Finite Group Databasebeta

← #32983343

Subgroups — #32983343

Order 18688.

486 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 117 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#22619011C211yesmaximal, characteristic
2#22615139C211yesmaximal, characteristic
3#22609924C211yesmaximal, characteristic
4#22608613C211yesmaximal, characteristic
5#22608611C211yesmaximal, characteristic
6#22607834C211yesmaximal, characteristic
7C73×#1303C211yesmaximal, characteristic
8C2×#14556591C2211yescharacteristic
9C2×C4×Dic146C2211yescharacteristic
10C8×Dic146—22no—
11#17988711—22no—
12#17988640C2211yescharacteristic
13#17988637—22no—
14#17988611C2211yescharacteristic
15C2×#14556509—21no—
16#17988508C414yes—
17#17988493—21no—
18#17988486—22no—
19#17988457—21no—
20#17988355—21no—
21#17988335—22no—
22#17988335—22no—
23#431×C73C2211yescharacteristic
24#423×C73C2211yescharacteristic
25C4×C4⋊C4×C73C2211yescharacteristic
26C22×Dic146C2×C412yes—
27C22×Dic146D411yescharacteristic
28C2×#11924012—21no—
29#14556591—21no—
30#14556591—21no—
31#14556591—21no—
32#14556591—21no—
33C4×Dic146—21no—
34C4×Dic146—21no—
35C4×Dic146—21no—
36C4×Dic146—21no—
37C2×C4⋊Dic73—24no—
38C2×C4⋊Dic73—21no—
39C2×C4⋊Dic73—21no—
40C2×C4⋊Dic73D411yescharacteristic
41C2×#11924007C2×C412yes—
42C2×C4×Dic73D412yes—
43C4⋊#10596831—21no—
44C4⋊#10596831—21no—
45C4⋊#10596831D412yes—
46#14556520—24no—
47#14556509—42no—
48C22⋊#10596831—21no—
49C4×#10596831—21no—
50C8×Dic73—24no—
51#14556498—24no—
52C2×M16×C73—21no—
53C2×C4⋊C4×C73—21no—
54C2×C42×C73—21no—
55C2×C42×C73C2311yescharacteristic
56C4⋊C8×C73—21no—
57C4⋊C8×C73—21no—
58C4⋊C8×C73D412yes—
59C22⋊C8×C73—21no—
60C4×C8×C73—21no—
61#95×C73C2×C412yes—
62C2×Dic146—21no—
63C2×Dic146—21no—
64C2×Dic146—21no—
65C2×Dic146—21no—
66C2×Dic146—22no—
67C2×Dic146—22no—
68C2×Dic146—82no—
69C2×Dic146SD1612yes—
70C2×Dic146Q1612yes—
71C22×Dic73—22no—
72C22×Dic73C22⋊C412yes—
73C22×Dic73C22⋊C412yes—
74#11924012—41no—
75#11924012—41no—
76C2×#10596831—22no—
77C2×#10596831—41no—
78C4⋊Dic73—21no—
79C4⋊Dic73—21no—
80C4⋊Dic73—41no—
81C4⋊Dic73—41no—
82C4⋊Dic73—41no—
83C4⋊Dic73—41no—
84C4⋊Dic73—84no—
85#11924007—22no—
86#11924007—22no—
87C4×Dic73—22no—
88C4×Dic73—22no—
89C22×C4×C73—22no—
90C22×C4×C73C22×C411yescharacteristic
91C22×C4×C73C2×D411yescharacteristic
92C22×C4×C73C2×D411yescharacteristic
93M16×C73—41no—
94M16×C73—41no—
95C2×C8×C73—22no—
96C2×C8×C73—41no—
97C4⋊C4×C73—24no—
98C42×C73—41no—
99C42×C73—41no—
100C42×C73C2×D411yescharacteristic
101C42×C73C2×D411yescharacteristic
102C42×C73#4111yescharacteristic
103C42×C73#4111yescharacteristic
104C23×C73C2×C22⋊C411yescharacteristic
105C2×C4×C73—22no—
106C2×C4×C73—24no—
107C2×C4×C73—41no—
108C2×C4×C73—42no—
109C2×C4×C73—42no—
110C2×C4×C73C4×D411yescharacteristic
111C2×C4×C73C4×D411yescharacteristic
112C2×C4×C73#12011yescharacteristic
113C2×C4×C73#12111yescharacteristic
114C2×C4×C73#12111yescharacteristic
115C2×C4×C73#12311yescharacteristic
116C2×C4×C73C2×SD1611yescharacteristic
117C2×C4×C73C2×Q1611yescharacteristic
118C2×C4×C73#13511yescharacteristic
119C2×C4×C73#13511yescharacteristic
120C2×Dic73—22no—
121C2×Dic73—22no—
122C2×Dic73—22no—
123C2×Dic73—42no—
124C2×Dic73—44no—
125C2×Dic73—42no—
126C2×Dic73#10314yes—
127Dic146—22no—
128Dic146—22no—
129Dic146—22no—
130Dic146—22no—
131Dic146—82no—
132Dic146—82no—
133C8×C73—42no—
134C8×C73—81no—
135#10596831—42no—
136#10596831—81no—
137C22×C73—21no—
138C22×C73—21no—
139C22×C73#38611yescharacteristic
140C22×C73C2×#10311yescharacteristic
141C22×C73#41611yescharacteristic
142C4×C73—21no—
143C4×C73—21no—
144C4×C73—21no—
145C4×C73—44no—
146C4×C73#45612yes—
147C4×C73#46511yescharacteristic
148C4×C73#46511yescharacteristic
149C4×C73#46711yescharacteristic
150C4×C73#46711yescharacteristic
151Dic73—24no—
152Dic73—42no—
153Dic73—82no—
154#9392—731nomaximal, Sylow
155C2×C73—21no—
156C2×C73—21no—
157C2×C73#188611yescharacteristic
158C2×C73#189211yescharacteristic
159C2×C73#191411yescharacteristic
160#2982—731no—
161#2567—731no—
162#1801—731no—
163#1548—731no—
164#1548—731no—
165#1303—731no—
166#1303D7311yescharacteristic
167C73#939211yescharacteristic, complemented, Sylow
168C2×C4⋊Q8—731no—
169C2×C4×Q8—731no—
170C8×Q8—1462no—
171C8×Q8—1462no—
172#431—731no—
173#431—1462no—
174#431C2×D7311yescharacteristic
175#423—731no—
176#423C2×D7311yescharacteristic
177C2×#101—1461no—
178#395—734no—
179#391—1461no—
180#389—1462no—
181#384—1461no—
182C4×C4⋊C4C2×D7311yescharacteristic
183#343—1461no—
184#333—1462no—
185#333—1462no—
186C22×Q8—731no—
187C22×Q8—732no—
188C2×M16—21no—
189C2×M16—1461no—
190C4⋊Q8—1461no—
191C4⋊Q8—1461no—
192C4⋊Q8—1461no—
193C4⋊Q8—1461no—
194C4×Q8—1461no—
195C4×Q8—1461no—
196C4×Q8—1461no—
197C4×Q8—1461no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—732no—
200C2×C4⋊C4—731no—
201C2×C4⋊C4—1461no—
202C2×C4⋊C4—1461no—
203C2×C4⋊C4—1464no—
204C2×C42—21no—
205C2×C42—732no—
206C2×C42C22×D7311yescharacteristic
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—732no—
210C4⋊C8—1464no—
211C4⋊C8—1461no—
212C4⋊C8—1461no—
213C4⋊C8D29212yes—
214#101—2922no—
215C22⋊C8—21no—
216C22⋊C8—1461no—
217C4×C8—21no—
218C4×C8—1464no—
219C4×C8—1461no—
220#95—1464no—
221#95C4×D7312yes—
222C2×Q8—5842no—
223C2×Q8—732no—
224C2×Q8—732no—
225C2×Q8—1462no—
226C2×Q8—1462no—
227C2×Q8—1461no—
228C2×Q8—1461no—
229C2×Q8—1461no—
230C2×Q8—1461no—
231C22×C4—22no—
232C22×C4—732no—
233C22×C4—732no—
234C22×C4—1462no—
235C22×C4C2×C4×D7311yescharacteristic
236C22×C4D4×D7311yescharacteristic
237C22×C4D4×D7311yescharacteristic
238M16—41no—
239M16—41no—
240M16—2921no—
241M16—2921no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—2921no—
245C2×C8—1462no—
246C4⋊C4—24no—
247C4⋊C4—2921no—
248C4⋊C4—2921no—
249C4⋊C4—2921no—
250C4⋊C4—2921no—
251C4⋊C4—5844no—
252C4⋊C4—1462no—
253C4⋊C4—1462no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C42—41no—
257C42—41no—
258C42—1462no—
259C42—1462no—
260C42D4×D7311yescharacteristic
261C42C2×D29211yescharacteristic
262C42#1192402811yescharacteristic
263C42#1192402911yescharacteristic
264C23C22⋊C4×D7311yescharacteristic
265Q8—5842no—
266Q8—5842no—
267Q8—1462no—
268Q8—1462no—
269Q8—1462no—
270Q8—1462no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—2922no—
277C2×C4—2924no—
278C2×C4—2922no—
279C2×C4—734no—
280C2×C4—1462no—
281C2×C4—1462no—
282C2×C4—1462no—
283C2×C4#1455655311yescharacteristic
284C2×C4C4×D29211yescharacteristic
285C2×C4#1455656111yescharacteristic
286C2×C4#1455656411yescharacteristic
287C2×C4#1455656611yescharacteristic
288C2×C4#1455657611yescharacteristic
289C2×C4SD16×D7311yescharacteristic
290C2×C4Q16×D7311yescharacteristic
291C2×C4#1455661011yescharacteristic
292C2×C4#1455661211yescharacteristic
293C8—42no—
294C8—81no—
295C8—2922no—
296C8—5841no—
297C22—21no—
298C22—21no—
299C22#1798846511yescharacteristic
300C22#103×D7311yescharacteristic
301C22#1798858011yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—44no—
306C4—2922no—
307C4—5842no—
308C4—1464no—
309C4#1798877112yes—
310C4#1798881511yescharacteristic
311C4#1798881711yescharacteristic
312C4#1798882711yescharacteristic
313C4#1798882911yescharacteristic
314C2—21no—
315C2—21no—
316C2#2261032311yescharacteristic
317C2#2261035311yescharacteristic
318C2#2261047711yescharacteristic
subgroupG/H
centerC22#17988465
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1303C2
socleC22×C73#386
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C42×C73C23
hypercenter#1303D73
hypocenterC73#9392
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
167. C73#9392semidirect

Maximal subgroups

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

subgroupindex
#226190112
#226151392
#226099242
#226086132
#226086112
#226078342
C73×#13032
#939273