Finite Group Databasebeta

← C41×#8984 #23785185

Subgroups — C41×#8984 #23785185

Order 10496.

592 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#474C211yesmaximal, characteristic
2C41×#2354C211yesmaximal, characteristic
3C41×#1990C211yesmaximal, characteristic, complemented
4C41×#1981C211yesmaximal, characteristic, complemented
5C2×C41×D4⋊C8C211yesmaximal, characteristic
6C41×#1296C211yesmaximal, characteristic, complemented
7C41×#1279C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C41C2211yescharacteristic
9C2×C4×D4×C41C2211yescharacteristic
10C2×#117×C41—21no—
11C41×#474—22no—
12C41×#474C414yescomplemented
13C2×#107×C41—21no—
14C2×C4⋊C8×C41C2211yescharacteristic
15C2×C4⋊C8×C41C2211yescharacteristic
16C2×#103×C41—21no—
17C2×#103×C41—21no—
18C2×#102×C41—21no—
19C2×C4×C8×C41C2211yescharacteristic
20C41×#390—21no—
21C41×#388—22no—
22C41×#384C2211yescharacteristic
23C41×#380—21no—
24C4×C4⋊C4×C41—21no—
25C4×C4⋊C4×C41C2211yescharacteristic
26C41×#340—22no—
27C41×D4⋊C8—22no—
28C22×Q8×C41—21no—
29C22×D4×C41D411yescharacteristic
30C23×C4×C41—21no—
31C22×C8×C41—21no—
32C22×C8×C41—21no—
33C22×C8×C41—21no—
34C4⋊Q8×C41—21no—
35C4⋊Q8×C41—21no—
36C4⋊Q8×C41—21no—
37C4⋊Q8×C41C2×C412yes—
38C4×D4×C41—21no—
39C4×D4×C41—21no—
40C4×D4×C41C2×C412yes—
41C4×D4×C41D412yes—
42#117×C41—42no—
43#117×C41—42no—
44C2×C4⋊C4×C41—21no—
45C2×C4⋊C4×C41—21no—
46C2×C4⋊C4×C41—21no—
47C2×C4⋊C4×C41—21no—
48C2×C4⋊C4×C41D411yescharacteristic
49C2×C4⋊C4×C41D411yescharacteristic
50C2×C4⋊C4×C41D411yescharacteristic
51C2×C4⋊C4×C41D412yes—
52C2×C22⋊C4×C41—21no—
53C2×C22⋊C4×C41—22no—
54C2×C22⋊C4×C41—22no—
55C2×C42×C41—22no—
56C2×C42×C41—21no—
57C2×C42×C41C2311yescharacteristic
58#107×C41—24no—
59C4⋊C8×C41—21no—
60C4⋊C8×C41—21no—
61C4⋊C8×C41—21no—
62C4⋊C8×C41C2×C412yes—
63#103×C41—42no—
64#103×C41—42no—
65#102×C41—24no—
66C4×C8×C41—21no—
67C4×C8×C41—21no—
68#95×C41—22no—
69#95×C41—21no—
70C24×C41—21no—
71C2×Q8×C41—22no—
72C2×Q8×C41—41no—
73C2×Q8×C41—41no—
74C2×Q8×C41—41no—
75C2×Q8×C41—41no—
76C2×Q8×C41—41no—
77C2×D4×C41—21no—
78C2×D4×C41—21no—
79C2×D4×C41—21no—
80C2×D4×C41—21no—
81C2×D4×C41—21no—
82C2×D4×C41C22⋊C412yes—
83C22×C4×C41—21no—
84C22×C4×C41—21no—
85C22×C4×C41—22no—
86C22×C4×C41—22no—
87C22×C4×C41—21no—
88C22×C4×C41—22no—
89C22×C4×C41—41no—
90C22×C4×C41—41no—
91C22×C4×C41—41no—
92C22×C4×C41—41no—
93C22×C4×C41—41no—
94C22×C4×C41C2×D411yescharacteristic
95C22×C4×C41C2×D411yescharacteristic
96C22×C4×C41C2×D411yescharacteristic
97C2×C8×C41—22no—
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—
106C4⋊C4×C41—21no—
107C4⋊C4×C41—21no—
108C4⋊C4×C41—22no—
109C4⋊C4×C41—22no—
110C4⋊C4×C41—21no—
111C4⋊C4×C41—21no—
112C4⋊C4×C41—42no—
113C4⋊C4×C41—41no—
114C4⋊C4×C41—41no—
115C4⋊C4×C41—41no—
116C4⋊C4×C41—41no—
117C4⋊C4×C41—41no—
118C4⋊C4×C41—41no—
119C4⋊C4×C41C22⋊C412yes—
120C4⋊C4×C41D812yes—
121C22⋊C4×C41—22no—
122C22⋊C4×C41—22no—
123C22⋊C4×C41—44no—
124C22⋊C4×C41—82no—
125C42×C41—44no—
126C42×C41—41no—
127C42×C41—41no—
128C42×C41C22×C411yescharacteristic
129C42×C41C2×D411yescharacteristic
130C42×C41#4111yescharacteristic
131C42×C41#4111yescharacteristic
132C23×C41—22no—
133C23×C41—41no—
134C23×C41—41no—
135C23×C41—41no—
136C23×C41—41no—
137C23×C41—41no—
138C23×C41—41no—
139C23×C41#12011yescharacteristic
140Q8×C41—42no—
141Q8×C41—42no—
142Q8×C41—81no—
143Q8×C41—81no—
144D4×C41—22no—
145D4×C41—22no—
146D4×C41—41no—
147D4×C41—41no—
148C2×C4×C41—21no—
149C2×C4×C41—21no—
150C2×C4×C41—22no—
151C2×C4×C41—22no—
152C2×C4×C41—41no—
153C2×C4×C41—41no—
154C2×C4×C41—41no—
155C2×C4×C41—41no—
156C2×C4×C41—42no—
157C2×C4×C41—42no—
158C2×C4×C41—42no—
159C2×C4×C41—42no—
160C2×C4×C41—42no—
161C2×C4×C41—42no—
162C2×C4×C41—41no—
163C2×C4×C41—41no—
164C2×C4×C41—42no—
165C2×C4×C41—41no—
166C2×C4×C41—42no—
167C2×C4×C41—81no—
168C2×C4×C41—81no—
169C2×C4×C41C2×C22⋊C411yescharacteristic
170C2×C4×C41C4×D411yescharacteristic
171C2×C4×C41C4×D411yescharacteristic
172C2×C4×C41#12111yescharacteristic
173C2×C4×C41#12111yescharacteristic
174C2×C4×C41#12311yescharacteristic
175C2×C4×C41C2×D811yescharacteristic
176C2×C4×C41#13511yescharacteristic
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
182C2×C4×C41#13711yescharacteristic
183C8×C41—42no—
184C8×C41—42no—
185C8×C41—81no—
186#8984C4111yesmaximal, characteristic, direct product factor, Sylow
187C22×C41—42no—
188C22×C41—42no—
189C22×C41—42no—
190C22×C41—81no—
191C22×C41—81no—
192C22×C41—81no—
193C22×C41—81no—
194C22×C41#38611yescharacteristic
195C22×C41#44711yescharacteristic
196C22×C41#44911yescharacteristic
197C22×C41#45211yescharacteristic
198C22×C41#45211yescharacteristic
199C22×C41#45511yescharacteristic
200C22×C41#45611yescharacteristic
201C4×C41—21no—
202C4×C41—21no—
203C4×C41—42no—
204C4×C41—42no—
205C4×C41—82no—
206C4×C41—82no—
207C4×C41—81no—
208C4×C41#41611yescharacteristic
209C4×C41#41911yescharacteristic
210C4×C41C4×D811yescharacteristic
211C4×C41#44211yescharacteristic
212C4×C41#45911yescharacteristic
213C4×C41#46311yescharacteristic
214C4×C41#48511yescharacteristic
215C4×C41#48511yescharacteristic
216C2×#474C2×C4111yescharacteristic
217#2354C2×C4111yescharacteristic
218#1990C2×C4111yescharacteristic, complemented
219#1981C2×C4111yescharacteristic, complemented
220C2×D4⋊C8C2×C4111yescharacteristic
221#1296C2×C4111yescharacteristic, complemented
222#1279C2×C4111yescharacteristic, complemented
223C2×C41—82no—
224C2×C41#164111yescharacteristic
225C2×C41#164611yescharacteristic
226C2×C41#164711yescharacteristic
227C2×C41#165211yescharacteristic
228C2×C41#187311yescharacteristic
229C2×C41#187911yescharacteristic
230C2×C41#188211yescharacteristic
231C2×C4⋊Q8C22×C4111yescharacteristic
232C2×C4×D4C22×C4111yescharacteristic
233C2×#117—21no—
234#474—22no—
235#474C4×C4114yescomplemented
236C2×#107—21no—
237C2×C4⋊C8C22×C4111yescharacteristic
238C2×C4⋊C8C22×C4111yescharacteristic
239C2×#103—21no—
240C2×#103—21no—
241C2×#102—21no—
242C2×C4×C8C22×C4111yescharacteristic
243#390—21no—
244#388—22no—
245#384C22×C4111yescharacteristic
246#380—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4C22×C4111yescharacteristic
249#340—22no—
250D4⋊C8—22no—
251C41#898411yescharacteristic, direct product factor, Sylow
252C22×Q8—21no—
253C22×D4D4×C4111yescharacteristic
254C23×C4—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8C2×C4×C4112yes—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4C2×C4×C4112yes—
265C4×D4D4×C4112yes—
266#117—42no—
267#117—42no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4D4×C4111yescharacteristic
273C2×C4⋊C4D4×C4111yescharacteristic
274C2×C4⋊C4D4×C4111yescharacteristic
275C2×C4⋊C4D4×C4112yes—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279C2×C42—22no—
280C2×C42—21no—
281C2×C42C23×C4111yescharacteristic
282#107—24no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8C2×C4×C4112yes—
287#103—42no—
288#103—42no—
289#102—24no—
290C4×C8—21no—
291C4×C8—21no—
292#95—22no—
293#95—21no—
294C24—21no—
295C2×Q8—22no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4C22⋊C4×C4112yes—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4C2×D4×C4111yescharacteristic
319C22×C4C2×D4×C4111yescharacteristic
320C22×C4C2×D4×C4111yescharacteristic
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—42no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4C22⋊C4×C4112yes—
344C4⋊C4D8×C4112yes—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—44no—
348C22⋊C4—82no—
349C42—44no—
350C42—41no—
351C42—41no—
352C42C22×C4×C4111yescharacteristic
353C42C2×D4×C4111yescharacteristic
354C42#41×C4111yescharacteristic
355C42#41×C4111yescharacteristic
356C23—22no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23#120×C4111yescharacteristic
364Q8—42no—
365Q8—42no—
366Q8—81no—
367Q8—81no—
368D4—22no—
369D4—22no—
370D4—41no—
371D4—41no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4C2×C22⋊C4×C4111yescharacteristic
394C2×C4C4×D4×C4111yescharacteristic
395C2×C4C4×D4×C4111yescharacteristic
396C2×C4#121×C4111yescharacteristic
397C2×C4#121×C4111yescharacteristic
398C2×C4#123×C4111yescharacteristic
399C2×C4C2×D8×C4111yescharacteristic
400C2×C4#135×C4111yescharacteristic
401C2×C4#135×C4111yescharacteristic
402C2×C4#135×C4111yescharacteristic
403C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
404C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
405C2×C4#137×C4111yescharacteristic
406C2×C4#137×C4111yescharacteristic
407C8—42no—
408C8—42no—
409C8—81no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22C41×#38611yescharacteristic
418C22C41×#44711yescharacteristic
419C22C41×#44911yescharacteristic
420C22C41×#45211yescharacteristic
421C22C41×#45211yescharacteristic
422C22C41×#45511yescharacteristic
423C22C41×#45611yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—42no—
428C4—82no—
429C4—82no—
430C4—81no—
431C4C41×#41611yescharacteristic
432C4C41×#41911yescharacteristic
433C4C4×D8×C4111yescharacteristic
434C4C41×#44211yescharacteristic
435C4C41×#45911yescharacteristic
436C4C41×#46311yescharacteristic
437C4C41×#48511yescharacteristic
438C4C41×#48511yescharacteristic
439C2—82no—
440C2C41×#164111yescharacteristic
441C2C41×#164611yescharacteristic
442C2C41×#164711yescharacteristic
443C2C41×#165211yescharacteristic
444C2C41×#187311yescharacteristic
445C2C41×#187911yescharacteristic
446C2C41×#188211yescharacteristic
subgroupG/H
center, socleC23×C41#120
commutatorC42C22×C4×C41
Frattini, cosocleC2×C42C23×C41
prime radicalC22×D4×C41D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C41×#1990C2semidirect
4. C41×#1981C2semidirect
6. C41×#1296C2semidirect
7. C41×#1279C2semidirect
12. C41×#474C4semidirect
186. #8984C41direct (N × H)
218. #1990C2×C41semidirect
219. #1981C2×C41semidirect
221. #1296C2×C41semidirect
222. #1279C2×C41semidirect
235. #474C4×C41semidirect
251. C41#8984direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4742
C41×#23542
C41×#19902
C41×#19812
C2×C41×D4⋊C82
C41×#12962
C41×#12792
#898441