Finite Group Databasebeta

← #3119×C211 #41010739

Subgroups — #3119×C211 #41010739

Order 27008.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#540×C211C211yesmaximal, characteristic, complemented
2#520×C211C211yesmaximal, characteristic, complemented
3#481×C211C211yesmaximal, characteristic, complemented
4#480×C211C211yesmaximal, characteristic, complemented
5#479×C211C211yesmaximal, characteristic, complemented
6#478×C211C211yesmaximal, characteristic, complemented
7#460×C211C211yesmaximal, characteristic, complemented
8#459×C211C211yesmaximal, characteristic, complemented
9#449×C211C211yesmaximal, characteristic, complemented
10#449×C211C211yesmaximal, characteristic, complemented
11#442×C211C211yesmaximal, characteristic, complemented
12#440×C211C211yesmaximal, characteristic, complemented
13C4×SD16×C211C211yesmaximal, characteristic, complemented
14C4×D8×C211C211yesmaximal, characteristic, complemented
15#433×C211C211yesmaximal, characteristic, complemented
16C2×#41×C211C2211yescharacteristic
17C2×SD16×C211C2211yescharacteristic
18C2×SD16×C211C2211yescharacteristic
19C2×D8×C211C2211yescharacteristic
20C2×D8×C211C2211yescharacteristic
21#127×C211C2211yescharacteristic
22#125×C211C2211yescharacteristic
23#123×C211—21no—
24#123×C211—21no—
25#121×C211—21no—
26#121×C211—21no—
27#121×C211C2211yescharacteristic
28#121×C211C2211yescharacteristic
29C4×Q8×C211C2211yescharacteristic
30C4×Q8×C211C2211yescharacteristic
31C4×D4×C211—21no—
32C4×D4×C211—21no—
33C4×D4×C211C2211yescharacteristic
34C4×D4×C211C2211yescharacteristic
35C4×D4×C211C2211yescharacteristic
36C4×D4×C211C2211yescharacteristic
37#117×C211—21no—
38#117×C211C2211yescharacteristic
39C2×C4⋊C4×C211—21no—
40C2×C4⋊C4×C211C2211yescharacteristic
41#107×C211C2211yescharacteristic
42#107×C211C2211yescharacteristic
43#106×C211C2211yescharacteristic
44#106×C211C2211yescharacteristic
45C4⋊C8×C211C2211yescharacteristic
46C4⋊C8×C211C2211yescharacteristic
47#103×C211C2211yescharacteristic
48#103×C211C2211yescharacteristic
49#102×C211C2211yescharacteristic
50#102×C211C2211yescharacteristic
51#102×C211C2211yescharacteristic
52#102×C211C2211yescharacteristic
53#102×C211C2211yescharacteristic
54#102×C211C2211yescharacteristic
55C22⋊C8×C211C2211yescharacteristic
56C22⋊C8×C211C2211yescharacteristic
57#97×C211C2211yescharacteristic
58C4×C8×C211C2211yescharacteristic
59#41×C211—22no—
60#41×C211—22no—
61C2×Q8×C211C2311yescharacteristic
62C2×D4×C211—21no—
63C2×D4×C211—21no—
64C2×D4×C211—21no—
65C2×D4×C211—21no—
66C2×D4×C211—21no—
67C2×D4×C211C2311yescharacteristic
68C2×D4×C211C2311yescharacteristic
69C2×D4×C211C2311yescharacteristic
70C22×C4×C211—21no—
71C22×C4×C211—21no—
72C22×C4×C211—21no—
73C22×C4×C211—21no—
74C22×C4×C211—21no—
75C22×C4×C211—21no—
76C22×C4×C211C2311yescharacteristic
77SD16×C211—22no—
78SD16×C211—22no—
79D8×C211—22no—
80D8×C211—22no—
81C2×C8×C211C2311yescharacteristic
82C2×C8×C211C2311yescharacteristic
83C2×C8×C211C2311yescharacteristic
84C2×C8×C211C2311yescharacteristic
85C4⋊C4×C211—21no—
86C4⋊C4×C211—21no—
87C4⋊C4×C211—21no—
88C4⋊C4×C211—21no—
89C4⋊C4×C211—21no—
90C4⋊C4×C211D411yescharacteristic
91C4⋊C4×C211D411yescharacteristic
92C4⋊C4×C211C2311yescharacteristic
93C4⋊C4×C211C2311yescharacteristic
94C4⋊C4×C211C2311yescharacteristic
95C4⋊C4×C211C2311yescharacteristic
96C22⋊C4×C211—21no—
97C22⋊C4×C211—21no—
98C22⋊C4×C211—21no—
99C22⋊C4×C211—21no—
100C22⋊C4×C211—21no—
101C22⋊C4×C211—21no—
102C22⋊C4×C211D411yescharacteristic
103C22⋊C4×C211D411yescharacteristic
104C42×C211—21no—
105C42×C211—21no—
106C42×C211C2311yescharacteristic
107C42×C211C2311yescharacteristic
108C23×C211—21no—
109C23×C211—21no—
110C23×C211—21no—
111C23×C211C2×D411yescharacteristic
112Q8×C211—21no—
113Q8×C211#4112yes—
114D4×C211—24no—
115D4×C211—21no—
116D4×C211—21no—
117D4×C211—21no—
118D4×C211—21no—
119D4×C211—21no—
120D4×C211—81no—
121D4×C211—81no—
122D4×C211—81no—
123D4×C211—81no—
124D4×C211#4112yes—
125C2×C4×C211—24no—
126C2×C4×C211—21no—
127C2×C4×C211—21no—
128C2×C4×C211—21no—
129C2×C4×C211—21no—
130C2×C4×C211—21no—
131C2×C4×C211—21no—
132C2×C4×C211—21no—
133C2×C4×C211—81no—
134C2×C4×C211—81no—
135C2×C4×C211—81no—
136C2×C4×C211—81no—
137C2×C4×C211—81no—
138C2×C4×C211C2×D411yescharacteristic
139C2×C4×C211C2×D411yescharacteristic
140C2×C4×C211C2×D411yescharacteristic
141C2×C4×C211C2×D411yescharacteristic
142C2×C4×C211C2×D411yescharacteristic
143C2×C4×C211C2411yescharacteristic
144C8×C211—21no—
145C8×C211—21no—
146C8×C211—21no—
147C8×C211—21no—
148C22×C211—21no—
149C22×C211—22no—
150C22×C211—21no—
151C22×C211—21no—
152C22×C211—41no—
153C22×C211—41no—
154C22×C211—41no—
155C22×C211—41no—
156C22×C211—41no—
157C22×C211—41no—
158C22×C211—41no—
159C22×C211—41no—
160C22×C211C22×D411yescharacteristic
161C4×C211—21no—
162C4×C211—22no—
163C4×C211—21no—
164C4×C211—21no—
165C4×C211—21no—
166C4×C211—21no—
167C4×C211—41no—
168C4×C211—41no—
169C4×C211—41no—
170C4×C211—41no—
171C4×C211C2×#4111yescharacteristic
172C4×C211C2×#4111yescharacteristic
173C2×C211—41no—
174C2×C211—42no—
175C2×C211—81no—
176C2×C211—81no—
177C2×C211#52511yescharacteristic
178C2×C211#57611yescharacteristic
179C2×C211#57711yescharacteristic
180C211#311911yescharacteristic, direct product factor, Sylow
181#3119C21111yesmaximal, characteristic, direct product factor, Sylow
182#540C2×C21111yescharacteristic, complemented
183#520C2×C21111yescharacteristic, complemented
184#481C2×C21111yescharacteristic, complemented
185#480C2×C21111yescharacteristic, complemented
186#479C2×C21111yescharacteristic, complemented
187#478C2×C21111yescharacteristic, complemented
188#460C2×C21111yescharacteristic, complemented
189#459C2×C21111yescharacteristic, complemented
190#449C2×C21111yescharacteristic, complemented
191#449C2×C21111yescharacteristic, complemented
192#442C2×C21111yescharacteristic, complemented
193#440C2×C21111yescharacteristic, complemented
194C4×SD16C2×C21111yescharacteristic, complemented
195C4×D8C2×C21111yescharacteristic, complemented
196#433C2×C21111yescharacteristic, complemented
197C2×#41C22×C21111yescharacteristic
198C2×SD16C22×C21111yescharacteristic
199C2×SD16C22×C21111yescharacteristic
200C2×D8C22×C21111yescharacteristic
201C2×D8C22×C21111yescharacteristic
202#127C22×C21111yescharacteristic
203#125C22×C21111yescharacteristic
204#123—21no—
205#123—21no—
206#121—21no—
207#121—21no—
208#121C22×C21111yescharacteristic
209#121C22×C21111yescharacteristic
210C4×Q8C22×C21111yescharacteristic
211C4×Q8C22×C21111yescharacteristic
212C4×D4—21no—
213C4×D4—21no—
214C4×D4C22×C21111yescharacteristic
215C4×D4C22×C21111yescharacteristic
216C4×D4C22×C21111yescharacteristic
217C4×D4C22×C21111yescharacteristic
218#117—21no—
219#117C22×C21111yescharacteristic
220C2×C4⋊C4—21no—
221C2×C4⋊C4C22×C21111yescharacteristic
222#107C22×C21111yescharacteristic
223#107C22×C21111yescharacteristic
224#106C22×C21111yescharacteristic
225#106C22×C21111yescharacteristic
226C4⋊C8C22×C21111yescharacteristic
227C4⋊C8C22×C21111yescharacteristic
228#103C22×C21111yescharacteristic
229#103C22×C21111yescharacteristic
230#102C22×C21111yescharacteristic
231#102C22×C21111yescharacteristic
232#102C22×C21111yescharacteristic
233#102C22×C21111yescharacteristic
234#102C22×C21111yescharacteristic
235#102C22×C21111yescharacteristic
236C22⋊C8C22×C21111yescharacteristic
237C22⋊C8C22×C21111yescharacteristic
238#97C22×C21111yescharacteristic
239C4×C8C22×C21111yescharacteristic
240#41—22no—
241#41—22no—
242C2×Q8C23×C21111yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C23×C21111yescharacteristic
249C2×D4C23×C21111yescharacteristic
250C2×D4C23×C21111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4C23×C21111yescharacteristic
258SD16—22no—
259SD16—22no—
260D8—22no—
261D8—22no—
262C2×C8C23×C21111yescharacteristic
263C2×C8C23×C21111yescharacteristic
264C2×C8C23×C21111yescharacteristic
265C2×C8C23×C21111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4D4×C21111yescharacteristic
272C4⋊C4D4×C21111yescharacteristic
273C4⋊C4C23×C21111yescharacteristic
274C4⋊C4C23×C21111yescharacteristic
275C4⋊C4C23×C21111yescharacteristic
276C4⋊C4C23×C21111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4D4×C21111yescharacteristic
284C22⋊C4D4×C21111yescharacteristic
285C42—21no—
286C42—21no—
287C42C23×C21111yescharacteristic
288C42C23×C21111yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292C23C2×D4×C21111yescharacteristic
293Q8—21no—
294Q8#41×C21112yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—81no—
302D4—81no—
303D4—81no—
304D4—81no—
305D4#41×C21112yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4C2×D4×C21111yescharacteristic
320C2×C4C2×D4×C21111yescharacteristic
321C2×C4C2×D4×C21111yescharacteristic
322C2×C4C2×D4×C21111yescharacteristic
323C2×C4C2×D4×C21111yescharacteristic
324C2×C4C24×C21111yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22C22×D4×C21111yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4C2×#41×C21111yescharacteristic
353C4C2×#41×C21111yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—81no—
358C2#525×C21111yescharacteristic
359C2#576×C21111yescharacteristic
360C2#577×C21111yescharacteristic
subgroupG/H
center, socleC22×C211C22×D4
commutator, Frattini, cosocleC2×C4C24×C211
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C211 ◁ #117×C211 ◁ G

Complements

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

NH ≅ G/Ntype
1. #540×C211C2semidirect
2. #520×C211C2semidirect
3. #481×C211C2semidirect
4. #480×C211C2semidirect
5. #479×C211C2semidirect
6. #478×C211C2semidirect
7. #460×C211C2semidirect
8. #459×C211C2semidirect
9. #449×C211C2semidirect
10. #449×C211C2semidirect
11. #442×C211C2semidirect
12. #440×C211C2semidirect
13. C4×SD16×C211C2semidirect
14. C4×D8×C211C2semidirect
15. #433×C211C2semidirect
180. C211#3119direct (N × H)
181. #3119C211direct (N × H)
182. #540C2×C211semidirect
183. #520C2×C211semidirect
184. #481C2×C211semidirect
185. #480C2×C211semidirect
186. #479C2×C211semidirect
187. #478C2×C211semidirect
188. #460C2×C211semidirect
189. #459C2×C211semidirect
190. #449C2×C211semidirect
191. #449C2×C211semidirect
192. #442C2×C211semidirect
193. #440C2×C211semidirect
194. C4×SD16C2×C211semidirect
195. C4×D8C2×C211semidirect
196. #433C2×C211semidirect

Maximal subgroups

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

subgroupindex
#540×C2112
#520×C2112
#481×C2112
#480×C2112
#479×C2112
#478×C2112
#460×C2112
#459×C2112
#449×C2112
#442×C2112
#440×C2112
C4×SD16×C2112
C4×D8×C2112
#433×C2112
#3119211