Finite Group Databasebeta

← C101×#24471 #38806622

Subgroups — C101×#24471 #38806622

Order 25856.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3488C211yesmaximal, characteristic
2C101×#3056C211yesmaximal, characteristic, complemented
3C2×#455×C101C211yesmaximal, characteristic, complemented
4C101×#3007C211yesmaximal, characteristic, complemented
5C2×#421×C101C211yesmaximal, characteristic, complemented
6C101×#2620C211yesmaximal, characteristic, complemented
7C101×#2039C211yesmaximal, characteristic, complemented
8C101×#2037C211yesmaximal, characteristic, complemented
9C101×#2007C211yesmaximal, characteristic, complemented
10C101×#2004C211yesmaximal, characteristic, complemented
11C101×#1900C211yesmaximal, characteristic, complemented
12C101×#1897C211yesmaximal, characteristic, complemented
13C101×#1882C211yesmaximal, characteristic, complemented
14C101×#1859C211yesmaximal, characteristic, complemented
15C101×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C101C2211yescharacteristic
17C22×#41×C101C2211yescharacteristic
18C2×#137×C101C2211yescharacteristic
19C2×#137×C101C2211yescharacteristic, complemented
20C2×#137×C101C2211yescharacteristic, complemented
21C22×M16×C101C2211yescharacteristic, complemented
22#550×C101—21no—
23#548×C101—21no—
24#546×C101—21no—
25#546×C101—22no—
26D42×C101—22no—
27D42×C101—21no—
28#537×C101—21no—
29#537×C101C2211yescharacteristic
30#535×C101—21no—
31#535×C101C2211yescharacteristic
32C2×#124×C101C2211yescharacteristic, complemented
33#525×C101—21no—
34#525×C101C2211yescharacteristic
35C2×C22⋊Q8×C101C2211yescharacteristic, complemented
36C2×#121×C101—21no—
37C2×#121×C101C2211yescharacteristic
38#520×C101C2211yescharacteristic
39C2×#117×C101C2211yescharacteristic, complemented
40#470×C101—21no—
41#468×C101—21no—
42#467×C101—21no—
43#465×C101—21no—
44#455×C101—24no—
45#452×C101—21no—
46#452×C101—21no—
47#451×C101—21no—
48#450×C101—21no—
49#428×C101C2211yescharacteristic, complemented
50#421×C101—24no—
51C2×#104×C101C2211yescharacteristic
52C2×#104×C101C2211yescharacteristic
53C2×#104×C101C2211yescharacteristic, complemented
54C2×#104×C101C2211yescharacteristic, complemented
55C2×#104×C101C2211yescharacteristic, complemented
56C2×#104×C101C2211yescharacteristic, complemented
57#419×C101C2211yescharacteristic, complemented
58#417×C101C2211yescharacteristic
59#417×C101C2211yescharacteristic, complemented
60#417×C101C2211yescharacteristic, complemented
61C2×#100×C101C2211yescharacteristic, complemented
62C2×#100×C101C2211yescharacteristic, complemented
63#407×C101C2211yescharacteristic, complemented
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
73H(5,𝔽2)×C101—22no—
74H(5,𝔽2)×C101—22no—
75H(5,𝔽2)×C101—41no—
76H(5,𝔽2)×C101—41no—
77C2×#41×C101—21no—
78C2×#41×C101—21no—
79C2×#41×C101—21no—
80C2×#41×C101—21no—
81C2×#41×C101—22no—
82C2×#41×C101—22no—
83C2×#41×C101—41no—
84C2×#41×C101—41no—
85C2×#41×C101D411yescharacteristic
86C2×#41×C101D411yescharacteristic
87C2×#41×C101C2311yescharacteristic
88C2×#41×C101C2311yescharacteristic
89C2×#41×C101C2311yescharacteristic
90C22×Q8×C101D411yescharacteristic
91C22×Q8×C101C2311yescharacteristic
92C22×D4×C101—21no—
93C22×D4×C101—22no—
94C22×D4×C101—22no—
95C22×D4×C101—21no—
96C22×D4×C101—21no—
97C22×D4×C101D411yescharacteristic
98C22×D4×C101D412yes—
99C22×D4×C101C2311yescharacteristic
100C23×C4×C101—21no—
101C23×C4×C101C2311yescharacteristic
102#137×C101—22no—
103#137×C101—22no—
104#137×C101—22no—
105#137×C101—41no—
106#137×C101—41no—
107#137×C101—41no—
108C2×Q16×C101—21no—
109C2×Q16×C101—21no—
110C2×Q16×C101—21no—
111C2×SD16×C101—21no—
112C2×SD16×C101—21no—
113C2×SD16×C101—21no—
114C2×M16×C101—21no—
115C2×M16×C101—22no—
116C2×M16×C101—41no—
117C2×M16×C101C2311yescharacteristic
118C2×M16×C101C2311yescharacteristic
119C2×M16×C101C2311yescharacteristic
120C2×M16×C101C2311yescharacteristic
121C22×C8×C101—21no—
122#127×C101—22no—
123#127×C101—21no—
124#124×C101—22no—
125#124×C101—21no—
126#124×C101—22no—
127#124×C101—41no—
128#123×C101—22no—
129#123×C101—21no—
130C22⋊Q8×C101—22no—
131C22⋊Q8×C101—21no—
132C22⋊Q8×C101—21no—
133C22⋊Q8×C101—21no—
134C22⋊Q8×C101—21no—
135C22⋊Q8×C101—21no—
136C22⋊Q8×C101—21no—
137C22⋊Q8×C101D411yescharacteristic
138C22⋊Q8×C101D411yescharacteristic
139#121×C101—22no—
140#121×C101—22no—
141#121×C101—22no—
142#121×C101—22no—
143#121×C101—22no—
144#121×C101—21no—
145#121×C101—21no—
146#121×C101—21no—
147#121×C101—21no—
148#121×C101—21no—
149#121×C101—21no—
150#121×C101—22no—
151#121×C101—21no—
152#121×C101—21no—
153#121×C101D411yescharacteristic
154#121×C101D411yescharacteristic
155#120×C101—22no—
156#120×C101—22no—
157#120×C101—22no—
158#120×C101—21no—
159#120×C101—22no—
160C4×Q8×C101—21no—
161C4×D4×C101—22no—
162C4×D4×C101—22no—
163C4×D4×C101—21no—
164C4×D4×C101—22no—
165C4×D4×C101—21no—
166C4×D4×C101—21no—
167#117×C101—21no—
168#117×C101—22no—
169#117×C101—41no—
170#117×C101C2311yescharacteristic
171C2×C4⋊C4×C101—21no—
172C2×C4⋊C4×C101—21no—
173C2×C4⋊C4×C101—21no—
174C2×C4⋊C4×C101—22no—
175C2×C4⋊C4×C101C2311yescharacteristic
176C2×C4⋊C4×C101C2311yescharacteristic
177C2×C22⋊C4×C101—22no—
178C2×C22⋊C4×C101—22no—
179C2×C22⋊C4×C101—21no—
180C2×C22⋊C4×C101—21no—
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#103×C101—21no—
197#103×C101—21no—
198#102×C101—21no—
199#102×C101—21no—
200#102×C101—21no—
201#100×C101—22no—
202#100×C101—41no—
203C22⋊C8×C101—21no—
204C22⋊C8×C101—21no—
205#95×C101—22no—
206C24×C101—22no—
207C24×C101—21no—
208C24×C101C2×D412yes—
209C24×C101C2×D411yescharacteristic
210#41×C101—21no—
211#41×C101—21no—
212#41×C101—22no—
213#41×C101—22no—
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—21no—
222#41×C101—42no—
223#41×C101—42no—
224#41×C101—41no—
225#41×C101—41no—
226#41×C101—42no—
227#41×C101—42no—
228#41×C101—42no—
229#41×C101—42no—
230#41×C101—42no—
231#41×C101—42no—
232#41×C101C2×D412yes—
233#41×C101#4112yes—
234C2×Q8×C101—21no—
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—41no—
243C2×Q8×C101C2×D411yescharacteristic
244C2×Q8×C101C2×D411yescharacteristic
245C2×Q8×C101C2×D411yescharacteristic
246C2×D4×C101—21no—
247C2×D4×C101—22no—
248C2×D4×C101—22no—
249C2×D4×C101—22no—
250C2×D4×C101—22no—
251C2×D4×C101—21no—
252C2×D4×C101—21no—
253C2×D4×C101—21no—
254C2×D4×C101—21no—
255C2×D4×C101—21no—
256C2×D4×C101—22no—
257C2×D4×C101—22no—
258C2×D4×C101—22no—
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—41no—
269C2×D4×C101—42no—
270C2×D4×C101—42no—
271C2×D4×C101—42no—
272C2×D4×C101—42no—
273C2×D4×C101—44no—
274C2×D4×C101—44no—
275C2×D4×C101—42no—
276C2×D4×C101—42no—
277C2×D4×C101—82no—
278C2×D4×C101—84no—
279C2×D4×C101C2×D411yescharacteristic
280C2×D4×C101C2×D411yescharacteristic
281C2×D4×C101C2×D411yescharacteristic
282C22×C4×C101—21no—
283C22×C4×C101—21no—
284C22×C4×C101—21no—
285C22×C4×C101—21no—
286C22×C4×C101—21no—
287C22×C4×C101—22no—
288C22×C4×C101—21no—
289C22×C4×C101—21no—
290C22×C4×C101—22no—
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—42no—
299C22×C4×C101—42no—
300C22×C4×C101C2×D411yescharacteristic
301C22×C4×C101C2×D411yescharacteristic
302C22×C4×C101C2×D411yescharacteristic
303C22×C4×C101C2×D411yescharacteristic
304C22×C4×C101C2×D411yescharacteristic
305C22×C4×C101C2×D412yes—
306C22×C4×C101C2411yescharacteristic
307Q16×C101—42no—
308Q16×C101—42no—
309Q16×C101—42no—
310SD16×C101—42no—
311SD16×C101—42no—
312SD16×C101—42no—
313M16×C101—21no—
314M16×C101—21no—
315M16×C101—21no—
316M16×C101—21no—
317M16×C101—21no—
318M16×C101—21no—
319M16×C101—21no—
320M16×C101—42no—
321M16×C101C2×D412yescomplemented
322C2×C8×C101—21no—
323C2×C8×C101—21no—
324C2×C8×C101—21no—
325C2×C8×C101—21no—
326C2×C8×C101—42no—
327C4⋊C4×C101—22no—
328C4⋊C4×C101—22no—
329C4⋊C4×C101—21no—
330C4⋊C4×C101—21no—
331C4⋊C4×C101—21no—
332C4⋊C4×C101—21no—
333C4⋊C4×C101—21no—
334C4⋊C4×C101—21no—
335C4⋊C4×C101—42no—
336C4⋊C4×C101—41no—
337C4⋊C4×C101—41no—
338C4⋊C4×C101—82no—
339C4⋊C4×C101C2×D411yescharacteristic
340C4⋊C4×C101C2×D411yescharacteristic
341C22⋊C4×C101—22no—
342C22⋊C4×C101—22no—
343C22⋊C4×C101—22no—
344C22⋊C4×C101—22no—
345C22⋊C4×C101—22no—
346C22⋊C4×C101—21no—
347C22⋊C4×C101—21no—
348C22⋊C4×C101—21no—
349C22⋊C4×C101—21no—
350C22⋊C4×C101—22no—
351C22⋊C4×C101—22no—
352C22⋊C4×C101—21no—
353C22⋊C4×C101—42no—
354C22⋊C4×C101—44no—
355C22⋊C4×C101—41no—
356C22⋊C4×C101—41no—
357C22⋊C4×C101—82no—
358C42×C101—22no—
359C42×C101—21no—
360C42×C101—21no—
361C42×C101—21no—
362C42×C101—21no—
363C42×C101C2×D412yescomplemented
364C23×C101—21no—
365C23×C101—21no—
366C23×C101—21no—
367C23×C101—22no—
368C23×C101—21no—
369C23×C101—21no—
370C23×C101—22no—
371C23×C101—22no—
372C23×C101—41no—
373C23×C101—41no—
374C23×C101—42no—
375C23×C101—42no—
376C23×C101—44no—
377C23×C101—42no—
378C23×C101—42no—
379C23×C101—81no—
380C23×C101—82no—
381C23×C101—82no—
382C23×C101#12011yescharacteristic
383C23×C101#12011yescharacteristic
384C23×C101C22×D411yescharacteristic
385Q8×C101—21no—
386Q8×C101—21no—
387Q8×C101—21no—
388Q8×C101—21no—
389Q8×C101—21no—
390Q8×C101—42no—
391Q8×C101—41no—
392Q8×C101—41no—
393Q8×C101—41no—
394Q8×C101—41no—
395Q8×C101#12112yes—
396D4×C101—22no—
397D4×C101—22no—
398D4×C101—21no—
399D4×C101—21no—
400D4×C101—21no—
401D4×C101—21no—
402D4×C101—21no—
403D4×C101—42no—
404D4×C101—42no—
405D4×C101—44no—
406D4×C101—42no—
407D4×C101—44no—
408D4×C101—44no—
409D4×C101—42no—
410D4×C101—41no—
411D4×C101—41no—
412D4×C101—41no—
413D4×C101—41no—
414D4×C101—41no—
415D4×C101—41no—
416D4×C101—41no—
417D4×C101—41no—
418D4×C101—81no—
419D4×C101—82no—
420D4×C101—82no—
421D4×C101—82no—
422D4×C101—82no—
423D4×C101#12112yes—
424C2×C4×C101—21no—
425C2×C4×C101—21no—
426C2×C4×C101—21no—
427C2×C4×C101—21no—
428C2×C4×C101—21no—
429C2×C4×C101—21no—
430C2×C4×C101—21no—
431C2×C4×C101—21no—
432C2×C4×C101—21no—
433C2×C4×C101—22no—
434C2×C4×C101—21no—
435C2×C4×C101—21no—
436C2×C4×C101—22no—
437C2×C4×C101—21no—
438C2×C4×C101—22no—
439C2×C4×C101—21no—
440C2×C4×C101—21no—
441C2×C4×C101—21no—
442C2×C4×C101—22no—
443C2×C4×C101—42no—
444C2×C4×C101—42no—
445C2×C4×C101—42no—
446C2×C4×C101—44no—
447C2×C4×C101—41no—
448C2×C4×C101—41no—
449C2×C4×C101—41no—
450C2×C4×C101—41no—
451C2×C4×C101—41no—
452C2×C4×C101—41no—
453C2×C4×C101—42no—
454C2×C4×C101—41no—
455C2×C4×C101—42no—
456C2×C4×C101—41no—
457C2×C4×C101—41no—
458C2×C4×C101—41no—
459C2×C4×C101—41no—
460C2×C4×C101—41no—
461C2×C4×C101—41no—
462C2×C4×C101—82no—
463C2×C4×C101#12011yescharacteristic
464C2×C4×C101#12011yescharacteristic
465C2×C4×C101C22×D411yescharacteristic
466C2×C4×C101C22×D411yescharacteristic
467C2×C4×C101C22×D411yescharacteristic
468C2×C4×C101C2×#4111yescharacteristic
469C2×C4×C101H(5,𝔽2)11yescharacteristic
470C2×C4×C101H(5,𝔽2)11yescharacteristic
471C8×C101—22no—
472C8×C101—41no—
473C8×C101—41no—
474C8×C101—41no—
475C22×C101—21no—
476C22×C101—21no—
477C22×C101—21no—
478C22×C101—21no—
479C22×C101—22no—
480C22×C101—21no—
481C22×C101—21no—
482C22×C101—21no—
483C22×C101—21no—
484C22×C101—41no—
485C22×C101—41no—
486C22×C101—41no—
487C22×C101—41no—
488C22×C101—42no—
489C22×C101—42no—
490C22×C101—41no—
491C22×C101—41no—
492C22×C101—41no—
493C22×C101—42no—
494C22×C101—41no—
495C22×C101—81no—
496C22×C101—81no—
497C22×C101—82no—
498C22×C101—82no—
499C22×C101—84no—
500C22×C101—164no—
501C22×C101C2×#12011yescharacteristic
502C22×C101D4211yescharacteristic
503C22×C101#54611yescharacteristic
504C4×C101—21no—
505C4×C101—21no—
506C4×C101—22no—
507C4×C101—42no—
508C4×C101—41no—
509C4×C101—41no—
510C4×C101—42no—
511C4×C101—41no—
512C4×C101—41no—
513C4×C101—81no—
514C4×C101—81no—
515C4×C101—81no—
516C4×C101C2×#12111yescharacteristic
517C4×C101#53411yescharacteristic
518C4×C101D4211yescharacteristic
519C4×C101#54611yescharacteristic
520#24471C10111yesmaximal, characteristic, direct product factor, Sylow
521C2×C101—21no—
522C2×C101—21no—
523C2×C101—41no—
524C2×C101—41no—
525C2×C101—42no—
526C2×C101—81no—
527C2×C101—82no—
528C2×C101—81no—
529C2×C101#241011yescharacteristic
530C2×C101#301911yescharacteristic
531C2×C101#302211yescharacteristic
532#3488C2×C10111yescharacteristic
533#3056C2×C10111yescharacteristic, complemented
534C2×#455C2×C10111yescharacteristic, complemented
535#3007C2×C10111yescharacteristic, complemented
536C2×#421C2×C10111yescharacteristic, complemented
537#2620C2×C10111yescharacteristic, complemented
538#2039C2×C10111yescharacteristic, complemented
539#2037C2×C10111yescharacteristic, complemented
540#2007C2×C10111yescharacteristic, complemented
541#2004C2×C10111yescharacteristic, complemented
542#1900C2×C10111yescharacteristic, complemented
543#1897C2×C10111yescharacteristic, complemented
544#1882C2×C10111yescharacteristic, complemented
545#1859C2×C10111yescharacteristic, complemented
546#1792C2×C10111yescharacteristic, complemented
547C101#2447111yescharacteristic, direct product factor, Sylow
548C2×H(5,𝔽2)C22×C10111yescharacteristic
549C22×#41C22×C10111yescharacteristic
550C2×#137C22×C10111yescharacteristic
551C2×#137C22×C10111yescharacteristic, complemented
552C2×#137C22×C10111yescharacteristic, complemented
553C22×M16C22×C10111yescharacteristic, complemented
554#550—21no—
555#548—21no—
556#546—21no—
557#546—22no—
558D42—22no—
559D42—21no—
560#537—21no—
561#537C22×C10111yescharacteristic
562#535—21no—
563#535C22×C10111yescharacteristic
564C2×#124C22×C10111yescharacteristic, complemented
565#525—21no—
566#525C22×C10111yescharacteristic
567C2×C22⋊Q8C22×C10111yescharacteristic, complemented
568C2×#121—21no—
569C2×#121C22×C10111yescharacteristic
570#520C22×C10111yescharacteristic
571C2×#117C22×C10111yescharacteristic, complemented
572#470—21no—
573#468—21no—
574#467—21no—
575#465—21no—
576#455—24no—
577#452—21no—
578#452—21no—
579#451—21no—
580#450—21no—
581#428C22×C10111yescharacteristic, complemented
582#421—24no—
583C2×#104C22×C10111yescharacteristic
584C2×#104C22×C10111yescharacteristic
585C2×#104C22×C10111yescharacteristic, complemented
586C2×#104C22×C10111yescharacteristic, complemented
587C2×#104C22×C10111yescharacteristic, complemented
588C2×#104C22×C10111yescharacteristic, complemented
589#419C22×C10111yescharacteristic, complemented
590#417C22×C10111yescharacteristic
591#417C22×C10111yescharacteristic, complemented
592#417C22×C10111yescharacteristic, complemented
593C2×#100C22×C10111yescharacteristic, complemented
594C2×#100C22×C10111yescharacteristic, complemented
595#407C22×C10111yescharacteristic, complemented
596#396—22no—
597#394—22no—
598#391C22×C10111yescharacteristic, complemented
599#390C22×C10111yescharacteristic, complemented
600#384C22×C10111yescharacteristic, complemented
601#343C22×C10111yescharacteristic, complemented
602#343C22×C10111yescharacteristic, complemented
603#339C22×C10111yescharacteristic, complemented
604#339C22×C10111yescharacteristic, complemented
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C10111yescharacteristic
618C2×#41D4×C10111yescharacteristic
619C2×#41C23×C10111yescharacteristic
620C2×#41C23×C10111yescharacteristic
621C2×#41C23×C10111yescharacteristic
622C22×Q8D4×C10111yescharacteristic
623C22×Q8C23×C10111yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C10111yescharacteristic
630C22×D4D4×C10112yes—
631C22×D4C23×C10111yescharacteristic
632C23×C4—21no—
633C23×C4C23×C10111yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C10111yescharacteristic
650C2×M16C23×C10111yescharacteristic
651C2×M16C23×C10111yescharacteristic
652C2×M16C23×C10111yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
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—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C10111yescharacteristic
686#121D4×C10111yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C10111yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C10111yescharacteristic
708C2×C4⋊C4C23×C10111yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C10112yes—
715C2×C42C23×C10111yescharacteristic
716C2×C42C23×C10111yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C10114yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C10112yes—
741C24C2×D4×C10111yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C10112yes—
765#41#41×C10112yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C10111yescharacteristic
776C2×Q8C2×D4×C10111yescharacteristic
777C2×Q8C2×D4×C10111yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C10111yescharacteristic
812C2×D4C2×D4×C10111yescharacteristic
813C2×D4C2×D4×C10111yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C10111yescharacteristic
833C22×C4C2×D4×C10111yescharacteristic
834C22×C4C2×D4×C10111yescharacteristic
835C22×C4C2×D4×C10111yescharacteristic
836C22×C4C2×D4×C10111yescharacteristic
837C22×C4C2×D4×C10112yes—
838C22×C4C24×C10111yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C10112yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C10111yescharacteristic
872C4⋊C4C2×D4×C10111yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C10112yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C10111yescharacteristic
915C23#120×C10111yescharacteristic
916C23C22×D4×C10111yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C10112yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—82no—
951D4—81no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C10112yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C10111yescharacteristic
996C2×C4#120×C10111yescharacteristic
997C2×C4C22×D4×C10111yescharacteristic
998C2×C4C22×D4×C10111yescharacteristic
999C2×C4C22×D4×C10111yescharacteristic
1000C2×C4C2×#41×C10111yescharacteristic
1001C2×C4H(5,𝔽2)×C10111yescharacteristic
1002C2×C4H(5,𝔽2)×C10111yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—22no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—42no—
1021C22—42no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C10111yescharacteristic
1034C22D42×C10111yescharacteristic
1035C22#546×C10111yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—41no—
1041C4—41no—
1042C4—42no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C10111yescharacteristic
1049C4#534×C10111yescharacteristic
1050C4D42×C10111yescharacteristic
1051C4#546×C10111yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C101×#241011yescharacteristic
1061C2C101×#301911yescharacteristic
1062C2C101×#302211yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#3488C2
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
2. C101×#3056C2semidirect
3. C2×#455×C101C2semidirect
4. C101×#3007C2semidirect
5. C2×#421×C101C2semidirect
6. C101×#2620C2semidirect
7. C101×#2039C2semidirect
8. C101×#2037C2semidirect
9. C101×#2007C2semidirect
10. C101×#2004C2semidirect
11. C101×#1900C2semidirect
12. C101×#1897C2semidirect
13. C101×#1882C2semidirect
14. C101×#1859C2semidirect
15. C101×#1792C2semidirect
19. C2×#137×C101C22semidirect
20. C2×#137×C101C22semidirect
21. C22×M16×C101C22semidirect
32. C2×#124×C101C22semidirect
35. C2×C22⋊Q8×C101C22semidirect
39. C2×#117×C101C22semidirect
49. #428×C101C22semidirect
53. C2×#104×C101C22semidirect
54. C2×#104×C101C22semidirect
55. C2×#104×C101C22semidirect
56. C2×#104×C101C22semidirect
57. #419×C101C22semidirect
59. #417×C101C22semidirect
60. #417×C101C22semidirect
61. C2×#100×C101C22semidirect
62. C2×#100×C101C22semidirect
63. #407×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
321. M16×C101C2×D4semidirect
363. C42×C101C2×D4semidirect
520. #24471C101direct (N × H)
533. #3056C2×C101semidirect
534. C2×#455C2×C101semidirect
535. #3007C2×C101semidirect
536. C2×#421C2×C101semidirect
537. #2620C2×C101semidirect
538. #2039C2×C101semidirect
539. #2037C2×C101semidirect
540. #2007C2×C101semidirect
541. #2004C2×C101semidirect
542. #1900C2×C101semidirect
543. #1897C2×C101semidirect
544. #1882C2×C101semidirect
545. #1859C2×C101semidirect
546. #1792C2×C101semidirect
547. C101#24471direct (N × H)
551. C2×#137C22×C101semidirect
552. C2×#137C22×C101semidirect
553. C22×M16C22×C101semidirect
564. C2×#124C22×C101semidirect
567. C2×C22⋊Q8C22×C101semidirect
571. C2×#117C22×C101semidirect
581. #428C22×C101semidirect
585. C2×#104C22×C101semidirect
586. C2×#104C22×C101semidirect
587. C2×#104C22×C101semidirect
588. C2×#104C22×C101semidirect
589. #419C22×C101semidirect
591. #417C22×C101semidirect
592. #417C22×C101semidirect
593. C2×#100C22×C101semidirect
594. C2×#100C22×C101semidirect
595. #407C22×C101semidirect
598. #391C22×C101semidirect
599. #390C22×C101semidirect
600. #384C22×C101semidirect
601. #343C22×C101semidirect
602. #343C22×C101semidirect
603. #339C22×C101semidirect
604. #339C22×C101semidirect
724. #104D4×C101semidirect
853. M16C2×D4×C101semidirect
895. C42C2×D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34882
C101×#30562
C2×#455×C1012
C101×#30072
C2×#421×C1012
C101×#26202
C101×#20392
C101×#20372
C101×#20072
C101×#20042
C101×#19002
C101×#18972
C101×#18822
C101×#18592
C101×#17922
#24471101