Finite Group Databasebeta

← C41×#9936 #23786137

Subgroups — C41×#9936 #23786137

Order 10496.

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

normal subgroups only

This group has 568 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×#3193C211yesmaximal, characteristic
2C41×#3095C211yesmaximal, characteristic, complemented
3C41×#2624C211yesmaximal, characteristic
4C41×#1996C211yesmaximal, characteristic, complemented
5C41×#1826C211yesmaximal, characteristic, complemented
6C41×#1507C211yesmaximal, characteristic
7C41×#1305C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C41C2211yescharacteristic
9C2×#121×C41C2211yescharacteristic
10C2×#117×C41C2211yescharacteristic
11C41×#485—22no—
12C41×#484—21no—
13C41×#484—21no—
14C41×#483—21no—
15C41×#480—21no—
16C41×#468—22no—
17C41×#450—21no—
18C41×#448—21no—
19C41×#428—21no—
20C41×#419—21no—
21C41×#407C2211yescharacteristic
22C41×#407C2211yescharacteristic
23C41×#399—21no—
24C41×#397—21no—
25C41×#394—22no—
26C41×#390—21no—
27C41×#389—21no—
28C41×#380C2211yescharacteristic
29C4×C22⋊C4×C41C2211yescharacteristic
30C41×#342—22no—
31C41×#339—22no—
32C41×#327—22no—
33C22×Q8×C41D411yescharacteristic
34C22×D4×C41—21no—
35C22×D4×C41D411yescharacteristic
36C23×C4×C41C2311yescharacteristic
37C2×SD16×C41—22no—
38C2×M16×C41—21no—
39C2×M16×C41D412yes—
40C22⋊Q8×C41—21no—
41C22⋊Q8×C41—21no—
42C22⋊Q8×C41—21no—
43C22⋊Q8×C41—21no—
44#121×C41—21no—
45#121×C41—21no—
46#121×C41—21no—
47#121×C41—21no—
48#117×C41—21no—
49#117×C41—21no—
50#117×C41—21no—
51#117×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×C41—22no—
64C2×C22⋊C4×C41—22no—
65C2×C22⋊C4×C41D412yes—
66C2×C42×C41—21no—
67C2×C42×C41—21no—
68#107×C41—22no—
69#107×C41—22no—
70#106×C41—22no—
71#103×C41—22no—
72#103×C41—22no—
73#103×C41—22no—
74#102×C41—22no—
75C22⋊C8×C41—21no—
76C22⋊C8×C41—21no—
77C22⋊C8×C41—21no—
78C22⋊C8×C41D412yes—
79#95×C41—22no—
80#95×C41—21no—
81#95×C41—21no—
82C24×C41—21no—
83C24×C41C2×D411yescharacteristic
84C2×Q8×C41—21no—
85C2×Q8×C41—21no—
86C2×Q8×C41—42no—
87C2×D4×C41—21no—
88C2×D4×C41—21no—
89C2×D4×C41—42no—
90C2×D4×C41—41no—
91C2×D4×C41—41no—
92C2×D4×C41—82no—
93C22×C4×C41—21no—
94C22×C4×C41—22no—
95C22×C4×C41—21no—
96C22×C4×C41—21no—
97C22×C4×C41—21no—
98C22×C4×C41—21no—
99C22×C4×C41—42no—
100C22×C4×C41—41no—
101C22×C4×C41C2×D411yescharacteristic
102C22×C4×C41C2×D411yescharacteristic
103C22×C4×C41C2×D411yescharacteristic
104C22×C4×C41C2×D411yescharacteristic
105C22×C4×C41C2×D411yescharacteristic
106C22×C4×C41#4111yescharacteristic
107SD16×C41—82no—
108M16×C41—42no—
109M16×C41—42no—
110C2×C8×C41—22no—
111C2×C8×C41—22no—
112C4⋊C4×C41—21no—
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—21no—
120C4⋊C4×C41—42no—
121C4⋊C4×C41—41no—
122C4⋊C4×C41—41no—
123C4⋊C4×C41—82no—
124C22⋊C4×C41—22no—
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—41no—
132C22⋊C4×C41—42no—
133C22⋊C4×C41—82no—
134C22⋊C4×C41—82no—
135C42×C41—42no—
136C42×C41—41no—
137C42×C41—41no—
138C23×C41—21no—
139C23×C41—21no—
140C23×C41—41no—
141C23×C41—41no—
142C23×C41—42no—
143C23×C41—42no—
144C23×C41—41no—
145C23×C41—41no—
146C23×C41—41no—
147C23×C41#12011yescharacteristic
148C23×C41#12111yescharacteristic
149C23×C41#12711yescharacteristic
150Q8×C41—42no—
151Q8×C41—42no—
152D4×C41—42no—
153D4×C41—81no—
154D4×C41—82no—
155D4×C41—82no—
156C2×C4×C41—22no—
157C2×C4×C41—22no—
158C2×C4×C41—22no—
159C2×C4×C41—41no—
160C2×C4×C41—41no—
161C2×C4×C41—41no—
162C2×C4×C41—42no—
163C2×C4×C41—41no—
164C2×C4×C41—42no—
165C2×C4×C41—42no—
166C2×C4×C41—41no—
167C2×C4×C41—42no—
168C2×C4×C41—41no—
169C2×C4×C41—41no—
170C2×C4×C41—41no—
171C2×C4×C41—41no—
172C2×C4×C41—41no—
173C2×C4×C41—42no—
174C2×C4×C41—41no—
175C2×C4×C41—41no—
176C2×C4×C41—81no—
177C2×C4×C41—81no—
178C2×C4×C41—81no—
179C2×C4×C41—81no—
180C2×C4×C41#12011yescharacteristic
181C2×C4×C41#12011yescharacteristic
182C2×C4×C41#12111yescharacteristic
183C2×C4×C41#12111yescharacteristic
184C8×C41—42no—
185C8×C41—42no—
186#9936C4111yesmaximal, characteristic, direct product factor, Sylow
187C22×C41—21no—
188C22×C41—21no—
189C22×C41—21no—
190C22×C41—21no—
191C22×C41—21no—
192C22×C41—21no—
193C22×C41—21no—
194C22×C41—21no—
195C22×C41—81no—
196C22×C41—81no—
197C22×C41—82no—
198C22×C41—82no—
199C22×C41—81no—
200C22×C41—81no—
201C22×C41—81no—
202C22×C41#39211yescharacteristic
203C22×C41#45511yescharacteristic
204C22×C41#45611yescharacteristic
205C4×C41—21no—
206C4×C41—21no—
207C4×C41—21no—
208C4×C41—82no—
209C4×C41—82no—
210C4×C41—81no—
211C4×C41—81no—
212C4×C41—81no—
213C4×C41—81no—
214C4×C41—81no—
215C4×C41#45812yes—
216#3193C2×C4111yescharacteristic
217#3095C2×C4111yescharacteristic, complemented
218#2624C2×C4111yescharacteristic
219#1996C2×C4111yescharacteristic, complemented
220#1826C2×C4111yescharacteristic, complemented
221#1507C2×C4111yescharacteristic
222#1305C2×C4111yescharacteristic, complemented
223C2×C41—21no—
224C2×C41—21no—
225C2×C41—41no—
226C2×C41—41no—
227C2×C41—161no—
228C2×C41#200711yescharacteristic
229C2×C41#200811yescharacteristic
230C2×C41#202211yescharacteristic
231C2×C22⋊Q8C22×C4111yescharacteristic
232C2×#121C22×C4111yescharacteristic
233C2×#117C22×C4111yescharacteristic
234#485—22no—
235#484—21no—
236#484—21no—
237#483—21no—
238#480—21no—
239#468—22no—
240#450—21no—
241#448—21no—
242#428—21no—
243#419—21no—
244#407C22×C4111yescharacteristic
245#407C22×C4111yescharacteristic
246#399—21no—
247#397—21no—
248#394—22no—
249#390—21no—
250#389—21no—
251#380C22×C4111yescharacteristic
252C4×C22⋊C4C22×C4111yescharacteristic
253#342—22no—
254#339—22no—
255#327—22no—
256C41#993611yescharacteristic, direct product factor, Sylow
257C22×Q8D4×C4111yescharacteristic
258C22×D4—21no—
259C22×D4D4×C4111yescharacteristic
260C23×C4C23×C4111yescharacteristic
261C2×SD16—22no—
262C2×M16—21no—
263C2×M16D4×C4112yes—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268#121—21no—
269#121—21no—
270#121—21no—
271#121—21no—
272#117—21no—
273#117—21no—
274#117—21no—
275#117—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4D4×C4111yescharacteristic
280C2×C4⋊C4D4×C4111yescharacteristic
281C2×C4⋊C4D4×C4111yescharacteristic
282C2×C4⋊C4D4×C4111yescharacteristic
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4D4×C4112yes—
290C2×C42—21no—
291C2×C42—21no—
292#107—22no—
293#107—22no—
294#106—22no—
295#103—22no—
296#103—22no—
297#103—22no—
298#102—22no—
299C22⋊C8—21no—
300C22⋊C8—21no—
301C22⋊C8—21no—
302C22⋊C8D4×C4112yes—
303#95—22no—
304#95—21no—
305#95—21no—
306C24—21no—
307C24C2×D4×C4111yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—42no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—42no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—82no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—42no—
324C22×C4—41no—
325C22×C4C2×D4×C4111yescharacteristic
326C22×C4C2×D4×C4111yescharacteristic
327C22×C4C2×D4×C4111yescharacteristic
328C22×C4C2×D4×C4111yescharacteristic
329C22×C4C2×D4×C4111yescharacteristic
330C22×C4#41×C4111yescharacteristic
331SD16—82no—
332M16—42no—
333M16—42no—
334C2×C8—22no—
335C2×C8—22no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—42no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—82no—
348C22⋊C4—22no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—42no—
357C22⋊C4—82no—
358C22⋊C4—82no—
359C42—42no—
360C42—41no—
361C42—41no—
362C23—21no—
363C23—21no—
364C23—41no—
365C23—41no—
366C23—42no—
367C23—42no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23#120×C4111yescharacteristic
372C23#121×C4111yescharacteristic
373C23#127×C4111yescharacteristic
374Q8—42no—
375Q8—42no—
376D4—42no—
377D4—81no—
378D4—82no—
379D4—82no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4#120×C4111yescharacteristic
405C2×C4#120×C4111yescharacteristic
406C2×C4#121×C4111yescharacteristic
407C2×C4#121×C4111yescharacteristic
408C8—42no—
409C8—42no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—81no—
419C22—81no—
420C22—82no—
421C22—82no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22C41×#39211yescharacteristic
426C22C41×#45511yescharacteristic
427C22C41×#45611yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—82no—
432C4—82no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4C41×#45812yes—
439C2—21no—
440C2—21no—
441C2—41no—
442C2—41no—
443C2—161no—
444C2C41×#200711yescharacteristic
445C2C41×#200811yescharacteristic
446C2C41×#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
2. C41×#3095C2semidirect
4. C41×#1996C2semidirect
5. C41×#1826C2semidirect
7. C41×#1305C2semidirect
186. #9936C41direct (N × H)
217. #3095C2×C41semidirect
219. #1996C2×C41semidirect
220. #1826C2×C41semidirect
222. #1305C2×C41semidirect
256. C41#9936direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#31932
C41×#30952
C41×#26242
C41×#19962
C41×#18262
C41×#15072
C41×#13052
#993641