Finite Group Databasebeta

← #13273478

Subgroups — #13273478

Order 1792.

484 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11733866C211yesmaximal, characteristic
2C7×#1856C211yesmaximal, characteristic
3#11729411C212yesmaximal
4#11725504C212yesmaximal
5#11725447C211yesmaximal, characteristic
6C7×#518C2211yescharacteristic
7C7×#428—21no—
8C2×C7×#100C2211yescharacteristic
9C7×#390C2211yescharacteristic
10#89992C2212yes—
11C2×#6408C2212yes—
12#89758—21no—
13#89722—22no—
14#89719—22no—
15#89718—22no—
16#89701—21no—
17C7×#339—21no—
18#89321—22no—
19#13463—71nomaximal, Sylow
20C22×C7×D4C2311yescharacteristic
21C23×Dic7D412yes—
22C22×Dic14—21no—
23C2×C7×M16—21no—
24C4×C7×D4—41no—
25C4×C7×D4—41no—
26C7×#117—21no—
27C2×C7×C4⋊C4D411yescharacteristic
28C2×C7×C22⋊C4—22no—
29C2×C7×C22⋊C4—22no—
30C2×C42×C7D411yescharacteristic
31C2×C22⋊Dic7—22no—
32C2×C22⋊Dic7—22no—
33C2×C22⋊Dic7D412yes—
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×Dic7⋊C4—42no—
37C7×#107—41no—
38C7×#106—41no—
39C7×#100—21no—
40C7×#100Q812yescomplemented
41#6408—22no—
42#6408Q814yescomplemented
43C7⋊#95—22no—
44C7⋊#95—21no—
45C7⋊#95—22no—
46C7⋊#95—22no—
47C7⋊#95—42no—
48#2804—71no—
49#1867—72no—
50#1856D711yescharacteristic
51#1393—71no—
52#1390—72no—
53C24×C7C2×D412yes—
54C2×C7×D4—41no—
55C2×C7×D4—41no—
56C2×C7×D4C2×Q811yescharacteristic
57C2×C7×D4C2×Q812yes—
58C2×C7×D4#4111yescharacteristic
59C22×C4×C7—21no—
60C22×C4×C7—21no—
61C22×C4×C7—22no—
62C22×C4×C7—22no—
63C22×C4×C7C2×D411yescharacteristic
64C22×Dic7—22no—
65C22×Dic7—22no—
66C22×Dic7—42no—
67C22×Dic7—42no—
68C22×Dic7—82no—
69C2×Dic14—42no—
70C2×Dic14—81no—
71C2×Dic14—81no—
72C7×M16—22no—
73C7×M16—41no—
74C2×C7×C8—41no—
75C7×C4⋊C4—21no—
76C7×C4⋊C4—21no—
77C7×C4⋊C4—41no—
78C7×C22⋊C4—44no—
79C7×C22⋊C4—42no—
80C7×C22⋊C4—41no—
81C42×C7—41no—
82C42×C7—41no—
83C22⋊Dic7—24no—
84C22⋊Dic7—42no—
85C22⋊Dic7—42no—
86C22⋊Dic7—82no—
87C4⋊Dic7—81no—
88C4⋊Dic7—81no—
89Dic7⋊C4—84no—
90#518C2×D711yescharacteristic
91#428—21no—
92C2×#100C2×D711yescharacteristic
93C2×#99—72no—
94#400—141no—
95#393—142no—
96#391—141no—
97#390C2×D711yescharacteristic
98#386—72no—
99#385—142no—
100#385—142no—
101#342—142no—
102#339—21no—
103C23×C7—22no—
104C23×C7—22no—
105C23×C7—42no—
106C23×C7—42no—
107C23×C7#12011yescharacteristic
108C23×C7C22⋊Q812yes—
109C23×C7C4⋊Q812yes—
110C7×D4—41no—
111C7×D4—42no—
112C7×D4—41no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7—22no—
116C2×C4×C7—41no—
117C2×C4×C7—41no—
118C2×C4×C7—42no—
119C2×C4×C7—41no—
120C2×C4×C7—41no—
121C2×C4×C7—41no—
122C2×C4×C7—82no—
123C2×C4×C7—82no—
124C2×C4×C7C22⋊Q811yescharacteristic
125C2×C4×C7C4⋊Q811yescharacteristic
126C2×Dic7—42no—
127C2×Dic7—44no—
128C2×Dic7—42no—
129C2×Dic7—42no—
130C2×Dic7—42no—
131C2×Dic7—44no—
132C2×Dic7—42no—
133C2×Dic7—42no—
134C2×Dic7—82no—
135C2×Dic7—82no—
136C2×Dic7—82no—
137Dic14—84no—
138C7×C8—42no—
139C22×Q8—141no—
140C22×D4C22×D711yescharacteristic
141C23×C4—72no—
142C2×M16—21no—
143C4×D4—41no—
144C4×D4—41no—
145#117—21no—
146C2×C4⋊C4—141no—
147C2×C4⋊C4—141no—
148C2×C4⋊C4—282no—
149C2×C4⋊C4C22⋊D711yescharacteristic
150C2×C22⋊C4—22no—
151C2×C22⋊C4—22no—
152C2×C22⋊C4—72no—
153C2×C22⋊C4—142no—
154C2×C22⋊C4—142no—
155C2×C42C22⋊D711yescharacteristic
156#107—41no—
157#106—41no—
158#100—21no—
159#100Dic1412yescomplemented
160#99—74no—
161#99—142no—
162#95—142no—
163#95—142no—
164#95—141no—
165#95—142no—
166#95—282no—
167C22×C7—21no—
168C22×C7—21no—
169C22×C7—22no—
170C22×C7—22no—
171C22×C7—42no—
172C22×C7—42no—
173C22×C7—42no—
174C22×C7—42no—
175C22×C7—82no—
176C22×C7#39511yescharacteristic
177C22×C7B(4,𝔽2)11yescharacteristic
178C22×C7#45811yescharacteristic
179C4×C7—21no—
180C4×C7—21no—
181C4×C7—42no—
182C4×C7—81no—
183C4×C7—81no—
184C4×C7—81no—
185Dic7—82no—
186Dic7—84no—
187Dic7—82no—
188C24D4×D712yes—
189C2×Q8—282no—
190C2×Q8—561no—
191C2×Q8—561no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4C2×Dic1411yescharacteristic
195C2×D4#115711yescharacteristic
196C2×D4Q8×D712yes—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—142no—
202C22×C4—142no—
203C22×C4—282no—
204C22×C4—282no—
205C22×C4—562no—
206C22×C4C2×C22⋊D711yescharacteristic
207M16—22no—
208M16—41no—
209C2×C8—41no—
210C4⋊C4—21no—
211C4⋊C4—21no—
212C4⋊C4—41no—
213C4⋊C4—561no—
214C4⋊C4—561no—
215C4⋊C4—564no—
216C22⋊C4—44no—
217C22⋊C4—42no—
218C22⋊C4—41no—
219C22⋊C4—144no—
220C22⋊C4—282no—
221C22⋊C4—282no—
222C22⋊C4—562no—
223C42—41no—
224C42—41no—
225C2×C7—21no—
226C2×C7—21no—
227C2×C7—42no—
228C2×C7—42no—
229C2×C7#206211yescharacteristic
230C2×C7#219811yescharacteristic
231C2×C7#219911yescharacteristic
232C23—22no—
233C23—22no—
234C23—42no—
235C23—42no—
236C23#645112yes—
237C23#645912yes—
238C23#650011yescharacteristic
239Q8—564no—
240D4—41no—
241D4—41no—
242D4—42no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4—284no—
255C2×C4—282no—
256C2×C4—282no—
257C2×C4—282no—
258C2×C4—282no—
259C2×C4—284no—
260C2×C4—282no—
261C2×C4—282no—
262C2×C4—562no—
263C2×C4—562no—
264C2×C4—562no—
265C2×C4#648711yescharacteristic
266C2×C4#650711yescharacteristic
267C8—42no—
268C7#1346311yescharacteristic, complemented, Sylow
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—82no—
278C22#8975111yescharacteristic
279C22#8980411yescharacteristic
280C22#8982511yescharacteristic
281C4—21no—
282C4—21no—
283C4—42no—
284C4—81no—
285C4—81no—
286C4—81no—
287C4—562no—
288C4—564no—
289C4—562no—
290C2—21no—
291C2—21no—
292C2—42no—
293C2—42no—
294C2#1172734811yescharacteristic
295C2#1172874011yescharacteristic
296C2#1172874511yescharacteristic
subgroupG/H
centerC22#89804
commutator, prime radical, cosocleC22×C7×D4C23
FrattiniC22×D4C22×D7
FittingC7×#1856C2
socleC22×C7B(4,𝔽2)
hypercenter#1856D7
hypocenterC7#13463
LCSG ▷ C22×C7×D4 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1856

Complements

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

NH ≅ G/Ntype
40. C7×#100Q8semidirect
42. #6408Q8semidirect
159. #100Dic14semidirect
268. C7#13463semidirect

Maximal subgroups

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

subgroupindex
#117338662
C7×#18562
#117294112
#117255042
#117254472
#134637