Finite Group Databasebeta

← #32979511

Subgroups — #32979511

Order 18688.

398 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 83 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#22612532C211yesmaximal, characteristic
2#22610009C211yesmaximal, characteristic
3#22610009C211yesmaximal, characteristic
4#22607840C211yesmaximal, characteristic
5#22607840C211yesmaximal, characteristic
6#22607839C211yesmaximal, characteristic
7C73×#1306C211yesmaximal, characteristic
8C22×C4⋊Dic73C2211yescharacteristic
9#17988551C2211yescharacteristic
10#17988551C2211yescharacteristic
11#17988472—22no—
12#17988470—22no—
13#17988450C2211yescharacteristic
14#17988445C412yes—
15C22⋊C4×Dic73C412yes—
16#17988355—22no—
17#17988355—22no—
18#407×C73C2211yescharacteristic
19#407×C73C2211yescharacteristic
20#381×C73C2211yescharacteristic
21C23×Dic73C2×C411yescharacteristic
22C23×Dic73C2×C411yescharacteristic
23C2×#11924012—21no—
24C2×#11924012—21no—
25C2×C4⋊Dic73—21no—
26C2×C4⋊Dic73—21no—
27C2×C4⋊Dic73—21no—
28C2×C4⋊Dic73—21no—
29C2×C4⋊Dic73D412yes—
30C2×C4⋊Dic73D412yes—
31C2×#11924007—22no—
32C2×C22⋊Dic73C2×C412yes—
33C2×C4×Dic73—22no—
34C22⋊#10596831—21no—
35C22⋊#10596831—21no—
36C22⋊#10596831—21no—
37C22⋊#10596831—21no—
38#14556498—22no—
39#14556498—22no—
40#14556498—21no—
41#14556498—21no—
42C23×C4×C73C2311yescharacteristic
43C2×M16×C73—21no—
44C2×M16×C73—21no—
45C2×C22⋊C4×C73C2×C412yes—
46C22⋊C8×C73—21no—
47C22⋊C8×C73—21no—
48C22⋊C8×C73—21no—
49C22⋊C8×C73—21no—
50#95×C73—21no—
51#95×C73—21no—
52C22×Dic73—21no—
53C22×Dic73—21no—
54C22×Dic73—21no—
55C22×Dic73—21no—
56C22×Dic73—22no—
57C22×Dic73—81no—
58C22×Dic73—81no—
59C22×Dic73C22⋊C412yes—
60C22×Dic73C22⋊C412yes—
61#11924012—42no—
62#11924012—42no—
63C2×#10596831—41no—
64C2×#10596831—41no—
65C4⋊Dic73—22no—
66C4⋊Dic73—22no—
67C4⋊Dic73—22no—
68C4⋊Dic73—22no—
69#11924007—82no—
70C22⋊Dic73—42no—
71C4×Dic73—82no—
72C24×C73C22×C411yescharacteristic
73C22×C4×C73—22no—
74C22×C4×C73—42no—
75C22×C4×C73C2×D411yescharacteristic
76C22×C4×C73C2×D411yescharacteristic
77C22×C4×C73#4111yescharacteristic
78C22×C4×C73#4111yescharacteristic
79C22×C4×C73#4111yescharacteristic
80C22×C4×C73#4111yescharacteristic
81M16×C73—42no—
82M16×C73—42no—
83C2×C8×C73—41no—
84C2×C8×C73—41no—
85C22⋊C4×C73—42no—
86C23×C73—22no—
87C23×C73—41no—
88C23×C73—41no—
89C23×C73C2×C22⋊C411yescharacteristic
90C23×C73#11711yescharacteristic
91C23×C73#11711yescharacteristic
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—41no—
95C2×C4×C73—41no—
96C2×C4×C73—41no—
97C2×C4×C73—41no—
98C2×C4×C73—42no—
99C2×C4×C73—42no—
100C2×C4×C73—42no—
101C2×C4×C73#12311yescharacteristic
102C2×C4×C73#12311yescharacteristic
103C2×C4×C73#12311yescharacteristic
104C2×C4×C73#12311yescharacteristic
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—42no—
108C2×Dic73—42no—
109C2×Dic73—42no—
110C2×Dic73—42no—
111C2×Dic73—42no—
112C2×Dic73—81no—
113C2×Dic73—81no—
114C2×Dic73—81no—
115C2×Dic73—81no—
116C8×C73—81no—
117C8×C73—81no—
118#10596831—81no—
119#10596831—81no—
120C22×C73—21no—
121C22×C73—21no—
122C22×C73—21no—
123C22×C73—21no—
124C22×C73—21no—
125C22×C73—21no—
126C22×C73—21no—
127C22×C73—21no—
128C22×C73—44no—
129C22×C73#38111yescharacteristic
130C22×C73#41012yes—
131C4×C73—21no—
132C4×C73—21no—
133C4×C73—21no—
134C4×C73—21no—
135C4×C73—82no—
136Dic73—42no—
137Dic73—42no—
138Dic73—82no—
139#8755—731nomaximal, Sylow
140C2×C73—22no—
141C2×C73—41no—
142C2×C73—41no—
143C2×C73#182011yescharacteristic
144C2×C73#182911yescharacteristic
145C2×C73#183011yescharacteristic
146#2313—731no—
147#1821—731no—
148#1821—731no—
149#1306—731no—
150#1306—731no—
151#1306—731no—
152#1306D7311yescharacteristic
153C73#875511yescharacteristic, complemented, Sylow
154C22×C4⋊C4—731no—
155#407—731no—
156#407—731no—
157#407C2×D7311yescharacteristic
158#407C2×D7311yescharacteristic
159#387—1462no—
160#387—1462no—
161#381—731no—
162#381C2×D7311yescharacteristic
163#380—732no—
164C4×C22⋊C4—732no—
165#343—1462no—
166#343—1462no—
167C23×C4—731no—
168C23×C4—731no—
169C23×C4C22×D7311yescharacteristic
170C2×M16—21no—
171C2×M16—21no—
172C2×M16—1461no—
173C2×M16—1461no—
174C2×C4⋊C4—732no—
175C2×C4⋊C4—732no—
176C2×C4⋊C4—1462no—
177C2×C4⋊C4—1461no—
178C2×C4⋊C4—1461no—
179C2×C4⋊C4—1461no—
180C2×C4⋊C4—1461no—
181C2×C22⋊C4—732no—
182C2×C22⋊C4C4×D7312yes—
183C2×C42—1462no—
184C22⋊C8—21no—
185C22⋊C8—21no—
186C22⋊C8—21no—
187C22⋊C8—21no—
188C22⋊C8—1461no—
189C22⋊C8—1461no—
190C22⋊C8—1461no—
191C22⋊C8—1461no—
192#95—21no—
193#95—21no—
194#95—1462no—
195#95—1462no—
196#95—1461no—
197#95—1461no—
198C24C2×C4×D7311yescharacteristic
199C22×C4—22no—
200C22×C4—42no—
201C22×C4—5841no—
202C22×C4—5841no—
203C22×C4—732no—
204C22×C4—732no—
205C22×C4—1462no—
206C22×C4—1461no—
207C22×C4—1461no—
208C22×C4—1461no—
209C22×C4—1461no—
210C22×C4D4×D7311yescharacteristic
211C22×C4D4×D7311yescharacteristic
212C22×C4#1192402711yescharacteristic
213C22×C4#1192402811yescharacteristic
214C22×C4#1192402811yescharacteristic
215C22×C4#1192402911yescharacteristic
216M16—42no—
217M16—42no—
218M16—2922no—
219M16—2922no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—2921no—
223C2×C8—2921no—
224C4⋊C4—5842no—
225C4⋊C4—1462no—
226C4⋊C4—1462no—
227C4⋊C4—1462no—
228C4⋊C4—1462no—
229C22⋊C4—42no—
230C22⋊C4—2922no—
231C42—5842no—
232C23—22no—
233C23—41no—
234C23—41no—
235C23C22⋊C4×D7311yescharacteristic
236C23#1455654811yescharacteristic
237C23#1455654911yescharacteristic
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—2922no—
248C2×C4—2922no—
249C2×C4—2922no—
250C2×C4—2922no—
251C2×C4—2922no—
252C2×C4—5841no—
253C2×C4—5841no—
254C2×C4—5841no—
255C2×C4—5841no—
256C2×C4—1462no—
257C2×C4—1462no—
258C2×C4#1455657311yescharacteristic
259C2×C4#1455657311yescharacteristic
260C2×C4#1455657611yescharacteristic
261C2×C4#1455657611yescharacteristic
262C8—81no—
263C8—81no—
264C8—5841no—
265C8—5841no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—44no—
275C22#1798844911yescharacteristic
276C22#1798855912yes—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—82no—
282C4—2922no—
283C4—2922no—
284C4—5842no—
285C2—22no—
286C2—41no—
287C2—41no—
288C2#2261000711yescharacteristic
289C2#2261004111yescharacteristic
290C2#2261004411yescharacteristic
subgroupG/H
centerC22#17988449
commutator, prime radicalC24×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#1306C2
socleC22×C73#381
cosocleC23×C4×C73C23
hypercenter#1306D73
hypocenterC73#8755
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
153. C73#8755semidirect

Maximal subgroups

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

subgroupindex
#226125322
#226100092
#226078402
#226078392
C73×#13062
#875573