Finite Group Databasebeta

← #32995390

Subgroups — #32995390

Order 18688.

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

normal subgroups only

This group has 434 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#22612555C211yesmaximal, characteristic
2#22608261C211yesmaximal, characteristic
3#22607876C212yesmaximal, complemented
4#22607874C212yesmaximal, complemented
5C73×#1463C211yesmaximal, characteristic
6C2×#14556550C411yescharacteristic
7C2×#14556550C411yescharacteristic
8#17988551—21no—
9#17988483—21no—
10#17988483—21no—
11#17988460—21no—
12#17988460—21no—
13#17988456C411yescharacteristic
14#17988456C2211yescharacteristic
15#17988452C411yescharacteristic
16#17988452C2211yescharacteristic
17#17988313—21no—
18#17988313C2212yes—
19C22×C4⋊C4×C73C2211yescharacteristic
20#407×C73—21no—
21#324×C73—21no—
22#324×C73C2212yes—
23C2×#11924012—41no—
24#14556550—22no—
25#14556550—22no—
26#14556550—41no—
27#14556550—41no—
28C2×C4⋊Dic73—21no—
29C2×C4⋊Dic73C2×C411yescharacteristic
30C2×C4⋊Dic73C2×C411yescharacteristic
31C2×#11924007—21no—
32C2×#11924007—21no—
33C2×#11924007—21no—
34C2×#11924007—21no—
35C2×C22⋊Dic73—21no—
36C2×C22⋊Dic73—21no—
37C2×C4×Dic73—21no—
38C2×C4×Dic73C2×C411yescharacteristic
39C2×C4×Dic73C2×C411yescharacteristic
40C22⋊#10596831—22no—
41C22⋊#10596831—41no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46C23×C4×C73C2×C411yescharacteristic
47C23×C4×C73D411yescharacteristic
48C23×C4×C73D411yescharacteristic
49C2×M16×C73—41no—
50C2×C4⋊C4×C73—41no—
51C2×C4⋊C4×C73—41no—
52C2×C4⋊C4×C73C2×C411yescharacteristic
53C2×C4⋊C4×C73D411yescharacteristic
54C2×C4⋊C4×C73D411yescharacteristic
55C2×C4⋊C4×C73C2311yescharacteristic
56C22⋊C8×C73—22no—
57C22⋊C8×C73—41no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62#11924012—82no—
63C2×#10596831—42no—
64C4⋊Dic73—24no—
65C4⋊Dic73—41no—
66C4⋊Dic73—41no—
67#11924007—81no—
68#11924007—81no—
69#11924007—81no—
70#11924007—81no—
71C22⋊Dic73—24no—
72C22⋊Dic73—41no—
73C22⋊Dic73—41no—
74C4×Dic73—21no—
75C4×Dic73—21no—
76C4×Dic73—42no—
77C4×Dic73M1612yescomplemented
78C4×Dic73M1612yescomplemented
79C24×C73C22⋊C411yescharacteristic
80C22×C4×C73—21no—
81C22×C4×C73—21no—
82C22×C4×C73—22no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73—21no—
86C22×C4×C73—21no—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73—81no—
90C22×C4×C73—81no—
91C22×C4×C73C22⋊C411yescharacteristic
92C22×C4×C73C22⋊C411yescharacteristic
93C22×C4×C73C22⋊C411yescharacteristic
94C22×C4×C73C22×C411yescharacteristic
95C22×C4×C73C2×D411yescharacteristic
96C22×C4×C73C2×D411yescharacteristic
97M16×C73—82no—
98C2×C8×C73—42no—
99C4⋊C4×C73—41no—
100C4⋊C4×C73—41no—
101C4⋊C4×C73—41no—
102C4⋊C4×C73—41no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—41no—
106C23×C73—41no—
107C23×C73#9911yescharacteristic
108C23×C73#9911yescharacteristic
109C23×C73C2×C22⋊C411yescharacteristic
110C2×C4×C73—22no—
111C2×C4×C73—22no—
112C2×C4×C73—22no—
113C2×C4×C73—22no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—42no—
123C2×C4×C73—42no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73—41no—
128C2×C4×C73—81no—
129C2×C4×C73—81no—
130C2×C4×C73#10112yes—
131C2×C4×C73C2×M1611yescharacteristic
132C2×C4×C73C2×M1611yescharacteristic
133C2×Dic73—22no—
134C2×Dic73—22no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73—42no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C8×C73—82no—
145#10596831—82no—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—42no—
155C22×C73—42no—
156C22×C73#40711yescharacteristic
157C22×C73C2×#9911yescharacteristic
158C22×C73C2×#10111yescharacteristic
159C4×C73—22no—
160C4×C73—21no—
161C4×C73—21no—
162C4×C73—41no—
163C4×C73—41no—
164C4×C73—41no—
165C4×C73—41no—
166Dic73—42no—
167Dic73—42no—
168Dic73—81no—
169Dic73—81no—
170#11514—731nomaximal, Sylow
171C2×C73—21no—
172C2×C73—21no—
173C2×C73—41no—
174C2×C73—41no—
175C2×C73#146311yescharacteristic
176C2×C73#212711yescharacteristic
177C2×C73#213311yescharacteristic
178#2317—731no—
179#1463—731no—
180#1463D7311yescharacteristic
181#1325—732no—
182#1324—732no—
183C73#1151411yescharacteristic, complemented, Sylow
184C2×#117—731no—
185C2×#117—731no—
186C22×C4⋊C4C2×D7311yescharacteristic
187#407—21no—
188#407—1461no—
189#389—1461no—
190#389—1461no—
191#385—1461no—
192#385—1461no—
193#384—731no—
194#384—731no—
195#382—731no—
196#382—731no—
197#324—21no—
198#324—732no—
199#324—1461no—
200#324C2×D7312yes—
201C23×C4C4×D7311yescharacteristic
202C23×C4D29211yescharacteristic
203C23×C4C22⋊D7311yescharacteristic
204C2×M16—41no—
205C2×M16—2921no—
206#117—2921no—
207#117—2921no—
208#117—1462no—
209#117—1462no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—731no—
213C2×C4⋊C4—731no—
214C2×C4⋊C4—1461no—
215C2×C4⋊C4—1461no—
216C2×C4⋊C4—1461no—
217C2×C4⋊C4—1461no—
218C2×C4⋊C4—1461no—
219C2×C4⋊C4C4×D7311yescharacteristic
220C2×C4⋊C4D29211yescharacteristic
221C2×C4⋊C4C22⋊D7311yescharacteristic
222C2×C4⋊C4C22×D7311yescharacteristic
223C2×C22⋊C4—1461no—
224C2×C22⋊C4—1461no—
225C2×C42—731no—
226C2×C42—731no—
227C2×C42—1461no—
228C22⋊C8—22no—
229C22⋊C8—41no—
230C22⋊C8—2921no—
231C22⋊C8—1462no—
232#95—1461no—
233#95—1461no—
234#95—1461no—
235#95—1461no—
236C24#1192400511yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4—1461no—
249C22×C4—1461no—
250C22×C4—1461no—
251C22×C4—1461no—
252C22×C4#1192400511yescharacteristic
253C22×C4#1192400511yescharacteristic
254C22×C4#1192400511yescharacteristic
255C22×C4C2×C4×D7311yescharacteristic
256C22×C4C2×C22⋊D7311yescharacteristic
257C22×C4C2×D29211yescharacteristic
258M16—82no—
259M16—5842no—
260C2×C8—42no—
261C2×C8—2922no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—2921no—
267C4⋊C4—2921no—
268C4⋊C4—5841no—
269C4⋊C4—5841no—
270C4⋊C4—5841no—
271C4⋊C4—5841no—
272C4⋊C4—1464no—
273C22⋊C4—2921no—
274C22⋊C4—2921no—
275C22⋊C4—1464no—
276C42—2922no—
277C42—732no—
278C42—732no—
279C42—1461no—
280C42—1461no—
281C23—21no—
282C23—21no—
283C23—41no—
284C23—41no—
285C23#1455650511yescharacteristic
286C23#1455650511yescharacteristic
287C23C2×#1192400511yescharacteristic
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—2921no—
309C2×C4—2921no—
310C2×C4—2921no—
311C2×C4—2921no—
312C2×C4—2921no—
313C2×C4—2921no—
314C2×C4—2922no—
315C2×C4—2921no—
316C2×C4—2921no—
317C2×C4—1462no—
318C2×C4—1462no—
319C2×C4#1455650912yes—
320C2×C4M16×D7311yescharacteristic
321C2×C4M16×D7311yescharacteristic
322C8—82no—
323C8—5842no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—42no—
333C22—42no—
334C22#1798855011yescharacteristic
335C22C2×#1455650511yescharacteristic
336C22C2×#1455650911yescharacteristic
337C4—22no—
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—2922no—
345C4—2922no—
346C4—5841no—
347C4—5841no—
348C2—21no—
349C2—21no—
350C2—41no—
351C2—41no—
352C2#2260826011yescharacteristic
353C2#2261159811yescharacteristic
354C2#2261161811yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1463C2
socleC22×C73C2×#99
prime radicalC24×C73C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1463D73
hypocenterC73#11514
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. #22607876C2semidirect
4. #22607874C2semidirect
77. C4×Dic73M16semidirect
78. C4×Dic73M16semidirect
183. C73#11514semidirect

Maximal subgroups

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

subgroupindex
#226125552
#226082612
#226078762
#226078742
C73×#14632
#1151473