Finite Group Databasebeta

← #13263274

Subgroups — #13263274

Order 1792.

412 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C4×#6507C211yesmaximal, characteristic
2C7×#1467C211yesmaximal, characteristic
3#11729379C211yesmaximal, characteristic
4#11725261C212yesmaximal
5#11725259C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×#6507C411yescharacteristic
8C2×C4×Dic14C411yescharacteristic
9C7×#432—21no—
10#90002C411yescharacteristic
11#89748C2211yescharacteristic
12#89746C2211yescharacteristic
13#89744—21no—
14#89744—21no—
15C4×Dic7⋊C4—21no—
16C4×Dic7⋊C4—21no—
17C42×Dic7C411yescharacteristic
18#89698—21no—
19C7×#324—21no—
20C7×#324C2212yes—
21#89323—21no—
22#89323C2212yes—
23#11532—71nomaximal, Sylow
24C22×C7×Q8C2×C411yescharacteristic
25C22×Dic14C2×C411yescharacteristic
26C4×C7×Q8—41no—
27C4×C7×Q8—41no—
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C7×C4⋊C4D411yescharacteristic
30C2×C7×C4⋊C4C2311yescharacteristic
31C2×C42×C7C2×C411yescharacteristic
32C2×C42×C7D411yescharacteristic
33C2×C42×C7D411yescharacteristic
34#6507—22no—
35#6507—22no—
36C2×C4⋊Dic7C2×C411yescharacteristic
37C2×Dic7⋊C4—21no—
38C2×Dic7⋊C4—21no—
39C2×Dic7⋊C4—21no—
40C2×Dic7⋊C4—21no—
41C2×Dic7⋊C4—21no—
42C2×C4×Dic7—21no—
43C2×C4×Dic7—21no—
44C2×C4×Dic7—21no—
45C2×C4×Dic7C2×C411yescharacteristic
46C2×C4×Dic7C2×C411yescharacteristic
47C4×Dic14—41no—
48C4×Dic14—41no—
49C7×C4⋊C8—41no—
50C7×C22⋊C8—22no—
51C7×#97—41no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95—21no—
56C22⋊(C7⋊C8)—22no—
57C4⋊(C7⋊C8)—41no—
58#6377—41no—
59C4×C4⋊Q8—71no—
60#1467—71no—
61#1467D711yescharacteristic
62#1325—72no—
63#1319—72no—
64C2×C7×Q8—21no—
65C2×C7×Q8—21no—
66C2×C7×Q8—41no—
67C2×C7×Q8—41no—
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22×C411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C22×C4×C7C2×D411yescharacteristic
75C22×Dic7—21no—
76C22×Dic7—21no—
77C22×Dic7—21no—
78C22×Dic7—21no—
79C2×Dic14—21no—
80C2×Dic14—41no—
81C2×Dic14—41no—
82C2×Dic14M1612yes—
83C2×C7×C8—42no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—41no—
87C42×C7—21no—
88C42×C7—21no—
89C42×C7—21no—
90C42×C7—21no—
91C42×C7—21no—
92C42×C7—21no—
93C4⋊Dic7—41no—
94Dic7⋊C4—24no—
95Dic7⋊C4—24no—
96Dic7⋊C4—42no—
97Dic7⋊C4—42no—
98Dic7⋊C4—42no—
99C4×Dic7—24no—
100C4×Dic7—21no—
101C4×Dic7—42no—
102C4×Dic7—41no—
103C4×Dic7—41no—
104C4×Dic7—41no—
105C4×Dic7M1612yes—
106C2×C7⋊C8—42no—
107C2×C4⋊Q8—71no—
108C2×C4×Q8—71no—
109C2×C4×Q8C2×D711yescharacteristic
110#432—21no—
111#432—141no—
112#391—71no—
113#391—71no—
114#389—141no—
115#389—141no—
116#384—71no—
117C4×C4⋊C4—141no—
118C4×C4⋊C4—141no—
119C43—71no—
120#324—21no—
121#324—72no—
122#324—141no—
123#324C2×D712yes—
124C23×C7C2×C22⋊C411yescharacteristic
125C7×Q8—42no—
126C7×Q8—42no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—22no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—41no—
140C2×C4×C7—41no—
141C2×C4×C7—41no—
142C2×C4×C7#9911yescharacteristic
143C2×C4×C7#9911yescharacteristic
144C2×C4×C7C2×M1611yescharacteristic
145C2×C4×C7C2×M1611yescharacteristic
146C2×Dic7—22no—
147C2×Dic7—22no—
148C2×Dic7—22no—
149C2×Dic7—22no—
150C2×Dic7—22no—
151C2×Dic7—41no—
152C2×Dic7—41no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158Dic14—42no—
159Dic14—42no—
160C7×C8—82no—
161C7⋊C8—82no—
162C22×Q8—71no—
163C22×Q8C4×D711yescharacteristic
164C4⋊Q8—142no—
165C4⋊Q8—142no—
166C4×Q8—41no—
167C4×Q8—41no—
168C4×Q8—281no—
169C4×Q8—281no—
170C2×C4⋊C4—71no—
171C2×C4⋊C4—141no—
172C2×C4⋊C4—141no—
173C2×C4⋊C4—141no—
174C2×C4⋊C4—141no—
175C2×C4⋊C4—141no—
176C2×C4⋊C4D2811yescharacteristic
177C2×C4⋊C4C22⋊D711yescharacteristic
178C2×C4⋊C4C22×D711yescharacteristic
179C2×C42—71no—
180C2×C42—71no—
181C2×C42—141no—
182C2×C42—141no—
183C2×C42—141no—
184C2×C42C4×D711yescharacteristic
185C2×C42D2811yescharacteristic
186C2×C42C22⋊D711yescharacteristic
187C4⋊C8—41no—
188C4⋊C8—281no—
189C22⋊C8—22no—
190C22⋊C8—142no—
191#97—41no—
192#97—281no—
193#95—141no—
194#95—141no—
195#95—141no—
196#95—141no—
197C22×C7—21no—
198C22×C7—21no—
199C22×C7#40711yescharacteristic
200C22×C7C2×#9911yescharacteristic
201C22×C7#41311yescharacteristic
202C4×C7—21no—
203C4×C7—21no—
204C4×C7—21no—
205C4×C7—41no—
206C4×C7—41no—
207C4×C7—41no—
208C4×C7—41no—
209C4×C7—41no—
210C4×C7#35612yes—
211Dic7—24no—
212Dic7—42no—
213Dic7—42no—
214Dic7—81no—
215C2×Q8—21no—
216C2×Q8—21no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8—72no—
220C2×Q8—141no—
221C2×Q8—281no—
222C2×Q8—281no—
223C22×C4—141no—
224C22×C4—141no—
225C22×C4—141no—
226C22×C4—141no—
227C22×C4(C2×D7)⋊C411yescharacteristic
228C22×C4(C2×D7)⋊C411yescharacteristic
229C22×C4(C2×D7)⋊C411yescharacteristic
230C22×C4(C2×D7)⋊C411yescharacteristic
231C22×C4C2×C4×D711yescharacteristic
232C22×C4C2×D2811yescharacteristic
233C22×C4C2×C22⋊D711yescharacteristic
234C2×C8—42no—
235C2×C8—282no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—144no—
240C4⋊C4—144no—
241C4⋊C4—281no—
242C4⋊C4—282no—
243C4⋊C4—282no—
244C4⋊C4—282no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—72no—
252C42—144no—
253C42—141no—
254C42—281no—
255C42—282no—
256C42—281no—
257C42—281no—
258C2×C7—21no—
259C2×C7—21no—
260C2×C7#146511yescharacteristic
261C2×C7#212611yescharacteristic
262C2×C7C2×#35611yescharacteristic
263C23C2×(C2×D7)⋊C411yescharacteristic
264Q8—42no—
265Q8—42no—
266Q8—282no—
267Q8—282no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—142no—
284C2×C4—142no—
285C2×C4—142no—
286C2×C4—142no—
287C2×C4—142no—
288C2×C4—281no—
289C2×C4—281no—
290C2×C4—281no—
291C2×C4—281no—
292C2×C4—281no—
293C2×C4—281no—
294C2×C4—281no—
295C2×C4#638011yescharacteristic
296C2×C4#638011yescharacteristic
297C2×C4D7×M1611yescharacteristic
298C2×C4D7×M1611yescharacteristic
299C8—82no—
300C8—562no—
301C7#1153211yescharacteristic, complemented, Sylow
302C22—21no—
303C22—21no—
304C22C2×#638011yescharacteristic
305C22#8989811yescharacteristic
306C22#8990411yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—144no—
316C4—282no—
317C4—282no—
318C4—561no—
319C4#8927312yes—
320C2—21no—
321C2—21no—
322C2#1172772211yescharacteristic
323C2#1172781411yescharacteristic
324C2C2×#8927311yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1467C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1467D7
hypocenterC7#11532
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
301. C7#11532semidirect

Maximal subgroups

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

subgroupindex
C4×#65072
C7×#14672
#117293792
#117252612
#117252592
#115327