Finite Group Databasebeta

← C41×#7781 #23783982

Subgroups — C41×#7781 #23783982

Order 10496.

536 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2733C211yesmaximal, characteristic
2C41×#2024C211yesmaximal, characteristic, complemented
3C41×#2023C211yesmaximal, characteristic, complemented
4C41×#2013C211yesmaximal, characteristic, complemented
5C41×#1272C211yesmaximal, characteristic, complemented
6C41×#1270C211yesmaximal, characteristic, complemented
7C41×#1270C211yesmaximal, characteristic, complemented
8C22×SD16×C41—21no—
9C2×C4⋊Q8×C41C2211yescharacteristic
10C2×#124×C41—21no—
11C2×#103×C41—21no—
12C2×#103×C41—21no—
13C2×#102×C41—21no—
14C41×#394—21no—
15C41×#392—21no—
16C41×#392—21no—
17C41×#391C2211yescharacteristic
18C41×#390C2211yescharacteristic
19C41×#390C2211yescharacteristic
20C41×#388—21no—
21C41×#388—21no—
22C41×#340—21no—
23C41×#340—21no—
24C41×#336C2211yescharacteristic
25C41×#336C2211yescharacteristic
26C41×#336C2211yescharacteristic
27C22×Q8×C41—21no—
28C22×Q8×C41D411yescharacteristic
29C22×D4×C41—21no—
30C22×D4×C41—21no—
31C22×D4×C41D411yescharacteristic
32C22×D4×C41D411yescharacteristic
33C2×SD16×C41—42no—
34C2×SD16×C41—42no—
35C2×SD16×C41—42no—
36C22×C8×C41—21no—
37C22×C8×C41—21no—
38C22×C8×C41—21no—
39C4⋊Q8×C41—42no—
40#124×C41—42no—
41#124×C41—42no—
42C2×C4⋊C4×C41—21no—
43C2×C4⋊C4×C41—21no—
44C2×C4⋊C4×C41D411yescharacteristic
45C2×C4⋊C4×C41D411yescharacteristic
46C2×C4⋊C4×C41D411yescharacteristic
47C2×C22⋊C4×C41—21no—
48C2×C22⋊C4×C41—21no—
49C2×C22⋊C4×C41—21no—
50C2×C22⋊C4×C41—21no—
51C2×C22⋊C4×C41—21no—
52C2×C22⋊C4×C41—21no—
53C2×C22⋊C4×C41—21no—
54C2×C22⋊C4×C41—21no—
55C2×C42×C41—21no—
56C2×C42×C41C2311yescharacteristic
57#103×C41—42no—
58#103×C41—42no—
59#102×C41—42no—
60#95×C41—21no—
61#95×C41—21no—
62#95×C41—21no—
63C24×C41—21no—
64C24×C41—21no—
65C2×Q8×C41—21no—
66C2×Q8×C41—22no—
67C2×Q8×C41—41no—
68C2×Q8×C41—41no—
69C2×Q8×C41—41no—
70C2×Q8×C41—41no—
71C2×Q8×C41—41no—
72C2×Q8×C41—41no—
73C2×Q8×C41—41no—
74C2×Q8×C41SD1612yescomplemented
75C2×D4×C41—21no—
76C2×D4×C41—21no—
77C2×D4×C41—21no—
78C2×D4×C41—21no—
79C2×D4×C41—41no—
80C2×D4×C41—41no—
81C2×D4×C41—41no—
82C2×D4×C41—41no—
83C2×D4×C41—42no—
84C2×D4×C41—81no—
85C2×D4×C41—81no—
86C2×D4×C41—81no—
87C2×D4×C41—81no—
88C2×D4×C41—81no—
89C22×C4×C41—21no—
90C22×C4×C41—21no—
91C22×C4×C41—21no—
92C22×C4×C41—21no—
93C22×C4×C41—41no—
94C22×C4×C41C2×D411yescharacteristic
95C22×C4×C41C2×D411yescharacteristic
96C22×C4×C41C2×D411yescharacteristic
97SD16×C41—48no—
98C2×C8×C41—22no—
99C2×C8×C41—41no—
100C2×C8×C41—41no—
101C2×C8×C41—41no—
102C2×C8×C41—41no—
103C2×C8×C41—41no—
104C2×C8×C41—41no—
105C2×C8×C41—41no—
106C2×C8×C41—41no—
107C4⋊C4×C41—22no—
108C4⋊C4×C41—22no—
109C4⋊C4×C41—41no—
110C4⋊C4×C41—41no—
111C4⋊C4×C41—41no—
112C4⋊C4×C41—41no—
113C4⋊C4×C41—41no—
114C22⋊C4×C41—42no—
115C22⋊C4×C41—42no—
116C22⋊C4×C41—41no—
117C22⋊C4×C41—41no—
118C22⋊C4×C41—41no—
119C22⋊C4×C41—41no—
120C22⋊C4×C41—41no—
121C22⋊C4×C41—41no—
122C22⋊C4×C41—41no—
123C22⋊C4×C41—41no—
124C22⋊C4×C41—81no—
125C22⋊C4×C41—81no—
126C42×C41—41no—
127C42×C41—42no—
128C23×C41—41no—
129C23×C41—41no—
130C23×C41—41no—
131C23×C41—41no—
132C23×C41—41no—
133C23×C41—41no—
134C23×C41—41no—
135C23×C41—41no—
136C23×C41—41no—
137C23×C41—41no—
138C23×C41—41no—
139C23×C41—41no—
140C23×C41—41no—
141C23×C41—41no—
142C23×C41#12011yescharacteristic
143Q8×C41—42no—
144Q8×C41—42no—
145Q8×C41—42no—
146Q8×C41—81no—
147Q8×C41—81no—
148Q8×C41—81no—
149D4×C41—42no—
150D4×C41—42no—
151D4×C41—81no—
152D4×C41—81no—
153D4×C41—84no—
154D4×C41—84no—
155C2×C4×C41—21no—
156C2×C4×C41—21no—
157C2×C4×C41—21no—
158C2×C4×C41—21no—
159C2×C4×C41—21no—
160C2×C4×C41—21no—
161C2×C4×C41—22no—
162C2×C4×C41—41no—
163C2×C4×C41—41no—
164C2×C4×C41—41no—
165C2×C4×C41—41no—
166C2×C4×C41—41no—
167C2×C4×C41—41no—
168C2×C4×C41—41no—
169C2×C4×C41—41no—
170C2×C4×C41—41no—
171C2×C4×C41—41no—
172C2×C4×C41—41no—
173C2×C4×C41—42no—
174C2×C4×C41—81no—
175C2×C4×C41—81no—
176C2×C4×C41C2×SD1611yescharacteristic
177C2×C4×C41#13511yescharacteristic
178C2×C4×C41#13511yescharacteristic
179C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C41#13711yescharacteristic
182C8×C41—42no—
183C8×C41—81no—
184C8×C41—81no—
185#7781C4111yesmaximal, characteristic, direct product factor, Sylow
186C22×C41—81no—
187C22×C41—81no—
188C22×C41—81no—
189C22×C41—81no—
190C22×C41—81no—
191C22×C41—81no—
192C22×C41—81no—
193C22×C41—81no—
194C22×C41—81no—
195C22×C41—81no—
196C22×C41—81no—
197C22×C41—81no—
198C22×C41—81no—
199C22×C41—81no—
200C22×C41#44911yescharacteristic
201C22×C41#45011yescharacteristic
202C22×C41#45211yescharacteristic
203C22×C41#45311yescharacteristic
204C22×C41#45511yescharacteristic
205C22×C41#45511yescharacteristic
206C22×C41B(4,𝔽2)11yescharacteristic
207C4×C41—21no—
208C4×C41—21no—
209C4×C41—21no—
210C4×C41—21no—
211C4×C41—21no—
212C4×C41—21no—
213C4×C41—42no—
214C4×C41—82no—
215C4×C41—81no—
216C4×C41—81no—
217C4×C41—81no—
218#2733C2×C4111yescharacteristic
219#2024C2×C4111yescharacteristic, complemented
220#2023C2×C4111yescharacteristic, complemented
221#2013C2×C4111yescharacteristic, complemented
222#1272C2×C4111yescharacteristic, complemented
223#1270C2×C4111yescharacteristic, complemented
224#1270C2×C4111yescharacteristic, complemented
225C2×C41—161no—
226C2×C41—161no—
227C2×C41#160011yescharacteristic
228C2×C41#160111yescharacteristic
229C2×C41#160611yescharacteristic
230C2×C41#163111yescharacteristic
231C2×C41#164211yescharacteristic
232C2×C41#164611yescharacteristic
233C2×C41#165911yescharacteristic
234C22×SD16—21no—
235C2×C4⋊Q8C22×C4111yescharacteristic
236C2×#124—21no—
237C2×#103—21no—
238C2×#103—21no—
239C2×#102—21no—
240#394—21no—
241#392—21no—
242#392—21no—
243#391C22×C4111yescharacteristic
244#390C22×C4111yescharacteristic
245#390C22×C4111yescharacteristic
246#388—21no—
247#388—21no—
248#340—21no—
249#340—21no—
250#336C22×C4111yescharacteristic
251#336C22×C4111yescharacteristic
252#336C22×C4111yescharacteristic
253C41#778111yescharacteristic, direct product factor, Sylow
254C22×Q8—21no—
255C22×Q8D4×C4111yescharacteristic
256C22×D4—21no—
257C22×D4—21no—
258C22×D4D4×C4111yescharacteristic
259C22×D4D4×C4111yescharacteristic
260C2×SD16—42no—
261C2×SD16—42no—
262C2×SD16—42no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C4⋊Q8—42no—
267#124—42no—
268#124—42no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4D4×C4111yescharacteristic
272C2×C4⋊C4D4×C4111yescharacteristic
273C2×C4⋊C4D4×C4111yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C42—21no—
283C2×C42C23×C4111yescharacteristic
284#103—42no—
285#103—42no—
286#102—42no—
287#95—21no—
288#95—21no—
289#95—21no—
290C24—21no—
291C24—21no—
292C2×Q8—21no—
293C2×Q8—22no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8SD16×C4112yescomplemented
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—42no—
311C2×D4—81no—
312C2×D4—81no—
313C2×D4—81no—
314C2×D4—81no—
315C2×D4—81no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4C2×D4×C4111yescharacteristic
322C22×C4C2×D4×C4111yescharacteristic
323C22×C4C2×D4×C4111yescharacteristic
324SD16—48no—
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—81no—
352C22⋊C4—81no—
353C42—41no—
354C42—42no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23#120×C4111yescharacteristic
370Q8—42no—
371Q8—42no—
372Q8—42no—
373Q8—81no—
374Q8—81no—
375Q8—81no—
376D4—42no—
377D4—42no—
378D4—81no—
379D4—81no—
380D4—84no—
381D4—84no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4C2×SD16×C4111yescharacteristic
404C2×C4#135×C4111yescharacteristic
405C2×C4#135×C4111yescharacteristic
406C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
407C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
408C2×C4#137×C4111yescharacteristic
409C8—42no—
410C8—81no—
411C8—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22C41×#44911yescharacteristic
427C22C41×#45011yescharacteristic
428C22C41×#45211yescharacteristic
429C22C41×#45311yescharacteristic
430C22C41×#45511yescharacteristic
431C22C41×#45511yescharacteristic
432C22C41×B(4,𝔽2)11yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—42no—
440C4—82no—
441C4—81no—
442C4—81no—
443C4—81no—
444C2—161no—
445C2—161no—
446C2C41×#160011yescharacteristic
447C2C41×#160111yescharacteristic
448C2C41×#160611yescharacteristic
449C2C41×#163111yescharacteristic
450C2C41×#164211yescharacteristic
451C2C41×#164611yescharacteristic
452C2C41×#165911yescharacteristic
subgroupG/H
center, socleC23×C41#120
commutator, Frattini, cosocleC2×C42C23×C41
prime radicalC41×#2733C2
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2024C2semidirect
3. C41×#2023C2semidirect
4. C41×#2013C2semidirect
5. C41×#1272C2semidirect
6. C41×#1270C2semidirect
7. C41×#1270C2semidirect
74. C2×Q8×C41SD16semidirect
185. #7781C41direct (N × H)
219. #2024C2×C41semidirect
220. #2023C2×C41semidirect
221. #2013C2×C41semidirect
222. #1272C2×C41semidirect
223. #1270C2×C41semidirect
224. #1270C2×C41semidirect
253. C41#7781direct (N × H)
301. C2×Q8SD16×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#27332
C41×#20242
C41×#20232
C41×#20132
C41×#12722
C41×#12702
#778141