Finite Group Databasebeta

← C109×#3225 #28360479

Subgroups — C109×#3225 #28360479

Order 13952.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#542×C109C211yesmaximal, characteristic, complemented
2#536×C109C211yesmaximal, characteristic, complemented
3#497×C109C211yesmaximal, characteristic, complemented
4#495×C109C211yesmaximal, characteristic, complemented
5#489×C109C211yesmaximal, characteristic, complemented
6#487×C109C211yesmaximal, characteristic, complemented
7#464×C109C211yesmaximal, characteristic, complemented
8#463×C109C211yesmaximal, characteristic, complemented
9#462×C109C211yesmaximal, characteristic, complemented
10#461×C109C211yesmaximal, characteristic, complemented
11#452×C109C211yesmaximal, characteristic, complemented
12#451×C109C211yesmaximal, characteristic, complemented
13#449×C109C211yesmaximal, characteristic
14#448×C109C211yesmaximal, characteristic, complemented
15#433×C109C211yesmaximal, characteristic, complemented
16C2×#41×C109C2211yescharacteristic
17C22×Q8×C109C2211yescharacteristic
18C2×Q16×C109C2211yescharacteristic
19C2×Q16×C109C2211yescharacteristic
20C2×Q16×C109C2211yescharacteristic
21C2×SD16×C109C2211yescharacteristic
22C2×SD16×C109C2211yescharacteristic
23C2×SD16×C109C2211yescharacteristic
24C2×SD16×C109C2211yescharacteristic
25C2×D8×C109C2211yescharacteristic
26C4⋊Q8×C109C2211yescharacteristic
27C4⋊Q8×C109C2211yescharacteristic
28C4⋊Q8×C109C2211yescharacteristic
29#126×C109—21no—
30#124×C109—21no—
31#124×C109C2211yescharacteristic
32#124×C109C2211yescharacteristic
33#124×C109C2211yescharacteristic
34#123×C109—21no—
35#123×C109—21no—
36#123×C109—21no—
37C22⋊Q8×C109—21no—
38C22⋊Q8×C109—21no—
39C22⋊Q8×C109—21no—
40C22⋊Q8×C109C2211yescharacteristic
41#121×C109C2211yescharacteristic
42C4×Q8×C109C2211yescharacteristic
43C4×D4×C109C2211yescharacteristic
44#117×C109C2211yescharacteristic
45C4⋊C8×C109C2211yescharacteristic
46C4⋊C8×C109C2211yescharacteristic
47#103×C109C2211yescharacteristic
48#103×C109C2211yescharacteristic
49#103×C109C2211yescharacteristic
50#103×C109C2211yescharacteristic
51#103×C109C2211yescharacteristic
52#103×C109C2211yescharacteristic
53#102×C109C2211yescharacteristic
54#102×C109C2211yescharacteristic
55C22⋊C8×C109C2211yescharacteristic
56C22⋊C8×C109C2211yescharacteristic
57#97×C109C2211yescharacteristic
58C4×C8×C109C2211yescharacteristic
59#41×C109—41no—
60#41×C109—41no—
61C2×Q8×C109—21no—
62C2×Q8×C109—21no—
63C2×Q8×C109—41no—
64C2×Q8×C109—41no—
65C2×Q8×C109C2311yescharacteristic
66C2×Q8×C109C2311yescharacteristic
67C2×Q8×C109C2311yescharacteristic
68C2×Q8×C109C2311yescharacteristic
69C2×D4×C109—21no—
70C2×D4×C109—21no—
71C2×D4×C109C2311yescharacteristic
72C2×D4×C109C2311yescharacteristic
73C22×C4×C109—21no—
74C22×C4×C109—21no—
75C22×C4×C109—21no—
76C22×C4×C109C2311yescharacteristic
77Q16×C109—41no—
78Q16×C109—41no—
79Q16×C109—41no—
80SD16×C109—41no—
81SD16×C109—41no—
82SD16×C109—41no—
83SD16×C109—41no—
84D8×C109—41no—
85C2×C8×C109C2311yescharacteristic
86C2×C8×C109C2311yescharacteristic
87C2×C8×C109C2311yescharacteristic
88C2×C8×C109C2311yescharacteristic
89C4⋊C4×C109—21no—
90C4⋊C4×C109—21no—
91C4⋊C4×C109—21no—
92C4⋊C4×C109—21no—
93C4⋊C4×C109—21no—
94C4⋊C4×C109—21no—
95C4⋊C4×C109—21no—
96C4⋊C4×C109D411yescharacteristic
97C4⋊C4×C109D411yescharacteristic
98C4⋊C4×C109C2311yescharacteristic
99C4⋊C4×C109C2311yescharacteristic
100C22⋊C4×C109—21no—
101C22⋊C4×C109—21no—
102C22⋊C4×C109—21no—
103C22⋊C4×C109—21no—
104C22⋊C4×C109—21no—
105C22⋊C4×C109—21no—
106C22⋊C4×C109—21no—
107C22⋊C4×C109—21no—
108C22⋊C4×C109—21no—
109C22⋊C4×C109D411yescharacteristic
110C22⋊C4×C109D411yescharacteristic
111C42×C109—21no—
112C42×C109C2311yescharacteristic
113C42×C109C2311yescharacteristic
114C23×C109—21no—
115C23×C109—21no—
116C23×C109C2×D411yescharacteristic
117Q8×C109—21no—
118Q8×C109—21no—
119Q8×C109—21no—
120Q8×C109—21no—
121Q8×C109—21no—
122Q8×C109—21no—
123Q8×C109—21no—
124Q8×C109—21no—
125Q8×C109—42no—
126Q8×C109—81no—
127D4×C109—21no—
128D4×C109—21no—
129D4×C109—21no—
130D4×C109—21no—
131D4×C109—42no—
132D4×C109—81no—
133C2×C4×C109—21no—
134C2×C4×C109—21no—
135C2×C4×C109—21no—
136C2×C4×C109—21no—
137C2×C4×C109—21no—
138C2×C4×C109—21no—
139C2×C4×C109—21no—
140C2×C4×C109—21no—
141C2×C4×C109—42no—
142C2×C4×C109—42no—
143C2×C4×C109—81no—
144C2×C4×C109C2×D411yescharacteristic
145C2×C4×C109C2×D411yescharacteristic
146C2×C4×C109C2×D411yescharacteristic
147C2×C4×C109C2×D411yescharacteristic
148C2×C4×C109C2×D411yescharacteristic
149C2×C4×C109C2411yescharacteristic
150C8×C109—21no—
151C8×C109—21no—
152C8×C109—21no—
153C8×C109—21no—
154C22×C109—21no—
155C22×C109—21no—
156C22×C109—21no—
157C22×C109—41no—
158C22×C109—41no—
159C22×C109—41no—
160C22×C109—41no—
161C22×C109—41no—
162C22×C109—41no—
163C22×C109C22×D411yescharacteristic
164C4×C109—21no—
165C4×C109—21no—
166C4×C109—21no—
167C4×C109—21no—
168C4×C109—21no—
169C4×C109—41no—
170C4×C109—41no—
171C4×C109—41no—
172C4×C109—41no—
173C4×C109—41no—
174C4×C109—41no—
175C4×C109H(5,𝔽2)11yescharacteristic
176C4×C109H(5,𝔽2)11yescharacteristic
177C2×C109—41no—
178C2×C109—81no—
179C2×C109—81no—
180C2×C109#53511yescharacteristic
181C2×C109#57711yescharacteristic
182C2×C109#57811yescharacteristic
183#3225C10911yesmaximal, characteristic, direct product factor, Sylow
184C109#322511yescharacteristic, direct product factor, Sylow
185#542C2×C10911yescharacteristic, complemented
186#536C2×C10911yescharacteristic, complemented
187#497C2×C10911yescharacteristic, complemented
188#495C2×C10911yescharacteristic, complemented
189#489C2×C10911yescharacteristic, complemented
190#487C2×C10911yescharacteristic, complemented
191#464C2×C10911yescharacteristic, complemented
192#463C2×C10911yescharacteristic, complemented
193#462C2×C10911yescharacteristic, complemented
194#461C2×C10911yescharacteristic, complemented
195#452C2×C10911yescharacteristic, complemented
196#451C2×C10911yescharacteristic, complemented
197#449C2×C10911yescharacteristic
198#448C2×C10911yescharacteristic, complemented
199#433C2×C10911yescharacteristic, complemented
200C2×#41C22×C10911yescharacteristic
201C22×Q8C22×C10911yescharacteristic
202C2×Q16C22×C10911yescharacteristic
203C2×Q16C22×C10911yescharacteristic
204C2×Q16C22×C10911yescharacteristic
205C2×SD16C22×C10911yescharacteristic
206C2×SD16C22×C10911yescharacteristic
207C2×SD16C22×C10911yescharacteristic
208C2×SD16C22×C10911yescharacteristic
209C2×D8C22×C10911yescharacteristic
210C4⋊Q8C22×C10911yescharacteristic
211C4⋊Q8C22×C10911yescharacteristic
212C4⋊Q8C22×C10911yescharacteristic
213#126—21no—
214#124—21no—
215#124C22×C10911yescharacteristic
216#124C22×C10911yescharacteristic
217#124C22×C10911yescharacteristic
218#123—21no—
219#123—21no—
220#123—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C22⋊Q8C22×C10911yescharacteristic
225#121C22×C10911yescharacteristic
226C4×Q8C22×C10911yescharacteristic
227C4×D4C22×C10911yescharacteristic
228#117C22×C10911yescharacteristic
229C4⋊C8C22×C10911yescharacteristic
230C4⋊C8C22×C10911yescharacteristic
231#103C22×C10911yescharacteristic
232#103C22×C10911yescharacteristic
233#103C22×C10911yescharacteristic
234#103C22×C10911yescharacteristic
235#103C22×C10911yescharacteristic
236#103C22×C10911yescharacteristic
237#102C22×C10911yescharacteristic
238#102C22×C10911yescharacteristic
239C22⋊C8C22×C10911yescharacteristic
240C22⋊C8C22×C10911yescharacteristic
241#97C22×C10911yescharacteristic
242C4×C8C22×C10911yescharacteristic
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8C23×C10911yescharacteristic
250C2×Q8C23×C10911yescharacteristic
251C2×Q8C23×C10911yescharacteristic
252C2×Q8C23×C10911yescharacteristic
253C2×D4—21no—
254C2×D4—21no—
255C2×D4C23×C10911yescharacteristic
256C2×D4C23×C10911yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4C23×C10911yescharacteristic
261Q16—41no—
262Q16—41no—
263Q16—41no—
264SD16—41no—
265SD16—41no—
266SD16—41no—
267SD16—41no—
268D8—41no—
269C2×C8C23×C10911yescharacteristic
270C2×C8C23×C10911yescharacteristic
271C2×C8C23×C10911yescharacteristic
272C2×C8C23×C10911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4D4×C10911yescharacteristic
281C4⋊C4D4×C10911yescharacteristic
282C4⋊C4C23×C10911yescharacteristic
283C4⋊C4C23×C10911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4D4×C10911yescharacteristic
294C22⋊C4D4×C10911yescharacteristic
295C42—21no—
296C42C23×C10911yescharacteristic
297C42C23×C10911yescharacteristic
298C23—21no—
299C23—21no—
300C23C2×D4×C10911yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—42no—
310Q8—81no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—81no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—81no—
328C2×C4C2×D4×C10911yescharacteristic
329C2×C4C2×D4×C10911yescharacteristic
330C2×C4C2×D4×C10911yescharacteristic
331C2×C4C2×D4×C10911yescharacteristic
332C2×C4C2×D4×C10911yescharacteristic
333C2×C4C24×C10911yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22C22×D4×C10911yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4H(5,𝔽2)×C10911yescharacteristic
360C4H(5,𝔽2)×C10911yescharacteristic
361C2—41no—
362C2—81no—
363C2—81no—
364C2#535×C10911yescharacteristic
365C2#577×C10911yescharacteristic
366C2#578×C10911yescharacteristic
subgroupG/H
center, socleC22×C109C22×D4
commutator, Frattini, cosocleC2×C4C24×C109
prime radical#449×C109C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ #117×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. #542×C109C2semidirect
2. #536×C109C2semidirect
3. #497×C109C2semidirect
4. #495×C109C2semidirect
5. #489×C109C2semidirect
6. #487×C109C2semidirect
7. #464×C109C2semidirect
8. #463×C109C2semidirect
9. #462×C109C2semidirect
10. #461×C109C2semidirect
11. #452×C109C2semidirect
12. #451×C109C2semidirect
14. #448×C109C2semidirect
15. #433×C109C2semidirect
183. #3225C109direct (N × H)
184. C109#3225direct (N × H)
185. #542C2×C109semidirect
186. #536C2×C109semidirect
187. #497C2×C109semidirect
188. #495C2×C109semidirect
189. #489C2×C109semidirect
190. #487C2×C109semidirect
191. #464C2×C109semidirect
192. #463C2×C109semidirect
193. #462C2×C109semidirect
194. #461C2×C109semidirect
195. #452C2×C109semidirect
196. #451C2×C109semidirect
198. #448C2×C109semidirect
199. #433C2×C109semidirect

Maximal subgroups

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

subgroupindex
#542×C1092
#536×C1092
#497×C1092
#495×C1092
#489×C1092
#487×C1092
#464×C1092
#463×C1092
#462×C1092
#461×C1092
#452×C1092
#451×C1092
#449×C1092
#448×C1092
#433×C1092
#3225109