Finite Group Databasebeta

← C101×#18224 #38800375

Subgroups — C101×#18224 #38800375

Order 25856.

1370 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3534C211yesmaximal, characteristic, complemented
2C101×#3003C211yesmaximal, characteristic, complemented
3C2×#447×C101C211yesmaximal, characteristic, complemented
4C101×#2613C211yesmaximal, characteristic, complemented
5C101×#1600C212yesmaximal, complemented
6C101×#1598C212yesmaximal, complemented
7C101×#1597C212yesmaximal, complemented
8C101×#1595C212yesmaximal, complemented
9C101×#1516C211yesmaximal, characteristic, complemented
10C101×#1510C211yesmaximal, characteristic, complemented
11C101×#1468C211yesmaximal, characteristic, complemented
12C23×D4×C101C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C101—21no—
14C22×D8×C101—21no—
15#562×C101—21no—
16#560×C101—21no—
17#553×C101—21no—
18#551×C101—21no—
19#546×C101—21no—
20#546×C101—21no—
21#546×C101—21no—
22D42×C101—21no—
23#540×C101—21no—
24#539×C101—21no—
25#539×C101C2211yescharacteristic, complemented
26#538×C101—21no—
27#538×C101C2211yescharacteristic, complemented
28#537×C101C2211yescharacteristic, complemented
29#534×C101—21no—
30#534×C101C2211yescharacteristic, complemented
31#525×C101C2211yescharacteristic
32C2×#123×C101C2211yescharacteristic
33C2×#121×C101C2211yescharacteristic
34C2×#120×C101—21no—
35#450×C101—21no—
36#450×C101C2212yescomplemented
37#447×C101—21no—
38#447×C101—21no—
39#447×C101—21no—
40#447×C101C2212yes—
41#447×C101C2212yescomplemented
42#447×C101C2212yescomplemented
43#418×C101—21no—
44C2×#102×C101—21no—
45#407×C101C2211yescharacteristic, complemented
46C2×C22⋊C8×C101C2211yescharacteristic, complemented
47#394×C101—21no—
48#394×C101C2212yescomplemented
49#392×C101—21no—
50#392×C101C2212yescomplemented
51#381×C101C2211yescharacteristic, complemented
52#379×C101—21no—
53#328×C101C2212yescomplemented
54#327×C101C2212yescomplemented
55#327×C101C2212yescomplemented
56#327×C101C2212yescomplemented
57#324×C101C2212yescomplemented
58#323×C101C2212yescomplemented
59C25×C101—21no—
60C2×#41×C101—21no—
61C2×#41×C101D411yescharacteristic, complemented
62C22×D4×C101—21no—
63C22×D4×C101—21no—
64C22×D4×C101—21no—
65C22×D4×C101—22no—
66C22×D4×C101—21no—
67C22×D4×C101—21no—
68C22×D4×C101—21no—
69C22×D4×C101—21no—
70C22×D4×C101—21no—
71C22×D4×C101—44no—
72C22×D4×C101D411yescharacteristic
73C22×D4×C101D411yescharacteristic, complemented
74C22×D4×C101C2312yes—
75C23×C4×C101C2311yescharacteristic
76AGL(1,ℤ/8)×C101—44no—
77C2×SD16×C101—22no—
78C2×D8×C101—22no—
79C2×D8×C101—22no—
80C2×D8×C101—22no—
81C2×D8×C101—44no—
82C2×M16×C101—21no—
83C22×C8×C101—21no—
84#127×C101—21no—
85#126×C101—21no—
86#126×C101—21no—
87#126×C101—21no—
88#126×C101—21no—
89#125×C101—21no—
90#125×C101—21no—
91#124×C101—21no—
92#124×C101—21no—
93#124×C101—21no—
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—
106#123×C101—21no—
107#123×C101—21no—
108C22⋊Q8×C101—21no—
109C22⋊Q8×C101—21no—
110C22⋊Q8×C101—21no—
111C22⋊Q8×C101—21no—
112C22⋊Q8×C101—21no—
113C22⋊Q8×C101D411yescharacteristic, complemented
114C22⋊Q8×C101C2311yescharacteristic
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×C101—21no—
127#121×C101—21no—
128#121×C101—21no—
129#121×C101—21no—
130#121×C101D411yescharacteristic, complemented
131#121×C101D411yescharacteristic, complemented
132#121×C101D411yescharacteristic, complemented
133#121×C101C2311yescharacteristic
134#121×C101C2311yescharacteristic
135#121×C101C2311yescharacteristic
136#120×C101—21no—
137#120×C101—21no—
138#120×C101—21no—
139#120×C101—21no—
140#120×C101—21no—
141#120×C101—21no—
142#120×C101—21no—
143#120×C101—21no—
144#120×C101—44no—
145C4×D4×C101—21no—
146C4×D4×C101—21no—
147C4×D4×C101—21no—
148C4×D4×C101—21no—
149C4×D4×C101—21no—
150C4×D4×C101—21no—
151C4×D4×C101—21no—
152C4×D4×C101—21no—
153#117×C101—21no—
154#117×C101D411yescharacteristic, complemented
155C2×C4⋊C4×C101D411yescharacteristic
156C2×C4⋊C4×C101D411yescharacteristic, complemented
157C2×C4⋊C4×C101C2311yescharacteristic
158C2×C22⋊C4×C101—21no—
159C2×C22⋊C4×C101—21no—
160C2×C22⋊C4×C101—21no—
161C2×C22⋊C4×C101—21no—
162C2×C22⋊C4×C101—22no—
163C2×C22⋊C4×C101—22no—
164C2×C22⋊C4×C101—22no—
165C2×C22⋊C4×C101D411yescharacteristic
166C2×C22⋊C4×C101D411yescharacteristic
167C2×C22⋊C4×C101C2311yescharacteristic
168#102×C101—22no—
169#102×C101—22no—
170#102×C101—22no—
171#102×C101—22no—
172C22⋊C8×C101—21no—
173C22⋊C8×C101—21no—
174C22⋊C8×C101C2312yes—
175C22⋊C8×C101C2312yes—
176#95×C101—21no—
177#95×C101C2312yes—
178C24×C101—24no—
179C24×C101—21no—
180C24×C101—22no—
181C24×C101—21no—
182C24×C101—42no—
183C24×C101—41no—
184C24×C101—41no—
185C24×C101—82no—
186C24×C101—82no—
187C24×C101C2×D411yescharacteristic
188C24×C101C2×D411yescharacteristic
189#41×C101—42no—
190#41×C101—82no—
191C2×Q8×C101—21no—
192C2×Q8×C101C2×D411yescharacteristic
193C2×D4×C101—24no—
194C2×D4×C101—24no—
195C2×D4×C101—21no—
196C2×D4×C101—21no—
197C2×D4×C101—21no—
198C2×D4×C101—21no—
199C2×D4×C101—21no—
200C2×D4×C101—21no—
201C2×D4×C101—21no—
202C2×D4×C101—21no—
203C2×D4×C101—21no—
204C2×D4×C101—21no—
205C2×D4×C101—21no—
206C2×D4×C101—21no—
207C2×D4×C101—21no—
208C2×D4×C101—21no—
209C2×D4×C101—21no—
210C2×D4×C101—21no—
211C2×D4×C101—21no—
212C2×D4×C101—22no—
213C2×D4×C101—22no—
214C2×D4×C101—42no—
215C2×D4×C101—42no—
216C2×D4×C101—42no—
217C2×D4×C101—44no—
218C2×D4×C101—44no—
219C2×D4×C101—44no—
220C2×D4×C101—44no—
221C2×D4×C101—42no—
222C2×D4×C101—44no—
223C2×D4×C101—41no—
224C2×D4×C101—41no—
225C2×D4×C101—82no—
226C2×D4×C101—82no—
227C2×D4×C101—82no—
228C2×D4×C101—82no—
229C2×D4×C101—82no—
230C2×D4×C101C2×D411yescharacteristic
231C2×D4×C101C2×D411yescharacteristic
232C2×D4×C101C2×D411yescharacteristic
233C22×C4×C101—21no—
234C22×C4×C101—21no—
235C22×C4×C101—21no—
236C22×C4×C101—21no—
237C22×C4×C101—21no—
238C22×C4×C101—21no—
239C22×C4×C101—21no—
240C22×C4×C101—22no—
241C22×C4×C101—42no—
242C22×C4×C101C2×D411yescharacteristic
243C22×C4×C101C2×D411yescharacteristic
244C22×C4×C101C2×D411yescharacteristic
245C22×C4×C101C2×D411yescharacteristic
246C22×C4×C101C2×D411yescharacteristic
247C22×C4×C101C2×D411yescharacteristic
248C22×C4×C101C2×D411yescharacteristic
249C22×C4×C101C2×D411yescharacteristic
250C22×C4×C101C2411yescharacteristic
251SD16×C101—44no—
252D8×C101—44no—
253D8×C101—44no—
254D8×C101—44no—
255M16×C101—42no—
256C2×C8×C101—22no—
257C2×C8×C101—22no—
258C2×C8×C101—42no—
259C4⋊C4×C101—21no—
260C4⋊C4×C101—21no—
261C4⋊C4×C101—21no—
262C4⋊C4×C101—21no—
263C4⋊C4×C101—21no—
264C4⋊C4×C101—21no—
265C4⋊C4×C101—21no—
266C4⋊C4×C101—21no—
267C4⋊C4×C101—21no—
268C4⋊C4×C101—21no—
269C4⋊C4×C101—21no—
270C4⋊C4×C101—21no—
271C4⋊C4×C101—21no—
272C4⋊C4×C101C2×D411yescharacteristic
273C4⋊C4×C101C2×D411yescharacteristic
274C4⋊C4×C101C2×D411yescharacteristic
275C4⋊C4×C101C2×D411yescharacteristic
276C22⋊C4×C101—21no—
277C22⋊C4×C101—21no—
278C22⋊C4×C101—21no—
279C22⋊C4×C101—21no—
280C22⋊C4×C101—21no—
281C22⋊C4×C101—21no—
282C22⋊C4×C101—21no—
283C22⋊C4×C101—21no—
284C22⋊C4×C101—21no—
285C22⋊C4×C101—21no—
286C22⋊C4×C101—21no—
287C22⋊C4×C101—21no—
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—44no—
302C22⋊C4×C101—42no—
303C22⋊C4×C101—82no—
304C22⋊C4×C101—82no—
305C42×C101—21no—
306C42×C101—21no—
307C42×C101—21no—
308C23×C101—22no—
309C23×C101—22no—
310C23×C101—24no—
311C23×C101—21no—
312C23×C101—21no—
313C23×C101—21no—
314C23×C101—21no—
315C23×C101—22no—
316C23×C101—41no—
317C23×C101—42no—
318C23×C101—42no—
319C23×C101—44no—
320C23×C101—42no—
321C23×C101—41no—
322C23×C101—41no—
323C23×C101—42no—
324C23×C101—42no—
325C23×C101—42no—
326C23×C101—44no—
327C23×C101—42no—
328C23×C101—81no—
329C23×C101—81no—
330C23×C101—82no—
331C23×C101—82no—
332C23×C101—82no—
333C23×C101—82no—
334C23×C101—88no—
335C23×C101—81no—
336C23×C101—81no—
337C23×C101—81no—
338C23×C101—88no—
339C23×C101#12011yescharacteristic
340C23×C101#12011yescharacteristic
341C23×C101C22×D411yescharacteristic
342Q8×C101—41no—
343Q8×C101—81no—
344D4×C101—24no—
345D4×C101—24no—
346D4×C101—41no—
347D4×C101—41no—
348D4×C101—41no—
349D4×C101—42no—
350D4×C101—42no—
351D4×C101—44no—
352D4×C101—44no—
353D4×C101—42no—
354D4×C101—42no—
355D4×C101—42no—
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—81no—
367D4×C101—81no—
368D4×C101—81no—
369D4×C101—81no—
370D4×C101—88no—
371C2×C4×C101—22no—
372C2×C4×C101—22no—
373C2×C4×C101—21no—
374C2×C4×C101—21no—
375C2×C4×C101—21no—
376C2×C4×C101—21no—
377C2×C4×C101—21no—
378C2×C4×C101—21no—
379C2×C4×C101—21no—
380C2×C4×C101—21no—
381C2×C4×C101—22no—
382C2×C4×C101—41no—
383C2×C4×C101—41no—
384C2×C4×C101—41no—
385C2×C4×C101—41no—
386C2×C4×C101—41no—
387C2×C4×C101—41no—
388C2×C4×C101—42no—
389C2×C4×C101—42no—
390C2×C4×C101—42no—
391C2×C4×C101—81no—
392C2×C4×C101—81no—
393C2×C4×C101—81no—
394C2×C4×C101—81no—
395C2×C4×C101—81no—
396C2×C4×C101—81no—
397C2×C4×C101—81no—
398C2×C4×C101#12011yescharacteristic
399C2×C4×C101#12011yescharacteristic
400C2×C4×C101C22×D411yescharacteristic
401C2×C4×C101C22×D411yescharacteristic
402C8×C101—42no—
403C8×C101—42no—
404C22×C101—21no—
405C22×C101—21no—
406C22×C101—21no—
407C22×C101—21no—
408C22×C101—21no—
409C22×C101—21no—
410C22×C101—21no—
411C22×C101—44no—
412C22×C101—44no—
413C22×C101—44no—
414C22×C101—41no—
415C22×C101—41no—
416C22×C101—41no—
417C22×C101—41no—
418C22×C101—41no—
419C22×C101—41no—
420C22×C101—41no—
421C22×C101—41no—
422C22×C101—41no—
423C22×C101—41no—
424C22×C101—44no—
425C22×C101—41no—
426C22×C101—41no—
427C22×C101—82no—
428C22×C101—82no—
429C22×C101—82no—
430C22×C101—88no—
431C22×C101—88no—
432C22×C101—82no—
433C22×C101—82no—
434C22×C101—162no—
435C22×C101—162no—
436C22×C101B(4,𝔽2)12yes—
437C22×C101C2×#12011yescharacteristic
438C22×C101#57612yes—
439C4×C101—21no—
440C4×C101—21no—
441C4×C101—21no—
442C4×C101—21no—
443C4×C101—41no—
444C4×C101—41no—
445C4×C101—41no—
446C4×C101—41no—
447C4×C101—41no—
448C4×C101—41no—
449C4×C101—41no—
450C4×C101—41no—
451C4×C101—82no—
452#18224C10111yesmaximal, characteristic, direct product factor, Sylow
453C2×C101—22no—
454C2×C101—22no—
455C2×C101—41no—
456C2×C101—84no—
457C2×C101—81no—
458C2×C101—81no—
459C2×C101—81no—
460C2×C101—81no—
461C2×C101#300811yescharacteristic
462C2×C101#302111yescharacteristic
463C2×C101C2×B(4,𝔽2)11yescharacteristic
464#3534C2×C10111yescharacteristic, complemented
465#3003C2×C10111yescharacteristic, complemented
466C2×#447C2×C10111yescharacteristic, complemented
467#2613C2×C10111yescharacteristic, complemented
468#1600C2×C10112yescomplemented
469#1598C2×C10112yescomplemented
470#1597C2×C10112yescomplemented
471#1595C2×C10112yescomplemented
472#1516C2×C10111yescharacteristic, complemented
473#1510C2×C10111yescharacteristic, complemented
474#1468C2×C10111yescharacteristic, complemented
475C101#1822411yescharacteristic, direct product factor, Sylow
476C23×D4C22×C10111yescharacteristic, complemented
477C2×AGL(1,ℤ/8)—21no—
478C22×D8—21no—
479#562—21no—
480#560—21no—
481#553—21no—
482#551—21no—
483#546—21no—
484#546—21no—
485#546—21no—
486D42—21no—
487#540—21no—
488#539—21no—
489#539C22×C10111yescharacteristic, complemented
490#538—21no—
491#538C22×C10111yescharacteristic, complemented
492#537C22×C10111yescharacteristic, complemented
493#534—21no—
494#534C22×C10111yescharacteristic, complemented
495#525C22×C10111yescharacteristic
496C2×#123C22×C10111yescharacteristic
497C2×#121C22×C10111yescharacteristic
498C2×#120—21no—
499#450—21no—
500#450C22×C10112yescomplemented
501#447—21no—
502#447—21no—
503#447—21no—
504#447C22×C10112yes—
505#447C22×C10112yescomplemented
506#447C22×C10112yescomplemented
507#418—21no—
508C2×#102—21no—
509#407C22×C10111yescharacteristic, complemented
510C2×C22⋊C8C22×C10111yescharacteristic, complemented
511#394—21no—
512#394C22×C10112yescomplemented
513#392—21no—
514#392C22×C10112yescomplemented
515#381C22×C10111yescharacteristic, complemented
516#379—21no—
517#328C22×C10112yescomplemented
518#327C22×C10112yescomplemented
519#327C22×C10112yescomplemented
520#327C22×C10112yescomplemented
521#324C22×C10112yescomplemented
522#323C22×C10112yescomplemented
523C25—21no—
524C2×#41—21no—
525C2×#41D4×C10111yescharacteristic, complemented
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—44no—
536C22×D4D4×C10111yescharacteristic
537C22×D4D4×C10111yescharacteristic, complemented
538C22×D4C23×C10112yes—
539C23×C4C23×C10111yescharacteristic
540AGL(1,ℤ/8)—44no—
541C2×SD16—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—44no—
546C2×M16—21no—
547C22×C8—21no—
548#127—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#126—21no—
553#125—21no—
554#125—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8D4×C10111yescharacteristic, complemented
578C22⋊Q8C23×C10111yescharacteristic
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
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#121D4×C10111yescharacteristic, complemented
595#121D4×C10111yescharacteristic, complemented
596#121D4×C10111yescharacteristic, complemented
597#121C23×C10111yescharacteristic
598#121C23×C10111yescharacteristic
599#121C23×C10111yescharacteristic
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607#120—21no—
608#120—44no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617#117—21no—
618#117D4×C10111yescharacteristic, complemented
619C2×C4⋊C4D4×C10111yescharacteristic
620C2×C4⋊C4D4×C10111yescharacteristic, complemented
621C2×C4⋊C4C23×C10111yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4D4×C10111yescharacteristic
630C2×C22⋊C4D4×C10111yescharacteristic
631C2×C22⋊C4C23×C10111yescharacteristic
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8C23×C10112yes—
639C22⋊C8C23×C10112yes—
640#95—21no—
641#95C23×C10112yes—
642C24—24no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—42no—
647C24—41no—
648C24—41no—
649C24—82no—
650C24—82no—
651C24C2×D4×C10111yescharacteristic
652C24C2×D4×C10111yescharacteristic
653#41—42no—
654#41—82no—
655C2×Q8—21no—
656C2×Q8C2×D4×C10111yescharacteristic
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
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—22no—
677C2×D4—22no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—82no—
693C2×D4—82no—
694C2×D4C2×D4×C10111yescharacteristic
695C2×D4C2×D4×C10111yescharacteristic
696C2×D4C2×D4×C10111yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—42no—
706C22×C4C2×D4×C10111yescharacteristic
707C22×C4C2×D4×C10111yescharacteristic
708C22×C4C2×D4×C10111yescharacteristic
709C22×C4C2×D4×C10111yescharacteristic
710C22×C4C2×D4×C10111yescharacteristic
711C22×C4C2×D4×C10111yescharacteristic
712C22×C4C2×D4×C10111yescharacteristic
713C22×C4C2×D4×C10111yescharacteristic
714C22×C4C24×C10111yescharacteristic
715SD16—44no—
716D8—44no—
717D8—44no—
718D8—44no—
719M16—42no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—42no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4C2×D4×C10111yescharacteristic
737C4⋊C4C2×D4×C10111yescharacteristic
738C4⋊C4C2×D4×C10111yescharacteristic
739C4⋊C4C2×D4×C10111yescharacteristic
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—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—82no—
768C22⋊C4—82no—
769C42—21no—
770C42—21no—
771C42—21no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—42no—
785C23—41no—
786C23—41no—
787C23—44no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—81no—
793C23—81no—
794C23—82no—
795C23—82no—
796C23—82no—
797C23—82no—
798C23—88no—
799C23—81no—
800C23—81no—
801C23—81no—
802C23—88no—
803C23#120×C10111yescharacteristic
804C23#120×C10111yescharacteristic
805C23C22×D4×C10111yescharacteristic
806Q8—41no—
807Q8—81no—
808D4—24no—
809D4—24no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—44no—
817D4—42no—
818D4—42no—
819D4—42no—
820D4—42no—
821D4—42no—
822D4—81no—
823D4—81no—
824D4—81no—
825D4—81no—
826D4—81no—
827D4—81no—
828D4—81no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833D4—81no—
834D4—88no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4#120×C10111yescharacteristic
863C2×C4#120×C10111yescharacteristic
864C2×C4C22×D4×C10111yescharacteristic
865C2×C4C22×D4×C10111yescharacteristic
866C8—42no—
867C8—42no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—44no—
889C22—41no—
890C22—41no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—88no—
895C22—88no—
896C22—82no—
897C22—82no—
898C22—162no—
899C22—162no—
900C22B(4,𝔽2)×C10112yes—
901C22C2×#120×C10111yescharacteristic
902C22#576×C10112yes—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—82no—
916C2—22no—
917C2—22no—
918C2—41no—
919C2—84no—
920C2—81no—
921C2—81no—
922C2—81no—
923C2—81no—
924C2C101×#300811yescharacteristic
925C2C101×#302111yescharacteristic
926C2C2×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×#3534C2semidirect
2. C101×#3003C2semidirect
3. C2×#447×C101C2semidirect
4. C101×#2613C2semidirect
5. C101×#1600C2semidirect
6. C101×#1598C2semidirect
7. C101×#1597C2semidirect
8. C101×#1595C2semidirect
9. C101×#1516C2semidirect
10. C101×#1510C2semidirect
11. C101×#1468C2semidirect
12. C23×D4×C101C22semidirect
25. #539×C101C22semidirect
27. #538×C101C22semidirect
28. #537×C101C22semidirect
30. #534×C101C22semidirect
36. #450×C101C22semidirect
41. #447×C101C22semidirect
42. #447×C101C22semidirect
45. #407×C101C22semidirect
46. C2×C22⋊C8×C101C22semidirect
48. #394×C101C22semidirect
50. #392×C101C22semidirect
51. #381×C101C22semidirect
53. #328×C101C22semidirect
54. #327×C101C22semidirect
55. #327×C101C22semidirect
56. #327×C101C22semidirect
57. #324×C101C22semidirect
58. #323×C101C22semidirect
61. C2×#41×C101D4semidirect
73. C22×D4×C101D4semidirect
113. C22⋊Q8×C101D4semidirect
130. #121×C101D4semidirect
131. #121×C101D4semidirect
132. #121×C101D4semidirect
154. #117×C101D4semidirect
156. C2×C4⋊C4×C101D4semidirect
452. #18224C101direct (N × H)
464. #3534C2×C101semidirect
465. #3003C2×C101semidirect
466. C2×#447C2×C101semidirect
467. #2613C2×C101semidirect
468. #1600C2×C101semidirect
469. #1598C2×C101semidirect
470. #1597C2×C101semidirect
471. #1595C2×C101semidirect
472. #1516C2×C101semidirect
473. #1510C2×C101semidirect
474. #1468C2×C101semidirect
475. C101#18224direct (N × H)
476. C23×D4C22×C101semidirect
489. #539C22×C101semidirect
491. #538C22×C101semidirect
492. #537C22×C101semidirect
494. #534C22×C101semidirect
500. #450C22×C101semidirect
505. #447C22×C101semidirect
506. #447C22×C101semidirect
509. #407C22×C101semidirect
510. C2×C22⋊C8C22×C101semidirect
512. #394C22×C101semidirect
514. #392C22×C101semidirect
515. #381C22×C101semidirect
517. #328C22×C101semidirect
518. #327C22×C101semidirect
519. #327C22×C101semidirect
520. #327C22×C101semidirect
521. #324C22×C101semidirect
522. #323C22×C101semidirect
525. C2×#41D4×C101semidirect
537. C22×D4D4×C101semidirect
577. C22⋊Q8D4×C101semidirect
594. #121D4×C101semidirect
595. #121D4×C101semidirect
596. #121D4×C101semidirect
618. #117D4×C101semidirect
620. 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×#35342
C101×#30032
C2×#447×C1012
C101×#26132
C101×#16002
C101×#15982
C101×#15972
C101×#15952
C101×#15162
C101×#15102
C101×#14682
#18224101