Finite Group Databasebeta

← #32996570

Subgroups — #32996570

Order 18688.

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

normal subgroups only

This group has 464 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
1#22614239C211yesmaximal, characteristic
2#22608269C211yesmaximal, characteristic
3#22607936C214yesmaximal, complemented
4C4×#100×C73C211yesmaximal, characteristic
5C2×#14556572—21no—
6C22×C4⋊Dic73C411yescharacteristic
7#17988551—21no—
8#17988517C2212yes—
9#17988512C412yes—
10#17988485—21no—
11#17988448—21no—
12#17988447—21no—
13#17988447C411yescharacteristic
14#17988313C2212yes—
15#17988311—21no—
16C2×C4×D4×C73C2211yescharacteristic
17C2×#100×C73—21no—
18C4×M16×C73—21no—
19#343×C73C2212yes—
20C23×Dic73—21no—
21C2×#11924012—41no—
22#14556572—44no—
23C2×C4⋊Dic73—21no—
24C2×C4⋊Dic73—21no—
25C2×C4⋊Dic73—41no—
26C2×C4⋊Dic73—41no—
27C2×C4⋊Dic73C2×C412yes—
28C2×#11924007—22no—
29C2×C22⋊Dic73—22no—
30C2×C22⋊Dic73—21no—
31C22⋊#10596831—22no—
32C22⋊#10596831—41no—
33#14556498—22no—
34#14556498—22no—
35#14556498C2×C412yes—
36C22×D4×C73D411yescharacteristic
37C23×C4×C73C2×C411yescharacteristic
38C23×C4×C73D411yescharacteristic
39C2×M16×C73—22no—
40C4×D4×C73—41no—
41C4×D4×C73—41no—
42C2×C4⋊C4×C73C2311yescharacteristic
43C2×C22⋊C4×C73C2×C411yescharacteristic
44C2×C22⋊C4×C73D411yescharacteristic
45C2×C42×C73D411yescharacteristic
46#100×C73—24no—
47#97×C73—41no—
48C4×C8×C73—41no—
49C22×Dic73—22no—
50C22×Dic73—22no—
51C22×Dic73—42no—
52C22×Dic73—42no—
53C22×Dic73—42no—
54#11924012—82no—
55C2×#10596831—42no—
56C4⋊Dic73—42no—
57C4⋊Dic73—41no—
58C4⋊Dic73—41no—
59C4⋊Dic73—42no—
60#11924007—44no—
61C22⋊Dic73—42no—
62C22⋊Dic73—44no—
63C24×C73C22⋊C411yescharacteristic
64C24×C73C22⋊C411yescharacteristic
65C2×D4×C73—22no—
66C2×D4×C73—22no—
67C2×D4×C73—41no—
68C22×C4×C73—21no—
69C22×C4×C73—21no—
70C22×C4×C73—21no—
71C22×C4×C73—21no—
72C22×C4×C73—42no—
73C22×C4×C73—42no—
74C22×C4×C73C22⋊C411yescharacteristic
75C22×C4×C73C22⋊C411yescharacteristic
76C22×C4×C73C22×C411yescharacteristic
77C22×C4×C73C2×D411yescharacteristic
78C22×C4×C73C2×D411yescharacteristic
79M16×C73—24no—
80M16×C73—42no—
81C2×C8×C73—42no—
82C4⋊C4×C73—41no—
83C22⋊C4×C73—41no—
84C22⋊C4×C73—41no—
85C42×C73—21no—
86C42×C73—21no—
87C23×C73—21no—
88C23×C73—21no—
89C23×C73—21no—
90C23×C73—21no—
91C23×C73—21no—
92C23×C73—41no—
93C23×C73—41no—
94C23×C73—41no—
95C23×C73—41no—
96C23×C73#10412yes—
97C23×C73C2×C22⋊C411yescharacteristic
98D4×C73—44no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—22no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—42no—
106C2×C4×C73—42no—
107C2×C4×C73—42no—
108C2×C4×C73—41no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—81no—
112C2×C4×C73#9911yescharacteristic
113C2×C4×C73#9911yescharacteristic
114C2×C4×C73AGL(1,ℤ/8)12yes—
115C2×Dic73—42no—
116C2×Dic73—42no—
117C2×Dic73—42no—
118C2×Dic73—42no—
119C2×Dic73—42no—
120C2×Dic73—42no—
121C2×Dic73—84no—
122C8×C73—44no—
123#10596831—82no—
124C22×C73—21no—
125C22×C73—21no—
126C22×C73—22no—
127C22×C73—42no—
128C22×C73—42no—
129C22×C73—42no—
130C22×C73—41no—
131C22×C73—41no—
132C22×C73—41no—
133C22×C73—41no—
134C22×C73—41no—
135C22×C73—81no—
136C22×C73C2×#9911yescharacteristic
137C22×C73#41811yescharacteristic
138C22×C73C2×#10411yescharacteristic
139C4×C73—21no—
140C4×C73—22no—
141C4×C73—41no—
142C4×C73—41no—
143C4×C73—41no—
144C4×C73#35212yes—
145Dic73—82no—
146Dic73—82no—
147#11780—731nomaximal, Sylow
148C2×C73—21no—
149C2×C73—21no—
150C2×C73—42no—
151C2×C73—81no—
152C2×C73#150711yescharacteristic
153C2×C73C2×#35211yescharacteristic
154C2×C73#213511yescharacteristic
155#2486—731no—
156C4×#100D7311yescharacteristic
157#1465—731no—
158#1346—734no—
159C73#1178011yescharacteristic, complemented, Sylow
160C2×#123—1461no—
161C2×C4×D4C2×D7311yescharacteristic
162C22×C4⋊C4—731no—
163C2×#100—21no—
164#407—1461no—
165C4×M16—21no—
166#398—732no—
167#397—732no—
168#389—1461no—
169#381—1461no—
170#380—731no—
171#380—1461no—
172#343C2×D7312yes—
173#324—732no—
174#323—1461no—
175C22×D4C22⋊D7311yescharacteristic
176C23×C4—1461no—
177C23×C4C4×D7311yescharacteristic
178C23×C4D29211yescharacteristic
179C2×M16—22no—
180C2×M16—2921no—
181#123—2924no—
182C4×D4—41no—
183C4×D4—41no—
184C2×C4⋊C4—2921no—
185C2×C4⋊C4—2921no—
186C2×C4⋊C4—732no—
187C2×C4⋊C4—1461no—
188C2×C4⋊C4—1461no—
189C2×C4⋊C4—1462no—
190C2×C4⋊C4C22×D7311yescharacteristic
191C2×C22⋊C4—1461no—
192C2×C22⋊C4—1462no—
193C2×C22⋊C4C4×D7311yescharacteristic
194C2×C22⋊C4D29211yescharacteristic
195C2×C42C22⋊D7311yescharacteristic
196#100—24no—
197C22⋊C8—2921no—
198C22⋊C8—1462no—
199#97—41no—
200C4×C8—41no—
201#95—732no—
202#95—1462no—
203#95—1462no—
204C24#1192400511yescharacteristic
205C24#1192400511yescharacteristic
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—41no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—2922no—
216C22×C4—2922no—
217C22×C4—2922no—
218C22×C4—1462no—
219C22×C4—1462no—
220C22×C4#1192400511yescharacteristic
221C22×C4#1192400511yescharacteristic
222C22×C4C2×C4×D7311yescharacteristic
223C22×C4C2×C22⋊D7311yescharacteristic
224C22×C4C2×D29211yescharacteristic
225M16—24no—
226M16—42no—
227M16—5842no—
228C2×C8—42no—
229C2×C8—2922no—
230C4⋊C4—41no—
231C4⋊C4—2922no—
232C4⋊C4—2922no—
233C4⋊C4—2921no—
234C4⋊C4—2921no—
235C4⋊C4—2924no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—2922no—
239C22⋊C4—2924no—
240C42—21no—
241C42—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23#1455651912yes—
252C23C2×#1192400511yescharacteristic
253D4—44no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—81no—
267C2×C4—2922no—
268C2×C4—2922no—
269C2×C4—2922no—
270C2×C4—2922no—
271C2×C4—2922no—
272C2×C4—2922no—
273C2×C4—5844no—
274C2×C4#1455650511yescharacteristic
275C2×C4#1455650511yescharacteristic
276C2×C4#1455661612yes—
277C8—44no—
278C8—5842no—
279C22—21no—
280C22—21no—
281C22—22no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—81no—
291C22C2×#1455650511yescharacteristic
292C22#1798859111yescharacteristic
293C22C2×#1455651911yescharacteristic
294C4—22no—
295C4—21no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—5842no—
300C4—5842no—
301C4#1798837812yes—
302C2—21no—
303C2—21no—
304C2—42no—
305C2—81no—
306C2#2260844611yescharacteristic
307C2C2×#1798837811yescharacteristic
308C2#2261162511yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC4×#100×C73C2
socleC22×C73C2×#99
prime radicalC22×D4×C73D4
cosocleC2×C4⋊C4×C73C23
hypercenterC4×#100D73
hypocenterC73#11780
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
3. #22607936C2semidirect
159. C73#11780semidirect

Maximal subgroups

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

subgroupindex
#226142392
#226082692
#226079362
C4×#100×C732
#1178073