—21no—
99#123×C101—21no—
100#123×C101—21no—
101#123×C101—21no—
102#123×C101—21no—
103#123×C101—21no—
104#123×C101—21no—
105#123×C101—21no—
106C22⋊Q8×C101—21no—
107C22⋊Q8×C101—21no—
108C22⋊Q8×C101—21no—
109C22⋊Q8×C101—21no—
110C22⋊Q8×C101—21no—
111C22⋊Q8×C101—21no—
112C22⋊Q8×C101—21no—
113C22⋊Q8×C101C2311yescharacteristic
114#121×C101—21no—
115#121×C101—21no—
116#121×C101—21no—
117#121×C101—21no—
118#121×C101—21no—
119#121×C101—21no—
120#121×C101—21no—
121#121×C101—21no—
122#121×C101—21no—
123#121×C101—21no—
124#121×C101—21no—
125#121×C101—21no—
126#121×C101C2311yescharacteristic
127#121×C101C2311yescharacteristic
128#121×C101C2311yescharacteristic
129#120×C101—21no—
130#120×C101—21no—
131#120×C101—21no—
132#120×C101—21no—
133#120×C101—21no—
134C4×Q8×C101D411yescharacteristic, complemented
135C4×D4×C101—21no—
136C4×D4×C101—21no—
137C4×D4×C101—21no—
138C4×D4×C101—21no—
139C4×D4×C101—21no—
140C4×D4×C101—21no—
141C4×D4×C101—21no—
142C4×D4×C101—21no—
143C4×D4×C101D411yescharacteristic, complemented
144C4×D4×C101D411yescharacteristic, complemented
145C4×D4×C101D411yescharacteristic, complemented
146#117×C101—21no—
147#117×C101—21no—
148C2×C4⋊C4×C101—21no—
149C2×C4⋊C4×C101D411yescharacteristic
150C2×C4⋊C4×C101D411yescharacteristic
151C2×C4⋊C4×C101C2311yescharacteristic
152C2×C22⋊C4×C101—21no—
153C2×C22⋊C4×C101—21no—
154C2×C22⋊C4×C101—22no—
155C2×C22⋊C4×C101—22no—
156C2×C22⋊C4×C101—22no—
157C2×C22⋊C4×C101D411yescharacteristic
158C2×C22⋊C4×C101D411yescharacteristic
159C2×C22⋊C4×C101C2311yescharacteristic
160C2×C42×C101C2311yescharacteristic
161C4⋊C8×C101—21no—
162C4⋊C8×C101—21no—
163#102×C101—22no—
164#102×C101—22no—
165#102×C101—22no—
166#102×C101—22no—
167C22⋊C8×C101C2312yes—
168C22⋊C8×C101C2312yes—
169#97×C101—21no—
170C4×C8×C101—21no—
171#95×C101—21no—
172#95×C101—21no—
173#95×C101C2312yes—
174C24×C101—21no—
175C24×C101—22no—
176C24×C101C2×D411yescharacteristic
177#41×C101—82no—
178#41×C101—82no—
179C2×Q8×C101—21no—
180C2×Q8×C101—21no—
181C2×Q8×C101C2×D411yescharacteristic
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—21no—
193C2×D4×C101—21no—
194C2×D4×C101—22no—
195C2×D4×C101—22no—
196C2×D4×C101—41no—
197C2×D4×C101—41no—
198C2×D4×C101—41no—
199C2×D4×C101—41no—
200C2×D4×C101—82no—
201C2×D4×C101—82no—
202C2×D4×C101—82no—
203C2×D4×C101—82no—
204C2×D4×C101—82no—
205C2×D4×C101—82no—
206C2×D4×C101—82no—
207C2×D4×C101C2×D411yescharacteristic
208C2×D4×C101C2×D411yescharacteristic
209C2×D4×C101C2×D411yescharacteristic
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—21no—
214C22×C4×C101—21no—
215C22×C4×C101—21no—
216C22×C4×C101—21no—
217C22×C4×C101—21no—
218C22×C4×C101—22no—
219C22×C4×C101C2×D411yescharacteristic
220C22×C4×C101C2×D411yescharacteristic
221C22×C4×C101C2×D411yescharacteristic
222C22×C4×C101C2×D411yescharacteristic
223C22×C4×C101C2×D411yescharacteristic
224C22×C4×C101C2411yescharacteristic
225SD16×C101—82no—
226D8×C101—82no—
227D8×C101—82no—
228D8×C101—82no—
229C2×C8×C101—22no—
230C2×C8×C101—22no—
231C4⋊C4×C101—21no—
232C4⋊C4×C101—21no—
233C4⋊C4×C101—21no—
234C4⋊C4×C101—21no—
235C4⋊C4×C101—21no—
236C4⋊C4×C101—21no—
237C4⋊C4×C101—21no—
238C4⋊C4×C101—21no—
239C4⋊C4×C101—21no—
240C4⋊C4×C101—21no—
241C4⋊C4×C101—21no—
242C4⋊C4×C101—21no—
243C4⋊C4×C101—21no—
244C4⋊C4×C101—21no—
245C4⋊C4×C101—21no—
246C4⋊C4×C101—21no—
247C4⋊C4×C101—21no—
248C4⋊C4×C101C2×D411yescharacteristic
249C4⋊C4×C101C2×D411yescharacteristic
250C4⋊C4×C101C2×D411yescharacteristic
251C4⋊C4×C101C2×D411yescharacteristic
252C22⋊C4×C101—21no—
253C22⋊C4×C101—21no—
254C22⋊C4×C101—21no—
255C22⋊C4×C101—21no—
256C22⋊C4×C101—21no—
257C22⋊C4×C101—21no—
258C22⋊C4×C101—21no—
259C22⋊C4×C101—21no—
260C22⋊C4×C101—21no—
261C22⋊C4×C101—21no—
262C22⋊C4×C101—21no—
263C22⋊C4×C101—21no—
264C22⋊C4×C101—21no—
265C22⋊C4×C101—21no—
266C22⋊C4×C101—21no—
267C22⋊C4×C101—21no—
268C22⋊C4×C101—21no—
269C22⋊C4×C101—21no—
270C22⋊C4×C101—21no—
271C22⋊C4×C101—21no—
272C22⋊C4×C101—21no—
273C22⋊C4×C101—21no—
274C22⋊C4×C101—21no—
275C22⋊C4×C101—21no—
276C22⋊C4×C101—21no—
277C22⋊C4×C101—82no—
278C22⋊C4×C101—82no—
279C22⋊C4×C101—82no—
280C42×C101—21no—
281C42×C101—21no—
282C42×C101—21no—
283C42×C101C2×D411yescharacteristic
284C42×C101C2×D411yescharacteristic
285C42×C101C2×D411yescharacteristic
286C42×C101C2×D411yescharacteristic
287C23×C101—21no—
288C23×C101—21no—
289C23×C101—21no—
290C23×C101—21no—
291C23×C101—22no—
292C23×C101—41no—
293C23×C101—41no—
294C23×C101—42no—
295C23×C101—42no—
296C23×C101—42no—
297C23×C101—42no—
298C23×C101—42no—
299C23×C101—42no—
300C23×C101—42no—
301C23×C101—81no—
302C23×C101—81no—
303C23×C101—81no—
304C23×C101C22×D411yescharacteristic
305Q8×C101—41no—
306Q8×C101—81no—
307Q8×C101—81no—
308D4×C101—41no—
309D4×C101—41no—
310D4×C101—41no—
311D4×C101—42no—
312D4×C101—42no—
313D4×C101—42no—
314D4×C101—42no—
315D4×C101—42no—
316D4×C101—42no—
317D4×C101—42no—
318D4×C101—81no—
319D4×C101—81no—
320D4×C101—82no—
321D4×C101—82no—
322D4×C101—82no—
323D4×C101—82no—
324D4×C101—81no—
325D4×C101—81no—
326D4×C101—81no—
327D4×C101—81no—
328D4×C101—81no—
329D4×C101—81no—
330D4×C101—81no—
331D4×C101—88no—
332C2×C4×C101—22no—
333C2×C4×C101—21no—
334C2×C4×C101—21no—
335C2×C4×C101—21no—
336C2×C4×C101—21no—
337C2×C4×C101—21no—
338C2×C4×C101—21no—
339C2×C4×C101—21no—
340C2×C4×C101—21no—
341C2×C4×C101—22no—
342C2×C4×C101—41no—
343C2×C4×C101—41no—
344C2×C4×C101—41no—
345C2×C4×C101—41no—
346C2×C4×C101—42no—
347C2×C4×C101—42no—
348C2×C4×C101—42no—
349C2×C4×C101—81no—
350C2×C4×C101—81no—
351C2×C4×C101—81no—
352C2×C4×C101—81no—
353C2×C4×C101—81no—
354C2×C4×C101—81no—
355C2×C4×C101—81no—
356C2×C4×C101—81no—
357C2×C4×C101#12011yescharacteristic
358C2×C4×C101#12011yescharacteristic
359C2×C4×C101#12011yescharacteristic
360C2×C4×C101#12011yescharacteristic
361C2×C4×C101C22×D411yescharacteristic
362C2×C4×C101C22×D411yescharacteristic
363C8×C101—42no—
364C8×C101—42no—
365C22×C101—21no—
366C22×C101—21no—
367C22×C101—41no—
368C22×C101—41no—
369C22×C101—41no—
370C22×C101—41no—
371C22×C101—41no—
372C22×C101—41no—
373C22×C101—41no—
374C22×C101—41no—
375C22×C101—41no—
376C22×C101—41no—
377C22×C101—41no—
378C22×C101—41no—
379C22×C101—82no—
380C22×C101—82no—
381C22×C101—82no—
382C22×C101—82no—
383C22×C101—82no—
384C22×C101—82no—
385C22×C101—82no—
386C22×C101—82no—
387C22×C101—162no—
388C22×C101C2×#12011yescharacteristic
389C22×C101#57612yes—
390C4×C101—21no—
391C4×C101—21no—
392C4×C101—21no—
393C4×C101—21no—
394C4×C101—21no—
395C4×C101—21no—
396C4×C101—41no—
397C4×C101—41no—
398C4×C101—41no—
399C4×C101—41no—
400C4×C101—41no—
401C4×C101—41no—
402C4×C101—41no—
403C4×C101—41no—
404C4×C101—82no—
405#18462C10111yesmaximal, characteristic, direct product factor, Sylow
406C2×C101—22no—
407C2×C101—81no—
408C2×C101—81no—
409C2×C101—81no—
410C2×C101—81no—
411C2×C101—162no—
412C2×C101#300811yescharacteristic
413C2×C101#302111yescharacteristic
414C2×C101#302711yescharacteristic
415#3560C2×C10111yescharacteristic, complemented
416#3217C2×C10111yescharacteristic, complemented
417#3205C2×C10111yescharacteristic, complemented
418#2818C2×C10111yescharacteristic, complemented
419#1600C2×C10112yescomplemented
420#1598C2×C10112yescomplemented
421#1597C2×C10112yescomplemented
422#1595C2×C10112yescomplemented
423#1521C2×C10111yescharacteristic, complemented
424#1514C2×C10111yescharacteristic, complemented
425#1473C2×C10111yescharacteristic, complemented
426C101#1846211yescharacteristic, direct product factor, Sylow
427#563—21no—
428#560—21no—
429#553—21no—
430#553—21no—
431#551—21no—
432#547—21no—
433#546—21no—
434#546—21no—
435#542—21no—
436#539—21no—
437#539C22×C10111yescharacteristic
438#538—21no—
439#538—21no—
440#538C22×C10111yescharacteristic
441#537C22×C10111yescharacteristic
442#534C22×C10111yescharacteristic
443#532C22×C10111yescharacteristic
444C2×#127C22×C10111yescharacteristic, complemented
445#529C22×C10111yescharacteristic
446C2×#126C22×C10111yescharacteristic
447#496—21no—
448#493—21no—
449#490—21no—
450#486—21no—
451#460—21no—
452#459—21no—
453#459—21no—
454#459—21no—
455#450C22×C10112yescomplemented
456#447C22×C10112yes—
457#447C22×C10112yes—
458#447C22×C10112yescomplemented
459#432C22×C10111yescharacteristic, complemented
460#431C22×C10111yescharacteristic, complemented
461#394—21no—
462#394—21no—
463#394C22×C10112yescomplemented
464#392—21no—
465#392—21no—
466#392C22×C10112yes—
467#383C22×C10111yescharacteristic, complemented
468#328C22×C10112yescomplemented
469#327C22×C10112yes—
470#327C22×C10112yes—
471#327C22×C10112yescomplemented
472#324C22×C10112yescomplemented
473#323C22×C10112yes—
474C2×#41—21no—
475C2×#41—21no—
476C22×D4—21no—
477C22×D4—22no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4C23×C10112yes—
481C2×SD16—22no—
482C2×D8—22no—
483C2×D8—22no—
484C2×D8—22no—
485C4⋊Q8—21no—
486C4⋊Q8D4×C10111yescharacteristic, complemented
487#127—21no—
488#127—21no—
489#127—21no—
490#127—21no—
491#127D4×C10111yescharacteristic, complemented
492#126—21no—
493#126—21no—
494#126—21no—
495#126—21no—
496#126—21no—
497#126—21no—
498#126—21no—
499#126—21no—
500#126—21no—
501#125—21no—
502#125—21no—
503#125D4×C10111yescharacteristic, complemented
504#124—21no—
505#124—21no—
506#124—21no—
507#124—21no—
508#124D4×C10111yescharacteristic, complemented
509#123—21no—
510#123—21no—
511#123—21no—
512#123—21no—
513#123—21no—
514#123—21no—
515#123—21no—
516#123—21no—
517#123—21no—
518#123—21no—
519#123—21no—
520#123—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527C22⋊Q8—21no—
528C22⋊Q8C23×C10111yescharacteristic
529#121—21no—
530#121—21no—
531#121—21no—
532#121—21no—
533#121—21no—
534#121—21no—
535#121—21no—
536#121—21no—
537#121—21no—
538#121—21no—
539#121—21no—
540#121—21no—
541#121C23×C10111yescharacteristic
542#121C23×C10111yescharacteristic
543#121C23×C10111yescharacteristic
544#120—21no—
545#120—21no—
546#120—21no—
547#120—21no—
548#120—21no—
549C4×Q8D4×C10111yescharacteristic, complemented
550C4×D4—21no—
551C4×D4—21no—
552C4×D4—21no—
553C4×D4—21no—
554C4×D4—21no—
555C4×D4—21no—
556C4×D4—21no—
557C4×D4—21no—
558C4×D4D4×C10111yescharacteristic, complemented
559C4×D4D4×C10111yescharacteristic, complemented
560C4×D4D4×C10111yescharacteristic, complemented
561#117—21no—
562#117—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4D4×C10111yescharacteristic
565C2×C4⋊C4D4×C10111yescharacteristic
566C2×C4⋊C4C23×C10111yescharacteristic
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4D4×C10111yescharacteristic
573C2×C22⋊C4D4×C10111yescharacteristic
574C2×C22⋊C4C23×C10111yescharacteristic
575C2×C42C23×C10111yescharacteristic
576C4⋊C8—21no—
577C4⋊C8—21no—
578#102—22no—
579#102—22no—
580#102—22no—
581#102—22no—
582C22⋊C8C23×C10112yes—
583C22⋊C8C23×C10112yes—
584#97—21no—
585C4×C8—21no—
586#95—21no—
587#95—21no—
588#95C23×C10112yes—
589C24—21no—
590C24—22no—
591C24C2×D4×C10111yescharacteristic
592#41—82no—
593#41—82no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8C2×D4×C10111yescharacteristic
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—82no—
616C2×D4—82no—
617C2×D4—82no—
618C2×D4—82no—
619C2×D4—82no—
620C2×D4—82no—
621C2×D4—82no—
622C2×D4C2×D4×C10111yescharacteristic
623C2×D4C2×D4×C10111yescharacteristic
624C2×D4C2×D4×C10111yescharacteristic
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4C2×D4×C10111yescharacteristic
635C22×C4C2×D4×C10111yescharacteristic
636C22×C4C2×D4×C10111yescharacteristic
637C22×C4C2×D4×C10111yescharacteristic
638C22×C4C2×D4×C10111yescharacteristic
639C22×C4C24×C10111yescharacteristic
640SD16—82no—
641D8—82no—
642D8—82no—
643D8—82no—
644C2×C8—22no—
645C2×C8—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4C2×D4×C10111yescharacteristic
664C4⋊C4C2×D4×C10111yescharacteristic
665C4⋊C4C2×D4×C10111yescharacteristic
666C4⋊C4C2×D4×C10111yescharacteristic
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42C2×D4×C10111yescharacteristic
699C42C2×D4×C10111yescharacteristic
700C42C2×D4×C10111yescharacteristic
701C42C2×D4×C10111yescharacteristic
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23C22×D4×C10111yescharacteristic
720Q8—41no—
721Q8—81no—
722Q8—81no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—81no—
734D4—81no—
735D4—82no—
736D4—82no—
737D4—82no—
738D4—82no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—88no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4#120×C10111yescharacteristic
773C2×C4#120×C10111yescharacteristic
774C2×C4#120×C10111yescharacteristic
775C2×C4#120×C10111yescharacteristic
776C2×C4C22×D4×C10111yescharacteristic
777C2×C4C22×D4×C10111yescharacteristic
778C8—42no—
779C8—42no—
780C22—21no—
781C22—21no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—162no—
803C22C2×#120×C10111yescharacteristic
804C22#576×C10112yes—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—82no—
820C2—22no—
821C2—81no—
822C2—81no—
823C2—81no—
824C2—81no—
825C2—162no—
826C2C101×#300811yescharacteristic
827C2C101×#302111yescharacteristic
828C2C101×#302711yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3560C2semidirect
2. C101×#3217C2semidirect
3. C101×#3205C2semidirect
4. C101×#2818C2semidirect
5. C101×#1600C2semidirect
6. C101×#1598C2semidirect
7. C101×#1597C2semidirect
8. C101×#1595C2semidirect
9. C101×#1521C2semidirect
10. C101×#1514C2semidirect
11. C101×#1473C2semidirect
29. C2×#127×C101C22semidirect
40. #450×C101C22semidirect
43. #447×C101C22semidirect
44. #432×C101C22semidirect
45. #431×C101C22semidirect
48. #394×C101C22semidirect
52. #383×C101C22semidirect
53. #328×C101C22semidirect
56. #327×C101C22semidirect
57. #324×C101C22semidirect
71. C4⋊Q8×C101D4semidirect
76. #127×C101D4semidirect
88. #125×C101D4semidirect
93. #124×C101D4semidirect
134. C4×Q8×C101D4semidirect
143. C4×D4×C101D4semidirect
144. C4×D4×C101D4semidirect
145. C4×D4×C101D4semidirect
405. #18462C101direct (N × H)
415. #3560C2×C101semidirect
416. #3217C2×C101semidirect
417. #3205C2×C101semidirect
418. #2818C2×C101semidirect
419. #1600C2×C101semidirect
420. #1598C2×C101semidirect
421. #1597C2×C101semidirect
422. #1595C2×C101semidirect
423. #1521C2×C101semidirect
424. #1514C2×C101semidirect
425. #1473C2×C101semidirect
426. C101#18462direct (N × H)
444. C2×#127C22×C101semidirect
455. #450C22×C101semidirect
458. #447C22×C101semidirect
459. #432C22×C101semidirect
460. #431C22×C101semidirect
463. #394C22×C101semidirect
467. #383C22×C101semidirect
468. #328C22×C101semidirect
471. #327C22×C101semidirect
472. #324C22×C101semidirect
486. C4⋊Q8D4×C101semidirect
491. #127D4×C101semidirect
503. #125D4×C101semidirect
508. #124D4×C101semidirect
549. C4×Q8D4×C101semidirect
558. C4×D4D4×C101semidirect
559. C4×D4D4×C101semidirect
560. C4×D4D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35602
C101×#32172
C101×#32052
C101×#28182
C101×#16002
C101×#15982
C101×#15972
C101×#15952
C101×#15212
C101×#15142
C101×#14732
#18462101