Finite Group Databasebeta

← C101×#19068 #38801219

Subgroups — C101×#19068 #38801219

Order 25856.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3545C211yesmaximal, characteristic, complemented
2C101×#3219C211yesmaximal, characteristic, complemented
3C101×#3213C211yesmaximal, characteristic, complemented
4C101×#3171C211yesmaximal, characteristic, complemented
5C101×#1664C211yesmaximal, characteristic, complemented
6C101×#1662C211yesmaximal, characteristic, complemented
7C101×#1661C211yesmaximal, characteristic, complemented
8C101×#1659C211yesmaximal, characteristic, complemented
9C101×#1657C211yesmaximal, characteristic, complemented
10C101×#1656C211yesmaximal, characteristic, complemented
11C101×#1656C211yesmaximal, characteristic, complemented
12C101×#1655C211yesmaximal, characteristic, complemented
13C101×#1535C211yesmaximal, characteristic, complemented
14C101×#1529C211yesmaximal, characteristic, complemented
15C101×#1527C211yesmaximal, characteristic, complemented
16#563×C101C2211yescharacteristic
17#562×C101C2211yescharacteristic
18#562×C101C2211yescharacteristic
19H(3,𝔽4)×C101C2211yescharacteristic
20#555×C101—21no—
21#551×C101—21no—
22#551×C101—21no—
23#551×C101—21no—
24#546×C101—21no—
25#546×C101—21no—
26#542×C101—21no—
27#542×C101—21no—
28#538×C101—21no—
29#538×C101—21no—
30#536×C101—21no—
31#534×C101—21no—
32#532×C101C2211yescharacteristic, complemented
33#529×C101C2211yescharacteristic
34#529×C101C2211yescharacteristic
35C2×#124×C101C2211yescharacteristic
36#501×C101C2211yescharacteristic, complemented
37#497×C101C2211yescharacteristic, complemented
38#496×C101C2211yescharacteristic
39#496×C101C2211yescharacteristic, complemented
40#496×C101C2211yescharacteristic, complemented
41#496×C101C2211yescharacteristic, complemented
42#491×C101C2211yescharacteristic, complemented
43#490×C101C2211yescharacteristic, complemented
44#490×C101C2211yescharacteristic, complemented
45#489×C101C2211yescharacteristic
46#489×C101C2211yescharacteristic, complemented
47#489×C101C2211yescharacteristic, complemented
48#469×C101—21no—
49#468×C101—21no—
50#464×C101—21no—
51#463×C101—21no—
52#463×C101—21no—
53#463×C101—21no—
54#452×C101—21no—
55#449×C101—21no—
56#448×C101—21no—
57#447×C101—21no—
58C4×SD16×C101—21no—
59C4×D8×C101—21no—
60#432×C101C2211yescharacteristic, complemented
61#432×C101C2211yescharacteristic, complemented
62C4×M16×C101C2211yescharacteristic, complemented
63#330×C101C2211yescharacteristic, complemented
64#330×C101C2211yescharacteristic, complemented
65#330×C101C2211yescharacteristic, complemented
66#330×C101C2211yescharacteristic, complemented
67#329×C101C2211yescharacteristic
68#329×C101C2211yescharacteristic
69#329×C101C2211yescharacteristic, complemented
70#329×C101C2211yescharacteristic, complemented
71#329×C101C2211yescharacteristic, complemented
72#329×C101C2211yescharacteristic, complemented
73#329×C101C2211yescharacteristic, complemented
74#329×C101C2211yescharacteristic, complemented
75C2×#41×C101—21no—
76C2×#41×C101—21no—
77C22×Q8×C101D411yescharacteristic
78C22×D4×C101—21no—
79C22×D4×C101D411yescharacteristic
80C2×Q16×C101—21no—
81C2×SD16×C101—21no—
82C2×SD16×C101—21no—
83C2×SD16×C101—21no—
84C2×SD16×C101—21no—
85C2×SD16×C101—21no—
86C2×D8×C101—21no—
87C2×D8×C101—21no—
88C2×D8×C101—21no—
89C2×D8×C101—21no—
90C2×M16×C101—21no—
91C4⋊Q8×C101—21no—
92C4⋊Q8×C101—21no—
93C4⋊Q8×C101C2311yescharacteristic
94#127×C101C2311yescharacteristic
95#126×C101—21no—
96#126×C101—21no—
97#126×C101—21no—
98#126×C101—21no—
99#126×C101—21no—
100#126×C101—21no—
101#125×C101C2311yescharacteristic
102#125×C101C2311yescharacteristic
103#124×C101—21no—
104#124×C101—21no—
105#124×C101—21no—
106#124×C101—21no—
107#124×C101—21no—
108#124×C101—21no—
109#124×C101—21no—
110#124×C101—21no—
111#124×C101—21no—
112#124×C101D411yescharacteristic
113#124×C101D411yescharacteristic
114#124×C101C2311yescharacteristic
115#124×C101C2311yescharacteristic
116#124×C101C2311yescharacteristic
117#124×C101C2311yescharacteristic
118#123×C101—21no—
119#123×C101—21no—
120#123×C101—21no—
121#123×C101—21no—
122#123×C101—21no—
123#123×C101—21no—
124#123×C101—21no—
125#123×C101—21no—
126#123×C101—21no—
127#123×C101—21no—
128#123×C101—21no—
129#123×C101—21no—
130C22⋊Q8×C101—21no—
131C22⋊Q8×C101—21no—
132C22⋊Q8×C101—21no—
133C22⋊Q8×C101—21no—
134C22⋊Q8×C101—21no—
135C22⋊Q8×C101—21no—
136C22⋊Q8×C101—21no—
137C22⋊Q8×C101—21no—
138C22⋊Q8×C101D411yescharacteristic
139C22⋊Q8×C101D411yescharacteristic
140#121×C101—21no—
141#121×C101—21no—
142#121×C101—21no—
143#121×C101—21no—
144#121×C101—21no—
145#121×C101—21no—
146#121×C101—21no—
147#121×C101—21no—
148#121×C101—21no—
149#121×C101—21no—
150#121×C101D411yescharacteristic
151#121×C101D411yescharacteristic
152#120×C101—21no—
153#120×C101—21no—
154#120×C101—21no—
155#120×C101—21no—
156#120×C101—21no—
157#120×C101—21no—
158C4×Q8×C101D411yescharacteristic
159C4×Q8×C101D411yescharacteristic
160C4×D4×C101—21no—
161C4×D4×C101—21no—
162C4×D4×C101—21no—
163C4×D4×C101—21no—
164C4×D4×C101—21no—
165C4×D4×C101—21no—
166C4×D4×C101—21no—
167C4×D4×C101—21no—
168C4×D4×C101D411yescharacteristic
169C4×D4×C101D411yescharacteristic
170#117×C101—21no—
171#117×C101—21no—
172#117×C101—21no—
173#117×C101—21no—
174#117×C101—21no—
175C2×C22⋊C4×C101—21no—
176C2×C22⋊C4×C101—21no—
177C2×C22⋊C4×C101—21no—
178C2×C22⋊C4×C101—21no—
179C2×C22⋊C4×C101—21no—
180C2×C42×C101C2311yescharacteristic
181#107×C101—21no—
182#106×C101—21no—
183C4⋊C8×C101—21no—
184C4⋊C8×C101—21no—
185#103×C101—21no—
186#103×C101—21no—
187#103×C101—21no—
188#103×C101—21no—
189#103×C101—21no—
190#102×C101—21no—
191#102×C101—21no—
192#102×C101—21no—
193#102×C101—21no—
194#102×C101—21no—
195#102×C101—21no—
196#102×C101—21no—
197C22⋊C8×C101—21no—
198C22⋊C8×C101—21no—
199#97×C101C2311yescharacteristic
200#97×C101C2311yescharacteristic
201#97×C101C2311yescharacteristic
202#97×C101C2311yescharacteristic
203#97×C101C2311yescharacteristic
204#97×C101C2311yescharacteristic
205C4×C8×C101—21no—
206C24×C101—21no—
207C24×C101—21no—
208#41×C101—82no—
209#41×C101—81no—
210#41×C101—81no—
211C2×Q8×C101—21no—
212C2×Q8×C101—21no—
213C2×Q8×C101—21no—
214C2×Q8×C101—81no—
215C2×Q8×C101C2×D411yescharacteristic
216C2×Q8×C101C2×D411yescharacteristic
217C2×Q8×C101C2×D411yescharacteristic
218C2×Q8×C101C2×D411yescharacteristic
219C2×D4×C101—21no—
220C2×D4×C101—21no—
221C2×D4×C101—21no—
222C2×D4×C101—21no—
223C2×D4×C101—21no—
224C2×D4×C101—21no—
225C2×D4×C101—21no—
226C2×D4×C101—21no—
227C2×D4×C101—21no—
228C2×D4×C101—21no—
229C2×D4×C101—21no—
230C2×D4×C101—21no—
231C2×D4×C101—21no—
232C2×D4×C101—41no—
233C2×D4×C101—81no—
234C2×D4×C101—82no—
235C2×D4×C101C2×D411yescharacteristic
236C2×D4×C101C2×D411yescharacteristic
237C2×D4×C101C2×D411yescharacteristic
238C2×D4×C101C2×D411yescharacteristic
239C22×C4×C101—21no—
240C22×C4×C101—21no—
241C22×C4×C101—21no—
242C22×C4×C101—21no—
243C22×C4×C101—21no—
244C22×C4×C101—21no—
245C22×C4×C101—21no—
246C22×C4×C101—21no—
247C22×C4×C101—41no—
248C22×C4×C101C2×D411yescharacteristic
249C22×C4×C101C2×D411yescharacteristic
250C22×C4×C101C2×D411yescharacteristic
251Q16×C101—81no—
252SD16×C101—42no—
253SD16×C101—81no—
254SD16×C101—81no—
255SD16×C101—81no—
256SD16×C101—81no—
257D8×C101—42no—
258D8×C101—81no—
259D8×C101—81no—
260D8×C101—81no—
261M16×C101—42no—
262C2×C8×C101—21no—
263C2×C8×C101—21no—
264C2×C8×C101—21no—
265C2×C8×C101—21no—
266C2×C8×C101—21no—
267C2×C8×C101—21no—
268C4⋊C4×C101—21no—
269C4⋊C4×C101—21no—
270C4⋊C4×C101—21no—
271C4⋊C4×C101—21no—
272C4⋊C4×C101—21no—
273C4⋊C4×C101—21no—
274C4⋊C4×C101—21no—
275C4⋊C4×C101—21no—
276C4⋊C4×C101—21no—
277C4⋊C4×C101—21no—
278C4⋊C4×C101—21no—
279C4⋊C4×C101—21no—
280C4⋊C4×C101—21no—
281C4⋊C4×C101—21no—
282C4⋊C4×C101—21no—
283C4⋊C4×C101—21no—
284C4⋊C4×C101C2×D411yescharacteristic
285C4⋊C4×C101C2×D411yescharacteristic
286C4⋊C4×C101C2×D411yescharacteristic
287C4⋊C4×C101C2×D411yescharacteristic
288C22⋊C4×C101—21no—
289C22⋊C4×C101—21no—
290C22⋊C4×C101—21no—
291C22⋊C4×C101—21no—
292C22⋊C4×C101—21no—
293C22⋊C4×C101—21no—
294C22⋊C4×C101—21no—
295C22⋊C4×C101—21no—
296C22⋊C4×C101—21no—
297C22⋊C4×C101—21no—
298C22⋊C4×C101—21no—
299C22⋊C4×C101—21no—
300C22⋊C4×C101—21no—
301C22⋊C4×C101—21no—
302C22⋊C4×C101—21no—
303C22⋊C4×C101—21no—
304C22⋊C4×C101—21no—
305C22⋊C4×C101—21no—
306C22⋊C4×C101—21no—
307C22⋊C4×C101—21no—
308C22⋊C4×C101—21no—
309C22⋊C4×C101—21no—
310C22⋊C4×C101—21no—
311C22⋊C4×C101—21no—
312C22⋊C4×C101—21no—
313C22⋊C4×C101—21no—
314C22⋊C4×C101—21no—
315C22⋊C4×C101—21no—
316C22⋊C4×C101—41no—
317C22⋊C4×C101—41no—
318C42×C101—21no—
319C42×C101—21no—
320C42×C101—21no—
321C42×C101—21no—
322C42×C101C2×D411yescharacteristic
323C42×C101C2×D411yescharacteristic
324C42×C101C2×D411yescharacteristic
325C42×C101C2411yescharacteristic
326C23×C101—21no—
327C23×C101—21no—
328C23×C101—21no—
329C23×C101—21no—
330C23×C101—42no—
331C23×C101—41no—
332C23×C101—81no—
333C23×C101—81no—
334C23×C101—81no—
335C23×C101—81no—
336C23×C101—81no—
337C23×C101#12011yescharacteristic
338Q8×C101—41no—
339Q8×C101—41no—
340Q8×C101—41no—
341Q8×C101—41no—
342Q8×C101—41no—
343Q8×C101—41no—
344Q8×C101—81no—
345Q8×C101—81no—
346D4×C101—41no—
347D4×C101—41no—
348D4×C101—41no—
349D4×C101—41no—
350D4×C101—41no—
351D4×C101—41no—
352D4×C101—41no—
353D4×C101—41no—
354D4×C101—41no—
355D4×C101—41no—
356D4×C101—42no—
357D4×C101—42no—
358D4×C101—81no—
359D4×C101—81no—
360D4×C101—81no—
361D4×C101—81no—
362D4×C101—81no—
363D4×C101—81no—
364D4×C101—81no—
365D4×C101—81no—
366D4×C101—82no—
367C2×C4×C101—21no—
368C2×C4×C101—21no—
369C2×C4×C101—21no—
370C2×C4×C101—21no—
371C2×C4×C101—21no—
372C2×C4×C101—21no—
373C2×C4×C101—21no—
374C2×C4×C101—21no—
375C2×C4×C101—41no—
376C2×C4×C101—41no—
377C2×C4×C101—41no—
378C2×C4×C101—42no—
379C2×C4×C101—41no—
380C2×C4×C101—81no—
381C2×C4×C101—81no—
382C2×C4×C101—82no—
383C2×C4×C101—81no—
384C2×C4×C101—81no—
385C2×C4×C101—81no—
386C2×C4×C101—81no—
387C2×C4×C101—81no—
388C2×C4×C101#12011yescharacteristic
389C2×C4×C101#12011yescharacteristic
390C2×C4×C101#12011yescharacteristic
391C2×C4×C101C22×D411yescharacteristic
392C2×C4×C101C22×D411yescharacteristic
393C2×C4×C101C22×D411yescharacteristic
394C8×C101—22no—
395C8×C101—41no—
396C8×C101—41no—
397C8×C101—41no—
398C8×C101—41no—
399C8×C101—41no—
400C22×C101—21no—
401C22×C101—21no—
402C22×C101—21no—
403C22×C101—41no—
404C22×C101—41no—
405C22×C101—41no—
406C22×C101—41no—
407C22×C101—41no—
408C22×C101—41no—
409C22×C101—41no—
410C22×C101—41no—
411C22×C101—41no—
412C22×C101—41no—
413C22×C101—41no—
414C22×C101—41no—
415C22×C101—81no—
416C22×C101—81no—
417C22×C101—81no—
418C22×C101—162no—
419C22×C101—162no—
420C22×C101C2×#12011yescharacteristic
421C4×C101—21no—
422C4×C101—21no—
423C4×C101—21no—
424C4×C101—21no—
425C4×C101—21no—
426C4×C101—21no—
427C4×C101—41no—
428C4×C101—41no—
429C4×C101—41no—
430C4×C101—41no—
431C4×C101—41no—
432C4×C101—41no—
433C4×C101—41no—
434C4×C101—41no—
435C4×C101—81no—
436#19068C10111yesmaximal, characteristic, direct product factor, Sylow
437C2×C101—41no—
438C2×C101—81no—
439C2×C101—81no—
440C2×C101—81no—
441C2×C101—81no—
442C2×C101—161no—
443C2×C101#301811yescharacteristic
444C2×C101#301911yescharacteristic
445C2×C101#302111yescharacteristic
446#3545C2×C10111yescharacteristic, complemented
447#3219C2×C10111yescharacteristic, complemented
448#3213C2×C10111yescharacteristic, complemented
449#3171C2×C10111yescharacteristic, complemented
450#1664C2×C10111yescharacteristic, complemented
451#1662C2×C10111yescharacteristic, complemented
452#1661C2×C10111yescharacteristic, complemented
453#1659C2×C10111yescharacteristic, complemented
454#1657C2×C10111yescharacteristic, complemented
455#1656C2×C10111yescharacteristic, complemented
456#1656C2×C10111yescharacteristic, complemented
457#1655C2×C10111yescharacteristic, complemented
458#1535C2×C10111yescharacteristic, complemented
459#1529C2×C10111yescharacteristic, complemented
460#1527C2×C10111yescharacteristic, complemented
461C101#1906811yescharacteristic, direct product factor, Sylow
462#563C22×C10111yescharacteristic
463#562C22×C10111yescharacteristic
464#562C22×C10111yescharacteristic
465H(3,𝔽4)C22×C10111yescharacteristic
466#555—21no—
467#551—21no—
468#551—21no—
469#551—21no—
470#546—21no—
471#546—21no—
472#542—21no—
473#542—21no—
474#538—21no—
475#538—21no—
476#536—21no—
477#534—21no—
478#532C22×C10111yescharacteristic, complemented
479#529C22×C10111yescharacteristic
480#529C22×C10111yescharacteristic
481C2×#124C22×C10111yescharacteristic
482#501C22×C10111yescharacteristic, complemented
483#497C22×C10111yescharacteristic, complemented
484#496C22×C10111yescharacteristic
485#496C22×C10111yescharacteristic, complemented
486#496C22×C10111yescharacteristic, complemented
487#496C22×C10111yescharacteristic, complemented
488#491C22×C10111yescharacteristic, complemented
489#490C22×C10111yescharacteristic, complemented
490#490C22×C10111yescharacteristic, complemented
491#489C22×C10111yescharacteristic
492#489C22×C10111yescharacteristic, complemented
493#489C22×C10111yescharacteristic, complemented
494#469—21no—
495#468—21no—
496#464—21no—
497#463—21no—
498#463—21no—
499#463—21no—
500#452—21no—
501#449—21no—
502#448—21no—
503#447—21no—
504C4×SD16—21no—
505C4×D8—21no—
506#432C22×C10111yescharacteristic, complemented
507#432C22×C10111yescharacteristic, complemented
508C4×M16C22×C10111yescharacteristic, complemented
509#330C22×C10111yescharacteristic, complemented
510#330C22×C10111yescharacteristic, complemented
511#330C22×C10111yescharacteristic, complemented
512#330C22×C10111yescharacteristic, complemented
513#329C22×C10111yescharacteristic
514#329C22×C10111yescharacteristic
515#329C22×C10111yescharacteristic, complemented
516#329C22×C10111yescharacteristic, complemented
517#329C22×C10111yescharacteristic, complemented
518#329C22×C10111yescharacteristic, complemented
519#329C22×C10111yescharacteristic, complemented
520#329C22×C10111yescharacteristic, complemented
521C2×#41—21no—
522C2×#41—21no—
523C22×Q8D4×C10111yescharacteristic
524C22×D4—21no—
525C22×D4D4×C10111yescharacteristic
526C2×Q16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C2×D8—21no—
536C2×M16—21no—
537C4⋊Q8—21no—
538C4⋊Q8—21no—
539C4⋊Q8C23×C10111yescharacteristic
540#127C23×C10111yescharacteristic
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#125C23×C10111yescharacteristic
548#125C23×C10111yescharacteristic
549#124—21no—
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#124D4×C10111yescharacteristic
559#124D4×C10111yescharacteristic
560#124C23×C10111yescharacteristic
561#124C23×C10111yescharacteristic
562#124C23×C10111yescharacteristic
563#124C23×C10111yescharacteristic
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8D4×C10111yescharacteristic
585C22⋊Q8D4×C10111yescharacteristic
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121D4×C10111yescharacteristic
597#121D4×C10111yescharacteristic
598#120—21no—
599#120—21no—
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604C4×Q8D4×C10111yescharacteristic
605C4×Q8D4×C10111yescharacteristic
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4D4×C10111yescharacteristic
615C4×D4D4×C10111yescharacteristic
616#117—21no—
617#117—21no—
618#117—21no—
619#117—21no—
620#117—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42C23×C10111yescharacteristic
627#107—21no—
628#106—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642#102—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645#97C23×C10111yescharacteristic
646#97C23×C10111yescharacteristic
647#97C23×C10111yescharacteristic
648#97C23×C10111yescharacteristic
649#97C23×C10111yescharacteristic
650#97C23×C10111yescharacteristic
651C4×C8—21no—
652C24—21no—
653C24—21no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8C2×D4×C10111yescharacteristic
662C2×Q8C2×D4×C10111yescharacteristic
663C2×Q8C2×D4×C10111yescharacteristic
664C2×Q8C2×D4×C10111yescharacteristic
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—41no—
679C2×D4—81no—
680C2×D4—82no—
681C2×D4C2×D4×C10111yescharacteristic
682C2×D4C2×D4×C10111yescharacteristic
683C2×D4C2×D4×C10111yescharacteristic
684C2×D4C2×D4×C10111yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4C2×D4×C10111yescharacteristic
695C22×C4C2×D4×C10111yescharacteristic
696C22×C4C2×D4×C10111yescharacteristic
697Q16—81no—
698SD16—42no—
699SD16—81no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703D8—42no—
704D8—81no—
705D8—81no—
706D8—81no—
707M16—42no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4C2×D4×C10111yescharacteristic
731C4⋊C4C2×D4×C10111yescharacteristic
732C4⋊C4C2×D4×C10111yescharacteristic
733C4⋊C4C2×D4×C10111yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42C2×D4×C10111yescharacteristic
769C42C2×D4×C10111yescharacteristic
770C42C2×D4×C10111yescharacteristic
771C42C24×C10111yescharacteristic
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—42no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23#120×C10111yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—82no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—82no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4#120×C10111yescharacteristic
835C2×C4#120×C10111yescharacteristic
836C2×C4#120×C10111yescharacteristic
837C2×C4C22×D4×C10111yescharacteristic
838C2×C4C22×D4×C10111yescharacteristic
839C2×C4C22×D4×C10111yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22—162no—
866C22C2×#120×C10111yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—81no—
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—161no—
888C2C101×#301811yescharacteristic
889C2C101×#301911yescharacteristic
890C2C101×#302111yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC42C24×C101
LCSG ▷ C42 ▷ 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×#3545C2semidirect
2. C101×#3219C2semidirect
3. C101×#3213C2semidirect
4. C101×#3171C2semidirect
5. C101×#1664C2semidirect
6. C101×#1662C2semidirect
7. C101×#1661C2semidirect
8. C101×#1659C2semidirect
9. C101×#1657C2semidirect
10. C101×#1656C2semidirect
11. C101×#1656C2semidirect
12. C101×#1655C2semidirect
13. C101×#1535C2semidirect
14. C101×#1529C2semidirect
15. C101×#1527C2semidirect
32. #532×C101C22semidirect
36. #501×C101C22semidirect
37. #497×C101C22semidirect
39. #496×C101C22semidirect
40. #496×C101C22semidirect
41. #496×C101C22semidirect
42. #491×C101C22semidirect
43. #490×C101C22semidirect
44. #490×C101C22semidirect
46. #489×C101C22semidirect
47. #489×C101C22semidirect
60. #432×C101C22semidirect
61. #432×C101C22semidirect
62. C4×M16×C101C22semidirect
63. #330×C101C22semidirect
64. #330×C101C22semidirect
65. #330×C101C22semidirect
66. #330×C101C22semidirect
69. #329×C101C22semidirect
70. #329×C101C22semidirect
71. #329×C101C22semidirect
72. #329×C101C22semidirect
73. #329×C101C22semidirect
74. #329×C101C22semidirect
436. #19068C101direct (N × H)
446. #3545C2×C101semidirect
447. #3219C2×C101semidirect
448. #3213C2×C101semidirect
449. #3171C2×C101semidirect
450. #1664C2×C101semidirect
451. #1662C2×C101semidirect
452. #1661C2×C101semidirect
453. #1659C2×C101semidirect
454. #1657C2×C101semidirect
455. #1656C2×C101semidirect
456. #1656C2×C101semidirect
457. #1655C2×C101semidirect
458. #1535C2×C101semidirect
459. #1529C2×C101semidirect
460. #1527C2×C101semidirect
461. C101#19068direct (N × H)
478. #532C22×C101semidirect
482. #501C22×C101semidirect
483. #497C22×C101semidirect
485. #496C22×C101semidirect
486. #496C22×C101semidirect
487. #496C22×C101semidirect
488. #491C22×C101semidirect
489. #490C22×C101semidirect
490. #490C22×C101semidirect
492. #489C22×C101semidirect
493. #489C22×C101semidirect
506. #432C22×C101semidirect
507. #432C22×C101semidirect
508. C4×M16C22×C101semidirect
509. #330C22×C101semidirect
510. #330C22×C101semidirect
511. #330C22×C101semidirect
512. #330C22×C101semidirect
515. #329C22×C101semidirect
516. #329C22×C101semidirect
517. #329C22×C101semidirect
518. #329C22×C101semidirect
519. #329C22×C101semidirect
520. #329C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35452
C101×#32192
C101×#32132
C101×#31712
C101×#16642
C101×#16622
C101×#16612
C101×#16592
C101×#16572
C101×#16562
C101×#16552
C101×#15352
C101×#15292
C101×#15272
#19068101