Finite Group Databasebeta

← #32975221

Subgroups — #32975221

Order 18688.

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

normal subgroups only

This group has 350 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#22617884C211yesmaximal, characteristic
2#22611490C211yesmaximal, characteristic
3#22611407C211yesmaximal, characteristic
4#22611341C211yesmaximal, characteristic
5#22607756C211yesmaximal, characteristic
6#22607755C211yesmaximal, characteristic
7C73×#1271C211yesmaximal, characteristic
8C2×#14556522—21no—
9C2×#14556516—21no—
10#17988526—21no—
11#17988526—21no—
12#17988508—21no—
13#17988493C2211yescharacteristic
14#17988486—21no—
15#17988485C2211yescharacteristic
16#17988474—21no—
17#17988473—21no—
18#17988457C2211yescharacteristic
19#17988350—21no—
20#17988350—21no—
21#17988350—21no—
22#17988349—21no—
23#17988342C2211yescharacteristic
24#389×C73C2211yescharacteristic
25#336×C73C2211yescharacteristic
26#336×C73C2211yescharacteristic
27C22×Dic146D411yescharacteristic
28C22×#10596831—21no—
29C2×C4⋊Dic73—21no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73—21no—
33C2×C4⋊Dic73—21no—
34C2×C4⋊Dic73D411yescharacteristic
35C2×C4⋊Dic73D411yescharacteristic
36C2×C4⋊Dic73D411yescharacteristic
37C2×#11924007—21no—
38C2×C4×Dic73—21no—
39#14556522—42no—
40#14556516—42no—
41#14556498—21no—
42#14556498—21no—
43#14556498—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—
56C2×Dic146—21no—
57C2×Dic146—21no—
58C2×Dic146—41no—
59C2×Dic146—41no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73—41no—
65C2×#10596831—22no—
66C2×#10596831—41no—
67C2×#10596831—41no—
68C4⋊Dic73—21no—
69C4⋊Dic73—21no—
70C4⋊Dic73—41no—
71C4⋊Dic73—41no—
72C4⋊Dic73—42no—
73C4⋊Dic73—41no—
74C4⋊Dic73—41no—
75C4⋊Dic73—41no—
76C4⋊Dic73—41no—
77C4⋊Dic73—81no—
78C4⋊Dic73—81no—
79#11924007—41no—
80#11924007—41no—
81C4×Dic73—81no—
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×C73#13511yescharacteristic
114C2×C4×C73#13511yescharacteristic
115C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C73#13711yescharacteristic
117C2×C4×C73#13711yescharacteristic
118C2×Dic73—41no—
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—
133Dic146—42no—
134Dic146—81no—
135C8×C73—81no—
136C8×C73—81no—
137#10596831—42no—
138C22×C73#44811yescharacteristic
139C22×C73#44911yescharacteristic
140C22×C73#45211yescharacteristic
141C22×C73#45411yescharacteristic
142C22×C73#45511yescharacteristic
143C22×C73#45611yescharacteristic
144C22×C73#45811yescharacteristic
145C4×C73—21no—
146C4×C73—21no—
147C4×C73—21no—
148C4×C73—21no—
149C4×C73—21no—
150C4×C73—21no—
151C4×C73—42no—
152C4×C73—81no—
153Dic73—81no—
154Dic73—81no—
155Dic73—81no—
156Dic73—81no—
157Dic73—161no—
158#7818—731nomaximal, Sylow
159C2×C73#161111yescharacteristic
160C2×C73#161211yescharacteristic
161C2×C73#161511yescharacteristic
162C2×C73#162611yescharacteristic
163C2×C73#164311yescharacteristic
164C2×C73#165211yescharacteristic
165C2×C73#166411yescharacteristic
166#2805—731no—
167#2099—731no—
168#2084—731no—
169#2072—731no—
170#1272—731no—
171#1271—731no—
172#1271D7311yescharacteristic
173C73#781811yescharacteristic, complemented, Sylow
174C2×#106—1461no—
175C2×#103—1461no—
176#400—1461no—
177#400—1461no—
178#395—1461no—
179#391—731no—
180#389—731no—
181#389—1461no—
182#389C2×D7311yescharacteristic
183#387—1461no—
184#387—1461no—
185#384—731no—
186#340—1461no—
187#340—1461no—
188#340—1461no—
189#340—1461no—
190#336—731no—
191#336C2×D7311yescharacteristic
192#336C2×D7311yescharacteristic
193C22×Q8—731no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—1461no—
197C2×C4⋊C4—21no—
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⋊C4D29211yescharacteristic
208C2×C4⋊C4D29211yescharacteristic
209C2×C42—1461no—
210C2×C42C22×D7311yescharacteristic
211#106—2922no—
212#103—2922no—
213#95—21no—
214#95—1461no—
215#95—1461no—
216#95—1461no—
217#95—1461no—
218#95—1461no—
219#95—1461no—
220#95—1461no—
221#95—1461no—
222C2×Q8—2921no—
223C2×Q8—2921no—
224C2×Q8—1461no—
225C2×Q8—1461no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—2921no—
229C22×C4—1461no—
230C22×C4—1461no—
231C22×C4—1461no—
232C22×C4—1461no—
233C22×C4D4×D7311yescharacteristic
234C22×C4D4×D7311yescharacteristic
235C22×C4C2×D29211yescharacteristic
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—2921no—
243C2×C8—2921no—
244C2×C8—1462no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—2921no—
250C4⋊C4—2921no—
251C4⋊C4—2922no—
252C4⋊C4—2921no—
253C4⋊C4—2921no—
254C4⋊C4—2921no—
255C4⋊C4—2921no—
256C4⋊C4—2921no—
257C4⋊C4—2921no—
258C4⋊C4—5841no—
259C4⋊C4—5841no—
260C4⋊C4—1461no—
261C4⋊C4—1461no—
262C4⋊C4#1192401712yes—
263C42—41no—
264C42—5841no—
265C23#1455656111yescharacteristic
266Q8—2922no—
267Q8—5841no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
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—2921no—
284C2×C4—2921no—
285C2×C4—2921no—
286C2×C4—2921no—
287C2×C4—2921no—
288C2×C4—2921no—
289C2×C4—2921no—
290C2×C4—2921no—
291C2×C4—2921no—
292C2×C4—5841no—
293C2×C4—5841no—
294C2×C4—5841no—
295C2×C4C2×#1192401711yescharacteristic
296C2×C4#1455661011yescharacteristic
297C2×C4#1455661411yescharacteristic
298C2×C4#1455661811yescharacteristic
299C2×C4#1455662011yescharacteristic
300C2×C4#1455662411yescharacteristic
301C8—81no—
302C8—81no—
303C8—2922no—
304C22#1798872811yescharacteristic
305C22#1798873511yescharacteristic
306C22#1798875011yescharacteristic
307C22#1798876111yescharacteristic
308C22#1798876611yescharacteristic
309C22#1798877211yescharacteristic
310C22#1798877811yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—42no—
318C4—81no—
319C4—5841no—
320C4—5841no—
321C4—5841no—
322C4—5841no—
323C4—11681no—
324C2#2260894111yescharacteristic
325C2#2260894811yescharacteristic
326C2#2260896311yescharacteristic
327C2#2260903011yescharacteristic
328C2#2260914011yescharacteristic
329C2#2260920211yescharacteristic
330C2#2260926711yescharacteristic
subgroupG/H
centerC23#14556561
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1271C2
socle, prime radicalC23×C73#120
hypercenter#1271D73
hypocenterC73#7818
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
173. C73#7818semidirect

Maximal subgroups

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

subgroupindex
#226178842
#226114902
#226114072
#226113412
#226077562
#226077552
C73×#12712
#781873