Finite Group Databasebeta

← #13242297

Subgroups — #13242297

Order 1792.

530 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2851C211yesmaximal, characteristic
2#11729283C211yesmaximal, characteristic
3C2×#89319C211yesmaximal, characteristic
4#11725444C212yesmaximal, complemented
5#11725444C212yesmaximal, complemented
6C2×C7×#125C411yescharacteristic
7C22×C42×C7C2211yescharacteristic
8C23×C7⋊C8—21no—
9C7×#389C2211yescharacteristic
10C7×#389C2211yescharacteristic
11C7×#387—21no—
12C7×#387—21no—
13C7×#385—21no—
14C7×#385—21no—
15C7×#382C411yescharacteristic
16C7×#380C411yescharacteristic
17C7×#380C411yescharacteristic
18C2×C22⋊(C7⋊C8)—21no—
19C2×#6377—21no—
20#89319—21no—
21#89319C2212yes—
22#89319C2212yes—
23#7691—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C7×#125—42no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4C2×C411yescharacteristic
33C2×C7×C4⋊C4C2×C411yescharacteristic
34C2×C7×C4⋊C4C2×C411yescharacteristic
35C2×C7×C4⋊C4C2×C411yescharacteristic
36C2×C7×C22⋊C4—21no—
37C2×C7×C22⋊C4—21no—
38C2×C42×C7—42no—
39C2×C42×C7C2×C411yescharacteristic
40C2×C42×C7D411yescharacteristic
41C2×C42×C7D411yescharacteristic
42C2×C42×C7C2311yescharacteristic
43C22×C7⋊C8—24no—
44C22×C7⋊C8—22no—
45C22×C7⋊C8—22no—
46C22×C7⋊C8—42no—
47C22×C7⋊C8—42no—
48C7×#95—21no—
49C7×#95—21no—
50C7×#95—21no—
51C7×#95—21no—
52C7×#95—21no—
53C7×#95—21no—
54C22⋊(C7⋊C8)—24no—
55#6377—42no—
56#2851D711yescharacteristic
57#1749—71no—
58C2×#336—71no—
59#1271—72no—
60#1271—72no—
61C24×C7C22⋊C411yescharacteristic
62C22×C4×C7—22no—
63C22×C4×C7—22no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—22no—
67C22×C4×C7—22no—
68C22×C4×C7—22no—
69C22×C4×C7—22no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—41no—
75C22×C4×C7—41no—
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22⋊C411yescharacteristic
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22×C411yescharacteristic
80C22×C4×C7C2×D411yescharacteristic
81C22×C4×C7C2×D411yescharacteristic
82C7×C4⋊C4—22no—
83C7×C4⋊C4—22no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—42no—
87C7×C4⋊C4—42no—
88C7×C4⋊C4—42no—
89C7×C4⋊C4—41no—
90C7×C4⋊C4—41no—
91C7×C22⋊C4—42no—
92C7×C22⋊C4—42no—
93C42×C7—22no—
94C42×C7—22no—
95C42×C7—41no—
96C42×C7—41no—
97C2×C7⋊C8—24no—
98C2×C7⋊C8—24no—
99C2×C7⋊C8—48no—
100C2×C7⋊C8—42no—
101C2×C7⋊C8—42no—
102C2×C7⋊C8—42no—
103C2×C7⋊C8—42no—
104C23×C8—141no—
105C2×#125Dic711yescharacteristic
106C22×C42C2×D711yescharacteristic
107C2×C22⋊C8—141no—
108C2×#97—141no—
109#389C2×D711yescharacteristic
110#389C2×D711yescharacteristic
111#387—21no—
112#387—21no—
113#385—21no—
114#385—21no—
115#382Dic711yescharacteristic
116#380Dic711yescharacteristic
117#380Dic711yescharacteristic
118#336—72no—
119#336—72no—
120#336—141no—
121C23×C7—21no—
122C23×C7—21no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7#10112yes—
126C23×C7#10412yes—
127C23×C7#10412yes—
128C23×C7C2×C22⋊C411yescharacteristic
129C2×C4×C7—24no—
130C2×C4×C7—24no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—21no—
144C2×C4×C7—21no—
145C2×C4×C7—44no—
146C2×C4×C7—44no—
147C2×C4×C7—41no—
148C2×C4×C7—41no—
149C2×C4×C7—41no—
150C2×C4×C7—41no—
151C2×C4×C7—41no—
152C2×C4×C7—41no—
153C2×C4×C7—41no—
154C2×C4×C7—41no—
155C2×C4×C7—41no—
156C2×C4×C7—41no—
157C2×C4×C7—41no—
158C2×C4×C7—41no—
159C2×C4×C7#9912yes—
160C2×C4×C7#13112yes—
161C2×C4×C7#13512yes—
162C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C7#13711yescharacteristic
164C7⋊C8—44no—
165C7⋊C8—44no—
166C23×C4C2×Dic711yescharacteristic
167C23×C4C22⋊D711yescharacteristic
168C23×C4C22⋊D711yescharacteristic
169C22×C8—144no—
170C22×C8—142no—
171C22×C8—142no—
172C22×C8—282no—
173C22×C8—282no—
174#125—42no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4C2×Dic711yescharacteristic
180C2×C4⋊C4C2×Dic711yescharacteristic
181C2×C4⋊C4C2×Dic711yescharacteristic
182C2×C4⋊C4C2×Dic711yescharacteristic
183C2×C22⋊C4—21no—
184C2×C22⋊C4—21no—
185C2×C42—42no—
186C2×C42C2×Dic711yescharacteristic
187C2×C42C22⋊D711yescharacteristic
188C2×C42C22⋊D711yescharacteristic
189C2×C42C22×D711yescharacteristic
190C22⋊C8—144no—
191#97—282no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198C22×C7—22no—
199C22×C7—22no—
200C22×C7—22no—
201C22×C7—22no—
202C22×C7—22no—
203C22×C7—22no—
204C22×C7#33014yes—
205C22×C7#40811yescharacteristic
206C22×C7C2×#9911yescharacteristic
207C22×C7C2×#10111yescharacteristic
208C22×C7#41611yescharacteristic
209C22×C7#41711yescharacteristic
210C22×C7C2×#10411yescharacteristic
211C22×C7C2×#10411yescharacteristic
212C4×C7—22no—
213C4×C7—22no—
214C4×C7—21no—
215C4×C7—22no—
216C4×C7—21no—
217C4×C7—41no—
218C4×C7—41no—
219C4×C7—81no—
220C4×C7—81no—
221C4×C7—81no—
222C4×C7—81no—
223C24C22⋊Dic711yescharacteristic
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4C22⋊Dic711yescharacteristic
239C22×C4C22⋊Dic711yescharacteristic
240C22×C4C22⋊Dic711yescharacteristic
241C22×C4C22×Dic711yescharacteristic
242C22×C4C2×C22⋊D711yescharacteristic
243C22×C4C2×C22⋊D711yescharacteristic
244C2×C8—144no—
245C2×C8—144no—
246C2×C8—282no—
247C2×C8—288no—
248C2×C8—282no—
249C2×C8—282no—
250C2×C8—282no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C42—22no—
263C42—22no—
264C42—41no—
265C42—41no—
266C2×C7—24no—
267C2×C7#147211yescharacteristic
268C2×C7#148311yescharacteristic
269C2×C7#149411yescharacteristic
270C2×C7#150111yescharacteristic
271C2×C7#150411yescharacteristic
272C2×C7C2×#33011yescharacteristic
273C2×C7#155211yescharacteristic
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23#641012yes—
279C23#641112yes—
280C23#641112yes—
281C23C2×C22⋊Dic711yescharacteristic
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4#640812yes—
313C2×C4#651112yes—
314C2×C4#651211yescharacteristic
315C2×C4#651312yes—
316C2×C4#651411yescharacteristic
317C8—284no—
318C8—284no—
319C7#769111yescharacteristic, complemented, Sylow
320C22—22no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22#8933814yes—
327C22C2×#640811yescharacteristic
328C22C2×#641011yescharacteristic
329C22#9000411yescharacteristic
330C22#9000511yescharacteristic
331C22#9000611yescharacteristic
332C22C2×#641111yescharacteristic
333C22C2×#641111yescharacteristic
334C4—22no—
335C4—22no—
336C4—21no—
337C4—22no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—81no—
345C2—24no—
346C2#1172944511yescharacteristic
347C2#1172946111yescharacteristic
348C2#1172946211yescharacteristic
349C2C2×#8933811yescharacteristic
350C2#1172950511yescharacteristic
351C2#1172950611yescharacteristic
352C2#1172958511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2851C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C22⋊C4
cosocleC2×C42×C7C23
hypercenter#2851D7
hypocenterC7#7691
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
4. #11725444C2semidirect
5. #11725444C2semidirect
319. C7#7691semidirect

Maximal subgroups

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

subgroupindex
C7×#28512
#117292832
C2×#893192
#117254442
#76917