Finite Group Databasebeta

← C41×#9497 #23785698

Subgroups — C41×#9497 #23785698

Order 10496.

1184 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2403C211yesmaximal, characteristic
2C41×#2309C211yesmaximal, characteristic, complemented
3C41×#1781C212yesmaximal, complemented
4C41×#1781C211yesmaximal, characteristic, complemented
5C41×#1304C212yesmaximal, complemented
6C23×D4×C41C2211yescharacteristic
7C23×D4×C41C2211yescharacteristic
8C2×#120×C41—21no—
9C2×#120×C41C412yescomplemented
10C2×#117×C41—21no—
11C2×#99×C41—22no—
12C2×#99×C41—24no—
13C41×#392—22no—
14C41×#390—24no—
15C41×#386—21no—
16C41×#386C412yescomplemented
17C41×#379—21no—
18C41×#379C2212yes—
19C41×#379C2211yescharacteristic
20C41×#379C2212yes—
21C25×C41C2×C411yescharacteristic
22C25×C41D411yescharacteristic
23C25×C41C2311yescharacteristic
24C22×D4×C41—21no—
25C22×D4×C41—22no—
26C22×D4×C41—22no—
27C22×D4×C41—22no—
28C22×D4×C41—21no—
29C22×D4×C41—22no—
30C22×D4×C41—22no—
31C22×D4×C41—44no—
32C22×D4×C41—44no—
33C22×D4×C41C2×C412yes—
34C22×D4×C41D412yes—
35C23×C4×C41C2×C411yescharacteristic
36C23×C4×C41D411yescharacteristic
37#120×C41—44no—
38#120×C41—44no—
39#117×C41—44no—
40C2×C4⋊C4×C41—22no—
41C2×C22⋊C4×C41—22no—
42C2×C22⋊C4×C41—22no—
43C2×C22⋊C4×C41—21no—
44C2×C22⋊C4×C41—22no—
45C2×C22⋊C4×C41—22no—
46C2×C22⋊C4×C41—22no—
47C2×C22⋊C4×C41—22no—
48C2×C22⋊C4×C41—22no—
49C2×C22⋊C4×C41—22no—
50C2×C22⋊C4×C41—21no—
51C2×C22⋊C4×C41—22no—
52C2×C22⋊C4×C41C2×C412yes—
53C2×C22⋊C4×C41D414yescomplemented
54C2×C42×C41—22no—
55#99×C41—48no—
56#99×C41—44no—
57#95×C41—22no—
58C24×C41—21no—
59C24×C41—21no—
60C24×C41—22no—
61C24×C41—21no—
62C24×C41—42no—
63C24×C41—42no—
64C24×C41—42no—
65C24×C41—42no—
66C24×C41—42no—
67C24×C41—42no—
68C24×C41—81no—
69C24×C41—81no—
70C24×C41—81no—
71C24×C41C22⋊C412yes—
72C24×C41C22×C411yescharacteristic
73C24×C41C2×D411yescharacteristic
74C24×C41C2×D411yescharacteristic
75C24×C41C2×D412yes—
76C24×C41#4112yes—
77C2×D4×C41—28no—
78C2×D4×C41—24no—
79C2×D4×C41—24no—
80C2×D4×C41—24no—
81C2×D4×C41—24no—
82C2×D4×C41—24no—
83C2×D4×C41—42no—
84C2×D4×C41—42no—
85C2×D4×C41—44no—
86C2×D4×C41—44no—
87C2×D4×C41—48no—
88C2×D4×C41—42no—
89C2×D4×C41—44no—
90C2×D4×C41—42no—
91C2×D4×C41—44no—
92C2×D4×C41—42no—
93C2×D4×C41—44no—
94C2×D4×C41—41no—
95C2×D4×C41—42no—
96C2×D4×C41—41no—
97C2×D4×C41—44no—
98C2×D4×C41—44no—
99C2×D4×C41—82no—
100C22×C4×C41—21no—
101C22×C4×C41—21no—
102C22×C4×C41—24no—
103C22×C4×C41—21no—
104C22×C4×C41—22no—
105C22×C4×C41—22no—
106C22×C4×C41—24no—
107C22×C4×C41—42no—
108C22×C4×C41—42no—
109C22×C4×C41C22⋊C412yes—
110C4⋊C4×C41—44no—
111C22⋊C4×C41—44no—
112C22⋊C4×C41—44no—
113C22⋊C4×C41—42no—
114C22⋊C4×C41—44no—
115C22⋊C4×C41—44no—
116C22⋊C4×C41—42no—
117C22⋊C4×C41—44no—
118C22⋊C4×C41—44no—
119C22⋊C4×C41—82no—
120C22⋊C4×C41—82no—
121C22⋊C4×C41—81no—
122C22⋊C4×C41—82no—
123C22⋊C4×C41—82no—
124C42×C41—44no—
125C23×C41—22no—
126C23×C41—22no—
127C23×C41—22no—
128C23×C41—22no—
129C23×C41—24no—
130C23×C41—22no—
131C23×C41—24no—
132C23×C41—22no—
133C23×C41—22no—
134C23×C41—22no—
135C23×C41—41no—
136C23×C41—41no—
137C23×C41—41no—
138C23×C41—42no—
139C23×C41—41no—
140C23×C41—42no—
141C23×C41—41no—
142C23×C41—42no—
143C23×C41—42no—
144C23×C41—42no—
145C23×C41—42no—
146C23×C41—42no—
147C23×C41—42no—
148C23×C41—41no—
149C23×C41—42no—
150C23×C41—42no—
151C23×C41—42no—
152C23×C41—42no—
153C23×C41—41no—
154C23×C41—42no—
155C23×C41—42no—
156C23×C41—81no—
157C23×C41—81no—
158C23×C41—82no—
159C23×C41—82no—
160C23×C41—88no—
161C23×C41—88no—
162C23×C41—88no—
163C23×C41C2×C22⋊C411yescharacteristic
164C23×C41C4×D412yes—
165C23×C41#12011yescharacteristic
166C23×C41#12112yes—
167C23×C41#12311yescharacteristic
168D4×C41—48no—
169D4×C41—48no—
170D4×C41—48no—
171D4×C41—44no—
172D4×C41—44no—
173D4×C41—88no—
174C2×C4×C41—22no—
175C2×C4×C41—22no—
176C2×C4×C41—24no—
177C2×C4×C41—22no—
178C2×C4×C41—22no—
179C2×C4×C41—22no—
180C2×C4×C41—24no—
181C2×C4×C41—41no—
182C2×C4×C41—42no—
183C2×C4×C41—41no—
184C2×C4×C41—44no—
185C2×C4×C41—42no—
186C2×C4×C41—44no—
187C2×C4×C41—42no—
188C2×C4×C41—42no—
189C2×C4×C41—44no—
190C2×C4×C41—82no—
191C2×C4×C41—82no—
192C2×C4×C41—82no—
193C2×C4×C41#9914yescomplemented
194#9497C4111yesmaximal, characteristic, direct product factor, Sylow
195C22×C41—21no—
196C22×C41—21no—
197C22×C41—21no—
198C22×C41—21no—
199C22×C41—22no—
200C22×C41—22no—
201C22×C41—21no—
202C22×C41—21no—
203C22×C41—22no—
204C22×C41—22no—
205C22×C41—22no—
206C22×C41—22no—
207C22×C41—21no—
208C22×C41—44no—
209C22×C41—44no—
210C22×C41—44no—
211C22×C41—44no—
212C22×C41—42no—
213C22×C41—42no—
214C22×C41—42no—
215C22×C41—42no—
216C22×C41—84no—
217C22×C41—82no—
218C22×C41—82no—
219C22×C41—84no—
220C22×C41—82no—
221C22×C41—84no—
222C22×C41—84no—
223C22×C41—84no—
224C22×C41—84no—
225C22×C41—81no—
226C22×C41—81no—
227C22×C41#38611yescharacteristic
228C22×C41C2×#9912yes—
229C22×C41B(4,𝔽2)12yes—
230C4×C41—24no—
231C4×C41—42no—
232C4×C41—84no—
233C4×C41—82no—
234C4×C41—162no—
235#2403C2×C4111yescharacteristic
236#2309C2×C4111yescharacteristic, complemented
237#1781C2×C4112yescomplemented
238#1781C2×C4111yescharacteristic, complemented
239#1304C2×C4112yescomplemented
240C2×C41—22no—
241C2×C41—22no—
242C2×C41—42no—
243C2×C41—42no—
244C2×C41—41no—
245C2×C41—82no—
246C2×C41—82no—
247C2×C41#188911yescharacteristic
248C2×C41#189811yescharacteristic
249C2×C41#191311yescharacteristic
250C23×D4C22×C4111yescharacteristic
251C23×D4C22×C4111yescharacteristic
252C2×#120—21no—
253C2×#120C4×C4112yescomplemented
254C2×#117—21no—
255C2×#99—22no—
256C2×#99—24no—
257#392—22no—
258#390—24no—
259#386—21no—
260#386C4×C4112yescomplemented
261#379—21no—
262#379C22×C4112yes—
263#379C22×C4111yescharacteristic
264#379C22×C4112yes—
265C41#949711yescharacteristic, direct product factor, Sylow
266C25C2×C4×C4111yescharacteristic
267C25D4×C4111yescharacteristic
268C25C23×C4111yescharacteristic
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4C2×C4×C4112yes—
279C22×D4D4×C4112yes—
280C23×C4C2×C4×C4111yescharacteristic
281C23×C4D4×C4111yescharacteristic
282#120—44no—
283#120—44no—
284#117—44no—
285C2×C4⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4C2×C4×C4112yes—
298C2×C22⋊C4D4×C4114yescomplemented
299C2×C42—22no—
300#99—48no—
301#99—44no—
302#95—22no—
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—42no—
308C24—42no—
309C24—42no—
310C24—42no—
311C24—42no—
312C24—42no—
313C24—81no—
314C24—81no—
315C24—81no—
316C24C22⋊C4×C4112yes—
317C24C22×C4×C4111yescharacteristic
318C24C2×D4×C4111yescharacteristic
319C24C2×D4×C4111yescharacteristic
320C24C2×D4×C4112yes—
321C24#41×C4112yes—
322C2×D4—28no—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—24no—
327C2×D4—24no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4—48no—
333C2×D4—42no—
334C2×D4—44no—
335C2×D4—42no—
336C2×D4—44no—
337C2×D4—42no—
338C2×D4—44no—
339C2×D4—41no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—82no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4C22⋊C4×C4112yes—
355C4⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—44no—
358C22⋊C4—42no—
359C22⋊C4—44no—
360C22⋊C4—44no—
361C22⋊C4—42no—
362C22⋊C4—44no—
363C22⋊C4—44no—
364C22⋊C4—82no—
365C22⋊C4—82no—
366C22⋊C4—81no—
367C22⋊C4—82no—
368C22⋊C4—82no—
369C42—44no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—24no—
375C23—22no—
376C23—24no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—41no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23—81no—
402C23—81no—
403C23—82no—
404C23—82no—
405C23—88no—
406C23—88no—
407C23—88no—
408C23C2×C22⋊C4×C4111yescharacteristic
409C23C4×D4×C4112yes—
410C23#120×C4111yescharacteristic
411C23#121×C4112yes—
412C23#123×C4111yescharacteristic
413D4—48no—
414D4—48no—
415D4—48no—
416D4—44no—
417D4—44no—
418D4—88no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4#99×C4114yescomplemented
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—22no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—21no—
452C22—44no—
453C22—44no—
454C22—44no—
455C22—44no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—84no—
461C22—82no—
462C22—82no—
463C22—84no—
464C22—82no—
465C22—84no—
466C22—84no—
467C22—84no—
468C22—84no—
469C22—81no—
470C22—81no—
471C22C41×#38611yescharacteristic
472C22C2×#99×C4112yes—
473C22C41×B(4,𝔽2)12yes—
474C4—24no—
475C4—42no—
476C4—82no—
477C4—84no—
478C4—162no—
479C2—22no—
480C2—22no—
481C2—42no—
482C2—42no—
483C2—41no—
484C2—82no—
485C2—82no—
486C2C41×#188911yescharacteristic
487C2C41×#189811yescharacteristic
488C2C41×#191311yescharacteristic
subgroupG/H
center, socleC22×C41#386
commutatorC24C22×C4×C41
Frattini, cosocleC25C23×C41
prime radicalC41×#2403C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C25×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2309C2semidirect
3. C41×#1781C2semidirect
4. C41×#1781C2semidirect
5. C41×#1304C2semidirect
9. C2×#120×C41C4semidirect
16. C41×#386C4semidirect
53. C2×C22⋊C4×C41D4semidirect
193. C2×C4×C41#99semidirect
194. #9497C41direct (N × H)
236. #2309C2×C41semidirect
237. #1781C2×C41semidirect
238. #1781C2×C41semidirect
239. #1304C2×C41semidirect
253. C2×#120C4×C41semidirect
260. #386C4×C41semidirect
265. C41#9497direct (N × H)
298. C2×C22⋊C4D4×C41semidirect
438. C2×C4#99×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#24032
C41×#23092
C41×#17812
C41×#13042
#949741