Finite Group Databasebeta

← #32995643

Subgroups — #32995643

Order 18688.

416 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 83 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#22615127C211yesmaximal, characteristic
2#22608269C211yesmaximal, characteristic
3#22607876C212yesmaximal, complemented
4#22607874C212yesmaximal, complemented
5C73×#1459C211yesmaximal, characteristic
6C2×#14556583C411yescharacteristic
7#17988551—21no—
8#17988510—21no—
9#17988510—21no—
10#17988490C411yescharacteristic
11#17988490C411yescharacteristic
12#17988460—21no—
13#17988460—21no—
14#17988456C2211yescharacteristic
15#17988452C2211yescharacteristic
16C4×C4⋊Dic73C411yescharacteristic
17#17988313C2212yes—
18#17988311—21no—
19C2×C4×D4×C73C2211yescharacteristic
20C2×C22⋊C8×C73—21no—
21#324×C73C2212yes—
22#323×C73—21no—
23C2×#11924012—41no—
24#14556583—41no—
25#14556583—41no—
26C2×C4⋊Dic73—21no—
27C2×C4⋊Dic73C2×C411yescharacteristic
28C2×C4⋊Dic73C2×C411yescharacteristic
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×#11924007—21no—
32C2×#11924007—21no—
33C2×C22⋊Dic73—21no—
34C2×C22⋊Dic73—21no—
35C2×C22⋊Dic73—21no—
36C2×C22⋊Dic73—21no—
37C2×C4×Dic73C2×C411yescharacteristic
38C2×C4×Dic73C2×C411yescharacteristic
39C22⋊#10596831—22no—
40C22⋊#10596831—41no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44C22×D4×C73C2×C411yescharacteristic
45C23×C4×C73D411yescharacteristic
46C23×C4×C73D411yescharacteristic
47C22×C8×C73—41no—
48C4×D4×C73—41no—
49C4×D4×C73—41no—
50C2×C4⋊C4×C73C2311yescharacteristic
51C2×C22⋊C4×C73D411yescharacteristic
52C2×C22⋊C4×C73D411yescharacteristic
53C2×C42×C73C2×C411yescharacteristic
54C22⋊C8×C73—22no—
55C22⋊C8×C73—41no—
56C22×Dic73—21no—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60#11924012—82no—
61C2×#10596831—42no—
62C4⋊Dic73—42no—
63C4⋊Dic73—41no—
64C4⋊Dic73—41no—
65#11924007—42no—
66#11924007—41no—
67#11924007—41no—
68#11924007—81no—
69#11924007—81no—
70C22⋊Dic73—42no—
71C22⋊Dic73—42no—
72C22⋊Dic73—81no—
73C22⋊Dic73—81no—
74C4×Dic73—22no—
75C4×Dic73—22no—
76C24×C73C22⋊C411yescharacteristic
77C24×C73C22⋊C411yescharacteristic
78C2×D4×C73—22no—
79C2×D4×C73—22no—
80C2×D4×C73—41no—
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73—81no—
86C22×C4×C73—81no—
87C22×C4×C73C22⋊C411yescharacteristic
88C22×C4×C73C22⋊C411yescharacteristic
89C22×C4×C73C22×C411yescharacteristic
90C22×C4×C73C2×D411yescharacteristic
91C22×C4×C73C2×D411yescharacteristic
92C2×C8×C73—42no—
93C2×C8×C73—82no—
94C4⋊C4×C73—41no—
95C22⋊C4×C73—41no—
96C22⋊C4×C73—41no—
97C42×C73—21no—
98C42×C73—21no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—41no—
105C23×C73—41no—
106C23×C73—41no—
107C23×C73—41no—
108C23×C73#10112yes—
109C23×C73C2×C22⋊C411yescharacteristic
110D4×C73—44no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—41no—
117C2×C4×C73—42no—
118C2×C4×C73—42no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73—81no—
123C2×C4×C73—81no—
124C2×C4×C73#9911yescharacteristic
125C2×C4×C73#9911yescharacteristic
126C2×C4×C73#13112yes—
127C2×Dic73—22no—
128C2×Dic73—41no—
129C2×Dic73—41no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C8×C73—82no—
140#10596831—82no—
141C22×C73—21no—
142C22×C73—21no—
143C22×C73—22no—
144C22×C73—42no—
145C22×C73—42no—
146C22×C73—41no—
147C22×C73—41no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—81no—
152C22×C73—81no—
153C22×C73#40811yescharacteristic
154C22×C73C2×#9911yescharacteristic
155C22×C73C2×#10111yescharacteristic
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—22no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73—41no—
162Dic73—42no—
163Dic73—81no—
164Dic73—81no—
165Dic73—81no—
166#11572—731nomaximal, Sylow
167C2×C73—21no—
168C2×C73—21no—
169C2×C73—42no—
170C2×C73—81no—
171C2×C73#147211yescharacteristic
172C2×C73#212711yescharacteristic
173C2×C73#213211yescharacteristic
174#2566—731no—
175#1465—731no—
176#1459D7311yescharacteristic
177#1325—732no—
178#1324—732no—
179C73#1157211yescharacteristic, complemented, Sylow
180C2×#125—731no—
181C2×C4×D4C2×D7311yescharacteristic
182#407—1461no—
183C2×C22⋊C8—21no—
184#396—1461no—
185#396—1461no—
186#390—731no—
187#390—731no—
188#385—1461no—
189#385—1461no—
190#384—731no—
191#382—731no—
192C4×C4⋊C4—731no—
193#324—732no—
194#324C2×D7312yes—
195#323—21no—
196#323—1461no—
197C22×D4C4×D7311yescharacteristic
198C23×C4D29211yescharacteristic
199C23×C4C22⋊D7311yescharacteristic
200C2×M16—2921no—
201C22×C8—41no—
202#125—2921no—
203#125—2921no—
204C4×D4—41no—
205C4×D4—41no—
206C2×C4⋊C4—731no—
207C2×C4⋊C4—731no—
208C2×C4⋊C4—1461no—
209C2×C4⋊C4—1461no—
210C2×C4⋊C4—1461no—
211C2×C4⋊C4—1461no—
212C2×C4⋊C4—1461no—
213C2×C4⋊C4C22×D7311yescharacteristic
214C2×C22⋊C4—1461no—
215C2×C22⋊C4—1461no—
216C2×C22⋊C4—1461no—
217C2×C22⋊C4—1461no—
218C2×C22⋊C4D29211yescharacteristic
219C2×C22⋊C4C22⋊D7311yescharacteristic
220C2×C42—731no—
221C2×C42—731no—
222C2×C42C4×D7311yescharacteristic
223C22⋊C8—22no—
224C22⋊C8—41no—
225C22⋊C8—2921no—
226C22⋊C8—1462no—
227#95—1461no—
228#95—1461no—
229#95—1461no—
230C24#1192400511yescharacteristic
231C24#1192400511yescharacteristic
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—41no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—81no—
240C22×C4—81no—
241C22×C4—1461no—
242C22×C4—1461no—
243C22×C4—1461no—
244C22×C4—1461no—
245C22×C4#1192400511yescharacteristic
246C22×C4#1192400511yescharacteristic
247C22×C4C2×C4×D7311yescharacteristic
248C22×C4C2×C22⋊D7311yescharacteristic
249C22×C4C2×D29211yescharacteristic
250M16—5842no—
251C2×C8—42no—
252C2×C8—82no—
253C2×C8—2922no—
254C4⋊C4—41no—
255C4⋊C4—2921no—
256C4⋊C4—2921no—
257C4⋊C4—2922no—
258C4⋊C4—2922no—
259C4⋊C4—2921no—
260C4⋊C4—2921no—
261C4⋊C4—5841no—
262C4⋊C4—5841no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—2922no—
266C22⋊C4—2922no—
267C22⋊C4—5841no—
268C22⋊C4—5841no—
269C42—21no—
270C42—21no—
271C42—1462no—
272C42—1462no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#1455650912yes—
283C23C2×#1192400511yescharacteristic
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—2921no—
299C2×C4—2921no—
300C2×C4—2921no—
301C2×C4—2921no—
302C2×C4—2921no—
303C2×C4—2921no—
304C2×C4—2921no—
305C2×C4—2921no—
306C2×C4—2921no—
307C2×C4—2921no—
308C2×C4—2921no—
309C2×C4—1462no—
310C2×C4#1455650511yescharacteristic
311C2×C4#1455650511yescharacteristic
312C2×C4#1455659712yes—
313C8—82no—
314C8—5842no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—81no—
326C22—81no—
327C22#1798855311yescharacteristic
328C22C2×#1455650511yescharacteristic
329C22C2×#1455650911yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—2922no—
337C4—5841no—
338C4—5841no—
339C4—5841no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#2260829411yescharacteristic
345C2#2261159811yescharacteristic
346C2#2261161411yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1459C2
socleC22×C73C2×#99
prime radicalC22×D4×C73C2×C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1459D73
hypocenterC73#11572
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #22607876C2semidirect
4. #22607874C2semidirect
179. C73#11572semidirect

Maximal subgroups

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

subgroupindex
#226151272
#226082692
#226078762
#226078742
C73×#14592
#1157273