Finite Group Databasebeta

← C101×#18228 #38800379

Subgroups — C101×#18228 #38800379

Order 25856.

1300 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3537C211yesmaximal, characteristic, complemented
2C101×#3006C211yesmaximal, characteristic, complemented
3C101×#3002C211yesmaximal, characteristic, complemented
4C101×#2615C211yesmaximal, characteristic, complemented
5C101×#1606C212yesmaximal, complemented
6C101×#1601C212yesmaximal, complemented
7C101×#1600C212yesmaximal, complemented
8C101×#1595C212yesmaximal, complemented
9C101×#1519C211yesmaximal, characteristic, complemented
10C101×#1513C211yesmaximal, characteristic, complemented
11C101×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C101C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C101—21no—
14C2×#135×C101—21no—
15#560×C101—22no—
16#553×C101—21no—
17#553×C101—21no—
18D42×C101—22no—
19D42×C101—21no—
20D42×C101—21no—
21#540×C101—21no—
22#538×C101—21no—
23#538×C101C2212yes—
24#535×C101—21no—
25#534×C101—21no—
26#534×C101C2212yes—
27#525×C101C2211yescharacteristic
28C2×#121×C101—21no—
29C2×#121×C101C2211yescharacteristic
30C2×#121×C101C2211yescharacteristic
31#452×C101—21no—
32#451×C101C2211yescharacteristic, complemented
33#450×C101C2211yescharacteristic, complemented
34#449×C101—21no—
35#449×C101—22no—
36#448×C101C2211yescharacteristic, complemented
37#448×C101C2212yescomplemented
38#447×C101C2211yescharacteristic, complemented
39#447×C101C2212yescomplemented
40#417×C101—21no—
41#416×C101—21no—
42#407×C101C2211yescharacteristic, complemented
43C2×C22⋊C8×C101C2211yescharacteristic, complemented
44#393×C101C2212yescomplemented
45#392×C101—22no—
46#392×C101C2212yescomplemented
47#380×C101—21no—
48#380×C101C2211yescharacteristic, complemented
49#328×C101C2212yescomplemented
50#327×C101C2212yescomplemented
51#327×C101C2212yescomplemented
52#327×C101C2212yescomplemented
53#323×C101C2212yescomplemented
54#323×C101C2212yescomplemented
55C2×#41×C101—21no—
56C2×#41×C101—21no—
57C2×#41×C101—21no—
58C2×#41×C101—21no—
59C2×#41×C101—44no—
60C2×#41×C101D411yescharacteristic, complemented
61C22×Q8×C101C2311yescharacteristic
62C22×D4×C101—22no—
63C22×D4×C101—21no—
64C22×D4×C101—21no—
65C22×D4×C101—22no—
66C22×D4×C101—21no—
67C22×D4×C101—22no—
68C22×D4×C101D411yescharacteristic
69C22×D4×C101D412yes—
70C22×D4×C101D411yescharacteristic, complemented
71C22×D4×C101C2311yescharacteristic
72C23×C4×C101—21no—
73C23×C4×C101C2311yescharacteristic
74AGL(1,ℤ/8)×C101—44no—
75#135×C101—44no—
76C2×Q16×C101—21no—
77C2×SD16×C101—21no—
78C2×SD16×C101—21no—
79C2×SD16×C101—22no—
80C2×D8×C101—21no—
81C2×D8×C101—22no—
82C2×M16×C101—21no—
83C22×C8×C101—21no—
84#127×C101—22no—
85#127×C101—21no—
86#126×C101—22no—
87#126×C101—22no—
88#125×C101—21no—
89#124×C101—22no—
90#123×C101—22no—
91#123×C101—21no—
92#123×C101—22no—
93#123×C101—22no—
94#123×C101—22no—
95C22⋊Q8×C101D411yescharacteristic, complemented
96C22⋊Q8×C101C2311yescharacteristic
97#121×C101—22no—
98#121×C101—21no—
99#121×C101—21no—
100#121×C101—22no—
101#121×C101—22no—
102#121×C101—22no—
103#121×C101—22no—
104#121×C101—21no—
105#121×C101—21no—
106#121×C101—21no—
107#121×C101—21no—
108#121×C101—21no—
109#121×C101—21no—
110#121×C101—22no—
111#121×C101—44no—
112#121×C101D412yescomplemented
113#121×C101D411yescharacteristic, complemented
114#121×C101C2312yes—
115#121×C101C2311yescharacteristic
116#120×C101—22no—
117#120×C101—22no—
118#120×C101—22no—
119#120×C101—21no—
120#120×C101—22no—
121#120×C101—22no—
122#120×C101—22no—
123C4×D4×C101—22no—
124C4×D4×C101—21no—
125C4×D4×C101—21no—
126C4×D4×C101—21no—
127C4×D4×C101—21no—
128C4×D4×C101—22no—
129#117×C101—21no—
130#117×C101D411yescharacteristic, complemented
131C2×C4⋊C4×C101—21no—
132C2×C4⋊C4×C101D411yescharacteristic
133C2×C4⋊C4×C101D411yescharacteristic, complemented
134C2×C22⋊C4×C101—21no—
135C2×C22⋊C4×C101—22no—
136C2×C22⋊C4×C101—21no—
137C2×C22⋊C4×C101—22no—
138C2×C22⋊C4×C101C2312yes—
139#103×C101—21no—
140#103×C101—21no—
141#103×C101—22no—
142#102×C101—21no—
143#102×C101—21no—
144#102×C101—22no—
145C22⋊C8×C101—21no—
146C22⋊C8×C101—21no—
147C22⋊C8×C101C2311yescharacteristic
148C22⋊C8×C101C2311yescharacteristic
149C22⋊C8×C101C2312yes—
150#95×C101—22no—
151#95×C101C2312yes—
152C24×C101—22no—
153C24×C101—21no—
154C24×C101—21no—
155C24×C101C2×D412yes—
156C24×C101C2×D411yescharacteristic
157#41×C101—24no—
158#41×C101—24no—
159#41×C101—42no—
160#41×C101—42no—
161#41×C101—42no—
162#41×C101—42no—
163#41×C101—42no—
164#41×C101—42no—
165#41×C101—42no—
166C2×Q8×C101—21no—
167C2×Q8×C101—21no—
168C2×Q8×C101—42no—
169C2×Q8×C101C2×D411yescharacteristic
170C2×D4×C101—22no—
171C2×D4×C101—21no—
172C2×D4×C101—21no—
173C2×D4×C101—22no—
174C2×D4×C101—22no—
175C2×D4×C101—22no—
176C2×D4×C101—22no—
177C2×D4×C101—22no—
178C2×D4×C101—22no—
179C2×D4×C101—21no—
180C2×D4×C101—22no—
181C2×D4×C101—22no—
182C2×D4×C101—21no—
183C2×D4×C101—21no—
184C2×D4×C101—21no—
185C2×D4×C101—21no—
186C2×D4×C101—21no—
187C2×D4×C101—42no—
188C2×D4×C101—42no—
189C2×D4×C101—42no—
190C2×D4×C101—42no—
191C2×D4×C101—42no—
192C2×D4×C101—41no—
193C2×D4×C101—41no—
194C2×D4×C101—44no—
195C2×D4×C101—82no—
196C2×D4×C101—82no—
197C2×D4×C101—82no—
198C2×D4×C101—82no—
199C2×D4×C101—81no—
200C2×D4×C101—81no—
201C2×D4×C101—82no—
202C2×D4×C101—82no—
203C2×D4×C101—84no—
204C2×D4×C101C2×D411yescharacteristic
205C2×D4×C101C2×D412yes—
206C22×C4×C101—24no—
207C22×C4×C101—21no—
208C22×C4×C101—22no—
209C22×C4×C101—22no—
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101—22no—
213C22×C4×C101—42no—
214C22×C4×C101—42no—
215C22×C4×C101—41no—
216C22×C4×C101—41no—
217C22×C4×C101C2×D411yescharacteristic
218C22×C4×C101C2×D411yescharacteristic
219C22×C4×C101C2×D411yescharacteristic
220C22×C4×C101C2×D412yes—
221C22×C4×C101C2×D411yescharacteristic
222C22×C4×C101C2×D411yescharacteristic
223C22×C4×C101C2411yescharacteristic
224Q16×C101—42no—
225SD16×C101—42no—
226SD16×C101—42no—
227SD16×C101—44no—
228D8×C101—42no—
229D8×C101—44no—
230M16×C101—42no—
231C2×C8×C101—21no—
232C2×C8×C101—21no—
233C2×C8×C101—22no—
234C2×C8×C101—42no—
235C4⋊C4×C101—22no—
236C4⋊C4×C101—22no—
237C4⋊C4×C101—21no—
238C4⋊C4×C101—21no—
239C4⋊C4×C101—21no—
240C4⋊C4×C101—21no—
241C4⋊C4×C101—21no—
242C4⋊C4×C101—42no—
243C4⋊C4×C101C2×D412yes—
244C4⋊C4×C101C2×D411yescharacteristic
245C4⋊C4×C101C2×D411yescharacteristic
246C22⋊C4×C101—22no—
247C22⋊C4×C101—22no—
248C22⋊C4×C101—22no—
249C22⋊C4×C101—22no—
250C22⋊C4×C101—22no—
251C22⋊C4×C101—21no—
252C22⋊C4×C101—21no—
253C22⋊C4×C101—21no—
254C22⋊C4×C101—22no—
255C22⋊C4×C101—21no—
256C22⋊C4×C101—22no—
257C22⋊C4×C101—22no—
258C22⋊C4×C101—22no—
259C22⋊C4×C101—21no—
260C22⋊C4×C101—44no—
261C22⋊C4×C101—81no—
262C22⋊C4×C101—82no—
263C42×C101—22no—
264C42×C101—21no—
265C23×C101—21no—
266C23×C101—21no—
267C23×C101—22no—
268C23×C101—22no—
269C23×C101—22no—
270C23×C101—21no—
271C23×C101—22no—
272C23×C101—22no—
273C23×C101—41no—
274C23×C101—41no—
275C23×C101—41no—
276C23×C101—41no—
277C23×C101—41no—
278C23×C101—42no—
279C23×C101—42no—
280C23×C101—42no—
281C23×C101—41no—
282C23×C101—41no—
283C23×C101—41no—
284C23×C101—81no—
285C23×C101—81no—
286C23×C101—82no—
287C23×C101—82no—
288C23×C101—82no—
289C23×C101#12011yescharacteristic
290C23×C101#12011yescharacteristic
291C23×C101C22×D411yescharacteristic
292Q8×C101—22no—
293Q8×C101—22no—
294Q8×C101—41no—
295Q8×C101—41no—
296Q8×C101—41no—
297D4×C101—22no—
298D4×C101—22no—
299D4×C101—42no—
300D4×C101—41no—
301D4×C101—41no—
302D4×C101—41no—
303D4×C101—44no—
304D4×C101—42no—
305D4×C101—44no—
306D4×C101—44no—
307D4×C101—42no—
308D4×C101—41no—
309D4×C101—42no—
310D4×C101—41no—
311D4×C101—42no—
312D4×C101—42no—
313D4×C101—81no—
314D4×C101—82no—
315D4×C101—82no—
316D4×C101—81no—
317D4×C101—82no—
318D4×C101—82no—
319D4×C101—82no—
320D4×C101—82no—
321D4×C101—82no—
322D4×C101—88no—
323C2×C4×C101—22no—
324C2×C4×C101—22no—
325C2×C4×C101—22no—
326C2×C4×C101—22no—
327C2×C4×C101—21no—
328C2×C4×C101—22no—
329C2×C4×C101—22no—
330C2×C4×C101—21no—
331C2×C4×C101—21no—
332C2×C4×C101—41no—
333C2×C4×C101—41no—
334C2×C4×C101—41no—
335C2×C4×C101—44no—
336C2×C4×C101—41no—
337C2×C4×C101—41no—
338C2×C4×C101—44no—
339C2×C4×C101—42no—
340C2×C4×C101—42no—
341C2×C4×C101—42no—
342C2×C4×C101—42no—
343C2×C4×C101—42no—
344C2×C4×C101—81no—
345C2×C4×C101—82no—
346C2×C4×C101—82no—
347C2×C4×C101#12011yescharacteristic
348C2×C4×C101#12011yescharacteristic
349C2×C4×C101C22×D411yescharacteristic
350C2×C4×C101C22×D411yescharacteristic
351C8×C101—41no—
352C8×C101—41no—
353C8×C101—42no—
354C22×C101—21no—
355C22×C101—21no—
356C22×C101—21no—
357C22×C101—21no—
358C22×C101—21no—
359C22×C101—21no—
360C22×C101—21no—
361C22×C101—21no—
362C22×C101—42no—
363C22×C101—42no—
364C22×C101—42no—
365C22×C101—42no—
366C22×C101—41no—
367C22×C101—42no—
368C22×C101—42no—
369C22×C101—41no—
370C22×C101—42no—
371C22×C101—41no—
372C22×C101—42no—
373C22×C101—42no—
374C22×C101—81no—
375C22×C101—81no—
376C22×C101—82no—
377C22×C101—82no—
378C22×C101—81no—
379C22×C101—81no—
380C22×C101—81no—
381C22×C101—81no—
382C22×C101—162no—
383C22×C101—164no—
384C22×C101C2×#12011yescharacteristic
385C22×C101#57611yescharacteristic
386C22×C101#57711yescharacteristic
387C4×C101—21no—
388C4×C101—21no—
389C4×C101—21no—
390C4×C101—42no—
391C4×C101—41no—
392C4×C101—42no—
393C4×C101—41no—
394C4×C101—42no—
395C4×C101—41no—
396C4×C101—82no—
397C4×C101B(4,𝔽2)12yes—
398#18228C10111yesmaximal, characteristic, direct product factor, Sylow
399C2×C101—21no—
400C2×C101—21no—
401C2×C101—41no—
402C2×C101—41no—
403C2×C101—82no—
404C2×C101—82no—
405C2×C101—82no—
406C2×C101—81no—
407C2×C101#301211yescharacteristic
408C2×C101#301911yescharacteristic
409C2×C101C2×B(4,𝔽2)11yescharacteristic
410#3537C2×C10111yescharacteristic, complemented
411#3006C2×C10111yescharacteristic, complemented
412#3002C2×C10111yescharacteristic, complemented
413#2615C2×C10111yescharacteristic, complemented
414#1606C2×C10112yescomplemented
415#1601C2×C10112yescomplemented
416#1600C2×C10112yescomplemented
417#1595C2×C10112yescomplemented
418#1519C2×C10111yescharacteristic, complemented
419#1513C2×C10111yescharacteristic, complemented
420#1471C2×C10111yescharacteristic, complemented
421C101#1822811yescharacteristic, direct product factor, Sylow
422C22×#41C22×C10111yescharacteristic, complemented
423C2×AGL(1,ℤ/8)—21no—
424C2×#135—21no—
425#560—22no—
426#553—21no—
427#553—21no—
428D42—22no—
429D42—21no—
430D42—21no—
431#540—21no—
432#538—21no—
433#538C22×C10112yes—
434#535—21no—
435#534—21no—
436#534C22×C10112yes—
437#525C22×C10111yescharacteristic
438C2×#121—21no—
439C2×#121C22×C10111yescharacteristic
440C2×#121C22×C10111yescharacteristic
441#452—21no—
442#451C22×C10111yescharacteristic, complemented
443#450C22×C10111yescharacteristic, complemented
444#449—21no—
445#449—22no—
446#448C22×C10111yescharacteristic, complemented
447#448C22×C10112yescomplemented
448#447C22×C10111yescharacteristic, complemented
449#447C22×C10112yescomplemented
450#417—21no—
451#416—21no—
452#407C22×C10111yescharacteristic, complemented
453C2×C22⋊C8C22×C10111yescharacteristic, complemented
454#393C22×C10112yescomplemented
455#392—22no—
456#392C22×C10112yescomplemented
457#380—21no—
458#380C22×C10111yescharacteristic, complemented
459#328C22×C10112yescomplemented
460#327C22×C10112yescomplemented
461#327C22×C10112yescomplemented
462#327C22×C10112yescomplemented
463#323C22×C10112yescomplemented
464#323C22×C10112yescomplemented
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—44no—
470C2×#41D4×C10111yescharacteristic, complemented
471C22×Q8C23×C10111yescharacteristic
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—22no—
478C22×D4D4×C10111yescharacteristic
479C22×D4D4×C10112yes—
480C22×D4D4×C10111yescharacteristic, complemented
481C22×D4C23×C10111yescharacteristic
482C23×C4—21no—
483C23×C4C23×C10111yescharacteristic
484AGL(1,ℤ/8)—44no—
485#135—44no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×D8—21no—
491C2×D8—22no—
492C2×M16—21no—
493C22×C8—21no—
494#127—22no—
495#127—21no—
496#126—22no—
497#126—22no—
498#125—21no—
499#124—22no—
500#123—22no—
501#123—21no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8D4×C10111yescharacteristic, complemented
506C22⋊Q8C23×C10111yescharacteristic
507#121—22no—
508#121—21no—
509#121—21no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—22no—
521#121—44no—
522#121D4×C10112yescomplemented
523#121D4×C10111yescharacteristic, complemented
524#121C23×C10112yes—
525#121C23×C10111yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529#120—21no—
530#120—22no—
531#120—22no—
532#120—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—22no—
539#117—21no—
540#117D4×C10111yescharacteristic, complemented
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C10111yescharacteristic
543C2×C4⋊C4D4×C10111yescharacteristic, complemented
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4C23×C10112yes—
549#103—21no—
550#103—21no—
551#103—22no—
552#102—21no—
553#102—21no—
554#102—22no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8C23×C10111yescharacteristic
558C22⋊C8C23×C10111yescharacteristic
559C22⋊C8C23×C10112yes—
560#95—22no—
561#95C23×C10112yes—
562C24—22no—
563C24—21no—
564C24—21no—
565C24C2×D4×C10112yes—
566C24C2×D4×C10111yescharacteristic
567#41—24no—
568#41—24no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8C2×D4×C10111yescharacteristic
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—84no—
614C2×D4C2×D4×C10111yescharacteristic
615C2×D4C2×D4×C10112yes—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×D4×C10111yescharacteristic
628C22×C4C2×D4×C10111yescharacteristic
629C22×C4C2×D4×C10111yescharacteristic
630C22×C4C2×D4×C10112yes—
631C22×C4C2×D4×C10111yescharacteristic
632C22×C4C2×D4×C10111yescharacteristic
633C22×C4C24×C10111yescharacteristic
634Q16—42no—
635SD16—42no—
636SD16—42no—
637SD16—44no—
638D8—42no—
639D8—44no—
640M16—42no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—42no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4C2×D4×C10112yes—
654C4⋊C4C2×D4×C10111yescharacteristic
655C4⋊C4C2×D4×C10111yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—81no—
672C22⋊C4—82no—
673C42—22no—
674C42—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23#120×C10111yescharacteristic
700C23#120×C10111yescharacteristic
701C23C22×D4×C10111yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—44no—
714D4—42no—
715D4—44no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4—82no—
732D4—88no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4#120×C10111yescharacteristic
758C2×C4#120×C10111yescharacteristic
759C2×C4C22×D4×C10111yescharacteristic
760C2×C4C22×D4×C10111yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—162no—
793C22—164no—
794C22C2×#120×C10111yescharacteristic
795C22#576×C10111yescharacteristic
796C22#577×C10111yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—82no—
807C4B(4,𝔽2)×C10112yes—
808C2—21no—
809C2—21no—
810C2—41no—
811C2—41no—
812C2—82no—
813C2—82no—
814C2—82no—
815C2—81no—
816C2C101×#301211yescharacteristic
817C2C101×#301911yescharacteristic
818C2C2×B(4,𝔽2)×C10111yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3537C2semidirect
2. C101×#3006C2semidirect
3. C101×#3002C2semidirect
4. C101×#2615C2semidirect
5. C101×#1606C2semidirect
6. C101×#1601C2semidirect
7. C101×#1600C2semidirect
8. C101×#1595C2semidirect
9. C101×#1519C2semidirect
10. C101×#1513C2semidirect
11. C101×#1471C2semidirect
12. C22×#41×C101C22semidirect
32. #451×C101C22semidirect
33. #450×C101C22semidirect
36. #448×C101C22semidirect
37. #448×C101C22semidirect
38. #447×C101C22semidirect
39. #447×C101C22semidirect
42. #407×C101C22semidirect
43. C2×C22⋊C8×C101C22semidirect
44. #393×C101C22semidirect
46. #392×C101C22semidirect
48. #380×C101C22semidirect
49. #328×C101C22semidirect
50. #327×C101C22semidirect
51. #327×C101C22semidirect
52. #327×C101C22semidirect
53. #323×C101C22semidirect
54. #323×C101C22semidirect
60. C2×#41×C101D4semidirect
70. C22×D4×C101D4semidirect
95. C22⋊Q8×C101D4semidirect
112. #121×C101D4semidirect
113. #121×C101D4semidirect
130. #117×C101D4semidirect
133. C2×C4⋊C4×C101D4semidirect
398. #18228C101direct (N × H)
410. #3537C2×C101semidirect
411. #3006C2×C101semidirect
412. #3002C2×C101semidirect
413. #2615C2×C101semidirect
414. #1606C2×C101semidirect
415. #1601C2×C101semidirect
416. #1600C2×C101semidirect
417. #1595C2×C101semidirect
418. #1519C2×C101semidirect
419. #1513C2×C101semidirect
420. #1471C2×C101semidirect
421. C101#18228direct (N × H)
422. C22×#41C22×C101semidirect
442. #451C22×C101semidirect
443. #450C22×C101semidirect
446. #448C22×C101semidirect
447. #448C22×C101semidirect
448. #447C22×C101semidirect
449. #447C22×C101semidirect
452. #407C22×C101semidirect
453. C2×C22⋊C8C22×C101semidirect
454. #393C22×C101semidirect
456. #392C22×C101semidirect
458. #380C22×C101semidirect
459. #328C22×C101semidirect
460. #327C22×C101semidirect
461. #327C22×C101semidirect
462. #327C22×C101semidirect
463. #323C22×C101semidirect
464. #323C22×C101semidirect
470. C2×#41D4×C101semidirect
480. C22×D4D4×C101semidirect
505. C22⋊Q8D4×C101semidirect
522. #121D4×C101semidirect
523. #121D4×C101semidirect
540. #117D4×C101semidirect
543. C2×C4⋊C4D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35372
C101×#30062
C101×#30022
C101×#26152
C101×#16062
C101×#16012
C101×#16002
C101×#15952
C101×#15192
C101×#15132
C101×#14712
#18228101