Finite Group Databasebeta

← C101×#23412 #38805563

Subgroups — C101×#23412 #38805563

Order 25856.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C101C211yesmaximal, characteristic, complemented
2C2×#575×C101C211yesmaximal, characteristic, complemented
3C101×#3449C211yesmaximal, characteristic, complemented
4C2×#421×C101C211yesmaximal, characteristic, complemented
5C101×#2896C211yesmaximal, characteristic, complemented
6C2×#410×C101C211yesmaximal, characteristic, complemented
7C101×#2009C214yesmaximal, complemented
8C101×#2008C214yesmaximal, complemented
9C2×#344×C101C211yesmaximal, characteristic, complemented
10C22×#41×C101C2211yescharacteristic
11C22×#41×C101C2211yescharacteristic
12C22×#41×C101C2211yescharacteristic
13#575×C101—22no—
14#575×C101—22no—
15#575×C101—22no—
16#575×C101—22no—
17#575×C101—22no—
18#575×C101—22no—
19#575×C101—22no—
20#575×C101C2214yes—
21C2×#137×C101—21no—
22C2×#137×C101—21no—
23C2×#137×C101—21no—
24C2×#137×C101C2212yescomplemented
25C2×AGL(1,ℤ/8)×C101—21no—
26C2×AGL(1,ℤ/8)×C101—21no—
27C2×AGL(1,ℤ/8)×C101—21no—
28C2×AGL(1,ℤ/8)×C101C2212yescomplemented
29C2×#135×C101—22no—
30C2×#135×C101—22no—
31C22×M16×C101C2211yescharacteristic
32C22×M16×C101C2211yescharacteristic
33#537×C101—22no—
34#536×C101—21no—
35#536×C101C2212yescomplemented
36#535×C101—21no—
37#535×C101C2212yescomplemented
38#534×C101—22no—
39#532×C101—22no—
40#525×C101—22no—
41#525×C101—22no—
42C2×#117×C101C2211yescharacteristic
43C2×#117×C101C2211yescharacteristic
44#421×C101—22no—
45#421×C101C2214yescomplemented
46C2×#104×C101—22no—
47#419×C101C2212yescomplemented
48#418×C101C2212yescomplemented
49#417×C101—22no—
50#416×C101—22no—
51#410×C101—22no—
52#410×C101C2214yescomplemented
53C2×#99×C101—22no—
54#344×C101C2214yescomplemented
55C2×#41×C101—21no—
56C2×#41×C101—21no—
57C2×#41×C101—21no—
58C2×#41×C101—21no—
59C2×#41×C101—21no—
60C2×#41×C101—21no—
61C2×#41×C101—21no—
62C2×#41×C101—21no—
63C2×#41×C101—21no—
64C2×#41×C101—21no—
65C2×#41×C101—21no—
66C2×#41×C101—21no—
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69C2×#41×C101—21no—
70C2×#41×C101—21no—
71C2×#41×C101—21no—
72C2×#41×C101—21no—
73C2×#41×C101—21no—
74C2×#41×C101—21no—
75C2×#41×C101—21no—
76C2×#41×C101—21no—
77C2×#41×C101—21no—
78C2×#41×C101—21no—
79C2×#41×C101—21no—
80C2×#41×C101—21no—
81C2×#41×C101—21no—
82C2×#41×C101—21no—
83C2×#41×C101—21no—
84C2×#41×C101—21no—
85C2×#41×C101D412yes—
86C2×#41×C101D412yes—
87C2×#41×C101D412yes—
88C2×#41×C101D412yescomplemented
89C2×#41×C101C2312yes—
90C2×#41×C101C2312yes—
91C22×Q8×C101D411yescharacteristic
92C22×Q8×C101D411yescharacteristic, complemented
93C22×Q8×C101C2311yescharacteristic
94C22×D4×C101—21no—
95C22×D4×C101—21no—
96C22×D4×C101—21no—
97C22×D4×C101D411yescharacteristic
98C22×D4×C101D411yescharacteristic, complemented
99C22×D4×C101C2311yescharacteristic
100C23×C4×C101—21no—
101C23×C4×C101—21no—
102C23×C4×C101—21no—
103C23×C4×C101C2311yescharacteristic
104#137×C101—24no—
105#137×C101—24no—
106#137×C101—24no—
107#137×C101—24no—
108#137×C101—24no—
109#137×C101—24no—
110#137×C101—24no—
111#137×C101—24no—
112AGL(1,ℤ/8)×C101—24no—
113AGL(1,ℤ/8)×C101—24no—
114AGL(1,ℤ/8)×C101—24no—
115AGL(1,ℤ/8)×C101—24no—
116AGL(1,ℤ/8)×C101—24no—
117AGL(1,ℤ/8)×C101—24no—
118AGL(1,ℤ/8)×C101—24no—
119AGL(1,ℤ/8)×C101—24no—
120#135×C101—28no—
121#135×C101—28no—
122#135×C101—28no—
123#135×C101—28no—
124C2×Q16×C101—22no—
125C2×Q16×C101—22no—
126C2×SD16×C101—22no—
127C2×SD16×C101—22no—
128C2×SD16×C101—22no—
129C2×SD16×C101—22no—
130C2×D8×C101—22no—
131C2×D8×C101—22no—
132C2×M16×C101—21no—
133C2×M16×C101—21no—
134C2×M16×C101—21no—
135C2×M16×C101—21no—
136C2×M16×C101—21no—
137C2×M16×C101—21no—
138C2×M16×C101—21no—
139C2×M16×C101D412yescomplemented
140C2×M16×C101D412yescomplemented
141C2×M16×C101D412yescomplemented
142C2×M16×C101C2312yes—
143C2×M16×C101C2312yes—
144C22×C8×C101—21no—
145C22×C8×C101D412yescomplemented
146C4⋊Q8×C101—22no—
147#127×C101—22no—
148#124×C101—22no—
149#124×C101—22no—
150#123×C101—24no—
151#123×C101—24no—
152C22⋊Q8×C101—24no—
153C22⋊Q8×C101—24no—
154#121×C101—24no—
155#121×C101—28no—
156#121×C101—24no—
157#120×C101—24no—
158#120×C101—24no—
159C4×D4×C101—28no—
160#117×C101—21no—
161#117×C101—21no—
162#117×C101—21no—
163#117×C101—21no—
164#117×C101—21no—
165#117×C101D412yes—
166#117×C101C2312yes—
167#117×C101C2312yes—
168C2×C4⋊C4×C101—21no—
169C2×C4⋊C4×C101—21no—
170C2×C22⋊C4×C101—21no—
171C2×C22⋊C4×C101D412yes—
172C2×C42×C101—21no—
173C2×C42×C101—21no—
174#104×C101—28no—
175#103×C101—24no—
176#102×C101—24no—
177#99×C101—28no—
178C24×C101—21no—
179C24×C101—21no—
180C24×C101—21no—
181C24×C101C2×D411yescharacteristic
182#41×C101—22no—
183#41×C101—22no—
184#41×C101—22no—
185#41×C101—22no—
186#41×C101—22no—
187#41×C101—22no—
188#41×C101—22no—
189#41×C101—22no—
190#41×C101—22no—
191#41×C101—22no—
192#41×C101—22no—
193#41×C101—22no—
194#41×C101—22no—
195#41×C101—22no—
196#41×C101—22no—
197#41×C101—22no—
198#41×C101—22no—
199#41×C101—22no—
200#41×C101—22no—
201#41×C101—22no—
202#41×C101—22no—
203#41×C101—22no—
204#41×C101—22no—
205#41×C101—22no—
206#41×C101—41no—
207#41×C101—41no—
208#41×C101—41no—
209#41×C101—41no—
210#41×C101—41no—
211#41×C101—41no—
212#41×C101—41no—
213#41×C101—41no—
214#41×C101—41no—
215#41×C101—41no—
216#41×C101—41no—
217#41×C101—41no—
218#41×C101—41no—
219#41×C101—41no—
220#41×C101—41no—
221#41×C101—41no—
222#41×C101—41no—
223#41×C101—41no—
224#41×C101—41no—
225#41×C101—41no—
226#41×C101—41no—
227#41×C101—41no—
228#41×C101—41no—
229#41×C101—41no—
230C2×Q8×C101—21no—
231C2×Q8×C101—21no—
232C2×Q8×C101—21no—
233C2×Q8×C101—21no—
234C2×Q8×C101—21no—
235C2×Q8×C101—21no—
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—21no—
244C2×Q8×C101—21no—
245C2×Q8×C101C2×D412yes—
246C2×Q8×C101C2×D412yes—
247C2×Q8×C101C2×D412yes—
248C2×D4×C101—22no—
249C2×D4×C101—22no—
250C2×D4×C101—22no—
251C2×D4×C101—22no—
252C2×D4×C101—22no—
253C2×D4×C101—22no—
254C2×D4×C101—28no—
255C2×D4×C101—21no—
256C2×D4×C101—21no—
257C2×D4×C101—21no—
258C2×D4×C101—21no—
259C2×D4×C101—21no—
260C2×D4×C101—21no—
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—21no—
270C2×D4×C101—41no—
271C2×D4×C101—41no—
272C2×D4×C101—41no—
273C2×D4×C101—41no—
274C2×D4×C101—41no—
275C2×D4×C101—41no—
276C2×D4×C101—41no—
277C2×D4×C101—41no—
278C2×D4×C101—41no—
279C2×D4×C101—41no—
280C2×D4×C101—41no—
281C2×D4×C101—41no—
282C2×D4×C101C2×D412yes—
283C2×D4×C101C2×D412yes—
284C2×D4×C101C2×D412yes—
285C22×C4×C101—21no—
286C22×C4×C101—21no—
287C22×C4×C101—21no—
288C22×C4×C101—22no—
289C22×C4×C101—22no—
290C22×C4×C101—22no—
291C22×C4×C101—22no—
292C22×C4×C101—22no—
293C22×C4×C101—22no—
294C22×C4×C101—22no—
295C22×C4×C101—41no—
296C22×C4×C101—41no—
297C22×C4×C101—41no—
298C22×C4×C101—41no—
299C22×C4×C101—41no—
300C22×C4×C101—41no—
301C22×C4×C101—41no—
302C22×C4×C101—41no—
303C22×C4×C101—41no—
304C22×C4×C101—41no—
305C22×C4×C101—41no—
306C22×C4×C101—41no—
307C22×C4×C101—41no—
308C22×C4×C101C2×D411yescharacteristic
309C22×C4×C101C2×D411yescharacteristic
310C22×C4×C101C2×D411yescharacteristic
311C22×C4×C101C2×D411yescharacteristic
312C22×C4×C101C2×D411yescharacteristic
313C22×C4×C101C2×D411yescharacteristic
314C22×C4×C101C2×D411yescharacteristic
315C22×C4×C101C2×D411yescharacteristic
316C22×C4×C101C2×D411yescharacteristic
317C22×C4×C101C2×D411yescharacteristic
318C22×C4×C101C2×D411yescharacteristic
319C22×C4×C101#4111yescharacteristic
320C22×C4×C101#4111yescharacteristic
321C22×C4×C101C2411yescharacteristic
322Q16×C101—28no—
323Q16×C101—28no—
324SD16×C101—28no—
325SD16×C101—28no—
326SD16×C101—28no—
327SD16×C101—28no—
328D8×C101—28no—
329D8×C101—28no—
330M16×C101—22no—
331M16×C101—22no—
332M16×C101—22no—
333M16×C101—22no—
334M16×C101—22no—
335M16×C101—22no—
336M16×C101—22no—
337M16×C101C2×D414yes—
338C2×C8×C101—22no—
339C2×C8×C101—22no—
340C2×C8×C101—22no—
341C2×C8×C101—22no—
342C2×C8×C101—22no—
343C2×C8×C101C2×D414yes—
344C4⋊C4×C101—28no—
345C4⋊C4×C101—22no—
346C4⋊C4×C101—22no—
347C4⋊C4×C101—22no—
348C4⋊C4×C101—41no—
349C22⋊C4×C101—28no—
350C22⋊C4×C101—28no—
351C22⋊C4×C101—22no—
352C22⋊C4×C101—22no—
353C22⋊C4×C101—41no—
354C22⋊C4×C101C2×D414yes—
355C42×C101—22no—
356C42×C101—22no—
357C42×C101—22no—
358C42×C101—41no—
359C23×C101—22no—
360C23×C101—22no—
361C23×C101—22no—
362C23×C101—41no—
363C23×C101—41no—
364C23×C101—41no—
365C23×C101—41no—
366C23×C101—41no—
367C23×C101—41no—
368C23×C101—81no—
369C23×C101—82no—
370C23×C101—82no—
371C23×C101—82no—
372C23×C101#12011yescharacteristic
373C23×C101#12011yescharacteristic
374C23×C101#12111yescharacteristic
375C23×C101#12111yescharacteristic
376C23×C101#12711yescharacteristic
377C23×C101#12711yescharacteristic
378C23×C101C22×D411yescharacteristic
379Q8×C101—22no—
380Q8×C101—22no—
381Q8×C101—22no—
382Q8×C101—22no—
383Q8×C101—22no—
384Q8×C101—22no—
385Q8×C101—41no—
386Q8×C101—41no—
387Q8×C101—41no—
388Q8×C101—41no—
389Q8×C101—41no—
390Q8×C101—41no—
391D4×C101—22no—
392D4×C101—22no—
393D4×C101—22no—
394D4×C101—22no—
395D4×C101—22no—
396D4×C101—22no—
397D4×C101—42no—
398D4×C101—42no—
399D4×C101—42no—
400D4×C101—42no—
401D4×C101—42no—
402D4×C101—42no—
403D4×C101—42no—
404D4×C101—42no—
405D4×C101—42no—
406D4×C101—42no—
407D4×C101—42no—
408D4×C101—42no—
409D4×C101—41no—
410D4×C101—41no—
411D4×C101—41no—
412D4×C101—41no—
413D4×C101—41no—
414D4×C101—41no—
415D4×C101—88no—
416C2×C4×C101—24no—
417C2×C4×C101—22no—
418C2×C4×C101—22no—
419C2×C4×C101—22no—
420C2×C4×C101—41no—
421C2×C4×C101—41no—
422C2×C4×C101—41no—
423C2×C4×C101—41no—
424C2×C4×C101—41no—
425C2×C4×C101—41no—
426C2×C4×C101—42no—
427C2×C4×C101—42no—
428C2×C4×C101—42no—
429C2×C4×C101—42no—
430C2×C4×C101—42no—
431C2×C4×C101—42no—
432C2×C4×C101—42no—
433C2×C4×C101—42no—
434C2×C4×C101—42no—
435C2×C4×C101—42no—
436C2×C4×C101—42no—
437C2×C4×C101—42no—
438C2×C4×C101—42no—
439C2×C4×C101—82no—
440C2×C4×C101—82no—
441C2×C4×C101#12011yescharacteristic
442C2×C4×C101#12011yescharacteristic
443C2×C4×C101#12011yescharacteristic
444C2×C4×C101#12011yescharacteristic
445C2×C4×C101#12011yescharacteristic
446C2×C4×C101#12011yescharacteristic
447C2×C4×C101#12011yescharacteristic
448C2×C4×C101#12011yescharacteristic
449C2×C4×C101#12011yescharacteristic
450C2×C4×C101#12011yescharacteristic
451C2×C4×C101#12111yescharacteristic
452C2×C4×C101#12111yescharacteristic
453C2×C4×C101#12111yescharacteristic
454C2×C4×C101#12111yescharacteristic
455C2×C4×C101#12111yescharacteristic
456C2×C4×C101#12111yescharacteristic
457C2×C4×C101#12111yescharacteristic
458C2×C4×C101#12111yescharacteristic
459C2×C4×C101#12111yescharacteristic
460C2×C4×C101#12111yescharacteristic
461C2×C4×C101#12711yescharacteristic
462C2×C4×C101#12711yescharacteristic
463C2×C4×C101C22×D411yescharacteristic
464C2×C4×C101C22×D411yescharacteristic
465C2×C4×C101C22×D411yescharacteristic
466C2×C4×C101C22×D411yescharacteristic
467C2×C4×C101C22×D411yescharacteristic
468C2×C4×C101C2×#4111yescharacteristic
469C8×C101—24no—
470C8×C101—24no—
471C22×C101—41no—
472C22×C101—41no—
473C22×C101—41no—
474C22×C101—41no—
475C22×C101—41no—
476C22×C101—41no—
477C22×C101—41no—
478C22×C101—44no—
479C22×C101—44no—
480C22×C101—42no—
481C22×C101—42no—
482C22×C101—42no—
483C22×C101—82no—
484C22×C101—82no—
485C22×C101—82no—
486C22×C101—82no—
487C22×C101—82no—
488C22×C101—82no—
489C22×C101—82no—
490C22×C101#39211yescharacteristic
491C22×C101#39211yescharacteristic
492C22×C101#39211yescharacteristic
493C22×C101#39211yescharacteristic
494C22×C101C2×#12011yescharacteristic
495C22×C101C2×#12111yescharacteristic
496C22×C101C2×#12711yescharacteristic
497C4×C101—44no—
498C4×C101—42no—
499C4×C101—42no—
500C4×C101—42no—
501C4×C101—82no—
502C4×C101#39211yescharacteristic
503C4×C101#39211yescharacteristic
504C4×C101#39211yescharacteristic
505C4×C101#39211yescharacteristic
506C4×C101C2×#12011yescharacteristic
507C4×C101C2×#12011yescharacteristic
508C4×C101C2×#12111yescharacteristic
509C4×C101C2×#12111yescharacteristic
510#23412C10111yesmaximal, characteristic, direct product factor, Sylow
511C2×C101—21no—
512C2×C101—21no—
513C2×C101—21no—
514C2×C101—21no—
515C2×C101—21no—
516C2×C101—21no—
517C2×C101—21no—
518C2×C101—82no—
519C2×C101—82no—
520C2×C101—82no—
521C2×C101C2×#39211yescharacteristic
522C2×#575C2×C10111yescharacteristic, complemented
523C2×#575C2×C10111yescharacteristic, complemented
524#3449C2×C10111yescharacteristic, complemented
525C2×#421C2×C10111yescharacteristic, complemented
526#2896C2×C10111yescharacteristic, complemented
527C2×#410C2×C10111yescharacteristic, complemented
528#2009C2×C10114yescomplemented
529#2008C2×C10114yescomplemented
530C2×#344C2×C10111yescharacteristic, complemented
531C101#2341211yescharacteristic, direct product factor, Sylow
532C22×#41C22×C10111yescharacteristic
533C22×#41C22×C10111yescharacteristic
534C22×#41C22×C10111yescharacteristic
535#575—22no—
536#575—22no—
537#575—22no—
538#575—22no—
539#575—22no—
540#575—22no—
541#575—22no—
542#575C22×C10114yes—
543C2×#137—21no—
544C2×#137—21no—
545C2×#137—21no—
546C2×#137C22×C10112yescomplemented
547C2×AGL(1,ℤ/8)—21no—
548C2×AGL(1,ℤ/8)—21no—
549C2×AGL(1,ℤ/8)—21no—
550C2×AGL(1,ℤ/8)C22×C10112yescomplemented
551C2×#135—22no—
552C2×#135—22no—
553C22×M16C22×C10111yescharacteristic
554C22×M16C22×C10111yescharacteristic
555#537—22no—
556#536—21no—
557#536C22×C10112yescomplemented
558#535—21no—
559#535C22×C10112yescomplemented
560#534—22no—
561#532—22no—
562#525—22no—
563#525—22no—
564C2×#117C22×C10111yescharacteristic
565C2×#117C22×C10111yescharacteristic
566#421—22no—
567#421C22×C10114yescomplemented
568C2×#104—22no—
569#419C22×C10112yescomplemented
570#418C22×C10112yescomplemented
571#417—22no—
572#416—22no—
573#410—22no—
574#410C22×C10114yescomplemented
575C2×#99—22no—
576#344C22×C10114yescomplemented
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—21no—
584C2×#41—21no—
585C2×#41—21no—
586C2×#41—21no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—21no—
607C2×#41D4×C10112yes—
608C2×#41D4×C10112yes—
609C2×#41D4×C10112yes—
610C2×#41D4×C10112yescomplemented
611C2×#41C23×C10112yes—
612C2×#41C23×C10112yes—
613C22×Q8D4×C10111yescharacteristic
614C22×Q8D4×C10111yescharacteristic, complemented
615C22×Q8C23×C10111yescharacteristic
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4D4×C10111yescharacteristic
620C22×D4D4×C10111yescharacteristic, complemented
621C22×D4C23×C10111yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C10111yescharacteristic
626#137—24no—
627#137—24no—
628#137—24no—
629#137—24no—
630#137—24no—
631#137—24no—
632#137—24no—
633#137—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—24no—
638AGL(1,ℤ/8)—24no—
639AGL(1,ℤ/8)—24no—
640AGL(1,ℤ/8)—24no—
641AGL(1,ℤ/8)—24no—
642#135—28no—
643#135—28no—
644#135—28no—
645#135—28no—
646C2×Q16—22no—
647C2×Q16—22no—
648C2×SD16—22no—
649C2×SD16—22no—
650C2×SD16—22no—
651C2×SD16—22no—
652C2×D8—22no—
653C2×D8—22no—
654C2×M16—21no—
655C2×M16—21no—
656C2×M16—21no—
657C2×M16—21no—
658C2×M16—21no—
659C2×M16—21no—
660C2×M16—21no—
661C2×M16D4×C10112yescomplemented
662C2×M16D4×C10112yescomplemented
663C2×M16D4×C10112yescomplemented
664C2×M16C23×C10112yes—
665C2×M16C23×C10112yes—
666C22×C8—21no—
667C22×C8D4×C10112yescomplemented
668C4⋊Q8—22no—
669#127—22no—
670#124—22no—
671#124—22no—
672#123—24no—
673#123—24no—
674C22⋊Q8—24no—
675C22⋊Q8—24no—
676#121—24no—
677#121—28no—
678#121—24no—
679#120—24no—
680#120—24no—
681C4×D4—28no—
682#117—21no—
683#117—21no—
684#117—21no—
685#117—21no—
686#117—21no—
687#117D4×C10112yes—
688#117C23×C10112yes—
689#117C23×C10112yes—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4D4×C10112yes—
694C2×C42—21no—
695C2×C42—21no—
696#104—28no—
697#103—24no—
698#102—24no—
699#99—28no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24C2×D4×C10111yescharacteristic
704#41—22no—
705#41—22no—
706#41—22no—
707#41—22no—
708#41—22no—
709#41—22no—
710#41—22no—
711#41—22no—
712#41—22no—
713#41—22no—
714#41—22no—
715#41—22no—
716#41—22no—
717#41—22no—
718#41—22no—
719#41—22no—
720#41—22no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—22no—
726#41—22no—
727#41—22no—
728#41—41no—
729#41—41no—
730#41—41no—
731#41—41no—
732#41—41no—
733#41—41no—
734#41—41no—
735#41—41no—
736#41—41no—
737#41—41no—
738#41—41no—
739#41—41no—
740#41—41no—
741#41—41no—
742#41—41no—
743#41—41no—
744#41—41no—
745#41—41no—
746#41—41no—
747#41—41no—
748#41—41no—
749#41—41no—
750#41—41no—
751#41—41no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8C2×D4×C10112yes—
768C2×Q8C2×D4×C10112yes—
769C2×Q8C2×D4×C10112yes—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—28no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—41no—
793C2×D4—41no—
794C2×D4—41no—
795C2×D4—41no—
796C2×D4—41no—
797C2×D4—41no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C2×D4—41no—
802C2×D4—41no—
803C2×D4—41no—
804C2×D4C2×D4×C10112yes—
805C2×D4C2×D4×C10112yes—
806C2×D4C2×D4×C10112yes—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4C2×D4×C10111yescharacteristic
831C22×C4C2×D4×C10111yescharacteristic
832C22×C4C2×D4×C10111yescharacteristic
833C22×C4C2×D4×C10111yescharacteristic
834C22×C4C2×D4×C10111yescharacteristic
835C22×C4C2×D4×C10111yescharacteristic
836C22×C4C2×D4×C10111yescharacteristic
837C22×C4C2×D4×C10111yescharacteristic
838C22×C4C2×D4×C10111yescharacteristic
839C22×C4C2×D4×C10111yescharacteristic
840C22×C4C2×D4×C10111yescharacteristic
841C22×C4#41×C10111yescharacteristic
842C22×C4#41×C10111yescharacteristic
843C22×C4C24×C10111yescharacteristic
844Q16—28no—
845Q16—28no—
846SD16—28no—
847SD16—28no—
848SD16—28no—
849SD16—28no—
850D8—28no—
851D8—28no—
852M16—22no—
853M16—22no—
854M16—22no—
855M16—22no—
856M16—22no—
857M16—22no—
858M16—22no—
859M16C2×D4×C10114yes—
860C2×C8—22no—
861C2×C8—22no—
862C2×C8—22no—
863C2×C8—22no—
864C2×C8—22no—
865C2×C8C2×D4×C10114yes—
866C4⋊C4—28no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—41no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—41no—
876C22⋊C4C2×D4×C10114yes—
877C42—22no—
878C42—22no—
879C42—22no—
880C42—41no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—81no—
891C23—82no—
892C23—82no—
893C23—82no—
894C23#120×C10111yescharacteristic
895C23#120×C10111yescharacteristic
896C23#121×C10111yescharacteristic
897C23#121×C10111yescharacteristic
898C23#127×C10111yescharacteristic
899C23#127×C10111yescharacteristic
900C23C22×D4×C10111yescharacteristic
901Q8—22no—
902Q8—22no—
903Q8—22no—
904Q8—22no—
905Q8—22no—
906Q8—22no—
907Q8—41no—
908Q8—41no—
909Q8—41no—
910Q8—41no—
911Q8—41no—
912Q8—41no—
913D4—22no—
914D4—22no—
915D4—22no—
916D4—22no—
917D4—22no—
918D4—22no—
919D4—42no—
920D4—42no—
921D4—42no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—88no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4#120×C10111yescharacteristic
964C2×C4#120×C10111yescharacteristic
965C2×C4#120×C10111yescharacteristic
966C2×C4#120×C10111yescharacteristic
967C2×C4#120×C10111yescharacteristic
968C2×C4#120×C10111yescharacteristic
969C2×C4#120×C10111yescharacteristic
970C2×C4#120×C10111yescharacteristic
971C2×C4#120×C10111yescharacteristic
972C2×C4#120×C10111yescharacteristic
973C2×C4#121×C10111yescharacteristic
974C2×C4#121×C10111yescharacteristic
975C2×C4#121×C10111yescharacteristic
976C2×C4#121×C10111yescharacteristic
977C2×C4#121×C10111yescharacteristic
978C2×C4#121×C10111yescharacteristic
979C2×C4#121×C10111yescharacteristic
980C2×C4#121×C10111yescharacteristic
981C2×C4#121×C10111yescharacteristic
982C2×C4#121×C10111yescharacteristic
983C2×C4#127×C10111yescharacteristic
984C2×C4#127×C10111yescharacteristic
985C2×C4C22×D4×C10111yescharacteristic
986C2×C4C22×D4×C10111yescharacteristic
987C2×C4C22×D4×C10111yescharacteristic
988C2×C4C22×D4×C10111yescharacteristic
989C2×C4C22×D4×C10111yescharacteristic
990C2×C4C2×#41×C10111yescharacteristic
991C8—24no—
992C8—24no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
1010C22—82no—
1011C22—82no—
1012C22#392×C10111yescharacteristic
1013C22#392×C10111yescharacteristic
1014C22#392×C10111yescharacteristic
1015C22#392×C10111yescharacteristic
1016C22C2×#120×C10111yescharacteristic
1017C22C2×#121×C10111yescharacteristic
1018C22C2×#127×C10111yescharacteristic
1019C4—44no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—82no—
1024C4#392×C10111yescharacteristic
1025C4#392×C10111yescharacteristic
1026C4#392×C10111yescharacteristic
1027C4#392×C10111yescharacteristic
1028C4C2×#120×C10111yescharacteristic
1029C4C2×#120×C10111yescharacteristic
1030C4C2×#121×C10111yescharacteristic
1031C4C2×#121×C10111yescharacteristic
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—21no—
1037C2—21no—
1038C2—21no—
1039C2—82no—
1040C2—82no—
1041C2—82no—
1042C2C2×#392×C10111yescharacteristic
subgroupG/H
centerC4×C101#392
commutator, Frattini, cosocleC22×C4C24×C101
socleC2×C101C2×#392
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#575×C101C2semidirect
2. C2×#575×C101C2semidirect
3. C101×#3449C2semidirect
4. C2×#421×C101C2semidirect
5. C101×#2896C2semidirect
6. C2×#410×C101C2semidirect
7. C101×#2009C2semidirect
8. C101×#2008C2semidirect
9. C2×#344×C101C2semidirect
24. C2×#137×C101C22semidirect
28. C2×AGL(1,ℤ/8)×C101C22semidirect
35. #536×C101C22semidirect
37. #535×C101C22semidirect
45. #421×C101C22semidirect
47. #419×C101C22semidirect
48. #418×C101C22semidirect
52. #410×C101C22semidirect
54. #344×C101C22semidirect
88. C2×#41×C101D4semidirect
92. C22×Q8×C101D4semidirect
98. C22×D4×C101D4semidirect
139. C2×M16×C101D4semidirect
140. C2×M16×C101D4semidirect
141. C2×M16×C101D4semidirect
145. C22×C8×C101D4semidirect
510. #23412C101direct (N × H)
522. C2×#575C2×C101semidirect
523. C2×#575C2×C101semidirect
524. #3449C2×C101semidirect
525. C2×#421C2×C101semidirect
526. #2896C2×C101semidirect
527. C2×#410C2×C101semidirect
528. #2009C2×C101semidirect
529. #2008C2×C101semidirect
530. C2×#344C2×C101semidirect
531. C101#23412direct (N × H)
546. C2×#137C22×C101semidirect
550. C2×AGL(1,ℤ/8)C22×C101semidirect
557. #536C22×C101semidirect
559. #535C22×C101semidirect
567. #421C22×C101semidirect
569. #419C22×C101semidirect
570. #418C22×C101semidirect
574. #410C22×C101semidirect
576. #344C22×C101semidirect
610. C2×#41D4×C101semidirect
614. C22×Q8D4×C101semidirect
620. C22×D4D4×C101semidirect
661. C2×M16D4×C101semidirect
662. C2×M16D4×C101semidirect
663. C2×M16D4×C101semidirect
667. C22×C8D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1012
C101×#34492
C2×#421×C1012
C101×#28962
C2×#410×C1012
C101×#20092
C101×#20082
C2×#344×C1012
#23412101