Finite Group Databasebeta

← C101×#18262 #38800413

Subgroups — C101×#18262 #38800413

Order 25856.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3534C211yesmaximal, characteristic
2C101×#3094C211yesmaximal, characteristic, complemented
3C101×#3091C211yesmaximal, characteristic, complemented
4C101×#2498C211yesmaximal, characteristic, complemented
5C101×#1618C211yesmaximal, characteristic, complemented
6C101×#1616C211yesmaximal, characteristic, complemented
7C101×#1615C211yesmaximal, characteristic, complemented
8C101×#1613C211yesmaximal, characteristic, complemented
9C101×#1612C211yesmaximal, characteristic, complemented
10C101×#1610C211yesmaximal, characteristic, complemented
11C101×#1609C211yesmaximal, characteristic, complemented
12C101×#1607C211yesmaximal, characteristic, complemented
13C101×#1504C211yesmaximal, characteristic, complemented
14C2×#327×C101C211yesmaximal, 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×#117×C101C2211yescharacteristic, complemented
36#485×C101—21no—
37#484×C101C2211yescharacteristic, complemented
38#483×C101C2211yescharacteristic, complemented
39#482×C101—21no—
40#482×C101—21no—
41#482×C101—21no—
42#481×C101C2211yescharacteristic
43#481×C101C2211yescharacteristic, complemented
44#481×C101C2211yescharacteristic, complemented
45#480×C101C2211yescharacteristic
46#480×C101C2211yescharacteristic, complemented
47#480×C101C2211yescharacteristic, complemented
48#428×C101—21no—
49#427×C101—21no—
50#418×C101—21no—
51#416×C101—21no—
52#407×C101C2211yescharacteristic, complemented
53C2×C22⋊C8×C101C2211yescharacteristic, complemented
54#400×C101C2211yescharacteristic, complemented
55#399×C101C2211yescharacteristic, complemented
56#398×C101C2211yescharacteristic, complemented
57#397×C101C2211yescharacteristic, complemented
58#388×C101—21no—
59#387×C101—21no—
60#386×C101—21no—
61#380×C101—21no—
62C2×#95×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
77C22×D4×C101—21no—
78C22×D4×C101—21no—
79C22×D4×C101—21no—
80C22×D4×C101D411yescharacteristic
81C22×D4×C101D411yescharacteristic
82C23×C4×C101—21no—
83C23×C4×C101C2311yescharacteristic
84C2×M16×C101—21no—
85C22×C8×C101—21no—
86#127×C101—21no—
87#126×C101—21no—
88#126×C101—21no—
89#126×C101—21no—
90#126×C101—21no—
91#125×C101—21no—
92#125×C101—21no—
93#124×C101—21no—
94#124×C101—21no—
95#124×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—
108#123×C101—21no—
109#123×C101—21no—
110C22⋊Q8×C101—21no—
111C22⋊Q8×C101—21no—
112C22⋊Q8×C101—21no—
113C22⋊Q8×C101—21no—
114C22⋊Q8×C101—21no—
115C22⋊Q8×C101D411yescharacteristic
116C22⋊Q8×C101C2311yescharacteristic
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×C101—21no—
131#121×C101—21no—
132#121×C101D411yescharacteristic
133#121×C101D411yescharacteristic
134#121×C101D411yescharacteristic
135#121×C101C2311yescharacteristic
136#121×C101C2311yescharacteristic
137#121×C101C2311yescharacteristic
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—21no—
145#120×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—
153C4×D4×C101—21no—
154#117×C101—21no—
155#117×C101—21no—
156#117×C101—21no—
157#117×C101—21no—
158#117×C101—21no—
159#117×C101D411yescharacteristic
160C2×C4⋊C4×C101—21no—
161C2×C4⋊C4×C101—21no—
162C2×C4⋊C4×C101D411yescharacteristic
163C2×C4⋊C4×C101D411yescharacteristic
164C2×C4⋊C4×C101C2311yescharacteristic
165C2×C4⋊C4×C101C2311yescharacteristic
166C2×C4⋊C4×C101C2311yescharacteristic
167C2×C22⋊C4×C101—21no—
168C2×C22⋊C4×C101—21no—
169C2×C22⋊C4×C101—21no—
170C2×C22⋊C4×C101—21no—
171C2×C22⋊C4×C101—21no—
172C2×C22⋊C4×C101—21no—
173C2×C22⋊C4×C101D411yescharacteristic
174C2×C22⋊C4×C101D411yescharacteristic
175C2×C22⋊C4×C101C2311yescharacteristic
176C2×C42×C101—21no—
177#107×C101—21no—
178#107×C101—21no—
179#107×C101—21no—
180#107×C101—21no—
181#106×C101—21no—
182#106×C101—21no—
183#106×C101—21no—
184#106×C101—21no—
185#103×C101—21no—
186#103×C101—21no—
187#102×C101—21no—
188#102×C101—21no—
189#102×C101—21no—
190#102×C101—21no—
191#102×C101—21no—
192#102×C101—21no—
193C22⋊C8×C101—21no—
194C22⋊C8×C101—21no—
195C22⋊C8×C101C2311yescharacteristic
196C22⋊C8×C101C2311yescharacteristic
197C22⋊C8×C101C2311yescharacteristic
198C22⋊C8×C101C2311yescharacteristic
199#95×C101—21no—
200#95×C101—21no—
201#95×C101—21no—
202#95×C101—21no—
203#95×C101—21no—
204#95×C101C2311yescharacteristic
205#95×C101C2311yescharacteristic
206C24×C101—21no—
207C24×C101—21no—
208C24×C101C2×D411yescharacteristic
209C24×C101C2×D411yescharacteristic
210#41×C101—42no—
211#41×C101—81no—
212#41×C101—81no—
213C2×Q8×C101—21no—
214C2×Q8×C101C2×D411yescharacteristic
215C2×D4×C101—21no—
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—42no—
233C2×D4×C101—42no—
234C2×D4×C101—81no—
235C2×D4×C101—81no—
236C2×D4×C101—81no—
237C2×D4×C101—81no—
238C2×D4×C101—82no—
239C2×D4×C101C2×D411yescharacteristic
240C2×D4×C101C2×D411yescharacteristic
241C2×D4×C101C2×D411yescharacteristic
242C22×C4×C101—21no—
243C22×C4×C101—21no—
244C22×C4×C101—21no—
245C22×C4×C101—21no—
246C22×C4×C101—21no—
247C22×C4×C101—21no—
248C22×C4×C101—21no—
249C22×C4×C101—21no—
250C22×C4×C101—21no—
251C22×C4×C101—21no—
252C22×C4×C101—21no—
253C22×C4×C101—42no—
254C22×C4×C101—42no—
255C22×C4×C101—42no—
256C22×C4×C101—81no—
257C22×C4×C101C2×D411yescharacteristic
258C22×C4×C101C2×D411yescharacteristic
259C22×C4×C101C2×D411yescharacteristic
260C22×C4×C101C2×D411yescharacteristic
261C22×C4×C101C2×D411yescharacteristic
262C22×C4×C101C2×D411yescharacteristic
263C22×C4×C101C2×D411yescharacteristic
264C22×C4×C101C2×D411yescharacteristic
265C22×C4×C101C2411yescharacteristic
266M16×C101—42no—
267C2×C8×C101—21no—
268C2×C8×C101—21no—
269C2×C8×C101—21no—
270C2×C8×C101—21no—
271C2×C8×C101—42no—
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×C101—21no—
285C4⋊C4×C101—21no—
286C4⋊C4×C101—21no—
287C4⋊C4×C101—21no—
288C4⋊C4×C101—21no—
289C4⋊C4×C101—42no—
290C4⋊C4×C101—81no—
291C4⋊C4×C101C2×D411yescharacteristic
292C4⋊C4×C101C2×D411yescharacteristic
293C4⋊C4×C101C2×D411yescharacteristic
294C4⋊C4×C101C2×D411yescharacteristic
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—21no—
317C22⋊C4×C101—21no—
318C22⋊C4×C101—21no—
319C22⋊C4×C101—21no—
320C22⋊C4×C101—42no—
321C22⋊C4×C101—41no—
322C22⋊C4×C101—41no—
323C22⋊C4×C101—81no—
324C42×C101—21no—
325C42×C101—21no—
326C42×C101—21no—
327C42×C101—41no—
328C42×C101—41no—
329C23×C101—21no—
330C23×C101—21no—
331C23×C101—22no—
332C23×C101—21no—
333C23×C101—21no—
334C23×C101—21no—
335C23×C101—21no—
336C23×C101—21no—
337C23×C101—21no—
338C23×C101—41no—
339C23×C101—41no—
340C23×C101—41no—
341C23×C101—42no—
342C23×C101—81no—
343C23×C101—81no—
344C23×C101—81no—
345C23×C101—81no—
346C23×C101—81no—
347C23×C101#12011yescharacteristic
348C23×C101#12011yescharacteristic
349C23×C101C22×D411yescharacteristic
350Q8×C101—41no—
351Q8×C101—81no—
352D4×C101—41no—
353D4×C101—41no—
354D4×C101—41no—
355D4×C101—41no—
356D4×C101—41no—
357D4×C101—41no—
358D4×C101—41no—
359D4×C101—41no—
360D4×C101—41no—
361D4×C101—42no—
362D4×C101—42no—
363D4×C101—81no—
364D4×C101—81no—
365D4×C101—81no—
366D4×C101—81no—
367D4×C101—81no—
368D4×C101—81no—
369D4×C101—81no—
370D4×C101—81no—
371D4×C101—81no—
372D4×C101—81no—
373D4×C101—81no—
374D4×C101—81no—
375C2×C4×C101—22no—
376C2×C4×C101—22no—
377C2×C4×C101—22no—
378C2×C4×C101—21no—
379C2×C4×C101—21no—
380C2×C4×C101—21no—
381C2×C4×C101—21no—
382C2×C4×C101—21no—
383C2×C4×C101—21no—
384C2×C4×C101—21no—
385C2×C4×C101—21no—
386C2×C4×C101—21no—
387C2×C4×C101—21no—
388C2×C4×C101—41no—
389C2×C4×C101—41no—
390C2×C4×C101—41no—
391C2×C4×C101—41no—
392C2×C4×C101—41no—
393C2×C4×C101—41no—
394C2×C4×C101—41no—
395C2×C4×C101—41no—
396C2×C4×C101—41no—
397C2×C4×C101—41no—
398C2×C4×C101—41no—
399C2×C4×C101—41no—
400C2×C4×C101—41no—
401C2×C4×C101—41no—
402C2×C4×C101—41no—
403C2×C4×C101—41no—
404C2×C4×C101—41no—
405C2×C4×C101—81no—
406C2×C4×C101—81no—
407C2×C4×C101—81no—
408C2×C4×C101—81no—
409C2×C4×C101—81no—
410C2×C4×C101—81no—
411C2×C4×C101—81no—
412C2×C4×C101—84no—
413C2×C4×C101#12011yescharacteristic
414C2×C4×C101#12011yescharacteristic
415C2×C4×C101C22×D411yescharacteristic
416C2×C4×C101C22×D411yescharacteristic
417C8×C101—41no—
418C8×C101—41no—
419C8×C101—41no—
420C8×C101—41no—
421C22×C101—21no—
422C22×C101—21no—
423C22×C101—21no—
424C22×C101—21no—
425C22×C101—21no—
426C22×C101—21no—
427C22×C101—21no—
428C22×C101—42no—
429C22×C101—42no—
430C22×C101—41no—
431C22×C101—41no—
432C22×C101—41no—
433C22×C101—41no—
434C22×C101—41no—
435C22×C101—41no—
436C22×C101—41no—
437C22×C101—41no—
438C22×C101—41no—
439C22×C101—41no—
440C22×C101—41no—
441C22×C101—41no—
442C22×C101—81no—
443C22×C101—81no—
444C22×C101—162no—
445C22×C101—162no—
446C22×C101#45812yes—
447C22×C101C2×#12011yescharacteristic
448C22×C101#57611yescharacteristic
449C22×C101#57711yescharacteristic
450C4×C101—21no—
451C4×C101—21no—
452C4×C101—21no—
453C4×C101—21no—
454C4×C101—42no—
455C4×C101—41no—
456C4×C101—41no—
457C4×C101—41no—
458C4×C101—41no—
459C4×C101—41no—
460C4×C101—41no—
461C4×C101—41no—
462C4×C101—41no—
463C4×C101—81no—
464C4×C101—81no—
465C4×C101—81no—
466#18262C10111yesmaximal, characteristic, direct product factor, Sylow
467C2×C101—21no—
468C2×C101—21no—
469C2×C101—22no—
470C2×C101—41no—
471C2×C101—81no—
472C2×C101—81no—
473C2×C101—81no—
474C2×C101—81no—
475C2×C101#301211yescharacteristic
476C2×C101#301811yescharacteristic
477C2×C101C2×#45811yescharacteristic
478#3534C2×C10111yescharacteristic
479#3094C2×C10111yescharacteristic, complemented
480#3091C2×C10111yescharacteristic, complemented
481#2498C2×C10111yescharacteristic, complemented
482#1618C2×C10111yescharacteristic, complemented
483#1616C2×C10111yescharacteristic, complemented
484#1615C2×C10111yescharacteristic, complemented
485#1613C2×C10111yescharacteristic, complemented
486#1612C2×C10111yescharacteristic, complemented
487#1610C2×C10111yescharacteristic, complemented
488#1609C2×C10111yescharacteristic, complemented
489#1607C2×C10111yescharacteristic, complemented
490#1504C2×C10111yescharacteristic, complemented
491C2×#327C2×C10111yescharacteristic, complemented
492#1468C2×C10111yescharacteristic, complemented
493C101#1826211yescharacteristic, direct product factor, Sylow
494#562—21no—
495#560—21no—
496#553—21no—
497#551—21no—
498#546—21no—
499#546—21no—
500#546—21no—
501D42—21no—
502#540—21no—
503#539—21no—
504#539C22×C10111yescharacteristic
505#538—21no—
506#538C22×C10111yescharacteristic
507#537C22×C10111yescharacteristic
508#534—21no—
509#534C22×C10111yescharacteristic
510#525C22×C10111yescharacteristic
511C2×#123C22×C10111yescharacteristic
512C2×#121C22×C10111yescharacteristic
513C2×#117C22×C10111yescharacteristic, complemented
514#485—21no—
515#484C22×C10111yescharacteristic, complemented
516#483C22×C10111yescharacteristic, complemented
517#482—21no—
518#482—21no—
519#482—21no—
520#481C22×C10111yescharacteristic
521#481C22×C10111yescharacteristic, complemented
522#481C22×C10111yescharacteristic, complemented
523#480C22×C10111yescharacteristic
524#480C22×C10111yescharacteristic, complemented
525#480C22×C10111yescharacteristic, complemented
526#428—21no—
527#427—21no—
528#418—21no—
529#416—21no—
530#407C22×C10111yescharacteristic, complemented
531C2×C22⋊C8C22×C10111yescharacteristic, complemented
532#400C22×C10111yescharacteristic, complemented
533#399C22×C10111yescharacteristic, complemented
534#398C22×C10111yescharacteristic, complemented
535#397C22×C10111yescharacteristic, complemented
536#388—21no—
537#387—21no—
538#386—21no—
539#380—21no—
540C2×#95C22×C10111yescharacteristic, complemented
541#328C22×C10111yescharacteristic, complemented
542#328C22×C10111yescharacteristic, complemented
543#327C22×C10111yescharacteristic
544#327C22×C10111yescharacteristic
545#327C22×C10111yescharacteristic, complemented
546#327C22×C10111yescharacteristic, complemented
547#327C22×C10111yescharacteristic, complemented
548#327C22×C10111yescharacteristic, complemented
549#324C22×C10111yescharacteristic, complemented
550#324C22×C10111yescharacteristic, complemented
551#323C22×C10111yescharacteristic, complemented
552#323C22×C10111yescharacteristic, complemented
553C2×#41—21no—
554C2×#41D4×C10111yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4D4×C10111yescharacteristic
559C22×D4D4×C10111yescharacteristic
560C23×C4—21no—
561C23×C4C23×C10111yescharacteristic
562C2×M16—21no—
563C22×C8—21no—
564#127—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#125—21no—
570#125—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8D4×C10111yescharacteristic
594C22⋊Q8C23×C10111yescharacteristic
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121D4×C10111yescharacteristic
611#121D4×C10111yescharacteristic
612#121D4×C10111yescharacteristic
613#121C23×C10111yescharacteristic
614#121C23×C10111yescharacteristic
615#121C23×C10111yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C10111yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C10111yescharacteristic
641C2×C4⋊C4D4×C10111yescharacteristic
642C2×C4⋊C4C23×C10111yescharacteristic
643C2×C4⋊C4C23×C10111yescharacteristic
644C2×C4⋊C4C23×C10111yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C10111yescharacteristic
652C2×C22⋊C4D4×C10111yescharacteristic
653C2×C22⋊C4C23×C10111yescharacteristic
654C2×C42—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C10111yescharacteristic
674C22⋊C8C23×C10111yescharacteristic
675C22⋊C8C23×C10111yescharacteristic
676C22⋊C8C23×C10111yescharacteristic
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95C23×C10111yescharacteristic
683#95C23×C10111yescharacteristic
684C24—21no—
685C24—21no—
686C24C2×D4×C10111yescharacteristic
687C24C2×D4×C10111yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
692C2×Q8C2×D4×C10111yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C10111yescharacteristic
718C2×D4C2×D4×C10111yescharacteristic
719C2×D4C2×D4×C10111yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C10111yescharacteristic
736C22×C4C2×D4×C10111yescharacteristic
737C22×C4C2×D4×C10111yescharacteristic
738C22×C4C2×D4×C10111yescharacteristic
739C22×C4C2×D4×C10111yescharacteristic
740C22×C4C2×D4×C10111yescharacteristic
741C22×C4C2×D4×C10111yescharacteristic
742C22×C4C2×D4×C10111yescharacteristic
743C22×C4C24×C10111yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C10111yescharacteristic
770C4⋊C4C2×D4×C10111yescharacteristic
771C4⋊C4C2×D4×C10111yescharacteristic
772C4⋊C4C2×D4×C10111yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23#120×C10111yescharacteristic
826C23#120×C10111yescharacteristic
827C23C22×D4×C10111yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4#120×C10111yescharacteristic
892C2×C4#120×C10111yescharacteristic
893C2×C4C22×D4×C10111yescharacteristic
894C2×C4C22×D4×C10111yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22#458×C10112yes—
925C22C2×#120×C10111yescharacteristic
926C22#576×C10111yescharacteristic
927C22#577×C10111yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C101×#301211yescharacteristic
953C2C101×#301811yescharacteristic
954C2C2×#458×C10111yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#3534C2
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
2. C101×#3094C2semidirect
3. C101×#3091C2semidirect
4. C101×#2498C2semidirect
5. C101×#1618C2semidirect
6. C101×#1616C2semidirect
7. C101×#1615C2semidirect
8. C101×#1613C2semidirect
9. C101×#1612C2semidirect
10. C101×#1610C2semidirect
11. C101×#1609C2semidirect
12. C101×#1607C2semidirect
13. C101×#1504C2semidirect
14. C2×#327×C101C2semidirect
15. C101×#1468C2semidirect
35. C2×#117×C101C22semidirect
37. #484×C101C22semidirect
38. #483×C101C22semidirect
43. #481×C101C22semidirect
44. #481×C101C22semidirect
46. #480×C101C22semidirect
47. #480×C101C22semidirect
52. #407×C101C22semidirect
53. C2×C22⋊C8×C101C22semidirect
54. #400×C101C22semidirect
55. #399×C101C22semidirect
56. #398×C101C22semidirect
57. #397×C101C22semidirect
62. C2×#95×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
466. #18262C101direct (N × H)
479. #3094C2×C101semidirect
480. #3091C2×C101semidirect
481. #2498C2×C101semidirect
482. #1618C2×C101semidirect
483. #1616C2×C101semidirect
484. #1615C2×C101semidirect
485. #1613C2×C101semidirect
486. #1612C2×C101semidirect
487. #1610C2×C101semidirect
488. #1609C2×C101semidirect
489. #1607C2×C101semidirect
490. #1504C2×C101semidirect
491. C2×#327C2×C101semidirect
492. #1468C2×C101semidirect
493. C101#18262direct (N × H)
513. C2×#117C22×C101semidirect
515. #484C22×C101semidirect
516. #483C22×C101semidirect
521. #481C22×C101semidirect
522. #481C22×C101semidirect
524. #480C22×C101semidirect
525. #480C22×C101semidirect
530. #407C22×C101semidirect
531. C2×C22⋊C8C22×C101semidirect
532. #400C22×C101semidirect
533. #399C22×C101semidirect
534. #398C22×C101semidirect
535. #397C22×C101semidirect
540. C2×#95C22×C101semidirect
541. #328C22×C101semidirect
542. #328C22×C101semidirect
545. #327C22×C101semidirect
546. #327C22×C101semidirect
547. #327C22×C101semidirect
548. #327C22×C101semidirect
549. #324C22×C101semidirect
550. #324C22×C101semidirect
551. #323C22×C101semidirect
552. #323C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35342
C101×#30942
C101×#30912
C101×#24982
C101×#16182
C101×#16162
C101×#16152
C101×#16132
C101×#16122
C101×#16102
C101×#16092
C101×#16072
C101×#15042
C2×#327×C1012
C101×#14682
#18262101