Finite Group Databasebeta

← C3×#89440 #13055108

Subgroups — C3×#89440 #13055108

Order 1344.

468 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D7C211yesmaximal, characteristic
2C2×C3×(C2×D7)⋊C4C211yesmaximal, characteristic
3C2×C3×(C2×D7)⋊C4C211yesmaximal, characteristic
4C2×C3×C4⋊Dic7C211yesmaximal, characteristic, complemented
5C2×C3×Dic7⋊C4C211yesmaximal, characteristic, complemented
6C3×C7×#95C211yesmaximal, characteristic, complemented
7C3×C7⋊#95C211yesmaximal, characteristic, complemented
8#89440C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×D7C2211yescharacteristic
10C22×C3×C4×C7C2211yescharacteristic
11C22×C3×C4×C7C2211yescharacteristic
12C22×C3×C4×C7C2211yescharacteristic
13C22×C3×Dic7C2211yescharacteristic
14C22×C3×Dic7C2211yescharacteristic
15C22×C3×Dic7C2211yescharacteristic
16C2×C3×C4×D7—22no—
17C2×C3×C4×D7—22no—
18C2×C3×C4×D7—22no—
19C3×(C2×D7)⋊C4—22no—
20C3×(C2×D7)⋊C4C414yescomplemented
21C3×C4⋊Dic7—22no—
22C3×Dic7⋊C4—22no—
23C22×C4×D7C2×C311yescharacteristic
24C2×(C2×D7)⋊C4C2×C311yescharacteristic
25C2×(C2×D7)⋊C4C2×C311yescharacteristic
26C2×C4⋊Dic7C2×C311yescharacteristic, complemented
27C2×Dic7⋊C4C2×C311yescharacteristic, complemented
28C7×#95C2×C311yescharacteristic, complemented
29C7⋊#95C2×C311yescharacteristic, complemented
30C3×#385—71nomaximal, Hall
31C23×C3×C7C2311yescharacteristic
32C22×C3×D7—21no—
33C22×C3×D7—21no—
34C22×C3×D7—21no—
35C22×C3×D7—21no—
36C22×C3×D7C2×C412yes—
37C22×C3×D7D412yes—
38C22×C3×D7Q812yes—
39C2×C3×C4×C7—21no—
40C2×C3×C4×C7—21no—
41C2×C3×C4×C7—21no—
42C2×C3×C4×C7—21no—
43C2×C3×C4×C7—21no—
44C2×C3×C4×C7—21no—
45C2×C3×C4×C7—21no—
46C2×C3×C4×C7C2×C412yescomplemented
47C2×C3×C4×C7D412yes—
48C2×C3×Dic7—21no—
49C2×C3×Dic7—21no—
50C2×C3×Dic7—21no—
51C2×C3×Dic7—21no—
52C2×C3×Dic7—21no—
53C2×C3×Dic7—21no—
54C2×C3×Dic7—21no—
55C2×C3×Dic7C2×C412yescomplemented
56C2×C3×Dic7D412yes—
57C3×C4×D7—28no—
58C23×D7C22×C311yescharacteristic
59C22×C4×C7C22×C311yescharacteristic
60C22×C4×C7C22×C311yescharacteristic
61C22×C4×C7C22×C311yescharacteristic
62C22×Dic7C22×C311yescharacteristic
63C22×Dic7C22×C311yescharacteristic
64C22×Dic7C22×C311yescharacteristic
65C2×C4×D7—22no—
66C2×C4×D7—22no—
67C2×C4×D7—22no—
68(C2×D7)⋊C4—22no—
69(C2×D7)⋊C4C3×C414yescomplemented
70C4⋊Dic7—22no—
71Dic7⋊C4—22no—
72C23×C3×C4—71no—
73C2×C3×C4⋊C4—71no—
74C2×C3×C4⋊C4—71no—
75C2×C3×C22⋊C4—71no—
76C2×C3×C22⋊C4—71no—
77C3×#95—71no—
78C3×#95D711yescharacteristic, complemented
79C22×C3×C7C22×C411yescharacteristic
80C22×C3×C7C2×D411yescharacteristic
81C22×C3×C7C2×D411yescharacteristic
82C22×C3×C7C2×D411yescharacteristic
83C22×C3×C7C2×Q811yescharacteristic
84C22×C3×C7#4111yescharacteristic
85C22×C3×C7#4111yescharacteristic
86C2×C3×D7—22no—
87C2×C3×D7—22no—
88C2×C3×D7—22no—
89C2×C3×D7—22no—
90C2×C3×D7—22no—
91C2×C3×D7—22no—
92C2×C3×D7C4⋊C414yescomplemented
93C3×C4×C7—22no—
94C3×C4×C7—22no—
95C3×C4×C7—41no—
96C3×Dic7—22no—
97C3×Dic7—22no—
98C3×Dic7—41no—
99#385—71noSylow
100C23×C7C23×C311yescharacteristic
101C22×D7—21no—
102C22×D7—21no—
103C22×D7—21no—
104C22×D7—21no—
105C22×D7C2×C3×C412yes—
106C22×D7C3×D412yes—
107C22×D7C3×Q812yes—
108C2×C4×C7—21no—
109C2×C4×C7—21no—
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7C2×C3×C412yescomplemented
116C2×C4×C7C3×D412yes—
117C2×Dic7—21no—
118C2×Dic7—21no—
119C2×Dic7—21no—
120C2×Dic7—21no—
121C2×Dic7—21no—
122C2×Dic7—21no—
123C2×Dic7—21no—
124C2×Dic7C2×C3×C412yescomplemented
125C2×Dic7C3×D412yes—
126C4×D7—28no—
127C24×C3—71no—
128C22×C3×C4—71no—
129C22×C3×C4—71no—
130C22×C3×C4—71no—
131C22×C3×C4—142no—
132C22×C3×C4—142no—
133C22×C3×C4—142no—
134C22×C3×C4C2×D711yescharacteristic
135C22×C3×C4C2×D711yescharacteristic
136C22×C3×C4C2×D711yescharacteristic
137C3×C4⋊C4—142no—
138C3×C4⋊C4—142no—
139C3×C22⋊C4—74no—
140C3×C22⋊C4—142no—
141C2×C3×C7C2×C4⋊C411yescharacteristic
142C2×C3×C7C4×D411yescharacteristic
143C2×C3×C7C4×D411yescharacteristic
144C2×C3×C7#12011yescharacteristic
145C2×C3×C7C22⋊Q811yescharacteristic
146C2×C3×C7C22⋊Q811yescharacteristic
147C2×C3×C7#12311yescharacteristic
148C3×D7—24no—
149C23×C4—71no—
150C2×C4⋊C4—71no—
151C2×C4⋊C4—71no—
152C2×C22⋊C4—71no—
153C2×C22⋊C4—71no—
154#95—71no—
155#95C3×D711yescharacteristic, complemented
156C22×C7C22×C3×C411yescharacteristic
157C22×C7C2×C3×D411yescharacteristic
158C22×C7C2×C3×D411yescharacteristic
159C22×C7C2×C3×D411yescharacteristic
160C22×C7C2×C3×Q811yescharacteristic
161C22×C7C3×#4111yescharacteristic
162C22×C7C3×#4111yescharacteristic
163C2×D7—22no—
164C2×D7—22no—
165C2×D7—22no—
166C2×D7—22no—
167C2×D7—22no—
168C2×D7—22no—
169C2×D7C3×C4⋊C414yescomplemented
170C4×C7—22no—
171C4×C7—22no—
172C4×C7—41no—
173Dic7—22no—
174Dic7—22no—
175Dic7—41no—
176C23×C3—72no—
177C23×C3—72no—
178C23×C3—72no—
179C23×C3—141no—
180C23×C3—141no—
181C23×C3—141no—
182C23×C3—141no—
183C23×C3C22×D711yescharacteristic
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—72no—
192C2×C3×C4—72no—
193C2×C3×C4—148no—
194C2×C3×C4—141no—
195C2×C3×C4—141no—
196C2×C3×C4—141no—
197C2×C3×C4—141no—
198C2×C3×C4—141no—
199C2×C3×C4—141no—
200C2×C3×C4—141no—
201C2×C3×C4C4×D712yescomplemented
202C2×C3×C4D2812yes—
203C3×C7#38511yescharacteristic, complemented, Hall
204C24—71no—
205C22×C4—71no—
206C22×C4—71no—
207C22×C4—71no—
208C22×C4—142no—
209C22×C4—142no—
210C22×C4—142no—
211C22×C4C2×C3×D711yescharacteristic
212C22×C4C2×C3×D711yescharacteristic
213C22×C4C2×C3×D711yescharacteristic
214C4⋊C4—142no—
215C4⋊C4—142no—
216C22⋊C4—74no—
217C22⋊C4—142no—
218C2×C7C2×C3×C4⋊C411yescharacteristic
219C2×C7C3×C4×D411yescharacteristic
220C2×C7C3×C4×D411yescharacteristic
221C2×C7C3×#12011yescharacteristic
222C2×C7C3×C22⋊Q811yescharacteristic
223C2×C7C3×C22⋊Q811yescharacteristic
224C2×C7C3×#12311yescharacteristic
225D7—24no—
226C22×C3—74no—
227C22×C3—142no—
228C22×C3—142no—
229C22×C3—142no—
230C22×C3—142no—
231C22×C3—142no—
232C22×C3—142no—
233C22×C3C2×C4×D711yescharacteristic
234C22×C3C2×D2811yescharacteristic
235C22×C3#115711yescharacteristic
236C22×C3D4×D711yescharacteristic
237C22×C3D4×D711yescharacteristic
238C22×C3#115911yescharacteristic
239C22×C3Q8×D711yescharacteristic
240C3×C4—22no—
241C3×C4—22no—
242C3×C4—41no—
243C3×C4—142no—
244C3×C4—142no—
245C3×C4—281no—
246C23—72no—
247C23—72no—
248C23—72no—
249C23—141no—
250C23—141no—
251C23—141no—
252C23—141no—
253C23C22×C3×D711yescharacteristic
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—72no—
262C2×C4—72no—
263C2×C4—148no—
264C2×C4—141no—
265C2×C4—141no—
266C2×C4—141no—
267C2×C4—141no—
268C2×C4—141no—
269C2×C4—141no—
270C2×C4—141no—
271C2×C4C3×C4×D712yescomplemented
272C2×C4C3×D2812yes—
273C7C3×#38511yescharacteristic, complemented, Sylow
274C2×C3—144no—
275C2×C3C4×D2811yescharacteristic
276C2×C3(C22⋊D7)⋊C411yescharacteristic
277C2×C3#644511yescharacteristic
278C2×C3#644611yescharacteristic
279C2×C3D7×C4⋊C411yescharacteristic
280C2×C3#645911yescharacteristic
281C2×C3#646011yescharacteristic
282C22—74no—
283C22—142no—
284C22—142no—
285C22—142no—
286C22—142no—
287C22—142no—
288C22—142no—
289C22C2×C3×C4×D711yescharacteristic
290C22C2×C3×D2811yescharacteristic
291C22C3×#115711yescharacteristic
292C22C3×D4×D711yescharacteristic
293C22C3×D4×D711yescharacteristic
294C22C3×#115911yescharacteristic
295C22C3×Q8×D711yescharacteristic
296C4—22no—
297C4—22no—
298C4—41no—
299C4—142no—
300C4—142no—
301C4—281no—
302C3#8944011yescharacteristic, direct product factor, Sylow
303C2—144no—
304C2C3×C4×D2811yescharacteristic
305C2C3×(C22⋊D7)⋊C411yescharacteristic
306C2C3×#644511yescharacteristic
307C2C3×#644611yescharacteristic
308C2C3×D7×C4⋊C411yescharacteristic
309C2C3×#645911yescharacteristic
310C2C3×#646011yescharacteristic
subgroupG/H
centerC23×C3C22×D7
commutatorC22×C7C22×C3×C4
FrattiniC23C22×C3×D7
FittingC3×C7×#95C2
socleC23×C3×C7C23
prime radicalC23×C3×D7C22
cosocleC23×C7C23×C3
hypercenterC3×#95D7
hypocenterC7C3×#385
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23×C3 ◁ C3×#95

Complements

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

NH ≅ G/Ntype
4. C2×C3×C4⋊Dic7C2semidirect
5. C2×C3×Dic7⋊C4C2semidirect
6. C3×C7×#95C2semidirect
7. C3×C7⋊#95C2semidirect
8. #89440C3direct (N × H)
20. C3×(C2×D7)⋊C4C4semidirect
26. C2×C4⋊Dic7C2×C3semidirect
27. C2×Dic7⋊C4C2×C3semidirect
28. C7×#95C2×C3semidirect
29. C7⋊#95C2×C3semidirect
46. C2×C3×C4×C7C2×C4semidirect
55. C2×C3×Dic7C2×C4semidirect
69. (C2×D7)⋊C4C3×C4semidirect
78. C3×#95D7semidirect
92. C2×C3×D7C4⋊C4semidirect
115. C2×C4×C7C2×C3×C4semidirect
124. C2×Dic7C2×C3×C4semidirect
155. #95C3×D7semidirect
169. C2×D7C3×C4⋊C4semidirect
201. C2×C3×C4C4×D7semidirect
203. C3×C7#385semidirect
271. C2×C4C3×C4×D7semidirect
273. C7C3×#385semidirect
302. C3#89440direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×D72
C2×C3×(C2×D7)⋊C42
C2×C3×C4⋊Dic72
C2×C3×Dic7⋊C42
C3×C7×#952
C3×C7⋊#952
#894403
C3×#3857