Finite Group Databasebeta

← #13258257

Subgroups — #13258257

Order 1792.

390 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2571C211yesmaximal, characteristic
2#11727328C211yesmaximal, characteristic
3#11727221C211yesmaximal, characteristic
4#11727220C211yesmaximal, characteristic
5#11725440C211yesmaximal, characteristic
6#11725425C211yesmaximal, characteristic
7#11725425C211yesmaximal, characteristic
8C7×#400—22no—
9C7×#389—21no—
10C7×#389—21no—
11C7×#384C2211yescharacteristic
12C7×#382—21no—
13C7×#382—21no—
14C4×C7×C4⋊C4C2211yescharacteristic
15C4×C7×C4⋊C4C2211yescharacteristic
16C2×#6382—21no—
17C2×#6381—21no—
18#89707C2211yescharacteristic
19C2×C4⋊(C7⋊C8)C2211yescharacteristic
20C2×C4⋊(C7⋊C8)C2211yescharacteristic
21C2×C4×C7⋊C8C2211yescharacteristic
22#89324—21no—
23#89324—21no—
24#89324—22no—
25#10578—71nomaximal, Sylow
26C2×C7×C4⋊C4—21no—
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4—22no—
29C2×C7×C4⋊C4D411yescharacteristic
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C7×C4⋊C4D411yescharacteristic
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C7×C4⋊C4D412yes—
34C2×C42×C7—21no—
35C2×C42×C7—21no—
36C2×C42×C7C2311yescharacteristic
37C2×C4⋊Dic7—21no—
38C2×C4⋊Dic7—21no—
39C2×C4⋊Dic7—21no—
40C22×C7⋊C8—21no—
41C22×C7⋊C8—21no—
42C22×C7⋊C8—21no—
43C7×#95—22no—
44C7×#95—22no—
45C7×#95—22no—
46C7×#95—21no—
47C7×#95—21no—
48#6382—42no—
49#6381—42no—
50C4⋊(C7⋊C8)—21no—
51C4⋊(C7⋊C8)—21no—
52C4⋊(C7⋊C8)Q812yes—
53C4⋊(C7⋊C8)Q812yes—
54C4×C7⋊C8—21no—
55C4×C7⋊C8Q812yes—
56#2571D711yescharacteristic
57#1948—71no—
58#1947—71no—
59#1834—71no—
60#1296—71no—
61#1279—71no—
62#1279—71no—
63C22×C4×C7—21no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—22no—
68C22×C4×C7C2×D411yescharacteristic
69C22×C4×C7C2×D411yescharacteristic
70C22×C4×C7C2×D411yescharacteristic
71C22×Dic7—41no—
72C7×C4⋊C4—21no—
73C7×C4⋊C4—21no—
74C7×C4⋊C4—21no—
75C7×C4⋊C4—21no—
76C7×C4⋊C4—21no—
77C7×C4⋊C4—21no—
78C7×C4⋊C4—21no—
79C7×C4⋊C4—21no—
80C7×C4⋊C4—42no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—41no—
83C7×C4⋊C4—41no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—82no—
86C42×C7—41no—
87C42×C7—41no—
88C42×C7—41no—
89C42×C7—41no—
90C42×C7C2×Q811yescharacteristic
91C42×C7C2×Q811yescharacteristic
92C42×C7C2×Q811yescharacteristic
93C42×C7#4111yescharacteristic
94C4⋊Dic7—42no—
95C4⋊Dic7—41no—
96C4⋊Dic7—41no—
97C4⋊Dic7—41no—
98C4⋊Dic7—41no—
99C2×C7⋊C8—22no—
100C2×C7⋊C8—22no—
101C2×C7⋊C8—22no—
102C2×C7⋊C8—41no—
103C2×C7⋊C8—41no—
104C2×C7⋊C8—41no—
105C2×C7⋊C8—41no—
106C2×C7⋊C8—41no—
107C2×C7⋊C8—41no—
108C2×#107—141no—
109C2×#106—141no—
110C2×C4⋊C8—71no—
111C2×C4⋊C8—71no—
112C2×C4×C8—71no—
113#400—22no—
114#389—21no—
115#389—21no—
116#384—71no—
117#384C2×D711yescharacteristic
118#382—21no—
119#382—21no—
120C4×C4⋊C4C2×D711yescharacteristic
121C4×C4⋊C4C2×D711yescharacteristic
122#340—142no—
123#340—141no—
124#340—141no—
125C23×C7#12011yescharacteristic
126C2×C4×C7—21no—
127C2×C4×C7—21no—
128C2×C4×C7—41no—
129C2×C4×C7—41no—
130C2×C4×C7—41no—
131C2×C4×C7—41no—
132C2×C4×C7—42no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7—41no—
137C2×C4×C7—42no—
138C2×C4×C7—41no—
139C2×C4×C7—41no—
140C2×C4×C7—42no—
141C2×C4×C7—41no—
142C2×C4×C7—41no—
143C2×C4×C7C22⋊Q811yescharacteristic
144C2×C4×C7C22⋊Q811yescharacteristic
145C2×C4×C7C22⋊Q811yescharacteristic
146C2×C4×C7C4⋊Q811yescharacteristic
147C2×C4×C7C4⋊Q811yescharacteristic
148C2×C4×C7C4⋊Q811yescharacteristic
149C2×C4×C7#13511yescharacteristic
150C2×C4×C7#13511yescharacteristic
151C2×C4×C7#13511yescharacteristic
152C2×C4×C7#13511yescharacteristic
153C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C7#13711yescharacteristic
156C2×C4×C7#13711yescharacteristic
157C2×Dic7—81no—
158C2×Dic7—81no—
159C2×Dic7—81no—
160C7⋊C8—42no—
161C7⋊C8—42no—
162C7⋊C8—42no—
163C22×C8—141no—
164C22×C8—141no—
165C22×C8—141no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—141no—
170C2×C4⋊C4—141no—
171C2×C4⋊C4—141no—
172C2×C4⋊C4C22⋊D711yescharacteristic
173C2×C4⋊C4C22⋊D711yescharacteristic
174C2×C4⋊C4C22⋊D711yescharacteristic
175C2×C4⋊C4C22⋊D711yescharacteristic
176C2×C4⋊C4C22⋊D712yes—
177C2×C42—21no—
178C2×C42—21no—
179C2×C42C22×D711yescharacteristic
180#107—282no—
181#106—282no—
182C4⋊C8—72no—
183C4⋊C8—72no—
184C4⋊C8—141no—
185C4⋊C8—141no—
186C4×C8—72no—
187C4×C8—141no—
188#95—22no—
189#95—22no—
190#95—22no—
191#95—21no—
192#95—21no—
193C22×C7#39511yescharacteristic
194C22×C7#44911yescharacteristic
195C22×C7#44911yescharacteristic
196C22×C7#45211yescharacteristic
197C22×C7#45211yescharacteristic
198C22×C7#45411yescharacteristic
199C22×C7#45511yescharacteristic
200C4×C7—21no—
201C4×C7—21no—
202C4×C7—81no—
203C4×C7—81no—
204C4×C7—82no—
205C4×C7—81no—
206C4×C7—81no—
207C4×C7#47811yescharacteristic
208C4×C7#47811yescharacteristic
209C4×C7#47911yescharacteristic
210C4×C7#47911yescharacteristic
211C4×C7#49911yescharacteristic
212C4×C7#49911yescharacteristic
213C4×C7#50111yescharacteristic
214C4×C7#50111yescharacteristic
215Dic7—161no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—281no—
222C22×C4C2×C22⋊D711yescharacteristic
223C22×C4C2×C22⋊D711yescharacteristic
224C22×C4C2×C22⋊D711yescharacteristic
225C2×C8—142no—
226C2×C8—142no—
227C2×C8—142no—
228C2×C8—281no—
229C2×C8—281no—
230C2×C8—281no—
231C2×C8—281no—
232C2×C8—281no—
233C2×C8—281no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—82no—
248C4⋊C4—282no—
249C4⋊C4—281no—
250C4⋊C4—281no—
251C4⋊C4—281no—
252C4⋊C4—281no—
253C42—41no—
254C42—41no—
255C42—41no—
256C42—41no—
257C42Q8×D711yescharacteristic
258C42Q8×D711yescharacteristic
259C42Q8×D711yescharacteristic
260C42#116111yescharacteristic
261C2×C7#162811yescharacteristic
262C2×C7#163811yescharacteristic
263C2×C7#164011yescharacteristic
264C2×C7#164611yescharacteristic
265C2×C7#205911yescharacteristic
266C2×C7#205911yescharacteristic
267C2×C7#206111yescharacteristic
268C23#651611yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—561no—
287C2×C4—561no—
288C2×C4—561no—
289C2×C4#650711yescharacteristic
290C2×C4#650711yescharacteristic
291C2×C4#650711yescharacteristic
292C2×C4#650911yescharacteristic
293C2×C4#650911yescharacteristic
294C2×C4#650911yescharacteristic
295C2×C4#651211yescharacteristic
296C2×C4#651211yescharacteristic
297C2×C4#651311yescharacteristic
298C2×C4#651311yescharacteristic
299C2×C4#651311yescharacteristic
300C2×C4#651311yescharacteristic
301C2×C4#651411yescharacteristic
302C2×C4#651411yescharacteristic
303C8—282no—
304C8—282no—
305C8—282no—
306C7#1057811yescharacteristic, complemented, Sylow
307C22#9000111yescharacteristic
308C22#9001011yescharacteristic
309C22#9001011yescharacteristic
310C22#9001111yescharacteristic
311C22#9001111yescharacteristic
312C22#9001411yescharacteristic
313C22#9001711yescharacteristic
314C4—21no—
315C4—21no—
316C4—81no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—82no—
321C4—1121no—
322C4#8983511yescharacteristic
323C4#8983511yescharacteristic
324C4#8983611yescharacteristic
325C4#8983611yescharacteristic
326C4#8983711yescharacteristic
327C4#8983711yescharacteristic
328C4#8983811yescharacteristic
329C4#8983811yescharacteristic
330C2#1172949311yescharacteristic
331C2#1172949311yescharacteristic
332C2#1172965511yescharacteristic
333C2#1172968311yescharacteristic
334C2#1172968511yescharacteristic
335C2#1172968611yescharacteristic
336C2#1172969911yescharacteristic
subgroupG/H
centerC23#6516
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#2571C2
socle, prime radicalC23×C7#120
hypercenter#2571D7
hypocenterC7#10578
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

Complements

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

NH ≅ G/Ntype
306. C7#10578semidirect

Maximal subgroups

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

subgroupindex
C7×#25712
#117273282
#117272212
#117272202
#117254402
#117254252
#105787