Finite Group Databasebeta

← #32975207

Subgroups — #32975207

Order 18688.

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

normal subgroups only

This group has 362 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#22617893C211yesmaximal, characteristic
2#22611340C211yesmaximal, characteristic
3#22611340C211yesmaximal, characteristic
4#22607756C211yesmaximal, characteristic
5#22607756C211yesmaximal, characteristic
6#22607754C211yesmaximal, characteristic
7C73×#2099C211yesmaximal, characteristic
8C2×#14556514—21no—
9C2×#14556514—21no—
10#17988520—21no—
11#17988519—21no—
12#17988507—21no—
13#17988493C2211yescharacteristic
14#17988493C2211yescharacteristic
15#17988491—21no—
16#17988486—21no—
17#17988473—21no—
18#17988349—21no—
19#17988349—21no—
20#17988342C2211yescharacteristic
21#17988342C2211yescharacteristic
22#389×C73C2211yescharacteristic
23#384×C73C2211yescharacteristic
24#340×C73—21no—
25#340×C73—21no—
26#336×C73C2211yescharacteristic
27C22×Dic146D411yescharacteristic
28C22×Dic146D411yescharacteristic
29C22×#10596831—21no—
30C22×#10596831—21no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73—21no—
33C2×C4⋊Dic73D411yescharacteristic
34C2×C4⋊Dic73D411yescharacteristic
35C2×#11924007—21no—
36C2×#11924007—21no—
37C2×C4×Dic73—21no—
38#14556514—42no—
39#14556514—42no—
40#14556498—21no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47C22×C8×C73—21no—
48C2×C4⋊C4×C73—21no—
49C2×C4⋊C4×C73—21no—
50C2×C4⋊C4×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—21no—
59C2×Dic146—41no—
60C2×Dic146—41no—
61C2×Dic146—41no—
62C2×Dic146—41no—
63C2×Dic146SD1612yes—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C2×#10596831—41no—
69C2×#10596831—41no—
70C2×#10596831—41no—
71C2×#10596831—41no—
72C2×#10596831—41no—
73C2×#10596831—41no—
74C4⋊Dic73—41no—
75C4⋊Dic73—41no—
76C4⋊Dic73—81no—
77C4⋊Dic73—81no—
78#11924007—81no—
79#11924007—81no—
80C4×Dic73—81no—
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73—41no—
84C22×C4×C73C2×D411yescharacteristic
85C22×C4×C73C2×D411yescharacteristic
86C22×C4×C73C2×D411yescharacteristic
87C2×C8×C73—41no—
88C2×C8×C73—41no—
89C2×C8×C73—41no—
90C4⋊C4×C73—21no—
91C4⋊C4×C73—41no—
92C4⋊C4×C73—42no—
93C4⋊C4×C73—41no—
94C4⋊C4×C73—41no—
95C4⋊C4×C73—41no—
96C4⋊C4×C73—41no—
97C4⋊C4×C73—41no—
98C4⋊C4×C73—41no—
99C4⋊C4×C73Q1612yes—
100C42×C73—41no—
101C23×C73#12011yescharacteristic
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—22no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—81no—
115C2×C4×C73—81no—
116C2×C4×C73—81no—
117C2×C4×C73C2×SD1611yescharacteristic
118C2×C4×C73C2×Q1611yescharacteristic
119C2×C4×C73#13511yescharacteristic
120C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C73#13711yescharacteristic
122C2×C4×C73#13711yescharacteristic
123C2×Dic73—22no—
124C2×Dic73—41no—
125C2×Dic73—41no—
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—
135Dic146—42no—
136Dic146—42no—
137Dic146—81no—
138Dic146—81no—
139C8×C73—81no—
140#10596831—81no—
141#10596831—81no—
142C22×C73#44811yescharacteristic
143C22×C73#44911yescharacteristic
144C22×C73#45111yescharacteristic
145C22×C73#45411yescharacteristic
146C22×C73#45511yescharacteristic
147C22×C73#45511yescharacteristic
148C22×C73#45811yescharacteristic
149C4×C73—21no—
150C4×C73—21no—
151C4×C73—21no—
152C4×C73—21no—
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—42no—
156C4×C73—81no—
157C4×C73—161no—
158Dic73—42no—
159Dic73—81no—
160Dic73—81no—
161Dic73—81no—
162#7816—731nomaximal, Sylow
163C2×C73#160811yescharacteristic
164C2×C73#161211yescharacteristic
165C2×C73#161711yescharacteristic
166C2×C73#162611yescharacteristic
167C2×C73#164411yescharacteristic
168C2×C73#164511yescharacteristic
169C2×C73#166211yescharacteristic
170#2806—731no—
171#2099D7311yescharacteristic
172#2072—731no—
173#2072—731no—
174#1272—731no—
175#1272—731no—
176#1271—731no—
177C73#781611yescharacteristic, complemented, Sylow
178C2×#103—1461no—
179C2×#103—1461no—
180#398—1461no—
181#398—1461no—
182#395—1461no—
183#391—731no—
184#391—731no—
185#391—1461no—
186#389—1461no—
187#389C2×D7311yescharacteristic
188#387—1461no—
189#384C2×D7311yescharacteristic
190#340—21no—
191#340—21no—
192#340—1461no—
193#340—1461no—
194#336—731no—
195#336—731no—
196#336C2×D7311yescharacteristic
197C22×Q8—731no—
198C22×Q8—731no—
199C22×C8—21no—
200C22×C8—1461no—
201C22×C8—1461no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
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⋊C4C22⋊D7311yescharacteristic
213C2×C4⋊C4C22⋊D7311yescharacteristic
214C2×C42—1461no—
215C2×C42C22×D7311yescharacteristic
216#103—2922no—
217#103—2922no—
218#95—21no—
219#95—1461no—
220#95—1461no—
221#95—1461no—
222#95—1461no—
223#95—1461no—
224#95—1461no—
225#95—1461no—
226C2×Q8—2921no—
227C2×Q8—2921no—
228C2×Q8—2921no—
229C2×Q8—2921no—
230C2×Q8—732no—
231C2×Q8—1461no—
232C2×Q8—1461no—
233C2×Q8—1461no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4—1461no—
238C22×C4—1461no—
239C22×C4—1461no—
240C22×C4—1461no—
241C22×C4D4×D7311yescharacteristic
242C22×C4D4×D7311yescharacteristic
243C22×C4C2×C22⋊D7311yescharacteristic
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—2921no—
248C2×C8—2921no—
249C2×C8—2921no—
250C2×C8—2921no—
251C2×C8—2921no—
252C2×C8—2921no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—2921no—
263C4⋊C4—2921no—
264C4⋊C4—5841no—
265C4⋊C4—5841no—
266C4⋊C4—5841no—
267C4⋊C4—5841no—
268C4⋊C4#1192401812yes—
269C42—41no—
270C42—5841no—
271C23#1455655911yescharacteristic
272Q8—2922no—
273Q8—2922no—
274Q8—5841no—
275Q8—5841no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
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—2921no—
301C2×C4—2921no—
302C2×C4—1462no—
303C2×C4SD16×D7311yescharacteristic
304C2×C4C2×#1192401811yescharacteristic
305C2×C4#1455661011yescharacteristic
306C2×C4#1455661511yescharacteristic
307C2×C4#1455662011yescharacteristic
308C2×C4#1455662111yescharacteristic
309C8—81no—
310C8—5841no—
311C8—5841no—
312C22#1798872411yescharacteristic
313C22#1798872911yescharacteristic
314C22#1798874211yescharacteristic
315C22#1798875911yescharacteristic
316C22#1798876311yescharacteristic
317C22#1798876311yescharacteristic
318C22#1798877611yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—81no—
327C4—161no—
328C4—2922no—
329C4—5841no—
330C4—5841no—
331C4—5841no—
332C2#2260892011yescharacteristic
333C2#2260894211yescharacteristic
334C2#2260897211yescharacteristic
335C2#2260902411yescharacteristic
336C2#2260914411yescharacteristic
337C2#2260915111yescharacteristic
338C2#2260925211yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2099C2
socle, prime radicalC23×C73#120
hypercenter#2099D73
hypocenterC73#7816
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
177. C73#7816semidirect

Maximal subgroups

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

subgroupindex
#226178932
#226113402
#226077562
#226077542
C73×#20992
#781673