Finite Group Databasebeta

← #13249517

Subgroups — #13249517

Order 1792.

738 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2855C211yesmaximal, characteristic
2C2×C4×C4⋊Dic7C211yesmaximal, characteristic
3C2×#89333C212yesmaximal
4#11729285C211yesmaximal, characteristic
5#11725430C212yesmaximal
6C2×C7×C22⋊Q8C2211yescharacteristic
7C22×C42×C7C2211yescharacteristic
8C22×C4⋊Dic7—21no—
9C22×C4×Dic7—21no—
10C7×#391C412yescomplemented
11C7×#389C412yescomplemented
12C7×#387—22no—
13C7×#385—21no—
14C7×#381—21no—
15C7×#380C2211yescharacteristic
16C2×C7⋊#95C2212yes—
17C2×C22⋊(C7⋊C8)C2212yes—
18C4×C4⋊Dic7—24no—
19#89333—24no—
20#89319—22no—
21#9144—71nomaximal, Sylow
22C22×C7×Q8C2×C411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C23×C4×C7D411yescharacteristic
25C23×C4×C7C2311yescharacteristic
26C23×Dic7—22no—
27C7×C22⋊Q8—22no—
28C7×C22⋊Q8—22no—
29C2×C7×C4⋊C4—22no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4C2×C411yescharacteristic
32C2×C7×C4⋊C4C2×C412yes—
33C2×C7×C22⋊C4—21no—
34C2×C7×C22⋊C4—21no—
35C2×C42×C7—22no—
36C2×C42×C7—22no—
37C2×C42×C7C2×C412yes—
38C2×C42×C7D412yes—
39C2×C4⋊Dic7—24no—
40C2×C4⋊Dic7—28no—
41C2×C4×Dic7—24no—
42C2×C4×Dic7—42no—
43C2×C4×Dic7—42no—
44C22×C7⋊C8—22no—
45C7×#95—22no—
46C7×#95—22no—
47C7×#95—22no—
48C7×#95—21no—
49C7⋊#95—22no—
50C7⋊#95D414yes—
51C22⋊(C7⋊C8)—22no—
52C22⋊(C7⋊C8)—22no—
53#2855D711yescharacteristic
54C2×C4×C4⋊C4—71no—
55#1817—71no—
56C2×#328—72no—
57#1294—72no—
58C24×C7C2×D411yescharacteristic
59C2×C7×Q8—22no—
60C2×C7×Q8—42no—
61C22×C4×C7—21no—
62C22×C4×C7—21no—
63C22×C4×C7—21no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—24no—
68C22×C4×C7—22no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—42no—
72C22×C4×C7C22⋊C412yes—
73C22×C4×C7C22⋊C412yes—
74C22×C4×C7SD1612yes—
75C22×C4×C7Q1612yes—
76C22×C4×C7C22×C411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×C4×C7C2×D412yes—
79C22×C4×C7#4112yes—
80C22×Dic7—28no—
81C22×Dic7—24no—
82C22×Dic7—44no—
83C22×Dic7—42no—
84C22×Dic7—42no—
85C7×C4⋊C4—22no—
86C7×C4⋊C4—42no—
87C7×C4⋊C4—44no—
88C7×C4⋊C4—42no—
89C7×C22⋊C4—41no—
90C7×C22⋊C4—41no—
91C7×C22⋊C4—41no—
92C7×C22⋊C4—41no—
93C42×C7—24no—
94C42×C7—24no—
95C4⋊Dic7—216no—
96C4×Dic7—48no—
97C2×C7⋊C8—44no—
98C2×C7⋊C8—42no—
99C2×C22⋊Q8C2×D711yescharacteristic
100C22×C4⋊C4—141no—
101C22×C42—141no—
102C22×C42C2×D711yescharacteristic
103C2×C22⋊C8—72no—
104#391Dic712yescomplemented
105#389Dic712yescomplemented
106#387—22no—
107#385—21no—
108#381—21no—
109#380C2×D711yescharacteristic
110C4×C4⋊C4—144no—
111C2×#95—72no—
112#336—142no—
113#328—144no—
114C23×C7—22no—
115C23×C7—22no—
116C23×C7C2×C22⋊C411yescharacteristic
117C23×C7#12011yescharacteristic
118C23×C7#12311yescharacteristic
119C23×C7C2×SD1611yescharacteristic
120C23×C7C2×Q1611yescharacteristic
121C23×C7AGL(1,ℤ/8)11yescharacteristic
122C23×C7#13711yescharacteristic
123C7×Q8—82no—
124C2×C4×C7—24no—
125C2×C4×C7—24no—
126C2×C4×C7—22no—
127C2×C4×C7—22no—
128C2×C4×C7—22no—
129C2×C4×C7—22no—
130C2×C4×C7—22no—
131C2×C4×C7—22no—
132C2×C4×C7—22no—
133C2×C4×C7—22no—
134C2×C4×C7—22no—
135C2×C4×C7—22no—
136C2×C4×C7—42no—
137C2×C4×C7—42no—
138C2×C4×C7—41no—
139C2×C4×C7—41no—
140C2×C4×C7—42no—
141C2×C4×C7—42no—
142C2×C4×C7—42no—
143C2×C4×C7—42no—
144C2×C4×C7—42no—
145C2×C4×C7#10314yes—
146C2×C4×C7#10414yes—
147C2×C4×C7C4×D412yes—
148C2×C4×C7#12112yes—
149C2×Dic7—28no—
150C2×Dic7—44no—
151C2×Dic7—48no—
152C2×Dic7—48no—
153C2×Dic7—44no—
154C7⋊C8—82no—
155C22×Q8C2×Dic711yescharacteristic
156C23×C4—142no—
157C23×C4C22⋊D711yescharacteristic
158C23×C4C22⋊D711yescharacteristic
159C23×C4C22×D711yescharacteristic
160C22×C8—142no—
161C22⋊Q8—22no—
162C22⋊Q8—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—148no—
166C2×C4⋊C4—144no—
167C2×C4⋊C4C2×Dic711yescharacteristic
168C2×C4⋊C4C2×Dic712yes—
169C2×C22⋊C4—21no—
170C2×C22⋊C4—21no—
171C2×C42—22no—
172C2×C42—22no—
173C2×C42—144no—
174C2×C42—282no—
175C2×C42—282no—
176C2×C42C2×Dic712yes—
177C2×C42C22⋊D712yes—
178C22⋊C8—142no—
179C22⋊C8—142no—
180#95—22no—
181#95—22no—
182#95—22no—
183#95—21no—
184#95—74no—
185#95—142no—
186C22×C7—21no—
187C22×C7—21no—
188C22×C7—21no—
189C22×C7—21no—
190C22×C7—22no—
191C22×C7—22no—
192C22×C7—22no—
193C22×C7—22no—
194C22×C7#38611yescharacteristic
195C22×C7#41012yes—
196C22×C7C2×#10311yescharacteristic
197C22×C7#41711yescharacteristic
198C22×C7C2×#10412yes—
199C22×C7#45011yescharacteristic
200C22×C7#45111yescharacteristic
201C22×C7#48311yescharacteristic
202C22×C7#48411yescharacteristic
203C4×C7—24no—
204C4×C7—24no—
205C4×C7—22no—
206C4×C7—22no—
207C4×C7—81no—
208C4×C7—81no—
209C4×C7—82no—
210Dic7—48no—
211C24C2×C22⋊D711yescharacteristic
212C2×Q8—22no—
213C2×Q8—42no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—24no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—42no—
225C22×C4—148no—
226C22×C4—144no—
227C22×C4—284no—
228C22×C4—282no—
229C22×C4—282no—
230C22×C4#114312yes—
231C22×C4#114412yes—
232C22×C4C22⋊Dic712yes—
233C22×C4C22⋊Dic712yes—
234C22×C4D4×D712yes—
235C22×C4#115912yes—
236C22×C4C22×Dic711yescharacteristic
237C22×C4C2×C22⋊D711yescharacteristic
238C2×C8—284no—
239C2×C8—282no—
240C4⋊C4—22no—
241C4⋊C4—42no—
242C4⋊C4—44no—
243C4⋊C4—42no—
244C4⋊C4—1416no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C42—24no—
250C42—24no—
251C42—288no—
252C2×C7—21no—
253C2×C7—21no—
254C2×C7—21no—
255C2×C7—21no—
256C2×C7#150312yes—
257C2×C7#150912yes—
258C2×C7#187211yescharacteristic
259C2×C7#189611yescharacteristic
260C2×C7#189911yescharacteristic
261C23—22no—
262C23—22no—
263C23#649811yescharacteristic
264C23#650011yescharacteristic
265C23C2×#114311yescharacteristic
266C23C2×#114411yescharacteristic
267C23#651211yescharacteristic
268C23#651411yescharacteristic
269C23C2×C22⋊Dic711yescharacteristic
270Q8—82no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—148no—
293C2×C4—284no—
294C2×C4—288no—
295C2×C4—288no—
296C2×C4—284no—
297C2×C4#640914yes—
298C2×C4#641114yes—
299C2×C4D4×Dic712yes—
300C2×C4#650212yes—
301C8—562no—
302C7#914411yescharacteristic, complemented, Sylow
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22#8981511yescharacteristic
312C22#8981611yescharacteristic
313C22#8981811yescharacteristic
314C22#8982211yescharacteristic
315C22#8999211yescharacteristic
316C22C2×#640911yescharacteristic
317C22#9000411yescharacteristic
318C22C2×#641112yes—
319C22#9001212yes—
320C4—24no—
321C4—22no—
322C4—22no—
323C4—24no—
324C4—81no—
325C4—81no—
326C4—82no—
327C4—288no—
328C2—21no—
329C2—21no—
330C2—21no—
331C2—21no—
332C2#1172944611yescharacteristic
333C2#1172945911yescharacteristic
334C2#1172946511yescharacteristic
335C2#1172950912yes—
336C2#1172958912yes—
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#2855C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenter#2855D7
hypocenterC7#9144
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
10. C7×#391C4semidirect
11. C7×#389C4semidirect
104. #391Dic7semidirect
105. #389Dic7semidirect
302. C7#9144semidirect

Maximal subgroups

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

subgroupindex
C7×#28552
C2×C4×C4⋊Dic72
C2×#893332
#117292852
#117254302
#91447