Finite Group Databasebeta

← C109×#3371 #28360625

Subgroups — C109×#3371 #28360625

Order 13952.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#559×C109C211yesmaximal, characteristic
2#557×C109C211yesmaximal, characteristic, complemented
3#490×C109C211yesmaximal, characteristic
4#489×C109C211yesmaximal, characteristic, complemented
5#488×C109C211yesmaximal, characteristic, complemented
6#479×C109C211yesmaximal, characteristic, complemented
7#478×C109C211yesmaximal, characteristic, complemented
8#476×C109C211yesmaximal, characteristic, complemented
9#464×C109C211yesmaximal, characteristic, complemented
10#464×C109C211yesmaximal, characteristic, complemented
11#460×C109C211yesmaximal, characteristic
12#446×C109C211yesmaximal, characteristic, complemented
13#441×C109C211yesmaximal, characteristic, complemented
14#440×C109C211yesmaximal, characteristic, complemented
15C4×SD16×C109C211yesmaximal, characteristic, complemented
16C2×Q16×C109C2211yescharacteristic
17C2×SD16×C109C2211yescharacteristic
18C2×SD16×C109C2211yescharacteristic
19C4⋊Q8×C109—21no—
20C4⋊Q8×C109C2211yescharacteristic
21#127×C109C2211yescharacteristic
22#125×C109—21no—
23#125×C109—21no—
24#125×C109C2211yescharacteristic
25#125×C109C2211yescharacteristic
26#124×C109—21no—
27#124×C109C2211yescharacteristic
28#124×C109C2211yescharacteristic
29#123×C109—21no—
30#123×C109—21no—
31C4×Q8×C109—21no—
32C4×Q8×C109C2211yescharacteristic
33C4×Q8×C109C2211yescharacteristic
34C4×Q8×C109C2211yescharacteristic
35C4×Q8×C109C2211yescharacteristic
36C4×Q8×C109C2211yescharacteristic
37C4×D4×C109—21no—
38C4×D4×C109C2211yescharacteristic
39C4×D4×C109C2211yescharacteristic
40#107×C109C2211yescharacteristic
41#106×C109C2211yescharacteristic
42#106×C109C2211yescharacteristic
43C4⋊C8×C109C2211yescharacteristic
44C4⋊C8×C109C2211yescharacteristic
45C4⋊C8×C109C2211yescharacteristic
46#103×C109C2211yescharacteristic
47#103×C109C2211yescharacteristic
48#103×C109C2211yescharacteristic
49#103×C109C2211yescharacteristic
50#102×C109C2211yescharacteristic
51#102×C109C2211yescharacteristic
52#102×C109C2211yescharacteristic
53#102×C109C2211yescharacteristic
54#102×C109C2211yescharacteristic
55#102×C109C2211yescharacteristic
56#97×C109C2211yescharacteristic
57#97×C109C2211yescharacteristic
58C4×C8×C109C2211yescharacteristic
59C2×Q8×C109—21no—
60C2×Q8×C109D411yescharacteristic
61C2×Q8×C109C2311yescharacteristic
62C2×Q8×C109C2311yescharacteristic
63C2×D4×C109—21no—
64C2×D4×C109—21no—
65C2×D4×C109C2311yescharacteristic
66C2×D4×C109C2311yescharacteristic
67C22×C4×C109—21no—
68C22×C4×C109—21no—
69Q16×C109—22no—
70SD16×C109—22no—
71SD16×C109—22no—
72C2×C8×C109C2311yescharacteristic
73C2×C8×C109C2311yescharacteristic
74C2×C8×C109C2311yescharacteristic
75C2×C8×C109C2311yescharacteristic
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×C109D411yescharacteristic
86C4⋊C4×C109D411yescharacteristic
87C4⋊C4×C109D411yescharacteristic
88C4⋊C4×C109C2311yescharacteristic
89C4⋊C4×C109C2311yescharacteristic
90C4⋊C4×C109C2311yescharacteristic
91C4⋊C4×C109C2311yescharacteristic
92C22⋊C4×C109—21no—
93C22⋊C4×C109—21no—
94C22⋊C4×C109—21no—
95C22⋊C4×C109—21no—
96C22⋊C4×C109—21no—
97C22⋊C4×C109—21no—
98C42×C109—21no—
99C42×C109—21no—
100C42×C109—21no—
101C42×C109—21no—
102C42×C109C2311yescharacteristic
103C42×C109C2311yescharacteristic
104C42×C109C2311yescharacteristic
105C23×C109—21no—
106C23×C109—21no—
107Q8×C109—21no—
108Q8×C109—21no—
109Q8×C109—21no—
110Q8×C109—41no—
111Q8×C109—42no—
112Q8×C109#4112yes—
113D4×C109—21no—
114D4×C109—21no—
115D4×C109—21no—
116D4×C109—21no—
117D4×C109—42no—
118D4×C109—81no—
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—81no—
126C2×C4×C109—81no—
127C2×C4×C109C2×D411yescharacteristic
128C2×C4×C109C2×D411yescharacteristic
129C2×C4×C109C2×D411yescharacteristic
130C2×C4×C109C2×D411yescharacteristic
131C2×C4×C109C2×D411yescharacteristic
132C2×C4×C109C2×D411yescharacteristic
133C2×C4×C109C2411yescharacteristic
134C8×C109—21no—
135C8×C109—21no—
136C8×C109—21no—
137C8×C109—21no—
138C22×C109—41no—
139C22×C109—41no—
140C22×C109—41no—
141C22×C109—41no—
142C22×C109—41no—
143C22×C109—41no—
144C22×C109C22×D411yescharacteristic
145C4×C109—22no—
146C4×C109—21no—
147C4×C109—21no—
148C4×C109—21no—
149C4×C109—21no—
150C4×C109—21no—
151C4×C109—21no—
152C4×C109—41no—
153C4×C109—41no—
154C4×C109—41no—
155C4×C109—41no—
156C4×C109—41no—
157C4×C109C2×#4111yescharacteristic
158C4×C1092−1+411yescharacteristic
159C2×C109—81no—
160C2×C109—81no—
161C2×C109#54811yescharacteristic
162C2×C109#57511yescharacteristic
163C2×C109#57711yescharacteristic
164#3371C10911yesmaximal, characteristic, direct product factor, Sylow
165C109#337111yescharacteristic, direct product factor, Sylow
166#559C2×C10911yescharacteristic
167#557C2×C10911yescharacteristic, complemented
168#490C2×C10911yescharacteristic
169#489C2×C10911yescharacteristic, complemented
170#488C2×C10911yescharacteristic, complemented
171#479C2×C10911yescharacteristic, complemented
172#478C2×C10911yescharacteristic, complemented
173#476C2×C10911yescharacteristic, complemented
174#464C2×C10911yescharacteristic, complemented
175#464C2×C10911yescharacteristic, complemented
176#460C2×C10911yescharacteristic
177#446C2×C10911yescharacteristic, complemented
178#441C2×C10911yescharacteristic, complemented
179#440C2×C10911yescharacteristic, complemented
180C4×SD16C2×C10911yescharacteristic, complemented
181C2×Q16C22×C10911yescharacteristic
182C2×SD16C22×C10911yescharacteristic
183C2×SD16C22×C10911yescharacteristic
184C4⋊Q8—21no—
185C4⋊Q8C22×C10911yescharacteristic
186#127C22×C10911yescharacteristic
187#125—21no—
188#125—21no—
189#125C22×C10911yescharacteristic
190#125C22×C10911yescharacteristic
191#124—21no—
192#124C22×C10911yescharacteristic
193#124C22×C10911yescharacteristic
194#123—21no—
195#123—21no—
196C4×Q8—21no—
197C4×Q8C22×C10911yescharacteristic
198C4×Q8C22×C10911yescharacteristic
199C4×Q8C22×C10911yescharacteristic
200C4×Q8C22×C10911yescharacteristic
201C4×Q8C22×C10911yescharacteristic
202C4×D4—21no—
203C4×D4C22×C10911yescharacteristic
204C4×D4C22×C10911yescharacteristic
205#107C22×C10911yescharacteristic
206#106C22×C10911yescharacteristic
207#106C22×C10911yescharacteristic
208C4⋊C8C22×C10911yescharacteristic
209C4⋊C8C22×C10911yescharacteristic
210C4⋊C8C22×C10911yescharacteristic
211#103C22×C10911yescharacteristic
212#103C22×C10911yescharacteristic
213#103C22×C10911yescharacteristic
214#103C22×C10911yescharacteristic
215#102C22×C10911yescharacteristic
216#102C22×C10911yescharacteristic
217#102C22×C10911yescharacteristic
218#102C22×C10911yescharacteristic
219#102C22×C10911yescharacteristic
220#102C22×C10911yescharacteristic
221#97C22×C10911yescharacteristic
222#97C22×C10911yescharacteristic
223C4×C8C22×C10911yescharacteristic
224C2×Q8—21no—
225C2×Q8D4×C10911yescharacteristic
226C2×Q8C23×C10911yescharacteristic
227C2×Q8C23×C10911yescharacteristic
228C2×D4—21no—
229C2×D4—21no—
230C2×D4C23×C10911yescharacteristic
231C2×D4C23×C10911yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234Q16—22no—
235SD16—22no—
236SD16—22no—
237C2×C8C23×C10911yescharacteristic
238C2×C8C23×C10911yescharacteristic
239C2×C8C23×C10911yescharacteristic
240C2×C8C23×C10911yescharacteristic
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⋊C4D4×C10911yescharacteristic
251C4⋊C4D4×C10911yescharacteristic
252C4⋊C4D4×C10911yescharacteristic
253C4⋊C4C23×C10911yescharacteristic
254C4⋊C4C23×C10911yescharacteristic
255C4⋊C4C23×C10911yescharacteristic
256C4⋊C4C23×C10911yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42C23×C10911yescharacteristic
268C42C23×C10911yescharacteristic
269C42C23×C10911yescharacteristic
270C23—21no—
271C23—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—41no—
276Q8—42no—
277Q8#41×C10912yes—
278D4—21no—
279D4—21no—
280D4—21no—
281D4—21no—
282D4—42no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C2×D4×C10911yescharacteristic
293C2×C4C2×D4×C10911yescharacteristic
294C2×C4C2×D4×C10911yescharacteristic
295C2×C4C2×D4×C10911yescharacteristic
296C2×C4C2×D4×C10911yescharacteristic
297C2×C4C2×D4×C10911yescharacteristic
298C2×C4C24×C10911yescharacteristic
299C8—21no—
300C8—21no—
301C8—21no—
302C8—21no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C22×D4×C10911yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4C2×#41×C10911yescharacteristic
323C42−1+4×C10911yescharacteristic
324C2—81no—
325C2—81no—
326C2#548×C10911yescharacteristic
327C2#575×C10911yescharacteristic
328C2#577×C10911yescharacteristic
subgroupG/H
center, socleC22×C109C22×D4
commutator, Frattini, cosocleC2×C4C24×C109
prime radical#127×C109C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C4×Q8×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. #557×C109C2semidirect
4. #489×C109C2semidirect
5. #488×C109C2semidirect
6. #479×C109C2semidirect
7. #478×C109C2semidirect
8. #476×C109C2semidirect
9. #464×C109C2semidirect
10. #464×C109C2semidirect
12. #446×C109C2semidirect
13. #441×C109C2semidirect
14. #440×C109C2semidirect
15. C4×SD16×C109C2semidirect
164. #3371C109direct (N × H)
165. C109#3371direct (N × H)
167. #557C2×C109semidirect
169. #489C2×C109semidirect
170. #488C2×C109semidirect
171. #479C2×C109semidirect
172. #478C2×C109semidirect
173. #476C2×C109semidirect
174. #464C2×C109semidirect
175. #464C2×C109semidirect
177. #446C2×C109semidirect
178. #441C2×C109semidirect
179. #440C2×C109semidirect
180. C4×SD16C2×C109semidirect

Maximal subgroups

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

subgroupindex
#559×C1092
#557×C1092
#490×C1092
#489×C1092
#488×C1092
#479×C1092
#478×C1092
#476×C1092
#464×C1092
#460×C1092
#446×C1092
#441×C1092
#440×C1092
C4×SD16×C1092
#3371109