Finite Group Databasebeta

← C101×#23972 #38806123

Subgroups — C101×#23972 #38806123

Order 25856.

1516 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C101C211yesmaximal, characteristic, complemented
2C2×#449×C101C211yesmaximal, characteristic, complemented
3C2×#417×C101C211yesmaximal, characteristic, complemented
4C101×#2407C211yesmaximal, characteristic, complemented
5C101×#2024C211yesmaximal, characteristic, complemented
6C101×#2023C211yesmaximal, characteristic, complemented
7C101×#2000C211yesmaximal, characteristic, complemented
8C101×#1999C211yesmaximal, characteristic, complemented
9C101×#1895C211yesmaximal, characteristic, complemented
10C101×#1879C211yesmaximal, characteristic, complemented
11C101×#1877C211yesmaximal, characteristic, complemented
12C101×#1874C211yesmaximal, characteristic, complemented
13C101×#1872C211yesmaximal, characteristic, complemented
14C101×#1870C211yesmaximal, characteristic, complemented
15C101×#1824C211yesmaximal, characteristic, complemented
16C22×#41×C101—21no—
17C22×#41×C101C2211yescharacteristic
18C22×SD16×C101C2211yescharacteristic
19C22×D8×C101C2211yescharacteristic
20C22×M16×C101C2211yescharacteristic
21#547×C101—24no—
22#547×C101—24no—
23C2×C4⋊Q8×C101C2211yescharacteristic
24C2×#123×C101—21no—
25C2×#123×C101—21no—
26C2×C22⋊Q8×C101—21no—
27C2×C22⋊Q8×C101C2211yescharacteristic
28C2×#121×C101C2211yescharacteristic
29C2×#121×C101C2211yescharacteristic
30C2×#121×C101C2211yescharacteristic
31C2×C4×D4×C101C2211yescharacteristic
32C2×C4×D4×C101C2211yescharacteristic
33C22×C4⋊C4×C101C2211yescharacteristic
34C22×C4⋊C4×C101C2211yescharacteristic
35#449×C101—24no—
36#417×C101—24no—
37C2×#103×C101C2211yescharacteristic
38C2×#103×C101C2211yescharacteristic
39C2×#103×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×C22⋊C8×C101C2211yescharacteristic
46C2×C22⋊C8×C101C2211yescharacteristic
47C2×C22⋊C8×C101C2211yescharacteristic
48#394×C101—21no—
49#392×C101—21no—
50#391×C101C2211yescharacteristic
51#390×C101C2211yescharacteristic
52#386×C101—21no—
53#385×C101—21no—
54#380×C101C2211yescharacteristic
55#340×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#336×C101C2211yescharacteristic
62#336×C101C2211yescharacteristic
63C2×#41×C101—28no—
64C2×#41×C101—22no—
65C2×#41×C101—22no—
66C2×#41×C101—22no—
67C2×#41×C101—22no—
68C2×#41×C101—41no—
69C2×#41×C101—41no—
70C2×#41×C101—44no—
71C2×#41×C101—44no—
72C22×Q8×C101—21no—
73C22×Q8×C101C2311yescharacteristic
74C22×D4×C101—21no—
75C22×D4×C101—21no—
76C22×D4×C101—21no—
77C22×D4×C101—21no—
78C22×D4×C101D411yescharacteristic
79C22×D4×C101C2311yescharacteristic
80C22×D4×C101C2311yescharacteristic
81C23×C4×C101—21no—
82C23×C4×C101—21no—
83C23×C4×C101—21no—
84C23×C4×C101—21no—
85C23×C4×C101C2311yescharacteristic
86C23×C4×C101C2311yescharacteristic
87C2×SD16×C101—22no—
88C2×SD16×C101—22no—
89C2×SD16×C101—41no—
90C2×D8×C101—22no—
91C2×D8×C101—22no—
92C2×D8×C101—41no—
93C2×M16×C101—22no—
94C2×M16×C101—41no—
95C2×M16×C101—41no—
96C22×C8×C101C2311yescharacteristic
97C22×C8×C101C2311yescharacteristic
98C22×C8×C101C2311yescharacteristic
99C22×C8×C101C2311yescharacteristic
100C4⋊Q8×C101—22no—
101C4⋊Q8×C101—22no—
102#123×C101—28no—
103#123×C101—28no—
104C22⋊Q8×C101—28no—
105C22⋊Q8×C101—22no—
106C22⋊Q8×C101—41no—
107#121×C101—22no—
108#121×C101—22no—
109#121×C101—22no—
110#121×C101—22no—
111#121×C101—41no—
112#121×C101D414yescomplemented
113C4×D4×C101—22no—
114C4×D4×C101—22no—
115C4×D4×C101—22no—
116C4×D4×C101—22no—
117C2×C4⋊C4×C101—21no—
118C2×C4⋊C4×C101—21no—
119C2×C4⋊C4×C101—22no—
120C2×C4⋊C4×C101—21no—
121C2×C4⋊C4×C101—22no—
122C2×C4⋊C4×C101—22no—
123C2×C4⋊C4×C101—21no—
124C2×C4⋊C4×C101D411yescharacteristic
125C2×C4⋊C4×C101D414yescomplemented
126C2×C4⋊C4×C101C2311yescharacteristic
127C2×C4⋊C4×C101C2311yescharacteristic
128C2×C4⋊C4×C101C2311yescharacteristic
129C2×C4⋊C4×C101C2311yescharacteristic
130C2×C4⋊C4×C101C2311yescharacteristic
131C2×C22⋊C4×C101—21no—
132C2×C22⋊C4×C101—21no—
133C2×C22⋊C4×C101—21no—
134C2×C22⋊C4×C101—21no—
135C2×C22⋊C4×C101—21no—
136C2×C22⋊C4×C101—21no—
137C2×C22⋊C4×C101—21no—
138C2×C22⋊C4×C101—21no—
139C2×C22⋊C4×C101D411yescharacteristic
140C2×C22⋊C4×C101D411yescharacteristic
141C2×C42×C101C2311yescharacteristic
142#103×C101—22no—
143#103×C101—22no—
144#103×C101—22no—
145#102×C101—22no—
146#102×C101—22no—
147#102×C101—22no—
148#102×C101—41no—
149#102×C101—41no—
150C22⋊C8×C101—22no—
151C22⋊C8×C101—41no—
152C22⋊C8×C101—41no—
153#95×C101—21no—
154#95×C101—21no—
155#95×C101—21no—
156C24×C101—21no—
157C24×C101—21no—
158C24×C101C2×D411yescharacteristic
159C24×C101C2×D411yescharacteristic
160#41×C101—28no—
161#41×C101—44no—
162#41×C101—44no—
163#41×C101—44no—
164#41×C101—432no—
165C2×Q8×C101—24no—
166C2×Q8×C101—21no—
167C2×Q8×C101—21no—
168C2×Q8×C101—21no—
169C2×Q8×C101—21no—
170C2×Q8×C101—21no—
171C2×Q8×C101—42no—
172C2×Q8×C101—42no—
173C2×Q8×C101#4112yescomplemented
174C2×D4×C101—22no—
175C2×D4×C101—22no—
176C2×D4×C101—24no—
177C2×D4×C101—24no—
178C2×D4×C101—22no—
179C2×D4×C101—21no—
180C2×D4×C101—21no—
181C2×D4×C101—21no—
182C2×D4×C101—21no—
183C2×D4×C101—21no—
184C2×D4×C101—21no—
185C2×D4×C101—21no—
186C2×D4×C101—21no—
187C2×D4×C101—21no—
188C2×D4×C101—21no—
189C2×D4×C101—42no—
190C2×D4×C101—42no—
191C2×D4×C101—42no—
192C2×D4×C101—42no—
193C2×D4×C101—42no—
194C2×D4×C101—42no—
195C2×D4×C101—42no—
196C2×D4×C101—42no—
197C2×D4×C101—42no—
198C2×D4×C101—81no—
199C2×D4×C101C2×D412yes—
200C2×D4×C101#4112yescomplemented
201C22×C4×C101—21no—
202C22×C4×C101—21no—
203C22×C4×C101—21no—
204C22×C4×C101—21no—
205C22×C4×C101—24no—
206C22×C4×C101—24no—
207C22×C4×C101—24no—
208C22×C4×C101—21no—
209C22×C4×C101—21no—
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—21no—
214C22×C4×C101—21no—
215C22×C4×C101—21no—
216C22×C4×C101—21no—
217C22×C4×C101—21no—
218C22×C4×C101—21no—
219C22×C4×C101—21no—
220C22×C4×C101—42no—
221C22×C4×C101—42no—
222C22×C4×C101—42no—
223C22×C4×C101—42no—
224C22×C4×C101—42no—
225C22×C4×C101—42no—
226C22×C4×C101—42no—
227C22×C4×C101—42no—
228C22×C4×C101—42no—
229C22×C4×C101C2×D411yescharacteristic
230C22×C4×C101C2×D411yescharacteristic
231C22×C4×C101C2×D411yescharacteristic
232C22×C4×C101C2×D412yes—
233C22×C4×C101C2×D412yes—
234C22×C4×C101C2×D411yescharacteristic
235C22×C4×C101C2411yescharacteristic
236SD16×C101—44no—
237D8×C101—44no—
238M16×C101—44no—
239C2×C8×C101—21no—
240C2×C8×C101—21no—
241C2×C8×C101—21no—
242C2×C8×C101—21no—
243C2×C8×C101—21no—
244C2×C8×C101—21no—
245C2×C8×C101—21no—
246C2×C8×C101—21no—
247C2×C8×C101—21no—
248C2×C8×C101—21no—
249C2×C8×C101—21no—
250C2×C8×C101—21no—
251C4⋊C4×C101—24no—
252C4⋊C4×C101—24no—
253C4⋊C4×C101—24no—
254C4⋊C4×C101—22no—
255C4⋊C4×C101—21no—
256C4⋊C4×C101—21no—
257C4⋊C4×C101—21no—
258C4⋊C4×C101—21no—
259C4⋊C4×C101—21no—
260C4⋊C4×C101—21no—
261C4⋊C4×C101—21no—
262C4⋊C4×C101—42no—
263C4⋊C4×C101C2×D412yes—
264C4⋊C4×C101C2×D412yes—
265C4⋊C4×C101C2×D412yes—
266C22⋊C4×C101—24no—
267C22⋊C4×C101—24no—
268C22⋊C4×C101—22no—
269C22⋊C4×C101—24no—
270C22⋊C4×C101—22no—
271C22⋊C4×C101—42no—
272C22⋊C4×C101—42no—
273C22⋊C4×C101—42no—
274C22⋊C4×C101—81no—
275C22⋊C4×C101—81no—
276C42×C101—21no—
277C42×C101—21no—
278C23×C101—21no—
279C23×C101—21no—
280C23×C101—21no—
281C23×C101—21no—
282C23×C101—21no—
283C23×C101—21no—
284C23×C101—21no—
285C23×C101—21no—
286C23×C101—21no—
287C23×C101—21no—
288C23×C101—21no—
289C23×C101—21no—
290C23×C101—22no—
291C23×C101—22no—
292C23×C101—41no—
293C23×C101—41no—
294C23×C101—41no—
295C23×C101—41no—
296C23×C101—41no—
297C23×C101—41no—
298C23×C101—41no—
299C23×C101—41no—
300C23×C101—41no—
301C23×C101—41no—
302C23×C101—41no—
303C23×C101—41no—
304C23×C101#12012yes—
305C23×C101AGL(1,ℤ/8)12yes—
306C23×C101C22×D411yescharacteristic
307Q8×C101—22no—
308Q8×C101—22no—
309Q8×C101—48no—
310Q8×C101—41no—
311Q8×C101—41no—
312D4×C101—28no—
313D4×C101—22no—
314D4×C101—22no—
315D4×C101—22no—
316D4×C101—22no—
317D4×C101—48no—
318D4×C101—48no—
319D4×C101—48no—
320D4×C101—41no—
321D4×C101—41no—
322D4×C101—41no—
323D4×C101—41no—
324D4×C101—84no—
325C2×C4×C101—21no—
326C2×C4×C101—21no—
327C2×C4×C101—21no—
328C2×C4×C101—21no—
329C2×C4×C101—22no—
330C2×C4×C101—22no—
331C2×C4×C101—22no—
332C2×C4×C101—22no—
333C2×C4×C101—21no—
334C2×C4×C101—21no—
335C2×C4×C101—22no—
336C2×C4×C101—22no—
337C2×C4×C101—22no—
338C2×C4×C101—21no—
339C2×C4×C101—22no—
340C2×C4×C101—21no—
341C2×C4×C101—21no—
342C2×C4×C101—21no—
343C2×C4×C101—48no—
344C2×C4×C101—48no—
345C2×C4×C101—48no—
346C2×C4×C101—48no—
347C2×C4×C101—41no—
348C2×C4×C101—41no—
349C2×C4×C101—41no—
350C2×C4×C101—41no—
351C2×C4×C101—41no—
352C2×C4×C101—41no—
353C2×C4×C101—41no—
354C2×C4×C101—41no—
355C2×C4×C101—41no—
356C2×C4×C101—41no—
357C2×C4×C101—41no—
358C2×C4×C101—41no—
359C2×C4×C101—41no—
360C2×C4×C101—41no—
361C2×C4×C101—41no—
362C2×C4×C101—41no—
363C2×C4×C101—41no—
364C2×C4×C101—41no—
365C2×C4×C101#12012yes—
366C2×C4×C101AGL(1,ℤ/8)12yes—
367C2×C4×C101C22×D411yescharacteristic
368C2×C4×C101C22×D411yescharacteristic
369C2×C4×C101C2×#4111yescharacteristic
370C2×C4×C101C2×#4111yescharacteristic
371C2×C4×C101H(5,𝔽2)11yescharacteristic
372C2×C4×C101H(5,𝔽2)11yescharacteristic
373C8×C101—41no—
374C8×C101—41no—
375C8×C101—41no—
376C8×C101—41no—
377C22×C101—22no—
378C22×C101—22no—
379C22×C101—22no—
380C22×C101—22no—
381C22×C101—22no—
382C22×C101—22no—
383C22×C101—41no—
384C22×C101—41no—
385C22×C101—41no—
386C22×C101—41no—
387C22×C101—41no—
388C22×C101—41no—
389C22×C101—41no—
390C22×C101—41no—
391C22×C101—42no—
392C22×C101—42no—
393C22×C101—42no—
394C22×C101—42no—
395C22×C101—42no—
396C22×C101—42no—
397C22×C101—81no—
398C22×C101—81no—
399C22×C101—81no—
400C22×C101—81no—
401C22×C101—81no—
402C22×C101—81no—
403C22×C101—81no—
404C22×C101—81no—
405C22×C101C2×#12011yescharacteristic
406C22×C101#54611yescharacteristic
407C22×C101#54611yescharacteristic
408C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C101#57711yescharacteristic
411C22×C101#57811yescharacteristic
412C4×C101—22no—
413C4×C101—22no—
414C4×C101—41no—
415C4×C101—42no—
416C4×C101—42no—
417C4×C101—42no—
418C4×C101—42no—
419C4×C101—41no—
420C4×C101—81no—
421C4×C101—81no—
422C4×C101#52511yescharacteristic
423C4×C101#53511yescharacteristic
424C4×C101#54611yescharacteristic
425C4×C101#54611yescharacteristic
426#23972C10111yesmaximal, characteristic, direct product factor, Sylow
427C2×C101—42no—
428C2×C101—42no—
429C2×C101—82no—
430C2×C101—82no—
431C2×C101#240411yescharacteristic
432C2×C101#300311yescharacteristic
433C2×C101#301311yescharacteristic
434C2×C101#330611yescharacteristic
435C2×C101#330811yescharacteristic
436C2×C101#333011yescharacteristic
437C2×C101#333211yescharacteristic
438C2×#547C2×C10111yescharacteristic, complemented
439C2×#449C2×C10111yescharacteristic, complemented
440C2×#417C2×C10111yescharacteristic, complemented
441#2407C2×C10111yescharacteristic, complemented
442#2024C2×C10111yescharacteristic, complemented
443#2023C2×C10111yescharacteristic, complemented
444#2000C2×C10111yescharacteristic, complemented
445#1999C2×C10111yescharacteristic, complemented
446#1895C2×C10111yescharacteristic, complemented
447#1879C2×C10111yescharacteristic, complemented
448#1877C2×C10111yescharacteristic, complemented
449#1874C2×C10111yescharacteristic, complemented
450#1872C2×C10111yescharacteristic, complemented
451#1870C2×C10111yescharacteristic, complemented
452#1824C2×C10111yescharacteristic, complemented
453C101#2397211yescharacteristic, direct product factor, Sylow
454C22×#41—21no—
455C22×#41C22×C10111yescharacteristic
456C22×SD16C22×C10111yescharacteristic
457C22×D8C22×C10111yescharacteristic
458C22×M16C22×C10111yescharacteristic
459#547—24no—
460#547—24no—
461C2×C4⋊Q8C22×C10111yescharacteristic
462C2×#123—21no—
463C2×#123—21no—
464C2×C22⋊Q8—21no—
465C2×C22⋊Q8C22×C10111yescharacteristic
466C2×#121C22×C10111yescharacteristic
467C2×#121C22×C10111yescharacteristic
468C2×#121C22×C10111yescharacteristic
469C2×C4×D4C22×C10111yescharacteristic
470C2×C4×D4C22×C10111yescharacteristic
471C22×C4⋊C4C22×C10111yescharacteristic
472C22×C4⋊C4C22×C10111yescharacteristic
473#449—24no—
474#417—24no—
475C2×#103C22×C10111yescharacteristic
476C2×#103C22×C10111yescharacteristic
477C2×#103C22×C10111yescharacteristic
478C2×#102C22×C10111yescharacteristic
479C2×#102C22×C10111yescharacteristic
480C2×#102C22×C10111yescharacteristic
481C2×#102C22×C10111yescharacteristic
482C2×#102C22×C10111yescharacteristic
483C2×C22⋊C8C22×C10111yescharacteristic
484C2×C22⋊C8C22×C10111yescharacteristic
485C2×C22⋊C8C22×C10111yescharacteristic
486#394—21no—
487#392—21no—
488#391C22×C10111yescharacteristic
489#390C22×C10111yescharacteristic
490#386—21no—
491#385—21no—
492#380C22×C10111yescharacteristic
493#340C22×C10111yescharacteristic
494#340C22×C10111yescharacteristic
495#340C22×C10111yescharacteristic
496#340C22×C10111yescharacteristic
497#340C22×C10111yescharacteristic
498#340C22×C10111yescharacteristic
499#336C22×C10111yescharacteristic
500#336C22×C10111yescharacteristic
501C2×#41—28no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—44no—
509C2×#41—44no—
510C22×Q8—21no—
511C22×Q8C23×C10111yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4D4×C10111yescharacteristic
517C22×D4C23×C10111yescharacteristic
518C22×D4C23×C10111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C23×C10111yescharacteristic
524C23×C4C23×C10111yescharacteristic
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—41no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C22×C8C23×C10111yescharacteristic
535C22×C8C23×C10111yescharacteristic
536C22×C8C23×C10111yescharacteristic
537C22×C8C23×C10111yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540#123—28no—
541#123—28no—
542C22⋊Q8—28no—
543C22⋊Q8—22no—
544C22⋊Q8—41no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—41no—
550#121D4×C10114yescomplemented
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4D4×C10111yescharacteristic
563C2×C4⋊C4D4×C10114yescomplemented
564C2×C4⋊C4C23×C10111yescharacteristic
565C2×C4⋊C4C23×C10111yescharacteristic
566C2×C4⋊C4C23×C10111yescharacteristic
567C2×C4⋊C4C23×C10111yescharacteristic
568C2×C4⋊C4C23×C10111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4D4×C10111yescharacteristic
578C2×C22⋊C4D4×C10111yescharacteristic
579C2×C42C23×C10111yescharacteristic
580#103—22no—
581#103—22no—
582#103—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—41no—
587#102—41no—
588C22⋊C8—22no—
589C22⋊C8—41no—
590C22⋊C8—41no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—21no—
595C24—21no—
596C24C2×D4×C10111yescharacteristic
597C24C2×D4×C10111yescharacteristic
598#41—28no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—432no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8#41×C10112yescomplemented
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4C2×D4×C10112yes—
638C2×D4#41×C10112yescomplemented
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C10111yescharacteristic
668C22×C4C2×D4×C10111yescharacteristic
669C22×C4C2×D4×C10111yescharacteristic
670C22×C4C2×D4×C10112yes—
671C22×C4C2×D4×C10112yes—
672C22×C4C2×D4×C10111yescharacteristic
673C22×C4C24×C10111yescharacteristic
674SD16—44no—
675D8—44no—
676M16—44no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—42no—
701C4⋊C4C2×D4×C10112yes—
702C4⋊C4C2×D4×C10112yes—
703C4⋊C4C2×D4×C10112yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—22no—
707C22⋊C4—24no—
708C22⋊C4—22no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23#120×C10112yes—
743C23AGL(1,ℤ/8)×C10112yes—
744C23C22×D4×C10111yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750D4—28no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4#120×C10112yes—
804C2×C4AGL(1,ℤ/8)×C10112yes—
805C2×C4C22×D4×C10111yescharacteristic
806C2×C4C22×D4×C10111yescharacteristic
807C2×C4C2×#41×C10111yescharacteristic
808C2×C4C2×#41×C10111yescharacteristic
809C2×C4H(5,𝔽2)×C10111yescharacteristic
810C2×C4H(5,𝔽2)×C10111yescharacteristic
811C8—41no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#120×C10111yescharacteristic
844C22#546×C10111yescharacteristic
845C22#546×C10111yescharacteristic
846C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
847C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
848C22#577×C10111yescharacteristic
849C22#578×C10111yescharacteristic
850C4—22no—
851C4—22no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—41no—
858C4—81no—
859C4—81no—
860C4#525×C10111yescharacteristic
861C4#535×C10111yescharacteristic
862C4#546×C10111yescharacteristic
863C4#546×C10111yescharacteristic
864C2—42no—
865C2—42no—
866C2—82no—
867C2—82no—
868C2C101×#240411yescharacteristic
869C2C101×#300311yescharacteristic
870C2C101×#301311yescharacteristic
871C2C101×#330611yescharacteristic
872C2C101×#330811yescharacteristic
873C2C101×#333011yescharacteristic
874C2C101×#333211yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C4×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#547×C101C2semidirect
2. C2×#449×C101C2semidirect
3. C2×#417×C101C2semidirect
4. C101×#2407C2semidirect
5. C101×#2024C2semidirect
6. C101×#2023C2semidirect
7. C101×#2000C2semidirect
8. C101×#1999C2semidirect
9. C101×#1895C2semidirect
10. C101×#1879C2semidirect
11. C101×#1877C2semidirect
12. C101×#1874C2semidirect
13. C101×#1872C2semidirect
14. C101×#1870C2semidirect
15. C101×#1824C2semidirect
112. #121×C101D4semidirect
125. C2×C4⋊C4×C101D4semidirect
173. C2×Q8×C101#41semidirect
200. C2×D4×C101#41semidirect
426. #23972C101direct (N × H)
438. C2×#547C2×C101semidirect
439. C2×#449C2×C101semidirect
440. C2×#417C2×C101semidirect
441. #2407C2×C101semidirect
442. #2024C2×C101semidirect
443. #2023C2×C101semidirect
444. #2000C2×C101semidirect
445. #1999C2×C101semidirect
446. #1895C2×C101semidirect
447. #1879C2×C101semidirect
448. #1877C2×C101semidirect
449. #1874C2×C101semidirect
450. #1872C2×C101semidirect
451. #1870C2×C101semidirect
452. #1824C2×C101semidirect
453. C101#23972direct (N × H)
550. #121D4×C101semidirect
563. C2×C4⋊C4D4×C101semidirect
611. C2×Q8#41×C101semidirect
638. C2×D4#41×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1012
C2×#449×C1012
C2×#417×C1012
C101×#24072
C101×#20242
C101×#20232
C101×#20002
C101×#19992
C101×#18952
C101×#18792
C101×#18772
C101×#18742
C101×#18722
C101×#18702
C101×#18242
#23972101