Finite Group Databasebeta

← C101×#23889 #38806040

Subgroups — C101×#23889 #38806040

Order 25856.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#578×C101C211yesmaximal, characteristic, complemented
2C2×#577×C101C211yesmaximal, characteristic, complemented
3C2×#454×C101C211yesmaximal, characteristic, complemented
4C2×#455×C101C211yesmaximal, characteristic, complemented
5C101×#3013C211yesmaximal, characteristic, complemented
6C101×#3012C211yesmaximal, characteristic, complemented
7C101×#2020C211yesmaximal, characteristic, complemented
8C101×#2019C211yesmaximal, characteristic, complemented
9C101×#2015C211yesmaximal, characteristic, complemented
10C101×#2007C211yesmaximal, characteristic, complemented
11C101×#1908C211yesmaximal, characteristic, complemented
12C101×#1907C211yesmaximal, characteristic, complemented
13C101×#1876C211yesmaximal, characteristic, complemented
14C101×#1876C211yesmaximal, characteristic, complemented
15C101×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C101C2211yescharacteristic
17C2×2−1+4×C101C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C101C2211yescharacteristic
19#578×C101—24no—
20#578×C101—24no—
21#577×C101—24no—
22#577×C101—24no—
23C2×#137×C101—21no—
24C2×#137×C101—21no—
25C2×#137×C101—21no—
26C2×#137×C101C2211yescharacteristic
27C2×#137×C101C2211yescharacteristic
28C2×#137×C101C2211yescharacteristic
29C2×#137×C101C2211yescharacteristic, complemented
30C2×AGL(1,ℤ/8)×C101—21no—
31C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
32C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
33C2×#135×C101—21no—
34C2×#135×C101—21no—
35C2×#135×C101C2211yescharacteristic
36C2×#135×C101C2211yescharacteristic
37C22×Q16×C101—21no—
38C22×Q16×C101C2211yescharacteristic, complemented
39C22×SD16×C101—21no—
40C22×SD16×C101C2211yescharacteristic
41C2×#131×C101C2211yescharacteristic
42C2×#131×C101C2211yescharacteristic, complemented
43#537×C101C2211yescharacteristic
44C2×#124×C101C2211yescharacteristic
45#455×C101—24no—
46#454×C101—24no—
47#452×C101—21no—
48#452×C101—21no—
49#451×C101—21no—
50#450×C101—21no—
51#449×C101—21no—
52#449×C101—21no—
53#448×C101—21no—
54#447×C101—21no—
55C2×#104×C101C2211yescharacteristic
56C2×#104×C101C2211yescharacteristic
57C2×#104×C101C2211yescharacteristic, complemented
58C2×#104×C101C2211yescharacteristic, complemented
59#417×C101C2211yescharacteristic
60#417×C101C2211yescharacteristic, complemented
61C2×#103×C101C2211yescharacteristic, complemented
62C2×#102×C101C2211yescharacteristic
63C2×#101×C101C2211yescharacteristic, complemented
64C2×#101×C101C2211yescharacteristic, complemented
65C2×#100×C101C2211yescharacteristic
66#408×C101C2211yescharacteristic
67#408×C101C2211yescharacteristic, complemented
68#391×C101C2211yescharacteristic, complemented
69#343×C101C2211yescharacteristic, complemented
70#341×C101C2211yescharacteristic, complemented
71#341×C101C2211yescharacteristic, complemented
72#336×C101C2211yescharacteristic, complemented
732−1+4×C101—22no—
742−1+4×C101—22no—
752−1+4×C101—22no—
762−1+4×C101—22no—
772−1+4×C101—22no—
782−1+4×C101—41no—
792−1+4×C101—41no—
802−1+4×C101D414yescomplemented
81H(5,𝔽2)×C101—22no—
82H(5,𝔽2)×C101—22no—
83H(5,𝔽2)×C101—22no—
84H(5,𝔽2)×C101—41no—
85C2×#41×C101—21no—
86C2×#41×C101—21no—
87C2×#41×C101—21no—
88C2×#41×C101—21no—
89C2×#41×C101—21no—
90C2×#41×C101—21no—
91C2×#41×C101—41no—
92C2×#41×C101—41no—
93C2×#41×C101C2311yescharacteristic
94C2×#41×C101C2311yescharacteristic
95C2×#41×C101C2311yescharacteristic
96C2×#41×C101C2311yescharacteristic
97C22×Q8×C101—21no—
98C22×Q8×C101—21no—
99C22×Q8×C101—21no—
100C22×Q8×C101—21no—
101C22×Q8×C101C2311yescharacteristic
102C22×Q8×C101C2311yescharacteristic
103C22×D4×C101—21no—
104C22×D4×C101—21no—
105C22×D4×C101—41no—
106C22×D4×C101C2311yescharacteristic
107#137×C101—28no—
108#137×C101—28no—
109#137×C101—28no—
110#137×C101—22no—
111#137×C101—22no—
112#137×C101—22no—
113#137×C101—22no—
114#137×C101—22no—
115#137×C101—22no—
116#137×C101—41no—
117#137×C101D414yescomplemented
118AGL(1,ℤ/8)×C101—28no—
119AGL(1,ℤ/8)×C101—22no—
120AGL(1,ℤ/8)×C101—22no—
121AGL(1,ℤ/8)×C101—41no—
122AGL(1,ℤ/8)×C101D414yescomplemented
123#135×C101—28no—
124#135×C101—28no—
125#135×C101—22no—
126#135×C101—22no—
127#135×C101—22no—
128#135×C101—22no—
129C2×Q16×C101—28no—
130C2×Q16×C101—21no—
131C2×Q16×C101—21no—
132C2×Q16×C101—22no—
133C2×Q16×C101—22no—
134C2×Q16×C101—21no—
135C2×Q16×C101—21no—
136C2×Q16×C101—21no—
137C2×Q16×C101—21no—
138C2×Q16×C101D411yescharacteristic
139C2×Q16×C101D411yescharacteristic
140C2×SD16×C101—28no—
141C2×SD16×C101—21no—
142C2×SD16×C101—22no—
143C2×SD16×C101—21no—
144C2×SD16×C101—22no—
145C2×SD16×C101—21no—
146C2×SD16×C101—21no—
147C2×SD16×C101—21no—
148C2×SD16×C101—21no—
149C2×SD16×C101—21no—
150C2×SD16×C101—21no—
151C2×SD16×C101D411yescharacteristic
152C2×SD16×C101D411yescharacteristic
153C2×SD16×C101D411yescharacteristic
154C2×SD16×C101D411yescharacteristic
155C2×D8×C101—21no—
156C2×D8×C101—21no—
157C2×D8×C101D411yescharacteristic
158C2×D8×C101D411yescharacteristic
159#131×C101—22no—
160#131×C101—22no—
161#131×C101—22no—
162#131×C101—22no—
163C2×M16×C101—21no—
164C2×M16×C101—21no—
165C2×M16×C101C2311yescharacteristic
166C2×M16×C101C2311yescharacteristic
167C2×M16×C101C2311yescharacteristic
168C2×M16×C101C2311yescharacteristic
169C22×C8×C101—21no—
170C22×C8×C101—21no—
171C22×C8×C101C2311yescharacteristic
172C22×C8×C101C2311yescharacteristic
173#124×C101—22no—
174#124×C101—22no—
175C22⋊Q8×C101—21no—
176C22⋊Q8×C101—21no—
177#121×C101—21no—
178#121×C101—21no—
179#121×C101—41no—
180C2×C4⋊C4×C101C2311yescharacteristic
181C2×C22⋊C4×C101—41no—
182C2×C42×C101C2311yescharacteristic
183#104×C101—22no—
184#104×C101—22no—
185#104×C101—22no—
186#104×C101—22no—
187#103×C101—21no—
188#103×C101—21no—
189#103×C101—21no—
190#103×C101—21no—
191#102×C101—21no—
192#102×C101—21no—
193#102×C101—21no—
194#102×C101—21no—
195#101×C101—22no—
196#101×C101—41no—
197#100×C101—22no—
198C22⋊C8×C101—21no—
199C22⋊C8×C101—21no—
200C22⋊C8×C101—21no—
201C22⋊C8×C101—21no—
202#95×C101—41no—
203C24×C101—21no—
204C24×C101—41no—
205#41×C101—21no—
206#41×C101—21no—
207#41×C101—21no—
208#41×C101—21no—
209#41×C101—24no—
210#41×C101—24no—
211#41×C101—24no—
212#41×C101—24no—
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—44no—
222#41×C101—42no—
223#41×C101—42no—
224#41×C101—42no—
225#41×C101—44no—
226#41×C101—42no—
227#41×C101—44no—
228#41×C101—42no—
229#41×C101—42no—
230#41×C101—44no—
231#41×C101—42no—
232#41×C101—42no—
233#41×C101C2×D412yes—
234#41×C101C2×D412yes—
235#41×C101C2×D412yes—
236#41×C101C2×D412yes—
237C2×Q8×C101—21no—
238C2×Q8×C101—21no—
239C2×Q8×C101—24no—
240C2×Q8×C101—24no—
241C2×Q8×C101—24no—
242C2×Q8×C101—21no—
243C2×Q8×C101—21no—
244C2×Q8×C101—21no—
245C2×Q8×C101—21no—
246C2×Q8×C101—21no—
247C2×Q8×C101—21no—
248C2×Q8×C101—21no—
249C2×Q8×C101—21no—
250C2×Q8×C101—41no—
251C2×Q8×C101—41no—
252C2×Q8×C101—42no—
253C2×Q8×C101—42no—
254C2×Q8×C101—42no—
255C2×Q8×C101—42no—
256C2×Q8×C101—42no—
257C2×Q8×C101C2×D411yescharacteristic
258C2×Q8×C101C2×D411yescharacteristic
259C2×Q8×C101C2×D412yes—
260C2×Q8×C101C2×D412yes—
261C2×Q8×C101C2×D411yescharacteristic
262C2×Q8×C101C2×D411yescharacteristic
263C2×D4×C101—21no—
264C2×D4×C101—21no—
265C2×D4×C101—24no—
266C2×D4×C101—21no—
267C2×D4×C101—21no—
268C2×D4×C101—21no—
269C2×D4×C101—21no—
270C2×D4×C101—21no—
271C2×D4×C101—21no—
272C2×D4×C101—21no—
273C2×D4×C101—42no—
274C2×D4×C101—41no—
275C2×D4×C101—41no—
276C2×D4×C101—42no—
277C2×D4×C101—44no—
278C2×D4×C101—44no—
279C2×D4×C101—41no—
280C2×D4×C101—41no—
281C2×D4×C101—42no—
282C2×D4×C101—41no—
283C2×D4×C101C2×D411yescharacteristic
284C2×D4×C101C2×D411yescharacteristic
285C2×D4×C101C2×D412yes—
286C2×D4×C101C2×D411yescharacteristic
287C2×D4×C101C2×D411yescharacteristic
288C22×C4×C101—21no—
289C22×C4×C101—21no—
290C22×C4×C101—21no—
291C22×C4×C101—21no—
292C22×C4×C101—21no—
293C22×C4×C101—21no—
294C22×C4×C101—21no—
295C22×C4×C101—21no—
296C22×C4×C101—41no—
297C22×C4×C101—41no—
298C22×C4×C101—41no—
299C22×C4×C101—41no—
300C22×C4×C101—41no—
301C22×C4×C101C2411yescharacteristic
302Q16×C101—24no—
303Q16×C101—24no—
304Q16×C101—24no—
305Q16×C101—24no—
306Q16×C101—22no—
307Q16×C101—24no—
308Q16×C101—22no—
309Q16×C101—42no—
310SD16×C101—24no—
311SD16×C101—24no—
312SD16×C101—24no—
313SD16×C101—24no—
314SD16×C101—22no—
315SD16×C101—24no—
316SD16×C101—22no—
317SD16×C101—24no—
318SD16×C101—22no—
319SD16×C101—22no—
320SD16×C101—42no—
321SD16×C101—42no—
322D8×C101—24no—
323D8×C101—22no—
324D8×C101—22no—
325D8×C101—42no—
326M16×C101—24no—
327M16×C101—24no—
328M16×C101—21no—
329M16×C101—21no—
330M16×C101—21no—
331M16×C101—21no—
332M16×C101—21no—
333M16×C101—21no—
334M16×C101C2×D412yes—
335M16×C101C2×D412yes—
336C2×C8×C101—24no—
337C2×C8×C101—24no—
338C2×C8×C101—21no—
339C2×C8×C101—21no—
340C2×C8×C101—21no—
341C2×C8×C101—21no—
342C2×C8×C101—21no—
343C2×C8×C101—21no—
344C2×C8×C101—21no—
345C2×C8×C101—21no—
346C2×C8×C101C2×D411yescharacteristic
347C2×C8×C101C2×D411yescharacteristic
348C2×C8×C101C2×D411yescharacteristic
349C2×C8×C101C2×D411yescharacteristic
350C4⋊C4×C101—21no—
351C4⋊C4×C101—21no—
352C4⋊C4×C101—41no—
353C22⋊C4×C101—44no—
354C22⋊C4×C101—41no—
355C22⋊C4×C101—41no—
356C42×C101—21no—
357C42×C101—21no—
358C23×C101—21no—
359C23×C101—21no—
360C23×C101—21no—
361C23×C101—21no—
362C23×C101—22no—
363C23×C101—44no—
364C23×C101—41no—
365C23×C101—41no—
366C23×C101—81no—
367C23×C101—81no—
368C23×C101—161no—
369C23×C101—161no—
370C23×C101H(5,𝔽2)11yescharacteristic
371Q8×C101—21no—
372Q8×C101—21no—
373Q8×C101—22no—
374Q8×C101—22no—
375Q8×C101—22no—
376Q8×C101—21no—
377Q8×C101—21no—
378Q8×C101—21no—
379Q8×C101—22no—
380Q8×C101—21no—
381Q8×C101—44no—
382Q8×C101—44no—
383Q8×C101—41no—
384Q8×C101—41no—
385Q8×C101—41no—
386Q8×C101—41no—
387Q8×C101#12012yes—
388Q8×C101#12012yes—
389D4×C101—22no—
390D4×C101—22no—
391D4×C101—22no—
392D4×C101—22no—
393D4×C101—22no—
394D4×C101—21no—
395D4×C101—21no—
396D4×C101—21no—
397D4×C101—21no—
398D4×C101—21no—
399D4×C101—22no—
400D4×C101—21no—
401D4×C101—44no—
402D4×C101—44no—
403D4×C101—44no—
404D4×C101—44no—
405D4×C101—41no—
406D4×C101—41no—
407D4×C101—41no—
408D4×C101—41no—
409D4×C101—41no—
410D4×C101—41no—
411D4×C101—161no—
412D4×C101#12012yes—
413D4×C101#12012yes—
414C2×C4×C101—21no—
415C2×C4×C101—21no—
416C2×C4×C101—22no—
417C2×C4×C101—22no—
418C2×C4×C101—22no—
419C2×C4×C101—22no—
420C2×C4×C101—22no—
421C2×C4×C101—22no—
422C2×C4×C101—21no—
423C2×C4×C101—21no—
424C2×C4×C101—44no—
425C2×C4×C101—44no—
426C2×C4×C101—44no—
427C2×C4×C101—44no—
428C2×C4×C101—44no—
429C2×C4×C101—41no—
430C2×C4×C101—41no—
431C2×C4×C101—41no—
432C2×C4×C101—41no—
433C2×C4×C101—41no—
434C2×C4×C101—41no—
435C2×C4×C101—41no—
436C2×C4×C101—41no—
437C2×C4×C101—41no—
438C2×C4×C101—41no—
439C2×C4×C101—41no—
440C2×C4×C101—41no—
441C2×C4×C101—81no—
442C2×C4×C101C22×D411yescharacteristic
443C2×C4×C101C22×D411yescharacteristic
444C2×C4×C101C22×D411yescharacteristic
445C2×C4×C101C22×D411yescharacteristic
446C2×C4×C101C22×D411yescharacteristic
447C2×C4×C101H(5,𝔽2)11yescharacteristic
448C8×C101—21no—
449C8×C101—21no—
450C8×C101—22no—
451C8×C101—22no—
452C8×C101—21no—
453C8×C101—21no—
454C8×C101—41no—
455C8×C101—41no—
456C22×C101—21no—
457C22×C101—21no—
458C22×C101—22no—
459C22×C101—22no—
460C22×C101—41no—
461C22×C101—41no—
462C22×C101—41no—
463C22×C101—41no—
464C22×C101—41no—
465C22×C101—41no—
466C22×C101—42no—
467C22×C101—41no—
468C22×C101—41no—
469C22×C101—41no—
470C22×C101—41no—
471C22×C101—82no—
472C22×C101—81no—
473C22×C101—81no—
474C22×C101—161no—
475C22×C101—164no—
476C22×C101#53411yescharacteristic
477C22×C101D4211yescharacteristic
478C22×C101D4211yescharacteristic
479C4×C101—22no—
480C4×C101—22no—
481C4×C101—41no—
482C4×C101—42no—
483C4×C101—42no—
484C4×C101—41no—
485C4×C101—81no—
486C4×C101—81no—
487C4×C101C2×#12011yescharacteristic
488C4×C101C2×#12011yescharacteristic
489C4×C101D4211yescharacteristic
490C4×C101D4211yescharacteristic
491#23889C10111yesmaximal, characteristic, direct product factor, Sylow
492C2×C101—21no—
493C2×C101—21no—
494C2×C101—42no—
495C2×C101—42no—
496C2×C101—81no—
497C2×C101—81no—
498C2×C101—82no—
499C2×C101#240311yescharacteristic
500C2×C101#328911yescharacteristic
501C2×C101#329011yescharacteristic
502C2×#578C2×C10111yescharacteristic, complemented
503C2×#577C2×C10111yescharacteristic, complemented
504C2×#454C2×C10111yescharacteristic, complemented
505C2×#455C2×C10111yescharacteristic, complemented
506#3013C2×C10111yescharacteristic, complemented
507#3012C2×C10111yescharacteristic, complemented
508#2020C2×C10111yescharacteristic, complemented
509#2019C2×C10111yescharacteristic, complemented
510#2015C2×C10111yescharacteristic, complemented
511#2007C2×C10111yescharacteristic, complemented
512#1908C2×C10111yescharacteristic, complemented
513#1907C2×C10111yescharacteristic, complemented
514#1876C2×C10111yescharacteristic, complemented
515#1876C2×C10111yescharacteristic, complemented
516#1793C2×C10111yescharacteristic, complemented
517C101#2388911yescharacteristic, direct product factor, Sylow
518C2×2−1+4C22×C10111yescharacteristic
519C2×2−1+4C22×C10111yescharacteristic, complemented
520C2×H(5,𝔽2)C22×C10111yescharacteristic
521#578—24no—
522#578—24no—
523#577—24no—
524#577—24no—
525C2×#137—21no—
526C2×#137—21no—
527C2×#137—21no—
528C2×#137C22×C10111yescharacteristic
529C2×#137C22×C10111yescharacteristic
530C2×#137C22×C10111yescharacteristic
531C2×#137C22×C10111yescharacteristic, complemented
532C2×AGL(1,ℤ/8)—21no—
533C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
534C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
535C2×#135—21no—
536C2×#135—21no—
537C2×#135C22×C10111yescharacteristic
538C2×#135C22×C10111yescharacteristic
539C22×Q16—21no—
540C22×Q16C22×C10111yescharacteristic, complemented
541C22×SD16—21no—
542C22×SD16C22×C10111yescharacteristic
543C2×#131C22×C10111yescharacteristic
544C2×#131C22×C10111yescharacteristic, complemented
545#537C22×C10111yescharacteristic
546C2×#124C22×C10111yescharacteristic
547#455—24no—
548#454—24no—
549#452—21no—
550#452—21no—
551#451—21no—
552#450—21no—
553#449—21no—
554#449—21no—
555#448—21no—
556#447—21no—
557C2×#104C22×C10111yescharacteristic
558C2×#104C22×C10111yescharacteristic
559C2×#104C22×C10111yescharacteristic, complemented
560C2×#104C22×C10111yescharacteristic, complemented
561#417C22×C10111yescharacteristic
562#417C22×C10111yescharacteristic, complemented
563C2×#103C22×C10111yescharacteristic, complemented
564C2×#102C22×C10111yescharacteristic
565C2×#101C22×C10111yescharacteristic, complemented
566C2×#101C22×C10111yescharacteristic, complemented
567C2×#100C22×C10111yescharacteristic
568#408C22×C10111yescharacteristic
569#408C22×C10111yescharacteristic, complemented
570#391C22×C10111yescharacteristic, complemented
571#343C22×C10111yescharacteristic, complemented
572#341C22×C10111yescharacteristic, complemented
573#341C22×C10111yescharacteristic, complemented
574#336C22×C10111yescharacteristic, complemented
5752−1+4—22no—
5762−1+4—22no—
5772−1+4—22no—
5782−1+4—22no—
5792−1+4—22no—
5802−1+4—41no—
5812−1+4—41no—
5822−1+4D4×C10114yescomplemented
583H(5,𝔽2)—22no—
584H(5,𝔽2)—22no—
585H(5,𝔽2)—22no—
586H(5,𝔽2)—41no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—41no—
594C2×#41—41no—
595C2×#41C23×C10111yescharacteristic
596C2×#41C23×C10111yescharacteristic
597C2×#41C23×C10111yescharacteristic
598C2×#41C23×C10111yescharacteristic
599C22×Q8—21no—
600C22×Q8—21no—
601C22×Q8—21no—
602C22×Q8—21no—
603C22×Q8C23×C10111yescharacteristic
604C22×Q8C23×C10111yescharacteristic
605C22×D4—21no—
606C22×D4—21no—
607C22×D4—41no—
608C22×D4C23×C10111yescharacteristic
609#137—28no—
610#137—28no—
611#137—28no—
612#137—22no—
613#137—22no—
614#137—22no—
615#137—22no—
616#137—22no—
617#137—22no—
618#137—41no—
619#137D4×C10114yescomplemented
620AGL(1,ℤ/8)—28no—
621AGL(1,ℤ/8)—22no—
622AGL(1,ℤ/8)—22no—
623AGL(1,ℤ/8)—41no—
624AGL(1,ℤ/8)D4×C10114yescomplemented
625#135—28no—
626#135—28no—
627#135—22no—
628#135—22no—
629#135—22no—
630#135—22no—
631C2×Q16—28no—
632C2×Q16—21no—
633C2×Q16—21no—
634C2×Q16—22no—
635C2×Q16—22no—
636C2×Q16—21no—
637C2×Q16—21no—
638C2×Q16—21no—
639C2×Q16—21no—
640C2×Q16D4×C10111yescharacteristic
641C2×Q16D4×C10111yescharacteristic
642C2×SD16—28no—
643C2×SD16—21no—
644C2×SD16—22no—
645C2×SD16—21no—
646C2×SD16—22no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—21no—
653C2×SD16D4×C10111yescharacteristic
654C2×SD16D4×C10111yescharacteristic
655C2×SD16D4×C10111yescharacteristic
656C2×SD16D4×C10111yescharacteristic
657C2×D8—21no—
658C2×D8—21no—
659C2×D8D4×C10111yescharacteristic
660C2×D8D4×C10111yescharacteristic
661#131—22no—
662#131—22no—
663#131—22no—
664#131—22no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16C23×C10111yescharacteristic
668C2×M16C23×C10111yescharacteristic
669C2×M16C23×C10111yescharacteristic
670C2×M16C23×C10111yescharacteristic
671C22×C8—21no—
672C22×C8—21no—
673C22×C8C23×C10111yescharacteristic
674C22×C8C23×C10111yescharacteristic
675#124—22no—
676#124—22no—
677C22⋊Q8—21no—
678C22⋊Q8—21no—
679#121—21no—
680#121—21no—
681#121—41no—
682C2×C4⋊C4C23×C10111yescharacteristic
683C2×C22⋊C4—41no—
684C2×C42C23×C10111yescharacteristic
685#104—22no—
686#104—22no—
687#104—22no—
688#104—22no—
689#103—21no—
690#103—21no—
691#103—21no—
692#103—21no—
693#102—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#101—22no—
698#101—41no—
699#100—22no—
700C22⋊C8—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8—21no—
704#95—41no—
705C24—21no—
706C24—41no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—24no—
712#41—24no—
713#41—24no—
714#41—24no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—44no—
724#41—42no—
725#41—42no—
726#41—42no—
727#41—44no—
728#41—42no—
729#41—44no—
730#41—42no—
731#41—42no—
732#41—44no—
733#41—42no—
734#41—42no—
735#41C2×D4×C10112yes—
736#41C2×D4×C10112yes—
737#41C2×D4×C10112yes—
738#41C2×D4×C10112yes—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—41no—
753C2×Q8—41no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8C2×D4×C10111yescharacteristic
760C2×Q8C2×D4×C10111yescharacteristic
761C2×Q8C2×D4×C10112yes—
762C2×Q8C2×D4×C10112yes—
763C2×Q8C2×D4×C10111yescharacteristic
764C2×Q8C2×D4×C10111yescharacteristic
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—42no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—41no—
782C2×D4—41no—
783C2×D4—42no—
784C2×D4—41no—
785C2×D4C2×D4×C10111yescharacteristic
786C2×D4C2×D4×C10111yescharacteristic
787C2×D4C2×D4×C10112yes—
788C2×D4C2×D4×C10111yescharacteristic
789C2×D4C2×D4×C10111yescharacteristic
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—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4C24×C10111yescharacteristic
804Q16—24no—
805Q16—24no—
806Q16—24no—
807Q16—24no—
808Q16—22no—
809Q16—24no—
810Q16—22no—
811Q16—42no—
812SD16—24no—
813SD16—24no—
814SD16—24no—
815SD16—24no—
816SD16—22no—
817SD16—24no—
818SD16—22no—
819SD16—24no—
820SD16—22no—
821SD16—22no—
822SD16—42no—
823SD16—42no—
824D8—24no—
825D8—22no—
826D8—22no—
827D8—42no—
828M16—24no—
829M16—24no—
830M16—21no—
831M16—21no—
832M16—21no—
833M16—21no—
834M16—21no—
835M16—21no—
836M16C2×D4×C10112yes—
837M16C2×D4×C10112yes—
838C2×C8—24no—
839C2×C8—24no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8C2×D4×C10111yescharacteristic
849C2×C8C2×D4×C10111yescharacteristic
850C2×C8C2×D4×C10111yescharacteristic
851C2×C8C2×D4×C10111yescharacteristic
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—41no—
855C22⋊C4—44no—
856C22⋊C4—41no—
857C22⋊C4—41no—
858C42—21no—
859C42—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—22no—
865C23—44no—
866C23—41no—
867C23—41no—
868C23—81no—
869C23—81no—
870C23—161no—
871C23—161no—
872C23H(5,𝔽2)×C10111yescharacteristic
873Q8—21no—
874Q8—21no—
875Q8—22no—
876Q8—22no—
877Q8—22no—
878Q8—21no—
879Q8—21no—
880Q8—21no—
881Q8—22no—
882Q8—21no—
883Q8—44no—
884Q8—44no—
885Q8—41no—
886Q8—41no—
887Q8—41no—
888Q8—41no—
889Q8#120×C10112yes—
890Q8#120×C10112yes—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—21no—
897D4—21no—
898D4—21no—
899D4—21no—
900D4—21no—
901D4—22no—
902D4—21no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—44no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—161no—
914D4#120×C10112yes—
915D4#120×C10112yes—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—81no—
944C2×C4C22×D4×C10111yescharacteristic
945C2×C4C22×D4×C10111yescharacteristic
946C2×C4C22×D4×C10111yescharacteristic
947C2×C4C22×D4×C10111yescharacteristic
948C2×C4C22×D4×C10111yescharacteristic
949C2×C4H(5,𝔽2)×C10111yescharacteristic
950C8—21no—
951C8—21no—
952C8—22no—
953C8—22no—
954C8—21no—
955C8—21no—
956C8—41no—
957C8—41no—
958C22—21no—
959C22—21no—
960C22—22no—
961C22—22no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—82no—
974C22—81no—
975C22—81no—
976C22—161no—
977C22—164no—
978C22#534×C10111yescharacteristic
979C22D42×C10111yescharacteristic
980C22D42×C10111yescharacteristic
981C4—22no—
982C4—22no—
983C4—41no—
984C4—42no—
985C4—42no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4C2×#120×C10111yescharacteristic
990C4C2×#120×C10111yescharacteristic
991C4D42×C10111yescharacteristic
992C4D42×C10111yescharacteristic
993C2—21no—
994C2—21no—
995C2—42no—
996C2—42no—
997C2—81no—
998C2—81no—
999C2—82no—
1000C2C101×#240311yescharacteristic
1001C2C101×#328911yescharacteristic
1002C2C101×#329011yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#578×C101C2semidirect
2. C2×#577×C101C2semidirect
3. C2×#454×C101C2semidirect
4. C2×#455×C101C2semidirect
5. C101×#3013C2semidirect
6. C101×#3012C2semidirect
7. C101×#2020C2semidirect
8. C101×#2019C2semidirect
9. C101×#2015C2semidirect
10. C101×#2007C2semidirect
11. C101×#1908C2semidirect
12. C101×#1907C2semidirect
13. C101×#1876C2semidirect
14. C101×#1876C2semidirect
15. C101×#1793C2semidirect
17. C2×2−1+4×C101C22semidirect
29. C2×#137×C101C22semidirect
38. C22×Q16×C101C22semidirect
42. C2×#131×C101C22semidirect
57. C2×#104×C101C22semidirect
58. C2×#104×C101C22semidirect
60. #417×C101C22semidirect
61. C2×#103×C101C22semidirect
63. C2×#101×C101C22semidirect
64. C2×#101×C101C22semidirect
67. #408×C101C22semidirect
68. #391×C101C22semidirect
69. #343×C101C22semidirect
70. #341×C101C22semidirect
71. #341×C101C22semidirect
72. #336×C101C22semidirect
80. 2−1+4×C101D4semidirect
117. #137×C101D4semidirect
122. AGL(1,ℤ/8)×C101D4semidirect
491. #23889C101direct (N × H)
502. C2×#578C2×C101semidirect
503. C2×#577C2×C101semidirect
504. C2×#454C2×C101semidirect
505. C2×#455C2×C101semidirect
506. #3013C2×C101semidirect
507. #3012C2×C101semidirect
508. #2020C2×C101semidirect
509. #2019C2×C101semidirect
510. #2015C2×C101semidirect
511. #2007C2×C101semidirect
512. #1908C2×C101semidirect
513. #1907C2×C101semidirect
514. #1876C2×C101semidirect
515. #1876C2×C101semidirect
516. #1793C2×C101semidirect
517. C101#23889direct (N × H)
519. C2×2−1+4C22×C101semidirect
531. C2×#137C22×C101semidirect
540. C22×Q16C22×C101semidirect
544. C2×#131C22×C101semidirect
559. C2×#104C22×C101semidirect
560. C2×#104C22×C101semidirect
562. #417C22×C101semidirect
563. C2×#103C22×C101semidirect
565. C2×#101C22×C101semidirect
566. C2×#101C22×C101semidirect
569. #408C22×C101semidirect
570. #391C22×C101semidirect
571. #343C22×C101semidirect
572. #341C22×C101semidirect
573. #341C22×C101semidirect
574. #336C22×C101semidirect
582. 2−1+4D4×C101semidirect
619. #137D4×C101semidirect
624. AGL(1,ℤ/8)D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#578×C1012
C2×#577×C1012
C2×#454×C1012
C2×#455×C1012
C101×#30132
C101×#30122
C101×#20202
C101×#20192
C101×#20152
C101×#20072
C101×#19082
C101×#19072
C101×#18762
C101×#17932
#23889101