Finite Group Databasebeta

← C109×#32425 #42150419

Subgroups — C109×#32425 #42150419

Order 27904.

596 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#2495C212yesmaximal
2C109×#2086C212yesmaximal, complemented
3C109×#2085C212yesmaximal, complemented
4C109×#2076C211yesmaximal, characteristic
5C109×#2075C211yesmaximal, characteristic
6C109×#1949C212yesmaximal, complemented
7C109×#1921C212yesmaximal, complemented
8C109×#1851C211yesmaximal, characteristic
9C109×#1809C212yesmaximal
10C22×M16×C109C2211yescharacteristic
11C2×#107×C109C2212yes—
12C2×#107×C109C2211yescharacteristic
13C2×#107×C109C2211yescharacteristic
14C2×#106×C109C2212yes—
15C2×C4⋊C8×C109C2212yes—
16C2×C22⋊C8×C109C2211yescharacteristic
17#400×C109—22no—
18#397×C109—22no—
19#389×C109C2212yes—
20#389×C109C2212yes—
21#388×C109—22no—
22#383×C109—22no—
23#382×C109C2212yes—
24#380×C109C2212yes—
25#380×C109C2212yes—
26C4×C4⋊C4×C109C2212yes—
27C4×C22⋊C4×C109C2211yescharacteristic
28#340×C109C2211yescharacteristic
29#340×C109C2212yes—
30#340×C109C2212yes—
31#340×C109C2212yes—
32#340×C109C2212yes—
33#340×C109C2211yescharacteristic
34#336×C109C2212yes—
35C23×C4×C109C2311yescharacteristic
36C2×M16×C109—24no—
37C2×M16×C109—41no—
38C22×C8×C109C2311yescharacteristic
39C22×C8×C109C2311yescharacteristic
40C22×C8×C109C2312yes—
41C2×C4⋊C4×C109—22no—
42C2×C4⋊C4×C109—22no—
43C2×C4⋊C4×C109C2312yes—
44C2×C4⋊C4×C109C2312yes—
45C2×C4⋊C4×C109C2312yes—
46C2×C4⋊C4×C109C2312yes—
47C2×C22⋊C4×C109—22no—
48C2×C22⋊C4×C109—22no—
49C2×C22⋊C4×C109D412yes—
50C2×C42×C109—22no—
51C2×C42×C109C2312yes—
52#107×C109—24no—
53#107×C109—41no—
54#107×C109—41no—
55#106×C109—42no—
56C4⋊C8×C109—24no—
57C22⋊C8×C109—41no—
58#95×C109—22no—
59#95×C109—22no—
60#95×C109—22no—
61#95×C109—22no—
62#95×C109—22no—
63#95×C109—22no—
64#95×C109—22no—
65#95×C109D411yescharacteristic
66#95×C109D411yescharacteristic
67C24×C109C2×D411yescharacteristic
68C22×C4×C109—22no—
69C22×C4×C109—21no—
70C22×C4×C109—21no—
71C22×C4×C109—22no—
72C22×C4×C109—22no—
73C22×C4×C109—22no—
74C22×C4×C109—22no—
75C22×C4×C109—22no—
76C22×C4×C109C2×D411yescharacteristic
77C22×C4×C109C2×D412yes—
78C22×C4×C109C2×D412yes—
79C22×C4×C109C2411yescharacteristic
80M16×C109—44no—
81C2×C8×C109—22no—
82C2×C8×C109—22no—
83C2×C8×C109—22no—
84C2×C8×C109—21no—
85C2×C8×C109—21no—
86C2×C8×C109—22no—
87C2×C8×C109#4114yes—
88C4⋊C4×C109—22no—
89C4⋊C4×C109—22no—
90C4⋊C4×C109—22no—
91C4⋊C4×C109—22no—
92C4⋊C4×C109—22no—
93C4⋊C4×C109—22no—
94C4⋊C4×C109—22no—
95C4⋊C4×C109—22no—
96C4⋊C4×C109—82no—
97C4⋊C4×C109—82no—
98C22⋊C4×C109—42no—
99C22⋊C4×C109—44no—
100C22⋊C4×C109—82no—
101C42×C109—22no—
102C42×C109—22no—
103C42×C109—44no—
104C23×C109—21no—
105C23×C109—22no—
106C23×C109—22no—
107C23×C109—21no—
108C23×C109—21no—
109C23×C109C22×D411yescharacteristic
110C2×C4×C109—21no—
111C2×C4×C109—22no—
112C2×C4×C109—22no—
113C2×C4×C109—22no—
114C2×C4×C109—22no—
115C2×C4×C109—22no—
116C2×C4×C109—22no—
117C2×C4×C109—22no—
118C2×C4×C109—42no—
119C2×C4×C109—41no—
120C2×C4×C109—41no—
121C2×C4×C109—42no—
122C2×C4×C109—42no—
123C2×C4×C109—42no—
124C2×C4×C109—42no—
125C2×C4×C109—42no—
126C2×C4×C109—42no—
127C2×C4×C109—42no—
128C2×C4×C109—42no—
129C2×C4×C109—42no—
130C2×C4×C109—42no—
131C2×C4×C109—42no—
132C2×C4×C109—42no—
133C2×C4×C109C2×#4112yes—
134C2×C4×C109H(5,𝔽2)11yescharacteristic
135C2×C4×C1092−1+411yescharacteristic
136C2×C4×C1092−1+412yes—
137C8×C109—24no—
138C8×C109—41no—
139C8×C109—41no—
140C22×C109—42no—
141C22×C109—42no—
142C22×C109—41no—
143C22×C109—41no—
144C22×C109—41no—
145C22×C109#53711yescharacteristic
146C22×C109#54712yes—
147C22×C109#57512yes—
148C22×C109#57611yescharacteristic
149C22×C109#57811yescharacteristic
150C4×C109—42no—
151C4×C109—42no—
152C4×C109—41no—
153C4×C109—82no—
154C4×C109—82no—
155C4×C109—82no—
156C4×C109—82no—
157C4×C109#54112yes—
158C4×C109#55111yescharacteristic
159C4×C109#56311yescharacteristic
160#32425C10911yesmaximal, characteristic, direct product factor, Sylow
161C2×C109—81no—
162C2×C109#272211yescharacteristic
163C2×C109#325611yescharacteristic
164C2×C109#326211yescharacteristic
165C2×C109#334712yes—
166C2×C109#335212yes—
167#2495C2×C10912yes—
168#2086C2×C10912yescomplemented
169#2085C2×C10912yescomplemented
170#2076C2×C10911yescharacteristic
171#2075C2×C10911yescharacteristic
172#1949C2×C10912yescomplemented
173#1921C2×C10912yescomplemented
174#1851C2×C10911yescharacteristic
175#1809C2×C10912yes—
176C109#3242511yescharacteristic, direct product factor, Sylow
177C22×M16C22×C10911yescharacteristic
178C2×#107C22×C10912yes—
179C2×#107C22×C10911yescharacteristic
180C2×#107C22×C10911yescharacteristic
181C2×#106C22×C10912yes—
182C2×C4⋊C8C22×C10912yes—
183C2×C22⋊C8C22×C10911yescharacteristic
184#400—22no—
185#397—22no—
186#389C22×C10912yes—
187#389C22×C10912yes—
188#388—22no—
189#383—22no—
190#382C22×C10912yes—
191#380C22×C10912yes—
192#380C22×C10912yes—
193C4×C4⋊C4C22×C10912yes—
194C4×C22⋊C4C22×C10911yescharacteristic
195#340C22×C10912yes—
196#340C22×C10912yes—
197#340C22×C10912yes—
198#340C22×C10911yescharacteristic
199#340C22×C10912yes—
200#340C22×C10911yescharacteristic
201#336C22×C10912yes—
202C23×C4C23×C10911yescharacteristic
203C2×M16—24no—
204C2×M16—41no—
205C22×C8C23×C10911yescharacteristic
206C22×C8C23×C10911yescharacteristic
207C22×C8C23×C10912yes—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4C23×C10912yes—
211C2×C4⋊C4C23×C10912yes—
212C2×C4⋊C4C23×C10912yes—
213C2×C4⋊C4C23×C10912yes—
214C2×C22⋊C4—22no—
215C2×C22⋊C4—22no—
216C2×C22⋊C4D4×C10912yes—
217C2×C42—22no—
218C2×C42C23×C10912yes—
219#107—24no—
220#107—41no—
221#107—41no—
222#106—42no—
223C4⋊C8—24no—
224C22⋊C8—41no—
225#95—22no—
226#95—22no—
227#95—22no—
228#95—22no—
229#95—22no—
230#95—22no—
231#95—22no—
232#95D4×C10911yescharacteristic
233#95D4×C10911yescharacteristic
234C24C2×D4×C10911yescharacteristic
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4C2×D4×C10911yescharacteristic
244C22×C4C2×D4×C10912yes—
245C22×C4C2×D4×C10912yes—
246C22×C4C24×C10911yescharacteristic
247M16—44no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—22no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—22no—
254C2×C8#41×C10914yes—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—82no—
264C4⋊C4—82no—
265C22⋊C4—42no—
266C22⋊C4—44no—
267C22⋊C4—82no—
268C42—22no—
269C42—22no—
270C42—44no—
271C23—21no—
272C23—22no—
273C23—22no—
274C23—21no—
275C23—21no—
276C23C22×D4×C10911yescharacteristic
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4C2×#41×C10912yes—
301C2×C4H(5,𝔽2)×C10911yescharacteristic
302C2×C42−1+4×C10911yescharacteristic
303C2×C42−1+4×C10912yes—
304C8—24no—
305C8—41no—
306C8—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—42no—
311C22—42no—
312C22#537×C10911yescharacteristic
313C22#547×C10912yes—
314C22#575×C10912yes—
315C22#576×C10911yescharacteristic
316C22#578×C10911yescharacteristic
317C4—41no—
318C4—42no—
319C4—42no—
320C4—82no—
321C4—82no—
322C4—82no—
323C4—82no—
324C4#541×C10912yes—
325C4#551×C10911yescharacteristic
326C4#563×C10911yescharacteristic
327C2—81no—
328C2C109×#272211yescharacteristic
329C2C109×#325611yescharacteristic
330C2C109×#326211yescharacteristic
331C2C109×#334712yes—
332C2C109×#335212yes—
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC24×C109C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C4×C22⋊C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C109×#2086C2semidirect
3. C109×#2085C2semidirect
6. C109×#1949C2semidirect
7. C109×#1921C2semidirect
160. #32425C109direct (N × H)
168. #2086C2×C109semidirect
169. #2085C2×C109semidirect
172. #1949C2×C109semidirect
173. #1921C2×C109semidirect
176. C109#32425direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#24952
C109×#20862
C109×#20852
C109×#20762
C109×#20752
C109×#19492
C109×#19212
C109×#18512
C109×#18092
#32425109