Finite Group Databasebeta

← C109×#3344 #28360598

Subgroups — C109×#3344 #28360598

Order 13952.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#554×C109C211yesmaximal, characteristic
2#552×C109C211yesmaximal, characteristic
3#501×C109C211yesmaximal, characteristic, complemented
4#485×C109C211yesmaximal, characteristic, complemented
5#484×C109C211yesmaximal, characteristic, complemented
6#483×C109C211yesmaximal, characteristic, complemented
7#483×C109C211yesmaximal, characteristic, complemented
8#479×C109C211yesmaximal, characteristic, complemented
9#475×C109C211yesmaximal, characteristic, complemented
10#470×C109C211yesmaximal, characteristic, complemented
11#467×C109C211yesmaximal, characteristic, complemented
12#441×C109C211yesmaximal, characteristic, complemented
13#435×C109C211yesmaximal, characteristic
14#428×C109C211yesmaximal, characteristic, complemented
15C2×#106×C109C211yesmaximal, characteristic, complemented
16C2×Q16×C109C2211yescharacteristic
17C2×M16×C109C2211yescharacteristic
18C22×C8×C109C2211yescharacteristic
19C4⋊Q8×C109C2211yescharacteristic
20#126×C109—21no—
21#125×C109—21no—
22#125×C109—21no—
23#125×C109C2211yescharacteristic
24#123×C109—21no—
25C22⋊Q8×C109—21no—
26C22⋊Q8×C109—21no—
27C22⋊Q8×C109C2211yescharacteristic
28C22⋊Q8×C109C2211yescharacteristic
29C22⋊Q8×C109C2211yescharacteristic
30C22⋊Q8×C109C2211yescharacteristic
31C4×Q8×C109C2211yescharacteristic
32C4×Q8×C109C2211yescharacteristic
33C4×D4×C109—21no—
34C4×D4×C109C2211yescharacteristic
35#117×C109—21no—
36#117×C109C2211yescharacteristic
37C2×C4⋊C4×C109C2211yescharacteristic
38C2×C4⋊C4×C109C2211yescharacteristic
39C2×C4⋊C4×C109C2211yescharacteristic
40#107×C109C2211yescharacteristic
41#107×C109C2211yescharacteristic
42#107×C109C2211yescharacteristic
43#106×C109C2211yescharacteristic
44#106×C109C2211yescharacteristic
45#106×C109C2211yescharacteristic
46#106×C109C2211yescharacteristic
47#106×C109C2211yescharacteristic
48#106×C109C2211yescharacteristic
49C4⋊C8×C109C2211yescharacteristic
50#103×C109C2211yescharacteristic
51#103×C109C2211yescharacteristic
52#103×C109C2211yescharacteristic
53#103×C109C2211yescharacteristic
54#103×C109C2211yescharacteristic
55#103×C109C2211yescharacteristic
56C22⋊C8×C109C2211yescharacteristic
57C22⋊C8×C109C2211yescharacteristic
58#97×C109C2211yescharacteristic
59C2×Q8×C109—21no—
60C2×Q8×C109C2311yescharacteristic
61C2×Q8×C109C2311yescharacteristic
62C2×D4×C109D411yescharacteristic
63C22×C4×C109—21no—
64C22×C4×C109—21no—
65C22×C4×C109—21no—
66C22×C4×C109C2311yescharacteristic
67C22×C4×C109C2311yescharacteristic
68Q16×C109—22no—
69M16×C109—22no—
70C2×C8×C109—22no—
71C2×C8×C109C2311yescharacteristic
72C2×C8×C109C2311yescharacteristic
73C2×C8×C109C2311yescharacteristic
74C2×C8×C109C2311yescharacteristic
75C4⋊C4×C109—21no—
76C4⋊C4×C109—21no—
77C4⋊C4×C109—21no—
78C4⋊C4×C109—21no—
79C4⋊C4×C109—21no—
80C4⋊C4×C109—21no—
81C4⋊C4×C109—21no—
82C4⋊C4×C109—21no—
83C4⋊C4×C109—21no—
84C4⋊C4×C109—21no—
85C4⋊C4×C109—21no—
86C4⋊C4×C109—21no—
87C4⋊C4×C109D411yescharacteristic
88C4⋊C4×C109C2311yescharacteristic
89C4⋊C4×C109C2311yescharacteristic
90C4⋊C4×C109C2311yescharacteristic
91C4⋊C4×C109C2311yescharacteristic
92C4⋊C4×C109C2311yescharacteristic
93C4⋊C4×C109C2311yescharacteristic
94C22⋊C4×C109—21no—
95C22⋊C4×C109—21no—
96C22⋊C4×C109—21no—
97C22⋊C4×C109—21no—
98C22⋊C4×C109—21no—
99C22⋊C4×C109D411yescharacteristic
100C22⋊C4×C109D411yescharacteristic
101C42×C109—21no—
102C42×C109—21no—
103C42×C109—21no—
104C42×C109C2311yescharacteristic
105C23×C109C2×D411yescharacteristic
106C23×C109C2×D411yescharacteristic
107Q8×C109—21no—
108Q8×C109—21no—
109Q8×C109—21no—
110Q8×C109—21no—
111Q8×C109—81no—
112D4×C109—22no—
113C2×C4×C109—21no—
114C2×C4×C109—21no—
115C2×C4×C109—21no—
116C2×C4×C109—21no—
117C2×C4×C109—21no—
118C2×C4×C109—21no—
119C2×C4×C109—21no—
120C2×C4×C109—21no—
121C2×C4×C109—21no—
122C2×C4×C109—21no—
123C2×C4×C109—21no—
124C2×C4×C109—21no—
125C2×C4×C109—42no—
126C2×C4×C109—81no—
127C2×C4×C109—81no—
128C2×C4×C109C2×D411yescharacteristic
129C2×C4×C109C2×D411yescharacteristic
130C2×C4×C109C2×D411yescharacteristic
131C2×C4×C109C2×D411yescharacteristic
132C2×C4×C109C2411yescharacteristic
133C8×C109—21no—
134C8×C109—21no—
135C8×C109—21no—
136C8×C109#4112yes—
137C22×C109—21no—
138C22×C109—21no—
139C22×C109—21no—
140C22×C109—21no—
141C22×C109—21no—
142C22×C109#13712yes—
143C22×C109C22×D411yescharacteristic
144C4×C109—21no—
145C4×C109—21no—
146C4×C109—21no—
147C4×C109—21no—
148C4×C109—41no—
149C4×C109—41no—
150C4×C109—41no—
151C4×C109—41no—
152C4×C109—41no—
153C4×C109—41no—
154C4×C109—41no—
155C4×C109—41no—
156C4×C109C2×#4111yescharacteristic
157C4×C1092−1+411yescharacteristic
158C2×C109—22no—
159C2×C109—41no—
160C2×C109#54711yescharacteristic
161C2×C109C2×#13711yescharacteristic
162C2×C109#57711yescharacteristic
163#3344C10911yesmaximal, characteristic, direct product factor, Sylow
164C109#334411yescharacteristic, direct product factor, Sylow
165#554C2×C10911yescharacteristic
166#552C2×C10911yescharacteristic
167#501C2×C10911yescharacteristic, complemented
168#485C2×C10911yescharacteristic, complemented
169#484C2×C10911yescharacteristic, complemented
170#483C2×C10911yescharacteristic, complemented
171#483C2×C10911yescharacteristic, complemented
172#479C2×C10911yescharacteristic, complemented
173#475C2×C10911yescharacteristic, complemented
174#470C2×C10911yescharacteristic, complemented
175#467C2×C10911yescharacteristic, complemented
176#441C2×C10911yescharacteristic, complemented
177#435C2×C10911yescharacteristic
178#428C2×C10911yescharacteristic, complemented
179C2×#106C2×C10911yescharacteristic, complemented
180C2×Q16C22×C10911yescharacteristic
181C2×M16C22×C10911yescharacteristic
182C22×C8C22×C10911yescharacteristic
183C4⋊Q8C22×C10911yescharacteristic
184#126—21no—
185#125—21no—
186#125—21no—
187#125C22×C10911yescharacteristic
188#123—21no—
189C22⋊Q8—21no—
190C22⋊Q8—21no—
191C22⋊Q8C22×C10911yescharacteristic
192C22⋊Q8C22×C10911yescharacteristic
193C22⋊Q8C22×C10911yescharacteristic
194C22⋊Q8C22×C10911yescharacteristic
195C4×Q8C22×C10911yescharacteristic
196C4×Q8C22×C10911yescharacteristic
197C4×D4—21no—
198C4×D4C22×C10911yescharacteristic
199#117—21no—
200#117C22×C10911yescharacteristic
201C2×C4⋊C4C22×C10911yescharacteristic
202C2×C4⋊C4C22×C10911yescharacteristic
203C2×C4⋊C4C22×C10911yescharacteristic
204#107C22×C10911yescharacteristic
205#107C22×C10911yescharacteristic
206#107C22×C10911yescharacteristic
207#106C22×C10911yescharacteristic
208#106C22×C10911yescharacteristic
209#106C22×C10911yescharacteristic
210#106C22×C10911yescharacteristic
211#106C22×C10911yescharacteristic
212#106C22×C10911yescharacteristic
213C4⋊C8C22×C10911yescharacteristic
214#103C22×C10911yescharacteristic
215#103C22×C10911yescharacteristic
216#103C22×C10911yescharacteristic
217#103C22×C10911yescharacteristic
218#103C22×C10911yescharacteristic
219#103C22×C10911yescharacteristic
220C22⋊C8C22×C10911yescharacteristic
221C22⋊C8C22×C10911yescharacteristic
222#97C22×C10911yescharacteristic
223C2×Q8—21no—
224C2×Q8C23×C10911yescharacteristic
225C2×Q8C23×C10911yescharacteristic
226C2×D4D4×C10911yescharacteristic
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4C23×C10911yescharacteristic
231C22×C4C23×C10911yescharacteristic
232Q16—22no—
233M16—22no—
234C2×C8—22no—
235C2×C8C23×C10911yescharacteristic
236C2×C8C23×C10911yescharacteristic
237C2×C8C23×C10911yescharacteristic
238C2×C8C23×C10911yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4D4×C10911yescharacteristic
252C4⋊C4C23×C10911yescharacteristic
253C4⋊C4C23×C10911yescharacteristic
254C4⋊C4C23×C10911yescharacteristic
255C4⋊C4C23×C10911yescharacteristic
256C4⋊C4C23×C10911yescharacteristic
257C4⋊C4C23×C10911yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4D4×C10911yescharacteristic
264C22⋊C4D4×C10911yescharacteristic
265C42—21no—
266C42—21no—
267C42—21no—
268C42C23×C10911yescharacteristic
269C23C2×D4×C10911yescharacteristic
270C23C2×D4×C10911yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—81no—
276D4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—42no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C2×D4×C10911yescharacteristic
293C2×C4C2×D4×C10911yescharacteristic
294C2×C4C2×D4×C10911yescharacteristic
295C2×C4C2×D4×C10911yescharacteristic
296C2×C4C24×C10911yescharacteristic
297C8—21no—
298C8—21no—
299C8—21no—
300C8#41×C10912yes—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22#137×C10912yes—
307C22C22×D4×C10911yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4C2×#41×C10911yescharacteristic
321C42−1+4×C10911yescharacteristic
322C2—22no—
323C2—41no—
324C2#547×C10911yescharacteristic
325C2C2×#137×C10911yescharacteristic
326C2#577×C10911yescharacteristic
subgroupG/H
center, socleC22×C109C22×D4
commutator, Frattini, cosocleC2×C4C24×C109
prime radicalC2×D4×C109D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C4×D4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
3. #501×C109C2semidirect
4. #485×C109C2semidirect
5. #484×C109C2semidirect
6. #483×C109C2semidirect
7. #483×C109C2semidirect
8. #479×C109C2semidirect
9. #475×C109C2semidirect
10. #470×C109C2semidirect
11. #467×C109C2semidirect
12. #441×C109C2semidirect
14. #428×C109C2semidirect
15. C2×#106×C109C2semidirect
163. #3344C109direct (N × H)
164. C109#3344direct (N × H)
167. #501C2×C109semidirect
168. #485C2×C109semidirect
169. #484C2×C109semidirect
170. #483C2×C109semidirect
171. #483C2×C109semidirect
172. #479C2×C109semidirect
173. #475C2×C109semidirect
174. #470C2×C109semidirect
175. #467C2×C109semidirect
176. #441C2×C109semidirect
178. #428C2×C109semidirect
179. C2×#106C2×C109semidirect

Maximal subgroups

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

subgroupindex
#554×C1092
#552×C1092
#501×C1092
#485×C1092
#484×C1092
#483×C1092
#479×C1092
#475×C1092
#470×C1092
#467×C1092
#441×C1092
#435×C1092
#428×C1092
C2×#106×C1092
#3344109