Finite Group Databasebeta

← #13258348

Subgroups — #13258348

Order 1792.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#1988C211yesmaximal, characteristic
2#11729539C211yesmaximal, characteristic
3C2×#89342C211yesmaximal, characteristic
4C2×#89274C211yesmaximal, characteristic
5#11727238C211yesmaximal, characteristic
6#11727220C211yesmaximal, characteristic
7#11725508C211yesmaximal, characteristic
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×C7×C4⋊C8C2211yescharacteristic
10C4×C7×C4⋊C4C2211yescharacteristic
11C2×#6409—21no—
12C2×#6409—21no—
13C2×#6381—21no—
14#89707C2211yescharacteristic
15C2×C4⋊(C7⋊C8)—21no—
16C2×C4⋊(C7⋊C8)C2211yescharacteristic
17C2×C4⋊(C7⋊C8)C2211yescharacteristic
18C2×C4×C7⋊C8C2211yescharacteristic
19C7×#340—21no—
20C7×#340—21no—
21#89342—22no—
22#89324—21no—
23#89319—21no—
24#89274—22no—
25#10592—71nomaximal, Sylow
26C22×C7×Q8—21no—
27C22×C7×C8—21no—
28C7×C4⋊Q8—21no—
29C7×C4⋊Q8—21no—
30C7×C4⋊Q8—21no—
31C7×C4⋊Q8Q812yes—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4D411yescharacteristic
35C2×C7×C4⋊C4D411yescharacteristic
36C2×C42×C7—21no—
37C2×C42×C7C2311yescharacteristic
38C2×C4⋊Dic7—21no—
39C2×C4⋊Dic7—21no—
40C2×C4⋊Dic7—21no—
41C22×C7⋊C8—21no—
42C22×C7⋊C8—21no—
43C22×C7⋊C8D411yescharacteristic
44C22×C7⋊C8D411yescharacteristic
45C7×C4⋊C8—21no—
46C7×C4⋊C8—21no—
47C7×#95—21no—
48#6409—42no—
49#6409—42no—
50#6381—42no—
51C4⋊(C7⋊C8)—21no—
52C4⋊(C7⋊C8)—21no—
53C4⋊(C7⋊C8)—21no—
54C4⋊(C7⋊C8)—42no—
55C4⋊(C7⋊C8)D412yes—
56C4×C7⋊C8—21no—
57C4×C7⋊C8—21no—
58#1988D711yescharacteristic
59#1956—71no—
60#1947—71no—
61#1939—71no—
62C2×#335—71no—
63C2×#332—71no—
64#1296—71no—
65C2×C7×Q8—22no—
66C2×C7×Q8—41no—
67C2×C7×Q8—41no—
68C2×C7×Q8—41no—
69C2×C7×Q8—41no—
70C2×C7×Q8—41no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—41no—
74C22×C4×C7C2×D411yescharacteristic
75C22×C4×C7C2×D411yescharacteristic
76C22×C4×C7#4111yescharacteristic
77C22×Dic7—41no—
78C2×C7×C8—41no—
79C2×C7×C8—41no—
80C2×C7×C8—41no—
81C7×C4⋊C4—21no—
82C7×C4⋊C4—22no—
83C7×C4⋊C4—22no—
84C7×C4⋊C4—21no—
85C7×C4⋊C4—21no—
86C7×C4⋊C4—41no—
87C7×C4⋊C4—41no—
88C7×C4⋊C4Q1612yes—
89C42×C7—41no—
90C42×C7—41no—
91C42×C7C2×D411yescharacteristic
92C42×C7C2×Q811yescharacteristic
93C42×C7#4111yescharacteristic
94C42×C7#4111yescharacteristic
95C4⋊Dic7—41no—
96C4⋊Dic7—41no—
97C4⋊Dic7—41no—
98C4⋊Dic7—41no—
99C4⋊Dic7—81no—
100C2×C7⋊C8—21no—
101C2×C7⋊C8—21no—
102C2×C7⋊C8—22no—
103C2×C7⋊C8—21no—
104C2×C7⋊C8—21no—
105C2×C7⋊C8—21no—
106C2×C7⋊C8—41no—
107C2×C7⋊C8—41no—
108C2×C7⋊C8—41no—
109C2×C7⋊C8—41no—
110C2×C7⋊C8—41no—
111C2×C7⋊C8D812yes—
112C2×C4⋊Q8C2×D711yescharacteristic
113C2×#107—141no—
114C2×C4⋊C8—71no—
115C2×C4⋊C8—71no—
116C2×C4⋊C8—141no—
117C2×C4⋊C8C2×D711yescharacteristic
118C2×#103—141no—
119C2×#103—141no—
120C2×C4×C8—71no—
121#384—71no—
122C4×C4⋊C4C2×D711yescharacteristic
123#340—21no—
124#340—21no—
125#340—141no—
126#336—141no—
127#335—142no—
128#332—142no—
129C23×C7#12111yescharacteristic
130C7×Q8—42no—
131C7×Q8—42no—
132C7×Q8—81no—
133C7×Q8—81no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—22no—
137C2×C4×C7—41no—
138C2×C4×C7—41no—
139C2×C4×C7—42no—
140C2×C4×C7—41no—
141C2×C4×C7—41no—
142C2×C4×C7—41no—
143C2×C4×C7—81no—
144C2×C4×C7—81no—
145C2×C4×C7#12111yescharacteristic
146C2×C4×C7#12111yescharacteristic
147C2×C4×C7C22⋊Q811yescharacteristic
148C2×C4×C7C22⋊Q811yescharacteristic
149C2×C4×C7C22⋊Q811yescharacteristic
150C2×C4×C7#12611yescharacteristic
151C2×C4×C7C2×D811yescharacteristic
152C2×C4×C7C2×Q1611yescharacteristic
153C2×C4×C7#13511yescharacteristic
154C2×C4×C7#13511yescharacteristic
155C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C7#13711yescharacteristic
158C2×C4×C7#13711yescharacteristic
159C2×Dic7—81no—
160C2×Dic7—81no—
161C2×Dic7—81no—
162C7×C8—81no—
163C7⋊C8—22no—
164C7⋊C8—42no—
165C7⋊C8—41no—
166C7⋊C8—81no—
167C22×Q8—21no—
168C22×C8—21no—
169C22×C8—71no—
170C22×C8—71no—
171C22×C8—141no—
172C22×C8—141no—
173C4⋊Q8—21no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176C4⋊Q8Dic1412yes—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—141no—
180C2×C4⋊C4—141no—
181C2×C4⋊C4—141no—
182C2×C4⋊C4C22⋊D711yescharacteristic
183C2×C4⋊C4C22⋊D711yescharacteristic
184C2×C42—21no—
185C2×C42C22×D711yescharacteristic
186#107—282no—
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—72no—
190C4⋊C8—141no—
191C4⋊C8—141no—
192C4⋊C8—141no—
193C4⋊C8—282no—
194#103—282no—
195#103—282no—
196C4×C8—141no—
197C4×C8—141no—
198#95—21no—
199C22×C7#39611yescharacteristic
200C22×C7#45911yescharacteristic
201C22×C7#46411yescharacteristic
202C22×C7#46711yescharacteristic
203C22×C7#46811yescharacteristic
204C22×C7#47111yescharacteristic
205C22×C7#47311yescharacteristic
206C4×C7—21no—
207C4×C7—21no—
208C4×C7—42no—
209C4×C7—82no—
210C4×C7—81no—
211C4×C7#46211yescharacteristic
212C4×C7#46311yescharacteristic
213C4×C7#46611yescharacteristic
214C4×C7#46811yescharacteristic
215C4×C7#47411yescharacteristic
216C4×C7#47711yescharacteristic
217C4×C7#47811yescharacteristic
218C4×C7#47911yescharacteristic
219Dic7—161no—
220C2×Q8—22no—
221C2×Q8—41no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×Q8—41no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—281no—
230C22×C4D4×D711yescharacteristic
231C22×C4#115911yescharacteristic
232C22×C4C2×C22⋊D711yescharacteristic
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—72no—
237C2×C8—141no—
238C2×C8—141no—
239C2×C8—141no—
240C2×C8—141no—
241C2×C8—141no—
242C2×C8—142no—
243C2×C8—281no—
244C2×C8—281no—
245C2×C8—281no—
246C2×C8—281no—
247C2×C8—281no—
248C4⋊C4—21no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—281no—
256C4⋊C4—281no—
257C4⋊C4—281no—
258C4⋊C4—281no—
259C4⋊C4—561no—
260C4⋊C4#114412yes—
261C42—41no—
262C42—41no—
263C42C2×Dic1411yescharacteristic
264C42#115711yescharacteristic
265C42D4×D711yescharacteristic
266C42#115911yescharacteristic
267C2×C7#166911yescharacteristic
268C2×C7#168411yescharacteristic
269C2×C7#168511yescharacteristic
270C2×C7#170011yescharacteristic
271C2×C7#206411yescharacteristic
272C2×C7#206711yescharacteristic
273C2×C7#206811yescharacteristic
274C23#650211yescharacteristic
275Q8—42no—
276Q8—42no—
277Q8—81no—
278Q8—81no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—561no—
291C2×C4—561no—
292C2×C4—561no—
293C2×C4#644111yescharacteristic
294C2×C4#644111yescharacteristic
295C2×C4#644211yescharacteristic
296C2×C4#644711yescharacteristic
297C2×C4D7×D811yescharacteristic
298C2×C4#647411yescharacteristic
299C2×C4#647811yescharacteristic
300C2×C4#647911yescharacteristic
301C2×C4#648711yescharacteristic
302C2×C4#650111yescharacteristic
303C2×C4#650511yescharacteristic
304C2×C4C2×#114411yescharacteristic
305C2×C4#651211yescharacteristic
306C2×C4#651311yescharacteristic
307C8—81no—
308C8—142no—
309C8—281no—
310C8—282no—
311C8—561no—
312C7#1059211yescharacteristic, complemented, Sylow
313C22#8972011yescharacteristic
314C22#8982111yescharacteristic
315C22#8982311yescharacteristic
316C22#8992211yescharacteristic
317C22#8993811yescharacteristic
318C22#8997511yescharacteristic
319C22#8997611yescharacteristic
320C4—21no—
321C4—21no—
322C4—42no—
323C4—82no—
324C4—81no—
325C4—1121no—
326C4#8953111yescharacteristic
327C4#8953511yescharacteristic
328C4#8954711yescharacteristic
329C4#8955211yescharacteristic
330C4#8979311yescharacteristic
331C4#8979411yescharacteristic
332C4#8982911yescharacteristic
333C4#8986211yescharacteristic
334C2#1172743711yescharacteristic
335C2#1172794811yescharacteristic
336C2#1172809111yescharacteristic
337C2#1172885511yescharacteristic
338C2#1172885811yescharacteristic
339C2#1172887311yescharacteristic
340C2#1172887611yescharacteristic
subgroupG/H
centerC23#6502
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1988C2
socle, prime radicalC23×C7#121
hypercenter#1988D7
hypocenterC7#10592
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
312. C7#10592semidirect

Maximal subgroups

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

subgroupindex
C7×#19882
#117295392
C2×#893422
C2×#892742
#117272382
#117272202
#117255082
#105927