Finite Group Databasebeta

← #13252828

Subgroups — #13252828

Order 1792.

570 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
1#11740698C211yesmaximal, characteristic
2C2×C7×#332C211yesmaximal, characteristic
3C2×#89342C211yesmaximal, characteristic
4#11728199C211yesmaximal, characteristic
5Dic7×C4⋊C8C211yesmaximal, characteristic
6C2×#89277C211yesmaximal, characteristic
7C2×#89281C211yesmaximal, characteristic
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×#6507—22no—
10C2×#6432C2211yescharacteristic
11C2×C7×C4⋊C8C2211yescharacteristic
12C2×C7×C4⋊C8C2211yescharacteristic
13C2×Dic7⋊C8—22no—
14C2×C8×Dic7—21no—
15#89748—21no—
16#89748—21no—
17#89748C414yes—
18C42×Dic7C2211yescharacteristic
19C2×C4⋊(C7⋊C8)C2211yescharacteristic
20C2×C4⋊(C7⋊C8)C2211yescharacteristic
21C7×#332—22no—
22#89345—21no—
23#89342—22no—
24#89281—22no—
25#89277—22no—
26#9692—71nomaximal, Sylow
27C22×C7×Q8—21no—
28C22×Dic14—21no—
29C22×C7×C8—21no—
30C22×C7×C8—21no—
31C7×C4⋊Q8—21no—
32C7×C4⋊Q8—21no—
33C7×C4⋊Q8—21no—
34C7×C4⋊Q8—21no—
35C2×C7×C4⋊C4—21no—
36C2×C7×C4⋊C4C2×C412yes—
37C2×C42×C7C2311yescharacteristic
38#6507—44no—
39#6507—44no—
40C2×C4⋊Dic7—21no—
41C2×C4⋊Dic7C2×C412yes—
42C2×Dic7⋊C4—24no—
43C2×Dic7⋊C4—24no—
44C2×C4×Dic7C2×C412yes—
45C2×C4×Dic7D411yescharacteristic
46C2×C4×Dic7D412yes—
47C2×C4×Dic7D411yescharacteristic
48C22×C7⋊C8—21no—
49C22×C7⋊C8—21no—
50#6432—21no—
51#6432—21no—
52#6432—21no—
53#6432—21no—
54C7×C4⋊C8—21no—
55C7×C4⋊C8—21no—
56C7×C4⋊C8—21no—
57C7×C4⋊C8D412yes—
58Dic7⋊C8—44no—
59C8×Dic7—42no—
60C4⋊(C7⋊C8)—21no—
61C4⋊(C7⋊C8)—21no—
62C4⋊(C7⋊C8)—21no—
63C4⋊(C7⋊C8)D412yes—
64#2868—71no—
65#1842—71no—
66C4×C4⋊C8—71no—
67C2×#332—71no—
68C2×#332—71no—
69C2×#332—71no—
70C2×#332D711yescharacteristic
71C2×C7×Q8—41no—
72C2×C7×Q8—41no—
73C2×C7×Q8—42no—
74C2×C7×Q8—42no—
75C22×C4×C7—22no—
76C22×C4×C7C22×C411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×Dic7—22no—
80C22×Dic7C22⋊C412yes—
81C22×Dic7C22⋊C412yes—
82C2×Dic14—41no—
83C2×Dic14—41no—
84C2×Dic14—42no—
85C2×Dic14—42no—
86C2×C7×C8—22no—
87C2×C7×C8—41no—
88C2×C7×C8—41no—
89C2×C7×C8—41no—
90C2×C7×C8—42no—
91C7×C4⋊C4—22no—
92C7×C4⋊C4—22no—
93C7×C4⋊C4—41no—
94C7×C4⋊C4—41no—
95C42×C7C2×D411yescharacteristic
96C42×C7C2×D411yescharacteristic
97C42×C7#4111yescharacteristic
98C42×C7#4111yescharacteristic
99C4⋊Dic7—22no—
100C4⋊Dic7—22no—
101C4⋊Dic7—41no—
102C4⋊Dic7—41no—
103Dic7⋊C4—48no—
104Dic7⋊C4—48no—
105C4×Dic7—21no—
106C4×Dic7—21no—
107C4×Dic7—24no—
108C4×Dic7D814yes—
109C4×Dic7SD1614yes—
110C4×Dic7SD1612yes—
111C4×Dic7Q1612yes—
112C2×C7⋊C8—22no—
113C2×C7⋊C8—41no—
114C2×C7⋊C8—41no—
115C2×C7⋊C8—41no—
116C2×C7⋊C8—42no—
117C2×C4⋊Q8—71no—
118C2×C4⋊Q8—142no—
119C2×C4⋊Q8C2×D711yescharacteristic
120C2×C4⋊C8—71no—
121C2×C4⋊C8—71no—
122C2×C4⋊C8—142no—
123C2×C4⋊C8C2×D711yescharacteristic
124C2×C4⋊C8C2×D711yescharacteristic
125C2×C4×C8—141no—
126#384—74no—
127#384—141no—
128#384—141no—
129C43—71no—
130#336—141no—
131#332—22no—
132#332—142no—
133#332—142no—
134#332—142no—
135C23×C7C2×C22⋊C411yescharacteristic
136C7×Q8—82no—
137C7×Q8—81no—
138C7×Q8—81no—
139C2×C4×C7—22no—
140C2×C4×C7—42no—
141C2×C4×C7—44no—
142C2×C4×C7C4×D411yescharacteristic
143C2×C4×C7C4×D411yescharacteristic
144C2×C4×C7#12111yescharacteristic
145C2×C4×C7#12111yescharacteristic
146C2×C4×C7#12411yescharacteristic
147C2×C4×C7#12711yescharacteristic
148C2×C4×C7C2×D812yes—
149C2×C4×C7C2×SD1611yescharacteristic
150C2×C4×C7C2×SD1612yes—
151C2×C4×C7C2×Q1611yescharacteristic
152C2×C4×C7#13711yescharacteristic
153C2×C4×C7#13711yescharacteristic
154C2×Dic7—22no—
155C2×Dic7—22no—
156C2×Dic7—42no—
157C2×Dic7—44no—
158C2×Dic7#10114yes—
159C2×Dic7#10214yes—
160C2×Dic7#10214yes—
161C2×Dic7#10314yes—
162Dic14—82no—
163Dic14—81no—
164Dic14—81no—
165C7×C8—42no—
166C7×C8—81no—
167C7⋊C8—42no—
168C7⋊C8—81no—
169C22×Q8—21no—
170C22×Q8—141no—
171C22×C8—21no—
172C22×C8—21no—
173C22×C8—141no—
174C22×C8—141no—
175C4⋊Q8—21no—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C4⋊Q8—141no—
180C4⋊Q8—141no—
181C4⋊Q8—141no—
182C4⋊Q8—141no—
183C4⋊Q8—284no—
184C4⋊Q8—284no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—72no—
187C2×C4⋊C4—144no—
188C2×C4⋊C4—144no—
189C2×C4⋊C4—141no—
190C2×C4⋊C4C4×D712yes—
191C2×C42—72no—
192C2×C42—71no—
193C2×C42—72no—
194C2×C42—71no—
195C2×C42C22×D711yescharacteristic
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—72no—
200C4⋊C8—141no—
201C4⋊C8—141no—
202C4⋊C8—141no—
203C4⋊C8—284no—
204C4⋊C8C22⋊D712yes—
205C4×C8—282no—
206C22×C7#39011yescharacteristic
207C22×C7C2×#10112yes—
208C22×C7C2×#10212yes—
209C22×C7C2×#10311yescharacteristic
210C22×C7#41911yescharacteristic
211C4×C7—21no—
212C4×C7—21no—
213C4×C7—82no—
214C4×C7#46111yescharacteristic
215C4×C7#46111yescharacteristic
216C4×C7#46211yescharacteristic
217C4×C7#46211yescharacteristic
218C4×C7#48612yes—
219C4×C7#49211yescharacteristic
220C4×C7#49311yescharacteristic
221Dic7—24no—
222Dic7—82no—
223Dic7#33218yescomplemented
224C2×Q8—41no—
225C2×Q8—42no—
226C2×Q8—42no—
227C2×Q8—41no—
228C2×Q8—281no—
229C2×Q8—282no—
230C2×Q8—282no—
231C2×Q8—281no—
232C22×C4—22no—
233C22×C4—72no—
234C22×C4—72no—
235C22×C4—142no—
236C22×C4C2×C4×D711yescharacteristic
237C22×C4D4×D711yescharacteristic
238C22×C4D4×D711yescharacteristic
239C2×C8—22no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—42no—
243C2×C8—41no—
244C2×C8—142no—
245C2×C8—281no—
246C2×C8—281no—
247C2×C8—282no—
248C2×C8—281no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—142no—
254C4⋊C4—142no—
255C4⋊C4—288no—
256C4⋊C4—288no—
257C4⋊C4—281no—
258C4⋊C4—281no—
259C42—74no—
260C42—72no—
261C42—74no—
262C42—72no—
263C42—144no—
264C42—141no—
265C42—141no—
266C42#115711yescharacteristic
267C42D4×D711yescharacteristic
268C42#115911yescharacteristic
269C42C2×C22⋊D711yescharacteristic
270C2×C7C2×#33212yes—
271C2×C7#154612yes—
272C2×C7#195711yescharacteristic
273C2×C7#196611yescharacteristic
274C2×C7#198111yescharacteristic
275C23D7×C22⋊C411yescharacteristic
276Q8—81no—
277Q8—81no—
278Q8—82no—
279Q8—561no—
280Q8—561no—
281Q8—562no—
282C2×C4—22no—
283C2×C4—42no—
284C2×C4—44no—
285C2×C4—74no—
286C2×C4—74no—
287C2×C4—74no—
288C2×C4—74no—
289C2×C4—142no—
290C2×C4—142no—
291C2×C4—282no—
292C2×C4—284no—
293C2×C4(C22⋊D7)⋊C411yescharacteristic
294C2×C4#644711yescharacteristic
295C2×C4#644811yescharacteristic
296C2×C4D7×D812yes—
297C2×C4D7×SD1611yescharacteristic
298C2×C4D7×SD1612yes—
299C2×C4#647811yescharacteristic
300C2×C4D7×Q1611yescharacteristic
301C2×C4#648111yescharacteristic
302C2×C4C4×C22⋊D711yescharacteristic
303C2×C4#650211yescharacteristic
304C2×C4#650311yescharacteristic
305C8—42no—
306C8—81no—
307C8—282no—
308C8—561no—
309C7#969211yescharacteristic, complemented, Sylow
310C22D7×#10112yes—
311C22D7×#10212yes—
312C22D7×#10311yescharacteristic
313C22#8957411yescharacteristic
314C22#8972911yescharacteristic
315C4—21no—
316C4—21no—
317C4—78no—
318C4—82no—
319C4—144no—
320C4—562no—
321C4#8953212yes—
322C4#8956511yescharacteristic
323C4#8959011yescharacteristic
324C4#8992311yescharacteristic
325C4#8993411yescharacteristic
326C4#8994711yescharacteristic
327C4#8995411yescharacteristic
328C2D7×#33212yes—
329C2#1172617412yes—
330C2#1172785211yescharacteristic
331C2#1172791111yescharacteristic
332C2#1172798311yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC2×C7×#332C2
socle, prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenterC2×#332D7
hypocenterC7#9692
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
223. Dic7#332semidirect
309. C7#9692semidirect

Maximal subgroups

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

subgroupindex
#117406982
C2×C7×#3322
C2×#893422
#117281992
Dic7×C4⋊C82
C2×#892772
C2×#892812
#96927