Finite Group Databasebeta

← #32975198

Subgroups — #32975198

Order 18688.

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

normal subgroups only

This group has 374 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#22616882C211yesmaximal, characteristic
2#22611488C211yesmaximal, characteristic
3#22611408C211yesmaximal, characteristic
4#22607754C211yesmaximal, characteristic
5#22607753C211yesmaximal, characteristic
6#22607753C211yesmaximal, characteristic
7C73×#2084C211yesmaximal, characteristic
8C2×#14556582—21no—
9C2×#14556522—21no—
10#17988520—21no—
11#17988520—21no—
12#17988519—21no—
13#17988485C2211yescharacteristic
14#17988485C2211yescharacteristic
15#17988484—21no—
16#17988473—21no—
17#17988349—21no—
18#17988349—21no—
19#17988349—21no—
20#17988342C2211yescharacteristic
21#17988342C2211yescharacteristic
22C2×#106×C73—21no—
23#389×C73C2211yescharacteristic
24#384×C73C2211yescharacteristic
25#340×C73—21no—
26#336×C73C2211yescharacteristic
27C22×#10596831—21no—
28C22×#10596831—21no—
29#14556582—42no—
30#14556582—42no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73—21no—
33C2×C4⋊Dic73D411yescharacteristic
34C2×C4⋊Dic73D411yescharacteristic
35C2×C4⋊Dic73D411yescharacteristic
36C2×C4⋊Dic73D411yescharacteristic
37C2×#11924007—21no—
38C2×#11924007—21no—
39C2×#11924007—21no—
40C2×#11924007—21no—
41C2×C4×Dic73—21no—
42#14556522—42no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48C22×C8×C73—21no—
49C2×C4⋊C4×C73—21no—
50C2×C4⋊C4×C73—21no—
51C2×C4⋊C4×C73—21no—
52C2×C4⋊C4×C73—21no—
53C2×C4⋊C4×C73D411yescharacteristic
54C2×C4⋊C4×C73D411yescharacteristic
55C2×C42×C73C2311yescharacteristic
56#106×C73—42no—
57#95×C73—21no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C2×#10596831—22no—
63C2×#10596831—41no—
64C2×#10596831—41no—
65C2×#10596831—41no—
66C2×#10596831—41no—
67C2×#10596831—41no—
68C4⋊Dic73—21no—
69C4⋊Dic73—21no—
70C4⋊Dic73—21no—
71C4⋊Dic73—42no—
72C4⋊Dic73—42no—
73C4⋊Dic73—41no—
74C4⋊Dic73—41no—
75C4⋊Dic73SD1612yes—
76#11924007—42no—
77#11924007—41no—
78#11924007—41no—
79#11924007—41no—
80#11924007—41no—
81#11924007—81no—
82C4×Dic73—42no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73—41no—
86C22×C4×C73C2×D411yescharacteristic
87C22×C4×C73C2×D411yescharacteristic
88C22×C4×C73C2×D411yescharacteristic
89C2×C8×C73—22no—
90C2×C8×C73—41no—
91C2×C8×C73—41no—
92C4⋊C4×C73—21no—
93C4⋊C4×C73—41no—
94C4⋊C4×C73—42no—
95C4⋊C4×C73—41no—
96C4⋊C4×C73—41no—
97C4⋊C4×C73—41no—
98C4⋊C4×C73—41no—
99C4⋊C4×C73—41no—
100C4⋊C4×C73—41no—
101C4⋊C4×C73SD1612yes—
102C42×C73—41no—
103C23×C73#12011yescharacteristic
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—22no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—41no—
116C2×C4×C73—81no—
117C2×C4×C73—81no—
118C2×C4×C73—81no—
119C2×C4×C73C2×SD1611yescharacteristic
120C2×C4×C73C2×SD1611yescharacteristic
121C2×C4×C73#13511yescharacteristic
122C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C73#13711yescharacteristic
125C2×Dic73—22no—
126C2×Dic73—41no—
127C2×Dic73—41no—
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—
137C8×C73—42no—
138#10596831—42no—
139#10596831—81no—
140C22×C73#44811yescharacteristic
141C22×C73#44911yescharacteristic
142C22×C73#45011yescharacteristic
143C22×C73#45411yescharacteristic
144C22×C73#45611yescharacteristic
145C22×C73#45611yescharacteristic
146C22×C73#45811yescharacteristic
147C4×C73—21no—
148C4×C73—21no—
149C4×C73—21no—
150C4×C73—21no—
151C4×C73—21no—
152C4×C73—21no—
153C4×C73—42no—
154C4×C73—81no—
155C4×C73—161no—
156Dic73—42no—
157Dic73—81no—
158Dic73—81no—
159Dic73—81no—
160#7815—731nomaximal, Sylow
161C2×C73#160911yescharacteristic
162C2×C73#161111yescharacteristic
163C2×C73#161611yescharacteristic
164C2×C73#162611yescharacteristic
165C2×C73#165111yescharacteristic
166C2×C73#165411yescharacteristic
167C2×C73#166311yescharacteristic
168#2726—731no—
169#2099—731no—
170#2084—731no—
171#2084D7311yescharacteristic
172#1271—731no—
173#1271—731no—
174#1271—731no—
175C73#781511yescharacteristic, complemented, Sylow
176C2×#125—1461no—
177C2×#106—21no—
178C2×#106—1461no—
179#398—1461no—
180#398—1461no—
181#398—1461no—
182#389—731no—
183#389—731no—
184#389—1461no—
185#389C2×D7311yescharacteristic
186#387—1461no—
187#384C2×D7311yescharacteristic
188#340—21no—
189#340—1461no—
190#340—1461no—
191#340—1461no—
192#336—731no—
193#336—731no—
194#336C2×D7311yescharacteristic
195C22×C8—21no—
196C22×C8—1461no—
197C22×C8—1461no—
198#125—2922no—
199#125—2922no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—731no—
205C2×C4⋊C4—731no—
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⋊C4—1461no—
214C2×C4⋊C4C22⋊D7311yescharacteristic
215C2×C4⋊C4C22⋊D7311yescharacteristic
216C2×C42—1461no—
217C2×C42C22×D7311yescharacteristic
218#106—42no—
219#106—2922no—
220#95—21no—
221#95—1461no—
222#95—1461no—
223#95—1461no—
224#95—1461no—
225#95—1461no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—1461no—
230C22×C4—1461no—
231C22×C4—1461no—
232C22×C4—1461no—
233C22×C4D4×D7311yescharacteristic
234C22×C4D4×D7311yescharacteristic
235C22×C4C2×C22⋊D7311yescharacteristic
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—2921no—
240C2×C8—2921no—
241C2×C8—2921no—
242C2×C8—2921no—
243C2×C8—2921no—
244C2×C8—1462no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—42no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—2921no—
255C4⋊C4—2921no—
256C4⋊C4—2922no—
257C4⋊C4—2922no—
258C4⋊C4—2922no—
259C4⋊C4—2921no—
260C4⋊C4—2921no—
261C4⋊C4—2921no—
262C4⋊C4—2921no—
263C4⋊C4—5841no—
264C4⋊C4—732no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4#1192401612yes—
269C42—41no—
270C42—2922no—
271C23#1455655911yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—2921no—
288C2×C4—2921no—
289C2×C4—2921no—
290C2×C4—2921no—
291C2×C4—2921no—
292C2×C4—2921no—
293C2×C4—2921no—
294C2×C4—2921no—
295C2×C4—2921no—
296C2×C4—2921no—
297C2×C4—2921no—
298C2×C4—1462no—
299C2×C4SD16×D7311yescharacteristic
300C2×C4C2×#1192401611yescharacteristic
301C2×C4#1455661211yescharacteristic
302C2×C4#1455661811yescharacteristic
303C2×C4#1455661811yescharacteristic
304C2×C4#1455662111yescharacteristic
305C8—42no—
306C8—2922no—
307C8—5841no—
308C22#1798872511yescharacteristic
309C22#1798873111yescharacteristic
310C22#1798873611yescharacteristic
311C22#1798875811yescharacteristic
312C22#1798876811yescharacteristic
313C22#1798876911yescharacteristic
314C22#1798877611yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—81no—
323C4—161no—
324C4—2922no—
325C4—5841no—
326C4—5841no—
327C4—5841no—
328C2#2260892711yescharacteristic
329C2#2260893811yescharacteristic
330C2#2260896611yescharacteristic
331C2#2260902611yescharacteristic
332C2#2260919211yescharacteristic
333C2#2260921211yescharacteristic
334C2#2260925811yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2084C2
socle, prime radicalC23×C73#120
hypercenter#2084D73
hypocenterC73#7815
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
175. C73#7815semidirect

Maximal subgroups

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

subgroupindex
#226168822
#226114882
#226114082
#226077542
#226077532
C73×#20842
#781573