Finite Group Databasebeta

← #32995639

Subgroups — #32995639

Order 18688.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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#22615119C211yesmaximal, characteristic
2#22608273C211yesmaximal, characteristic
3#22608253C211yesmaximal, characteristic
4#22607877C211yesmaximal, characteristic
5#22607874C211yesmaximal, characteristic
6#22607874C211yesmaximal, characteristic
7C73×#1325C211yesmaximal, characteristic
8C2×#14556582C411yescharacteristic
9C2×#14556556C2211yescharacteristic
10#17988641—21no—
11#17988637—21no—
12#17988518—21no—
13#17988518—21no—
14#17988493C411yescharacteristic
15#17988492C411yescharacteristic
16#17988473—21no—
17#17988473—21no—
18#17988452C2211yescharacteristic
19C4×#11924007C411yescharacteristic
20#17988313C2211yescharacteristic
21#17988313C2211yescharacteristic
22#17988312—21no—
23#17988312—21no—
24#384×C73C2211yescharacteristic
25#324×C73C2211yescharacteristic
26#324×C73C2211yescharacteristic
27C22×Dic146C2×C411yescharacteristic
28#14556582—41no—
29#14556582—41no—
30#14556556—41no—
31#14556556—41no—
32C2×C4⋊Dic73—21no—
33C2×C4⋊Dic73C2×C411yescharacteristic
34C2×#11924007—21no—
35C2×#11924007—21no—
36C2×#11924007D411yescharacteristic
37C2×#11924007D411yescharacteristic
38C2×C4×Dic73C2×C411yescharacteristic
39C2×C4×Dic73C2×C411yescharacteristic
40C2×C4×Dic73D411yescharacteristic
41C2×C4×Dic73D411yescharacteristic
42#14556520—41no—
43#14556520—41no—
44C22⋊#10596831—21no—
45C22⋊#10596831—21no—
46#14556501—41no—
47C8×Dic73—41no—
48#14556498—21no—
49#14556498—21no—
50#14556498—21no—
51#14556498—21no—
52#14556498—21no—
53#14556498—21no—
54#14556498—21no—
55C2×C4⋊C4×C73—21no—
56C2×C4⋊C4×C73—21no—
57C2×C4⋊C4×C73C2×C411yescharacteristic
58C2×C4⋊C4×C73C2311yescharacteristic
59C2×C42×C73C2×C411yescharacteristic
60C22⋊C8×C73—21no—
61C22⋊C8×C73—21no—
62C2×Dic146—21no—
63C2×Dic146—21no—
64C2×Dic146—22no—
65C2×Dic146—41no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73C22⋊C411yescharacteristic
69C22×Dic73C22⋊C411yescharacteristic
70C22×Dic73C22⋊C411yescharacteristic
71C22×Dic73C22⋊C411yescharacteristic
72C2×#10596831—41no—
73C2×#10596831—41no—
74C4⋊Dic73—41no—
75C4⋊Dic73—41no—
76C4⋊Dic73—41no—
77#11924007—41no—
78#11924007—41no—
79#11924007—42no—
80#11924007—42no—
81C4×Dic73—21no—
82C4×Dic73—21no—
83C4×Dic73—21no—
84C4×Dic73—21no—
85C4×Dic73—21no—
86C4×Dic73—21no—
87C4×Dic73—21no—
88C4×Dic73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73C22×C411yescharacteristic
92C22×C4×C73C2×D411yescharacteristic
93C22×C4×C73C2×D411yescharacteristic
94C2×C8×C73—41no—
95C2×C8×C73—41no—
96C4⋊C4×C73—41no—
97C4⋊C4×C73—41no—
98C4⋊C4×C73—42no—
99C4⋊C4×C73—42no—
100C42×C73—21no—
101C42×C73—21no—
102C23×C73C2×C22⋊C411yescharacteristic
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—22no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—41no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73#13111yescharacteristic
116C2×C4×C73#13111yescharacteristic
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—41no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126C2×Dic73—41no—
127C2×Dic73—42no—
128C2×Dic73—41no—
129C2×Dic73—41no—
130C2×Dic73#9911yescharacteristic
131C2×Dic73#9911yescharacteristic
132C2×Dic73#10112yes—
133Dic146—42no—
134Dic146—42no—
135C8×C73—81no—
136C8×C73—81no—
137#10596831—81no—
138#10596831—81no—
139C22×C73—21no—
140C22×C73—21no—
141C22×C73#40811yescharacteristic
142C22×C73C2×#9911yescharacteristic
143C22×C73C2×#10111yescharacteristic
144C4×C73—21no—
145C4×C73—21no—
146C4×C73—42no—
147C4×C73—41no—
148C4×C73—41no—
149C4×C73—81no—
150Dic73—21no—
151Dic73—21no—
152Dic73—22no—
153Dic73—41no—
154Dic73—41no—
155Dic73—81no—
156Dic73—81no—
157#11571—731nomaximal, Sylow
158C2×C73—21no—
159C2×C73—21no—
160C2×C73#147211yescharacteristic
161C2×C73#212611yescharacteristic
162C2×C73#213311yescharacteristic
163#2565—731no—
164#1467—731no—
165#1461—731no—
166#1325—731no—
167#1325D7311yescharacteristic
168#1324—731no—
169#1324—731no—
170C73#1157111yescharacteristic, complemented, Sylow
171C2×#125—731no—
172C2×C4×Q8—731no—
173#432—1461no—
174#431—1461no—
175#398—1461no—
176#398—1461no—
177#391—731no—
178#391—731no—
179#387—1461no—
180#387—1461no—
181#384C2×D7311yescharacteristic
182#382—731no—
183C4×C4⋊C4—731no—
184#324—731no—
185#324—731no—
186#324—1461no—
187#324—1461no—
188#324C2×D7311yescharacteristic
189#324C2×D7311yescharacteristic
190C22×Q8—731no—
191#125—2921no—
192#125—2921no—
193C4×Q8—2921no—
194C4×Q8—2921no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—731no—
198C2×C4⋊C4—731no—
199C2×C4⋊C4—731no—
200C2×C4⋊C4—1461no—
201C2×C4⋊C4—1461no—
202C2×C4⋊C4—1461no—
203C2×C4⋊C4C4×D7311yescharacteristic
204C2×C4⋊C4C22×D7311yescharacteristic
205C2×C42—731no—
206C2×C42—731no—
207C2×C42—731no—
208C2×C42—731no—
209C2×C42C4×D7311yescharacteristic
210C4⋊C8—2921no—
211C4⋊C8—2921no—
212C22⋊C8—21no—
213C22⋊C8—21no—
214C22⋊C8—1461no—
215C22⋊C8—1461no—
216#97—2921no—
217C4×C8—2921no—
218#95—1461no—
219#95—1461no—
220#95—1461no—
221#95—1461no—
222#95—1461no—
223#95—1461no—
224#95—1461no—
225C2×Q8—2921no—
226C2×Q8—1462no—
227C2×Q8—1461no—
228C2×Q8—1461no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—731no—
232C22×C4—731no—
233C22×C4—731no—
234C22×C4—731no—
235C22×C4—1461no—
236C22×C4—1461no—
237C22×C4C2×C4×D7311yescharacteristic
238C22×C4D4×D7311yescharacteristic
239C22×C4D4×D7311yescharacteristic
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—2921no—
243C2×C8—2921no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—2921no—
249C4⋊C4—2922no—
250C4⋊C4—2921no—
251C4⋊C4—2921no—
252C4⋊C4—2921no—
253C4⋊C4—2921no—
254C4⋊C4—2922no—
255C42—21no—
256C42—21no—
257C42—1461no—
258C42—1461no—
259C42—1461no—
260C42—1461no—
261C42—1461no—
262C42—1461no—
263C42—1461no—
264C42—1461no—
265C23C22⋊C4×D7311yescharacteristic
266Q8—2922no—
267Q8—2922no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—2921no—
281C2×C4—2921no—
282C2×C4—2921no—
283C2×C4—2922no—
284C2×C4—2921no—
285C2×C4—2921no—
286C2×C4—2921no—
287C2×C4—731no—
288C2×C4—731no—
289C2×C4—732no—
290C2×C4—1461no—
291C2×C4—1461no—
292C2×C4—1461no—
293C2×C4—1461no—
294C2×C4—1461no—
295C2×C4—1461no—
296C2×C4#1455659711yescharacteristic
297C2×C4#1455659911yescharacteristic
298C8—81no—
299C8—81no—
300C8—5841no—
301C8—5841no—
302C22—21no—
303C22—21no—
304C22#1798855211yescharacteristic
305C22#99×D7311yescharacteristic
306C22#101×D7311yescharacteristic
307C4—21no—
308C4—21no—
309C4—42no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4—2921no—
314C4—2921no—
315C4—5841no—
316C4—5841no—
317C4—1461no—
318C4—1461no—
319C4—1462no—
320C2—21no—
321C2—21no—
322C2#2260829311yescharacteristic
323C2#2261159311yescharacteristic
324C2#2261161911yescharacteristic
subgroupG/H
centerC22#99×D73
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1325C2
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1325D73
hypocenterC73#11571
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
170. C73#11571semidirect

Maximal subgroups

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

subgroupindex
#226151192
#226082732
#226082532
#226078772
#226078742
C73×#13252
#1157173