Finite Group Databasebeta

← C41×#9098 #23785299

Subgroups — C41×#9098 #23785299

Order 10496.

488 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2965C211yesmaximal, characteristic
2C4×#137×C41C211yesmaximal, characteristic
3C41×#1477C211yesmaximal, characteristic
4C2×C41×Q8⋊C8C211yesmaximal, characteristic, complemented
5C41×#1461C211yesmaximal, characteristic, complemented
6C41×#1283C211yesmaximal, characteristic, complemented
7C41×#1278C211yesmaximal, characteristic, complemented
8C2×#137×C41C411yescharacteristic
9C4×#41×C41C2211yescharacteristic
10C2×C4×Q8×C41C2211yescharacteristic
11C41×#446—21no—
12C41×#441—21no—
13C41×#440—21no—
14C4×Q16×C41—21no—
15C4×SD16×C41—21no—
16C41×#436—21no—
17C41×#435—22no—
18C41×#431—21no—
19C41×#431C2211yescharacteristic
20C41×#431C2211yescharacteristic
21C41×#428C411yescharacteristic
22C2×C4⋊C8×C41C2211yescharacteristic
23C41×#419C411yescharacteristic
24C41×#417C411yescharacteristic
25C4×M16×C41—21no—
26C4×M16×C41C2211yescharacteristic
27C2×C4×C8×C41C2211yescharacteristic
28C41×Q8⋊C8—21no—
29C41×Q8⋊C8—21no—
30C41×Q8⋊C8—21no—
31C41×D4⋊C8—21no—
32C41×#324—22no—
33C2×#41×C41C2×C411yescharacteristic
34C22×Q8×C41C2×C411yescharacteristic
35#137×C41—22no—
36#137×C41—22no—
37C2×Q16×C41—21no—
38C2×SD16×C41—21no—
39C2×M16×C41—22no—
40C2×M16×C41C2×C411yescharacteristic
41C2×M16×C41C2×C411yescharacteristic
42C22×C8×C41—21no—
43C22×C8×C41—21no—
44C4×Q8×C41—21no—
45C4×Q8×C41—21no—
46C4×Q8×C41—21no—
47C4×Q8×C41—21no—
48C4×Q8×C41D411yescharacteristic
49C4×Q8×C41D411yescharacteristic
50C4×D4×C41—21no—
51C4×D4×C41—21no—
52C4×D4×C41D411yescharacteristic
53C4×D4×C41D411yescharacteristic
54#117×C41—21no—
55#117×C41C2×C411yescharacteristic
56C2×C4⋊C4×C41—21no—
57C2×C4⋊C4×C41C2×C411yescharacteristic
58C2×C42×C41—21no—
59C2×C42×C41—21no—
60C2×C42×C41C2311yescharacteristic
61#107×C41—21no—
62#106×C41—21no—
63C4⋊C8×C41—22no—
64C4⋊C8×C41—21no—
65C4⋊C8×C41—21no—
66C4⋊C8×C41—21no—
67C4⋊C8×C41—21no—
68#103×C41—21no—
69#103×C41—21no—
70#103×C41—21no—
71#102×C41—21no—
72C22⋊C8×C41—22no—
73C22⋊C8×C41—21no—
74C22⋊C8×C41D412yes—
75#97×C41—22no—
76#97×C41—21no—
77C4×C8×C41—21no—
78C4×C8×C41—21no—
79C4×C8×C41—21no—
80C4×C8×C41—21no—
81C4×C8×C41D411yescharacteristic
82C4×C8×C41D411yescharacteristic
83#41×C41—21no—
84#41×C41—21no—
85#41×C41—21no—
86#41×C41—21no—
87C2×Q8×C41—21no—
88C2×Q8×C41—21no—
89C2×Q8×C41—21no—
90C2×Q8×C41—21no—
91C2×Q8×C41—21no—
92C2×Q8×C41C22⋊C411yescharacteristic
93C2×Q8×C41M1612yescomplemented
94C2×D4×C41—21no—
95C2×D4×C41C22⋊C411yescharacteristic
96C22×C4×C41—21no—
97C22×C4×C41—21no—
98C22×C4×C41—21no—
99C22×C4×C41—21no—
100C22×C4×C41—21no—
101C22×C4×C41C22×C411yescharacteristic
102C22×C4×C41C2×D411yescharacteristic
103C22×C4×C41#4111yescharacteristic
104Q16×C41—24no—
105SD16×C41—24no—
106M16×C41—21no—
107M16×C41—21no—
108M16×C41—21no—
109M16×C41—44no—
110M16×C41M1612yescomplemented
111C2×C8×C41—21no—
112C2×C8×C41—21no—
113C2×C8×C41—21no—
114C2×C8×C41—21no—
115C2×C8×C41—22no—
116C2×C8×C41—42no—
117C2×C8×C41—41no—
118C2×C8×C41—41no—
119C2×C8×C41—81no—
120C4⋊C4×C41—21no—
121C4⋊C4×C41—21no—
122C4⋊C4×C41—21no—
123C4⋊C4×C41—21no—
124C4⋊C4×C41—41no—
125C4⋊C4×C41—41no—
126C4⋊C4×C41C22⋊C411yescharacteristic
127C4⋊C4×C41C22⋊C411yescharacteristic
128C22⋊C4×C41—21no—
129C22⋊C4×C41—21no—
130C22⋊C4×C41—21no—
131C42×C41—21no—
132C42×C41—21no—
133C42×C41—21no—
134C42×C41—41no—
135C42×C41—41no—
136C42×C41C2×D411yescharacteristic
137C42×C41C2×D411yescharacteristic
138C42×C41C2×D411yescharacteristic
139C42×C41#4111yescharacteristic
140C23×C41—21no—
141C23×C41C4×D411yescharacteristic
142Q8×C41—22no—
143Q8×C41—21no—
144Q8×C41—21no—
145Q8×C41—22no—
146Q8×C41—41no—
147Q8×C41—41no—
148D4×C41—21no—
149D4×C41—21no—
150D4×C41—41no—
151D4×C41—41no—
152C2×C4×C41—21no—
153C2×C4×C41—21no—
154C2×C4×C41—21no—
155C2×C4×C41—21no—
156C2×C4×C41—21no—
157C2×C4×C41—22no—
158C2×C4×C41—41no—
159C2×C4×C41—42no—
160C2×C4×C41—41no—
161C2×C4×C41—41no—
162C2×C4×C41—41no—
163C2×C4×C41—41no—
164C2×C4×C41—41no—
165C2×C4×C41—41no—
166C2×C4×C41—41no—
167C2×C4×C41—81no—
168C2×C4×C41C2×C22⋊C411yescharacteristic
169C2×C4×C41C4×D411yescharacteristic
170C2×C4×C41#12011yescharacteristic
171C2×C4×C41#12111yescharacteristic
172C2×C4×C41#12111yescharacteristic
173C2×C4×C41#12311yescharacteristic
174C2×C4×C41C2×M1611yescharacteristic
175C2×C4×C41C2×M1611yescharacteristic
176C2×C4×C41#13111yescharacteristic
177C2×C4×C41#13111yescharacteristic
178C8×C41—22no—
179C8×C41—22no—
180C8×C41—41no—
181C8×C41—42no—
182C8×C41—41no—
183C8×C41—81no—
184C8×C41—81no—
185#9098C4111yesmaximal, characteristic, direct product factor, Sylow
186C22×C41—21no—
187C22×C41—21no—
188C22×C41—41no—
189C22×C41—41no—
190C22×C41—41no—
191C22×C41#38611yescharacteristic
192C22×C41#43511yescharacteristic
193C22×C41#43611yescharacteristic
194C4×C41—21no—
195C4×C41—21no—
196C4×C41—21no—
197C4×C41—41no—
198C4×C41—42no—
199C4×C41—41no—
200C4×C41—41no—
201C4×C41—81no—
202C4×C41#40711yescharacteristic
203C4×C41#40811yescharacteristic
204C4×C41#43511yescharacteristic
205C4×C41#43611yescharacteristic
206C4×C41#47111yescharacteristic
207C4×C41#47311yescharacteristic
208#2965C2×C4111yescharacteristic
209C4×#137C2×C4111yescharacteristic
210#1477C2×C4111yescharacteristic
211C2×Q8⋊C8C2×C4111yescharacteristic, complemented
212#1461C2×C4111yescharacteristic, complemented
213#1283C2×C4111yescharacteristic, complemented
214#1278C2×C4111yescharacteristic, complemented
215C2×C41—21no—
216C2×C41—21no—
217C2×C41—81no—
218C2×C41#187011yescharacteristic
219C2×C41#190611yescharacteristic
220C2×C41#190811yescharacteristic
221C2×#137C4×C4111yescharacteristic
222C4×#41C22×C4111yescharacteristic
223C2×C4×Q8C22×C4111yescharacteristic
224#446—21no—
225#441—21no—
226#440—21no—
227C4×Q16—21no—
228C4×SD16—21no—
229#436—21no—
230#435—22no—
231#431—21no—
232#431C22×C4111yescharacteristic
233#431C22×C4111yescharacteristic
234#428C4×C4111yescharacteristic
235C2×C4⋊C8C22×C4111yescharacteristic
236#419C4×C4111yescharacteristic
237#417C4×C4111yescharacteristic
238C4×M16—21no—
239C4×M16C22×C4111yescharacteristic
240C2×C4×C8C22×C4111yescharacteristic
241Q8⋊C8—21no—
242Q8⋊C8—21no—
243Q8⋊C8—21no—
244D4⋊C8—21no—
245#324—22no—
246C41#909811yescharacteristic, direct product factor, Sylow
247C2×#41C2×C4×C4111yescharacteristic
248C22×Q8C2×C4×C4111yescharacteristic
249#137—22no—
250#137—22no—
251C2×Q16—21no—
252C2×SD16—21no—
253C2×M16—22no—
254C2×M16C2×C4×C4111yescharacteristic
255C2×M16C2×C4×C4111yescharacteristic
256C22×C8—21no—
257C22×C8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8D4×C4111yescharacteristic
263C4×Q8D4×C4111yescharacteristic
264C4×D4—21no—
265C4×D4—21no—
266C4×D4D4×C4111yescharacteristic
267C4×D4D4×C4111yescharacteristic
268#117—21no—
269#117C2×C4×C4111yescharacteristic
270C2×C4⋊C4—21no—
271C2×C4⋊C4C2×C4×C4111yescharacteristic
272C2×C42—21no—
273C2×C42—21no—
274C2×C42C23×C4111yescharacteristic
275#107—21no—
276#106—21no—
277C4⋊C8—22no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282#103—21no—
283#103—21no—
284#103—21no—
285#102—21no—
286C22⋊C8—22no—
287C22⋊C8—21no—
288C22⋊C8D4×C4112yes—
289#97—22no—
290#97—21no—
291C4×C8—21no—
292C4×C8—21no—
293C4×C8—21no—
294C4×C8—21no—
295C4×C8D4×C4111yescharacteristic
296C4×C8D4×C4111yescharacteristic
297#41—21no—
298#41—21no—
299#41—21no—
300#41—21no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8C22⋊C4×C4111yescharacteristic
307C2×Q8M16×C4112yescomplemented
308C2×D4—21no—
309C2×D4C22⋊C4×C4111yescharacteristic
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4C22×C4×C4111yescharacteristic
316C22×C4C2×D4×C4111yescharacteristic
317C22×C4#41×C4111yescharacteristic
318Q16—24no—
319SD16—24no—
320M16—21no—
321M16—21no—
322M16—21no—
323M16—44no—
324M16M16×C4112yescomplemented
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—22no—
330C2×C8—42no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—81no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4C22⋊C4×C4111yescharacteristic
341C4⋊C4C22⋊C4×C4111yescharacteristic
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42—41no—
349C42—41no—
350C42C2×D4×C4111yescharacteristic
351C42C2×D4×C4111yescharacteristic
352C42C2×D4×C4111yescharacteristic
353C42#41×C4111yescharacteristic
354C23—21no—
355C23C4×D4×C4111yescharacteristic
356Q8—22no—
357Q8—21no—
358Q8—21no—
359Q8—22no—
360Q8—41no—
361Q8—41no—
362D4—21no—
363D4—21no—
364D4—41no—
365D4—41no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4C2×C22⋊C4×C4111yescharacteristic
383C2×C4C4×D4×C4111yescharacteristic
384C2×C4#120×C4111yescharacteristic
385C2×C4#121×C4111yescharacteristic
386C2×C4#121×C4111yescharacteristic
387C2×C4#123×C4111yescharacteristic
388C2×C4C2×M16×C4111yescharacteristic
389C2×C4C2×M16×C4111yescharacteristic
390C2×C4#131×C4111yescharacteristic
391C2×C4#131×C4111yescharacteristic
392C8—22no—
393C8—22no—
394C8—41no—
395C8—42no—
396C8—41no—
397C8—81no—
398C8—81no—
399C22—21no—
400C22—21no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22C41×#38611yescharacteristic
405C22C41×#43511yescharacteristic
406C22C41×#43611yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—41no—
411C4—42no—
412C4—41no—
413C4—41no—
414C4—81no—
415C4C41×#40711yescharacteristic
416C4C41×#40811yescharacteristic
417C4C41×#43511yescharacteristic
418C4C41×#43611yescharacteristic
419C4C41×#47111yescharacteristic
420C4C41×#47311yescharacteristic
421C2—21no—
422C2—21no—
423C2—81no—
424C2C41×#187011yescharacteristic
425C2C41×#190611yescharacteristic
426C2C41×#190811yescharacteristic
subgroupG/H
centerC2×C4×C41#121
commutatorC22×C4C22×C4×C41
Frattini, cosocleC2×C42C23×C41
socleC22×C41#386
prime radicalC2×#41×C41C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C41×Q8⋊C8C2semidirect
5. C41×#1461C2semidirect
6. C41×#1283C2semidirect
7. C41×#1278C2semidirect
93. C2×Q8×C41M16semidirect
110. M16×C41M16semidirect
185. #9098C41direct (N × H)
211. C2×Q8⋊C8C2×C41semidirect
212. #1461C2×C41semidirect
213. #1283C2×C41semidirect
214. #1278C2×C41semidirect
246. C41#9098direct (N × H)
307. C2×Q8M16×C41semidirect
324. M16M16×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#29652
C4×#137×C412
C41×#14772
C2×C41×Q8⋊C82
C41×#14612
C41×#12832
C41×#12782
#909841