Finite Group Databasebeta

← #32988725

Subgroups — #32988725

Order 18688.

516 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 103 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#22621072C211yesmaximal, characteristic
2#22620876C211yesmaximal, characteristic
3#22618309C211yesmaximal, characteristic
4#22608613C211yesmaximal, characteristic
5#22608604C211yesmaximal, characteristic
6#22607764C211yesmaximal, characteristic
7C73×#1994C211yesmaximal, characteristic
8C2×#14556591C2211yescharacteristic
9C2×#14556591C2211yescharacteristic
10#17988983—21no—
11#17988966—21no—
12#17988939—21no—
13#17988937—21no—
14#17988915—22no—
15#17988872—22no—
16#17988797—22no—
17#17988742—22no—
18#17988640C2211yescharacteristic
19#17988640C2211yescharacteristic
20#17988493—22no—
21#17988493—22no—
22#17988453—22no—
23#17988335—22no—
24#17988334—22no—
25#533×C73C2211yescharacteristic
26#423×C73C2211yescharacteristic
27C43×C73C2211yescharacteristic
28#339×C73—22no—
29C22×Dic146—21no—
30C22×Dic146D412yes—
31C2×#11924018—24no—
32#14556591—21no—
33#14556591—21no—
34#14556591—21no—
35#14556591—21no—
36#14556591—21no—
37#14556591—21no—
38#14556591—21no—
39#14556591—21no—
40C2×C4⋊Dic73—21no—
41C2×C4⋊Dic73—21no—
42C2×C4⋊Dic73—21no—
43C2×C4⋊Dic73D412yes—
44#14556522—24no—
45C4⋊#10596831D412yes—
46C4⋊#10596831D412yes—
47#14556515—24no—
48#14556514—24no—
49C22⋊#10596831—21no—
50C22⋊#10596831—21no—
51C4×#10596831—21no—
52C4×#10596831—21no—
53#14556498—28no—
54C2×M16×C73—21no—
55C4⋊Q8×C73D411yescharacteristic
56C4⋊Q8×C73D411yescharacteristic
57#125×C73—21no—
58C22⋊Q8×C73—21no—
59C22⋊Q8×C73—21no—
60C4×Q8×C73—21no—
61C4×Q8×C73—21no—
62#117×C73—21no—
63C2×C42×C73—21no—
64C2×C42×C73—21no—
65C2×C42×C73D412yes—
66C2×C42×C73C2311yescharacteristic
67C4⋊C8×C73—21no—
68C4⋊C8×C73—21no—
69C2×Dic146—22no—
70C2×Dic146—22no—
71C2×Dic146—44no—
72C2×Dic146—41no—
73C2×Dic146—41no—
74C2×Dic146—42no—
75C2×Dic146—42no—
76C22×Dic73—22no—
77C22×Dic73—22no—
78#11924018—84no—
79C2×#10596831—22no—
80C2×#10596831—22no—
81C4⋊Dic73—22no—
82C4⋊Dic73—22no—
83C4⋊Dic73—41no—
84C4⋊Dic73—41no—
85C4⋊Dic73—41no—
86C4⋊Dic73—41no—
87C4⋊Dic73—41no—
88C4⋊Dic73—41no—
89C2×Q8×C73—21no—
90C2×Q8×C73—21no—
91C22×C4×C73—22no—
92C22×C4×C73C2×D411yescharacteristic
93C22×C4×C73C2×D411yescharacteristic
94C22×C4×C73C2×D411yescharacteristic
95M16×C73—42no—
96C2×C8×C73—41no—
97C4⋊C4×C73—21no—
98C4⋊C4×C73—21no—
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73—41no—
102C4⋊C4×C73—41no—
103C22⋊C4×C73—41no—
104C42×C73—24no—
105C42×C73—22no—
106C42×C73—22no—
107C42×C73—42no—
108C42×C73—41no—
109C42×C73C2×D411yescharacteristic
110C42×C73C2×D411yescharacteristic
111C42×C73C2×D411yescharacteristic
112C42×C73#4111yescharacteristic
113C23×C73#12011yescharacteristic
114Q8×C73—42no—
115Q8×C73—42no—
116C2×C4×C73—22no—
117C2×C4×C73—22no—
118C2×C4×C73—24no—
119C2×C4×C73—42no—
120C2×C4×C73—42no—
121C2×C4×C73—41no—
122C2×C4×C73—41no—
123C2×C4×C73#12011yescharacteristic
124C2×C4×C73#12011yescharacteristic
125C2×C4×C73#12111yescharacteristic
126C2×C4×C73#12111yescharacteristic
127C2×C4×C73#12111yescharacteristic
128C2×C4×C73#12711yescharacteristic
129C2×C4×C73#13512yes—
130C2×C4×C73#13712yes—
131C2×Dic73—44no—
132C2×Dic73—42no—
133C2×Dic73—42no—
134C2×Dic73—44no—
135Dic146—44no—
136Dic146—82no—
137Dic146—81no—
138Dic146—81no—
139Dic146—82no—
140C8×C73—81no—
141#10596831—42no—
142#10596831—42no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73#39211yescharacteristic
146C22×C73#45212yes—
147C4×C73—21no—
148C4×C73—21no—
149C4×C73—44no—
150C4×C73—81no—
151C4×C73—81no—
152C4×C73#45512yes—
153C4×C73#45612yes—
154C4×C73#46412yes—
155C4×C73#49511yescharacteristic
156C4×C73#49711yescharacteristic
157Dic73—82no—
158Dic73—82no—
159#10298—731nomaximal, Sylow
160C2×C73—22no—
161C2×C73#200411yescharacteristic
162C2×C73#200511yescharacteristic
163C2×C73#201511yescharacteristic
164#3229—731no—
165#3209—731no—
166#2862—731no—
167#1994D7311yescharacteristic
168#1548—731no—
169#1546—731no—
170#1276—731no—
171C73#1029811yescharacteristic, complemented, Sylow
172#533C2×D7311yescharacteristic
173C2×C4⋊Q8—731no—
174C2×C4⋊Q8—731no—
175#498—1461no—
176#494—1461no—
177#487—1461no—
178#487—1461no—
179#483—1462no—
180#475—1462no—
181#462—1462no—
182#451—1462no—
183#431—731no—
184#431—731no—
185#423C2×D7311yescharacteristic
186#391—1462no—
187#391—1462no—
188#382—1462no—
189C43C2×D7311yescharacteristic
190#339—22no—
191#333—1462no—
192#332—1462no—
193C22×Q8—732no—
194C22×Q8—1461no—
195C2×Q16—1464no—
196C2×M16—21no—
197C4⋊Q8—1461no—
198C4⋊Q8—1461no—
199C4⋊Q8—1461no—
200C4⋊Q8—1461no—
201C4⋊Q8—1461no—
202C4⋊Q8—1461no—
203C4⋊Q8—1461no—
204C4⋊Q8—1461no—
205C4⋊Q8D29211yescharacteristic
206C4⋊Q8D29211yescharacteristic
207#125—21no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C4×Q8—21no—
211C4×Q8—21no—
212#117—21no—
213C2×C4⋊C4—732no—
214C2×C4⋊C4—1461no—
215C2×C4⋊C4—1461no—
216C2×C4⋊C4—1461no—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42C22⋊D7312yes—
220C2×C42C22×D7311yescharacteristic
221#106—1464no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—732no—
225C4⋊C8—732no—
226#103—1464no—
227#103—1464no—
228C22⋊C8—1461no—
229C22⋊C8—1461no—
230C4×C8—1461no—
231C4×C8—1461no—
232#95—1468no—
233C2×Q8—21no—
234C2×Q8—21no—
235C2×Q8—2924no—
236C2×Q8—2921no—
237C2×Q8—2921no—
238C2×Q8—2922no—
239C2×Q8—2922no—
240C2×Q8—1462no—
241C2×Q8—1462no—
242C22×C4—22no—
243C22×C4—1462no—
244C22×C4—1462no—
245C22×C4D4×D7311yescharacteristic
246C22×C4D4×D7311yescharacteristic
247C22×C4C2×C22⋊D7311yescharacteristic
248Q16—5844no—
249M16—42no—
250C2×C8—41no—
251C2×C8—1462no—
252C2×C8—1462no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—2921no—
260C4⋊C4—2921no—
261C4⋊C4—2921no—
262C4⋊C4—2921no—
263C4⋊C4—2921no—
264C4⋊C4—2921no—
265C4⋊C4—1462no—
266C4⋊C4—1462no—
267C22⋊C4—41no—
268C42—24no—
269C42—22no—
270C42—22no—
271C42—42no—
272C42—41no—
273C42D4×D7311yescharacteristic
274C42D4×D7311yescharacteristic
275C42C2×D29211yescharacteristic
276C42#1192402811yescharacteristic
277C23#1455655911yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—2924no—
281Q8—5842no—
282Q8—5841no—
283Q8—5841no—
284Q8—5842no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—2924no—
293C2×C4—2924no—
294C2×C4—2922no—
295C2×C4—2922no—
296C2×C4#1455656111yescharacteristic
297C2×C4#1455656111yescharacteristic
298C2×C4#1455656411yescharacteristic
299C2×C4#1455656411yescharacteristic
300C2×C4#1455656511yescharacteristic
301C2×C4#1455658711yescharacteristic
302C2×C4#1455661112yes—
303C2×C4#1455662212yes—
304C8—81no—
305C8—2922no—
306C8—2922no—
307C22—21no—
308C22—21no—
309C22#1798849611yescharacteristic
310C22#1798874712yes—
311C4—21no—
312C4—21no—
313C4—44no—
314C4—81no—
315C4—81no—
316C4—5842no—
317C4—5842no—
318C4#1798876612yes—
319C4#1798877112yes—
320C4#1798880912yes—
321C4#1798896911yescharacteristic
322C4#1798897911yescharacteristic
323C2—22no—
324C2#2261095911yescharacteristic
325C2#2261096611yescharacteristic
326C2#2261102411yescharacteristic
subgroupG/H
centerC22#17988496
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1994C2
socleC22×C73#392
prime radicalC23×C73#120
hypercenter#1994D73
hypocenterC73#10298
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
171. C73#10298semidirect

Maximal subgroups

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

subgroupindex
#226210722
#226208762
#226183092
#226086132
#226086042
#226077642
C73×#19942
#1029873