Finite Group Databasebeta

← #13272488

Subgroups — #13272488

Order 1792.

396 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 103 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
1#11739922C211yesmaximal, characteristic
2C4×C7×#101C211yesmaximal, characteristic
3#11729391C211yesmaximal, characteristic
4#11725505C212yesmaximal
5#11725505C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×#6433C411yescharacteristic
8C2×C7×#101C2212yes—
9C4×C7×M16—21no—
10#90002C2211yescharacteristic
11#90002C2211yescharacteristic
12C2×#6410C2212yes—
13#89756—21no—
14#89756—21no—
15#89749C411yescharacteristic
16#89748C411yescharacteristic
17C4×C4⋊Dic7C411yescharacteristic
18#89705—21no—
19#89705—21no—
20#89696—21no—
21C7×#343—21no—
22#89325—21no—
23#13303—71nomaximal, Sylow
24C22×C7×Q8C2311yescharacteristic
25C2×C7×M16—22no—
26C4×C7×Q8—41no—
27C4×C7×Q8—41no—
28C2×C7×C4⋊C4C2×C411yescharacteristic
29C2×C7×C4⋊C4D411yescharacteristic
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C42×C7C2×C411yescharacteristic
32C2×C42×C7D411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7C2×C411yescharacteristic
36C2×C4⋊Dic7C2×C411yescharacteristic
37C2×Dic7⋊C4—21no—
38C2×Dic7⋊C4—21no—
39C2×Dic7⋊C4—21no—
40C2×Dic7⋊C4—21no—
41C2×C4×Dic7C2×C411yescharacteristic
42C2×C4×Dic7C2×C411yescharacteristic
43C2×#1136—22no—
44#6433—41no—
45#6433—41no—
46C7×#101—22no—
47C7×#101Q814yes—
48C7×#97—41no—
49C4×C7×C8—41no—
50#6410—24no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95—21no—
56C7⋊#95—21no—
57C7⋊#95—21no—
58C4⋊(C7⋊C8)—41no—
59C4⋊(C7⋊C8)—41no—
60#2565—71no—
61#1801—71no—
62C4×#101D711yescharacteristic
63#1394—72no—
64#1394—72no—
65C2×C7×Q8—41no—
66C2×C7×Q8—41no—
67C2×C7×Q8C2×Q812yes—
68C2×C7×Q8#4112yes—
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22×C411yescharacteristic
74C22×C4×C7C2×D411yescharacteristic
75C22×C4×C7C2×D411yescharacteristic
76C22×Dic7—21no—
77C22×Dic7—21no—
78C22×Dic7—21no—
79C22×Dic7—21no—
80C7×M16—24no—
81C7×M16—42no—
82C2×C7×C8—42no—
83C7×C4⋊C4—41no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—41no—
86C42×C7—21no—
87C42×C7—21no—
88C42×C7—21no—
89C42×C7—21no—
90C42×C7—21no—
91C42×C7—21no—
92C4⋊Dic7—42no—
93C4⋊Dic7—41no—
94C4⋊Dic7—41no—
95Dic7⋊C4—42no—
96Dic7⋊C4—42no—
97Dic7⋊C4—42no—
98Dic7⋊C4—41no—
99Dic7⋊C4—41no—
100C4×Dic7—41no—
101C4×Dic7—41no—
102#1136—42no—
103#1136—42no—
104C2×C7⋊C8—42no—
105C2×#125—71no—
106C2×C4×Q8C2×D711yescharacteristic
107#423—141no—
108C2×#101—72no—
109C2×#101C2×D712yes—
110C4×M16—21no—
111#398—141no—
112#398—141no—
113#391—71no—
114#391—71no—
115#387—141no—
116#387—141no—
117#384—71no—
118#382—71no—
119C4×C4⋊C4—71no—
120#343—21no—
121#343—141no—
122C23×C7C2×C22⋊C411yescharacteristic
123C7×Q8—42no—
124C7×Q8—42no—
125C2×C4×C7—21no—
126C2×C4×C7—21no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7—41no—
137C2×C4×C7—41no—
138C2×C4×C7#9911yescharacteristic
139C2×C4×C7#9911yescharacteristic
140C2×C4×C7C4×Q812yes—
141C2×C4×C7C22⋊Q812yes—
142C2×C4×C7#12411yescharacteristic
143C2×C4×C7C4⋊Q811yescharacteristic
144C2×Dic7—22no—
145C2×Dic7—41no—
146C2×Dic7—41no—
147C2×Dic7—41no—
148C2×Dic7—41no—
149C2×Dic7—41no—
150C2×Dic7—41no—
151C2×Dic7—42no—
152C2×Dic7—41no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C7×C8—44no—
156C7⋊C8—82no—
157C22×Q8C22×D711yescharacteristic
158C2×M16—22no—
159C2×M16—142no—
160#125—281no—
161#125—281no—
162C4×Q8—41no—
163C4×Q8—41no—
164C2×C4⋊C4—71no—
165C2×C4⋊C4—71no—
166C2×C4⋊C4—141no—
167C2×C4⋊C4—141no—
168C2×C4⋊C4—141no—
169C2×C4⋊C4—141no—
170C2×C4⋊C4—141no—
171C2×C4⋊C4C4×D711yescharacteristic
172C2×C4⋊C4D2811yescharacteristic
173C2×C4⋊C4C22⋊D711yescharacteristic
174C2×C42—71no—
175C2×C42—71no—
176C2×C42C4×D711yescharacteristic
177C2×C42D2811yescharacteristic
178C2×C42C22⋊D711yescharacteristic
179C4⋊C8—281no—
180C4⋊C8—281no—
181#101—22no—
182#101—144no—
183#101Dic1414yes—
184#97—41no—
185C4×C8—41no—
186#95—141no—
187#95—141no—
188#95—141no—
189#95—141no—
190#95—141no—
191#95—141no—
192#95—141no—
193C22×C7—21no—
194C22×C7—21no—
195C22×C7#39111yescharacteristic
196C22×C7C2×#9911yescharacteristic
197C22×C7#41011yescharacteristic
198C4×C7—21no—
199C4×C7—21no—
200C4×C7—21no—
201C4×C7—22no—
202C4×C7—22no—
203C4×C7—21no—
204C4×C7—41no—
205C4×C7—41no—
206C4×C7—41no—
207Dic7—42no—
208Dic7—81no—
209Dic7—81no—
210Dic7—81no—
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8C2×Dic1412yes—
214C2×Q8#115712yes—
215C22×C4—141no—
216C22×C4—141no—
217C22×C4—141no—
218C22×C4—141no—
219C22×C4(C2×D7)⋊C411yescharacteristic
220C22×C4(C2×D7)⋊C411yescharacteristic
221C22×C4(C2×D7)⋊C411yescharacteristic
222C22×C4(C2×D7)⋊C411yescharacteristic
223C22×C4C2×C4×D711yescharacteristic
224C22×C4C2×D2811yescharacteristic
225C22×C4C2×C22⋊D711yescharacteristic
226M16—24no—
227M16—42no—
228M16—282no—
229M16—282no—
230C2×C8—42no—
231C2×C8—282no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—281no—
236C4⋊C4—281no—
237C4⋊C4—282no—
238C4⋊C4—282no—
239C4⋊C4—282no—
240C4⋊C4—282no—
241C4⋊C4—281no—
242C4⋊C4—281no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—281no—
250C42—281no—
251C2×C7—21no—
252C2×C7—21no—
253C2×C7#199611yescharacteristic
254C2×C7#213211yescharacteristic
255C2×C7#213311yescharacteristic
256C23C2×(C2×D7)⋊C411yescharacteristic
257Q8—42no—
258Q8—42no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—142no—
273C2×C4—281no—
274C2×C4—281no—
275C2×C4—281no—
276C2×C4—281no—
277C2×C4—281no—
278C2×C4—281no—
279C2×C4—282no—
280C2×C4—281no—
281C2×C4—281no—
282C2×C4—281no—
283C2×C4#638011yescharacteristic
284C2×C4#638011yescharacteristic
285C2×C4C4×Dic1412yes—
286C2×C4#643211yescharacteristic
287C2×C4#643811yescharacteristic
288C2×C4#648712yes—
289C8—44no—
290C8—562no—
291C7#1330311yescharacteristic, complemented, Sylow
292C22—21no—
293C22—21no—
294C22#8970111yescharacteristic
295C22C2×#638011yescharacteristic
296C22#8977811yescharacteristic
297C4—21no—
298C4—21no—
299C4—22no—
300C4—21no—
301C4—22no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—282no—
307C4—561no—
308C4—561no—
309C4—561no—
310C2—21no—
311C2—21no—
312C2#1172721111yescharacteristic
313C2#1172788211yescharacteristic
314C2#1172790211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC22×Q8C22×D7
FittingC4×C7×#101C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC22×C7×Q8C23
hypercenterC4×#101D7
hypocenterC7#13303
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
291. C7#13303semidirect

Maximal subgroups

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

subgroupindex
#117399222
C4×C7×#1012
#117293912
#117255052
#133037