Finite Group Databasebeta

← C41×#9941 #23786142

Subgroups — C41×#9941 #23786142

Order 10496.

600 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3094C211yesmaximal, characteristic
2C41×#2591C211yesmaximal, characteristic
3C41×#2484C211yesmaximal, characteristic, complemented
4C41×#1826C211yesmaximal, characteristic, complemented
5C41×#1510C211yesmaximal, characteristic
6C41×#1463C211yesmaximal, characteristic, complemented
7C41×#1284C211yesmaximal, characteristic, complemented
8C2×#121×C41C2211yescharacteristic
9C2×#117×C41C2211yescharacteristic
10C22×C4⋊C4×C41C2211yescharacteristic
11C41×#482—22no—
12C41×#481—21no—
13C41×#480—21no—
14C41×#428—21no—
15C41×#418—21no—
16C41×#407C2211yescharacteristic
17C41×#407C2211yescharacteristic
18C41×#400—21no—
19C41×#400—21no—
20C41×#398—21no—
21C41×#394—21no—
22C41×#388—22no—
23C41×#387—22no—
24C41×#386—21no—
25C41×#386—21no—
26C41×#385—21no—
27C41×#381—21no—
28C41×#381C2211yescharacteristic
29C4×C22⋊C4×C41C2211yescharacteristic
30C41×#339—22no—
31C41×#327—22no—
32C41×#324—22no—
33C22×D4×C41—21no—
34C22×D4×C41D411yescharacteristic
35C23×C4×C41D411yescharacteristic
36C23×C4×C41D411yescharacteristic
37C23×C4×C41C2311yescharacteristic
38C2×M16×C41—21no—
39C2×M16×C41—21no—
40#121×C41—21no—
41#121×C41—21no—
42#121×C41—21no—
43#121×C41—21no—
44#117×C41—21no—
45#117×C41—21no—
46#117×C41—21no—
47#117×C41—21no—
48C2×C4⋊C4×C41—22no—
49C2×C4⋊C4×C41—21no—
50C2×C4⋊C4×C41—21no—
51C2×C4⋊C4×C41—21no—
52C2×C4⋊C4×C41—21no—
53C2×C4⋊C4×C41—21no—
54C2×C4⋊C4×C41—21no—
55C2×C4⋊C4×C41D411yescharacteristic
56C2×C4⋊C4×C41D411yescharacteristic
57C2×C4⋊C4×C41D411yescharacteristic
58C2×C22⋊C4×C41—22no—
59C2×C22⋊C4×C41—21no—
60C2×C22⋊C4×C41—21no—
61C2×C22⋊C4×C41—21no—
62C2×C22⋊C4×C41—21no—
63C2×C22⋊C4×C41—22no—
64C2×C42×C41—21no—
65C2×C42×C41D412yes—
66#107×C41—22no—
67#106×C41—22no—
68#102×C41—22no—
69#102×C41—22no—
70C22⋊C8×C41—21no—
71C22⋊C8×C41—21no—
72C22⋊C8×C41—21no—
73C22⋊C8×C41D412yes—
74#95×C41—22no—
75#95×C41—22no—
76#95×C41—22no—
77#95×C41—22no—
78#95×C41—22no—
79#95×C41—21no—
80#95×C41—21no—
81#95×C41D412yes—
82C24×C41—21no—
83C24×C41C2×D411yescharacteristic
84C2×D4×C41—21no—
85C2×D4×C41—21no—
86C2×D4×C41—42no—
87C2×D4×C41—44no—
88C2×D4×C41—41no—
89C2×D4×C41—41no—
90C22×C4×C41—21no—
91C22×C4×C41—21no—
92C22×C4×C41—21no—
93C22×C4×C41—22no—
94C22×C4×C41—21no—
95C22×C4×C41—21no—
96C22×C4×C41—21no—
97C22×C4×C41—22no—
98C22×C4×C41—21no—
99C22×C4×C41—21no—
100C22×C4×C41—21no—
101C22×C4×C41—42no—
102C22×C4×C41—42no—
103C22×C4×C41—42no—
104C22×C4×C41C2×D411yescharacteristic
105C22×C4×C41C2×D411yescharacteristic
106C22×C4×C41C2×D411yescharacteristic
107C22×C4×C41C2×D411yescharacteristic
108C22×C4×C41C2×D411yescharacteristic
109C22×C4×C41#4111yescharacteristic
110M16×C41—42no—
111M16×C41—42no—
112C2×C8×C41—22no—
113C2×C8×C41—41no—
114C4⋊C4×C41—21no—
115C4⋊C4×C41—21no—
116C4⋊C4×C41—21no—
117C4⋊C4×C41—21no—
118C4⋊C4×C41—21no—
119C4⋊C4×C41—21no—
120C4⋊C4×C41—44no—
121C4⋊C4×C41—41no—
122C4⋊C4×C41—41no—
123C4⋊C4×C41—41no—
124C4⋊C4×C41—41no—
125C22⋊C4×C41—44no—
126C22⋊C4×C41—42no—
127C22⋊C4×C41—42no—
128C22⋊C4×C41—41no—
129C22⋊C4×C41—41no—
130C22⋊C4×C41—41no—
131C22⋊C4×C41—41no—
132C22⋊C4×C41—82no—
133C42×C41—42no—
134C42×C41—41no—
135C42×C41—41no—
136C23×C41—22no—
137C23×C41—22no—
138C23×C41—41no—
139C23×C41—42no—
140C23×C41—42no—
141C23×C41—41no—
142C23×C41—42no—
143C23×C41#12011yescharacteristic
144C23×C41#12011yescharacteristic
145C23×C41#12111yescharacteristic
146D4×C41—42no—
147D4×C41—81no—
148D4×C41—82no—
149D4×C41—82no—
150C2×C4×C41—22no—
151C2×C4×C41—22no—
152C2×C4×C41—22no—
153C2×C4×C41—22no—
154C2×C4×C41—22no—
155C2×C4×C41—41no—
156C2×C4×C41—41no—
157C2×C4×C41—41no—
158C2×C4×C41—41no—
159C2×C4×C41—41no—
160C2×C4×C41—41no—
161C2×C4×C41—41no—
162C2×C4×C41—41no—
163C2×C4×C41—42no—
164C2×C4×C41—42no—
165C2×C4×C41—42no—
166C2×C4×C41—42no—
167C2×C4×C41—42no—
168C2×C4×C41—42no—
169C2×C4×C41—42no—
170C2×C4×C41—41no—
171C2×C4×C41—41no—
172C2×C4×C41—41no—
173C2×C4×C41—41no—
174C2×C4×C41—42no—
175C2×C4×C41—42no—
176C2×C4×C41—42no—
177C2×C4×C41—42no—
178C2×C4×C41—81no—
179C2×C4×C41#12011yescharacteristic
180C2×C4×C41#12111yescharacteristic
181C2×C4×C41#12111yescharacteristic
182C2×C4×C41#12711yescharacteristic
183C8×C41—42no—
184C8×C41—81no—
185#9941C4111yesmaximal, characteristic, direct product factor, Sylow
186C22×C41—21no—
187C22×C41—21no—
188C22×C41—21no—
189C22×C41—21no—
190C22×C41—21no—
191C22×C41—21no—
192C22×C41—21no—
193C22×C41—44no—
194C22×C41—84no—
195C22×C41—81no—
196C22×C41—81no—
197C22×C41—81no—
198C22×C41#39211yescharacteristic
199C22×C41#45412yes—
200C22×C41#45812yes—
201C4×C41—21no—
202C4×C41—21no—
203C4×C41—21no—
204C4×C41—21no—
205C4×C41—42no—
206C4×C41—82no—
207C4×C41—82no—
208C4×C41—81no—
209C4×C41—81no—
210C4×C41—81no—
211C4×C41—81no—
212#3094C2×C4111yescharacteristic
213#2591C2×C4111yescharacteristic
214#2484C2×C4111yescharacteristic, complemented
215#1826C2×C4111yescharacteristic, complemented
216#1510C2×C4111yescharacteristic
217#1463C2×C4111yescharacteristic, complemented
218#1284C2×C4111yescharacteristic, complemented
219C2×C41—22no—
220C2×C41—22no—
221C2×C41—41no—
222C2×C41—161no—
223C2×C41#200311yescharacteristic
224C2×C41#201011yescharacteristic
225C2×C41#202211yescharacteristic
226C2×#121C22×C4111yescharacteristic
227C2×#117C22×C4111yescharacteristic
228C22×C4⋊C4C22×C4111yescharacteristic
229#482—22no—
230#481—21no—
231#480—21no—
232#428—21no—
233#418—21no—
234#407C22×C4111yescharacteristic
235#407C22×C4111yescharacteristic
236#400—21no—
237#400—21no—
238#398—21no—
239#394—21no—
240#388—22no—
241#387—22no—
242#386—21no—
243#386—21no—
244#385—21no—
245#381—21no—
246#381C22×C4111yescharacteristic
247C4×C22⋊C4C22×C4111yescharacteristic
248#339—22no—
249#327—22no—
250#324—22no—
251C41#994111yescharacteristic, direct product factor, Sylow
252C22×D4—21no—
253C22×D4D4×C4111yescharacteristic
254C23×C4D4×C4111yescharacteristic
255C23×C4D4×C4111yescharacteristic
256C23×C4C23×C4111yescharacteristic
257C2×M16—21no—
258C2×M16—21no—
259#121—21no—
260#121—21no—
261#121—21no—
262#121—21no—
263#117—21no—
264#117—21no—
265#117—21no—
266#117—21no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4D4×C4111yescharacteristic
275C2×C4⋊C4D4×C4111yescharacteristic
276C2×C4⋊C4D4×C4111yescharacteristic
277C2×C22⋊C4—22no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—22no—
283C2×C42—21no—
284C2×C42D4×C4112yes—
285#107—22no—
286#106—22no—
287#102—22no—
288#102—22no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8D4×C4112yes—
293#95—22no—
294#95—22no—
295#95—22no—
296#95—22no—
297#95—22no—
298#95—21no—
299#95—21no—
300#95D4×C4112yes—
301C24—21no—
302C24C2×D4×C4111yescharacteristic
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—42no—
306C2×D4—44no—
307C2×D4—41no—
308C2×D4—41no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4C2×D4×C4111yescharacteristic
324C22×C4C2×D4×C4111yescharacteristic
325C22×C4C2×D4×C4111yescharacteristic
326C22×C4C2×D4×C4111yescharacteristic
327C22×C4C2×D4×C4111yescharacteristic
328C22×C4#41×C4111yescharacteristic
329M16—42no—
330M16—42no—
331C2×C8—22no—
332C2×C8—41no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—44no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C22⋊C4—44no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—82no—
352C42—42no—
353C42—41no—
354C42—41no—
355C23—22no—
356C23—22no—
357C23—41no—
358C23—42no—
359C23—42no—
360C23—41no—
361C23—42no—
362C23#120×C4111yescharacteristic
363C23#120×C4111yescharacteristic
364C23#121×C4111yescharacteristic
365D4—42no—
366D4—81no—
367D4—82no—
368D4—82no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—81no—
398C2×C4#120×C4111yescharacteristic
399C2×C4#121×C4111yescharacteristic
400C2×C4#121×C4111yescharacteristic
401C2×C4#127×C4111yescharacteristic
402C8—42no—
403C8—81no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—44no—
412C22—84no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22C41×#39211yescharacteristic
417C22C41×#45412yes—
418C22C41×#45812yes—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—82no—
425C4—82no—
426C4—81no—
427C4—81no—
428C4—81no—
429C4—81no—
430C2—22no—
431C2—22no—
432C2—41no—
433C2—161no—
434C2C41×#200311yescharacteristic
435C2C41×#201011yescharacteristic
436C2C41×#202211yescharacteristic
subgroupG/H
center, socleC22×C41#392
commutator, Frattini, cosocleC23×C4C23×C41
prime radicalC2×#121×C41C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C41×#2484C2semidirect
4. C41×#1826C2semidirect
6. C41×#1463C2semidirect
7. C41×#1284C2semidirect
185. #9941C41direct (N × H)
214. #2484C2×C41semidirect
215. #1826C2×C41semidirect
217. #1463C2×C41semidirect
218. #1284C2×C41semidirect
251. C41#9941direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#30942
C41×#25912
C41×#24842
C41×#18262
C41×#15102
C41×#14632
C41×#12842
#994141