Finite Group Databasebeta

← #13248870

Subgroups — #13248870

Order 1792.

484 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 107 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×#2983C211yesmaximal, characteristic
2#11739912C211yesmaximal, characteristic
3C4×#6410C211yesmaximal, characteristic
4#11728556C212yesmaximal
5#11725554C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×C4×Dic14C2211yescharacteristic
8C7×#446—24no—
9C7×#432—21no—
10C7×#432C2212yes—
11C7×#431—21no—
12#90001—21no—
13C2×#6410—21no—
14#89755C411yescharacteristic
15#89755C411yescharacteristic
16#89752—21no—
17#89751C411yescharacteristic
18#89751C411yescharacteristic
19#89704C2211yescharacteristic
20C4×Dic7⋊C4—21no—
21C4×Dic7⋊C4—21no—
22C4×#1136C2212yes—
23#89325—21no—
24#89279—24no—
25#9030—71nomaximal, Sylow
26C22×C7×Q8D411yescharacteristic
27C22×Dic14C2×C411yescharacteristic
28C4×C7×Q8—22no—
29C4×C7×Q8—22no—
30C2×C7×C4⋊C4C2×C411yescharacteristic
31C2×C7×C4⋊C4C2×C411yescharacteristic
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C42×C7D411yescharacteristic
35C2×C42×C7C2311yescharacteristic
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×#1136—22no—
45C4×Dic14—22no—
46C4×Dic14—22no—
47C7×C4⋊C8—22no—
48C7×C4⋊C8—22no—
49C7×C4⋊C8D414yes—
50C7×C22⋊C8—22no—
51C7×#97—22no—
52C7×#97—22no—
53C4×C7×C8—22no—
54#6410—24no—
55C7⋊#95—21no—
56C7⋊#95—21no—
57C7⋊#95—21no—
58C7⋊#95—21no—
59C7⋊#95—21no—
60C7⋊#95C2×C411yescharacteristic
61C7⋊#95C2×C411yescharacteristic
62#6377—22no—
63C4×C7⋊C8—22no—
64#2983D711yescharacteristic
65#2399—71no—
66C4×#101—71no—
67#1491—72no—
68#1300—72no—
69C2×C7×Q8—22no—
70C2×C7×Q8—22no—
71C2×C7×Q8—41no—
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22×C411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—21no—
82C22×Dic7—21no—
83C2×Dic14—22no—
84C2×Dic14—42no—
85C2×C7×C8—24no—
86C7×C4⋊C4—22no—
87C7×C4⋊C4—22no—
88C7×C4⋊C4—22no—
89C42×C7—21no—
90C42×C7—21no—
91C42×C7—21no—
92C42×C7—21no—
93C42×C7C2×D412yes—
94C42×C7#4112yes—
95C4⋊Dic7—22no—
96Dic7⋊C4—42no—
97Dic7⋊C4—42no—
98Dic7⋊C4—42no—
99Dic7⋊C4—42no—
100Dic7⋊C4—42no—
101C4×Dic7—24no—
102C4×Dic7—41no—
103C4×Dic7—41no—
104#1136—24no—
105#1136—42no—
106C2×C7⋊C8—42no—
107C2×C4×Q8—71no—
108C2×C4×Q8C2×D711yescharacteristic
109#446—24no—
110#432—21no—
111#432C2×D712yes—
112#431—21no—
113C2×#101—141no—
114C4×M16—72no—
115#398—71no—
116#398—71no—
117#398—141no—
118#395—71no—
119#395—71no—
120#395—141no—
121C4×C4⋊C4—141no—
122C4×C4⋊C4—141no—
123#376—71no—
124#343—141no—
125Q8⋊C8—144no—
126C23×C7C2×C22⋊C411yescharacteristic
127C7×Q8—44no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
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—21no—
137C2×C4×C7—21no—
138C2×C4×C7—41no—
139C2×C4×C7—41no—
140C2×C4×C7—41no—
141C2×C4×C7#10412yes—
142C2×C4×C7C4×D412yes—
143C2×C4×C7#12011yescharacteristic
144C2×C4×C7#12112yes—
145C2×C4×C7#12311yescharacteristic
146C2×Dic7—22no—
147C2×Dic7—22no—
148C2×Dic7—22no—
149C2×Dic7—41no—
150C2×Dic7—41no—
151C2×Dic7—41no—
152C2×Dic7—41no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158Dic14—24no—
159Dic14—42no—
160C7×C8—44no—
161C7⋊C8—44no—
162C22×Q8—71no—
163C22×Q8D2811yescharacteristic
164C2×M16—142no—
165C4×Q8—22no—
166C4×Q8—22no—
167C4×Q8—142no—
168C4×Q8—142no—
169C2×C4⋊C4—71no—
170C2×C4⋊C4—141no—
171C2×C4⋊C4—141no—
172C2×C4⋊C4—141no—
173C2×C4⋊C4—141no—
174C2×C4⋊C4—141no—
175C2×C4⋊C4C4×D711yescharacteristic
176C2×C4⋊C4C4×D711yescharacteristic
177C2×C4⋊C4D2811yescharacteristic
178C2×C42—141no—
179C2×C42—141no—
180C2×C42C22⋊D711yescharacteristic
181C2×C42C22⋊D711yescharacteristic
182C2×C42C22×D711yescharacteristic
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8C22⋊D714yes—
186#101—144no—
187C22⋊C8—22no—
188#97—22no—
189#97—22no—
190#97—142no—
191C4×C8—22no—
192C4×C8—142no—
193#95—71no—
194#95—71no—
195#95—141no—
196#95—141no—
197#95—141no—
198#95—141no—
199#95—141no—
200C22×C7—21no—
201C22×C7—21no—
202C22×C7#38611yescharacteristic
203C22×C7C2×#10411yescharacteristic
204C22×C7#42111yescharacteristic
205C4×C7—22no—
206C4×C7—22no—
207C4×C7—21no—
208C4×C7—22no—
209C4×C7—41no—
210C4×C7—41no—
211C4×C7—41no—
212C4×C7#45612yes—
213Dic7—42no—
214Dic7—42no—
215Dic7—42no—
216Dic7—81no—
217C2×Q8—22no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—142no—
221C2×Q8—282no—
222C22×C4—141no—
223C22×C4—141no—
224C22×C4—141no—
225C22×C4—141no—
226C22×C4(C2×D7)⋊C411yescharacteristic
227C22×C4(C2×D7)⋊C411yescharacteristic
228C22×C4(C2×D7)⋊C411yescharacteristic
229C22×C4(C2×D7)⋊C411yescharacteristic
230C22×C4C2×C4×D711yescharacteristic
231C22×C4C2×D2811yescharacteristic
232C22×C4C2×C22⋊D711yescharacteristic
233M16—144no—
234M16—282no—
235C2×C8—24no—
236C2×C8—282no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—22no—
240C4⋊C4—142no—
241C4⋊C4—282no—
242C4⋊C4—282no—
243C4⋊C4—282no—
244C4⋊C4—282no—
245C4⋊C4—282no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—144no—
251C42—281no—
252C42—281no—
253C42#115712yes—
254C42C2×C22⋊D712yes—
255C2×C7—21no—
256C2×C7—21no—
257C2×C7#187111yescharacteristic
258C2×C7#188611yescharacteristic
259C2×C7#189111yescharacteristic
260C23C2×(C2×D7)⋊C411yescharacteristic
261Q8—44no—
262Q8—144no—
263Q8—282no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—142no—
278C2×C4—142no—
279C2×C4—142no—
280C2×C4—281no—
281C2×C4—281no—
282C2×C4—281no—
283C2×C4—281no—
284C2×C4—281no—
285C2×C4—281no—
286C2×C4—281no—
287C2×C4—281no—
288C2×C4—281no—
289C2×C4#639912yes—
290C2×C4C4×C22⋊D712yes—
291C2×C4#649211yescharacteristic
292C2×C4#649312yes—
293C2×C4#651611yescharacteristic
294C8—44no—
295C8—284no—
296C7#903011yescharacteristic, complemented, Sylow
297C22—21no—
298C22—21no—
299C22C2×#639911yescharacteristic
300C22#8991111yescharacteristic
301C22#8998511yescharacteristic
302C4—21no—
303C4—22no—
304C4—22no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—282no—
310C4—282no—
311C4—282no—
312C4—561no—
313C4#9001812yes—
314C2—21no—
315C2—21no—
316C2#1172941411yescharacteristic
317C2#1172973811yescharacteristic
318C2#1172978311yescharacteristic
subgroupG/H
centerC2×C4#6516
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2983C2
socleC22×C7#386
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#2983D7
hypocenterC7#9030
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
296. C7#9030semidirect

Maximal subgroups

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

subgroupindex
C7×#29832
#117399122
C4×#64102
#117285562
#117255542
#90307