Finite Group Databasebeta

← #32975151

Subgroups — #32975151

Order 18688.

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

normal subgroups only

This group has 366 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#22611473C211yesmaximal, characteristic
3#22611409C211yesmaximal, characteristic
4#22611402C211yesmaximal, characteristic
5#22607756C211yesmaximal, characteristic
6#22607755C211yesmaximal, characteristic
7C73×#1271C211yesmaximal, characteristic
8C2×#14556524—21no—
9C2×#14556523—21no—
10C2×#14556523—21no—
11C2×#14556516—21no—
12#17988526—21no—
13#17988526—21no—
14#17988508—21no—
15#17988493C2211yescharacteristic
16#17988486—21no—
17#17988485C2211yescharacteristic
18#17988474—21no—
19#17988473—21no—
20#17988457C2211yescharacteristic
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#14556524—42no—
40#14556523—42no—
41#14556523—42no—
42#14556516—42no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49#14556498—21no—
50#14556498—21no—
51C22×C8×C73—21no—
52C22×C8×C73—21no—
53C2×C4⋊C4×C73—21no—
54C2×C4⋊C4×C73D411yescharacteristic
55C2×C4⋊C4×C73D411yescharacteristic
56C2×C42×C73C2311yescharacteristic
57#95×C73—21no—
58C2×Dic146—21no—
59C2×Dic146—21no—
60C2×Dic146—41no—
61C2×Dic146—41no—
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C22×Dic73—41no—
67C2×#10596831—22no—
68C2×#10596831—41no—
69C2×#10596831—41no—
70C4⋊Dic73—21no—
71C4⋊Dic73—21no—
72C4⋊Dic73—41no—
73C4⋊Dic73—41no—
74C4⋊Dic73—41no—
75C4⋊Dic73—41no—
76C4⋊Dic73—41no—
77C4⋊Dic73—41no—
78C4⋊Dic73—41no—
79C4⋊Dic73—41no—
80C4⋊Dic73—81no—
81C4⋊Dic73—81no—
82#11924007—41no—
83#11924007—41no—
84C4×Dic73—81no—
85C22×C4×C73—21no—
86C22×C4×C73—21no—
87C22×C4×C73C2×D411yescharacteristic
88C22×C4×C73C2×D411yescharacteristic
89C22×C4×C73C2×D411yescharacteristic
90C2×C8×C73—22no—
91C2×C8×C73—22no—
92C2×C8×C73—41no—
93C2×C8×C73—41no—
94C2×C8×C73—41no—
95C2×C8×C73—41no—
96C4⋊C4×C73—21no—
97C4⋊C4×C73—41no—
98C4⋊C4×C73—41no—
99C4⋊C4×C73—41no—
100C4⋊C4×C73SD1612yes—
101C42×C73—41no—
102C23×C73#12011yescharacteristic
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—22no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73C2×SD1611yescharacteristic
116C2×C4×C73#13511yescharacteristic
117C2×C4×C73#13511yescharacteristic
118C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C73#13711yescharacteristic
120C2×C4×C73#13711yescharacteristic
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—41no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—81no—
134C2×Dic73—81no—
135C2×Dic73—81no—
136Dic146—42no—
137Dic146—81no—
138C8×C73—42no—
139C8×C73—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—42no—
155C4×C73—81no—
156Dic73—81no—
157Dic73—81no—
158Dic73—81no—
159Dic73—81no—
160Dic73—161no—
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#2096—731no—
171#2084—731no—
172#2083—731no—
173#1272—731no—
174#1271—731no—
175#1271D7311yescharacteristic
176C73#780711yescharacteristic, complemented, Sylow
177C2×#107—1461no—
178C2×#106—1461no—
179C2×#106—1461no—
180C2×#103—1461no—
181#400—1461no—
182#400—1461no—
183#395—1461no—
184#391—731no—
185#389—731no—
186#389—1461no—
187#389C2×D7311yescharacteristic
188#387—1461no—
189#387—1461no—
190#384—731no—
191#340—1461no—
192#340—1461no—
193#336—731no—
194#336C2×D7311yescharacteristic
195#336C2×D7311yescharacteristic
196C22×Q8—731no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—1461no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—731no—
202C2×C4⋊C4—731no—
203C2×C4⋊C4—731no—
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#107—2922no—
215#106—2922no—
216#106—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—
226#95—1461no—
227C2×Q8—2921no—
228C2×Q8—2921no—
229C2×Q8—1461no—
230C2×Q8—1461no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—2921no—
234C22×C4—1461no—
235C22×C4—1461no—
236C22×C4—1461no—
237C22×C4—1461no—
238C22×C4D4×D7311yescharacteristic
239C22×C4D4×D7311yescharacteristic
240C22×C4C2×D29211yescharacteristic
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—2921no—
248C2×C8—2921no—
249C2×C8—1462no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—2921no—
255C4⋊C4—2921no—
256C4⋊C4—2921no—
257C4⋊C4—2921no—
258C4⋊C4—2921no—
259C4⋊C4—2921no—
260C4⋊C4—2921no—
261C4⋊C4—2921no—
262C4⋊C4—2921no—
263C4⋊C4—2921no—
264C4⋊C4—5841no—
265C4⋊C4—5841no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4#1192401712yes—
269C42—41no—
270C42—5841no—
271C23#1455656111yescharacteristic
272Q8—2922no—
273Q8—5841no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—2921no—
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—5841no—
299C2×C4—5841no—
300C2×C4—5841no—
301C2×C4C2×#1192401711yescharacteristic
302C2×C4#1455661211yescharacteristic
303C2×C4#1455661211yescharacteristic
304C2×C4#1455661511yescharacteristic
305C2×C4#1455662311yescharacteristic
306C2×C4#1455662411yescharacteristic
307C8—42no—
308C8—42no—
309C8—2922no—
310C22#1798872811yescharacteristic
311C22#1798873311yescharacteristic
312C22#1798875211yescharacteristic
313C22#1798875611yescharacteristic
314C22#1798877111yescharacteristic
315C22#1798877211yescharacteristic
316C22#1798877811yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—42no—
324C4—81no—
325C4—5841no—
326C4—5841no—
327C4—5841no—
328C4—5841no—
329C4—11681no—
330C2#2260892911yescharacteristic
331C2#2260894111yescharacteristic
332C2#2260898211yescharacteristic
333C2#2260900511yescharacteristic
334C2#2260918811yescharacteristic
335C2#2260921011yescharacteristic
336C2#2260924411yescharacteristic
subgroupG/H
centerC23#14556561
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1271C2
socle, prime radicalC23×C73#120
hypercenter#1271D73
hypocenterC73#7807
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
176. C73#7807semidirect

Maximal subgroups

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

subgroupindex
#226178842
#226114732
#226114092
#226114022
#226077562
#226077552
C73×#12712
#780773