Finite Group Databasebeta

← C101×#24366 #38806517

Subgroups — C101×#24366 #38806517

Order 25856.

1662 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C101C211yesmaximal, characteristic, complemented
2C2×#463×C101C211yesmaximal, characteristic, complemented
3C2×#459×C101C211yesmaximal, characteristic, complemented
4C2×#447×C101C211yesmaximal, characteristic, complemented
5C101×#2431C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C101C211yesmaximal, characteristic, complemented
7C101×#2055C211yesmaximal, characteristic, complemented
8C101×#2054C211yesmaximal, characteristic, complemented
9C101×#2012C211yesmaximal, characteristic, complemented
10C101×#2011C211yesmaximal, characteristic, complemented
11C101×#1895C211yesmaximal, characteristic, complemented
12C101×#1879C211yesmaximal, characteristic, complemented
13C101×#1877C211yesmaximal, characteristic, complemented
14C101×#1851C211yesmaximal, characteristic, complemented
15C101×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×D4×C101C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C101—24no—
19C2×AGL(1,ℤ/8)×C101—24no—
20C2×AGL(1,ℤ/8)×C101—24no—
21C22×SD16×C101C2211yescharacteristic
22C22×SD16×C101C2211yescharacteristic
23C22×D8×C101C2211yescharacteristic
24C22×D8×C101C2211yescharacteristic
25C22×D8×C101C2211yescharacteristic
26C22×D8×C101C2211yescharacteristic
27C22×M16×C101C2211yescharacteristic
28C2×#127×C101C2211yescharacteristic, complemented
29C2×#124×C101C2211yescharacteristic, complemented
30C2×#121×C101C2211yescharacteristic
31C2×C4×D4×C101C2211yescharacteristic
32C2×C4×D4×C101C2211yescharacteristic
33C22×C22⋊C4×C101—21no—
34#463×C101—24no—
35#459×C101—24no—
36#447×C101—24no—
37C2×C4⋊C8×C101C2211yescharacteristic, complemented
38C2×C4⋊C8×C101C2211yescharacteristic, complemented
39C2×#103×C101C2211yescharacteristic, complemented
40C2×#103×C101C2211yescharacteristic, complemented
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic, complemented
44C2×#102×C101C2211yescharacteristic, complemented
45C2×#102×C101C2211yescharacteristic, complemented
46C2×#102×C101C2211yescharacteristic, complemented
47C2×C22⋊C8×C101C2211yescharacteristic
48#392×C101—21no—
49#392×C101—21no—
50#391×C101C2211yescharacteristic, complemented
51#390×C101C2211yescharacteristic
52#390×C101C2211yescharacteristic
53#390×C101C2211yescharacteristic, complemented
54#386×C101—21no—
55#386×C101—21no—
56#386×C101—21no—
57#386×C101—21no—
58#380×C101C2211yescharacteristic
59#379×C101—21no—
60C4×C22⋊C4×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic, complemented
62#340×C101C2211yescharacteristic, complemented
63#336×C101C2211yescharacteristic, complemented
64#336×C101C2211yescharacteristic, complemented
65C25×C101—21no—
66C2×#41×C101—22no—
67C2×#41×C101—22no—
68C2×#41×C101—22no—
69C2×#41×C101—22no—
70C2×#41×C101—41no—
71C2×#41×C101—41no—
72C22×Q8×C101C2311yescharacteristic
73C22×D4×C101—22no—
74C22×D4×C101—22no—
75C22×D4×C101—21no—
76C22×D4×C101—21no—
77C22×D4×C101—21no—
78C22×D4×C101—21no—
79C22×D4×C101—21no—
80C22×D4×C101—22no—
81C22×D4×C101—41no—
82C22×D4×C101—41no—
83C22×D4×C101D414yescomplemented
84C22×D4×C101C2311yescharacteristic
85C22×D4×C101C2311yescharacteristic
86C22×D4×C101C2311yescharacteristic
87C22×D4×C101C2311yescharacteristic
88C23×C4×C101—21no—
89C23×C4×C101—21no—
90C23×C4×C101—21no—
91C23×C4×C101C2311yescharacteristic
92AGL(1,ℤ/8)×C101—232no—
93C2×SD16×C101—22no—
94C2×SD16×C101—22no—
95C2×SD16×C101—22no—
96C2×SD16×C101—22no—
97C2×SD16×C101—22no—
98C2×SD16×C101D414yescomplemented
99C2×D8×C101—22no—
100C2×D8×C101—22no—
101C2×D8×C101—22no—
102C2×D8×C101—22no—
103C2×D8×C101—22no—
104C2×D8×C101—22no—
105C2×D8×C101—22no—
106C2×D8×C101—22no—
107C2×D8×C101—22no—
108C2×D8×C101—41no—
109C2×D8×C101—41no—
110C2×D8×C101D414yescomplemented
111C2×M16×C101—22no—
112C2×M16×C101—22no—
113C2×M16×C101—22no—
114C22×C8×C101C2311yescharacteristic
115C22×C8×C101C2311yescharacteristic
116C22×C8×C101C2311yescharacteristic
117C22×C8×C101C2311yescharacteristic
118#127×C101—22no—
119#127×C101—41no—
120#124×C101—22no—
121#124×C101—41no—
122#121×C101—22no—
123#121×C101—22no—
124C4×D4×C101—22no—
125C4×D4×C101—22no—
126C4×D4×C101—41no—
127C4×D4×C101—41no—
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×C101—21no—
140C2×C22⋊C4×C101—21no—
141C2×C22⋊C4×C101—21no—
142C2×C22⋊C4×C101—21no—
143C2×C22⋊C4×C101—44no—
144C2×C22⋊C4×C101D411yescharacteristic
145C2×C22⋊C4×C101D411yescharacteristic
146C2×C42×C101C2311yescharacteristic
147C2×C42×C101C2311yescharacteristic
148C4⋊C8×C101—22no—
149C4⋊C8×C101—22no—
150#103×C101—22no—
151#103×C101—41no—
152#102×C101—22no—
153#102×C101—22no—
154#102×C101—22no—
155#102×C101—22no—
156#102×C101—22no—
157#102×C101—41no—
158C22⋊C8×C101—22no—
159#95×C101—21no—
160#95×C101—21no—
161#95×C101—21no—
162#95×C101D411yescharacteristic
163#95×C101D411yescharacteristic
164C24×C101—21no—
165C24×C101—21no—
166C24×C101—21no—
167C24×C101—24no—
168C24×C101—21no—
169C24×C101—42no—
170C24×C101—42no—
171C24×C101—42no—
172C24×C101—42no—
173C24×C101—81no—
174C24×C101—81no—
175C24×C101C2×D411yescharacteristic
176#41×C101—28no—
177#41×C101—44no—
178#41×C101—44no—
179#41×C101—44no—
180C2×Q8×C101—21no—
181C2×Q8×C101—21no—
182C2×Q8×C101—21no—
183C2×Q8×C101—21no—
184C2×Q8×C101—21no—
185C2×Q8×C101C2×D412yes—
186C2×D4×C101—28no—
187C2×D4×C101—24no—
188C2×D4×C101—21no—
189C2×D4×C101—21no—
190C2×D4×C101—21no—
191C2×D4×C101—21no—
192C2×D4×C101—21no—
193C2×D4×C101—21no—
194C2×D4×C101—21no—
195C2×D4×C101—21no—
196C2×D4×C101—21no—
197C2×D4×C101—21no—
198C2×D4×C101—21no—
199C2×D4×C101—21no—
200C2×D4×C101—21no—
201C2×D4×C101—21no—
202C2×D4×C101—21no—
203C2×D4×C101—21no—
204C2×D4×C101—21no—
205C2×D4×C101—21no—
206C2×D4×C101—21no—
207C2×D4×C101—44no—
208C2×D4×C101—44no—
209C2×D4×C101—44no—
210C2×D4×C101—42no—
211C2×D4×C101—42no—
212C2×D4×C101—42no—
213C2×D4×C101—42no—
214C2×D4×C101—42no—
215C2×D4×C101—42no—
216C2×D4×C101—42no—
217C2×D4×C101—42no—
218C2×D4×C101—42no—
219C2×D4×C101—42no—
220C2×D4×C101—81no—
221C2×D4×C101—81no—
222C2×D4×C101—81no—
223C2×D4×C101—81no—
224C2×D4×C101C2×D412yes—
225C2×D4×C101C2×D412yes—
226C2×D4×C101C2×D412yes—
227C2×D4×C101C2×D412yes—
228C2×D4×C101C2×D412yes—
229C22×C4×C101—21no—
230C22×C4×C101—21no—
231C22×C4×C101—21no—
232C22×C4×C101—21no—
233C22×C4×C101—21no—
234C22×C4×C101—21no—
235C22×C4×C101—21no—
236C22×C4×C101—21no—
237C22×C4×C101—42no—
238C22×C4×C101—42no—
239C22×C4×C101—42no—
240C22×C4×C101—42no—
241C22×C4×C101—42no—
242C22×C4×C101—42no—
243C22×C4×C101—42no—
244C22×C4×C101—81no—
245C22×C4×C101—81no—
246C22×C4×C101C2×D411yescharacteristic
247C22×C4×C101C2×D411yescharacteristic
248C22×C4×C101C2×D411yescharacteristic
249C22×C4×C101C2×D411yescharacteristic
250C22×C4×C101C2×D412yes—
251C22×C4×C101C2×D411yescharacteristic
252C22×C4×C101#4112yes—
253C22×C4×C101C2411yescharacteristic
254SD16×C101—28no—
255SD16×C101—28no—
256D8×C101—28no—
257D8×C101—28no—
258D8×C101—44no—
259D8×C101—44no—
260M16×C101—28no—
261C2×C8×C101—21no—
262C2×C8×C101—21no—
263C2×C8×C101—21no—
264C2×C8×C101—21no—
265C2×C8×C101—21no—
266C2×C8×C101—21no—
267C2×C8×C101—21no—
268C2×C8×C101—21no—
269C2×C8×C101—21no—
270C2×C8×C101—21no—
271C2×C8×C101C2×D412yes—
272C2×C8×C101C2×D412yes—
273C4⋊C4×C101—21no—
274C4⋊C4×C101—21no—
275C4⋊C4×C101—21no—
276C4⋊C4×C101—21no—
277C4⋊C4×C101—21no—
278C4⋊C4×C101—21no—
279C22⋊C4×C101—22no—
280C22⋊C4×C101—41no—
281C22⋊C4×C101—42no—
282C22⋊C4×C101—42no—
283C22⋊C4×C101—42no—
284C22⋊C4×C101—42no—
285C22⋊C4×C101—42no—
286C22⋊C4×C101—42no—
287C22⋊C4×C101—42no—
288C22⋊C4×C101—42no—
289C22⋊C4×C101—81no—
290C22⋊C4×C101—81no—
291C22⋊C4×C101—81no—
292C22⋊C4×C101—81no—
293C42×C101—21no—
294C42×C101—21no—
295C42×C101—21no—
296C42×C101—21no—
297C23×C101—22no—
298C23×C101—22no—
299C23×C101—22no—
300C23×C101—21no—
301C23×C101—21no—
302C23×C101—21no—
303C23×C101—21no—
304C23×C101—21no—
305C23×C101—21no—
306C23×C101—22no—
307C23×C101—22no—
308C23×C101—48no—
309C23×C101—48no—
310C23×C101—41no—
311C23×C101—41no—
312C23×C101—41no—
313C23×C101—41no—
314C23×C101—41no—
315C23×C101—41no—
316C23×C101—41no—
317C23×C101—41no—
318C23×C101—41no—
319C23×C101—41no—
320C23×C101—41no—
321C23×C101—41no—
322C23×C101—41no—
323C23×C101—41no—
324C23×C101—41no—
325C23×C101—41no—
326C23×C101—41no—
327C23×C101—41no—
328C23×C101—41no—
329C23×C101—41no—
330C23×C101—41no—
331C23×C101—41no—
332C23×C101—41no—
333C23×C101—84no—
334C23×C101—84no—
335C23×C101—84no—
336C23×C101—84no—
337C23×C101—84no—
338C23×C101#12112yes—
339C23×C101C22×D411yescharacteristic
340Q8×C101—22no—
341Q8×C101—22no—
342Q8×C101—41no—
343Q8×C101—41no—
344D4×C101—22no—
345D4×C101—22no—
346D4×C101—22no—
347D4×C101—22no—
348D4×C101—22no—
349D4×C101—22no—
350D4×C101—22no—
351D4×C101—48no—
352D4×C101—48no—
353D4×C101—41no—
354D4×C101—41no—
355D4×C101—41no—
356D4×C101—41no—
357D4×C101—41no—
358D4×C101—41no—
359D4×C101—41no—
360D4×C101—41no—
361D4×C101—84no—
362D4×C101—84no—
363D4×C101—84no—
364D4×C101#12014yes—
365C2×C4×C101—21no—
366C2×C4×C101—21no—
367C2×C4×C101—21no—
368C2×C4×C101—21no—
369C2×C4×C101—22no—
370C2×C4×C101—22no—
371C2×C4×C101—22no—
372C2×C4×C101—22no—
373C2×C4×C101—21no—
374C2×C4×C101—21no—
375C2×C4×C101—21no—
376C2×C4×C101—22no—
377C2×C4×C101—21no—
378C2×C4×C101—21no—
379C2×C4×C101—21no—
380C2×C4×C101—21no—
381C2×C4×C101—21no—
382C2×C4×C101—21no—
383C2×C4×C101—48no—
384C2×C4×C101—41no—
385C2×C4×C101—41no—
386C2×C4×C101—41no—
387C2×C4×C101—41no—
388C2×C4×C101—41no—
389C2×C4×C101—41no—
390C2×C4×C101—41no—
391C2×C4×C101—41no—
392C2×C4×C101—41no—
393C2×C4×C101—41no—
394C2×C4×C101—41no—
395C2×C4×C101—84no—
396C2×C4×C101—84no—
397C2×C4×C101#12112yes—
398C2×C4×C101AGL(1,ℤ/8)12yescomplemented
399C2×C4×C101C22×D411yescharacteristic
400C2×C4×C101C22×D411yescharacteristic
401C2×C4×C101C22×D411yescharacteristic
402C2×C4×C101C2×#4111yescharacteristic
403C2×C4×C101H(5,𝔽2)11yescharacteristic
404C2×C4×C101H(5,𝔽2)11yescharacteristic
405C8×C101—22no—
406C8×C101—22no—
407C8×C101—41no—
408C8×C101—41no—
409C22×C101—22no—
410C22×C101—24no—
411C22×C101—22no—
412C22×C101—22no—
413C22×C101—42no—
414C22×C101—41no—
415C22×C101—41no—
416C22×C101—42no—
417C22×C101—41no—
418C22×C101—42no—
419C22×C101—42no—
420C22×C101—41no—
421C22×C101—42no—
422C22×C101—42no—
423C22×C101—42no—
424C22×C101—42no—
425C22×C101—42no—
426C22×C101—42no—
427C22×C101—42no—
428C22×C101—42no—
429C22×C101—816no—
430C22×C101—81no—
431C22×C101—81no—
432C22×C101—81no—
433C22×C101—81no—
434C22×C101—81no—
435C22×C101—81no—
436C22×C101—81no—
437C22×C101—81no—
438C22×C101—81no—
439C22×C101—81no—
440C22×C101—81no—
441C22×C101—81no—
442C22×C101—81no—
443C22×C101—81no—
444C22×C101—81no—
445C22×C101C2×#12111yescharacteristic
446C22×C101D4211yescharacteristic
447C22×C101D4211yescharacteristic
448C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
449C22×C101#57511yescharacteristic
450C22×C101#57611yescharacteristic
451C22×C101#57611yescharacteristic
452C4×C101—22no—
453C4×C101—22no—
454C4×C101—42no—
455C4×C101—41no—
456C4×C101—41no—
457C4×C101—41no—
458C4×C101—81no—
459C4×C101—81no—
460C4×C101—81no—
461C4×C101C2×#12011yescharacteristic
462C4×C101#53411yescharacteristic
463C4×C101#54611yescharacteristic
464C4×C101#54611yescharacteristic
465#24366C10111yesmaximal, characteristic, direct product factor, Sylow
466C2×C101—42no—
467C2×C101—44no—
468C2×C101—82no—
469C2×C101—82no—
470C2×C101—161no—
471C2×C101#241011yescharacteristic
472C2×C101#303611yescharacteristic
473C2×C101#304111yescharacteristic
474C2×C101#326411yescharacteristic
475C2×C101#326811yescharacteristic
476C2×C101#327311yescharacteristic
477C2×C101#327411yescharacteristic
478C22×AGL(1,ℤ/8)C2×C10111yescharacteristic, complemented
479C2×#463C2×C10111yescharacteristic, complemented
480C2×#459C2×C10111yescharacteristic, complemented
481C2×#447C2×C10111yescharacteristic, complemented
482#2431C2×C10111yescharacteristic, complemented
483D4×C22⋊C4C2×C10111yescharacteristic, complemented
484#2055C2×C10111yescharacteristic, complemented
485#2054C2×C10111yescharacteristic, complemented
486#2012C2×C10111yescharacteristic, complemented
487#2011C2×C10111yescharacteristic, complemented
488#1895C2×C10111yescharacteristic, complemented
489#1879C2×C10111yescharacteristic, complemented
490#1877C2×C10111yescharacteristic, complemented
491#1851C2×C10111yescharacteristic, complemented
492#1788C2×C10111yescharacteristic, complemented
493C101#2436611yescharacteristic, direct product factor, Sylow
494C22×#41C22×C10111yescharacteristic
495C23×D4C22×C10111yescharacteristic
496C2×AGL(1,ℤ/8)—24no—
497C2×AGL(1,ℤ/8)—24no—
498C2×AGL(1,ℤ/8)—24no—
499C22×SD16C22×C10111yescharacteristic
500C22×SD16C22×C10111yescharacteristic
501C22×D8C22×C10111yescharacteristic
502C22×D8C22×C10111yescharacteristic
503C22×D8C22×C10111yescharacteristic
504C22×D8C22×C10111yescharacteristic
505C22×M16C22×C10111yescharacteristic
506C2×#127C22×C10111yescharacteristic, complemented
507C2×#124C22×C10111yescharacteristic, complemented
508C2×#121C22×C10111yescharacteristic
509C2×C4×D4C22×C10111yescharacteristic
510C2×C4×D4C22×C10111yescharacteristic
511C22×C22⋊C4—21no—
512#463—24no—
513#459—24no—
514#447—24no—
515C2×C4⋊C8C22×C10111yescharacteristic, complemented
516C2×C4⋊C8C22×C10111yescharacteristic, complemented
517C2×#103C22×C10111yescharacteristic, complemented
518C2×#103C22×C10111yescharacteristic, complemented
519C2×#102C22×C10111yescharacteristic
520C2×#102C22×C10111yescharacteristic
521C2×#102C22×C10111yescharacteristic, complemented
522C2×#102C22×C10111yescharacteristic, complemented
523C2×#102C22×C10111yescharacteristic, complemented
524C2×#102C22×C10111yescharacteristic, complemented
525C2×C22⋊C8C22×C10111yescharacteristic
526#392—21no—
527#392—21no—
528#391C22×C10111yescharacteristic, complemented
529#390C22×C10111yescharacteristic
530#390C22×C10111yescharacteristic
531#390C22×C10111yescharacteristic, complemented
532#386—21no—
533#386—21no—
534#386—21no—
535#386—21no—
536#380C22×C10111yescharacteristic
537#379—21no—
538C4×C22⋊C4C22×C10111yescharacteristic
539#340C22×C10111yescharacteristic, complemented
540#340C22×C10111yescharacteristic, complemented
541#336C22×C10111yescharacteristic, complemented
542#336C22×C10111yescharacteristic, complemented
543C25—21no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—41no—
549C2×#41—41no—
550C22×Q8C23×C10111yescharacteristic
551C22×D4—22no—
552C22×D4—22no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4D4×C10114yescomplemented
562C22×D4C23×C10111yescharacteristic
563C22×D4C23×C10111yescharacteristic
564C22×D4C23×C10111yescharacteristic
565C22×D4C23×C10111yescharacteristic
566C23×C4—21no—
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C10111yescharacteristic
570AGL(1,ℤ/8)—232no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16D4×C10114yescomplemented
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—41no—
587C2×D8—41no—
588C2×D8D4×C10114yescomplemented
589C2×M16—22no—
590C2×M16—22no—
591C2×M16—22no—
592C22×C8C23×C10111yescharacteristic
593C22×C8C23×C10111yescharacteristic
594C22×C8C23×C10111yescharacteristic
595C22×C8C23×C10111yescharacteristic
596#127—22no—
597#127—41no—
598#124—22no—
599#124—41no—
600#121—22no—
601#121—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—41no—
605C4×D4—41no—
606C2×C4⋊C4C23×C10111yescharacteristic
607C2×C4⋊C4C23×C10111yescharacteristic
608C2×C4⋊C4C23×C10111yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—44no—
622C2×C22⋊C4D4×C10111yescharacteristic
623C2×C22⋊C4D4×C10111yescharacteristic
624C2×C42C23×C10111yescharacteristic
625C2×C42C23×C10111yescharacteristic
626C4⋊C8—22no—
627C4⋊C8—22no—
628#103—22no—
629#103—41no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95D4×C10111yescharacteristic
641#95D4×C10111yescharacteristic
642C24—21no—
643C24—21no—
644C24—21no—
645C24—24no—
646C24—21no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—81no—
652C24—81no—
653C24C2×D4×C10111yescharacteristic
654#41—28no—
655#41—44no—
656#41—44no—
657#41—44no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8C2×D4×C10112yes—
664C2×D4—28no—
665C2×D4—24no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C2×D4×C10112yes—
703C2×D4C2×D4×C10112yes—
704C2×D4C2×D4×C10112yes—
705C2×D4C2×D4×C10112yes—
706C2×D4C2×D4×C10112yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—81no—
723C22×C4—81no—
724C22×C4C2×D4×C10111yescharacteristic
725C22×C4C2×D4×C10111yescharacteristic
726C22×C4C2×D4×C10111yescharacteristic
727C22×C4C2×D4×C10111yescharacteristic
728C22×C4C2×D4×C10112yes—
729C22×C4C2×D4×C10111yescharacteristic
730C22×C4#41×C10112yes—
731C22×C4C24×C10111yescharacteristic
732SD16—28no—
733SD16—28no—
734D8—28no—
735D8—28no—
736D8—44no—
737D8—44no—
738M16—28no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8C2×D4×C10112yes—
750C2×C8C2×D4×C10112yes—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C22⋊C4—22no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4—81no—
769C22⋊C4—81no—
770C22⋊C4—81no—
771C42—21no—
772C42—21no—
773C42—21no—
774C42—21no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—48no—
787C23—48no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23#121×C10112yes—
817C23C22×D4×C10111yescharacteristic
818Q8—22no—
819Q8—22no—
820Q8—41no—
821Q8—41no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—48no—
830D4—48no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4#120×C10114yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—84no—
874C2×C4—84no—
875C2×C4#121×C10112yes—
876C2×C4AGL(1,ℤ/8)×C10112yescomplemented
877C2×C4C22×D4×C10111yescharacteristic
878C2×C4C22×D4×C10111yescharacteristic
879C2×C4C22×D4×C10111yescharacteristic
880C2×C4C2×#41×C10111yescharacteristic
881C2×C4H(5,𝔽2)×C10111yescharacteristic
882C2×C4H(5,𝔽2)×C10111yescharacteristic
883C8—22no—
884C8—22no—
885C8—41no—
886C8—41no—
887C22—22no—
888C22—24no—
889C22—22no—
890C22—22no—
891C22—42no—
892C22—41no—
893C22—41no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—816no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22C2×#121×C10111yescharacteristic
924C22D42×C10111yescharacteristic
925C22D42×C10111yescharacteristic
926C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
927C22#575×C10111yescharacteristic
928C22#576×C10111yescharacteristic
929C22#576×C10111yescharacteristic
930C4—22no—
931C4—22no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C4C2×#120×C10111yescharacteristic
940C4#534×C10111yescharacteristic
941C4#546×C10111yescharacteristic
942C4#546×C10111yescharacteristic
943C2—42no—
944C2—44no—
945C2—82no—
946C2—82no—
947C2—161no—
948C2C101×#241011yescharacteristic
949C2C101×#303611yescharacteristic
950C2C101×#304111yescharacteristic
951C2C101×#326411yescharacteristic
952C2C101×#326811yescharacteristic
953C2C101×#327311yescharacteristic
954C2C101×#327411yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C4×C22⋊C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C101C2semidirect
2. C2×#463×C101C2semidirect
3. C2×#459×C101C2semidirect
4. C2×#447×C101C2semidirect
5. C101×#2431C2semidirect
6. D4×C22⋊C4×C101C2semidirect
7. C101×#2055C2semidirect
8. C101×#2054C2semidirect
9. C101×#2012C2semidirect
10. C101×#2011C2semidirect
11. C101×#1895C2semidirect
12. C101×#1879C2semidirect
13. C101×#1877C2semidirect
14. C101×#1851C2semidirect
15. C101×#1788C2semidirect
28. C2×#127×C101C22semidirect
29. C2×#124×C101C22semidirect
37. C2×C4⋊C8×C101C22semidirect
38. C2×C4⋊C8×C101C22semidirect
39. C2×#103×C101C22semidirect
40. C2×#103×C101C22semidirect
43. C2×#102×C101C22semidirect
44. C2×#102×C101C22semidirect
45. C2×#102×C101C22semidirect
46. C2×#102×C101C22semidirect
50. #391×C101C22semidirect
53. #390×C101C22semidirect
61. #340×C101C22semidirect
62. #340×C101C22semidirect
63. #336×C101C22semidirect
64. #336×C101C22semidirect
83. C22×D4×C101D4semidirect
98. C2×SD16×C101D4semidirect
110. C2×D8×C101D4semidirect
398. C2×C4×C101AGL(1,ℤ/8)semidirect
465. #24366C101direct (N × H)
478. C22×AGL(1,ℤ/8)C2×C101semidirect
479. C2×#463C2×C101semidirect
480. C2×#459C2×C101semidirect
481. C2×#447C2×C101semidirect
482. #2431C2×C101semidirect
483. D4×C22⋊C4C2×C101semidirect
484. #2055C2×C101semidirect
485. #2054C2×C101semidirect
486. #2012C2×C101semidirect
487. #2011C2×C101semidirect
488. #1895C2×C101semidirect
489. #1879C2×C101semidirect
490. #1877C2×C101semidirect
491. #1851C2×C101semidirect
492. #1788C2×C101semidirect
493. C101#24366direct (N × H)
506. C2×#127C22×C101semidirect
507. C2×#124C22×C101semidirect
515. C2×C4⋊C8C22×C101semidirect
516. C2×C4⋊C8C22×C101semidirect
517. C2×#103C22×C101semidirect
518. C2×#103C22×C101semidirect
521. C2×#102C22×C101semidirect
522. C2×#102C22×C101semidirect
523. C2×#102C22×C101semidirect
524. C2×#102C22×C101semidirect
528. #391C22×C101semidirect
531. #390C22×C101semidirect
539. #340C22×C101semidirect
540. #340C22×C101semidirect
541. #336C22×C101semidirect
542. #336C22×C101semidirect
561. C22×D4D4×C101semidirect
576. C2×SD16D4×C101semidirect
588. C2×D8D4×C101semidirect
876. C2×C4AGL(1,ℤ/8)×C101semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1012
C2×#463×C1012
C2×#459×C1012
C2×#447×C1012
C101×#24312
D4×C22⋊C4×C1012
C101×#20552
C101×#20542
C101×#20122
C101×#20112
C101×#18952
C101×#18792
C101×#18772
C101×#18512
C101×#17882
#24366101