Finite Group Databasebeta

← #32989591

Subgroups — #32989591

Order 18688.

408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#17988794C211yesmaximal, characteristic
2#22609924C211yesmaximal, characteristic
3#22608706C211yesmaximal, characteristic
4#22608603C211yesmaximal, characteristic
5#22608325C211yesmaximal, characteristic
6#22607826C211yesmaximal, characteristic
7C73×#1546C211yesmaximal, characteristic
8C22×#11924018—21no—
9C2×C4×Dic146C2211yescharacteristic
10#17988794—22no—
11#17988794—22no—
12#17988640C2211yescharacteristic
13#17988611C2211yescharacteristic
14C2×C4⋊#10596831C2211yescharacteristic
15C2×#14556515—21no—
16C2×#14556509—21no—
17#17988355—21no—
18#17988340—22no—
19#17988333—22no—
20#17988317—22no—
21C2×C4⋊Q8×C73C2211yescharacteristic
22#431×C73C2211yescharacteristic
23#423×C73C2211yescharacteristic
24#332×C73—22no—
25C22×Dic146D411yescharacteristic
26C2×#11924018—24no—
27C2×#11924018—42no—
28C2×#11924018—42no—
29C2×#11924012—21no—
30C22×#10596831—21no—
31C4×Dic146—21no—
32C4×Dic146—21no—
33C4×Dic146—21no—
34C4×Dic146—21no—
35C2×C4⋊Dic73D411yescharacteristic
36C2×#11924007—21no—
37C2×C4×Dic73—21no—
38C4⋊#10596831—21no—
39C4⋊#10596831—21no—
40C4⋊#10596831—21no—
41C4⋊#10596831—21no—
42C4⋊#10596831D412yes—
43#14556515—24no—
44#14556509—42no—
45C22⋊#10596831—21no—
46C4×#10596831—21no—
47C22×Q8×C73—21no—
48C2×M16×C73—21no—
49C4⋊Q8×C73—21no—
50C4⋊Q8×C73—21no—
51C4⋊Q8×C73—21no—
52C4⋊Q8×C73D412yes—
53C2×C4⋊C4×C73—21no—
54C2×C4⋊C4×C73—21no—
55C2×C42×C73C2311yescharacteristic
56C4⋊C8×C73—21no—
57C4⋊C8×C73—21no—
58C4⋊C8×C73D412yes—
59C22⋊C8×C73—21no—
60C4×C8×C73—21no—
61C2×Dic146—21no—
62C2×Dic146—21no—
63C2×Dic146—21no—
64C2×Dic146—21no—
65C2×Dic146—21no—
66C2×Dic146D812yes—
67C22×Dic73—21no—
68C22×Dic73—21no—
69#11924018—48no—
70#11924012—41no—
71#11924012—41no—
72C2×#10596831—22no—
73C2×#10596831—41no—
74C2×#10596831—41no—
75C2×#10596831—41no—
76C2×#10596831—41no—
77C4⋊Dic73—21no—
78C4⋊Dic73—21no—
79#11924007—41no—
80#11924007—41no—
81C4×Dic73—41no—
82C4×Dic73—41no—
83C2×Q8×C73—22no—
84C2×Q8×C73—41no—
85C2×Q8×C73—41no—
86C2×Q8×C73—41no—
87C2×Q8×C73—41no—
88C2×Q8×C73—41no—
89C22×C4×C73—41no—
90C22×C4×C73C2×D411yescharacteristic
91C22×C4×C73#4111yescharacteristic
92C22×C4×C73#4111yescharacteristic
93M16×C73—41no—
94M16×C73—41no—
95C2×C8×C73—22no—
96C2×C8×C73—41no—
97C4⋊C4×C73—22no—
98C4⋊C4×C73—22no—
99C4⋊C4×C73—41no—
100C4⋊C4×C73—41no—
101C42×C73C2×D411yescharacteristic
102C42×C73C2×D411yescharacteristic
103C42×C73C2×D411yescharacteristic
104C42×C73#4111yescharacteristic
105C23×C73#12311yescharacteristic
106Q8×C73—42no—
107Q8×C73—42no—
108Q8×C73—81no—
109Q8×C73—81no—
110C2×C4×C73—22no—
111C2×C4×C73—41no—
112C2×C4×C73—42no—
113C2×C4×C73—81no—
114C2×C4×C73—81no—
115C2×C4×C73#12011yescharacteristic
116C2×C4×C73#12111yescharacteristic
117C2×C4×C73#12111yescharacteristic
118C2×C4×C73#12111yescharacteristic
119C2×C4×C73#12311yescharacteristic
120C2×C4×C73#12411yescharacteristic
121C2×C4×C73C2×D811yescharacteristic
122C2×C4×C73#13511yescharacteristic
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—81no—
130Dic146—22no—
131Dic146—22no—
132Dic146—41no—
133Dic146—41no—
134C8×C73—42no—
135C8×C73—81no—
136#10596831—42no—
137#10596831—81no—
138#10596831—81no—
139C22×C73—21no—
140C22×C73—21no—
141C22×C73#39411yescharacteristic
142C22×C73#48011yescharacteristic
143C22×C73#48211yescharacteristic
144C4×C73—21no—
145C4×C73—21no—
146C4×C73—21no—
147C4×C73—82no—
148C4×C73#44711yescharacteristic
149C4×C73#45211yescharacteristic
150C4×C73#46611yescharacteristic
151C4×C73#46811yescharacteristic
152C4×C73#47312yes—
153Dic73—42no—
154Dic73—81no—
155#10446—731nomaximal, Sylow
156C2×C73—21no—
157C2×C73—21no—
158C2×C73#203311yescharacteristic
159C2×C73#204711yescharacteristic
160C2×C73#204911yescharacteristic
161C2×#462—731no—
162#1801—731no—
163#1571—731no—
164#1546—731no—
165#1546D7311yescharacteristic
166#1479—731no—
167#1301—731no—
168C73#1044611yescharacteristic, complemented, Sylow
169C22×Q16—1461no—
170C2×C4⋊Q8C2×D7311yescharacteristic
171C2×C4×Q8—731no—
172#462—1462no—
173#462—1462no—
174#431—731no—
175#431C2×D7311yescharacteristic
176#423—731no—
177#423C2×D7311yescharacteristic
178C2×C4⋊C8—731no—
179C2×#103—1461no—
180C2×#101—1461no—
181#343—1461no—
182#335—1462no—
183#332—22no—
184#332—1462no—
185Q8⋊C8—1462no—
186C22×Q8—21no—
187C22×Q8—731no—
188C2×Q16—2922no—
189C2×Q16—2922no—
190C2×Q16—1464no—
191C2×M16—21no—
192C2×M16—1461no—
193C22×C8—1461no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8D29212yes—
198C4×Q8—1461no—
199C4×Q8—1461no—
200C4×Q8—1461no—
201C4×Q8—1461no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—731no—
205C2×C4⋊C4—1461no—
206C2×C42—1461no—
207C2×C42C22×D7311yescharacteristic
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—732no—
211C4⋊C8—1461no—
212C4⋊C8—1461no—
213C4⋊C8—1461no—
214C4⋊C8—1461no—
215C4⋊C8C22⋊D7312yes—
216#103—1464no—
217#101—2922no—
218C22⋊C8—21no—
219C22⋊C8—1461no—
220C4×C8—21no—
221C4×C8—1461no—
222C2×Q8—22no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—732no—
229C2×Q8—1461no—
230C2×Q8—1461no—
231C2×Q8—1461no—
232C2×Q8—1461no—
233C2×Q8—1461no—
234C22×C4—41no—
235C22×C4—1461no—
236C22×C4—1461no—
237C22×C4D4×D7311yescharacteristic
238C22×C4#1192402711yescharacteristic
239C22×C4#1192402811yescharacteristic
240Q16—2928no—
241M16—41no—
242M16—41no—
243M16—2921no—
244M16—2921no—
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—2921no—
248C2×C8—2921no—
249C2×C8—2921no—
250C2×C8—2921no—
251C2×C8—1462no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—2921no—
257C4⋊C4—2921no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
260C42—2921no—
261C42—2921no—
262C42D4×D7311yescharacteristic
263C42C2×C22⋊D7311yescharacteristic
264C42C2×D29211yescharacteristic
265C42#1192402711yescharacteristic
266C23#1455657311yescharacteristic
267Q8—42no—
268Q8—42no—
269Q8—81no—
270Q8—81no—
271Q8—2921no—
272Q8—2921no—
273Q8—1462no—
274Q8—1462no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—2921no—
281C2×C4—2921no—
282C2×C4—2921no—
283C2×C4—5841no—
284C2×C4—1462no—
285C2×C4#1455656111yescharacteristic
286C2×C4#1455656211yescharacteristic
287C2×C4#1455656311yescharacteristic
288C2×C4#1455656511yescharacteristic
289C2×C4#1455657511yescharacteristic
290C2×C4#1455657711yescharacteristic
291C2×C4D8×D7311yescharacteristic
292C2×C4#1455661011yescharacteristic
293C2×C4#1455661811yescharacteristic
294C2×C4#1455662011yescharacteristic
295C8—42no—
296C8—81no—
297C8—2922no—
298C8—5841no—
299C8—5841no—
300C22—21no—
301C22—21no—
302C22#1798850311yescharacteristic
303C22#1798889911yescharacteristic
304C22#1798890911yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—82no—
309C4—2922no—
310C4—5841no—
311C4#1798872211yescharacteristic
312C4#1798875011yescharacteristic
313C4#1798882011yescharacteristic
314C4#1798883011yescharacteristic
315C4#1798886012yes—
316C2—21no—
317C2—21no—
318C2#2261111211yescharacteristic
319C2#2261119811yescharacteristic
320C2#2261121011yescharacteristic
subgroupG/H
centerC22#17988503
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1546C2
socleC22×C73#394
prime radicalC23×C73#123
hypercenter#1546D73
hypocenterC73#10446
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
168. C73#10446semidirect

Maximal subgroups

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

subgroupindex
C2×#179887942
#226099242
#226087062
#226086032
#226083252
#226078262
C73×#15462
#1044673