Finite Group Databasebeta

← #13257413

Subgroups — #13257413

Order 1792.

408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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×#89621C211yesmaximal, characteristic
2C7×#1570C211yesmaximal, characteristic
3#11728532C211yesmaximal, characteristic
4#11728520C211yesmaximal, characteristic
5#11728282C211yesmaximal, characteristic
6#11728260C211yesmaximal, characteristic
7#11725513C211yesmaximal, characteristic
8C22×Dic28—21no—
9C2×#6432C2211yescharacteristic
10C2×C4×Dic14C2211yescharacteristic
11C7×#431C2211yescharacteristic
12C7×#423C2211yescharacteristic
13C2×C7×C4⋊C8C2211yescharacteristic
14C2×#6398—21no—
15C2×#6390—21no—
16#89697C2211yescharacteristic
17#89696C2211yescharacteristic
18#89621—22no—
19#89621—22no—
20C7×#334—22no—
21#89349—21no—
22#89281—22no—
23#89279—22no—
24#89277—22no—
25#10447—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—
37C2×Dic28—24no—
38C2×Dic28—42no—
39C2×Dic28—42no—
40#6432—21no—
41#6432—21no—
42#6432—21no—
43#6432D412yes—
44C4×Dic14—21no—
45C4×Dic14—21no—
46C4×Dic14—21no—
47C4×Dic14—21no—
48C7×C4⋊C8—21no—
49C7×C4⋊C8—21no—
50C7×C4⋊C8—21no—
51C7×C4⋊C8D412yes—
52C7×C4⋊C8D412yes—
53C7×C22⋊C8—21no—
54C4×C7×C8—21no—
55C22⋊(C7⋊C8)—21no—
56#6398—42no—
57#6390—24no—
58C4⋊(C7⋊C8)—21no—
59C4⋊(C7⋊C8)—21no—
60C4⋊(C7⋊C8)—21no—
61C4×C7⋊C8—21no—
62C2×#462—71no—
63#1801—71no—
64#1570D711yescharacteristic
65#1546—71no—
66#1546—71no—
67#1479—71no—
68#1301—71no—
69C22×C4×C7C2×D411yescharacteristic
70C22×C4×C7#4111yescharacteristic
71C22×C4×C7#4111yescharacteristic
72C22×Dic7—21no—
73C22×Dic7—21no—
74C22×Dic7—41no—
75C2×Dic14—21no—
76C2×Dic14—21no—
77C2×Dic14—21no—
78C2×Dic14—21no—
79C2×Dic14—21no—
80C2×Dic14—22no—
81C2×Dic14—41no—
82C2×Dic14—41no—
83C2×Dic14—41no—
84C2×Dic14—41no—
85C2×Dic14—41no—
86C2×Dic14SD1612yes—
87C7×M16—41no—
88C7×M16—41no—
89C2×C7×C8—22no—
90C2×C7×C8—22no—
91C2×C7×C8—41no—
92C2×C7×C8—41no—
93C2×C7×C8—41no—
94C42×C7C2×D411yescharacteristic
95C42×C7C2×D411yescharacteristic
96C42×C7C2×D411yescharacteristic
97C42×C7#4111yescharacteristic
98C4⋊Dic7—21no—
99C4⋊Dic7—21no—
100C4⋊Dic7—22no—
101C4⋊Dic7—22no—
102C4⋊Dic7—41no—
103C4⋊Dic7—41no—
104Dic7⋊C4—41no—
105Dic7⋊C4—41no—
106C4×Dic7—41no—
107C4×Dic7—41no—
108#1136—41no—
109#1136—41no—
110C2×C7⋊C8—41no—
111C2×C7⋊C8—41no—
112Dic28—48no—
113C22×Q16—141no—
114C2×C4⋊Q8—71no—
115C2×C4×Q8—71no—
116#462—142no—
117#462—142no—
118#431—71no—
119#431C2×D711yescharacteristic
120#423—71no—
121#423C2×D711yescharacteristic
122C2×C4⋊C8C2×D711yescharacteristic
123C2×#103—141no—
124C2×#101—141no—
125#343—141no—
126#334—22no—
127#332—142no—
128#332—142no—
129Q8⋊C8—142no—
130C23×C7#12311yescharacteristic
131C2×C4×C7—22no—
132C2×C4×C7—41no—
133C2×C4×C7#12011yescharacteristic
134C2×C4×C7#12111yescharacteristic
135C2×C4×C7#12111yescharacteristic
136C2×C4×C7#12111yescharacteristic
137C2×C4×C7#12311yescharacteristic
138C2×C4×C7#12411yescharacteristic
139C2×C4×C7C2×SD1611yescharacteristic
140C2×C4×C7#13511yescharacteristic
141C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
143C2×Dic7—22no—
144C2×Dic7—41no—
145C2×Dic7—41no—
146C2×Dic7—41no—
147C2×Dic7—42no—
148C2×Dic7—81no—
149C2×Dic7—81no—
150C2×Dic7—81no—
151Dic14—22no—
152Dic14—22no—
153Dic14—41no—
154Dic14—41no—
155Dic14—42no—
156Dic14—42no—
157Dic14—81no—
158Dic14—81no—
159C7×C8—42no—
160C7×C8—42no—
161C7×C8—81no—
162C7⋊C8—81no—
163C7⋊C8—81no—
164C22×Q8—71no—
165C22×Q8—141no—
166C2×Q16—144no—
167C2×Q16—282no—
168C2×Q16—282no—
169C2×M16—21no—
170C2×M16—141no—
171C22×C8—21no—
172C4⋊Q8—72no—
173C4⋊Q8—141no—
174C4⋊Q8—141no—
175C4⋊Q8—141no—
176C4×Q8—141no—
177C4×Q8—141no—
178C4×Q8—141no—
179C4×Q8—141no—
180C2×C4⋊C4—71no—
181C2×C4⋊C4—141no—
182C2×C4⋊C4—141no—
183C2×C4⋊C4—141no—
184C2×C42—141no—
185C2×C42C22×D711yescharacteristic
186C4⋊C8—21no—
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—141no—
190C4⋊C8—141no—
191C4⋊C8—141no—
192C4⋊C8D2812yes—
193C4⋊C8C22⋊D712yes—
194#103—144no—
195#101—282no—
196C22⋊C8—21no—
197C22⋊C8—141no—
198C4×C8—21no—
199C4×C8—141no—
200C22×C7—21no—
201C22×C7—21no—
202C22×C7#39411yescharacteristic
203C22×C7#48111yescharacteristic
204C22×C7#48211yescharacteristic
205C4×C7—21no—
206C4×C7—21no—
207C4×C7—21no—
208C4×C7#44911yescharacteristic
209C4×C7#45011yescharacteristic
210C4×C7#46511yescharacteristic
211C4×C7#46911yescharacteristic
212C4×C7#47312yes—
213Dic7—42no—
214Dic7—81no—
215Dic7—82no—
216C2×Q8—72no—
217C2×Q8—141no—
218C2×Q8—141no—
219C2×Q8—141no—
220C2×Q8—141no—
221C2×Q8—141no—
222C2×Q8—142no—
223C2×Q8—281no—
224C2×Q8—281no—
225C2×Q8—281no—
226C2×Q8—281no—
227C2×Q8—281no—
228C22×C4—141no—
229C22×C4—141no—
230C22×C4—281no—
231C22×C4#115711yescharacteristic
232C22×C4D4×D711yescharacteristic
233C22×C4#116111yescharacteristic
234Q16—288no—
235M16—41no—
236M16—41no—
237M16—281no—
238M16—281no—
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—281no—
245C2×C8—281no—
246C4⋊C4—142no—
247C4⋊C4—141no—
248C4⋊C4—142no—
249C4⋊C4—141no—
250C4⋊C4—281no—
251C4⋊C4—281no—
252C4⋊C4—281no—
253C4⋊C4—281no—
254C42—281no—
255C42—281no—
256C42C2×D2811yescharacteristic
257C42D4×D711yescharacteristic
258C42#116111yescharacteristic
259C42C2×C22⋊D711yescharacteristic
260C2×C7—21no—
261C2×C7—21no—
262C2×C7#203411yescharacteristic
263C2×C7#204711yescharacteristic
264C2×C7#204911yescharacteristic
265C23#645711yescharacteristic
266Q8—142no—
267Q8—142no—
268Q8—281no—
269Q8—281no—
270Q8—282no—
271Q8—282no—
272Q8—561no—
273Q8—561no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—142no—
277C2×C4—281no—
278C2×C4—281no—
279C2×C4—281no—
280C2×C4—282no—
281C2×C4—561no—
282C2×C4—561no—
283C2×C4—561no—
284C2×C4#645711yescharacteristic
285C2×C4#645811yescharacteristic
286C2×C4#645811yescharacteristic
287C2×C4D7×SD1611yescharacteristic
288C2×C4#647711yescharacteristic
289C2×C4#647711yescharacteristic
290C2×C4#647911yescharacteristic
291C2×C4#649311yescharacteristic
292C2×C4#650011yescharacteristic
293C2×C4#651011yescharacteristic
294C8—42no—
295C8—42no—
296C8—81no—
297C8—561no—
298C8—561no—
299C7#1044711yescharacteristic, complemented, Sylow
300C22—21no—
301C22—21no—
302C22#8963511yescharacteristic
303C22#8963811yescharacteristic
304C22#8976311yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—282no—
309C4—561no—
310C4—562no—
311C4#8963611yescharacteristic
312C4#8963711yescharacteristic
313C4#8991512yes—
314C4#8994111yescharacteristic
315C4#8994411yescharacteristic
316C2—21no—
317C2—21no—
318C2#1172829711yescharacteristic
319C2#1172833511yescharacteristic
320C2#1172849111yescharacteristic
subgroupG/H
centerC22#89763
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1570C2
socleC22×C7#394
prime radicalC23×C7#123
hypercenter#1570D7
hypocenterC7#10447
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
299. C7#10447semidirect

Maximal subgroups

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

subgroupindex
C2×#896212
C7×#15702
#117285322
#117285202
#117282822
#117282602
#117255132
#104477