Finite Group Databasebeta

← #13272122

Subgroups — #13272122

Order 1792.

472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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#11739920C211yesmaximal, characteristic
2C4×C7×#101C211yesmaximal, characteristic
3#11729391C211yesmaximal, characteristic
4C2×#89273C214yesmaximal
5C2×C4×C7×Q8C2211yescharacteristic
6C2×#6507C2212yes—
7C2×#6432C411yescharacteristic
8C2×C7×#101C2212yes—
9C4×C7×M16—21no—
10C2×#6410C2212yes—
11#89755—21no—
12#89755—21no—
13#89746C412yes—
14C4×C4⋊Dic7C411yescharacteristic
15#89700—21no—
16#89700—21no—
17#89696—21no—
18C7×#343—21no—
19#89325—21no—
20#89273—28no—
21#13227—71nomaximal, Sylow
22C22×C7×Q8C2311yescharacteristic
23C22×Dic14C2×C412yes—
24C2×C7×M16—22no—
25C4×C7×Q8—41no—
26C4×C7×Q8—41no—
27C2×C7×C4⋊C4C2×C411yescharacteristic
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C7×C4⋊C4D411yescharacteristic
30C2×C42×C7C2×C411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C42×C7D411yescharacteristic
33#6507—24no—
34#6507—24no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—21no—
38C2×Dic7⋊C4—22no—
39C2×Dic7⋊C4—22no—
40C2×C4×Dic7C2×C412yes—
41C2×#1136—22no—
42#6432—41no—
43#6432—41no—
44C7×#101—22no—
45C7×#101D414yes—
46C7×#97—41no—
47C4×C7×C8—41no—
48#6410—24no—
49C7⋊#95—22no—
50C7⋊#95—22no—
51C7⋊#95—21no—
52C4⋊(C7⋊C8)—41no—
53C4⋊(C7⋊C8)—41no—
54#2546—71no—
55C2×#356—74no—
56#1801—71no—
57C4×#101D711yescharacteristic
58C2×C7×Q8—41no—
59C2×C7×Q8—41no—
60C2×C7×Q8C2×D412yes—
61C2×C7×Q8#4112yes—
62C22×C4×C7C22⋊C411yescharacteristic
63C22×C4×C7C22⋊C411yescharacteristic
64C22×C4×C7C22⋊C411yescharacteristic
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C22×C411yescharacteristic
67C22×C4×C7C2×D411yescharacteristic
68C22×C4×C7C2×D411yescharacteristic
69C22×Dic7—22no—
70C22×Dic7—22no—
71C2×Dic14—24no—
72C2×Dic14—42no—
73C2×Dic14—42no—
74C7×M16—24no—
75C7×M16—42no—
76C2×C7×C8—42no—
77C7×C4⋊C4—41no—
78C7×C4⋊C4—41no—
79C7×C4⋊C4—41no—
80C42×C7—21no—
81C42×C7—21no—
82C42×C7—21no—
83C42×C7—21no—
84C42×C7—21no—
85C42×C7—21no—
86C4⋊Dic7—24no—
87C4⋊Dic7—42no—
88C4⋊Dic7—41no—
89C4⋊Dic7—41no—
90Dic7⋊C4—44no—
91Dic7⋊C4—42no—
92Dic7⋊C4—42no—
93C4×Dic7—24no—
94#1136—42no—
95#1136—42no—
96C2×C7⋊C8—42no—
97C2×C4⋊Q8—72no—
98C2×C4⋊Q8—71no—
99C2×C4×Q8C2×D711yescharacteristic
100#423—141no—
101C2×#101—72no—
102C2×#101C2×D712yes—
103C4×M16—21no—
104#398—141no—
105#398—141no—
106#391—72no—
107#389—141no—
108#389—141no—
109C4×C4⋊C4—71no—
110#356—148no—
111#343—21no—
112#343—141no—
113C23×C7C2×C22⋊C411yescharacteristic
114C7×Q8—42no—
115C7×Q8—42no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
122C2×C4×C7—22no—
123C2×C4×C7—21no—
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—41no—
127C2×C4×C7—41no—
128C2×C4×C7—41no—
129C2×C4×C7#9911yescharacteristic
130C2×C4×C7#9911yescharacteristic
131C2×C4×C7C4×D412yes—
132C2×C4×C7#12112yes—
133C2×C4×C7#12411yescharacteristic
134C2×C4×C7#12711yescharacteristic
135C2×Dic7—24no—
136C2×Dic7—42no—
137C2×Dic7—42no—
138C2×Dic7—42no—
139C2×Dic7—42no—
140C2×Dic7—42no—
141Dic14—84no—
142C7×C8—44no—
143C7⋊C8—82no—
144C22×Q8—72no—
145C22×Q8C22×D711yescharacteristic
146C2×M16—22no—
147C2×M16—142no—
148C4⋊Q8—144no—
149C4⋊Q8—144no—
150C4⋊Q8—281no—
151C4⋊Q8—281no—
152C4×Q8—41no—
153C4×Q8—41no—
154C2×C4⋊C4—141no—
155C2×C4⋊C4—141no—
156C2×C4⋊C4—141no—
157C2×C4⋊C4—142no—
158C2×C4⋊C4—142no—
159C2×C4⋊C4C4×D711yescharacteristic
160C2×C4⋊C4D2811yescharacteristic
161C2×C4⋊C4C22⋊D711yescharacteristic
162C2×C42—72no—
163C2×C42C4×D711yescharacteristic
164C2×C42D2811yescharacteristic
165C2×C42C22⋊D711yescharacteristic
166C4⋊C8—281no—
167C4⋊C8—281no—
168#101—22no—
169#101—144no—
170#101D2814yes—
171#97—41no—
172C4×C8—41no—
173#95—141no—
174#95—142no—
175#95—142no—
176C22×C7—21no—
177C22×C7—21no—
178C22×C7#39011yescharacteristic
179C22×C7C2×#9911yescharacteristic
180C22×C7#41011yescharacteristic
181C4×C7—21no—
182C4×C7—21no—
183C4×C7—22no—
184C4×C7—22no—
185C4×C7—21no—
186C4×C7—41no—
187C4×C7—41no—
188C4×C7—41no—
189C4×C7#35612yescomplemented
190Dic7—44no—
191Dic7—82no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—144no—
195C2×Q8—282no—
196C2×Q8—282no—
197C2×Q8C2×D2812yes—
198C2×Q8#115712yes—
199C22×C4—142no—
200C22×C4—142no—
201C22×C4(C2×D7)⋊C411yescharacteristic
202C22×C4(C2×D7)⋊C411yescharacteristic
203C22×C4(C2×D7)⋊C411yescharacteristic
204C22×C4(C2×D7)⋊C411yescharacteristic
205C22×C4C2×C4×D711yescharacteristic
206C22×C4C2×D2811yescharacteristic
207C22×C4C2×C22⋊D711yescharacteristic
208M16—24no—
209M16—42no—
210M16—282no—
211M16—282no—
212C2×C8—42no—
213C2×C8—282no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—144no—
218C4⋊C4—282no—
219C4⋊C4—282no—
220C4⋊C4—282no—
221C4⋊C4—284no—
222C4⋊C4—281no—
223C4⋊C4—281no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—144no—
231C2×C7—21no—
232C2×C7—21no—
233C2×C7#196411yescharacteristic
234C2×C7C2×#35611yescharacteristic
235C2×C7#213511yescharacteristic
236C23C2×(C2×D7)⋊C411yescharacteristic
237Q8—42no—
238Q8—42no—
239Q8—564no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—144no—
254C2×C4—282no—
255C2×C4—282no—
256C2×C4—282no—
257C2×C4—282no—
258C2×C4—282no—
259C2×C4#638011yescharacteristic
260C2×C4#638011yescharacteristic
261C2×C4C4×D2812yes—
262C2×C4#643711yescharacteristic
263C2×C4#643811yescharacteristic
264C2×C4#649312yes—
265C8—44no—
266C8—562no—
267C7#1322711yescharacteristic, complemented, Sylow
268C22—21no—
269C22—21no—
270C22#8971111yescharacteristic
271C22C2×#638011yescharacteristic
272C22#8977811yescharacteristic
273C4—21no—
274C4—22no—
275C4—21no—
276C4—22no—
277C4—21no—
278C4—41no—
279C4—41no—
280C4—41no—
281C4—284no—
282C4—562no—
283C4#8927312yescomplemented
284C2—21no—
285C2—21no—
286C2#1172721011yescharacteristic
287C2C2×#8927311yescharacteristic
288C2#1172790411yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC22×Q8C22×D7
FittingC4×C7×#101C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC22×C7×Q8C23
hypercenterC4×#101D7
hypocenterC7#13227
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
189. C4×C7#356semidirect
267. C7#13227semidirect
283. C4#89273semidirect

Maximal subgroups

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

subgroupindex
#117399202
C4×C7×#1012
#117293912
C2×#892732
#132277