Finite Group Databasebeta

← C2×C109×#1346 #42129690

Subgroups — C2×C109×#1346 #42129690

Order 27904.

544 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
1C2×#398×C109C211yesmaximal, characteristic
2C2×#343×C109C211yesmaximal, characteristic
3C2×#324×C109C211yesmaximal, characteristic
4C109×#1346C214yesmaximal, direct product factor
5C22×M16×C109—21no—
6C22×C4⋊C4×C109—21no—
7C22×C4⋊C4×C109C411yescharacteristic
8C22×C4⋊C4×C109C2211yescharacteristic
9C2×C22⋊C8×C109—21no—
10#398×C109—21no—
11#398×C109—21no—
12#398×C109C412yes—
13#398×C109C2212yes—
14C2×#95×C109—21no—
15C2×#95×C109C411yescharacteristic
16#343×C109—21no—
17#343×C109C2212yes—
18#324×C109—21no—
19#324×C109C2212yes—
20C23×C4×C109—21no—
21C23×C4×C109—21no—
22C23×C4×C109C2×C411yescharacteristic
23C23×C4×C109D411yescharacteristic
24C23×C4×C109D411yescharacteristic
25C2×M16×C109—24no—
26C2×M16×C109—22no—
27C2×M16×C109—41no—
28C2×M16×C109—42no—
29C22×C8×C109—41no—
30C22×C8×C109—41no—
31C2×C4⋊C4×C109—22no—
32C2×C4⋊C4×C109—21no—
33C2×C4⋊C4×C109—22no—
34C2×C4⋊C4×C109—41no—
35C2×C4⋊C4×C109—41no—
36C2×C4⋊C4×C109—41no—
37C2×C4⋊C4×C109—41no—
38C2×C4⋊C4×C109—42no—
39C2×C4⋊C4×C109—42no—
40C2×C4⋊C4×C109C2×C412yes—
41C2×C4⋊C4×C109C2×C411yescharacteristic
42C2×C4⋊C4×C109D411yescharacteristic
43C2×C4⋊C4×C109D411yescharacteristic
44C2×C4⋊C4×C109C2311yescharacteristic
45C22⋊C8×C109—22no—
46C22⋊C8×C109—41no—
47#95×C109—22no—
48#95×C109—21no—
49#95×C109—22no—
50#95×C109C2×C412yes—
51C24×C109C22⋊C411yescharacteristic
52C22×C4×C109—21no—
53C22×C4×C109—21no—
54C22×C4×C109—22no—
55C22×C4×C109—24no—
56C22×C4×C109—21no—
57C22×C4×C109—21no—
58C22×C4×C109—21no—
59C22×C4×C109—22no—
60C22×C4×C109—21no—
61C22×C4×C109—22no—
62C22×C4×C109—42no—
63C22×C4×C109—42no—
64C22×C4×C109—42no—
65C22×C4×C109—42no—
66C22×C4×C109—41no—
67C22×C4×C109—41no—
68C22×C4×C109—42no—
69C22×C4×C109—42no—
70C22×C4×C109C22⋊C411yescharacteristic
71C22×C4×C109C22⋊C411yescharacteristic
72C22×C4×C109C22⋊C411yescharacteristic
73C22×C4×C109D812yes—
74C22×C4×C109SD1612yes—
75C22×C4×C109C22×C411yescharacteristic
76C22×C4×C109C2×D411yescharacteristic
77C22×C4×C109C2×D411yescharacteristic
78M16×C109—24no—
79M16×C109—44no—
80M16×C109—42no—
81C2×C8×C109—44no—
82C2×C8×C109—42no—
83C2×C8×C109—42no—
84C2×C8×C109—82no—
85C4⋊C4×C109—41no—
86C4⋊C4×C109—41no—
87C4⋊C4×C109—41no—
88C4⋊C4×C109—41no—
89C4⋊C4×C109—42no—
90C4⋊C4×C109—42no—
91C4⋊C4×C109—44no—
92C4⋊C4×C109—42no—
93C4⋊C4×C109—42no—
94C23×C109—22no—
95C23×C109—22no—
96C23×C109#9911yescharacteristic
97C23×C109#9911yescharacteristic
98C23×C109#10212yes—
99C23×C109#10412yes—
100C23×C109C2×C22⋊C411yescharacteristic
101C2×C4×C109—22no—
102C2×C4×C109—22no—
103C2×C4×C109—22no—
104C2×C4×C109—22no—
105C2×C4×C109—21no—
106C2×C4×C109—21no—
107C2×C4×C109—21no—
108C2×C4×C109—21no—
109C2×C4×C109—24no—
110C2×C4×C109—21no—
111C2×C4×C109—21no—
112C2×C4×C109—21no—
113C2×C4×C109—21no—
114C2×C4×C109—48no—
115C2×C4×C109—42no—
116C2×C4×C109—42no—
117C2×C4×C109—42no—
118C2×C4×C109—42no—
119C2×C4×C109—42no—
120C2×C4×C109—41no—
121C2×C4×C109—41no—
122C2×C4×C109—41no—
123C2×C4×C109—41no—
124C2×C4×C109—42no—
125C2×C4×C109—42no—
126C2×C4×C109—42no—
127C2×C4×C109—81no—
128C2×C4×C109—82no—
129C2×C4×C109—82no—
130C2×C4×C109#10212yes—
131C2×C4×C109C2×D811yescharacteristic
132C2×C4×C109C2×SD1611yescharacteristic
133C8×C109—44no—
134C8×C109—82no—
135C22×C109—24no—
136C22×C109—24no—
137C22×C109—21no—
138C22×C109—21no—
139C22×C109—21no—
140C22×C109—21no—
141C22×C109#32712yes—
142C22×C109#32712yes—
143C22×C109#35212yes—
144C22×C109#35612yes—
145C22×C109C2×#9911yescharacteristic
146C22×C109C2×#10211yescharacteristic
147C22×C109C2×#10411yescharacteristic
148C4×C109—21no—
149C4×C109—22no—
150C4×C109—21no—
151C4×C109—44no—
152C4×C109—41no—
153C4×C109—41no—
154C4×C109—41no—
155C4×C109—41no—
156C4×C109—82no—
157C2×#1346C10911yesmaximal, characteristic, direct product factor, Sylow
158C2×C109—21no—
159C2×C109—22no—
160C2×C109—21no—
161C2×C109#134614yesdirect product factor
162C2×C109C2×#32711yescharacteristic
163C2×C109C2×#35211yescharacteristic
164C2×C109C2×#35611yescharacteristic
165C2×#398C2×C10911yescharacteristic
166C2×#343C2×C10911yescharacteristic
167C2×#324C2×C10911yescharacteristic
168#1346C2×C10914yesdirect product factor
169C109C2×#134611yescharacteristic, direct product factor, Sylow
170C22×M16—21no—
171C22×C4⋊C4—21no—
172C22×C4⋊C4C4×C10911yescharacteristic
173C22×C4⋊C4C22×C10911yescharacteristic
174C2×C22⋊C8—21no—
175#398—21no—
176#398—21no—
177#398C4×C10912yes—
178#398C22×C10912yes—
179C2×#95—21no—
180C2×#95C4×C10911yescharacteristic
181#343—21no—
182#343C22×C10912yes—
183#324—21no—
184#324C22×C10912yes—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4C2×C4×C10911yescharacteristic
188C23×C4D4×C10911yescharacteristic
189C23×C4D4×C10911yescharacteristic
190C2×M16—24no—
191C2×M16—22no—
192C2×M16—41no—
193C2×M16—42no—
194C22×C8—41no—
195C22×C8—41no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—41no—
200C2×C4⋊C4—41no—
201C2×C4⋊C4—41no—
202C2×C4⋊C4—41no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4—42no—
205C2×C4⋊C4C2×C4×C10912yes—
206C2×C4⋊C4C2×C4×C10911yescharacteristic
207C2×C4⋊C4D4×C10911yescharacteristic
208C2×C4⋊C4D4×C10911yescharacteristic
209C2×C4⋊C4C23×C10911yescharacteristic
210C22⋊C8—22no—
211C22⋊C8—41no—
212#95—22no—
213#95—21no—
214#95—22no—
215#95C2×C4×C10912yes—
216C24C22⋊C4×C10911yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—24no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4C22⋊C4×C10911yescharacteristic
236C22×C4C22⋊C4×C10911yescharacteristic
237C22×C4C22⋊C4×C10911yescharacteristic
238C22×C4D8×C10912yes—
239C22×C4SD16×C10912yes—
240C22×C4C22×C4×C10911yescharacteristic
241C22×C4C2×D4×C10911yescharacteristic
242C22×C4C2×D4×C10911yescharacteristic
243M16—24no—
244M16—44no—
245M16—42no—
246C2×C8—44no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—82no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—44no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C23—22no—
260C23—22no—
261C23#99×C10911yescharacteristic
262C23#99×C10911yescharacteristic
263C23#102×C10912yes—
264C23#104×C10912yes—
265C23C2×C22⋊C4×C10911yescharacteristic
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—24no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—48no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—81no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4#102×C10912yes—
296C2×C4C2×D8×C10911yescharacteristic
297C2×C4C2×SD16×C10911yescharacteristic
298C8—44no—
299C8—82no—
300C22—24no—
301C22—24no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22#327×C10912yes—
307C22#327×C10912yes—
308C22#352×C10912yes—
309C22#356×C10912yes—
310C22C2×#99×C10911yescharacteristic
311C22C2×#102×C10911yescharacteristic
312C22C2×#104×C10911yescharacteristic
313C4—21no—
314C4—22no—
315C4—21no—
316C4—44no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—82no—
322C2—21no—
323C2—22no—
324C2—21no—
325C2C109×#134614yesdirect product factor
326C2C2×#327×C10911yescharacteristic
327C2C2×#352×C10911yescharacteristic
328C2C2×#356×C10911yescharacteristic
subgroupG/H
center, socleC23×C109#99
commutatorC22×C4C22×C4×C109
Frattini, cosocleC2×C4⋊C4C23×C109
prime radicalC24×C109C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C24×C109 ◁ C22×C4⋊C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
4. C109×#1346C2direct (N × H)
157. C2×#1346C109direct (N × H)
161. C2×C109#1346direct (N × H)
168. #1346C2×C109direct (N × H)
169. C109C2×#1346direct (N × H)
325. C2C109×#1346direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#398×C1092
C2×#343×C1092
C2×#324×C1092
C109×#13462
C2×#1346109