Finite Group Databasebeta

← #13257442

Subgroups — #13257442

Order 1792.

376 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#89623C211yesmaximal, characteristic
2#11728533C211yesmaximal, characteristic
3#11728521C211yesmaximal, characteristic
4#11728282C211yesmaximal, characteristic
5#11728262C211yesmaximal, characteristic
6#11728176C211yesmaximal, characteristic
7C7×#1301C211yesmaximal, characteristic
8C2×#6432C2211yescharacteristic
9C2×C4×Dic14C2211yescharacteristic
10C7×#431C2211yescharacteristic
11C7×#423C2211yescharacteristic
12C2×C7×C4⋊C8C2211yescharacteristic
13C2×#6398—21no—
14C2×#6391—21no—
15C2×#6390—21no—
16#89697C2211yescharacteristic
17#89696C2211yescharacteristic
18#89623—22no—
19#89623—22no—
20#89349—21no—
21#89281—22no—
22#89276—22no—
23#89274—22no—
24#89251—22no—
25#10451—71nomaximal, Sylow
26C22×Dic14—21no—
27C22×Dic14D411yescharacteristic
28C2×C7×M16—21no—
29C22×C7×C8—21no—
30C2×C42×C7C2311yescharacteristic
31C2×C4⋊Dic7—21no—
32C2×C4⋊Dic7—21no—
33C2×C4⋊Dic7D411yescharacteristic
34C2×Dic7⋊C4—21no—
35C2×C4×Dic7—21no—
36C2×#1136—21no—
37#6432—21no—
38#6432—21no—
39#6432—21no—
40#6432D412yes—
41C4×Dic14—21no—
42C4×Dic14—21no—
43C4×Dic14—21no—
44C4×Dic14—21no—
45C7×C4⋊C8—21no—
46C7×C4⋊C8—21no—
47C7×C4⋊C8—21no—
48C7×C4⋊C8—21no—
49C7×C4⋊C8D412yes—
50C7×C22⋊C8—21no—
51C4×C7×C8—21no—
52C22⋊(C7⋊C8)—21no—
53#6398—42no—
54#6391—24no—
55#6390—24no—
56C4⋊(C7⋊C8)—21no—
57C4⋊(C7⋊C8)—21no—
58C4⋊(C7⋊C8)D412yes—
59C4×C7⋊C8—21no—
60C2×#475—71no—
61#1801—71no—
62#1571—71no—
63#1549—71no—
64#1548—71no—
65#1479—71no—
66#1301D711yescharacteristic
67C22×C4×C7C2×D411yescharacteristic
68C22×C4×C7#4111yescharacteristic
69C22×C4×C7#4111yescharacteristic
70C22×Dic7—21no—
71C22×Dic7—21no—
72C22×Dic7—41no—
73C2×Dic14—21no—
74C2×Dic14—21no—
75C2×Dic14—21no—
76C2×Dic14—21no—
77C2×Dic14—21no—
78C2×Dic14—22no—
79C2×Dic14—41no—
80C2×Dic14—82no—
81C2×Dic14Q1612yes—
82C7×M16—41no—
83C7×M16—41no—
84C2×C7×C8—22no—
85C2×C7×C8—41no—
86C2×C7×C8—41no—
87C2×C7×C8—41no—
88C2×C7×C8—41no—
89C42×C7C2×D411yescharacteristic
90C42×C7C2×D411yescharacteristic
91C42×C7C2×D411yescharacteristic
92C42×C7#4111yescharacteristic
93C4⋊Dic7—21no—
94C4⋊Dic7—22no—
95C4⋊Dic7—21no—
96C4⋊Dic7—22no—
97C4⋊Dic7—41no—
98C4⋊Dic7—41no—
99Dic7⋊C4—41no—
100Dic7⋊C4—41no—
101C4×Dic7—41no—
102C4×Dic7—41no—
103#1136—41no—
104#1136—41no—
105C2×C7⋊C8—22no—
106C2×C7⋊C8—41no—
107C2×C4⋊Q8—71no—
108C2×C4×Q8—71no—
109#475—142no—
110#475—142no—
111#431—71no—
112#431C2×D711yescharacteristic
113C2×#106—141no—
114#423—71no—
115#423C2×D711yescharacteristic
116C2×C4⋊C8C2×D711yescharacteristic
117C2×#103—141no—
118C2×#101—141no—
119#343—141no—
120#335—142no—
121#333—142no—
122#332—142no—
123Q8⋊C8—142no—
124C23×C7#12311yescharacteristic
125C2×C4×C7—22no—
126C2×C4×C7—41no—
127C2×C4×C7#12011yescharacteristic
128C2×C4×C7#12111yescharacteristic
129C2×C4×C7#12111yescharacteristic
130C2×C4×C7#12111yescharacteristic
131C2×C4×C7#12311yescharacteristic
132C2×C4×C7#12411yescharacteristic
133C2×C4×C7C2×Q1611yescharacteristic
134C2×C4×C7#13511yescharacteristic
135C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C7#13711yescharacteristic
137C2×Dic7—22no—
138C2×Dic7—41no—
139C2×Dic7—41no—
140C2×Dic7—41no—
141C2×Dic7—42no—
142C2×Dic7—82no—
143C2×Dic7—81no—
144Dic14—22no—
145Dic14—22no—
146Dic14—41no—
147Dic14—41no—
148Dic14—82no—
149Dic14—82no—
150C7×C8—42no—
151C7×C8—81no—
152C7×C8—81no—
153C7⋊C8—42no—
154C7⋊C8—81no—
155C22×Q8—71no—
156C22×Q8—141no—
157C2×M16—21no—
158C2×M16—141no—
159C22×C8—21no—
160C4⋊Q8—72no—
161C4⋊Q8—141no—
162C4⋊Q8—141no—
163C4⋊Q8—141no—
164C4×Q8—141no—
165C4×Q8—141no—
166C4×Q8—141no—
167C4×Q8—141no—
168C2×C4⋊C4—71no—
169C2×C4⋊C4—141no—
170C2×C4⋊C4—141no—
171C2×C4⋊C4—141no—
172C2×C42—141no—
173C2×C42C22×D711yescharacteristic
174#106—144no—
175C4⋊C8—21no—
176C4⋊C8—21no—
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8—72no—
180C4⋊C8—141no—
181C4⋊C8—141no—
182C4⋊C8D2812yes—
183#103—144no—
184#101—282no—
185C22⋊C8—21no—
186C22⋊C8—141no—
187C4×C8—21no—
188C4×C8—141no—
189C22×C7—21no—
190C22×C7—21no—
191C22×C7#39411yescharacteristic
192C22×C7#48411yescharacteristic
193C22×C7#48511yescharacteristic
194C4×C7—21no—
195C4×C7—21no—
196C4×C7—21no—
197C4×C7#44911yescharacteristic
198C4×C7#45111yescharacteristic
199C4×C7#46711yescharacteristic
200C4×C7#46811yescharacteristic
201C4×C7#47112yes—
202Dic7—42no—
203Dic7—81no—
204Dic7—82no—
205C2×Q8—72no—
206C2×Q8—141no—
207C2×Q8—141no—
208C2×Q8—141no—
209C2×Q8—142no—
210C2×Q8—141no—
211C2×Q8—141no—
212C2×Q8—281no—
213C2×Q8—562no—
214C22×C4—141no—
215C22×C4—141no—
216C22×C4—281no—
217C22×C4#115711yescharacteristic
218C22×C4D4×D711yescharacteristic
219C22×C4#116111yescharacteristic
220M16—41no—
221M16—41no—
222M16—281no—
223M16—281no—
224C2×C8—22no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—142no—
230C2×C8—281no—
231C4⋊C4—142no—
232C4⋊C4—141no—
233C4⋊C4—141no—
234C4⋊C4—142no—
235C4⋊C4—281no—
236C4⋊C4—281no—
237C4⋊C4—281no—
238C4⋊C4—281no—
239C42—281no—
240C42—281no—
241C42C2×D2811yescharacteristic
242C42#115711yescharacteristic
243C42D4×D711yescharacteristic
244C42D4×D711yescharacteristic
245C2×C7—21no—
246C2×C7—21no—
247C2×C7#203611yescharacteristic
248C2×C7#204611yescharacteristic
249C2×C7#204911yescharacteristic
250C23#645711yescharacteristic
251Q8—142no—
252Q8—142no—
253Q8—281no—
254Q8—281no—
255Q8—562no—
256Q8—562no—
257C2×C4—22no—
258C2×C4—41no—
259C2×C4—142no—
260C2×C4—281no—
261C2×C4—281no—
262C2×C4—281no—
263C2×C4—282no—
264C2×C4—562no—
265C2×C4—561no—
266C2×C4#643811yescharacteristic
267C2×C4#644511yescharacteristic
268C2×C4#644711yescharacteristic
269C2×C4#644711yescharacteristic
270C2×C4#645711yescharacteristic
271C2×C4#645811yescharacteristic
272C2×C4#647411yescharacteristic
273C2×C4#647811yescharacteristic
274C2×C4#647911yescharacteristic
275C2×C4D7×Q1611yescharacteristic
276C8—42no—
277C8—81no—
278C8—81no—
279C8—282no—
280C8—561no—
281C7#1045111yescharacteristic, complemented, Sylow
282C22—21no—
283C22—21no—
284C22#8944411yescharacteristic
285C22#8963911yescharacteristic
286C22#8965611yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—282no—
291C4—562no—
292C4—561no—
293C4#8955211yescharacteristic
294C4#8955311yescharacteristic
295C4#8958011yescharacteristic
296C4#8958511yescharacteristic
297C4#8967012yes—
298C2—21no—
299C2—21no—
300C2#1172657911yescharacteristic
301C2#1172668711yescharacteristic
302C2#1172677311yescharacteristic
subgroupG/H
centerC22#89444
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1301C2
socleC22×C7#394
prime radicalC23×C7#123
hypercenter#1301D7
hypocenterC7#10451
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
281. C7#10451semidirect

Maximal subgroups

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

subgroupindex
C2×#896232
#117285332
#117285212
#117282822
#117282622
#117281762
C7×#13012
#104517