Finite Group Databasebeta

← #32995404

Subgroups — #32995404

Order 18688.

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

normal subgroups only

This group has 446 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#22612413C211yesmaximal, characteristic
2#22608265C211yesmaximal, characteristic
3#22607880C212yesmaximal
4#22607878C212yesmaximal
5C73×#1464C211yesmaximal, characteristic
6C2×#14556550C411yescharacteristic
7C22×C4×Dic73C411yescharacteristic
8#17988644—21no—
9#17988483—21no—
10#17988483—21no—
11#17988459C411yescharacteristic
12#17988459C411yescharacteristic
13#17988459C2211yescharacteristic
14#17988459C2211yescharacteristic
15C4×#11924007—21no—
16C4×#11924007—21no—
17#17988313—21no—
18#17988311C2212yes—
19C2×#117×C73C2211yescharacteristic
20#432×C73—21no—
21#324×C73—21no—
22#323×C73C2212yes—
23C23×Dic73C2×C411yescharacteristic
24C23×Dic73C2×C411yescharacteristic
25#14556550—22no—
26#14556550—22no—
27C2×C4⋊Dic73—21no—
28C2×#11924007—21no—
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×#11924007—21no—
32C2×C22⋊Dic73C2×C411yescharacteristic
33C2×C22⋊Dic73C2×C411yescharacteristic
34C2×C4×Dic73—21no—
35C2×C4×Dic73—21no—
36C2×C4×Dic73—21no—
37C2×C4×Dic73—41no—
38C2×C4×Dic73—41no—
39C4⋊#10596831—41no—
40C22⋊#10596831—22no—
41#14556502—41no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46C23×C4×C73C2×C411yescharacteristic
47#117×C73—41no—
48#117×C73—41no—
49C2×C4⋊C4×C73D411yescharacteristic
50C2×C4⋊C4×C73D411yescharacteristic
51C2×C22⋊C4×C73C2×C411yescharacteristic
52C2×C22⋊C4×C73C2311yescharacteristic
53C2×C42×C73D411yescharacteristic
54C2×C42×C73D411yescharacteristic
55C4⋊C8×C73—41no—
56C22⋊C8×C73—22no—
57#97×C73—41no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—42no—
63C22×Dic73—42no—
64C22×Dic73—41no—
65C22×Dic73—41no—
66C2×#10596831—42no—
67C4⋊Dic73—24no—
68#11924007—42no—
69#11924007—42no—
70#11924007—42no—
71#11924007—42no—
72C22⋊Dic73—21no—
73C22⋊Dic73—21no—
74C22⋊Dic73M1612yes—
75C22⋊Dic73M1612yes—
76C4×Dic73—24no—
77C4×Dic73—42no—
78C4×Dic73—41no—
79C4×Dic73—41no—
80C24×C73C22×C411yescharacteristic
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73—22no—
86C22×C4×C73C22⋊C411yescharacteristic
87C22×C4×C73C22⋊C411yescharacteristic
88C22×C4×C73C22⋊C411yescharacteristic
89C22×C4×C73C22⋊C411yescharacteristic
90C22×C4×C73C2×D411yescharacteristic
91C22×C4×C73C2×D411yescharacteristic
92C2×C8×C73—42no—
93C4⋊C4×C73—41no—
94C4⋊C4×C73—41no—
95C22⋊C4×C73—41no—
96C22⋊C4×C73—41no—
97C42×C73—21no—
98C42×C73—21no—
99C42×C73—21no—
100C42×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—41no—
104C23×C73—41no—
105C23×C73C2×C22⋊C411yescharacteristic
106C23×C73C2×M1611yescharacteristic
107C23×C73C2×M1611yescharacteristic
108C2×C4×C73—22no—
109C2×C4×C73—22no—
110C2×C4×C73—22no—
111C2×C4×C73—22no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
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—41no—
121C2×C4×C73—41no—
122C2×C4×C73—41no—
123C2×C4×C73—41no—
124C2×C4×C73#9911yescharacteristic
125C2×C4×C73#9911yescharacteristic
126C2×C4×C73#10112yes—
127C2×Dic73—22no—
128C2×Dic73—22no—
129C2×Dic73—22no—
130C2×Dic73—22no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—42no—
138C2×Dic73—42no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73—42no—
142C2×Dic73—42no—
143C8×C73—82no—
144#10596831—82no—
145C22×C73—21no—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—42no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73#40711yescharacteristic
155C22×C73C2×#9911yescharacteristic
156C22×C73C2×#10111yescharacteristic
157C4×C73—21no—
158C4×C73—21no—
159C4×C73—22no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73—41no—
164Dic73—42no—
165Dic73—42no—
166Dic73—42no—
167Dic73—42no—
168#11518—731nomaximal, Sylow
169C2×C73—21no—
170C2×C73—21no—
171C2×C73—41no—
172C2×C73—41no—
173C2×C73#146311yescharacteristic
174C2×C73#212011yescharacteristic
175C2×C73#212011yescharacteristic
176#2296—731no—
177#1464—731no—
178#1464D7311yescharacteristic
179#1326—732no—
180#1326—732no—
181C73#1151811yescharacteristic, complemented, Sylow
182C2×#117—731no—
183C2×#117C2×D7311yescharacteristic
184C22×C42—731no—
185#432—21no—
186#432—1461no—
187#389—1461no—
188#389—1461no—
189#385—731no—
190#385—731no—
191#385—731no—
192#385—731no—
193C4×C4⋊C4—1461no—
194C4×C4⋊C4—1461no—
195#324—21no—
196#324—1461no—
197#323—732no—
198#323C2×D7312yes—
199C23×C4—731no—
200C23×C4—731no—
201C23×C4C4×D7311yescharacteristic
202#117—41no—
203#117—41no—
204#117—1462no—
205#117—1462no—
206C2×C4⋊C4—1461no—
207C2×C4⋊C4—1461no—
208C2×C4⋊C4—1461no—
209C2×C4⋊C4—1461no—
210C2×C4⋊C4—1461no—
211C2×C4⋊C4D29211yescharacteristic
212C2×C4⋊C4C22⋊D7311yescharacteristic
213C2×C22⋊C4—731no—
214C2×C22⋊C4—731no—
215C2×C22⋊C4C4×D7311yescharacteristic
216C2×C22⋊C4C22×D7311yescharacteristic
217C2×C42—2921no—
218C2×C42—2921no—
219C2×C42—1461no—
220C2×C42—1461no—
221C2×C42—1461no—
222C2×C42D29211yescharacteristic
223C2×C42C22⋊D7311yescharacteristic
224C4⋊C8—41no—
225C4⋊C8—2921no—
226C22⋊C8—22no—
227C22⋊C8—1462no—
228#97—41no—
229#97—2921no—
230#95—1461no—
231#95—1461no—
232#95—1461no—
233#95—1461no—
234C24C2×C4×D7311yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—2921no—
241C22×C4—2921no—
242C22×C4—2922no—
243C22×C4—2922no—
244C22×C4—1461no—
245C22×C4—1461no—
246C22×C4—1461no—
247C22×C4—1461no—
248C22×C4#1192400511yescharacteristic
249C22×C4#1192400511yescharacteristic
250C22×C4#1192400511yescharacteristic
251C22×C4#1192400511yescharacteristic
252C22×C4C2×C22⋊D7311yescharacteristic
253C22×C4C2×D29211yescharacteristic
254C2×C8—42no—
255C2×C8—2922no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—2922no—
259C4⋊C4—2922no—
260C4⋊C4—2922no—
261C4⋊C4—2922no—
262C4⋊C4—1464no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—732no—
266C22⋊C4—732no—
267C22⋊C4—1461no—
268C22⋊C4—1461no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—2922no—
274C42—2921no—
275C42—2921no—
276C42—1464no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23C2×#1192400511yescharacteristic
282C23M16×D7311yescharacteristic
283C23M16×D7311yescharacteristic
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—2921no—
301C2×C4—2921no—
302C2×C4—2921no—
303C2×C4—2921no—
304C2×C4—2921no—
305C2×C4—2921no—
306C2×C4—2922no—
307C2×C4—2922no—
308C2×C4—2921no—
309C2×C4—2921no—
310C2×C4—2922no—
311C2×C4—2922no—
312C2×C4—1462no—
313C2×C4—1462no—
314C2×C4—1462no—
315C2×C4—1462no—
316C2×C4#1455650511yescharacteristic
317C2×C4#1455650511yescharacteristic
318C2×C4#1455650912yes—
319C8—82no—
320C8—5842no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—41no—
326C22—41no—
327C22—42no—
328C22—41no—
329C22—41no—
330C22#1798855011yescharacteristic
331C22C2×#1455650511yescharacteristic
332C22C2×#1455650911yescharacteristic
333C4—21no—
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—2922no—
341C4—2922no—
342C4—2922no—
343C4—2922no—
344C2—21no—
345C2—21no—
346C2—41no—
347C2—41no—
348C2#2260826011yescharacteristic
349C2#2261157011yescharacteristic
350C2#2261157311yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutator, prime radicalC24×C73C22×C4
FrattiniC2×C22⋊C4C22×D73
FittingC73×#1464C2
socleC22×C73C2×#99
cosocleC2×C22⋊C4×C73C23
hypercenter#1464D73
hypocenterC73#11518
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
181. C73#11518semidirect

Maximal subgroups

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

subgroupindex
#226124132
#226082652
#226078802
#226078782
C73×#14642
#1151873