Finite Group Databasebeta

← #13252865

Subgroups — #13252865

Order 1792.

478 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740697C211yesmaximal, characteristic
2C2×C7×#332C211yesmaximal, characteristic
3C2×#89342C211yesmaximal, characteristic
4#11728197C211yesmaximal, characteristic
5Dic7×C4⋊C8C211yesmaximal, characteristic
6C2×#89277C211yesmaximal, characteristic
7C2×#89281C211yesmaximal, characteristic
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×#6432C2211yescharacteristic
10C2×C7×C4⋊C8C2211yescharacteristic
11C2×C7×C4⋊C8C2211yescharacteristic
12#90002—22no—
13C2×C8×Dic7—21no—
14#89749C414yes—
15#89746—21no—
16#89746—21no—
17C42×Dic7C2211yescharacteristic
18C2×C4⋊(C7⋊C8)C2211yescharacteristic
19C2×C4⋊(C7⋊C8)C2211yescharacteristic
20C7×#332—22no—
21#89345—21no—
22#89345—22no—
23#89342—22no—
24#89281—22no—
25#89277—22no—
26#9700—71nomaximal, Sylow
27C22×C7×Q8—21no—
28C22×Dic14—21no—
29C22×C7×C8—21no—
30C22×C7×C8—21no—
31C7×C4⋊Q8—21no—
32C7×C4⋊Q8—21no—
33C7×C4⋊Q8—21no—
34C7×C4⋊Q8—21no—
35C2×C7×C4⋊C4—21no—
36C2×C7×C4⋊C4C2×C412yes—
37C2×C42×C7C2311yescharacteristic
38C2×C4⋊Dic7—21no—
39C2×C4⋊Dic7C2×C412yes—
40C2×C4×Dic7C2×C412yes—
41C2×C4×Dic7D411yescharacteristic
42C2×C4×Dic7D412yes—
43C2×C4×Dic7D411yescharacteristic
44C22×C7⋊C8—21no—
45C22×C7⋊C8—21no—
46#6432—21no—
47#6432—21no—
48#6432—21no—
49#6432—21no—
50C7×C4⋊C8—21no—
51C7×C4⋊C8—21no—
52C7×C4⋊C8—21no—
53C7×C4⋊C8D412yes—
54C7⋊#95—24no—
55C7⋊#95—24no—
56C8×Dic7—42no—
57C4⋊(C7⋊C8)—21no—
58C4⋊(C7⋊C8)—21no—
59C4⋊(C7⋊C8)—21no—
60C4⋊(C7⋊C8)D412yes—
61#2862—71no—
62#1831—71no—
63C4×C4⋊C8—71no—
64C2×#332—71no—
65C2×#332—71no—
66C2×#332—71no—
67C2×#332D711yescharacteristic
68C2×C7×Q8—41no—
69C2×C7×Q8—41no—
70C2×C7×Q8—42no—
71C2×C7×Q8—42no—
72C22×C4×C7—22no—
73C22×C4×C7C22×C411yescharacteristic
74C22×C4×C7C2×D411yescharacteristic
75C22×C4×C7C2×D411yescharacteristic
76C22×Dic7—22no—
77C22×Dic7C22⋊C412yes—
78C22×Dic7C22⋊C412yes—
79C2×Dic14—41no—
80C2×Dic14—41no—
81C2×Dic14—41no—
82C2×Dic14—41no—
83C2×Dic14—41no—
84C2×Dic14—41no—
85C2×C7×C8—22no—
86C2×C7×C8—41no—
87C2×C7×C8—41no—
88C2×C7×C8—41no—
89C2×C7×C8—42no—
90C7×C4⋊C4—22no—
91C7×C4⋊C4—22no—
92C7×C4⋊C4—41no—
93C7×C4⋊C4—41no—
94C42×C7C2×D411yescharacteristic
95C42×C7C2×D411yescharacteristic
96C42×C7#4111yescharacteristic
97C42×C7#4111yescharacteristic
98C4⋊Dic7—22no—
99C4⋊Dic7—22no—
100C4⋊Dic7—41no—
101C4⋊Dic7—41no—
102C4×Dic7—22no—
103C4×Dic7—22no—
104C4×Dic7—21no—
105C4×Dic7—21no—
106C4×Dic7—21no—
107C4×Dic7—21no—
108C4×Dic7—24no—
109C2×C7⋊C8—22no—
110C2×C7⋊C8—41no—
111C2×C7⋊C8—41no—
112C2×C7⋊C8—41no—
113C2×C7⋊C8—42no—
114C2×C4⋊Q8—71no—
115C2×C4⋊Q8C2×D711yescharacteristic
116C2×C4⋊C8—71no—
117C2×C4⋊C8—71no—
118C2×C4⋊C8C2×D711yescharacteristic
119C2×C4⋊C8C2×D711yescharacteristic
120C2×C4×C8—141no—
121#391—141no—
122#391—141no—
123#391—142no—
124#382—74no—
125C43—71no—
126#336—142no—
127#336—141no—
128#332—22no—
129#332—142no—
130#332—142no—
131#332—142no—
132C23×C7C2×C22⋊C411yescharacteristic
133C7×Q8—82no—
134C7×Q8—81no—
135C7×Q8—81no—
136C2×C4×C7—22no—
137C2×C4×C7—42no—
138C2×C4×C7—44no—
139C2×C4×C7C4×D411yescharacteristic
140C2×C4×C7C4×D411yescharacteristic
141C2×C4×C7#12111yescharacteristic
142C2×C4×C7#12111yescharacteristic
143C2×C4×C7#12411yescharacteristic
144C2×C4×C7#12711yescharacteristic
145C2×C4×C7#13512yes—
146C2×C4×C7#13511yescharacteristic
147C2×C4×C7#13512yes—
148C2×C4×C7#13511yescharacteristic
149C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C7#13711yescharacteristic
151C2×Dic7—22no—
152C2×Dic7—22no—
153C2×Dic7—22no—
154C2×Dic7—22no—
155C2×Dic7—22no—
156C2×Dic7—42no—
157C2×Dic7—42no—
158C2×Dic7—42no—
159C2×Dic7#10114yes—
160Dic14—81no—
161Dic14—81no—
162Dic14—81no—
163Dic14—81no—
164C7×C8—42no—
165C7×C8—81no—
166C7⋊C8—42no—
167C7⋊C8—81no—
168C22×Q8—21no—
169C22×Q8—141no—
170C22×C8—21no—
171C22×C8—21no—
172C22×C8—141no—
173C22×C8—141no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—141no—
179C4⋊Q8—141no—
180C4⋊Q8—141no—
181C4⋊Q8—141no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—72no—
184C2×C4⋊C4—141no—
185C2×C4⋊C4C4×D712yes—
186C2×C42—72no—
187C2×C42—72no—
188C2×C42—71no—
189C2×C42—71no—
190C2×C42C22×D711yescharacteristic
191C4⋊C8—21no—
192C4⋊C8—21no—
193C4⋊C8—21no—
194C4⋊C8—72no—
195C4⋊C8—141no—
196C4⋊C8—141no—
197C4⋊C8—141no—
198C4⋊C8C22⋊D712yes—
199C4×C8—282no—
200#95—144no—
201#95—144no—
202C22×C7#39011yescharacteristic
203C22×C7C2×#10112yes—
204C22×C7#41612yes—
205C22×C7#41611yescharacteristic
206C22×C7#41711yescharacteristic
207C4×C7—21no—
208C4×C7—21no—
209C4×C7—82no—
210C4×C7#46311yescharacteristic
211C4×C7#46311yescharacteristic
212C4×C7#46411yescharacteristic
213C4×C7#46411yescharacteristic
214C4×C7#48812yes—
215C4×C7#49511yescharacteristic
216C4×C7#49511yescharacteristic
217Dic7—24no—
218Dic7—42no—
219Dic7—82no—
220C2×Q8—41no—
221C2×Q8—42no—
222C2×Q8—42no—
223C2×Q8—41no—
224C2×Q8—281no—
225C2×Q8—281no—
226C2×Q8—281no—
227C2×Q8—281no—
228C2×Q8—281no—
229C2×Q8—281no—
230C22×C4—22no—
231C22×C4—72no—
232C22×C4—72no—
233C22×C4—142no—
234C22×C4C2×C4×D711yescharacteristic
235C22×C4D4×D711yescharacteristic
236C22×C4D4×D711yescharacteristic
237C2×C8—22no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—42no—
241C2×C8—41no—
242C2×C8—142no—
243C2×C8—281no—
244C2×C8—281no—
245C2×C8—282no—
246C2×C8—281no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—142no—
252C4⋊C4—142no—
253C4⋊C4—281no—
254C4⋊C4—281no—
255C42—144no—
256C42—142no—
257C42—141no—
258C42—142no—
259C42—141no—
260C42—141no—
261C42—141no—
262C42#115711yescharacteristic
263C42D4×D711yescharacteristic
264C42#115911yescharacteristic
265C42C2×C22⋊D711yescharacteristic
266C2×C7#154412yes—
267C2×C7#155212yes—
268C2×C7#195811yescharacteristic
269C2×C7#196611yescharacteristic
270C2×C7#198311yescharacteristic
271C23D7×C22⋊C411yescharacteristic
272Q8—81no—
273Q8—81no—
274Q8—82no—
275Q8—561no—
276Q8—561no—
277Q8—561no—
278Q8—561no—
279C2×C4—22no—
280C2×C4—42no—
281C2×C4—44no—
282C2×C4—74no—
283C2×C4—142no—
284C2×C4—142no—
285C2×C4—142no—
286C2×C4—142no—
287C2×C4—142no—
288C2×C4—282no—
289C2×C4—282no—
290C2×C4—282no—
291C2×C4(C22⋊D7)⋊C411yescharacteristic
292C2×C4#644711yescharacteristic
293C2×C4#644811yescharacteristic
294C2×C4#647512yes—
295C2×C4#647711yescharacteristic
296C2×C4#647911yescharacteristic
297C2×C4#647912yes—
298C2×C4#648111yescharacteristic
299C2×C4#648211yescharacteristic
300C2×C4C4×C22⋊D711yescharacteristic
301C2×C4#650211yescharacteristic
302C2×C4#650311yescharacteristic
303C8—42no—
304C8—81no—
305C8—282no—
306C8—561no—
307C7#970011yescharacteristic, complemented, Sylow
308C22D7×#10112yes—
309C22#8954412yes—
310C22#8957511yescharacteristic
311C22#8957611yescharacteristic
312C22#8972911yescharacteristic
313C4—21no—
314C4—21no—
315C4—82no—
316C4—144no—
317C4—282no—
318C4—562no—
319C4#8954012yes—
320C4#8957011yescharacteristic
321C4#8959111yescharacteristic
322C4#8992711yescharacteristic
323C4#8993711yescharacteristic
324C4#8994011yescharacteristic
325C4#8995711yescharacteristic
326C2#1172617312yes—
327C2#1172617812yes—
328C2#1172785211yescharacteristic
329C2#1172791211yescharacteristic
330C2#1172798411yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC2×C7×#332C2
socle, prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenterC2×#332D7
hypocenterC7#9700
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
307. C7#9700semidirect

Maximal subgroups

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

subgroupindex
#117406972
C2×C7×#3322
C2×#893422
#117281972
Dic7×C4⋊C82
C2×#892772
C2×#892812
#97007