Finite Group Databasebeta

← #32975272

Subgroups — #32975272

Order 18688.

358 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 85 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#22616883C211yesmaximal, characteristic
2#22611495C211yesmaximal, characteristic
3#22611495C211yesmaximal, characteristic
4#22611494C211yesmaximal, characteristic
5#22607753C211yesmaximal, characteristic
6#22607753C211yesmaximal, characteristic
7C73×#1271C211yesmaximal, characteristic
8C2×#14556581—21no—
9#17988519—21no—
10#17988517—21no—
11#17988517—21no—
12#17988486—21no—
13#17988485C2211yescharacteristic
14#17988485C2211yescharacteristic
15#17988472—21no—
16#17988457C2211yescharacteristic
17#17988350—21no—
18#17988350—21no—
19#17988350—21no—
20#17988350—21no—
21#17988349—21no—
22#17988349—21no—
23#17988342C2211yescharacteristic
24#389×C73C2211yescharacteristic
25#336×C73C2211yescharacteristic
26#336×C73C2211yescharacteristic
27C22×#10596831—21no—
28#14556581—42no—
29#14556581—42no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73—21no—
33C2×C4⋊Dic73—21no—
34C2×C4⋊Dic73—21no—
35C2×C4⋊Dic73D411yescharacteristic
36C2×C4⋊Dic73D411yescharacteristic
37C2×C4⋊Dic73D411yescharacteristic
38C2×C4⋊Dic73D411yescharacteristic
39C2×#11924007—21no—
40C2×#11924007—21no—
41C2×#11924007—21no—
42C2×#11924007—21no—
43C2×C4×Dic73—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49C22×C8×C73—21no—
50C22×C8×C73—21no—
51C2×C4⋊C4×C73—21no—
52C2×C4⋊C4×C73D411yescharacteristic
53C2×C4⋊C4×C73D411yescharacteristic
54C2×C42×C73C2311yescharacteristic
55#95×C73—21no—
56C22×Dic73—21no—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73—41no—
61C2×#10596831—41no—
62C2×#10596831—41no—
63C2×#10596831—41no—
64C4⋊Dic73—21no—
65C4⋊Dic73—21no—
66C4⋊Dic73—21no—
67C4⋊Dic73—42no—
68C4⋊Dic73—41no—
69C4⋊Dic73—41no—
70C4⋊Dic73—42no—
71C4⋊Dic73—42no—
72C4⋊Dic73—42no—
73C4⋊Dic73—81no—
74C4⋊Dic73Q1612yes—
75#11924007—42no—
76#11924007—42no—
77#11924007—41no—
78#11924007—41no—
79#11924007—41no—
80#11924007—41no—
81C4×Dic73—42no—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73C2×D411yescharacteristic
85C22×C4×C73C2×D411yescharacteristic
86C22×C4×C73C2×D411yescharacteristic
87C2×C8×C73—41no—
88C2×C8×C73—41no—
89C2×C8×C73—41no—
90C2×C8×C73—41no—
91C2×C8×C73—41no—
92C2×C8×C73—41no—
93C4⋊C4×C73—21no—
94C4⋊C4×C73—41no—
95C4⋊C4×C73—41no—
96C4⋊C4×C73—41no—
97C4⋊C4×C73SD1612yes—
98C42×C73—41no—
99C23×C73#12011yescharacteristic
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—22no—
107C2×C4×C73—41no—
108C2×C4×C73—41no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73C2×SD1611yescharacteristic
113C2×C4×C73C2×Q1611yescharacteristic
114C2×C4×C73#13511yescharacteristic
115C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C73#13711yescharacteristic
117C2×C4×C73#13711yescharacteristic
118C2×Dic73—22no—
119C2×Dic73—41no—
120C2×Dic73—41no—
121C2×Dic73—41no—
122C2×Dic73—41no—
123C2×Dic73—41no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126C2×Dic73—41no—
127C2×Dic73—41no—
128C2×Dic73—41no—
129C2×Dic73—41no—
130C2×Dic73—81no—
131C2×Dic73—81no—
132C2×Dic73—81no—
133C8×C73—81no—
134C8×C73—81no—
135#10596831—81no—
136C22×C73#45011yescharacteristic
137C22×C73#45111yescharacteristic
138C22×C73#45211yescharacteristic
139C22×C73#45411yescharacteristic
140C22×C73#45411yescharacteristic
141C22×C73#45411yescharacteristic
142C22×C73#45811yescharacteristic
143C4×C73—21no—
144C4×C73—21no—
145C4×C73—21no—
146C4×C73—21no—
147C4×C73—21no—
148C4×C73—21no—
149C4×C73—42no—
150C4×C73—81no—
151Dic73—42no—
152Dic73—81no—
153Dic73—81no—
154Dic73—81no—
155Dic73—161no—
156#7827—731nomaximal, Sylow
157C2×C73#161511yescharacteristic
158C2×C73#161611yescharacteristic
159C2×C73#161711yescharacteristic
160C2×C73#163511yescharacteristic
161C2×C73#163611yescharacteristic
162C2×C73#163711yescharacteristic
163C2×C73#165811yescharacteristic
164#2726—731no—
165#2100—731no—
166#2100—731no—
167#2100—731no—
168#1271—731no—
169#1271—731no—
170#1271D7311yescharacteristic
171C73#782711yescharacteristic, complemented, Sylow
172C2×#125—1461no—
173#398—1461no—
174#398—1461no—
175#398—1461no—
176#389—731no—
177#389—731no—
178#389—1461no—
179#389C2×D7311yescharacteristic
180#387—1461no—
181#384—731no—
182#340—1461no—
183#340—1461no—
184#340—1461no—
185#340—1461no—
186#340—1461no—
187#340—1461no—
188#336—731no—
189#336C2×D7311yescharacteristic
190#336C2×D7311yescharacteristic
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—1461no—
194#125—2922no—
195#125—2922no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—731no—
198C2×C4⋊C4—731no—
199C2×C4⋊C4—731no—
200C2×C4⋊C4—731no—
201C2×C4⋊C4—1461no—
202C2×C4⋊C4—1461no—
203C2×C4⋊C4—1461no—
204C2×C4⋊C4—1461no—
205C2×C4⋊C4—1461no—
206C2×C4⋊C4—1461no—
207C2×C4⋊C4—1461no—
208C2×C4⋊C4—1461no—
209C2×C4⋊C4—1461no—
210C2×C4⋊C4D29211yescharacteristic
211C2×C4⋊C4D29211yescharacteristic
212C2×C42—1461no—
213C2×C42C22×D7311yescharacteristic
214#95—21no—
215#95—1461no—
216#95—1461no—
217#95—1461no—
218#95—1461no—
219#95—1461no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—2921no—
223C22×C4—1461no—
224C22×C4—1461no—
225C22×C4—1461no—
226C22×C4—1461no—
227C22×C4D4×D7311yescharacteristic
228C22×C4D4×D7311yescharacteristic
229C22×C4C2×D29211yescharacteristic
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—2921no—
237C2×C8—2921no—
238C2×C8—2921no—
239C4⋊C4—21no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—2921no—
244C4⋊C4—2921no—
245C4⋊C4—2922no—
246C4⋊C4—2922no—
247C4⋊C4—2922no—
248C4⋊C4—2922no—
249C4⋊C4—2922no—
250C4⋊C4—2922no—
251C4⋊C4—2921no—
252C4⋊C4—2921no—
253C4⋊C4—2921no—
254C4⋊C4—2921no—
255C4⋊C4—5841no—
256C4⋊C4—732no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
260C4⋊C4#1192401712yes—
261C42—41no—
262C42—2922no—
263C23#1455656111yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—2921no—
277C2×C4—2921no—
278C2×C4—2921no—
279C2×C4—2921no—
280C2×C4—2921no—
281C2×C4—2921no—
282C2×C4—2921no—
283C2×C4—2921no—
284C2×C4—2921no—
285C2×C4—2921no—
286C2×C4—2921no—
287C2×C4—5841no—
288C2×C4—5841no—
289C2×C4—5841no—
290C2×C4—1462no—
291C2×C4C2×#1192401711yescharacteristic
292C2×C4Q16×D7311yescharacteristic
293C2×C4#1455661011yescharacteristic
294C2×C4#1455661911yescharacteristic
295C2×C4#1455662011yescharacteristic
296C2×C4#1455662011yescharacteristic
297C8—81no—
298C8—81no—
299C8—5841no—
300C22#1798874011yescharacteristic
301C22#1798874411yescharacteristic
302C22#1798875011yescharacteristic
303C22#1798876111yescharacteristic
304C22#1798876111yescharacteristic
305C22#1798876211yescharacteristic
306C22#1798877811yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—81no—
315C4—2922no—
316C4—5841no—
317C4—5841no—
318C4—5841no—
319C4—11681no—
320C2#2260896311yescharacteristic
321C2#2260897011yescharacteristic
322C2#2260897411yescharacteristic
323C2#2260908411yescharacteristic
324C2#2260909011yescharacteristic
325C2#2260909811yescharacteristic
326C2#2260923411yescharacteristic
subgroupG/H
centerC23#14556561
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1271C2
socle, prime radicalC23×C73#120
hypercenter#1271D73
hypocenterC73#7827
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
171. C73#7827semidirect

Maximal subgroups

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

subgroupindex
#226168832
#226114952
#226114942
#226077532
C73×#12712
#782773