Finite Group Databasebeta

← C101×#24469 #38806620

Subgroups — C101×#24469 #38806620

Order 25856.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3489C211yesmaximal, characteristic, complemented
2C101×#3055C211yesmaximal, characteristic, complemented
3C2×#454×C101C211yesmaximal, characteristic, complemented
4C101×#3006C211yesmaximal, characteristic, complemented
5C2×#421×C101C211yesmaximal, characteristic, complemented
6C101×#2620C211yesmaximal, characteristic, complemented
7C101×#2039C211yesmaximal, characteristic, complemented
8C101×#2038C211yesmaximal, characteristic, complemented
9C101×#2006C211yesmaximal, characteristic, complemented
10C101×#2003C211yesmaximal, characteristic, complemented
11C101×#1901C211yesmaximal, characteristic, complemented
12C101×#1897C211yesmaximal, characteristic, complemented
13C101×#1883C211yesmaximal, characteristic, complemented
14C101×#1859C211yesmaximal, characteristic, complemented
15C101×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C101C2211yescharacteristic
17C22×#41×C101C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C101C2211yescharacteristic, complemented
21C22×M16×C101C2211yescharacteristic
22D4×Q8×C101—21no—
23#548×C101—21no—
24#547×C101—21no—
25#547×C101—22no—
26#546×C101—21no—
27#546×C101—22no—
28#537×C101—21no—
29#537×C101C2211yescharacteristic
30#536×C101—21no—
31#536×C101C2211yescharacteristic
32C2×#124×C101C2211yescharacteristic, complemented
33#525×C101—21no—
34#525×C101C2211yescharacteristic
35C2×C22⋊Q8×C101—21no—
36C2×C22⋊Q8×C101C2211yescharacteristic
37C2×#121×C101C2211yescharacteristic
38#520×C101C2211yescharacteristic
39C2×#117×C101C2211yescharacteristic
40#469×C101—21no—
41#468×C101—21no—
42#466×C101—21no—
43#465×C101—21no—
44#454×C101—24no—
45#449×C101—21no—
46#449×C101—21no—
47#448×C101—21no—
48#447×C101—21no—
49#428×C101C2211yescharacteristic, complemented
50#421×C101—24no—
51C2×#104×C101C2211yescharacteristic
52C2×#104×C101C2211yescharacteristic
53C2×#104×C101C2211yescharacteristic
54C2×#104×C101C2211yescharacteristic
55C2×#104×C101C2211yescharacteristic, complemented
56C2×#104×C101C2211yescharacteristic, complemented
57#418×C101C2211yescharacteristic, complemented
58#417×C101C2211yescharacteristic
59#417×C101C2211yescharacteristic
60#417×C101C2211yescharacteristic, complemented
61C2×#101×C101C2211yescharacteristic, complemented
62C2×#101×C101C2211yescharacteristic, complemented
63#407×C101C2211yescharacteristic
64#396×C101—22no—
65#394×C101—22no—
66#391×C101C2211yescharacteristic, complemented
67#390×C101C2211yescharacteristic, complemented
68#384×C101C2211yescharacteristic, complemented
69#343×C101C2211yescharacteristic, complemented
70#343×C101C2211yescharacteristic, complemented
71#339×C101C2211yescharacteristic, complemented
72#339×C101C2211yescharacteristic, complemented
732−1+4×C101—22no—
742−1+4×C101—22no—
752−1+4×C101—41no—
762−1+4×C101—41no—
77C2×#41×C101—21no—
78C2×#41×C101—21no—
79C2×#41×C101—21no—
80C2×#41×C101—22no—
81C2×#41×C101—21no—
82C2×#41×C101—22no—
83C2×#41×C101—22no—
84C2×#41×C101—41no—
85C2×#41×C101—41no—
86C2×#41×C101D411yescharacteristic
87C2×#41×C101D411yescharacteristic
88C2×#41×C101C2311yescharacteristic
89C2×#41×C101C2311yescharacteristic
90C2×#41×C101C2311yescharacteristic
91C22×Q8×C101—21no—
92C22×Q8×C101—21no—
93C22×Q8×C101D411yescharacteristic
94C22×Q8×C101C2311yescharacteristic
95C22×D4×C101—21no—
96C22×D4×C101—21no—
97C22×D4×C101D411yescharacteristic
98C22×D4×C101C2311yescharacteristic
99C23×C4×C101—21no—
100C23×C4×C101C2311yescharacteristic
101AGL(1,ℤ/8)×C101—22no—
102AGL(1,ℤ/8)×C101—22no—
103AGL(1,ℤ/8)×C101—22no—
104AGL(1,ℤ/8)×C101—41no—
105AGL(1,ℤ/8)×C101—41no—
106AGL(1,ℤ/8)×C101—41no—
107C2×SD16×C101—21no—
108C2×SD16×C101—21no—
109C2×SD16×C101—21no—
110C2×D8×C101—21no—
111C2×D8×C101—21no—
112C2×D8×C101—21no—
113C2×M16×C101—21no—
114C2×M16×C101—22no—
115C2×M16×C101—41no—
116C2×M16×C101C2311yescharacteristic
117C2×M16×C101C2311yescharacteristic
118C2×M16×C101C2311yescharacteristic
119C2×M16×C101C2311yescharacteristic
120C22×C8×C101—21no—
121C4⋊Q8×C101—22no—
122C4⋊Q8×C101—21no—
123#124×C101—22no—
124#124×C101—21no—
125#124×C101—22no—
126#124×C101—41no—
127#123×C101—22no—
128#123×C101—22no—
129#123×C101—22no—
130#123×C101—21no—
131#123×C101—22no—
132C22⋊Q8×C101—22no—
133C22⋊Q8×C101—22no—
134C22⋊Q8×C101—22no—
135C22⋊Q8×C101—21no—
136C22⋊Q8×C101—21no—
137C22⋊Q8×C101—21no—
138C22⋊Q8×C101—21no—
139C22⋊Q8×C101—21no—
140C22⋊Q8×C101—21no—
141C22⋊Q8×C101—21no—
142C22⋊Q8×C101—21no—
143C22⋊Q8×C101D411yescharacteristic
144C22⋊Q8×C101D411yescharacteristic
145#121×C101—22no—
146#121×C101—22no—
147#121×C101—22no—
148#121×C101—21no—
149#121×C101—21no—
150#121×C101—22no—
151#121×C101—21no—
152#121×C101—21no—
153#121×C101—21no—
154#121×C101—21no—
155#121×C101D411yescharacteristic
156#121×C101D411yescharacteristic
157#120×C101—22no—
158#120×C101—21no—
159C4×Q8×C101—21no—
160C4×D4×C101—22no—
161C4×D4×C101—22no—
162C4×D4×C101—21no—
163C4×D4×C101—22no—
164C4×D4×C101—21no—
165C4×D4×C101—21no—
166#117×C101—21no—
167#117×C101—22no—
168#117×C101—41no—
169#117×C101C2311yescharacteristic
170C2×C4⋊C4×C101—22no—
171C2×C4⋊C4×C101—21no—
172C2×C4⋊C4×C101—21no—
173C2×C4⋊C4×C101—22no—
174C2×C4⋊C4×C101D412yes—
175C2×C4⋊C4×C101C2311yescharacteristic
176C2×C4⋊C4×C101C2311yescharacteristic
177C2×C22⋊C4×C101—22no—
178C2×C22⋊C4×C101—21no—
179C2×C22⋊C4×C101—21no—
180C2×C22⋊C4×C101—22no—
181C2×C22⋊C4×C101—22no—
182C2×C22⋊C4×C101D412yes—
183C2×C42×C101C2311yescharacteristic
184C2×C42×C101C2311yescharacteristic
185#107×C101—21no—
186#106×C101—21no—
187#104×C101—22no—
188#104×C101—22no—
189#104×C101—22no—
190#104×C101—22no—
191#104×C101—41no—
192#104×C101D414yescomplemented
193#103×C101—21no—
194#103×C101—21no—
195#103×C101—21no—
196#102×C101—21no—
197#102×C101—21no—
198#102×C101—21no—
199#102×C101—21no—
200#102×C101—21no—
201#101×C101—22no—
202#101×C101—41no—
203C22⋊C8×C101—21no—
204C22⋊C8×C101—21no—
205#95×C101—22no—
206C24×C101—21no—
207C24×C101—21no—
208C24×C101C2×D411yescharacteristic
209#41×C101—21no—
210#41×C101—21no—
211#41×C101—22no—
212#41×C101—22no—
213#41×C101—21no—
214#41×C101—21no—
215#41×C101—21no—
216#41×C101—21no—
217#41×C101—21no—
218#41×C101—21no—
219#41×C101—21no—
220#41×C101—21no—
221#41×C101—42no—
222#41×C101—42no—
223#41×C101—41no—
224#41×C101—41no—
225#41×C101—42no—
226#41×C101—42no—
227#41×C101—42no—
228#41×C101—42no—
229#41×C101—44no—
230#41×C101—44no—
231#41×C101—42no—
232#41×C101—42no—
233#41×C101C2×D412yes—
234#41×C101#4112yes—
235C2×Q8×C101—22no—
236C2×Q8×C101—21no—
237C2×Q8×C101—21no—
238C2×Q8×C101—21no—
239C2×Q8×C101—21no—
240C2×Q8×C101—21no—
241C2×Q8×C101—21no—
242C2×Q8×C101—21no—
243C2×Q8×C101—22no—
244C2×Q8×C101—41no—
245C2×Q8×C101—42no—
246C2×Q8×C101—42no—
247C2×Q8×C101—42no—
248C2×Q8×C101—42no—
249C2×Q8×C101C2×D411yescharacteristic
250C2×Q8×C101C2×D411yescharacteristic
251C2×Q8×C101C2×D411yescharacteristic
252C2×D4×C101—21no—
253C2×D4×C101—22no—
254C2×D4×C101—22no—
255C2×D4×C101—21no—
256C2×D4×C101—21no—
257C2×D4×C101—21no—
258C2×D4×C101—21no—
259C2×D4×C101—21no—
260C2×D4×C101—22no—
261C2×D4×C101—21no—
262C2×D4×C101—21no—
263C2×D4×C101—21no—
264C2×D4×C101—21no—
265C2×D4×C101—21no—
266C2×D4×C101—21no—
267C2×D4×C101—21no—
268C2×D4×C101—21no—
269C2×D4×C101—41no—
270C2×D4×C101—42no—
271C2×D4×C101—42no—
272C2×D4×C101—41no—
273C2×D4×C101—41no—
274C2×D4×C101—82no—
275C2×D4×C101C2×D411yescharacteristic
276C2×D4×C101C2×D411yescharacteristic
277C2×D4×C101C2×D411yescharacteristic
278C22×C4×C101—21no—
279C22×C4×C101—21no—
280C22×C4×C101—21no—
281C22×C4×C101—21no—
282C22×C4×C101—21no—
283C22×C4×C101—22no—
284C22×C4×C101—22no—
285C22×C4×C101—21no—
286C22×C4×C101—21no—
287C22×C4×C101—22no—
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—42no—
295C22×C4×C101—42no—
296C22×C4×C101C2×D412yes—
297C22×C4×C101C2×D411yescharacteristic
298C22×C4×C101C2×D411yescharacteristic
299C22×C4×C101C2×D411yescharacteristic
300C22×C4×C101C2×D411yescharacteristic
301C22×C4×C101C2×D411yescharacteristic
302C22×C4×C101C2×D412yes—
303C22×C4×C101C2411yescharacteristic
304SD16×C101—42no—
305SD16×C101—42no—
306SD16×C101—42no—
307D8×C101—42no—
308D8×C101—42no—
309D8×C101—42no—
310M16×C101—21no—
311M16×C101—21no—
312M16×C101—21no—
313M16×C101—21no—
314M16×C101—21no—
315M16×C101—21no—
316M16×C101—21no—
317M16×C101—42no—
318M16×C101C2×D412yes—
319C2×C8×C101—21no—
320C2×C8×C101—21no—
321C2×C8×C101—21no—
322C2×C8×C101—21no—
323C2×C8×C101—42no—
324C4⋊C4×C101—22no—
325C4⋊C4×C101—22no—
326C4⋊C4×C101—22no—
327C4⋊C4×C101—22no—
328C4⋊C4×C101—21no—
329C4⋊C4×C101—22no—
330C4⋊C4×C101—22no—
331C4⋊C4×C101—21no—
332C4⋊C4×C101—21no—
333C4⋊C4×C101—21no—
334C4⋊C4×C101—21no—
335C4⋊C4×C101—21no—
336C4⋊C4×C101—42no—
337C4⋊C4×C101—82no—
338C4⋊C4×C101C2×D411yescharacteristic
339C4⋊C4×C101C2×D411yescharacteristic
340C22⋊C4×C101—22no—
341C22⋊C4×C101—22no—
342C22⋊C4×C101—22no—
343C22⋊C4×C101—22no—
344C22⋊C4×C101—22no—
345C22⋊C4×C101—21no—
346C22⋊C4×C101—22no—
347C22⋊C4×C101—22no—
348C22⋊C4×C101—21no—
349C22⋊C4×C101—21no—
350C22⋊C4×C101—21no—
351C22⋊C4×C101—21no—
352C22⋊C4×C101—44no—
353C22⋊C4×C101—42no—
354C22⋊C4×C101—41no—
355C22⋊C4×C101—41no—
356C22⋊C4×C101—82no—
357C42×C101—22no—
358C42×C101—21no—
359C42×C101—21no—
360C42×C101—21no—
361C42×C101—21no—
362C42×C101C2×D412yes—
363C23×C101—21no—
364C23×C101—21no—
365C23×C101—21no—
366C23×C101—21no—
367C23×C101—21no—
368C23×C101—41no—
369C23×C101—41no—
370C23×C101—42no—
371C23×C101—42no—
372C23×C101—42no—
373C23×C101—42no—
374C23×C101—41no—
375C23×C101—41no—
376C23×C101—41no—
377C23×C101—81no—
378C23×C101#12011yescharacteristic
379C23×C101#12011yescharacteristic
380C23×C101C22×D411yescharacteristic
381Q8×C101—21no—
382Q8×C101—21no—
383Q8×C101—21no—
384Q8×C101—21no—
385Q8×C101—21no—
386Q8×C101—42no—
387Q8×C101—44no—
388Q8×C101—41no—
389Q8×C101—41no—
390Q8×C101—41no—
391Q8×C101—41no—
392Q8×C101#12112yes—
393D4×C101—22no—
394D4×C101—22no—
395D4×C101—21no—
396D4×C101—21no—
397D4×C101—21no—
398D4×C101—21no—
399D4×C101—21no—
400D4×C101—42no—
401D4×C101—42no—
402D4×C101—42no—
403D4×C101—42no—
404D4×C101—44no—
405D4×C101—41no—
406D4×C101—41no—
407D4×C101—41no—
408D4×C101—41no—
409D4×C101—41no—
410D4×C101—41no—
411D4×C101—41no—
412D4×C101—41no—
413D4×C101—81no—
414D4×C101—82no—
415D4×C101—82no—
416D4×C101—82no—
417D4×C101#12112yes—
418C2×C4×C101—21no—
419C2×C4×C101—21no—
420C2×C4×C101—21no—
421C2×C4×C101—21no—
422C2×C4×C101—21no—
423C2×C4×C101—21no—
424C2×C4×C101—21no—
425C2×C4×C101—21no—
426C2×C4×C101—21no—
427C2×C4×C101—22no—
428C2×C4×C101—21no—
429C2×C4×C101—21no—
430C2×C4×C101—22no—
431C2×C4×C101—21no—
432C2×C4×C101—22no—
433C2×C4×C101—21no—
434C2×C4×C101—21no—
435C2×C4×C101—22no—
436C2×C4×C101—21no—
437C2×C4×C101—22no—
438C2×C4×C101—22no—
439C2×C4×C101—22no—
440C2×C4×C101—42no—
441C2×C4×C101—42no—
442C2×C4×C101—42no—
443C2×C4×C101—44no—
444C2×C4×C101—41no—
445C2×C4×C101—41no—
446C2×C4×C101—44no—
447C2×C4×C101—41no—
448C2×C4×C101—41no—
449C2×C4×C101—41no—
450C2×C4×C101—41no—
451C2×C4×C101—42no—
452C2×C4×C101—41no—
453C2×C4×C101—42no—
454C2×C4×C101—41no—
455C2×C4×C101—41no—
456C2×C4×C101—41no—
457C2×C4×C101—82no—
458C2×C4×C101#12011yescharacteristic
459C2×C4×C101#12011yescharacteristic
460C2×C4×C101C22×D411yescharacteristic
461C2×C4×C101C22×D411yescharacteristic
462C2×C4×C101C22×D411yescharacteristic
463C2×C4×C101C2×#4111yescharacteristic
464C2×C4×C101H(5,𝔽2)11yescharacteristic
465C2×C4×C101H(5,𝔽2)11yescharacteristic
466C8×C101—22no—
467C8×C101—41no—
468C8×C101—41no—
469C8×C101—41no—
470C22×C101—21no—
471C22×C101—21no—
472C22×C101—21no—
473C22×C101—21no—
474C22×C101—22no—
475C22×C101—21no—
476C22×C101—21no—
477C22×C101—21no—
478C22×C101—21no—
479C22×C101—41no—
480C22×C101—41no—
481C22×C101—41no—
482C22×C101—41no—
483C22×C101—41no—
484C22×C101—41no—
485C22×C101—41no—
486C22×C101—41no—
487C22×C101—81no—
488C22×C101—81no—
489C22×C101—82no—
490C22×C101—82no—
491C22×C101—84no—
492C22×C101—81no—
493C22×C101—81no—
494C22×C101—81no—
495C22×C101C2×#12011yescharacteristic
496C22×C101D4211yescharacteristic
497C22×C101#54611yescharacteristic
498C4×C101—21no—
499C4×C101—21no—
500C4×C101—22no—
501C4×C101—42no—
502C4×C101—42no—
503C4×C101—41no—
504C4×C101—41no—
505C4×C101—41no—
506C4×C101—42no—
507C4×C101—41no—
508C4×C101—81no—
509C4×C101—81no—
510C4×C101C2×#12111yescharacteristic
511C4×C101#53411yescharacteristic
512C4×C101D4211yescharacteristic
513C4×C101#54611yescharacteristic
514#24469C10111yesmaximal, characteristic, direct product factor, Sylow
515C2×C101—21no—
516C2×C101—21no—
517C2×C101—41no—
518C2×C101—41no—
519C2×C101—42no—
520C2×C101—81no—
521C2×C101—81no—
522C2×C101—161no—
523C2×C101#241011yescharacteristic
524C2×C101#302011yescharacteristic
525C2×C101#302111yescharacteristic
526#3489C2×C10111yescharacteristic, complemented
527#3055C2×C10111yescharacteristic, complemented
528C2×#454C2×C10111yescharacteristic, complemented
529#3006C2×C10111yescharacteristic, complemented
530C2×#421C2×C10111yescharacteristic, complemented
531#2620C2×C10111yescharacteristic, complemented
532#2039C2×C10111yescharacteristic, complemented
533#2038C2×C10111yescharacteristic, complemented
534#2006C2×C10111yescharacteristic, complemented
535#2003C2×C10111yescharacteristic, complemented
536#1901C2×C10111yescharacteristic, complemented
537#1897C2×C10111yescharacteristic, complemented
538#1883C2×C10111yescharacteristic, complemented
539#1859C2×C10111yescharacteristic, complemented
540#1793C2×C10111yescharacteristic, complemented
541C101#2446911yescharacteristic, direct product factor, Sylow
542C2×2−1+4C22×C10111yescharacteristic
543C22×#41C22×C10111yescharacteristic
544C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
545C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
546C2×AGL(1,ℤ/8)C22×C10111yescharacteristic, complemented
547C22×M16C22×C10111yescharacteristic
548D4×Q8—21no—
549#548—21no—
550#547—21no—
551#547—22no—
552#546—21no—
553#546—22no—
554#537—21no—
555#537C22×C10111yescharacteristic
556#536—21no—
557#536C22×C10111yescharacteristic
558C2×#124C22×C10111yescharacteristic, complemented
559#525—21no—
560#525C22×C10111yescharacteristic
561C2×C22⋊Q8—21no—
562C2×C22⋊Q8C22×C10111yescharacteristic
563C2×#121C22×C10111yescharacteristic
564#520C22×C10111yescharacteristic
565C2×#117C22×C10111yescharacteristic
566#469—21no—
567#468—21no—
568#466—21no—
569#465—21no—
570#454—24no—
571#449—21no—
572#449—21no—
573#448—21no—
574#447—21no—
575#428C22×C10111yescharacteristic, complemented
576#421—24no—
577C2×#104C22×C10111yescharacteristic
578C2×#104C22×C10111yescharacteristic
579C2×#104C22×C10111yescharacteristic
580C2×#104C22×C10111yescharacteristic
581C2×#104C22×C10111yescharacteristic, complemented
582C2×#104C22×C10111yescharacteristic, complemented
583#418C22×C10111yescharacteristic, complemented
584#417C22×C10111yescharacteristic
585#417C22×C10111yescharacteristic
586#417C22×C10111yescharacteristic, complemented
587C2×#101C22×C10111yescharacteristic, complemented
588C2×#101C22×C10111yescharacteristic, complemented
589#407C22×C10111yescharacteristic
590#396—22no—
591#394—22no—
592#391C22×C10111yescharacteristic, complemented
593#390C22×C10111yescharacteristic, complemented
594#384C22×C10111yescharacteristic, complemented
595#343C22×C10111yescharacteristic, complemented
596#343C22×C10111yescharacteristic, complemented
597#339C22×C10111yescharacteristic, complemented
598#339C22×C10111yescharacteristic, complemented
5992−1+4—22no—
6002−1+4—22no—
6012−1+4—41no—
6022−1+4—41no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—22no—
607C2×#41—21no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—41no—
611C2×#41—41no—
612C2×#41D4×C10111yescharacteristic
613C2×#41D4×C10111yescharacteristic
614C2×#41C23×C10111yescharacteristic
615C2×#41C23×C10111yescharacteristic
616C2×#41C23×C10111yescharacteristic
617C22×Q8—21no—
618C22×Q8—21no—
619C22×Q8D4×C10111yescharacteristic
620C22×Q8C23×C10111yescharacteristic
621C22×D4—21no—
622C22×D4—21no—
623C22×D4D4×C10111yescharacteristic
624C22×D4C23×C10111yescharacteristic
625C23×C4—21no—
626C23×C4C23×C10111yescharacteristic
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—41no—
631AGL(1,ℤ/8)—41no—
632AGL(1,ℤ/8)—41no—
633C2×SD16—21no—
634C2×SD16—21no—
635C2×SD16—21no—
636C2×D8—21no—
637C2×D8—21no—
638C2×D8—21no—
639C2×M16—21no—
640C2×M16—22no—
641C2×M16—41no—
642C2×M16C23×C10111yescharacteristic
643C2×M16C23×C10111yescharacteristic
644C2×M16C23×C10111yescharacteristic
645C2×M16C23×C10111yescharacteristic
646C22×C8—21no—
647C4⋊Q8—22no—
648C4⋊Q8—21no—
649#124—22no—
650#124—21no—
651#124—22no—
652#124—41no—
653#123—22no—
654#123—22no—
655#123—22no—
656#123—21no—
657#123—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C10111yescharacteristic
670C22⋊Q8D4×C10111yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—22no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121D4×C10111yescharacteristic
682#121D4×C10111yescharacteristic
683#120—22no—
684#120—21no—
685C4×Q8—21no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—22no—
690C4×D4—21no—
691C4×D4—21no—
692#117—21no—
693#117—22no—
694#117—41no—
695#117C23×C10111yescharacteristic
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4D4×C10112yes—
701C2×C4⋊C4C23×C10111yescharacteristic
702C2×C4⋊C4C23×C10111yescharacteristic
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4D4×C10112yes—
709C2×C42C23×C10111yescharacteristic
710C2×C42C23×C10111yescharacteristic
711#107—21no—
712#106—21no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—22no—
717#104—41no—
718#104D4×C10114yescomplemented
719#103—21no—
720#103—21no—
721#103—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#102—21no—
727#101—22no—
728#101—41no—
729C22⋊C8—21no—
730C22⋊C8—21no—
731#95—22no—
732C24—21no—
733C24—21no—
734C24C2×D4×C10111yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41C2×D4×C10112yes—
760#41#41×C10112yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×D4×C10111yescharacteristic
776C2×Q8C2×D4×C10111yescharacteristic
777C2×Q8C2×D4×C10111yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—82no—
801C2×D4C2×D4×C10111yescharacteristic
802C2×D4C2×D4×C10111yescharacteristic
803C2×D4C2×D4×C10111yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4C2×D4×C10112yes—
823C22×C4C2×D4×C10111yescharacteristic
824C22×C4C2×D4×C10111yescharacteristic
825C22×C4C2×D4×C10111yescharacteristic
826C22×C4C2×D4×C10111yescharacteristic
827C22×C4C2×D4×C10111yescharacteristic
828C22×C4C2×D4×C10112yes—
829C22×C4C24×C10111yescharacteristic
830SD16—42no—
831SD16—42no—
832SD16—42no—
833D8—42no—
834D8—42no—
835D8—42no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—42no—
844M16C2×D4×C10112yes—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—42no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—42no—
863C4⋊C4—82no—
864C4⋊C4C2×D4×C10111yescharacteristic
865C4⋊C4C2×D4×C10111yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—44no—
879C22⋊C4—42no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—82no—
883C42—22no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42C2×D4×C10112yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23#120×C10111yescharacteristic
905C23#120×C10111yescharacteristic
906C23C22×D4×C10111yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8#121×C10112yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—44no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4#121×C10112yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—44no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4#120×C10111yescharacteristic
985C2×C4#120×C10111yescharacteristic
986C2×C4C22×D4×C10111yescharacteristic
987C2×C4C22×D4×C10111yescharacteristic
988C2×C4C22×D4×C10111yescharacteristic
989C2×C4C2×#41×C10111yescharacteristic
990C2×C4H(5,𝔽2)×C10111yescharacteristic
991C2×C4H(5,𝔽2)×C10111yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×#120×C10111yescharacteristic
1022C22D42×C10111yescharacteristic
1023C22#546×C10111yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—42no—
1029C4—41no—
1030C4—41no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×#121×C10111yescharacteristic
1037C4#534×C10111yescharacteristic
1038C4D42×C10111yescharacteristic
1039C4#546×C10111yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2C101×#241011yescharacteristic
1049C2C101×#302011yescharacteristic
1050C2C101×#302111yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3489C2semidirect
2. C101×#3055C2semidirect
3. C2×#454×C101C2semidirect
4. C101×#3006C2semidirect
5. C2×#421×C101C2semidirect
6. C101×#2620C2semidirect
7. C101×#2039C2semidirect
8. C101×#2038C2semidirect
9. C101×#2006C2semidirect
10. C101×#2003C2semidirect
11. C101×#1901C2semidirect
12. C101×#1897C2semidirect
13. C101×#1883C2semidirect
14. C101×#1859C2semidirect
15. C101×#1793C2semidirect
20. C2×AGL(1,ℤ/8)×C101C22semidirect
32. C2×#124×C101C22semidirect
49. #428×C101C22semidirect
55. C2×#104×C101C22semidirect
56. C2×#104×C101C22semidirect
57. #418×C101C22semidirect
60. #417×C101C22semidirect
61. C2×#101×C101C22semidirect
62. C2×#101×C101C22semidirect
66. #391×C101C22semidirect
67. #390×C101C22semidirect
68. #384×C101C22semidirect
69. #343×C101C22semidirect
70. #343×C101C22semidirect
71. #339×C101C22semidirect
72. #339×C101C22semidirect
192. #104×C101D4semidirect
514. #24469C101direct (N × H)
526. #3489C2×C101semidirect
527. #3055C2×C101semidirect
528. C2×#454C2×C101semidirect
529. #3006C2×C101semidirect
530. C2×#421C2×C101semidirect
531. #2620C2×C101semidirect
532. #2039C2×C101semidirect
533. #2038C2×C101semidirect
534. #2006C2×C101semidirect
535. #2003C2×C101semidirect
536. #1901C2×C101semidirect
537. #1897C2×C101semidirect
538. #1883C2×C101semidirect
539. #1859C2×C101semidirect
540. #1793C2×C101semidirect
541. C101#24469direct (N × H)
546. C2×AGL(1,ℤ/8)C22×C101semidirect
558. C2×#124C22×C101semidirect
575. #428C22×C101semidirect
581. C2×#104C22×C101semidirect
582. C2×#104C22×C101semidirect
583. #418C22×C101semidirect
586. #417C22×C101semidirect
587. C2×#101C22×C101semidirect
588. C2×#101C22×C101semidirect
592. #391C22×C101semidirect
593. #390C22×C101semidirect
594. #384C22×C101semidirect
595. #343C22×C101semidirect
596. #343C22×C101semidirect
597. #339C22×C101semidirect
598. #339C22×C101semidirect
718. #104D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34892
C101×#30552
C2×#454×C1012
C101×#30062
C2×#421×C1012
C101×#26202
C101×#20392
C101×#20382
C101×#20062
C101×#20032
C101×#19012
C101×#18972
C101×#18832
C101×#18592
C101×#17932
#24469101