Finite Group Databasebeta

← #32988976

Subgroups — #32988976

Order 18688.

640 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 109 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#22609865C212yesmaximal
2#22608201C211yesmaximal, characteristic
3#22607809C212yesmaximal
4#22607774C211yesmaximal, characteristic
5C73×#2646C211yesmaximal, characteristic
6C23×Dic146C2211yescharacteristic
7C2×#14556514—22no—
8C2×#14556514—22no—
9C2×C22⋊#10596831C2212yes—
10C2×#14556498—22no—
11C2×#14556498C2211yescharacteristic
12#400×C73—22no—
13#398×C73—22no—
14#385×C73—22no—
15#380×C73C2212yes—
16C2×#95×C73C2211yescharacteristic
17C22×Dic146—22no—
18C22×Dic146—21no—
19C22×Dic146—22no—
20C22×Dic146—44no—
21C22×Dic146Q812yes—
22C23×Dic73—21no—
23C23×Dic73—21no—
24C22×#10596831—22no—
25#14556514—44no—
26#14556514—44no—
27C22⋊#10596831—22no—
28C22⋊#10596831—22no—
29#14556498—22no—
30#14556498—44no—
31C23×C4×C73D412yes—
32C23×C4×C73C2311yescharacteristic
33C2×C4⋊C4×C73—22no—
34C2×C4⋊C4×C73—22no—
35C2×C4⋊C4×C73D412yes—
36C2×C4⋊C4×C73D412yes—
37C2×C22⋊C4×C73—22no—
38#95×C73—22no—
39#95×C73—22no—
40#95×C73—22no—
41#95×C73—22no—
42C2×Dic146—24no—
43C2×Dic146—24no—
44C2×Dic146—24no—
45C2×Dic146—44no—
46C2×Dic146—48no—
47C2×Dic146—44no—
48C2×Dic146—42no—
49C2×Dic146—42no—
50C2×Dic146—42no—
51C22×Dic73—24no—
52C22×Dic73—22no—
53C22×Dic73—22no—
54C22×Dic73—42no—
55C22×Dic73—41no—
56C22×Dic73—41no—
57C22×Dic73—42no—
58C22×Dic73—41no—
59C22×Dic73—41no—
60C22×Dic73—42no—
61C2×#10596831—42no—
62C2×#10596831—42no—
63C2×#10596831—42no—
64C24×C73C2×D411yescharacteristic
65C22×C4×C73—22no—
66C22×C4×C73—22no—
67C22×C4×C73—22no—
68C22×C4×C73—22no—
69C22×C4×C73—22no—
70C22×C4×C73—42no—
71C22×C4×C73—42no—
72C22×C4×C73—42no—
73C22×C4×C73C2×D412yes—
74C22×C4×C73C2×Q811yescharacteristic
75C22×C4×C73#4112yes—
76C22×C4×C73#4111yescharacteristic
77C4⋊C4×C73—42no—
78C4⋊C4×C73—42no—
79C4⋊C4×C73—82no—
80C4⋊C4×C73—82no—
81C22⋊C4×C73—42no—
82C22⋊C4×C73—42no—
83C23×C73—21no—
84C23×C73—21no—
85C23×C73—22no—
86C23×C73#12011yescharacteristic
87C23×C73C22⋊Q811yescharacteristic
88C23×C73#12411yescharacteristic
89C23×C73#13512yes—
90C23×C73#13712yes—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—41no—
94C2×C4×C73—41no—
95C2×C4×C73—42no—
96C2×C4×C73—44no—
97C2×C4×C73—42no—
98C2×C4×C73—42no—
99C2×C4×C73—42no—
100C2×C4×C73—42no—
101C2×C4×C73—42no—
102C2×C4×C73—42no—
103C2×C4×C73—42no—
104C2×C4×C73—42no—
105C2×C4×C73—42no—
106C2×C4×C73—82no—
107C2×C4×C73C22⋊Q812yes—
108C2×C4×C73#12412yes—
109C2×Dic73—24no—
110C2×Dic73—42no—
111C2×Dic73—44no—
112C2×Dic73—42no—
113C2×Dic73—44no—
114C2×Dic73—44no—
115C2×Dic73—42no—
116C2×Dic73—82no—
117C2×Dic73—81no—
118C2×Dic73—81no—
119Dic146—28no—
120Dic146—44no—
121Dic146—44no—
122Dic146—44no—
123#10596831—82no—
124C22×C73—22no—
125C22×C73—22no—
126C22×C73—22no—
127C22×C73—22no—
128C22×C73—21no—
129C22×C73—21no—
130C22×C73—21no—
131C22×C73—21no—
132C22×C73#39311yescharacteristic
133C22×C73#45212yes—
134C22×C73#45511yescharacteristic
135C22×C73#45611yescharacteristic
136C22×C73B(4,𝔽2)12yes—
137C22×C73#47912yes—
138C22×C73#48811yescharacteristic
139C22×C73#49111yescharacteristic
140C4×C73—22no—
141C4×C73—22no—
142C4×C73—82no—
143C4×C73—82no—
144C4×C73—82no—
145Dic73—44no—
146Dic73—82no—
147#10345—731nomaximal, Sylow
148C2×C73—21no—
149C2×C73—22no—
150C2×C73—21no—
151C2×C73#160312yes—
152C2×C73#160612yes—
153C2×C73#202611yescharacteristic
154C2×C73#202811yescharacteristic
155C2×C73#202911yescharacteristic
156#2646D7311yescharacteristic
157#1787—732no—
158#1446—731no—
159#1294—732no—
160#1280—731no—
161C73#1034511yescharacteristic, complemented, Sylow
162C23×Q8—731no—
163C2×#103—1462no—
164C2×#103—1462no—
165C2×C22⋊C8—732no—
166#400—22no—
167#398—22no—
168#385—22no—
169#380C2×D7312yes—
170C2×#95—731no—
171C2×#95—1462no—
172C2×#95C2×D7311yescharacteristic
173C22×Q8—2924no—
174C22×Q8—732no—
175C22×Q8—1462no—
176C22×Q8—1462no—
177C22×Q8—1461no—
178C23×C4—1461no—
179C23×C4—1461no—
180C23×C4C22⋊D7312yes—
181C23×C4C22×D7311yescharacteristic
182C22×C8—1462no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4C22⋊D7312yes—
186C2×C4⋊C4C22⋊D7312yes—
187C2×C22⋊C4—22no—
188#103—2924no—
189#103—2924no—
190C22⋊C8—1462no—
191C22⋊C8—1462no—
192#95—22no—
193#95—22no—
194#95—22no—
195#95—22no—
196#95—2924no—
197#95—1462no—
198C24C2×C22⋊D7311yescharacteristic
199C2×Q8—2922no—
200C2×Q8—2922no—
201C2×Q8—2928no—
202C2×Q8—2924no—
203C2×Q8—2924no—
204C2×Q8—2922no—
205C2×Q8—1464no—
206C2×Q8—1464no—
207C2×Q8—1464no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—2922no—
217C22×C4—2921no—
218C22×C4—2921no—
219C22×C4—2922no—
220C22×C4—2921no—
221C22×C4—2921no—
222C22×C4—2922no—
223C22×C4—1462no—
224C22×C4—1464no—
225C22×C4—1462no—
226C22×C4C2×C22⋊D7312yes—
227C22×C4Q8×D7311yescharacteristic
228C22×C4#1192402912yes—
229C22×C4#1192402911yescharacteristic
230C2×C8—2922no—
231C2×C8—2922no—
232C2×C8—2922no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—82no—
236C4⋊C4—82no—
237C22⋊C4—42no—
238C22⋊C4—42no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23#1455656011yescharacteristic
243C23#1455656711yescharacteristic
244C23#1455658011yescharacteristic
245C23#1455661112yes—
246C23#1455662112yes—
247Q8—2924no—
248Q8—2924no—
249Q8—2924no—
250Q8—1468no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—82no—
267C2×C4—2924no—
268C2×C4—2922no—
269C2×C4—2922no—
270C2×C4—2924no—
271C2×C4—2922no—
272C2×C4—2924no—
273C2×C4—5842no—
274C2×C4—5841no—
275C2×C4—5841no—
276C2×C4—1464no—
277C2×C4#1455656712yes—
278C2×C4#1455658012yes—
279C8—5842no—
280C22—22no—
281C22—22no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—22no—
287C22—22no—
288C22#1798849811yescharacteristic
289C22#1798874912yes—
290C22#1798876511yescharacteristic
291C22#1798877011yescharacteristic
292C22#1798877412yes—
293C22#1798889112yes—
294C22#1798894411yescharacteristic
295C22#1798895711yescharacteristic
296C4—22no—
297C4—22no—
298C4—82no—
299C4—82no—
300C4—82no—
301C4—2924no—
302C4—5842no—
303C2—21no—
304C2—22no—
305C2—21no—
306C2#2260889412yes—
307C2#2260891112yes—
308C2#2261107911yescharacteristic
309C2#2261108911yescharacteristic
310C2#2261109411yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC23×C4×C73C23
FrattiniC23×C4C22×D73
FittingC73×#2646C2
socleC23×C73#120
prime radicalC24×C73C2×D4
hypercenter#2646D73
hypocenterC73#10345
LCSG ▷ C23×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2646

Complements

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

NH ≅ G/Ntype
161. C73#10345semidirect

Maximal subgroups

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

subgroupindex
#226098652
#226082012
#226078092
#226077742
C73×#26462
#1034573