Finite Group Databasebeta

← C41×#9937 #23786138

Subgroups — C41×#9937 #23786138

Order 10496.

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

normal subgroups only

This group has 526 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×#3195C211yesmaximal, characteristic
2C41×#3095C211yesmaximal, characteristic
3C41×#2625C211yesmaximal, characteristic
4C41×#1996C211yesmaximal, characteristic
5C41×#1826C211yesmaximal, characteristic
6C41×#1508C211yesmaximal, characteristic
7C41×#1305C211yesmaximal, characteristic
8C2×C22⋊Q8×C41C2211yescharacteristic
9C2×C22⋊Q8×C41C2211yescharacteristic
10C2×#117×C41C2211yescharacteristic
11C41×#485—22no—
12C41×#484—21no—
13C41×#483—21no—
14C41×#483—21no—
15C41×#483—21no—
16C41×#470—22no—
17C41×#451—21no—
18C41×#451—21no—
19C41×#428—21no—
20C41×#419—21no—
21C41×#407C2211yescharacteristic
22C41×#407C2211yescharacteristic
23C41×#400—21no—
24C41×#398—21no—
25C41×#397—22no—
26C41×#391—21no—
27C41×#389—21no—
28C41×#380C2211yescharacteristic
29C4×C22⋊C4×C41C2211yescharacteristic
30C41×#342—22no—
31C41×#339—22no—
32C41×#328—22no—
33C22×Q8×C41D411yescharacteristic
34C22×Q8×C41D411yescharacteristic
35C23×C4×C41C2311yescharacteristic
36C2×Q16×C41—22no—
37C2×M16×C41—21no—
38C2×M16×C41D412yes—
39C22⋊Q8×C41—21no—
40C22⋊Q8×C41—21no—
41C22⋊Q8×C41—21no—
42C22⋊Q8×C41—21no—
43C22⋊Q8×C41—21no—
44C22⋊Q8×C41—21no—
45C22⋊Q8×C41—21no—
46C22⋊Q8×C41—21no—
47#117×C41—21no—
48#117×C41—21no—
49#117×C41—21no—
50#117×C41—21no—
51C2×C4⋊C4×C41—21no—
52C2×C4⋊C4×C41—21no—
53C2×C4⋊C4×C41—21no—
54C2×C4⋊C4×C41—22no—
55C2×C4⋊C4×C41D411yescharacteristic
56C2×C4⋊C4×C41D411yescharacteristic
57C2×C4⋊C4×C41D411yescharacteristic
58C2×C4⋊C4×C41D411yescharacteristic
59C2×C22⋊C4×C41—21no—
60C2×C22⋊C4×C41—21no—
61C2×C22⋊C4×C41—21no—
62C2×C22⋊C4×C41—21no—
63C2×C22⋊C4×C41D412yes—
64C2×C42×C41—21no—
65C2×C42×C41—21no—
66#107×C41—22no—
67#106×C41—22no—
68#106×C41—22no—
69#103×C41—22no—
70#103×C41—22no—
71#103×C41—22no—
72#103×C41—22no—
73C22⋊C8×C41—21no—
74C22⋊C8×C41—21no—
75C22⋊C8×C41—21no—
76C22⋊C8×C41D412yes—
77#95×C41—22no—
78#95×C41—22no—
79#95×C41—22no—
80#95×C41—21no—
81#95×C41—21no—
82C24×C41C2×D411yescharacteristic
83C2×Q8×C41—21no—
84C2×Q8×C41—21no—
85C2×Q8×C41—21no—
86C2×Q8×C41—21no—
87C2×Q8×C41—42no—
88C2×Q8×C41—42no—
89C22×C4×C41—21no—
90C22×C4×C41—21no—
91C22×C4×C41—22no—
92C22×C4×C41—21no—
93C22×C4×C41—21no—
94C22×C4×C41—21no—
95C22×C4×C41—21no—
96C22×C4×C41—42no—
97C22×C4×C41—41no—
98C22×C4×C41C2×D411yescharacteristic
99C22×C4×C41C2×D411yescharacteristic
100C22×C4×C41C2×D411yescharacteristic
101C22×C4×C41C2×D411yescharacteristic
102C22×C4×C41C2×D411yescharacteristic
103C22×C4×C41#4111yescharacteristic
104Q16×C41—82no—
105M16×C41—42no—
106M16×C41—42no—
107C2×C8×C41—22no—
108C2×C8×C41—22no—
109C4⋊C4×C41—21no—
110C4⋊C4×C41—21no—
111C4⋊C4×C41—21no—
112C4⋊C4×C41—21no—
113C4⋊C4×C41—21no—
114C4⋊C4×C41—21no—
115C4⋊C4×C41—21no—
116C4⋊C4×C41—21no—
117C4⋊C4×C41—42no—
118C4⋊C4×C41—41no—
119C4⋊C4×C41—41no—
120C4⋊C4×C41—41no—
121C4⋊C4×C41—41no—
122C4⋊C4×C41—82no—
123C22⋊C4×C41—22no—
124C22⋊C4×C41—41no—
125C22⋊C4×C41—41no—
126C22⋊C4×C41—41no—
127C22⋊C4×C41—41no—
128C22⋊C4×C41—41no—
129C22⋊C4×C41—41no—
130C22⋊C4×C41—41no—
131C22⋊C4×C41—42no—
132C42×C41—42no—
133C42×C41—41no—
134C42×C41—41no—
135C23×C41—21no—
136C23×C41—21no—
137C23×C41—41no—
138C23×C41—41no—
139C23×C41#12011yescharacteristic
140C23×C41#12111yescharacteristic
141C23×C41#12711yescharacteristic
142Q8×C41—42no—
143Q8×C41—42no—
144Q8×C41—42no—
145Q8×C41—81no—
146C2×C4×C41—22no—
147C2×C4×C41—22no—
148C2×C4×C41—22no—
149C2×C4×C41—41no—
150C2×C4×C41—41no—
151C2×C4×C41—41no—
152C2×C4×C41—42no—
153C2×C4×C41—42no—
154C2×C4×C41—42no—
155C2×C4×C41—42no—
156C2×C4×C41—42no—
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—41no—
165C2×C4×C41—41no—
166C2×C4×C41—41no—
167C2×C4×C41—41no—
168C2×C4×C41—81no—
169C2×C4×C41—81no—
170C2×C4×C41—81no—
171C2×C4×C41—81no—
172C2×C4×C41#12011yescharacteristic
173C2×C4×C41#12011yescharacteristic
174C2×C4×C41#12111yescharacteristic
175C2×C4×C41#12111yescharacteristic
176C8×C41—42no—
177C8×C41—42no—
178#9937C4111yesmaximal, characteristic, direct product factor, Sylow
179C22×C41—21no—
180C22×C41—21no—
181C22×C41—21no—
182C22×C41—21no—
183C22×C41—21no—
184C22×C41—21no—
185C22×C41—21no—
186C22×C41—21no—
187C22×C41—81no—
188C22×C41—81no—
189C22×C41#39211yescharacteristic
190C22×C41#45511yescharacteristic
191C22×C41#45611yescharacteristic
192C4×C41—21no—
193C4×C41—21no—
194C4×C41—21no—
195C4×C41—82no—
196C4×C41—82no—
197C4×C41—81no—
198C4×C41—81no—
199C4×C41—81no—
200C4×C41—81no—
201C4×C41—81no—
202C4×C41—81no—
203C4×C41#45812yes—
204#3195C2×C4111yescharacteristic
205#3095C2×C4111yescharacteristic
206#2625C2×C4111yescharacteristic
207#1996C2×C4111yescharacteristic
208#1826C2×C4111yescharacteristic
209#1508C2×C4111yescharacteristic
210#1305C2×C4111yescharacteristic
211C2×C41—21no—
212C2×C41—21no—
213C2×C41—41no—
214C2×C41—41no—
215C2×C41#200711yescharacteristic
216C2×C41#200911yescharacteristic
217C2×C41#202211yescharacteristic
218C2×C22⋊Q8C22×C4111yescharacteristic
219C2×C22⋊Q8C22×C4111yescharacteristic
220C2×#117C22×C4111yescharacteristic
221#485—22no—
222#484—21no—
223#483—21no—
224#483—21no—
225#483—21no—
226#470—22no—
227#451—21no—
228#451—21no—
229#428—21no—
230#419—21no—
231#407C22×C4111yescharacteristic
232#407C22×C4111yescharacteristic
233#400—21no—
234#398—21no—
235#397—22no—
236#391—21no—
237#389—21no—
238#380C22×C4111yescharacteristic
239C4×C22⋊C4C22×C4111yescharacteristic
240#342—22no—
241#339—22no—
242#328—22no—
243C41#993711yescharacteristic, direct product factor, Sylow
244C22×Q8D4×C4111yescharacteristic
245C22×Q8D4×C4111yescharacteristic
246C23×C4C23×C4111yescharacteristic
247C2×Q16—22no—
248C2×M16—21no—
249C2×M16D4×C4112yes—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258#117—21no—
259#117—21no—
260#117—21no—
261#117—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4D4×C4111yescharacteristic
267C2×C4⋊C4D4×C4111yescharacteristic
268C2×C4⋊C4D4×C4111yescharacteristic
269C2×C4⋊C4D4×C4111yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4D4×C4112yes—
275C2×C42—21no—
276C2×C42—21no—
277#107—22no—
278#106—22no—
279#106—22no—
280#103—22no—
281#103—22no—
282#103—22no—
283#103—22no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8D4×C4112yes—
288#95—22no—
289#95—22no—
290#95—22no—
291#95—21no—
292#95—21no—
293C24C2×D4×C4111yescharacteristic
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—42no—
299C2×Q8—42no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—41no—
309C22×C4C2×D4×C4111yescharacteristic
310C22×C4C2×D4×C4111yescharacteristic
311C22×C4C2×D4×C4111yescharacteristic
312C22×C4C2×D4×C4111yescharacteristic
313C22×C4C2×D4×C4111yescharacteristic
314C22×C4#41×C4111yescharacteristic
315Q16—82no—
316M16—42no—
317M16—42no—
318C2×C8—22no—
319C2×C8—22no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—42no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—82no—
334C22⋊C4—22no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—42no—
343C42—42no—
344C42—41no—
345C42—41no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23#120×C4111yescharacteristic
351C23#121×C4111yescharacteristic
352C23#127×C4111yescharacteristic
353Q8—42no—
354Q8—42no—
355Q8—42no—
356Q8—81no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4#120×C4111yescharacteristic
384C2×C4#120×C4111yescharacteristic
385C2×C4#121×C4111yescharacteristic
386C2×C4#121×C4111yescharacteristic
387C8—42no—
388C8—42no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—81no—
398C22—81no—
399C22C41×#39211yescharacteristic
400C22C41×#45511yescharacteristic
401C22C41×#45611yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—82no—
406C4—82no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4C41×#45812yes—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2C41×#200711yescharacteristic
419C2C41×#200911yescharacteristic
420C2C41×#202211yescharacteristic
subgroupG/H
center, socleC22×C41#392
commutator, Frattini, cosocleC23×C4C23×C41
prime radicalC24×C41C2×D4
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
178. #9937C41direct (N × H)
243. C41#9937direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#31952
C41×#30952
C41×#26252
C41×#19962
C41×#18262
C41×#15082
C41×#13052
#993741