Finite Group Databasebeta

← C101×#24044 #38806195

Subgroups — C101×#24044 #38806195

Order 25856.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C101C211yesmaximal, characteristic
2C2×#482×C101C211yesmaximal, characteristic, complemented
3C2×#418×C101C211yesmaximal, characteristic, complemented
4C101×#2485C211yesmaximal, characteristic, complemented
5C101×#2041C211yesmaximal, characteristic, complemented
6C101×#2041C211yesmaximal, characteristic, complemented
7C101×#2034C211yesmaximal, characteristic, complemented
8C101×#2033C211yesmaximal, characteristic, complemented
9C101×#1895C211yesmaximal, characteristic, complemented
10C101×#1870C211yesmaximal, characteristic, complemented
11C101×#1864C211yesmaximal, characteristic, complemented
12C101×#1862C211yesmaximal, characteristic, complemented
13C101×#1786C211yesmaximal, characteristic, complemented
14C101×#1786C211yesmaximal, characteristic, complemented
15C101×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C101—21no—
17C23×D4×C101C2211yescharacteristic
18C23×D4×C101C2211yescharacteristic
19C22×M16×C101C2211yescharacteristic, complemented
20D42×C101—24no—
21D42×C101—24no—
22C2×#127×C101C2211yescharacteristic
23C2×#121×C101—21no—
24C2×#121×C101C2211yescharacteristic
25C2×#121×C101C2211yescharacteristic
26C2×#120×C101—21no—
27C2×#120×C101—21no—
28C2×C4×D4×C101C2211yescharacteristic
29C2×C4×D4×C101C2211yescharacteristic
30C2×#117×C101C2211yescharacteristic, complemented
31#482×C101—24no—
32C2×#107×C101C2211yescharacteristic, complemented
33C2×#106×C101C2211yescharacteristic, complemented
34#418×C101—24no—
35C2×#102×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic, complemented
40C2×#102×C101C2211yescharacteristic, complemented
41C2×#102×C101C2211yescharacteristic, complemented
42C2×#102×C101C2211yescharacteristic, complemented
43C2×#102×C101C2211yescharacteristic, complemented
44C2×#102×C101C2211yescharacteristic, complemented
45C2×#102×C101C2211yescharacteristic, complemented
46C2×#102×C101C2211yescharacteristic, complemented
47C2×C22⋊C8×C101C2211yescharacteristic, complemented
48C2×C22⋊C8×C101C2211yescharacteristic, complemented
49C2×C22⋊C8×C101C2211yescharacteristic, complemented
50#397×C101—21no—
51#394×C101—21no—
52#389×C101C2211yescharacteristic, complemented
53#389×C101C2211yescharacteristic, complemented
54#388×C101—21no—
55#387×C101—21no—
56#380×C101C2211yescharacteristic, complemented
57#380×C101C2211yescharacteristic, complemented
58#380×C101C2211yescharacteristic, complemented
59#340×C101C2211yescharacteristic, complemented
60#340×C101C2211yescharacteristic, complemented
61#336×C101C2211yescharacteristic, complemented
62#336×C101C2211yescharacteristic, complemented
63C25×C101—21no—
64C25×C101—21no—
65C22×D4×C101—22no—
66C22×D4×C101—22no—
67C22×D4×C101—28no—
68C22×D4×C101—21no—
69C22×D4×C101—21no—
70C22×D4×C101—22no—
71C22×D4×C101—22no—
72C22×D4×C101—22no—
73C22×D4×C101—22no—
74C22×D4×C101—21no—
75C22×D4×C101—21no—
76C22×D4×C101—21no—
77C22×D4×C101—22no—
78C22×D4×C101—21no—
79C22×D4×C101—41no—
80C22×D4×C101—41no—
81C22×D4×C101—41no—
82C22×D4×C101—41no—
83C22×D4×C101—44no—
84C22×D4×C101—44no—
85C22×D4×C101D411yescharacteristic
86C22×D4×C101D414yes—
87C22×D4×C101C2311yescharacteristic
88C22×D4×C101C2311yescharacteristic
89C22×D4×C101C2311yescharacteristic
90C23×C4×C101—21no—
91C23×C4×C101C2311yescharacteristic
92C23×C4×C101C2311yescharacteristic
93C2×M16×C101—22no—
94C2×M16×C101—41no—
95C2×M16×C101—41no—
96C22×C8×C101C2311yescharacteristic
97C22×C8×C101C2311yescharacteristic
98C22×C8×C101C2311yescharacteristic
99C22×C8×C101C2311yescharacteristic
100#127×C101—22no—
101#127×C101—22no—
102#121×C101—28no—
103#121×C101—22no—
104#121×C101—22no—
105#121×C101—22no—
106#121×C101D414yes—
107#120×C101—28no—
108#120×C101—28no—
109C4×D4×C101—22no—
110C4×D4×C101—22no—
111C4×D4×C101—22no—
112C4×D4×C101—22no—
113#117×C101—22no—
114#117×C101—22no—
115C2×C4⋊C4×C101—21no—
116C2×C4⋊C4×C101—21no—
117C2×C4⋊C4×C101D411yescharacteristic
118C2×C4⋊C4×C101C2311yescharacteristic
119C2×C4⋊C4×C101C2311yescharacteristic
120C2×C4⋊C4×C101C2311yescharacteristic
121C2×C4⋊C4×C101C2311yescharacteristic
122C2×C4⋊C4×C101C2311yescharacteristic
123C2×C22⋊C4×C101—21no—
124C2×C22⋊C4×C101—21no—
125C2×C22⋊C4×C101—21no—
126C2×C22⋊C4×C101—21no—
127C2×C22⋊C4×C101—21no—
128C2×C22⋊C4×C101—21no—
129C2×C22⋊C4×C101—21no—
130C2×C22⋊C4×C101D411yescharacteristic
131C2×C22⋊C4×C101D411yescharacteristic
132C2×C42×C101—21no—
133C2×C42×C101C2311yescharacteristic
134#107×C101—22no—
135#106×C101—22no—
136#102×C101—22no—
137#102×C101—22no—
138#102×C101—22no—
139#102×C101—22no—
140#102×C101—22no—
141#102×C101—22no—
142#102×C101—22no—
143#102×C101—22no—
144#102×C101—41no—
145#102×C101—41no—
146#102×C101—41no—
147#102×C101—41no—
148C22⋊C8×C101—22no—
149C22⋊C8×C101—41no—
150C22⋊C8×C101—41no—
151#95×C101—21no—
152#95×C101—21no—
153#95×C101—21no—
154#95×C101—21no—
155#95×C101—21no—
156C24×C101—21no—
157C24×C101—24no—
158C24×C101—21no—
159C24×C101—21no—
160C24×C101—24no—
161C24×C101—42no—
162C24×C101—42no—
163C24×C101—42no—
164C24×C101—42no—
165C24×C101—42no—
166C24×C101—42no—
167C24×C101—42no—
168C24×C101—42no—
169C24×C101—81no—
170C24×C101—81no—
171C24×C101—81no—
172C24×C101—81no—
173C24×C101C2×D411yescharacteristic
174C24×C101C2×D411yescharacteristic
175C2×D4×C101—22no—
176C2×D4×C101—22no—
177C2×D4×C101—28no—
178C2×D4×C101—24no—
179C2×D4×C101—24no—
180C2×D4×C101—24no—
181C2×D4×C101—24no—
182C2×D4×C101—24no—
183C2×D4×C101—24no—
184C2×D4×C101—22no—
185C2×D4×C101—21no—
186C2×D4×C101—21no—
187C2×D4×C101—21no—
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—44no—
199C2×D4×C101—44no—
200C2×D4×C101—44no—
201C2×D4×C101—42no—
202C2×D4×C101—42no—
203C2×D4×C101—42no—
204C2×D4×C101—42no—
205C2×D4×C101—42no—
206C2×D4×C101—44no—
207C2×D4×C101—44no—
208C2×D4×C101—432no—
209C2×D4×C101—44no—
210C2×D4×C101—42no—
211C2×D4×C101—42no—
212C2×D4×C101—42no—
213C2×D4×C101—42no—
214C2×D4×C101—44no—
215C2×D4×C101—42no—
216C2×D4×C101—81no—
217C2×D4×C101—81no—
218C2×D4×C101C2×D412yes—
219C2×D4×C101C2×D412yes—
220C2×D4×C101C2×D412yes—
221C2×D4×C101#4112yes—
222C2×D4×C101#4112yes—
223C22×C4×C101—21no—
224C22×C4×C101—21no—
225C22×C4×C101—21no—
226C22×C4×C101—21no—
227C22×C4×C101—24no—
228C22×C4×C101—21no—
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—21no—
238C22×C4×C101—21no—
239C22×C4×C101—42no—
240C22×C4×C101—42no—
241C22×C4×C101C2×D411yescharacteristic
242C22×C4×C101C2×D411yescharacteristic
243C22×C4×C101C2×D411yescharacteristic
244C22×C4×C101C2×D412yes—
245C22×C4×C101C2×D412yes—
246C22×C4×C101C2×D411yescharacteristic
247C22×C4×C101C2411yescharacteristic
248M16×C101—44no—
249C2×C8×C101—21no—
250C2×C8×C101—21no—
251C2×C8×C101—21no—
252C2×C8×C101—21no—
253C2×C8×C101—21no—
254C2×C8×C101—21no—
255C2×C8×C101—21no—
256C2×C8×C101—21no—
257C2×C8×C101—21no—
258C2×C8×C101—21no—
259C2×C8×C101—21no—
260C2×C8×C101—21no—
261C4⋊C4×C101—22no—
262C4⋊C4×C101—21no—
263C4⋊C4×C101—21no—
264C4⋊C4×C101—21no—
265C4⋊C4×C101—21no—
266C4⋊C4×C101—21no—
267C4⋊C4×C101—21no—
268C4⋊C4×C101—21no—
269C4⋊C4×C101—21no—
270C4⋊C4×C101—21no—
271C4⋊C4×C101—42no—
272C4⋊C4×C101—81no—
273C4⋊C4×C101C2×D412yes—
274C22⋊C4×C101—24no—
275C22⋊C4×C101—24no—
276C22⋊C4×C101—22no—
277C22⋊C4×C101—24no—
278C22⋊C4×C101—22no—
279C22⋊C4×C101—42no—
280C22⋊C4×C101—42no—
281C22⋊C4×C101—81no—
282C22⋊C4×C101—81no—
283C42×C101—21no—
284C42×C101—21no—
285C42×C101—42no—
286C23×C101—21no—
287C23×C101—22no—
288C23×C101—21no—
289C23×C101—21no—
290C23×C101—21no—
291C23×C101—21no—
292C23×C101—22no—
293C23×C101—22no—
294C23×C101—21no—
295C23×C101—21no—
296C23×C101—21no—
297C23×C101—21no—
298C23×C101—21no—
299C23×C101—21no—
300C23×C101—21no—
301C23×C101—22no—
302C23×C101—22no—
303C23×C101—48no—
304C23×C101—48no—
305C23×C101—48no—
306C23×C101—48no—
307C23×C101—41no—
308C23×C101—41no—
309C23×C101—41no—
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—84no—
324C23×C101—84no—
325C23×C101—84no—
326C23×C101—84no—
327C23×C101—84no—
328C23×C101—84no—
329C23×C101—84no—
330C23×C101—84no—
331C23×C101—84no—
332C23×C101—84no—
333C23×C101#12012yes—
334C23×C101AGL(1,ℤ/8)12yes—
335C23×C101C22×D411yescharacteristic
336D4×C101—28no—
337D4×C101—22no—
338D4×C101—22no—
339D4×C101—22no—
340D4×C101—22no—
341D4×C101—22no—
342D4×C101—22no—
343D4×C101—22no—
344D4×C101—48no—
345D4×C101—48no—
346D4×C101—48no—
347D4×C101—48no—
348D4×C101—48no—
349D4×C101—41no—
350D4×C101—41no—
351D4×C101—41no—
352D4×C101—41no—
353D4×C101—84no—
354D4×C101#12314yes—
355C2×C4×C101—21no—
356C2×C4×C101—21no—
357C2×C4×C101—21no—
358C2×C4×C101—21no—
359C2×C4×C101—22no—
360C2×C4×C101—22no—
361C2×C4×C101—22no—
362C2×C4×C101—22no—
363C2×C4×C101—21no—
364C2×C4×C101—21no—
365C2×C4×C101—22no—
366C2×C4×C101—21no—
367C2×C4×C101—21no—
368C2×C4×C101—21no—
369C2×C4×C101—21no—
370C2×C4×C101—48no—
371C2×C4×C101—41no—
372C2×C4×C101—41no—
373C2×C4×C101—41no—
374C2×C4×C101—41no—
375C2×C4×C101—41no—
376C2×C4×C101—41no—
377C2×C4×C101—41no—
378C2×C4×C101—41no—
379C2×C4×C101—41no—
380C2×C4×C101—41no—
381C2×C4×C101—41no—
382C2×C4×C101—41no—
383C2×C4×C101—41no—
384C2×C4×C101—41no—
385C2×C4×C101—41no—
386C2×C4×C101—41no—
387C2×C4×C101—41no—
388C2×C4×C101—41no—
389C2×C4×C101#12012yes—
390C2×C4×C101AGL(1,ℤ/8)12yes—
391C2×C4×C101C22×D411yescharacteristic
392C2×C4×C101C22×D411yescharacteristic
393C2×C4×C101C2×#4111yescharacteristic
394C2×C4×C101C2×#4111yescharacteristic
395C2×C4×C101H(5,𝔽2)11yescharacteristic
396C2×C4×C101H(5,𝔽2)11yescharacteristic
397C8×C101—41no—
398C8×C101—41no—
399C8×C101—41no—
400C8×C101—41no—
401C22×C101—22no—
402C22×C101—24no—
403C22×C101—22no—
404C22×C101—22no—
405C22×C101—22no—
406C22×C101—22no—
407C22×C101—22no—
408C22×C101—41no—
409C22×C101—42no—
410C22×C101—41no—
411C22×C101—42no—
412C22×C101—41no—
413C22×C101—42no—
414C22×C101—41no—
415C22×C101—42no—
416C22×C101—41no—
417C22×C101—41no—
418C22×C101—42no—
419C22×C101—41no—
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—816no—
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×C101C2×#12011yescharacteristic
439C22×C101#54611yescharacteristic
440C22×C101#54611yescharacteristic
441C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
442C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
443C22×C101#57611yescharacteristic
444C22×C101#57711yescharacteristic
445C4×C101—22no—
446C4×C101—22no—
447C4×C101—41no—
448C4×C101—42no—
449C4×C101—41no—
450C4×C101—81no—
451C4×C101—81no—
452C4×C101—81no—
453C4×C101—81no—
454C4×C101C2×#12311yescharacteristic
455C4×C101#53411yescharacteristic
456C4×C101#54611yescharacteristic
457C4×C101#54611yescharacteristic
458#24044C10111yesmaximal, characteristic, direct product factor, Sylow
459C2×C101—42no—
460C2×C101—42no—
461C2×C101—44no—
462C2×C101—82no—
463C2×C101—82no—
464C2×C101#240511yescharacteristic
465C2×C101#300311yescharacteristic
466C2×C101#301211yescharacteristic
467C2×C101#331011yescharacteristic
468C2×C101#331811yescharacteristic
469C2×C101#332411yescharacteristic
470C2×C101#332511yescharacteristic
471C2×D42C2×C10111yescharacteristic
472C2×#482C2×C10111yescharacteristic, complemented
473C2×#418C2×C10111yescharacteristic, complemented
474#2485C2×C10111yescharacteristic, complemented
475#2041C2×C10111yescharacteristic, complemented
476#2041C2×C10111yescharacteristic, complemented
477#2034C2×C10111yescharacteristic, complemented
478#2033C2×C10111yescharacteristic, complemented
479#1895C2×C10111yescharacteristic, complemented
480#1870C2×C10111yescharacteristic, complemented
481#1864C2×C10111yescharacteristic, complemented
482#1862C2×C10111yescharacteristic, complemented
483#1786C2×C10111yescharacteristic, complemented
484#1786C2×C10111yescharacteristic, complemented
485#1786C2×C10111yescharacteristic, complemented
486C101#2404411yescharacteristic, direct product factor, Sylow
487C23×D4—21no—
488C23×D4C22×C10111yescharacteristic
489C23×D4C22×C10111yescharacteristic
490C22×M16C22×C10111yescharacteristic, complemented
491D42—24no—
492D42—24no—
493C2×#127C22×C10111yescharacteristic
494C2×#121—21no—
495C2×#121C22×C10111yescharacteristic
496C2×#121C22×C10111yescharacteristic
497C2×#120—21no—
498C2×#120—21no—
499C2×C4×D4C22×C10111yescharacteristic
500C2×C4×D4C22×C10111yescharacteristic
501C2×#117C22×C10111yescharacteristic, complemented
502#482—24no—
503C2×#107C22×C10111yescharacteristic, complemented
504C2×#106C22×C10111yescharacteristic, complemented
505#418—24no—
506C2×#102C22×C10111yescharacteristic
507C2×#102C22×C10111yescharacteristic
508C2×#102C22×C10111yescharacteristic
509C2×#102C22×C10111yescharacteristic
510C2×#102C22×C10111yescharacteristic, complemented
511C2×#102C22×C10111yescharacteristic, complemented
512C2×#102C22×C10111yescharacteristic, complemented
513C2×#102C22×C10111yescharacteristic, complemented
514C2×#102C22×C10111yescharacteristic, complemented
515C2×#102C22×C10111yescharacteristic, complemented
516C2×#102C22×C10111yescharacteristic, complemented
517C2×#102C22×C10111yescharacteristic, complemented
518C2×C22⋊C8C22×C10111yescharacteristic, complemented
519C2×C22⋊C8C22×C10111yescharacteristic, complemented
520C2×C22⋊C8C22×C10111yescharacteristic, complemented
521#397—21no—
522#394—21no—
523#389C22×C10111yescharacteristic, complemented
524#389C22×C10111yescharacteristic, complemented
525#388—21no—
526#387—21no—
527#380C22×C10111yescharacteristic, complemented
528#380C22×C10111yescharacteristic, complemented
529#380C22×C10111yescharacteristic, complemented
530#340C22×C10111yescharacteristic, complemented
531#340C22×C10111yescharacteristic, complemented
532#336C22×C10111yescharacteristic, complemented
533#336C22×C10111yescharacteristic, complemented
534C25—21no—
535C25—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—28no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4—44no—
555C22×D4—44no—
556C22×D4D4×C10111yescharacteristic
557C22×D4D4×C10114yes—
558C22×D4C23×C10111yescharacteristic
559C22×D4C23×C10111yescharacteristic
560C22×D4C23×C10111yescharacteristic
561C23×C4—21no—
562C23×C4C23×C10111yescharacteristic
563C23×C4C23×C10111yescharacteristic
564C2×M16—22no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C23×C10111yescharacteristic
568C22×C8C23×C10111yescharacteristic
569C22×C8C23×C10111yescharacteristic
570C22×C8C23×C10111yescharacteristic
571#127—22no—
572#127—22no—
573#121—28no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121D4×C10114yes—
578#120—28no—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C10111yescharacteristic
589C2×C4⋊C4C23×C10111yescharacteristic
590C2×C4⋊C4C23×C10111yescharacteristic
591C2×C4⋊C4C23×C10111yescharacteristic
592C2×C4⋊C4C23×C10111yescharacteristic
593C2×C4⋊C4C23×C10111yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C10111yescharacteristic
602C2×C22⋊C4D4×C10111yescharacteristic
603C2×C42—21no—
604C2×C42C23×C10111yescharacteristic
605#107—22no—
606#106—22no—
607#102—22no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616#102—41no—
617#102—41no—
618#102—41no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—21no—
631C24—24no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24—81no—
641C24—81no—
642C24—81no—
643C24—81no—
644C24C2×D4×C10111yescharacteristic
645C24C2×D4×C10111yescharacteristic
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—432no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4C2×D4×C10112yes—
690C2×D4C2×D4×C10112yes—
691C2×D4C2×D4×C10112yes—
692C2×D4#41×C10112yes—
693C2×D4#41×C10112yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4C2×D4×C10111yescharacteristic
713C22×C4C2×D4×C10111yescharacteristic
714C22×C4C2×D4×C10111yescharacteristic
715C22×C4C2×D4×C10112yes—
716C22×C4C2×D4×C10112yes—
717C22×C4C2×D4×C10111yescharacteristic
718C22×C4C24×C10111yescharacteristic
719M16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C4⋊C4—22no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—42no—
743C4⋊C4—81no—
744C4⋊C4C2×D4×C10112yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—24no—
749C22⋊C4—22no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C22⋊C4—81no—
754C42—21no—
755C42—21no—
756C42—42no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23#120×C10112yes—
805C23AGL(1,ℤ/8)×C10112yes—
806C23C22×D4×C10111yescharacteristic
807D4—28no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—84no—
825D4#123×C10114yes—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—48no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4#120×C10112yes—
861C2×C4AGL(1,ℤ/8)×C10112yes—
862C2×C4C22×D4×C10111yescharacteristic
863C2×C4C22×D4×C10111yescharacteristic
864C2×C4C2×#41×C10111yescharacteristic
865C2×C4C2×#41×C10111yescharacteristic
866C2×C4H(5,𝔽2)×C10111yescharacteristic
867C2×C4H(5,𝔽2)×C10111yescharacteristic
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C22—22no—
873C22—24no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—42no—
885C22—41no—
886C22—42no—
887C22—41no—
888C22—41no—
889C22—42no—
890C22—41no—
891C22—41no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—816no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×#120×C10111yescharacteristic
910C22#546×C10111yescharacteristic
911C22#546×C10111yescharacteristic
912C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
913C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
914C22#576×C10111yescharacteristic
915C22#577×C10111yescharacteristic
916C4—22no—
917C4—22no—
918C4—41no—
919C4—42no—
920C4—41no—
921C4—81no—
922C4—81no—
923C4—81no—
924C4—81no—
925C4C2×#123×C10111yescharacteristic
926C4#534×C10111yescharacteristic
927C4#546×C10111yescharacteristic
928C4#546×C10111yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—82no—
934C2C101×#240511yescharacteristic
935C2C101×#300311yescharacteristic
936C2C101×#301211yescharacteristic
937C2C101×#331011yescharacteristic
938C2C101×#331811yescharacteristic
939C2C101×#332411yescharacteristic
940C2C101×#332511yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×D42×C101C2
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
2. C2×#482×C101C2semidirect
3. C2×#418×C101C2semidirect
4. C101×#2485C2semidirect
5. C101×#2041C2semidirect
6. C101×#2041C2semidirect
7. C101×#2034C2semidirect
8. C101×#2033C2semidirect
9. C101×#1895C2semidirect
10. C101×#1870C2semidirect
11. C101×#1864C2semidirect
12. C101×#1862C2semidirect
13. C101×#1786C2semidirect
14. C101×#1786C2semidirect
15. C101×#1786C2semidirect
19. C22×M16×C101C22semidirect
30. C2×#117×C101C22semidirect
32. C2×#107×C101C22semidirect
33. C2×#106×C101C22semidirect
39. C2×#102×C101C22semidirect
40. C2×#102×C101C22semidirect
41. C2×#102×C101C22semidirect
42. C2×#102×C101C22semidirect
43. C2×#102×C101C22semidirect
44. C2×#102×C101C22semidirect
45. C2×#102×C101C22semidirect
46. C2×#102×C101C22semidirect
47. C2×C22⋊C8×C101C22semidirect
48. C2×C22⋊C8×C101C22semidirect
49. C2×C22⋊C8×C101C22semidirect
52. #389×C101C22semidirect
53. #389×C101C22semidirect
56. #380×C101C22semidirect
57. #380×C101C22semidirect
58. #380×C101C22semidirect
59. #340×C101C22semidirect
60. #340×C101C22semidirect
61. #336×C101C22semidirect
62. #336×C101C22semidirect
458. #24044C101direct (N × H)
472. C2×#482C2×C101semidirect
473. C2×#418C2×C101semidirect
474. #2485C2×C101semidirect
475. #2041C2×C101semidirect
476. #2041C2×C101semidirect
477. #2034C2×C101semidirect
478. #2033C2×C101semidirect
479. #1895C2×C101semidirect
480. #1870C2×C101semidirect
481. #1864C2×C101semidirect
482. #1862C2×C101semidirect
483. #1786C2×C101semidirect
484. #1786C2×C101semidirect
485. #1786C2×C101semidirect
486. C101#24044direct (N × H)
490. C22×M16C22×C101semidirect
501. C2×#117C22×C101semidirect
503. C2×#107C22×C101semidirect
504. C2×#106C22×C101semidirect
510. C2×#102C22×C101semidirect
511. C2×#102C22×C101semidirect
512. C2×#102C22×C101semidirect
513. C2×#102C22×C101semidirect
514. C2×#102C22×C101semidirect
515. C2×#102C22×C101semidirect
516. C2×#102C22×C101semidirect
517. C2×#102C22×C101semidirect
518. C2×C22⋊C8C22×C101semidirect
519. C2×C22⋊C8C22×C101semidirect
520. C2×C22⋊C8C22×C101semidirect
523. #389C22×C101semidirect
524. #389C22×C101semidirect
527. #380C22×C101semidirect
528. #380C22×C101semidirect
529. #380C22×C101semidirect
530. #340C22×C101semidirect
531. #340C22×C101semidirect
532. #336C22×C101semidirect
533. #336C22×C101semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1012
C2×#482×C1012
C2×#418×C1012
C101×#24852
C101×#20412
C101×#20342
C101×#20332
C101×#18952
C101×#18702
C101×#18642
C101×#18622
C101×#17862
#24044101