Finite Group Databasebeta

← C41×#8458 #23784659

Subgroups — C41×#8458 #23784659

Order 10496.

766 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3506C211yesmaximal, characteristic
2C41×#1955C211yesmaximal, characteristic, complemented
3C41×#1552C211yesmaximal, characteristic, complemented
4C41×#1551C211yesmaximal, characteristic, complemented
5C41×#1531C211yesmaximal, characteristic, complemented
6C41×#1530C211yesmaximal, characteristic, complemented
7C41×#1466C211yesmaximal, characteristic, complemented
8C41×#559—22no—
9C41×#556—21no—
10C41×#555—21no—
11C41×#553—22no—
12C41×#550—21no—
13C41×#547—21no—
14C41×#538—22no—
15C41×#535C412yes—
16C41×#533C2211yescharacteristic
17C41×#532C2211yescharacteristic
18C41×#525—22no—
19C41×#520C412yes—
20C2×C4×D4×C41C2211yescharacteristic
21C41×#432C2211yescharacteristic
22C41×#432C2211yescharacteristic
23C2×C4⋊C8×C41C2211yescharacteristic
24C2×C22⋊C8×C41—22no—
25C2×#97×C41C2211yescharacteristic
26C41×#333—21no—
27C41×#332—21no—
28C41×#332—21no—
29C41×#331—21no—
30C41×#330—22no—
31C41×#329—22no—
32C41×#323—22no—
33C2×#41×C41—22no—
34C2×#41×C41C2×C412yes—
35C22×D4×C41C2×C411yescharacteristic
36C23×C4×C41D412yes—
37C22×C8×C41—21no—
38C22×C8×C41—21no—
39C4⋊Q8×C41D411yescharacteristic
40C4⋊Q8×C41D411yescharacteristic
41C4⋊Q8×C41D411yescharacteristic
42#127×C41—22no—
43#127×C41D411yescharacteristic
44#126×C41—24no—
45#125×C41D412yes—
46#124×C41—24no—
47#124×C41—22no—
48#124×C41D412yes—
49#123×C41—24no—
50#123×C41—24no—
51C22⋊Q8×C41—22no—
52C22⋊Q8×C41—21no—
53C22⋊Q8×C41—21no—
54#121×C41—22no—
55#121×C41—24no—
56#121×C41—21no—
57#121×C41—21no—
58#121×C41—22no—
59#121×C41—22no—
60#120×C41—24no—
61C4×Q8×C41—22no—
62C4×Q8×C41—21no—
63C4×Q8×C41—21no—
64C4×D4×C41—24no—
65C4×D4×C41—22no—
66C4×D4×C41—24no—
67C4×D4×C41—21no—
68C4×D4×C41—21no—
69C4×D4×C41—21no—
70C4×D4×C41—21no—
71C4×D4×C41—21no—
72C4×D4×C41—21no—
73#117×C41—22no—
74#117×C41—22no—
75#117×C41C2×C412yes—
76C2×C4⋊C4×C41—22no—
77C2×C4⋊C4×C41C2×C411yescharacteristic
78C2×C22⋊C4×C41D412yes—
79C2×C42×C41C2311yescharacteristic
80C4⋊C8×C41—21no—
81C4⋊C8×C41—21no—
82C4⋊C8×C41—21no—
83C4⋊C8×C41—21no—
84C22⋊C8×C41—21no—
85C22⋊C8×C41—21no—
86C22⋊C8×C41—44no—
87#97×C41—21no—
88#97×C41—21no—
89#97×C41—21no—
90#97×C41—21no—
91C24×C41C22⋊C412yes—
92#41×C41—44no—
93#41×C41—82no—
94#41×C41—82no—
95C2×Q8×C41—21no—
96C2×Q8×C41—21no—
97C2×Q8×C41C22⋊C412yes—
98C2×D4×C41—22no—
99C2×D4×C41—24no—
100C2×D4×C41—24no—
101C2×D4×C41—21no—
102C2×D4×C41—21no—
103C2×D4×C41—21no—
104C2×D4×C41—21no—
105C2×D4×C41—42no—
106C2×D4×C41C22⋊C412yes—
107C22×C4×C41—24no—
108C22×C4×C41—22no—
109C22×C4×C41—22no—
110C22×C4×C41—22no—
111C22×C4×C41—42no—
112C22×C4×C41—42no—
113C22×C4×C41C22⋊C412yes—
114C22×C4×C41C22×C411yescharacteristic
115C22×C4×C41C2×D411yescharacteristic
116C22×C4×C41C2×D411yescharacteristic
117C2×C8×C41—22no—
118C2×C8×C41—41no—
119C2×C8×C41—41no—
120C2×C8×C41—42no—
121C2×C8×C41—41no—
122C2×C8×C41—41no—
123C2×C8×C41—41no—
124C4⋊C4×C41—24no—
125C4⋊C4×C41—21no—
126C4⋊C4×C41—21no—
127C4⋊C4×C41—21no—
128C4⋊C4×C41—21no—
129C4⋊C4×C41—22no—
130C4⋊C4×C41—21no—
131C4⋊C4×C41—22no—
132C4⋊C4×C41—21no—
133C4⋊C4×C41C22⋊C412yes—
134C4⋊C4×C41C22⋊C412yes—
135C22⋊C4×C41—24no—
136C22⋊C4×C41—24no—
137C22⋊C4×C41—24no—
138C22⋊C4×C41—22no—
139C22⋊C4×C41—22no—
140C22⋊C4×C41—22no—
141C22⋊C4×C41—22no—
142C22⋊C4×C41—22no—
143C42×C41—24no—
144C42×C41—22no—
145C42×C41C2×D411yescharacteristic
146C42×C41C2×D411yescharacteristic
147C42×C41C2×D411yescharacteristic
148C42×C41C2×D411yescharacteristic
149C23×C41—22no—
150C23×C41—22no—
151C23×C41—22no—
152C23×C41—22no—
153C23×C41—42no—
154C23×C41—42no—
155C23×C41C2×C22⋊C411yescharacteristic
156Q8×C41—42no—
157Q8×C41—41no—
158Q8×C41—41no—
159Q8×C41—81no—
160D4×C41—42no—
161D4×C41—42no—
162D4×C41—42no—
163D4×C41—44no—
164D4×C41—41no—
165D4×C41—41no—
166D4×C41—81no—
167D4×C41—84no—
168D4×C41—84no—
169C2×C4×C41—22no—
170C2×C4×C41—21no—
171C2×C4×C41—21no—
172C2×C4×C41—22no—
173C2×C4×C41—22no—
174C2×C4×C41—22no—
175C2×C4×C41—22no—
176C2×C4×C41—41no—
177C2×C4×C41—44no—
178C2×C4×C41—42no—
179C2×C4×C41—42no—
180C2×C4×C41—42no—
181C2×C4×C41—82no—
182C2×C4×C41—84no—
183C2×C4×C41C2×C22⋊C411yescharacteristic
184C2×C4×C41C2×C22⋊C411yescharacteristic
185C2×C4×C41#12011yescharacteristic
186C2×C4×C41#12011yescharacteristic
187C2×C4×C41#12011yescharacteristic
188C2×C4×C41#12011yescharacteristic
189C8×C41—42no—
190C8×C41—81no—
191C8×C41—81no—
192C8×C41—81no—
193#8458C4111yesmaximal, characteristic, direct product factor, Sylow
194C22×C41—21no—
195C22×C41—21no—
196C22×C41—44no—
197C22×C41—42no—
198C22×C41—42no—
199C22×C41—42no—
200C22×C41—42no—
201C22×C41—42no—
202C22×C41—42no—
203C22×C41—82no—
204C22×C41#37911yescharacteristic
205C22×C41#41312yes—
206C4×C41—21no—
207C4×C41—21no—
208C4×C41—21no—
209C4×C41—21no—
210C4×C41—21no—
211C4×C41—42no—
212C4×C41—42no—
213C4×C41—42no—
214C4×C41—42no—
215C4×C41#45311yescharacteristic
216C4×C41#45511yescharacteristic
217#3506C2×C4111yescharacteristic
218#1955C2×C4111yescharacteristic, complemented
219#1552C2×C4111yescharacteristic, complemented
220#1551C2×C4111yescharacteristic, complemented
221#1531C2×C4111yescharacteristic, complemented
222#1530C2×C4111yescharacteristic, complemented
223#1466C2×C4111yescharacteristic, complemented
224C2×C41—22no—
225C2×C41—82no—
226C2×C41—82no—
227C2×C41#178511yescharacteristic
228C2×C41#179211yescharacteristic
229C2×C41#179411yescharacteristic
230#559—22no—
231#556—21no—
232#555—21no—
233#553—22no—
234#550—21no—
235#547—21no—
236#538—22no—
237#535C4×C4112yes—
238#533C22×C4111yescharacteristic
239#532C22×C4111yescharacteristic
240#525—22no—
241#520C4×C4112yes—
242C2×C4×D4C22×C4111yescharacteristic
243#432C22×C4111yescharacteristic
244#432C22×C4111yescharacteristic
245C2×C4⋊C8C22×C4111yescharacteristic
246C2×C22⋊C8—22no—
247C2×#97C22×C4111yescharacteristic
248#333—21no—
249#332—21no—
250#332—21no—
251#331—21no—
252#330—22no—
253#329—22no—
254#323—22no—
255C41#845811yescharacteristic, direct product factor, Sylow
256C2×#41—22no—
257C2×#41C2×C4×C4112yes—
258C22×D4C2×C4×C4111yescharacteristic
259C23×C4D4×C4112yes—
260C22×C8—21no—
261C22×C8—21no—
262C4⋊Q8D4×C4111yescharacteristic
263C4⋊Q8D4×C4111yescharacteristic
264C4⋊Q8D4×C4111yescharacteristic
265#127—22no—
266#127D4×C4111yescharacteristic
267#126—24no—
268#125D4×C4112yes—
269#124—24no—
270#124—22no—
271#124D4×C4112yes—
272#123—24no—
273#123—24no—
274C22⋊Q8—22no—
275C22⋊Q8—21no—
276C22⋊Q8—21no—
277#121—22no—
278#121—24no—
279#121—21no—
280#121—21no—
281#121—22no—
282#121—22no—
283#120—24no—
284C4×Q8—22no—
285C4×Q8—21no—
286C4×Q8—21no—
287C4×D4—24no—
288C4×D4—22no—
289C4×D4—24no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—21no—
296#117—22no—
297#117—22no—
298#117C2×C4×C4112yes—
299C2×C4⋊C4—22no—
300C2×C4⋊C4C2×C4×C4111yescharacteristic
301C2×C22⋊C4D4×C4112yes—
302C2×C42C23×C4111yescharacteristic
303C4⋊C8—21no—
304C4⋊C8—21no—
305C4⋊C8—21no—
306C4⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8—44no—
310#97—21no—
311#97—21no—
312#97—21no—
313#97—21no—
314C24C22⋊C4×C4112yes—
315#41—44no—
316#41—82no—
317#41—82no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8C22⋊C4×C4112yes—
321C2×D4—22no—
322C2×D4—24no—
323C2×D4—24no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—42no—
329C2×D4C22⋊C4×C4112yes—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4C22⋊C4×C4112yes—
337C22×C4C22×C4×C4111yescharacteristic
338C22×C4C2×D4×C4111yescharacteristic
339C22×C4C2×D4×C4111yescharacteristic
340C2×C8—22no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—42no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C4⋊C4—24no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—22no—
353C4⋊C4—21no—
354C4⋊C4—22no—
355C4⋊C4—21no—
356C4⋊C4C22⋊C4×C4112yes—
357C4⋊C4C22⋊C4×C4112yes—
358C22⋊C4—24no—
359C22⋊C4—24no—
360C22⋊C4—24no—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C42—24no—
367C42—22no—
368C42C2×D4×C4111yescharacteristic
369C42C2×D4×C4111yescharacteristic
370C42C2×D4×C4111yescharacteristic
371C42C2×D4×C4111yescharacteristic
372C23—22no—
373C23—22no—
374C23—22no—
375C23—22no—
376C23—42no—
377C23—42no—
378C23C2×C22⋊C4×C4111yescharacteristic
379Q8—42no—
380Q8—41no—
381Q8—41no—
382Q8—81no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—44no—
387D4—41no—
388D4—41no—
389D4—81no—
390D4—84no—
391D4—84no—
392C2×C4—22no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—82no—
405C2×C4—84no—
406C2×C4C2×C22⋊C4×C4111yescharacteristic
407C2×C4C2×C22⋊C4×C4111yescharacteristic
408C2×C4#120×C4111yescharacteristic
409C2×C4#120×C4111yescharacteristic
410C2×C4#120×C4111yescharacteristic
411C2×C4#120×C4111yescharacteristic
412C8—42no—
413C8—81no—
414C8—81no—
415C8—81no—
416C22—21no—
417C22—21no—
418C22—44no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—82no—
426C22C41×#37911yescharacteristic
427C22C41×#41312yes—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—42no—
434C4—42no—
435C4—42no—
436C4—42no—
437C4C41×#45311yescharacteristic
438C4C41×#45511yescharacteristic
439C2—22no—
440C2—82no—
441C2—82no—
442C2C41×#178511yescharacteristic
443C2C41×#179211yescharacteristic
444C2C41×#179411yescharacteristic
subgroupG/H
center, socleC22×C41#379
commutatorC22×C4C22×C4×C41
Frattini, cosocleC2×C42C23×C41
prime radicalC41×#3506C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#1955C2semidirect
3. C41×#1552C2semidirect
4. C41×#1551C2semidirect
5. C41×#1531C2semidirect
6. C41×#1530C2semidirect
7. C41×#1466C2semidirect
193. #8458C41direct (N × H)
218. #1955C2×C41semidirect
219. #1552C2×C41semidirect
220. #1551C2×C41semidirect
221. #1531C2×C41semidirect
222. #1530C2×C41semidirect
223. #1466C2×C41semidirect
255. C41#8458direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35062
C41×#19552
C41×#15522
C41×#15512
C41×#15312
C41×#15302
C41×#14662
#845841