Finite Group Databasebeta

← #13272080

Subgroups — #13272080

Order 1792.

536 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C7×#2486C211yesmaximal, characteristic
2C2×#89334C214yesmaximal
3#11729373C211yesmaximal, characteristic
4C4×#6407C211yesmaximal, characteristic
5C2×C7×#123C2212yes—
6C2×C4×C7×D4C2211yescharacteristic
7C22×C7×C4⋊C4C411yescharacteristic, complemented
8C7×#398—21no—
9C7×#397—21no—
10C7×#389—21no—
11C7×#381C412yescomplemented
12C7×#380—21no—
13C7×#380C411yescharacteristic, complemented
14C2×#6408C2212yes—
15C2×#6407C2212yes—
16#89984—21no—
17C4×#1136—21no—
18#89334—28no—
19#89325—21no—
20#89321—21no—
21#13217—71nomaximal, Sylow
22C22×C7×D4C2311yescharacteristic
23C23×C4×C7C2×C412yes—
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C7×#123—24no—
27C7×#123—24no—
28C4×C7×D4—41no—
29C4×C7×D4—41no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—22no—
34C2×C7×C4⋊C4—41no—
35C2×C7×C4⋊C4—41no—
36C2×C7×C4⋊C4D411yescharacteristic
37C2×C7×C22⋊C4—22no—
38C2×C7×C22⋊C4C2×C412yes—
39C2×C7×C22⋊C4C2×C411yescharacteristic
40C2×C7×C22⋊C4D411yescharacteristic
41C2×C42×C7D411yescharacteristic
42C2×C22⋊Dic7—22no—
43C2×C4⋊Dic7—41no—
44C2×#1136—22no—
45C7×#95—22no—
46C7×#95—21no—
47C7×#95—22no—
48#6408—24no—
49#6407—22no—
50#6407D414yes—
51C7⋊#95—41no—
52#6377—41no—
53C4×C7⋊C8—41no—
54#2486D711yescharacteristic
55C2×#352—74no—
56#1799—71no—
57C4×#100—71no—
58C24×C7C22×C411yescharacteristic
59C24×C7C2×D411yescharacteristic
60C2×C7×D4—41no—
61C2×C7×D4—41no—
62C2×C7×D4C2×D412yes—
63C2×C7×D4#4112yes—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—21no—
68C22×C4×C7—22no—
69C22×C4×C7—22no—
70C22×C4×C7—24no—
71C22×C4×C7—42no—
72C22×C4×C7—42no—
73C22×C4×C7—42no—
74C22×C4×C7—42no—
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22⋊C411yescharacteristic
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C2×D411yescharacteristic
80C22×Dic7—42no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—42no—
83C7×C4⋊C4—42no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—44no—
87C7×C22⋊C4—24no—
88C7×C22⋊C4—41no—
89C7×C22⋊C4—41no—
90C7×C22⋊C4—42no—
91C7×C22⋊C4—42no—
92C42×C7—21no—
93C42×C7—21no—
94C22⋊Dic7—42no—
95C22⋊Dic7—42no—
96C4⋊Dic7—82no—
97#1136—24no—
98#1136—42no—
99C2×C7⋊C8—42no—
100C2×#123C2×D712yes—
101C2×C4×D4C2×D711yescharacteristic
102C22×C4⋊C4Dic711yescharacteristic, complemented
103C2×#100—72no—
104C2×#99—72no—
105C4×M16—141no—
106#398—21no—
107#397—21no—
108#389—21no—
109#381Dic712yescomplemented
110#380—21no—
111#380—141no—
112#380Dic711yescharacteristic, complemented
113#352—148no—
114#343—141no—
115#342—141no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7—41no—
121C23×C7—41no—
122C23×C7—41no—
123C23×C7—41no—
124C23×C7C2×C22⋊C411yescharacteristic
125C23×C7C4×D412yes—
126C23×C7#12411yescharacteristic
127C23×C7#12711yescharacteristic
128C7×D4—42no—
129C7×D4—42no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—22no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—42no—
137C2×C4×C7—42no—
138C2×C4×C7—42no—
139C2×C4×C7—41no—
140C2×C4×C7—41no—
141C2×C4×C7—41no—
142C2×C4×C7—42no—
143C2×C4×C7—42no—
144C2×C4×C7—42no—
145C2×C4×C7—42no—
146C2×C4×C7—42no—
147C2×C4×C7—42no—
148C2×C4×C7—81no—
149C2×C4×C7—84no—
150C2×C4×C7#9911yescharacteristic
151C2×C4×C7#9911yescharacteristic
152C2×C4×C7#12112yes—
153C2×Dic7—82no—
154C2×Dic7—82no—
155C2×Dic7—82no—
156C7⋊C8—44no—
157C22×D4C22×D711yescharacteristic
158C23×C4C2×Dic712yes—
159C23×C4C2×Dic711yescharacteristic
160C23×C4C22⋊D711yescharacteristic
161C2×M16—142no—
162#123—24no—
163#123—24no—
164C4×D4—41no—
165C4×D4—41no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—281no—
173C2×C4⋊C4C22⋊D711yescharacteristic
174C2×C22⋊C4—22no—
175C2×C22⋊C4—142no—
176C2×C22⋊C4C2×Dic712yes—
177C2×C22⋊C4C2×Dic711yescharacteristic
178C2×C22⋊C4C22⋊D711yescharacteristic
179C2×C42C22⋊D711yescharacteristic
180#100—74no—
181#100—142no—
182#99—144no—
183#97—281no—
184C4×C8—281no—
185#95—22no—
186#95—21no—
187#95—22no—
188#95—281no—
189C22×C7—21no—
190C22×C7—21no—
191C22×C7—21no—
192C22×C7—22no—
193C22×C7—21no—
194C22×C7—42no—
195C22×C7—41no—
196C22×C7—41no—
197C22×C7—42no—
198C22×C7—41no—
199C22×C7—41no—
200C22×C7—41no—
201C22×C7—41no—
202C22×C7—81no—
203C22×C7#39011yescharacteristic
204C22×C7C2×#9911yescharacteristic
205C22×C7#41011yescharacteristic
206C4×C7—21no—
207C4×C7—22no—
208C4×C7—41no—
209C4×C7—41no—
210C4×C7—41no—
211C4×C7—82no—
212C4×C7—82no—
213C4×C7#35212yescomplemented
214Dic7—162no—
215C24C22×Dic711yescharacteristic
216C24C2×C22⋊D711yescharacteristic
217C2×D4—41no—
218C2×D4—41no—
219C2×D4D4×D712yes—
220C2×D4#115912yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—24no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—282no—
233C22×C4C22⋊Dic711yescharacteristic
234C22×C4C22⋊Dic711yescharacteristic
235C22×C4C22⋊Dic711yescharacteristic
236C22×C4C22⋊Dic711yescharacteristic
237C22×C4C2×C22⋊D711yescharacteristic
238M16—144no—
239M16—282no—
240C2×C8—282no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—44no—
247C4⋊C4—562no—
248C22⋊C4—24no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—282no—
254C22⋊C4—282no—
255C42—21no—
256C42—21no—
257C2×C7—21no—
258C2×C7—21no—
259C2×C7—41no—
260C2×C7—42no—
261C2×C7—41no—
262C2×C7#196411yescharacteristic
263C2×C7C2×#35211yescharacteristic
264C2×C7#212311yescharacteristic
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23D4×Dic712yes—
274C23#649911yescharacteristic
275C23#650311yescharacteristic
276C23C2×C22⋊Dic711yescharacteristic
277D4—42no—
278D4—42no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—84no—
299C2×C4—562no—
300C2×C4—562no—
301C2×C4—562no—
302C2×C4#640811yescharacteristic
303C2×C4#640811yescharacteristic
304C2×C4#650112yes—
305C8—284no—
306C7#1321711yescharacteristic, complemented, Sylow
307C22—21no—
308C22—21no—
309C22—22no—
310C22—21no—
311C22—21no—
312C22—42no—
313C22—41no—
314C22—41no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22C2×#640811yescharacteristic
322C22#8999311yescharacteristic
323C22#9001211yescharacteristic
324C4—22no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—82no—
330C4—82no—
331C4—1122no—
332C4#8933412yescomplemented
333C2—21no—
334C2—21no—
335C2—41no—
336C2—42no—
337C2—41no—
338C2#1172944011yescharacteristic
339C2C2×#8933411yescharacteristic
340C2#1172962411yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC24×C7C22×C4
FrattiniC22×D4C22×D7
FittingC7×#2486C2
socleC22×C7C2×#99
prime radical, cosocleC22×C7×D4C23
hypercenter#2486D7
hypocenterC7#13217
LCSG ▷ C24×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2486

Complements

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

NH ≅ G/Ntype
7. C22×C7×C4⋊C4C4semidirect
11. C7×#381C4semidirect
13. C7×#380C4semidirect
102. C22×C4⋊C4Dic7semidirect
109. #381Dic7semidirect
112. #380Dic7semidirect
213. C4×C7#352semidirect
306. C7#13217semidirect
332. C4#89334semidirect

Maximal subgroups

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

subgroupindex
C7×#24862
C2×#893342
#117293732
C4×#64072
#132177