Finite Group Databasebeta

← C41×#9944 #23786145

Subgroups — C41×#9944 #23786145

Order 10496.

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

normal subgroups only

This group has 654 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×#3095C211yesmaximal, characteristic, complemented
2C41×#2561C211yesmaximal, characteristic
3C41×#2482C211yesmaximal, characteristic
4C41×#1826C211yesmaximal, characteristic, complemented
5C41×#1511C211yesmaximal, characteristic, complemented
6C41×#1462C211yesmaximal, characteristic
7C41×#1284C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C41C2211yescharacteristic
9C2×#117×C41C2211yescharacteristic
10C22×C22⋊C4×C41C2211yescharacteristic
11C41×#485—22no—
12C41×#484—21no—
13C41×#483—21no—
14C41×#428—21no—
15C41×#419—21no—
16C41×#407C2211yescharacteristic
17C41×#407C2211yescharacteristic
18C41×#399—21no—
19C41×#397—21no—
20C41×#397—21no—
21C41×#393—21no—
22C41×#388—22no—
23C41×#388—22no—
24C41×#385—21no—
25C41×#381—21no—
26C41×#381C2211yescharacteristic
27C41×#379—21no—
28C41×#379—21no—
29C4×C22⋊C4×C41C2211yescharacteristic
30C41×#339—22no—
31C41×#328—22no—
32C41×#323—22no—
33C25×C41D411yescharacteristic
34C22×Q8×C41D411yescharacteristic
35C23×C4×C41D411yescharacteristic
36C23×C4×C41C2311yescharacteristic
37C2×M16×C41—21no—
38C2×M16×C41—21no—
39C22⋊Q8×C41—21no—
40C22⋊Q8×C41—21no—
41C22⋊Q8×C41—21no—
42C22⋊Q8×C41—21no—
43#117×C41—21no—
44#117×C41—21no—
45#117×C41—21no—
46#117×C41—21no—
47C2×C4⋊C4×C41—21no—
48C2×C4⋊C4×C41—22no—
49C2×C4⋊C4×C41D411yescharacteristic
50C2×C4⋊C4×C41D411yescharacteristic
51C2×C4⋊C4×C41D411yescharacteristic
52C2×C22⋊C4×C41—22no—
53C2×C22⋊C4×C41—22no—
54C2×C22⋊C4×C41—21no—
55C2×C22⋊C4×C41—21no—
56C2×C22⋊C4×C41—21no—
57C2×C22⋊C4×C41—21no—
58C2×C22⋊C4×C41—21no—
59C2×C22⋊C4×C41—21no—
60C2×C22⋊C4×C41—21no—
61C2×C22⋊C4×C41—21no—
62C2×C22⋊C4×C41—21no—
63C2×C22⋊C4×C41—21no—
64C2×C22⋊C4×C41—22no—
65C2×C22⋊C4×C41—22no—
66C2×C42×C41—21no—
67C2×C42×C41D412yes—
68#107×C41—22no—
69#106×C41—22no—
70#103×C41—22no—
71#103×C41—22no—
72C22⋊C8×C41—21no—
73C22⋊C8×C41—21no—
74C22⋊C8×C41—21no—
75C22⋊C8×C41D412yes—
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×C41—21no—
84C24×C41—21no—
85C24×C41—42no—
86C24×C41—42no—
87C24×C41—42no—
88C24×C41C2×D411yescharacteristic
89C2×Q8×C41—21no—
90C2×Q8×C41—21no—
91C2×Q8×C41—42no—
92C22×C4×C41—21no—
93C22×C4×C41—22no—
94C22×C4×C41—22no—
95C22×C4×C41—21no—
96C22×C4×C41—21no—
97C22×C4×C41—21no—
98C22×C4×C41—21no—
99C22×C4×C41—21no—
100C22×C4×C41—21no—
101C22×C4×C41—42no—
102C22×C4×C41—42no—
103C22×C4×C41C2×D411yescharacteristic
104C22×C4×C41C2×D411yescharacteristic
105C22×C4×C41C2×D411yescharacteristic
106C22×C4×C41C2×D411yescharacteristic
107C22×C4×C41C2×D411yescharacteristic
108C22×C4×C41#4111yescharacteristic
109M16×C41—42no—
110M16×C41—42no—
111C2×C8×C41—22no—
112C2×C8×C41—41no—
113C4⋊C4×C41—21no—
114C4⋊C4×C41—21no—
115C4⋊C4×C41—21no—
116C4⋊C4×C41—21no—
117C4⋊C4×C41—21no—
118C4⋊C4×C41—21no—
119C4⋊C4×C41—41no—
120C4⋊C4×C41—41no—
121C4⋊C4×C41—82no—
122C22⋊C4×C41—42no—
123C22⋊C4×C41—42no—
124C22⋊C4×C41—44no—
125C22⋊C4×C41—44no—
126C22⋊C4×C41—41no—
127C22⋊C4×C41—41no—
128C22⋊C4×C41—41no—
129C22⋊C4×C41—41no—
130C22⋊C4×C41—41no—
131C22⋊C4×C41—41no—
132C22⋊C4×C41—41no—
133C22⋊C4×C41—41no—
134C22⋊C4×C41—82no—
135C22⋊C4×C41—82no—
136C42×C41—42no—
137C42×C41—41no—
138C42×C41—41no—
139C23×C41—22no—
140C23×C41—22no—
141C23×C41—22no—
142C23×C41—22no—
143C23×C41—22no—
144C23×C41—41no—
145C23×C41—42no—
146C23×C41—41no—
147C23×C41—41no—
148C23×C41—42no—
149C23×C41—41no—
150C23×C41—41no—
151C23×C41—42no—
152C23×C41—42no—
153C23×C41—81no—
154C23×C41—81no—
155C23×C41—88no—
156C23×C41#12011yescharacteristic
157C23×C41#12011yescharacteristic
158C23×C41#12111yescharacteristic
159Q8×C41—42no—
160Q8×C41—81no—
161C2×C4×C41—22no—
162C2×C4×C41—22no—
163C2×C4×C41—41no—
164C2×C4×C41—41no—
165C2×C4×C41—41no—
166C2×C4×C41—41no—
167C2×C4×C41—42no—
168C2×C4×C41—42no—
169C2×C4×C41—42no—
170C2×C4×C41—42no—
171C2×C4×C41—42no—
172C2×C4×C41—42no—
173C2×C4×C41—42no—
174C2×C4×C41—41no—
175C2×C4×C41—41no—
176C2×C4×C41—41no—
177C2×C4×C41—41no—
178C2×C4×C41—41no—
179C2×C4×C41—42no—
180C2×C4×C41—42no—
181C2×C4×C41—42no—
182C2×C4×C41—42no—
183C2×C4×C41—42no—
184C2×C4×C41—81no—
185C2×C4×C41#12011yescharacteristic
186C2×C4×C41#12111yescharacteristic
187C2×C4×C41#12111yescharacteristic
188C2×C4×C41#12711yescharacteristic
189C8×C41—42no—
190C8×C41—81no—
191#9944C4111yesmaximal, characteristic, direct product factor, Sylow
192C22×C41—21no—
193C22×C41—21no—
194C22×C41—21no—
195C22×C41—21no—
196C22×C41—21no—
197C22×C41—21no—
198C22×C41—21no—
199C22×C41—44no—
200C22×C41—44no—
201C22×C41—44no—
202C22×C41—42no—
203C22×C41—82no—
204C22×C41—82no—
205C22×C41—82no—
206C22×C41—82no—
207C22×C41—81no—
208C22×C41—81no—
209C22×C41#39211yescharacteristic
210C22×C41#45512yes—
211C22×C41#45812yes—
212C4×C41—21no—
213C4×C41—21no—
214C4×C41—21no—
215C4×C41—21no—
216C4×C41—82no—
217C4×C41—82no—
218C4×C41—81no—
219C4×C41—81no—
220C4×C41—81no—
221C4×C41—81no—
222C4×C41—81no—
223#3095C2×C4111yescharacteristic, complemented
224#2561C2×C4111yescharacteristic
225#2482C2×C4111yescharacteristic
226#1826C2×C4111yescharacteristic, complemented
227#1511C2×C4111yescharacteristic, complemented
228#1462C2×C4111yescharacteristic
229#1284C2×C4111yescharacteristic, complemented
230C2×C41—22no—
231C2×C41—22no—
232C2×C41—41no—
233C2×C41—82no—
234C2×C41#200411yescharacteristic
235C2×C41#201011yescharacteristic
236C2×C41#202211yescharacteristic
237C2×C22⋊Q8C22×C4111yescharacteristic
238C2×#117C22×C4111yescharacteristic
239C22×C22⋊C4C22×C4111yescharacteristic
240#485—22no—
241#484—21no—
242#483—21no—
243#428—21no—
244#419—21no—
245#407C22×C4111yescharacteristic
246#407C22×C4111yescharacteristic
247#399—21no—
248#397—21no—
249#397—21no—
250#393—21no—
251#388—22no—
252#388—22no—
253#385—21no—
254#381—21no—
255#381C22×C4111yescharacteristic
256#379—21no—
257#379—21no—
258C4×C22⋊C4C22×C4111yescharacteristic
259#339—22no—
260#328—22no—
261#323—22no—
262C41#994411yescharacteristic, direct product factor, Sylow
263C25D4×C4111yescharacteristic
264C22×Q8D4×C4111yescharacteristic
265C23×C4D4×C4111yescharacteristic
266C23×C4C23×C4111yescharacteristic
267C2×M16—21no—
268C2×M16—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273#117—21no—
274#117—21no—
275#117—21no—
276#117—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4D4×C4111yescharacteristic
280C2×C4⋊C4D4×C4111yescharacteristic
281C2×C4⋊C4D4×C4111yescharacteristic
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C42—21no—
297C2×C42D4×C4112yes—
298#107—22no—
299#106—22no—
300#103—22no—
301#103—22no—
302C22⋊C8—21no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8D4×C4112yes—
306#95—22no—
307#95—22no—
308#95—22no—
309#95—21no—
310#95—21no—
311#95D4×C4112yes—
312C24—21no—
313C24—21no—
314C24—21no—
315C24—42no—
316C24—42no—
317C24—42no—
318C24C2×D4×C4111yescharacteristic
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—42no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4C2×D4×C4111yescharacteristic
334C22×C4C2×D4×C4111yescharacteristic
335C22×C4C2×D4×C4111yescharacteristic
336C22×C4C2×D4×C4111yescharacteristic
337C22×C4C2×D4×C4111yescharacteristic
338C22×C4#41×C4111yescharacteristic
339M16—42no—
340M16—42no—
341C2×C8—22no—
342C2×C8—41no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—82no—
352C22⋊C4—42no—
353C22⋊C4—42no—
354C22⋊C4—44no—
355C22⋊C4—44no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—82no—
365C22⋊C4—82no—
366C42—42no—
367C42—41no—
368C42—41no—
369C23—22no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—41no—
375C23—42no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—42no—
382C23—42no—
383C23—81no—
384C23—81no—
385C23—88no—
386C23#120×C4111yescharacteristic
387C23#120×C4111yescharacteristic
388C23#121×C4111yescharacteristic
389Q8—42no—
390Q8—81no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—81no—
415C2×C4#120×C4111yescharacteristic
416C2×C4#121×C4111yescharacteristic
417C2×C4#121×C4111yescharacteristic
418C2×C4#127×C4111yescharacteristic
419C8—42no—
420C8—81no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—44no—
429C22—44no—
430C22—44no—
431C22—42no—
432C22—82no—
433C22—82no—
434C22—82no—
435C22—82no—
436C22—81no—
437C22—81no—
438C22C41×#39211yescharacteristic
439C22C41×#45512yes—
440C22C41×#45812yes—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—82no—
446C4—82no—
447C4—81no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—81no—
452C2—22no—
453C2—22no—
454C2—41no—
455C2—82no—
456C2C41×#200411yescharacteristic
457C2C41×#201011yescharacteristic
458C2C41×#202211yescharacteristic
subgroupG/H
center, socleC22×C41#392
commutator, Frattini, cosocleC23×C4C23×C41
prime radicalC25×C41D4
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
1. C41×#3095C2semidirect
4. C41×#1826C2semidirect
5. C41×#1511C2semidirect
7. C41×#1284C2semidirect
191. #9944C41direct (N × H)
223. #3095C2×C41semidirect
226. #1826C2×C41semidirect
227. #1511C2×C41semidirect
229. #1284C2×C41semidirect
262. C41#9944direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#30952
C41×#25612
C41×#24822
C41×#18262
C41×#15112
C41×#14622
C41×#12842
#994441