Finite Group Databasebeta

← #32982522

Subgroups — #32982522

Order 18688.

428 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22621072C211yesmaximal, characteristic
2#22610775C211yesmaximal, characteristic
3#22608621C211yesmaximal, characteristic
4C2×#17988334C211yesmaximal, characteristic
5#22607828C211yesmaximal, characteristic
6#22607782C211yesmaximal, characteristic
7C73×#2962C211yesmaximal, characteristic
8C2×#14556591C2211yescharacteristic
9#17988983—21no—
10#17988937—21no—
11#17988915C414yes—
12#17988872—22no—
13#17988640C2211yescharacteristic
14#17988611C2211yescharacteristic
15C2×C4⋊#10596831C2211yescharacteristic
16C2×#14556509—21no—
17C2×#14556509—21no—
18#17988336—21no—
19#17988334—21no—
20#17988334—21no—
21#17988333—21no—
22#533×C73C2211yescharacteristic
23#446×C73—22no—
24#446×C73—21no—
25C8×Q8×C73—21no—
26#424×C73—21no—
27C2×C4⋊C8×C73C2211yescharacteristic
28#405×C73—21no—
29C4×M16×C73C2211yescharacteristic
30C22×Dic146—21no—
31C2×#11924012—21no—
32C22×#10596831—21no—
33#14556591—21no—
34#14556591—21no—
35#14556591—21no—
36#14556591—21no—
37C2×C4⋊Dic73—21no—
38C2×C4⋊Dic73C2×C412yes—
39#14556522—24no—
40C4⋊#10596831—21no—
41C4⋊#10596831—21no—
42C4⋊#10596831—21no—
43C4⋊#10596831—21no—
44C4⋊#10596831—21no—
45#14556515—24no—
46#14556509—42no—
47#14556509—42no—
48C22⋊#10596831C2×C412yes—
49C4×#10596831—21no—
50C2×M16×C73D411yescharacteristic
51C2×M16×C73D411yescharacteristic
52C22×C8×C73—21no—
53C4⋊Q8×C73D411yescharacteristic
54C4⋊Q8×C73D411yescharacteristic
55#125×C73—21no—
56C22⋊Q8×C73—21no—
57C22⋊Q8×C73C2×C412yes—
58C4×Q8×C73—21no—
59C4×Q8×C73D412yes—
60#117×C73—21no—
61C2×C42×C73C2311yescharacteristic
62C4⋊C8×C73—22no—
63C4⋊C8×C73—22no—
64C4⋊C8×C73—21no—
65C4⋊C8×C73D411yescharacteristic
66C4⋊C8×C73D411yescharacteristic
67#97×C73—22no—
68#97×C73—21no—
69C4×C8×C73—22no—
70C4×C8×C73—21no—
71C2×Dic146—41no—
72C2×Dic146—41no—
73C2×Dic146—41no—
74C2×Dic146—41no—
75C2×Dic146—41no—
76C2×Dic146—41no—
77C22×Dic73—22no—
78#11924012—41no—
79#11924012—41no—
80C2×#10596831—22no—
81C2×#10596831—41no—
82C2×#10596831—41no—
83C2×#10596831—81no—
84C4⋊Dic73—22no—
85C4⋊Dic73—22no—
86C4⋊Dic73—41no—
87C4⋊Dic73—41no—
88C2×Q8×C73—21no—
89C2×Q8×C73C22⋊C412yes—
90C22×C4×C73C22×C411yescharacteristic
91C22×C4×C73C2×D411yescharacteristic
92C22×C4×C73#4111yescharacteristic
93M16×C73—21no—
94M16×C73—21no—
95M16×C73—21no—
96M16×C73SD1612yes—
97C2×C8×C73—21no—
98C2×C8×C73—21no—
99C2×C8×C73—21no—
100C2×C8×C73—21no—
101C2×C8×C73—41no—
102C2×C8×C73—41no—
103C4⋊C4×C73—22no—
104C4⋊C4×C73—21no—
105C4⋊C4×C73—21no—
106C4⋊C4×C73—21no—
107C4⋊C4×C73—22no—
108C4⋊C4×C73C22⋊C412yes—
109C22⋊C4×C73—22no—
110C42×C73—22no—
111C42×C73C2×D411yescharacteristic
112C42×C73C2×D411yescharacteristic
113C42×C73C2×D411yescharacteristic
114C42×C73#4111yescharacteristic
115C23×C73C4×D411yescharacteristic
116Q8×C73—42no—
117Q8×C73—41no—
118Q8×C73—41no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—22no—
122C2×C4×C73—22no—
123C2×C4×C73—41no—
124C2×C4×C73C2×C22⋊C411yescharacteristic
125C2×C4×C73C4×D411yescharacteristic
126C2×C4×C73#12011yescharacteristic
127C2×C4×C73#12111yescharacteristic
128C2×C4×C73#12111yescharacteristic
129C2×C4×C73#12311yescharacteristic
130C2×C4×C73C2×SD1611yescharacteristic
131C2×C4×C73#13511yescharacteristic
132C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C73#13711yescharacteristic
134C2×Dic73—42no—
135C2×Dic73—42no—
136C2×Dic73—42no—
137Dic146—81no—
138Dic146—81no—
139Dic146—81no—
140Dic146—81no—
141C8×C73—22no—
142C8×C73—41no—
143C8×C73—41no—
144C8×C73—41no—
145#10596831—42no—
146#10596831—81no—
147#10596831—81no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C73#38611yescharacteristic
151C22×C73C4×SD1611yescharacteristic
152C22×C73#44011yescharacteristic
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—21no—
156C4×C73—42no—
157C4×C73—42no—
158C4×C73#44811yescharacteristic
159C4×C73#44911yescharacteristic
160C4×C73#46011yescharacteristic
161C4×C73#46411yescharacteristic
162C4×C73#47111yescharacteristic
163C4×C73#47311yescharacteristic
164Dic73—82no—
165#9272—731nomaximal, Sylow
166C2×C73—21no—
167C2×C73—21no—
168C2×C73#188011yescharacteristic
169C2×C73#190811yescharacteristic
170C2×C73#191511yescharacteristic
171#3229—731no—
172#2962D7311yescharacteristic
173#1966—731no—
174#1550—731no—
175C2×#332—731no—
176#1301—731no—
177#1283—731no—
178C73#927211yescharacteristic, complemented, Sylow
179#533C2×D7311yescharacteristic
180C2×C4⋊Q8—731no—
181#498—1461no—
182#487—1461no—
183#483—734no—
184#475—1462no—
185#446—22no—
186#446—21no—
187C8×Q8—21no—
188#431—731no—
189#424—21no—
190#423—731no—
191C2×C4⋊C8—731no—
192C2×C4⋊C8C2×D7311yescharacteristic
193C2×#101—1461no—
194C2×#101—1461no—
195#405—21no—
196C4×M16C2×D7311yescharacteristic
197#333—1461no—
198#332—1461no—
199#332—1461no—
200#332—1461no—
201C22×Q8—1461no—
202C2×M16—1461no—
203C2×M16C22⋊D7311yescharacteristic
204C2×M16C22⋊D7311yescharacteristic
205C22×C8—21no—
206C22×C8—1461no—
207C4⋊Q8—1461no—
208C4⋊Q8—1461no—
209C4⋊Q8—1461no—
210C4⋊Q8—1461no—
211C4⋊Q8D29211yescharacteristic
212C4⋊Q8D29211yescharacteristic
213#125—21no—
214C22⋊Q8—21no—
215C22⋊Q8C4×D7312yes—
216C4×Q8—21no—
217C4×Q8C22⋊D7312yes—
218#117—21no—
219C2×C4⋊C4—732no—
220C2×C4⋊C4—1461no—
221C2×C42C22×D7311yescharacteristic
222#106—1464no—
223C4⋊C8—22no—
224C4⋊C8—22no—
225C4⋊C8—21no—
226C4⋊C8—1461no—
227C4⋊C8—1461no—
228C4⋊C8—1461no—
229C4⋊C8—1461no—
230C4⋊C8—1461no—
231C4⋊C8C22⋊D7311yescharacteristic
232C4⋊C8C22⋊D7311yescharacteristic
233#103—1464no—
234#101—2922no—
235#101—2922no—
236C22⋊C8—732no—
237#97—22no—
238#97—21no—
239C4×C8—22no—
240C4×C8—21no—
241C4×C8—1461no—
242C2×Q8—21no—
243C2×Q8—2921no—
244C2×Q8—2921no—
245C2×Q8—2921no—
246C2×Q8—2921no—
247C2×Q8—2921no—
248C2×Q8—2921no—
249C2×Q8#1192400512yes—
250C22×C4—1462no—
251C22×C4C2×C4×D7311yescharacteristic
252C22×C4C2×C22⋊D7311yescharacteristic
253C22×C4#1192402811yescharacteristic
254M16—21no—
255M16—21no—
256M16—21no—
257M16—2921no—
258M16—2921no—
259M16#1192401512yes—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—2921no—
267C2×C8—2921no—
268C2×C8—5841no—
269C2×C8—1462no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—2921no—
276C4⋊C4—2921no—
277C4⋊C4—1462no—
278C4⋊C4—1462no—
279C4⋊C4#1192400512yes—
280C22⋊C4—22no—
281C42—22no—
282C42C2×C22⋊D7311yescharacteristic
283C42C2×C22⋊D7311yescharacteristic
284C42C2×D29211yescharacteristic
285C42#1192402811yescharacteristic
286C23C4×C22⋊D7311yescharacteristic
287Q8—42no—
288Q8—41no—
289Q8—41no—
290Q8—5841no—
291Q8—5841no—
292Q8—5841no—
293Q8—5841no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—2922no—
300C2×C4—2922no—
301C2×C4—2922no—
302C2×C4C2×#1192400511yescharacteristic
303C2×C4C4×C22⋊D7311yescharacteristic
304C2×C4#1455656011yescharacteristic
305C2×C4#1455656511yescharacteristic
306C2×C4#1455656511yescharacteristic
307C2×C4#1455657411yescharacteristic
308C2×C4C2×#1192401511yescharacteristic
309C2×C4#1455661111yescharacteristic
310C2×C4#1455661611yescharacteristic
311C2×C4#1455662211yescharacteristic
312C8—22no—
313C8—41no—
314C8—41no—
315C8—41no—
316C8—2922no—
317C8—5841no—
318C8—5841no—
319C22—21no—
320C22—21no—
321C22#1798846611yescharacteristic
322C22C4×#1192401511yescharacteristic
323C22#1798868511yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—42no—
328C4—42no—
329C4—5842no—
330C4#1798872611yescharacteristic
331C4#1798873211yescharacteristic
332C4#1798878711yescharacteristic
333C4#1798880911yescharacteristic
334C4#1798885011yescharacteristic
335C4#1798886211yescharacteristic
336C2—21no—
337C2—21no—
338C2#2261028611yescharacteristic
339C2#2261044611yescharacteristic
340C2#2261048311yescharacteristic
subgroupG/H
centerC22#17988466
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#2962C2
socleC22×C73#386
prime radicalC23×C73C4×D4
cosocleC2×C42×C73C23
hypercenter#2962D73
hypocenterC73#9272
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
178. C73#9272semidirect

Maximal subgroups

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

subgroupindex
#226210722
#226107752
#226086212
C2×#179883342
#226078282
#226077822
C73×#29622
#927273