Finite Group Databasebeta

← #32988726

Subgroups — #32988726

Order 18688.

516 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 105 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#22621075C211yesmaximal, characteristic
2#22620879C211yesmaximal, characteristic
3#22610908C211yesmaximal, characteristic
4#22608612C211yesmaximal, characteristic
5#22608603C211yesmaximal, characteristic
6#22607764C211yesmaximal, characteristic
7C73×#2862C211yesmaximal, characteristic
8#17989144C2211yescharacteristic
9#17988983—21no—
10#17988966—21no—
11#17988939—21no—
12#17988937—21no—
13#17988917—22no—
14#17988869—22no—
15#17988794—22no—
16#17988743—22no—
17#17988640C2211yescharacteristic
18#17988640C2211yescharacteristic
19#17988611C2211yescharacteristic
20#17988347—22no—
21#17988336—22no—
22#17988333—22no—
23C2×C4⋊Q8×C73C2211yescharacteristic
24C2×C4⋊Q8×C73C2211yescharacteristic
25#391×C73—22no—
26#391×C73—22no—
27#382×C73—22no—
28C43×C73C2211yescharacteristic
29C2×#11924018—24no—
30C2×#11924012—21no—
31#14556591D411yescharacteristic
32#14556591D411yescharacteristic
33#14556583—21no—
34#14556570—21no—
35#14556570—21no—
36C4×Dic146—21no—
37C4×Dic146—21no—
38#14556550—21no—
39#14556522—24no—
40C4⋊#10596831—21no—
41C4⋊#10596831—21no—
42C4⋊#10596831D412yes—
43C4⋊#10596831D412yes—
44#14556515—24no—
45#14556514—24no—
46C22⋊#10596831—21no—
47C22⋊#10596831—21no—
48C4×#10596831—21no—
49C4×#10596831—21no—
50C22×Q8×C73—21no—
51C22×Q8×C73D412yes—
52C4⋊Q8×C73—21no—
53C4⋊Q8×C73—21no—
54C4⋊Q8×C73—21no—
55C4⋊Q8×C73—21no—
56C4⋊Q8×C73—21no—
57C4⋊Q8×C73—21no—
58C4⋊Q8×C73—21no—
59C4⋊Q8×C73—21no—
60C2×C4⋊C4×C73—21no—
61C2×C4⋊C4×C73—21no—
62C2×C4⋊C4×C73—21no—
63C2×C4⋊C4×C73D412yes—
64C2×C42×C73—21no—
65C2×C42×C73—21no—
66C2×C42×C73D412yes—
67C2×C42×C73C2311yescharacteristic
68#95×C73—28no—
69C2×Dic146—21no—
70C2×Dic146—21no—
71#11924018—84no—
72#11924012—42no—
73C2×#10596831—22no—
74C2×#10596831—22no—
75C2×#10596831—41no—
76C4⋊Dic73—21no—
77C4⋊Dic73—21no—
78C4⋊Dic73—21no—
79C4⋊Dic73—21no—
80#11924007—41no—
81#11924007—41no—
82C22⋊Dic73—41no—
83C4×Dic73—41no—
84C2×Q8×C73—22no—
85C2×Q8×C73—22no—
86C2×Q8×C73—44no—
87C2×Q8×C73—41no—
88C2×Q8×C73—41no—
89C2×Q8×C73—42no—
90C2×Q8×C73—42no—
91C22×C4×C73—22no—
92C22×C4×C73—22no—
93C22×C4×C73—22no—
94C22×C4×C73C2×D411yescharacteristic
95C22×C4×C73C2×D411yescharacteristic
96C22×C4×C73C2×D411yescharacteristic
97C4⋊C4×C73—22no—
98C4⋊C4×C73—22no—
99C4⋊C4×C73—41no—
100C4⋊C4×C73—41no—
101C4⋊C4×C73—41no—
102C4⋊C4×C73—41no—
103C4⋊C4×C73—41no—
104C4⋊C4×C73—41no—
105C42×C73—24no—
106C42×C73—22no—
107C42×C73—22no—
108C42×C73—42no—
109C42×C73C2×D411yescharacteristic
110C42×C73C2×D411yescharacteristic
111C42×C73C2×D411yescharacteristic
112C42×C73#4111yescharacteristic
113C23×C73#12011yescharacteristic
114Q8×C73—44no—
115Q8×C73—82no—
116Q8×C73—82no—
117Q8×C73—81no—
118Q8×C73—81no—
119C2×C4×C73—22no—
120C2×C4×C73—22no—
121C2×C4×C73—24no—
122C2×C4×C73—42no—
123C2×C4×C73—42no—
124C2×C4×C73—44no—
125C2×C4×C73—42no—
126C2×C4×C73—42no—
127C2×C4×C73—44no—
128C2×C4×C73#12011yescharacteristic
129C2×C4×C73#12011yescharacteristic
130C2×C4×C73#12111yescharacteristic
131C2×C4×C73#12111yescharacteristic
132C2×C4×C73#12111yescharacteristic
133C2×C4×C73#12711yescharacteristic
134C2×C4×C73#13512yes—
135C2×C4×C73#13712yes—
136C2×Dic73—41no—
137C2×Dic73—41no—
138Dic146—42no—
139Dic146—42no—
140#10596831—42no—
141#10596831—42no—
142#10596831—81no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73#39211yescharacteristic
146C22×C73#45212yes—
147C4×C73—21no—
148C4×C73—21no—
149C4×C73—44no—
150C4×C73—82no—
151C4×C73—82no—
152C4×C73#45512yes—
153C4×C73#45612yes—
154C4×C73#46412yes—
155C4×C73#49511yescharacteristic
156C4×C73#49711yescharacteristic
157Dic73—81no—
158Dic73—81no—
159#10298—731nomaximal, Sylow
160C2×C73—22no—
161C2×C73#200411yescharacteristic
162C2×C73#200511yescharacteristic
163C2×C73#201511yescharacteristic
164#3229—731no—
165#3209—731no—
166#2862D7311yescharacteristic
167#1994—731no—
168#1548—731no—
169#1546—731no—
170#1276—731no—
171C73#1029811yescharacteristic, complemented, Sylow
172#533—731no—
173C2×C4⋊Q8C2×D7311yescharacteristic
174C2×C4⋊Q8C2×D7311yescharacteristic
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#423—731no—
186#391—22no—
187#391—22no—
188#382—22no—
189C43C2×D7311yescharacteristic
190#339—1462no—
191#333—1462no—
192#332—1462no—
193C22×Q8—21no—
194C22×Q8C22⋊D7312yes—
195C2×Q16—1464no—
196C2×M16—1461no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—731no—
206C4⋊Q8—731no—
207#125—1461no—
208C22⋊Q8—1461no—
209C22⋊Q8—1461no—
210C4×Q8—1461no—
211C4×Q8—1461no—
212#117—1461no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4C22⋊D7312yes—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42C22⋊D7312yes—
220C2×C42C22×D7311yescharacteristic
221#106—1464no—
222C4⋊C8—732no—
223C4⋊C8—732no—
224C4⋊C8—1461no—
225C4⋊C8—1461no—
226#103—1464no—
227#103—1464no—
228C22⋊C8—1461no—
229C22⋊C8—1461no—
230C4×C8—1461no—
231C4×C8—1461no—
232#95—28no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—44no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×Q8—1461no—
241C2×Q8—1461no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4C2×C22⋊D7311yescharacteristic
246C22×C4C2×C22⋊D7311yescharacteristic
247C22×C4C2×C22⋊D7311yescharacteristic
248Q16—5844no—
249M16—2922no—
250C2×C8—2921no—
251C2×C8—1462no—
252C2×C8—1462no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—2921no—
262C4⋊C4—2921no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C22⋊C4—2921no—
268C42—24no—
269C42—22no—
270C42—22no—
271C42—42no—
272C42—2921no—
273C42D4×D7311yescharacteristic
274C42D4×D7311yescharacteristic
275C42D4×D7311yescharacteristic
276C42#1192402711yescharacteristic
277C23#1455656011yescharacteristic
278Q8—44no—
279Q8—82no—
280Q8—81no—
281Q8—81no—
282Q8—82no—
283Q8—2922no—
284Q8—2922no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—2921no—
295C2×C4—2921no—
296C2×C4#1455655911yescharacteristic
297C2×C4#1455655911yescharacteristic
298C2×C4#1455656211yescharacteristic
299C2×C4#1455656311yescharacteristic
300C2×C4#1455656311yescharacteristic
301C2×C4#1455658711yescharacteristic
302C2×C4#1455661112yes—
303C2×C4#1455662112yes—
304C8—2922no—
305C8—2922no—
306C8—5841no—
307C22—21no—
308C22—21no—
309C22#1798849511yescharacteristic
310C22#1798874912yes—
311C4—21no—
312C4—21no—
313C4—44no—
314C4—82no—
315C4—82no—
316C4—5841no—
317C4—5841no—
318C4#1798876412yes—
319C4#1798876912yes—
320C4#1798880612yes—
321C4#1798896911yescharacteristic
322C4#1798898211yescharacteristic
323C2—22no—
324C2#2261096011yescharacteristic
325C2#2261096711yescharacteristic
326C2#2261102511yescharacteristic
subgroupG/H
centerC22#17988495
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2862C2
socleC22×C73#392
prime radicalC23×C73#120
hypercenter#2862D73
hypocenterC73#10298
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2862

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
#226210752
#226208792
#226109082
#226086122
#226086032
#226077642
C73×#28622
#1029873