Finite Group Databasebeta

← #32983403

Subgroups — #32983403

Order 18688.

450 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 109 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#22619014C211yesmaximal, characteristic
2#22615146C211yesmaximal, characteristic
3#22609924C211yesmaximal, characteristic
4#22608617C211yesmaximal, characteristic
5#22608615C211yesmaximal, characteristic
6#22607834C211yesmaximal, characteristic
7C73×#1303C211yesmaximal, characteristic
8C2×#14556591C2211yescharacteristic
9C2×C4×Dic146C2211yescharacteristic
10#17988717—22no—
11#17988714—22no—
12#17988641—22no—
13#17988640C2211yescharacteristic
14#17988611C2211yescharacteristic
15C2×#14556509—21no—
16#17988527C414yes—
17#17988493—21no—
18#17988492—22no—
19#17988453—21no—
20#17988355—21no—
21#17988334—22no—
22#17988332—22no—
23#431×C73C2211yescharacteristic
24#423×C73C2211yescharacteristic
25C4×C4⋊C4×C73C2211yescharacteristic
26C22×Dic146—21no—
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—21no—
38C2×C4⋊Dic73C2×C412yes—
39C2×C4⋊Dic73D411yescharacteristic
40C2×#11924007C2×C412yes—
41C2×C4×Dic73D412yes—
42C4⋊#10596831—21no—
43C4⋊#10596831—21no—
44C4⋊#10596831D412yes—
45#14556520—24no—
46#14556509—42no—
47C22⋊#10596831—21no—
48#14556501—24no—
49C4×#10596831—21no—
50#14556498—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—21no—
67C2×Dic146—21no—
68C2×Dic146—44no—
69C2×Dic146—41no—
70C2×Dic146—41no—
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—22no—
81C4⋊Dic73—22no—
82C4⋊Dic73—41no—
83C4⋊Dic73—41no—
84#11924007—22no—
85#11924007—22no—
86C4×Dic73—22no—
87C4×Dic73—22no—
88C22×C4×C73—22no—
89C22×C4×C73C22×C411yescharacteristic
90C22×C4×C73C2×D411yescharacteristic
91C22×C4×C73C2×D411yescharacteristic
92M16×C73—41no—
93M16×C73—41no—
94C2×C8×C73—22no—
95C2×C8×C73—41no—
96C4⋊C4×C73—42no—
97C42×C73—41no—
98C42×C73—41no—
99C42×C73C2×D411yescharacteristic
100C42×C73C2×D411yescharacteristic
101C42×C73#4111yescharacteristic
102C42×C73#4111yescharacteristic
103C23×C73C2×C22⋊C411yescharacteristic
104C2×C4×C73—22no—
105C2×C4×C73—41no—
106C2×C4×C73—42no—
107C2×C4×C73—42no—
108C2×C4×C73—42no—
109C2×C4×C73C4×D411yescharacteristic
110C2×C4×C73C4×D411yescharacteristic
111C2×C4×C73#12011yescharacteristic
112C2×C4×C73#12111yescharacteristic
113C2×C4×C73#12111yescharacteristic
114C2×C4×C73#12311yescharacteristic
115C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C73#13711yescharacteristic
117C2×C4×C73#13711yescharacteristic
118C2×C4×C73#13711yescharacteristic
119C2×Dic73—22no—
120C2×Dic73—22no—
121C2×Dic73—22no—
122C2×Dic73—22no—
123C2×Dic73—42no—
124C2×Dic73—44no—
125C2×Dic73—42no—
126Dic146—41no—
127Dic146—41no—
128Dic146—41no—
129Dic146—41no—
130Dic146—82no—
131Dic146—82no—
132C8×C73—42no—
133C8×C73—81no—
134#10596831—42no—
135#10596831—81no—
136C22×C73—21no—
137C22×C73—21no—
138C22×C73#38611yescharacteristic
139C22×C73#41711yescharacteristic
140C22×C73#41911yescharacteristic
141C4×C73—21no—
142C4×C73—21no—
143C4×C73—21no—
144C4×C73—82no—
145C4×C73#45412yes—
146C4×C73#46811yescharacteristic
147C4×C73#46811yescharacteristic
148C4×C73#47011yescharacteristic
149C4×C73#47011yescharacteristic
150Dic73—42no—
151Dic73—42no—
152Dic73—82no—
153#9404—731nomaximal, Sylow
154C2×C73—21no—
155C2×C73—21no—
156C2×C73#188811yescharacteristic
157C2×C73#189411yescharacteristic
158C2×C73#191511yescharacteristic
159#2983—731no—
160#2568—731no—
161#1801—731no—
162#1549—731no—
163#1549—731no—
164#1303—731no—
165#1303D7311yescharacteristic
166C73#940411yescharacteristic, complemented, Sylow
167C2×C4⋊Q8—731no—
168C2×C4×Q8—731no—
169#446—1462no—
170#446—1462no—
171#432—1462no—
172#431—731no—
173#431C2×D7311yescharacteristic
174#423—731no—
175#423C2×D7311yescharacteristic
176C2×#101—1461no—
177#400—734no—
178#391—1461no—
179#391—1462no—
180#382—1461no—
181C4×C4⋊C4C2×D7311yescharacteristic
182#343—1461no—
183#332—1462no—
184#332—1462no—
185C22×Q8—731no—
186C22×Q8—1461no—
187C2×M16—21no—
188C2×M16—1461no—
189C4⋊Q8—1461no—
190C4⋊Q8—1461no—
191C4⋊Q8—1461no—
192C4⋊Q8—1461no—
193C4×Q8—1461no—
194C4×Q8—1461no—
195C4×Q8—1461no—
196C4×Q8—1461no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—732no—
199C2×C4⋊C4—731no—
200C2×C4⋊C4—732no—
201C2×C4⋊C4—1461no—
202C2×C42—21no—
203C2×C42—732no—
204C2×C42C22×D7311yescharacteristic
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—732no—
208C4⋊C8—1464no—
209C4⋊C8—1461no—
210C4⋊C8—1461no—
211C4⋊C8D29212yes—
212#101—2922no—
213C22⋊C8—21no—
214C22⋊C8—1461no—
215#97—1464no—
216C4×C8—21no—
217C4×C8—1461no—
218#95—1464no—
219#95—1464no—
220#95C4×D7312yes—
221C2×Q8—2924no—
222C2×Q8—2921no—
223C2×Q8—2921no—
224C2×Q8—1461no—
225C2×Q8—1461no—
226C2×Q8—1461no—
227C2×Q8—1461no—
228C2×Q8—1461no—
229C2×Q8—1461no—
230C22×C4—22no—
231C22×C4—732no—
232C22×C4—732no—
233C22×C4—1462no—
234C22×C4C2×C4×D7311yescharacteristic
235C22×C4D4×D7311yescharacteristic
236C22×C4D4×D7311yescharacteristic
237M16—41no—
238M16—41no—
239M16—2921no—
240M16—2921no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—2921no—
244C2×C8—1462no—
245C4⋊C4—42no—
246C4⋊C4—2921no—
247C4⋊C4—2921no—
248C4⋊C4—1462no—
249C4⋊C4—1462no—
250C4⋊C4—1462no—
251C4⋊C4—1462no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C42—41no—
255C42—41no—
256C42—1462no—
257C42—1462no—
258C42D4×D7311yescharacteristic
259C42C2×D29211yescharacteristic
260C42#1192402811yescharacteristic
261C42#1192402911yescharacteristic
262C23C22⋊C4×D7311yescharacteristic
263Q8—2921no—
264Q8—2921no—
265Q8—2921no—
266Q8—2921no—
267Q8—5842no—
268Q8—5842no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—2922no—
275C2×C4—2924no—
276C2×C4—2922no—
277C2×C4—1462no—
278C2×C4—1462no—
279C2×C4—1462no—
280C2×C4—1462no—
281C2×C4#1455655311yescharacteristic
282C2×C4C4×D29211yescharacteristic
283C2×C4#1455656111yescharacteristic
284C2×C4#1455656411yescharacteristic
285C2×C4#1455656611yescharacteristic
286C2×C4#1455657611yescharacteristic
287C2×C4#1455661511yescharacteristic
288C2×C4#1455662011yescharacteristic
289C2×C4#1455662011yescharacteristic
290C2×C4#1455662311yescharacteristic
291C8—42no—
292C8—81no—
293C8—2922no—
294C8—5841no—
295C22—21no—
296C22—21no—
297C22#1798846511yescharacteristic
298C22#1798858511yescharacteristic
299C22#1798859411yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—82no—
304C4—2922no—
305C4—2922no—
306C4—5842no—
307C4#1798876112yes—
308C4#1798883211yescharacteristic
309C4#1798883411yescharacteristic
310C4#1798884411yescharacteristic
311C4#1798884611yescharacteristic
312C2—21no—
313C2—21no—
314C2#2261033311yescharacteristic
315C2#2261036311yescharacteristic
316C2#2261048211yescharacteristic
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#9404
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
166. C73#9404semidirect

Maximal subgroups

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

subgroupindex
#226190142
#226151462
#226099242
#226086172
#226086152
#226078342
C73×#13032
#940473