Finite Group Databasebeta

← #32989761

Subgroups — #32989761

Order 18688.

366 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 95 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#22619736C211yesmaximal, characteristic
2#22609946C211yesmaximal, characteristic
3#22608702C211yesmaximal, characteristic
4#22608586C211yesmaximal, characteristic
5#22608496C211yesmaximal, characteristic
6#22607790C211yesmaximal, characteristic
7C73×#1461C211yesmaximal, characteristic
8#17989144C2211yescharacteristic
9#17988894—22no—
10#17988882—21no—
11#17988872—21no—
12#17988627—21no—
13#17988611C2211yescharacteristic
14C2×C4⋊#10596831C2211yescharacteristic
15#17988596—21no—
16C2×#14556515—21no—
17#17988453C2211yescharacteristic
18#17988349—21no—
19#17988338—22no—
20#17988335—21no—
21#17988334—21no—
22#17988325—22no—
23C2×C4×Q8×C73C2211yescharacteristic
24#431×C73C2211yescharacteristic
25#431×C73C2211yescharacteristic
26#324×C73—22no—
27C2×#11924012—21no—
28C22×#10596831—21no—
29#14556591D411yescharacteristic
30#14556591D411yescharacteristic
31#14556583—21no—
32#14556570—21no—
33#14556570—21no—
34C4×Dic146—21no—
35C4×Dic146—21no—
36#14556550—21no—
37C2×C4⋊Dic73—21no—
38#14556524—22no—
39#14556522—22no—
40C4⋊#10596831—21no—
41C4⋊#10596831—21no—
42C4⋊#10596831—21no—
43C4⋊#10596831D412yes—
44#14556515—22no—
45#14556515—22no—
46#14556515—42no—
47#14556498—21no—
48#14556498—21no—
49C22×Q8×C73D411yescharacteristic
50C4×Q8×C73—21no—
51C4×Q8×C73—21no—
52C4×Q8×C73—21no—
53C4×Q8×C73—21no—
54C2×C4⋊C4×C73—21no—
55C2×C4⋊C4×C73D411yescharacteristic
56C2×C42×C73—21no—
57C2×C42×C73C2311yescharacteristic
58C4⋊C8×C73—21no—
59C4⋊C8×C73—21no—
60C22⋊C8×C73—21no—
61C22⋊C8×C73D412yes—
62C4×C8×C73—21no—
63C4×C8×C73—21no—
64C2×Dic146—21no—
65C2×Dic146—21no—
66C22×Dic73—41no—
67#11924012—41no—
68#11924012—41no—
69C2×#10596831—22no—
70C2×#10596831—41no—
71C2×#10596831—41no—
72C2×#10596831—41no—
73C4⋊Dic73—21no—
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73—21no—
77C4⋊Dic73—41no—
78C4⋊Dic73—41no—
79#11924007—41no—
80#11924007—41no—
81C22⋊Dic73—41no—
82C4×Dic73—41no—
83C2×Q8×C73—21no—
84C2×Q8×C73—21no—
85C2×Q8×C73—21no—
86C2×Q8×C73—21no—
87C2×Q8×C73—21no—
88C2×Q8×C73SD1612yes—
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73C2×D411yescharacteristic
92C22×C4×C73C2×D411yescharacteristic
93C22×C4×C73#4111yescharacteristic
94C2×C8×C73—22no—
95C2×C8×C73—41no—
96C4⋊C4×C73—21no—
97C4⋊C4×C73—21no—
98C4⋊C4×C73—41no—
99C4⋊C4×C73—41no—
100C42×C73—41no—
101C42×C73—41no—
102C42×C73C2×D411yescharacteristic
103C42×C73C2×D411yescharacteristic
104C42×C73#4111yescharacteristic
105C42×C73#4111yescharacteristic
106C23×C73#12111yescharacteristic
107Q8×C73—22no—
108Q8×C73—22no—
109Q8×C73—41no—
110Q8×C73—41no—
111C2×C4×C73—22no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—41no—
116C2×C4×C73—41no—
117C2×C4×C73—81no—
118C2×C4×C73#12011yescharacteristic
119C2×C4×C73#12111yescharacteristic
120C2×C4×C73#12111yescharacteristic
121C2×C4×C73#12311yescharacteristic
122C2×C4×C73#12311yescharacteristic
123C2×C4×C73#12411yescharacteristic
124C2×C4×C73C2×SD1611yescharacteristic
125C2×C4×C73#13511yescharacteristic
126C2×C4×C73#13711yescharacteristic
127C2×C4×C73#13711yescharacteristic
128C2×Dic73—41no—
129C2×Dic73—41no—
130C2×Dic73—81no—
131C2×Dic73—81no—
132C2×Dic73—81no—
133Dic146—81no—
134Dic146—81no—
135C8×C73—42no—
136C8×C73—81no—
137#10596831—42no—
138#10596831—81no—
139C22×C73—21no—
140C22×C73—21no—
141C22×C73#39411yescharacteristic
142C22×C73#46511yescharacteristic
143C22×C73#47011yescharacteristic
144C4×C73—21no—
145C4×C73—21no—
146C4×C73—21no—
147C4×C73—21no—
148C4×C73—42no—
149C4×C73—81no—
150C4×C73#44811yescharacteristic
151C4×C73#45211yescharacteristic
152C4×C73#48311yescharacteristic
153C4×C73#48511yescharacteristic
154Dic73—81no—
155Dic73—81no—
156Dic73—161no—
157#10470—731nomaximal, Sylow
158C2×C73—21no—
159C2×C73—21no—
160C2×C73#203511yescharacteristic
161C2×C73#204911yescharacteristic
162C2×C73#205311yescharacteristic
163#3078—731no—
164#1805—731no—
165#1570—731no—
166#1542—731no—
167#1518—731no—
168#1461D7311yescharacteristic
169#1286—731no—
170C73#1047011yescharacteristic, complemented, Sylow
171#533—731no—
172C2×C4×Q8C2×D7311yescharacteristic
173#479—1462no—
174#477—1461no—
175#475—1461no—
176#431C2×D7311yescharacteristic
177#431C2×D7311yescharacteristic
178#428—1461no—
179#423—731no—
180C2×C4⋊C8—731no—
181#419—1461no—
182C2×#103—1461no—
183#382—731no—
184#340—1461no—
185#334—1462no—
186#333—1461no—
187#332—1461no—
188#328—1462no—
189#324—22no—
190C22×Q8D29211yescharacteristic
191C2×M16—1461no—
192C22×C8—1461no—
193C4⋊Q8—731no—
194C4⋊Q8—731no—
195#125—1461no—
196C22⋊Q8—1461no—
197C22⋊Q8—1461no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8—21no—
202C4×Q8—1461no—
203C4×Q8—1461no—
204#117—1461no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—1461no—
207C2×C4⋊C4D29211yescharacteristic
208C2×C42—21no—
209C2×C42C22×D7311yescharacteristic
210#107—1462no—
211#106—1462no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—732no—
215C4⋊C8—1461no—
216C4⋊C8—1461no—
217C4⋊C8—1461no—
218#103—2922no—
219#103—1462no—
220#103—1462no—
221C22⋊C8—21no—
222C22⋊C8C22⋊D7312yes—
223C4×C8—21no—
224C4×C8—21no—
225#95—1461no—
226#95—1461no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—1461no—
233C2×Q8—1461no—
234C2×Q8#1192401712yes—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—2921no—
238C22×C4C2×C22⋊D7311yescharacteristic
239C22×C4C2×D29211yescharacteristic
240C22×C4#1192402811yescharacteristic
241M16—2921no—
242M16—2921no—
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—2921no—
246C2×C8—2921no—
247C2×C8—2921no—
248C2×C8—1462no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—2921no—
254C4⋊C4—2921no—
255C4⋊C4—2921no—
256C4⋊C4—2921no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
260C4⋊C4—1461no—
261C22⋊C4—2921no—
262C42—41no—
263C42—41no—
264C42—2921no—
265C42D4×D7311yescharacteristic
266C42D4×D7311yescharacteristic
267C42#1192402711yescharacteristic
268C42#1192402711yescharacteristic
269C23#1455656511yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274Q8—5841no—
275Q8—5841no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—2921no—
284C2×C4—2921no—
285C2×C4—5841no—
286C2×C4—5841no—
287C2×C4—5841no—
288C2×C4#1455656111yescharacteristic
289C2×C4#1455656211yescharacteristic
290C2×C4#1455656311yescharacteristic
291C2×C4#1455657311yescharacteristic
292C2×C4#1455657511yescharacteristic
293C2×C4#1455657711yescharacteristic
294C2×C4C2×#1192401711yescharacteristic
295C2×C4#1455661311yescharacteristic
296C2×C4#1455662411yescharacteristic
297C2×C4#1455662411yescharacteristic
298C8—42no—
299C8—81no—
300C8—2922no—
301C8—5841no—
302C22—21no—
303C22—21no—
304C22#1798850311yescharacteristic
305C22#1798881611yescharacteristic
306C22#1798884511yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—42no—
312C4—81no—
313C4—5841no—
314C4—5841no—
315C4—11681no—
316C4#1798872811yescharacteristic
317C4#1798875111yescharacteristic
318C4#1798891811yescharacteristic
319C4#1798892911yescharacteristic
320C2—21no—
321C2—21no—
322C2#2261112811yescharacteristic
323C2#2261121011yescharacteristic
324C2#2261123611yescharacteristic
subgroupG/H
centerC22#17988503
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1461C2
socleC22×C73#394
prime radicalC23×C73#121
hypercenter#1461D73
hypocenterC73#10470
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
170. C73#10470semidirect

Maximal subgroups

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

subgroupindex
#226197362
#226099462
#226087022
#226085862
#226084962
#226077902
C73×#14612
#1047073