Finite Group Databasebeta

← #33005335

Subgroups — #33005335

Order 18688.

482 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988971C211yesmaximal, characteristic
2C2×#17988390C211yesmaximal, characteristic, complemented
3C2×#17988390C211yesmaximal, characteristic, complemented
4C2×#17988387C211yesmaximal, characteristic
5C2×#17988387C211yesmaximal, characteristic
6#22608009C211yesmaximal, characteristic, complemented
7C73×#1942C211yesmaximal, characteristic, complemented
8C22×Dic292C2211yescharacteristic
9C22×#11924017—21no—
10C22×D584C2211yescharacteristic
11C2×#14556579—21no—
12C22×#11924003C2211yescharacteristic
13C22×#11924003C2211yescharacteristic
14#17988971—22no—
15#17988971—22no—
16#17988390—22no—
17#17988390—22no—
18#17988387—22no—
19#17988387—22no—
20C2×#107×C73C2211yescharacteristic
21C2×#107×C73C2211yescharacteristic
22C2×C4×C8×C73C2211yescharacteristic
23#389×C73—21no—
24#340×C73—21no—
25C22×Dic146—21no—
26C22×D292—21no—
27C2×Dic292—21no—
28C2×Dic292—21no—
29C2×Dic292—21no—
30C2×Dic292—21no—
31C2×Dic292—21no—
32C2×Dic292D412yes—
33C2×#11924017—24no—
34C2×#11924017—42no—
35C2×#11924017—42no—
36C2×D584—21no—
37C2×D584—21no—
38C2×D584—21no—
39C2×D584—21no—
40C2×D584—21no—
41C2×D584D412yes—
42#14556579—24no—
43#14556579—42no—
44C2×#11924005—41no—
45C2×#11924005—41no—
46C2×#11924003—21no—
47C2×#11924003—21no—
48C2×#11924003—21no—
49C2×#11924003—21no—
50C2×#11924003—21no—
51C2×#11924003—21no—
52C22×C8×C73D411yescharacteristic
53C22×C8×C73C2311yescharacteristic
54C2×C4⋊C4×C73—21no—
55C2×C4⋊C4×C73—21no—
56C2×C4⋊C4×C73—41no—
57C2×C42×C73D411yescharacteristic
58#107×C73—21no—
59#107×C73—21no—
60#107×C73—21no—
61#107×C73D412yes—
62C4×C8×C73—21no—
63C4×C8×C73—21no—
64#95×C73—41no—
65C23×D73—41no—
66C2×Dic146—22no—
67C2×Dic146—41no—
68C2×Dic146—41no—
69C2×Dic146—41no—
70C2×Dic146—41no—
71C2×Dic146—41no—
72C2×D292—22no—
73C2×D292—41no—
74C2×D292—41no—
75C2×D292—41no—
76C2×D292—41no—
77C2×D292—41no—
78C22×Dic73—41no—
79Dic292—22no—
80Dic292—22no—
81Dic292—41no—
82Dic292—41no—
83#11924017—48no—
84D584—22no—
85D584—22no—
86D584—41no—
87D584—41no—
88#11924005—44no—
89#11924005—44no—
90#11924003—41no—
91#11924003—41no—
92C22×C4×C73—41no—
93C22×C4×C73—41no—
94C22×C4×C73D811yescharacteristic
95C22×C4×C73D811yescharacteristic
96C22×C4×C73C2×D411yescharacteristic
97C2×C8×C73—21no—
98C2×C8×C73—21no—
99C2×C8×C73SD1612yes—
100C2×C8×C73C2×D411yescharacteristic
101C2×C8×C73C2×D411yescharacteristic
102C2×C8×C73C2×D411yescharacteristic
103C2×C8×C73#4111yescharacteristic
104C2×C8×C73#4111yescharacteristic
105C2×C8×C73#4111yescharacteristic
106C4⋊C4×C73—22no—
107C4⋊C4×C73—41no—
108C4⋊C4×C73—41no—
109C4⋊C4×C73—41no—
110C4⋊C4×C73—82no—
111C42×C73—21no—
112C42×C73—21no—
113C23×C73C2×D811yescharacteristic
114C22×D73—42no—
115C22×D73—81no—
116C22×D73—81no—
117C22×D73—81no—
118C22×D73—81no—
119C22×D73—81no—
120C22×D73—81no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—42no—
128C2×C4×C73—81no—
129C2×C4×C73—81no—
130C2×C4×C73—81no—
131C2×C4×C73—81no—
132C2×C4×C73—81no—
133C2×C4×C73#12011yescharacteristic
134C2×C4×C73#12111yescharacteristic
135C2×C4×C73#12411yescharacteristic
136C2×C4×C73C2×SD1611yescharacteristic
137C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
139C2×Dic73—42no—
140C2×Dic73—81no—
141C2×Dic73—81no—
142D292—42no—
143D292—42no—
144D292—81no—
145D292—81no—
146Dic146—42no—
147Dic146—42no—
148Dic146—81no—
149Dic146—81no—
150C8×C73—22no—
151C8×C73#12111yescharacteristic
152C8×C73#12111yescharacteristic
153C8×C73#12311yescharacteristic
154C8×C73#12311yescharacteristic
155C22×C73#44711yescharacteristic
156C22×C73#45911yescharacteristic
157C22×C73#48611yescharacteristic
158C22×C73#50811yescharacteristic
159C22×C73#50811yescharacteristic
160C22×C73#50911yescharacteristic
161C22×C73#51011yescharacteristic
162C2×D73—82no—
163C2×D73—82no—
164C2×D73—82no—
165C2×D73—161no—
166C2×D73—161no—
167C2×D73—161no—
168C2×D73—161no—
169C4×C73—41no—
170C4×C73—41no—
171C4×C73—82no—
172C4×C73—161no—
173C4×C73#39411yescharacteristic
174C4×C73#45011yescharacteristic
175C4×C73#46011yescharacteristic
176C4×C73#49011yescharacteristic
177Dic73—82no—
178#13408—731nomaximal, Sylow
179C2×C73#204111yescharacteristic
180C2×C73#218611yescharacteristic
181C2×C73#218911yescharacteristic
182C2×C73#221011yescharacteristic
183C2×C73#221111yescharacteristic
184C2×C73#224211yescharacteristic
185C2×C73#224311yescharacteristic
186D73—162no—
187C2×#495—731no—
188C2×#358—731no—
189C2×#358—731no—
190C2×#357—731no—
191C2×#357—731no—
192#1942D7311yescharacteristic, complemented
193#1374—731no—
194C73#1340811yescharacteristic, complemented, Sylow
195C22×Q16—731no—
196C22×SD16—1461no—
197C22×D8—731no—
198C2×#124—1461no—
199C22×C16—731no—
200C22×C16—731no—
201#495—1462no—
202#495—1462no—
203C2×#107C2×D7311yescharacteristic
204C2×#107C2×D7311yescharacteristic
205C2×C4×C8C2×D7311yescharacteristic
206#389—21no—
207#358—1462no—
208#358—1462no—
209#357—1462no—
210#357—1462no—
211#340—21no—
212C22×Q8—1461no—
213C22×D4—1461no—
214C2×Q16—732no—
215C2×Q16—1461no—
216C2×Q16—1461no—
217C2×Q16—1461no—
218C2×Q16—1461no—
219C2×Q16—1461no—
220C2×SD16—2922no—
221C2×SD16—2922no—
222C2×SD16—1464no—
223C2×D8—732no—
224C2×D8—1461no—
225C2×D8—1461no—
226C2×D8—1461no—
227C2×D8—1461no—
228C2×D8—1461no—
229C22×C8C22⋊D7311yescharacteristic
230C22×C8C22×D7311yescharacteristic
231#124—2922no—
232#124—1464no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—41no—
236C2×C22⋊C4—2921no—
237C2×C22⋊C4—2921no—
238C2×C42C22⋊D7311yescharacteristic
239C2×C16—1461no—
240C2×C16—1461no—
241C2×C16—1461no—
242C2×C16—1461no—
243C2×C16—1461no—
244C2×C16—1461no—
245#107—21no—
246#107—21no—
247#107—21no—
248#107D29212yes—
249C4×C8—21no—
250C4×C8—21no—
251#95—41no—
252C24—2921no—
253C2×Q8—2921no—
254C2×Q8—2921no—
255C2×Q8—2921no—
256C2×Q8—2921no—
257C2×Q8—2921no—
258C2×Q8—1462no—
259C2×D4—2921no—
260C2×D4—2921no—
261C2×D4—2921no—
262C2×D4—2921no—
263C2×D4—2921no—
264C2×D4—1462no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—2921no—
268C22×C4#1192401311yescharacteristic
269C22×C4#1192401311yescharacteristic
270C22×C4C2×C22⋊D7311yescharacteristic
271Q16—2921no—
272Q16—2921no—
273Q16—1462no—
274Q16—1462no—
275SD16—2928no—
276D8—2921no—
277D8—2921no—
278D8—1462no—
279D8—1462no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8#1192401512yes—
283C2×C8D4×D7311yescharacteristic
284C2×C8D4×D7311yescharacteristic
285C2×C8C2×D29211yescharacteristic
286C2×C8#1192402811yescharacteristic
287C2×C8#1192402911yescharacteristic
288C2×C8#1192402911yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—82no—
294C22⋊C4—2924no—
295C22⋊C4—2924no—
296C42—21no—
297C42—21no—
298C16—2921no—
299C16—2921no—
300C23—2922no—
301C23—5841no—
302C23—5841no—
303C23—5841no—
304C23—5841no—
305C23—5841no—
306C23—5841no—
307C23C2×#1192401311yescharacteristic
308Q8—2922no—
309Q8—2922no—
310Q8—5841no—
311Q8—5841no—
312D4—2922no—
313D4—2922no—
314D4—5841no—
315D4—5841no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—2922no—
329C2×C4—5841no—
330C2×C4—5841no—
331C2×C4#1455655911yescharacteristic
332C2×C4#1455656511yescharacteristic
333C2×C4#1455658011yescharacteristic
334C2×C4C2×#1192401511yescharacteristic
335C2×C4#1455661611yescharacteristic
336C2×C4#1455661611yescharacteristic
337C8—22no—
338C8#1455656611yescharacteristic
339C8#1455656611yescharacteristic
340C8#1455657611yescharacteristic
341C8#1455657611yescharacteristic
342C22—5842no—
343C22—5842no—
344C22—5842no—
345C22—11681no—
346C22—11681no—
347C22—11681no—
348C22—11681no—
349C22#1798872011yescharacteristic
350C22#1798878211yescharacteristic
351C22#1798893511yescharacteristic
352C22#1798901711yescharacteristic
353C22#1798901711yescharacteristic
354C22#1798902311yescharacteristic
355C22#1798902811yescharacteristic
356C4—41no—
357C4—41no—
358C4—82no—
359C4—161no—
360C4—5842no—
361C4#1798850411yescharacteristic
362C4#1798873711yescharacteristic
363C4#1798878711yescharacteristic
364C4#1798895311yescharacteristic
365C2—11682no—
366C2#2261116511yescharacteristic
367C2#2261185211yescharacteristic
368C2#2261186911yescharacteristic
369C2#2261198611yescharacteristic
370C2#2261199311yescharacteristic
371C2#2261216511yescharacteristic
372C2#2261217011yescharacteristic
subgroupG/H
centerC23C2×#11924013
commutator, cosocleC22×C8×C73C23
FrattiniC22×C8C22×D73
FittingC73×#1942C2
socleC23×C73C2×D8
prime radicalC22×D584C22
hypercenter#1942D73
hypocenterC73#13408
LCSG ▷ C22×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1942

Complements

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

NH ≅ G/Ntype
2. C2×#17988390C2semidirect
3. C2×#17988390C2semidirect
6. #22608009C2semidirect
7. C73×#1942C2semidirect
192. #1942D73semidirect
194. C73#13408semidirect

Maximal subgroups

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

subgroupindex
C2×#179889712
C2×#179883902
C2×#179883872
#226080092
C73×#19422
#1340873