Finite Group Databasebeta

← C101×#18414 #38800565

Subgroups — C101×#18414 #38800565

Order 25856.

1042 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3534C211yesmaximal, characteristic, complemented
2C101×#3194C211yesmaximal, characteristic, complemented
3C101×#3186C211yesmaximal, characteristic, complemented
4C101×#2661C211yesmaximal, characteristic, complemented
5C101×#1612C211yesmaximal, characteristic, complemented
6C101×#1610C211yesmaximal, characteristic, complemented
7C101×#1609C211yesmaximal, characteristic, complemented
8C101×#1607C211yesmaximal, characteristic, complemented
9C101×#1600C211yesmaximal, characteristic, complemented
10C101×#1598C211yesmaximal, characteristic, complemented
11C101×#1597C211yesmaximal, characteristic, complemented
12C101×#1595C211yesmaximal, characteristic, complemented
13C101×#1507C211yesmaximal, characteristic, complemented
14C101×#1501C211yesmaximal, characteristic, complemented
15C101×#1468C211yesmaximal, characteristic, complemented
16#562×C101—21no—
17#560×C101—21no—
18#553×C101—21no—
19#551×C101—21no—
20#546×C101—21no—
21#546×C101—21no—
22#546×C101—21no—
23D42×C101—21no—
24#540×C101—21no—
25#539×C101—21no—
26#539×C101C2211yescharacteristic
27#538×C101—21no—
28#538×C101C2211yescharacteristic
29#537×C101C2211yescharacteristic
30#534×C101—21no—
31#534×C101C2211yescharacteristic
32#525×C101C2211yescharacteristic
33C2×#123×C101C2211yescharacteristic
34C2×#121×C101C2211yescharacteristic
35C2×#121×C101C2211yescharacteristic, complemented
36#483×C101C2211yescharacteristic, complemented
37#482×C101—21no—
38#480×C101—21no—
39#480×C101C2211yescharacteristic
40#480×C101C2211yescharacteristic, complemented
41#480×C101C2211yescharacteristic, complemented
42#469×C101—21no—
43#468×C101—21no—
44#466×C101—21no—
45#466×C101—21no—
46#450×C101C2211yescharacteristic, complemented
47#449×C101—21no—
48#447×C101—21no—
49#447×C101C2211yescharacteristic
50#447×C101C2211yescharacteristic, complemented
51#447×C101C2211yescharacteristic, complemented
52#407×C101C2211yescharacteristic, complemented
53C2×C22⋊C8×C101C2211yescharacteristic, complemented
54#398×C101C2211yescharacteristic, complemented
55#397×C101C2211yescharacteristic, complemented
56#394×C101—21no—
57#394×C101C2211yescharacteristic, complemented
58#392×C101—21no—
59#392×C101C2211yescharacteristic, complemented
60#390×C101—21no—
61#388×C101—21no—
62C4×C22⋊C4×C101C2211yescharacteristic, complemented
63#328×C101C2211yescharacteristic, complemented
64#328×C101C2211yescharacteristic, complemented
65#327×C101C2211yescharacteristic
66#327×C101C2211yescharacteristic
67#327×C101C2211yescharacteristic, complemented
68#327×C101C2211yescharacteristic, complemented
69#327×C101C2211yescharacteristic, complemented
70#327×C101C2211yescharacteristic, complemented
71#324×C101C2211yescharacteristic, complemented
72#324×C101C2211yescharacteristic, complemented
73#323×C101C2211yescharacteristic, complemented
74#323×C101C2211yescharacteristic, complemented
75C2×#41×C101—21no—
76C2×#41×C101D411yescharacteristic, complemented
77C22×D4×C101—21no—
78C22×D4×C101—21no—
79C22×D4×C101—21no—
80C22×D4×C101—21no—
81C22×D4×C101—21no—
82C22×D4×C101D411yescharacteristic
83C22×D4×C101D411yescharacteristic, complemented
84C22×D4×C101C2311yescharacteristic
85C23×C4×C101C2311yescharacteristic
86C2×SD16×C101—21no—
87C2×D8×C101—21no—
88C2×D8×C101—21no—
89C2×D8×C101—21no—
90C2×M16×C101—21no—
91C22×C8×C101—21no—
92#127×C101—21no—
93#126×C101—21no—
94#126×C101—21no—
95#126×C101—21no—
96#126×C101—21no—
97#125×C101—21no—
98#125×C101—21no—
99#124×C101—21no—
100#124×C101—21no—
101#124×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—
108#123×C101—21no—
109#123×C101—21no—
110#123×C101—21no—
111#123×C101—21no—
112#123×C101—21no—
113#123×C101—21no—
114#123×C101—21no—
115#123×C101—21no—
116C22⋊Q8×C101—21no—
117C22⋊Q8×C101—21no—
118C22⋊Q8×C101—21no—
119C22⋊Q8×C101—21no—
120C22⋊Q8×C101—21no—
121C22⋊Q8×C101D411yescharacteristic, complemented
122C22⋊Q8×C101C2311yescharacteristic
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×C101—21no—
131#121×C101—21no—
132#121×C101—21no—
133#121×C101—21no—
134#121×C101—21no—
135#121×C101—21no—
136#121×C101—21no—
137#121×C101—21no—
138#121×C101—21no—
139#121×C101—21no—
140#121×C101—21no—
141#121×C101—21no—
142#121×C101D411yescharacteristic, complemented
143#121×C101D411yescharacteristic, complemented
144#121×C101D411yescharacteristic, complemented
145#121×C101C2311yescharacteristic
146#121×C101C2311yescharacteristic
147#121×C101C2311yescharacteristic
148#120×C101—21no—
149#120×C101—21no—
150#120×C101—21no—
151#120×C101—21no—
152#120×C101—21no—
153#120×C101—21no—
154#120×C101—21no—
155#120×C101—21no—
156C4×D4×C101—21no—
157C4×D4×C101—21no—
158C4×D4×C101—21no—
159C4×D4×C101—21no—
160C4×D4×C101—21no—
161C4×D4×C101—21no—
162C4×D4×C101—21no—
163C4×D4×C101—21no—
164#117×C101—21no—
165#117×C101D411yescharacteristic, complemented
166C2×C4⋊C4×C101—21no—
167C2×C4⋊C4×C101D411yescharacteristic
168C2×C4⋊C4×C101D411yescharacteristic, complemented
169C2×C4⋊C4×C101C2311yescharacteristic
170C2×C4⋊C4×C101C2311yescharacteristic
171C2×C22⋊C4×C101—21no—
172C2×C22⋊C4×C101—21no—
173C2×C22⋊C4×C101—21no—
174C2×C22⋊C4×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×C22⋊C4×C101D411yescharacteristic
181C2×C22⋊C4×C101D411yescharacteristic
182C2×C22⋊C4×C101C2311yescharacteristic
183C2×C42×C101—21no—
184#107×C101—21no—
185#107×C101—21no—
186#107×C101—21no—
187#106×C101—21no—
188#103×C101—21no—
189#102×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—
196C22⋊C8×C101—21no—
197C22⋊C8×C101—21no—
198C22⋊C8×C101C2311yescharacteristic
199C22⋊C8×C101C2311yescharacteristic
200C22⋊C8×C101C2311yescharacteristic
201C22⋊C8×C101C2311yescharacteristic
202#95×C101—21no—
203#95×C101—21no—
204#95×C101C2311yescharacteristic
205#95×C101C2311yescharacteristic
206C24×C101—21no—
207C24×C101—21no—
208C24×C101—21no—
209C24×C101C2×D411yescharacteristic
210C24×C101C2×D411yescharacteristic
211#41×C101—81no—
212#41×C101—81no—
213#41×C101—81no—
214C2×Q8×C101—21no—
215C2×Q8×C101C2×D411yescharacteristic
216C2×D4×C101—21no—
217C2×D4×C101—21no—
218C2×D4×C101—21no—
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—21no—
233C2×D4×C101—21no—
234C2×D4×C101—21no—
235C2×D4×C101—42no—
236C2×D4×C101—41no—
237C2×D4×C101—41no—
238C2×D4×C101—81no—
239C2×D4×C101—81no—
240C2×D4×C101—81no—
241C2×D4×C101—81no—
242C2×D4×C101—81no—
243C2×D4×C101—81no—
244C2×D4×C101—81no—
245C2×D4×C101—81no—
246C2×D4×C101—81no—
247C2×D4×C101—81no—
248C2×D4×C101—81no—
249C2×D4×C101—82no—
250C2×D4×C101C2×D411yescharacteristic
251C2×D4×C101C2×D411yescharacteristic
252C2×D4×C101C2×D411yescharacteristic
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—81no—
264C22×C4×C101C2×D411yescharacteristic
265C22×C4×C101C2×D411yescharacteristic
266C22×C4×C101C2×D411yescharacteristic
267C22×C4×C101C2×D411yescharacteristic
268C22×C4×C101C2×D411yescharacteristic
269C22×C4×C101C2×D411yescharacteristic
270C22×C4×C101C2×D411yescharacteristic
271C22×C4×C101C2×D411yescharacteristic
272C22×C4×C101C2411yescharacteristic
273SD16×C101—81no—
274D8×C101—81no—
275D8×C101—81no—
276D8×C101—81no—
277M16×C101—81no—
278C2×C8×C101—21no—
279C2×C8×C101—21no—
280C2×C8×C101—21no—
281C2×C8×C101—21no—
282C2×C8×C101—81no—
283C4⋊C4×C101—21no—
284C4⋊C4×C101—21no—
285C4⋊C4×C101—21no—
286C4⋊C4×C101—21no—
287C4⋊C4×C101—21no—
288C4⋊C4×C101—21no—
289C4⋊C4×C101—21no—
290C4⋊C4×C101—21no—
291C4⋊C4×C101—21no—
292C4⋊C4×C101—21no—
293C4⋊C4×C101—21no—
294C4⋊C4×C101—21no—
295C4⋊C4×C101—21no—
296C4⋊C4×C101—21no—
297C4⋊C4×C101—21no—
298C4⋊C4×C101—81no—
299C4⋊C4×C101C2×D411yescharacteristic
300C4⋊C4×C101C2×D411yescharacteristic
301C4⋊C4×C101C2×D411yescharacteristic
302C4⋊C4×C101C2×D411yescharacteristic
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—21no—
317C22⋊C4×C101—21no—
318C22⋊C4×C101—21no—
319C22⋊C4×C101—21no—
320C22⋊C4×C101—21no—
321C22⋊C4×C101—21no—
322C22⋊C4×C101—21no—
323C22⋊C4×C101—21no—
324C22⋊C4×C101—21no—
325C22⋊C4×C101—21no—
326C22⋊C4×C101—21no—
327C22⋊C4×C101—21no—
328C22⋊C4×C101—42no—
329C22⋊C4×C101—42no—
330C22⋊C4×C101—41no—
331C22⋊C4×C101—41no—
332C22⋊C4×C101—81no—
333C22⋊C4×C101—81no—
334C22⋊C4×C101—81no—
335C42×C101—21no—
336C42×C101—21no—
337C42×C101—21no—
338C42×C101—81no—
339C23×C101—21no—
340C23×C101—21no—
341C23×C101—21no—
342C23×C101—21no—
343C23×C101—21no—
344C23×C101—21no—
345C23×C101—21no—
346C23×C101—21no—
347C23×C101—41no—
348C23×C101—41no—
349C23×C101—42no—
350C23×C101—41no—
351C23×C101—41no—
352C23×C101—41no—
353C23×C101—41no—
354C23×C101—41no—
355C23×C101—41no—
356C23×C101—41no—
357C23×C101—41no—
358C23×C101—41no—
359C23×C101—81no—
360C23×C101—81no—
361C23×C101—81no—
362C23×C101—81no—
363C23×C101—81no—
364C23×C101#12011yescharacteristic
365C23×C101#12011yescharacteristic
366C23×C101C22×D411yescharacteristic
367Q8×C101—41no—
368Q8×C101—81no—
369D4×C101—41no—
370D4×C101—41no—
371D4×C101—41no—
372D4×C101—41no—
373D4×C101—41no—
374D4×C101—41no—
375D4×C101—41no—
376D4×C101—42no—
377D4×C101—42no—
378D4×C101—41no—
379D4×C101—41no—
380D4×C101—41no—
381D4×C101—41no—
382D4×C101—41no—
383D4×C101—41no—
384D4×C101—81no—
385D4×C101—81no—
386D4×C101—81no—
387D4×C101—81no—
388D4×C101—81no—
389D4×C101—81no—
390D4×C101—81no—
391D4×C101—81no—
392D4×C101—81no—
393D4×C101—81no—
394D4×C101—81no—
395D4×C101—81no—
396D4×C101—84no—
397D4×C101—82no—
398D4×C101—82no—
399C2×C4×C101—22no—
400C2×C4×C101—21no—
401C2×C4×C101—21no—
402C2×C4×C101—21no—
403C2×C4×C101—21no—
404C2×C4×C101—21no—
405C2×C4×C101—21no—
406C2×C4×C101—21no—
407C2×C4×C101—21no—
408C2×C4×C101—21no—
409C2×C4×C101—21no—
410C2×C4×C101—41no—
411C2×C4×C101—41no—
412C2×C4×C101—41no—
413C2×C4×C101—41no—
414C2×C4×C101—41no—
415C2×C4×C101—41no—
416C2×C4×C101—41no—
417C2×C4×C101—41no—
418C2×C4×C101—41no—
419C2×C4×C101—41no—
420C2×C4×C101—41no—
421C2×C4×C101—41no—
422C2×C4×C101—41no—
423C2×C4×C101—41no—
424C2×C4×C101—41no—
425C2×C4×C101—41no—
426C2×C4×C101—81no—
427C2×C4×C101—81no—
428C2×C4×C101—81no—
429C2×C4×C101—81no—
430C2×C4×C101—81no—
431C2×C4×C101—81no—
432C2×C4×C101—81no—
433C2×C4×C101#12011yescharacteristic
434C2×C4×C101#12011yescharacteristic
435C2×C4×C101C22×D411yescharacteristic
436C2×C4×C101C22×D411yescharacteristic
437C8×C101—41no—
438C8×C101—41no—
439C8×C101—41no—
440C8×C101—41no—
441C22×C101—21no—
442C22×C101—21no—
443C22×C101—21no—
444C22×C101—21no—
445C22×C101—21no—
446C22×C101—21no—
447C22×C101—21no—
448C22×C101—21no—
449C22×C101—41no—
450C22×C101—41no—
451C22×C101—41no—
452C22×C101—41no—
453C22×C101—41no—
454C22×C101—41no—
455C22×C101—41no—
456C22×C101—41no—
457C22×C101—41no—
458C22×C101—41no—
459C22×C101—41no—
460C22×C101—41no—
461C22×C101—81no—
462C22×C101—81no—
463C22×C101—81no—
464C22×C101—81no—
465C22×C101—81no—
466C22×C101—81no—
467C22×C101—81no—
468C22×C101—81no—
469C22×C101—81no—
470C22×C101—81no—
471C22×C101—81no—
472C22×C101—162no—
473C22×C101—162no—
474C22×C101C2×#12011yescharacteristic
475C22×C101#57611yescharacteristic
476C22×C101#57611yescharacteristic
477C4×C101—21no—
478C4×C101—21no—
479C4×C101—21no—
480C4×C101—21no—
481C4×C101—42no—
482C4×C101—41no—
483C4×C101—41no—
484C4×C101—41no—
485C4×C101—41no—
486C4×C101—41no—
487C4×C101—41no—
488C4×C101—41no—
489C4×C101—41no—
490C4×C101—81no—
491C4×C101—81no—
492#18414C10111yesmaximal, characteristic, direct product factor, Sylow
493C2×C101—21no—
494C2×C101—21no—
495C2×C101—41no—
496C2×C101—41no—
497C2×C101—81no—
498C2×C101—81no—
499C2×C101—81no—
500C2×C101—81no—
501C2×C101—161no—
502C2×C101#300811yescharacteristic
503C2×C101#301811yescharacteristic
504C2×C101#302611yescharacteristic
505#3534C2×C10111yescharacteristic, complemented
506#3194C2×C10111yescharacteristic, complemented
507#3186C2×C10111yescharacteristic, complemented
508#2661C2×C10111yescharacteristic, complemented
509#1612C2×C10111yescharacteristic, complemented
510#1610C2×C10111yescharacteristic, complemented
511#1609C2×C10111yescharacteristic, complemented
512#1607C2×C10111yescharacteristic, complemented
513#1600C2×C10111yescharacteristic, complemented
514#1598C2×C10111yescharacteristic, complemented
515#1597C2×C10111yescharacteristic, complemented
516#1595C2×C10111yescharacteristic, complemented
517#1507C2×C10111yescharacteristic, complemented
518#1501C2×C10111yescharacteristic, complemented
519#1468C2×C10111yescharacteristic, complemented
520C101#1841411yescharacteristic, direct product factor, Sylow
521#562—21no—
522#560—21no—
523#553—21no—
524#551—21no—
525#546—21no—
526#546—21no—
527#546—21no—
528D42—21no—
529#540—21no—
530#539—21no—
531#539C22×C10111yescharacteristic
532#538—21no—
533#538C22×C10111yescharacteristic
534#537C22×C10111yescharacteristic
535#534—21no—
536#534C22×C10111yescharacteristic
537#525C22×C10111yescharacteristic
538C2×#123C22×C10111yescharacteristic
539C2×#121C22×C10111yescharacteristic
540C2×#121C22×C10111yescharacteristic, complemented
541#483C22×C10111yescharacteristic, complemented
542#482—21no—
543#480—21no—
544#480C22×C10111yescharacteristic
545#480C22×C10111yescharacteristic, complemented
546#480C22×C10111yescharacteristic, complemented
547#469—21no—
548#468—21no—
549#466—21no—
550#466—21no—
551#450C22×C10111yescharacteristic, complemented
552#449—21no—
553#447—21no—
554#447C22×C10111yescharacteristic
555#447C22×C10111yescharacteristic, complemented
556#447C22×C10111yescharacteristic, complemented
557#407C22×C10111yescharacteristic, complemented
558C2×C22⋊C8C22×C10111yescharacteristic, complemented
559#398C22×C10111yescharacteristic, complemented
560#397C22×C10111yescharacteristic, complemented
561#394—21no—
562#394C22×C10111yescharacteristic, complemented
563#392—21no—
564#392C22×C10111yescharacteristic, complemented
565#390—21no—
566#388—21no—
567C4×C22⋊C4C22×C10111yescharacteristic, complemented
568#328C22×C10111yescharacteristic, complemented
569#328C22×C10111yescharacteristic, complemented
570#327C22×C10111yescharacteristic
571#327C22×C10111yescharacteristic
572#327C22×C10111yescharacteristic, complemented
573#327C22×C10111yescharacteristic, complemented
574#327C22×C10111yescharacteristic, complemented
575#327C22×C10111yescharacteristic, complemented
576#324C22×C10111yescharacteristic, complemented
577#324C22×C10111yescharacteristic, complemented
578#323C22×C10111yescharacteristic, complemented
579#323C22×C10111yescharacteristic, complemented
580C2×#41—21no—
581C2×#41D4×C10111yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C10111yescharacteristic
588C22×D4D4×C10111yescharacteristic, complemented
589C22×D4C23×C10111yescharacteristic
590C23×C4C23×C10111yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C10111yescharacteristic, complemented
627C22⋊Q8C23×C10111yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C10111yescharacteristic, complemented
648#121D4×C10111yescharacteristic, complemented
649#121D4×C10111yescharacteristic, complemented
650#121C23×C10111yescharacteristic
651#121C23×C10111yescharacteristic
652#121C23×C10111yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C10111yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4D4×C10111yescharacteristic
673C2×C4⋊C4D4×C10111yescharacteristic, complemented
674C2×C4⋊C4C23×C10111yescharacteristic
675C2×C4⋊C4C23×C10111yescharacteristic
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4D4×C10111yescharacteristic
686C2×C22⋊C4D4×C10111yescharacteristic
687C2×C22⋊C4C23×C10111yescharacteristic
688C2×C42—21no—
689#107—21no—
690#107—21no—
691#107—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C10111yescharacteristic
704C22⋊C8C23×C10111yescharacteristic
705C22⋊C8C23×C10111yescharacteristic
706C22⋊C8C23×C10111yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C10111yescharacteristic
710#95C23×C10111yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C10111yescharacteristic
715C24C2×D4×C10111yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C10111yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C10111yescharacteristic
756C2×D4C2×D4×C10111yescharacteristic
757C2×D4C2×D4×C10111yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C10111yescharacteristic
770C22×C4C2×D4×C10111yescharacteristic
771C22×C4C2×D4×C10111yescharacteristic
772C22×C4C2×D4×C10111yescharacteristic
773C22×C4C2×D4×C10111yescharacteristic
774C22×C4C2×D4×C10111yescharacteristic
775C22×C4C2×D4×C10111yescharacteristic
776C22×C4C2×D4×C10111yescharacteristic
777C22×C4C24×C10111yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4C2×D4×C10111yescharacteristic
805C4⋊C4C2×D4×C10111yescharacteristic
806C4⋊C4C2×D4×C10111yescharacteristic
807C4⋊C4C2×D4×C10111yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—41no—
836C22⋊C4—41no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—81no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C10111yescharacteristic
870C23#120×C10111yescharacteristic
871C23C22×D4×C10111yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—84no—
902D4—82no—
903D4—82no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C10111yescharacteristic
939C2×C4#120×C10111yescharacteristic
940C2×C4C22×D4×C10111yescharacteristic
941C2×C4C22×D4×C10111yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C10111yescharacteristic
980C22#576×C10111yescharacteristic
981C22#576×C10111yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C101×#300811yescharacteristic
1007C2C101×#301811yescharacteristic
1008C2C101×#302611yescharacteristic
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×#3194C2semidirect
3. C101×#3186C2semidirect
4. C101×#2661C2semidirect
5. C101×#1612C2semidirect
6. C101×#1610C2semidirect
7. C101×#1609C2semidirect
8. C101×#1607C2semidirect
9. C101×#1600C2semidirect
10. C101×#1598C2semidirect
11. C101×#1597C2semidirect
12. C101×#1595C2semidirect
13. C101×#1507C2semidirect
14. C101×#1501C2semidirect
15. C101×#1468C2semidirect
35. C2×#121×C101C22semidirect
36. #483×C101C22semidirect
40. #480×C101C22semidirect
41. #480×C101C22semidirect
46. #450×C101C22semidirect
50. #447×C101C22semidirect
51. #447×C101C22semidirect
52. #407×C101C22semidirect
53. C2×C22⋊C8×C101C22semidirect
54. #398×C101C22semidirect
55. #397×C101C22semidirect
57. #394×C101C22semidirect
59. #392×C101C22semidirect
62. C4×C22⋊C4×C101C22semidirect
63. #328×C101C22semidirect
64. #328×C101C22semidirect
67. #327×C101C22semidirect
68. #327×C101C22semidirect
69. #327×C101C22semidirect
70. #327×C101C22semidirect
71. #324×C101C22semidirect
72. #324×C101C22semidirect
73. #323×C101C22semidirect
74. #323×C101C22semidirect
76. C2×#41×C101D4semidirect
83. C22×D4×C101D4semidirect
121. C22⋊Q8×C101D4semidirect
142. #121×C101D4semidirect
143. #121×C101D4semidirect
144. #121×C101D4semidirect
165. #117×C101D4semidirect
168. C2×C4⋊C4×C101D4semidirect
492. #18414C101direct (N × H)
505. #3534C2×C101semidirect
506. #3194C2×C101semidirect
507. #3186C2×C101semidirect
508. #2661C2×C101semidirect
509. #1612C2×C101semidirect
510. #1610C2×C101semidirect
511. #1609C2×C101semidirect
512. #1607C2×C101semidirect
513. #1600C2×C101semidirect
514. #1598C2×C101semidirect
515. #1597C2×C101semidirect
516. #1595C2×C101semidirect
517. #1507C2×C101semidirect
518. #1501C2×C101semidirect
519. #1468C2×C101semidirect
520. C101#18414direct (N × H)
540. C2×#121C22×C101semidirect
541. #483C22×C101semidirect
545. #480C22×C101semidirect
546. #480C22×C101semidirect
551. #450C22×C101semidirect
555. #447C22×C101semidirect
556. #447C22×C101semidirect
557. #407C22×C101semidirect
558. C2×C22⋊C8C22×C101semidirect
559. #398C22×C101semidirect
560. #397C22×C101semidirect
562. #394C22×C101semidirect
564. #392C22×C101semidirect
567. C4×C22⋊C4C22×C101semidirect
568. #328C22×C101semidirect
569. #328C22×C101semidirect
572. #327C22×C101semidirect
573. #327C22×C101semidirect
574. #327C22×C101semidirect
575. #327C22×C101semidirect
576. #324C22×C101semidirect
577. #324C22×C101semidirect
578. #323C22×C101semidirect
579. #323C22×C101semidirect
581. C2×#41D4×C101semidirect
588. C22×D4D4×C101semidirect
626. C22⋊Q8D4×C101semidirect
647. #121D4×C101semidirect
648. #121D4×C101semidirect
649. #121D4×C101semidirect
670. #117D4×C101semidirect
673. 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×#31942
C101×#31862
C101×#26612
C101×#16122
C101×#16102
C101×#16092
C101×#16072
C101×#16002
C101×#15982
C101×#15972
C101×#15952
C101×#15072
C101×#15012
C101×#14682
#18414101