Finite Group Databasebeta

← #13251173

Subgroups — #13251173

Order 1792.

470 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 117 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#11740689C211yesmaximal, characteristic
2#11736708C211yesmaximal, characteristic
3C7×#1549C211yesmaximal, characteristic
4#11729529C211yesmaximal, characteristic
5#11728282C211yesmaximal, characteristic
6#11725552C211yesmaximal, characteristic
7#11725521C211yesmaximal, characteristic
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×C4×Dic14C2211yescharacteristic
10C7×#431C2211yescharacteristic
11C7×#423C2211yescharacteristic
12#90002—22no—
13C2×#6398—21no—
14#89754C414yes—
15#89749—21no—
16#89746—21no—
17C4×C4⋊Dic7C2211yescharacteristic
18#89697C2211yescharacteristic
19#89696C2211yescharacteristic
20#89602—22no—
21#89490—22no—
22C8×Dic14—22no—
23C7×#332—22no—
24#89349—21no—
25#89342—22no—
26#9396—71nomaximal, Sylow
27C22×C7×Q8—21no—
28C22×Dic14D411yescharacteristic
29C2×C7×M16—21no—
30C7×C4⋊Q8—21no—
31C7×C4⋊Q8—21no—
32C7×C4⋊Q8—21no—
33C7×C4⋊Q8—21no—
34C2×C7×C4⋊C4—21no—
35C2×C7×C4⋊C4C2×C412yes—
36C2×C42×C7C2311yescharacteristic
37C2×C4⋊Dic7—21no—
38C2×C4⋊Dic7D411yescharacteristic
39C2×Dic7⋊C4C2×C412yes—
40C2×C4×Dic7—21no—
41C2×C4×Dic7D412yes—
42C2×#1136—21no—
43C4×Dic14—21no—
44C4×Dic14—21no—
45C4×Dic14—21no—
46C4×Dic14—21no—
47C7×C4⋊C8—21no—
48C7×C4⋊C8—21no—
49C7×C4⋊C8D412yes—
50C7×C22⋊C8—21no—
51C4×C7×C8—21no—
52C7⋊#95—24no—
53C7⋊#95—24no—
54C7⋊#95C2×C412yes—
55C22⋊(C7⋊C8)—21no—
56#6398—42no—
57Dic7⋊C8—24no—
58C8×Dic7—24no—
59C4⋊(C7⋊C8)—21no—
60C4⋊(C7⋊C8)—21no—
61C4⋊(C7⋊C8)D412yes—
62C4×C7⋊C8—21no—
63#2982—71no—
64#2568—71no—
65#1801—71no—
66#1549—71no—
67#1549D711yescharacteristic
68#1303—71no—
69#1303—71no—
70C2×C7×Q8—44no—
71C2×C7×Q8—41no—
72C2×C7×Q8—41no—
73C22×C4×C7—22no—
74C22×C4×C7C22×C411yescharacteristic
75C22×C4×C7C2×D411yescharacteristic
76C22×C4×C7C2×D411yescharacteristic
77C22×Dic7—22no—
78C22×Dic7C22⋊C412yes—
79C22×Dic7C22⋊C412yes—
80C2×Dic14—21no—
81C2×Dic14—21no—
82C2×Dic14—21no—
83C2×Dic14—21no—
84C2×Dic14SD1612yes—
85C2×Dic14Q1612yes—
86C7×M16—41no—
87C7×M16—41no—
88C2×C7×C8—22no—
89C2×C7×C8—41no—
90C7×C4⋊C4—22no—
91C7×C4⋊C4—22no—
92C7×C4⋊C4—41no—
93C7×C4⋊C4—41no—
94C42×C7C2×D411yescharacteristic
95C42×C7C2×D411yescharacteristic
96C42×C7#4111yescharacteristic
97C42×C7#4111yescharacteristic
98C4⋊Dic7—21no—
99C4⋊Dic7—21no—
100C4⋊Dic7—42no—
101Dic7⋊C4—22no—
102Dic7⋊C4—22no—
103C4×Dic7—22no—
104C4×Dic7—22no—
105C4×Dic7—41no—
106C4×Dic7—41no—
107#1136—41no—
108#1136—41no—
109C2×C7⋊C8—22no—
110C2×C7⋊C8—41no—
111C2×C4⋊Q8C2×D711yescharacteristic
112C2×C4×Q8—71no—
113C8×Q8—142no—
114C8×Q8—142no—
115#431—71no—
116#431—142no—
117#431C2×D711yescharacteristic
118#423—71no—
119#423C2×D711yescharacteristic
120C2×#101—141no—
121#400—74no—
122#391—142no—
123#391—141no—
124#382—141no—
125C4×C4⋊C4—71no—
126#343—141no—
127#332—22no—
128#332—142no—
129C23×C7C2×C22⋊C411yescharacteristic
130C7×Q8—82no—
131C7×Q8—82no—
132C2×C4×C7—22no—
133C2×C4×C7—41no—
134C2×C4×C7—44no—
135C2×C4×C7—42no—
136C2×C4×C7C4×D411yescharacteristic
137C2×C4×C7C4×D411yescharacteristic
138C2×C4×C7#12011yescharacteristic
139C2×C4×C7#12111yescharacteristic
140C2×C4×C7#12111yescharacteristic
141C2×C4×C7#12311yescharacteristic
142C2×C4×C7C2×SD1611yescharacteristic
143C2×C4×C7C2×Q1611yescharacteristic
144C2×C4×C7#13511yescharacteristic
145C2×C4×C7#13511yescharacteristic
146C2×Dic7—22no—
147C2×Dic7—22no—
148C2×Dic7—22no—
149C2×Dic7—42no—
150C2×Dic7—42no—
151C2×Dic7—42no—
152C2×Dic7—42no—
153C2×Dic7#10314yes—
154Dic14—22no—
155Dic14—22no—
156Dic14—22no—
157Dic14—22no—
158C7×C8—42no—
159C7×C8—81no—
160C7⋊C8—42no—
161C7⋊C8—81no—
162C22×Q8—21no—
163C22×Q8—71no—
164C2×M16—21no—
165C2×M16—141no—
166C4⋊Q8—21no—
167C4⋊Q8—21no—
168C4⋊Q8—21no—
169C4⋊Q8—21no—
170C4×Q8—141no—
171C4×Q8—141no—
172C4×Q8—141no—
173C4×Q8—141no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—72no—
176C2×C4⋊C4—71no—
177C2×C4⋊C4—141no—
178C2×C4⋊C4C4×D712yes—
179C2×C42—72no—
180C2×C42—141no—
181C2×C42C22×D711yescharacteristic
182C4⋊C8—21no—
183C4⋊C8—21no—
184C4⋊C8—72no—
185C4⋊C8—144no—
186C4⋊C8—141no—
187C4⋊C8—141no—
188C4⋊C8C22⋊D712yes—
189#101—282no—
190C22⋊C8—21no—
191C22⋊C8—141no—
192C4×C8—21no—
193C4×C8—144no—
194C4×C8—141no—
195#95—72no—
196#95—144no—
197#95—144no—
198C22×C7—21no—
199C22×C7—21no—
200C22×C7#38611yescharacteristic
201C22×C7C2×#10311yescharacteristic
202C22×C7#41611yescharacteristic
203C4×C7—21no—
204C4×C7—21no—
205C4×C7—21no—
206C4×C7—82no—
207C4×C7#45412yes—
208C4×C7#46511yescharacteristic
209C4×C7#46511yescharacteristic
210C4×C7#46711yescharacteristic
211C4×C7#46711yescharacteristic
212Dic7—24no—
213Dic7—42no—
214Dic7—82no—
215C2×Q8—44no—
216C2×Q8—41no—
217C2×Q8—41no—
218C2×Q8—72no—
219C2×Q8—72no—
220C2×Q8—141no—
221C2×Q8—141no—
222C2×Q8—141no—
223C2×Q8—141no—
224C22×C4—22no—
225C22×C4—72no—
226C22×C4—72no—
227C22×C4—142no—
228C22×C4C2×C4×D711yescharacteristic
229C22×C4D4×D711yescharacteristic
230C22×C4D4×D711yescharacteristic
231M16—41no—
232M16—41no—
233M16—281no—
234M16—281no—
235C2×C8—22no—
236C2×C8—41no—
237C2×C8—142no—
238C2×C8—281no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—142no—
244C4⋊C4—141no—
245C4⋊C4—142no—
246C4⋊C4—141no—
247C4⋊C4—282no—
248C42—142no—
249C42—142no—
250C42—281no—
251C42—281no—
252C42#115711yescharacteristic
253C42D4×D711yescharacteristic
254C42#115911yescharacteristic
255C42C2×C22⋊D711yescharacteristic
256C2×C7—21no—
257C2×C7—21no—
258C2×C7#188811yescharacteristic
259C2×C7#189211yescharacteristic
260C2×C7#191511yescharacteristic
261C23D7×C22⋊C411yescharacteristic
262Q8—82no—
263Q8—82no—
264Q8—142no—
265Q8—142no—
266Q8—142no—
267Q8—142no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—44no—
271C2×C4—42no—
272C2×C4—74no—
273C2×C4—142no—
274C2×C4—142no—
275C2×C4—142no—
276C2×C4—282no—
277C2×C4—282no—
278C2×C4—282no—
279C2×C4—282no—
280C2×C4(C22⋊D7)⋊C411yescharacteristic
281C2×C4#644611yescharacteristic
282C2×C4#644711yescharacteristic
283C2×C4D7×SD1611yescharacteristic
284C2×C4#647911yescharacteristic
285C2×C4D7×Q1611yescharacteristic
286C2×C4#648211yescharacteristic
287C2×C4C4×C22⋊D711yescharacteristic
288C2×C4#650011yescharacteristic
289C2×C4#650111yescharacteristic
290C8—42no—
291C8—81no—
292C8—282no—
293C8—561no—
294C7#939611yescharacteristic, complemented, Sylow
295C22—21no—
296C22—21no—
297C22D7×#10311yescharacteristic
298C22#8957611yescharacteristic
299C22#8972811yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—82no—
304C4—144no—
305C4—282no—
306C4—562no—
307C4#8957911yescharacteristic
308C4#8958511yescharacteristic
309C4#8994311yescharacteristic
310C4#8996011yescharacteristic
311C4#8997312yes—
312C2—21no—
313C2—21no—
314C2#1172787811yescharacteristic
315C2#1172802411yescharacteristic
316C2#1172807911yescharacteristic
subgroupG/H
centerC22#89728
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1549C2
socleC22×C7#386
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1549D7
hypocenterC7#9396
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
294. C7#9396semidirect

Maximal subgroups

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

subgroupindex
#117406892
#117367082
C7×#15492
#117295292
#117282822
#117255522
#117255212
#93967