Finite Group Databasebeta

← #32975148

Subgroups — #32975148

Order 18688.

366 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 81 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#22617886C211yesmaximal, characteristic
2#22611408C211yesmaximal, characteristic
3#22611403C211yesmaximal, characteristic
4#22607757C211yesmaximal, characteristic
5#22607755C211yesmaximal, characteristic
6#22607753C211yesmaximal, characteristic
7C73×#2096C211yesmaximal, characteristic
8C2×#14556524—21no—
9C2×#14556522—21no—
10#17988529—21no—
11#17988527—21no—
12#17988506—21no—
13#17988485C2211yescharacteristic
14#17988485C2211yescharacteristic
15#17988484—21no—
16#17988470—21no—
17#17988468—21no—
18#17988349—21no—
19#17988349—21no—
20#17988342C2211yescharacteristic
21#17988342C2211yescharacteristic
22C2×#106×C73—21no—
23C2×#103×C73—21no—
24#391×C73C2211yescharacteristic
25#384×C73C2211yescharacteristic
26#336×C73C2211yescharacteristic
27C22×#10596831—21no—
28C22×#10596831—21no—
29C2×C4⋊Dic73D411yescharacteristic
30C2×C4⋊Dic73D411yescharacteristic
31C2×C4⋊Dic73D411yescharacteristic
32C2×C4⋊Dic73D411yescharacteristic
33C2×#11924007—21no—
34C2×#11924007—21no—
35C2×#11924007—21no—
36C2×#11924007—21no—
37C2×C4×Dic73—21no—
38#14556524—42no—
39#14556522—42no—
40#14556498—21no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47C22×Q8×C73D411yescharacteristic
48C22×C8×C73—21no—
49C2×C4⋊C4×C73—21no—
50C2×C4⋊C4×C73—21no—
51C2×C4⋊C4×C73—21no—
52C2×C4⋊C4×C73D411yescharacteristic
53C2×C42×C73C2311yescharacteristic
54#106×C73—42no—
55#103×C73—42no—
56#95×C73—21no—
57#95×C73—21no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C2×#10596831—22no—
63C2×#10596831—22no—
64C2×#10596831—41no—
65C2×#10596831—41no—
66C2×#10596831—41no—
67C2×#10596831—41no—
68C4⋊Dic73—21no—
69C4⋊Dic73—21no—
70C4⋊Dic73—21no—
71C4⋊Dic73—41no—
72C4⋊Dic73—41no—
73C4⋊Dic73SD1612yes—
74#11924007—41no—
75#11924007—41no—
76#11924007—41no—
77#11924007—41no—
78#11924007—81no—
79#11924007—81no—
80C4×Dic73—81no—
81C2×Q8×C73—21no—
82C2×Q8×C73—21no—
83C2×Q8×C73—41no—
84C2×Q8×C73—41no—
85C22×C4×C73—21no—
86C22×C4×C73—21no—
87C22×C4×C73—41no—
88C22×C4×C73C2×D411yescharacteristic
89C22×C4×C73C2×D411yescharacteristic
90C22×C4×C73C2×D411yescharacteristic
91C2×C8×C73—22no—
92C2×C8×C73—41no—
93C2×C8×C73—41no—
94C4⋊C4×C73—41no—
95C4⋊C4×C73—41no—
96C4⋊C4×C73—41no—
97C4⋊C4×C73—41no—
98C4⋊C4×C73—41no—
99C4⋊C4×C73—41no—
100C4⋊C4×C73—41no—
101C42×C73—41no—
102C23×C73#12011yescharacteristic
103Q8×C73—42no—
104Q8×C73—81no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—41no—
116C2×C4×C73—41no—
117C2×C4×C73—81no—
118C2×C4×C73—81no—
119C2×C4×C73—81no—
120C2×C4×C73C2×SD1611yescharacteristic
121C2×C4×C73#13511yescharacteristic
122C2×C4×C73#13511yescharacteristic
123C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C73#13711yescharacteristic
125C2×C4×C73#13711yescharacteristic
126C2×Dic73—22no—
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—
137C2×Dic73—41no—
138C8×C73—42no—
139#10596831—42no—
140#10596831—42no—
141C22×C73#44811yescharacteristic
142C22×C73#44911yescharacteristic
143C22×C73#45211yescharacteristic
144C22×C73#45311yescharacteristic
145C22×C73#45611yescharacteristic
146C22×C73#45611yescharacteristic
147C22×C73#45811yescharacteristic
148C4×C73—21no—
149C4×C73—21no—
150C4×C73—21no—
151C4×C73—21no—
152C4×C73—21no—
153C4×C73—21no—
154C4×C73—81no—
155C4×C73—81no—
156C4×C73—161no—
157Dic73—42no—
158Dic73—81no—
159Dic73—81no—
160Dic73—81no—
161#7807—731nomaximal, Sylow
162C2×C73#160911yescharacteristic
163C2×C73#161111yescharacteristic
164C2×C73#161811yescharacteristic
165C2×C73#162211yescharacteristic
166C2×C73#165011yescharacteristic
167C2×C73#165311yescharacteristic
168C2×C73#166011yescharacteristic
169#2805—731no—
170#2096D7311yescharacteristic
171#2084—731no—
172#2083—731no—
173#1272—731no—
174#1271—731no—
175#1271—731no—
176C73#780711yescharacteristic, complemented, Sylow
177C2×#107—1461no—
178C2×#106—21no—
179C2×#106—1461no—
180C2×#103—21no—
181#400—1461no—
182#400—1461no—
183#395—1461no—
184#391C2×D7311yescharacteristic
185#389—731no—
186#389—731no—
187#389—1461no—
188#387—1461no—
189#387—1461no—
190#384C2×D7311yescharacteristic
191#340—1461no—
192#340—1461no—
193#336—731no—
194#336—731no—
195#336C2×D7311yescharacteristic
196C22×Q8C22⋊D7311yescharacteristic
197C22×C8—21no—
198C22×C8—1461no—
199C22×C8—1461no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—731no—
204C2×C4⋊C4—731no—
205C2×C4⋊C4—731no—
206C2×C4⋊C4—731no—
207C2×C4⋊C4—1461no—
208C2×C4⋊C4—1461no—
209C2×C4⋊C4—1461no—
210C2×C4⋊C4—1461no—
211C2×C4⋊C4C22⋊D7311yescharacteristic
212C2×C42—1461no—
213C2×C42C22×D7311yescharacteristic
214#107—2922no—
215#106—42no—
216#106—2922no—
217#103—42no—
218#95—21no—
219#95—21no—
220#95—1461no—
221#95—1461no—
222#95—1461no—
223#95—1461no—
224#95—1461no—
225#95—1461no—
226#95—1461no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—41no—
230C2×Q8—41no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—1461no—
235C22×C4—1461no—
236C22×C4—1461no—
237C22×C4—1461no—
238C22×C4D4×D7311yescharacteristic
239C22×C4D4×D7311yescharacteristic
240C22×C4C2×C22⋊D7311yescharacteristic
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—2921no—
245C2×C8—2921no—
246C2×C8—2921no—
247C2×C8—2921no—
248C2×C8—1462no—
249C2×C8—1462no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—2921no—
258C4⋊C4—2921no—
259C4⋊C4—2921no—
260C4⋊C4—2921no—
261C4⋊C4—2921no—
262C4⋊C4—2921no—
263C4⋊C4—5841no—
264C4⋊C4—5841no—
265C4⋊C4—732no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C42—41no—
270C42—5841no—
271C23#1455655911yescharacteristic
272Q8—42no—
273Q8—81no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
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—2921no—
299C2×C4—2921no—
300C2×C4—1462no—
301C2×C4SD16×D7311yescharacteristic
302C2×C4#1455661111yescharacteristic
303C2×C4#1455661211yescharacteristic
304C2×C4#1455661811yescharacteristic
305C2×C4#1455662011yescharacteristic
306C2×C4#1455662211yescharacteristic
307C8—42no—
308C8—2922no—
309C8—2922no—
310C22#1798872411yescharacteristic
311C22#1798873111yescharacteristic
312C22#1798874711yescharacteristic
313C22#1798875411yescharacteristic
314C22#1798876811yescharacteristic
315C22#1798876811yescharacteristic
316C22#1798877611yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—81no—
325C4—161no—
326C4—2922no—
327C4—5841no—
328C4—5841no—
329C4—5841no—
330C2#2260892711yescharacteristic
331C2#2260893711yescharacteristic
332C2#2260897711yescharacteristic
333C2#2260900011yescharacteristic
334C2#2260918611yescharacteristic
335C2#2260920711yescharacteristic
336C2#2260924011yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2096C2
socle, prime radicalC23×C73#120
hypercenter#2096D73
hypocenterC73#7807
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2096

Complements

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

NH ≅ G/Ntype
176. C73#7807semidirect

Maximal subgroups

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

subgroupindex
#226178862
#226114082
#226114032
#226077572
#226077552
#226077532
C73×#20962
#780773