Finite Group Databasebeta

← #33005582

Subgroups — #33005582

Order 18688.

446 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556534C211yesmaximal, characteristic
2C2×#17988405C211yesmaximal, characteristic, complemented
3C2×#17988389C211yesmaximal, characteristic
4#22610795C211yesmaximal, characteristic
5#22610793C211yesmaximal, characteristic, complemented
6#22608022C211yesmaximal, characteristic, complemented
7C2×#358×C73C211yesmaximal, characteristic, complemented
8C22×D584C2211yescharacteristic
9C2×#14556534—22no—
10C2×#14556534—22no—
11C2×#14556534—22no—
12C22×#11924003C2211yescharacteristic
13C2×#14556525C2211yescharacteristic
14C2×#14556515—21no—
15C2×#14556511—21no—
16C2×C8×Dic73C2211yescharacteristic
17#17988494—21no—
18#17988488—21no—
19#17988405—22no—
20#17988389—22no—
21C22×Q16×C73C2211yescharacteristic
22C22×C16×C73C2211yescharacteristic
23C2×#107×C73C2211yescharacteristic
24#358×C73—22no—
25C22×D292—21no—
26C2×D584—21no—
27C2×D584—21no—
28C2×D584—21no—
29C2×D584—21no—
30C2×D584—21no—
31C2×D584D412yes—
32C22×#10596831D411yescharacteristic
33C2×C4⋊Dic73—21no—
34C2×#11924005—41no—
35C2×#11924005—41no—
36C2×C4×Dic73D411yescharacteristic
37#14556534—28no—
38C2×#11924003—21no—
39C2×#11924003—21no—
40C2×#11924003D412yes—
41#14556525—21no—
42#14556525—21no—
43#14556515—42no—
44#14556511—42no—
45C8×Dic73—21no—
46C8×Dic73—21no—
47#14556498—41no—
48#14556498—41no—
49C22×Q8×C73—21no—
50C2×Q16×C73—21no—
51C2×Q16×C73—21no—
52C2×Q16×C73—21no—
53C2×Q16×C73—21no—
54C2×Q16×C73—21no—
55C2×Q16×C73D412yes—
56C22×C8×C73C2311yescharacteristic
57C2×C4⋊C4×C73—21no—
58C2×C16×C73—21no—
59C2×C16×C73—21no—
60C2×C16×C73—21no—
61#107×C73—21no—
62#107×C73—21no—
63C23×D73—41no—
64C2×D292—22no—
65C2×D292—41no—
66C2×D292—41no—
67C2×D292—41no—
68C2×D292—41no—
69C2×D292—41no—
70C22×Dic73—41no—
71C22×Dic73D811yescharacteristic
72C22×Dic73D811yescharacteristic
73D584—22no—
74D584—22no—
75D584—41no—
76D584—41no—
77C2×#10596831—21no—
78C2×#10596831—21no—
79C2×#10596831—21no—
80C4⋊Dic73—41no—
81C4⋊Dic73—41no—
82#11924005—82no—
83#11924005—82no—
84C4×Dic73—21no—
85C4×Dic73—21no—
86#11924003—22no—
87C2×Q8×C73—22no—
88C2×Q8×C73—41no—
89C2×Q8×C73—41no—
90C2×Q8×C73—41no—
91C2×Q8×C73—41no—
92C2×Q8×C73—41no—
93C22×C4×C73—41no—
94C22×C4×C73—41no—
95C22×C4×C73C2×D411yescharacteristic
96Q16×C73—22no—
97Q16×C73—22no—
98Q16×C73—41no—
99Q16×C73—41no—
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—41no—
107C4⋊C4×C73—41no—
108C16×C73—41no—
109C23×C73C2×D811yescharacteristic
110C22×D73—42no—
111C22×D73—81no—
112C22×D73—81no—
113C22×D73—81no—
114C22×D73—81no—
115C22×D73—81no—
116C22×D73—81no—
117Q8×C73—42no—
118Q8×C73—42no—
119Q8×C73—81no—
120Q8×C73—81no—
121C2×C4×C73—42no—
122C2×C4×C73—81no—
123C2×C4×C73—81no—
124C2×C4×C73—81no—
125C2×C4×C73—81no—
126C2×C4×C73—81no—
127C2×C4×C73#12111yescharacteristic
128C2×C4×C73#12111yescharacteristic
129C2×C4×C73#12111yescharacteristic
130C2×C4×C73#13511yescharacteristic
131C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—81no—
139C2×Dic73—81no—
140C2×Dic73—81no—
141C2×Dic73SD3212yescomplemented
142D292—42no—
143D292—42no—
144D292—81no—
145D292—81no—
146C8×C73#12011yescharacteristic
147C8×C73#12311yescharacteristic
148C8×C73#12311yescharacteristic
149C8×C73#12411yescharacteristic
150#10596831—41no—
151C22×C73#45911yescharacteristic
152C22×C73#45911yescharacteristic
153C22×C73#46611yescharacteristic
154C22×C73C2×SD3211yescharacteristic
155C22×C73#50811yescharacteristic
156C22×C73#50911yescharacteristic
157C22×C73#51011yescharacteristic
158C2×D73—82no—
159C2×D73—82no—
160C2×D73—82no—
161C2×D73—161no—
162C2×D73—161no—
163C2×D73—161no—
164C2×D73—161no—
165C4×C73—82no—
166C4×C73—161no—
167C4×C73#39411yescharacteristic
168C4×C73#46311yescharacteristic
169C4×C73#46311yescharacteristic
170C4×C73#46911yescharacteristic
171Dic73—22no—
172Dic73—41no—
173Dic73—161no—
174#13449—731nomaximal, Sylow
175C2×C73#205411yescharacteristic
176C2×C73#220711yescharacteristic
177C2×C73#220811yescharacteristic
178C2×C73#221011yescharacteristic
179C2×C73#221111yescharacteristic
180C2×C73#221711yescharacteristic
181C2×C73#222011yescharacteristic
182D73—162no—
183C22×SD32—731no—
184C2×C4⋊C16—731no—
185C2×#358D7311yescharacteristic, complemented
186C2×#357—731no—
187#1970—731no—
188#1969—731no—
189#1380—731no—
190C73#1344911yescharacteristic, complemented, Sylow
191C22×Q16C2×D7311yescharacteristic
192C22×D8—731no—
193C2×SD32—1462no—
194C2×SD32—1462no—
195C2×SD32—1462no—
196C22×C16—731no—
197C22×C16C2×D7311yescharacteristic
198C2×#107—731no—
199C2×#107C2×D7311yescharacteristic
200C2×#103—1461no—
201C2×#102—1461no—
202C2×C4×C8—731no—
203#391—1461no—
204#390—1461no—
205C4⋊C16—1462no—
206#358—22no—
207#357—1462no—
208C22×Q8—21no—
209C22×D4—1461no—
210C2×Q16—21no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16C22⋊D7312yes—
216C2×D8—732no—
217C2×D8—1461no—
218C2×D8—1461no—
219C2×D8—1461no—
220C2×D8—1461no—
221C2×D8—1461no—
222C22×C8—731no—
223C22×C8C22×D7311yescharacteristic
224C2×C4⋊C4—21no—
225C2×C4⋊C4—1461no—
226C2×C22⋊C4—2921no—
227C2×C22⋊C4—2921no—
228C2×C42—731no—
229SD32—1468no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—732no—
234C2×C16—1461no—
235C2×C16—1461no—
236#107—21no—
237#107—21no—
238#107—1461no—
239#107—1461no—
240#103—2922no—
241#102—2922no—
242C4×C8—1461no—
243C4×C8—1461no—
244#95—2921no—
245#95—2921no—
246C24—2921no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×D4—2921no—
254C2×D4—2921no—
255C2×D4—2921no—
256C2×D4—2921no—
257C2×D4—2921no—
258C2×D4—1462no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—2921no—
262C22×C4—731no—
263C22×C4—731no—
264C22×C4D4×D7311yescharacteristic
265Q16—22no—
266Q16—22no—
267Q16—41no—
268Q16—41no—
269D8—2921no—
270D8—2921no—
271D8—1462no—
272D8—1462no—
273C2×C8—1461no—
274C2×C8—1461no—
275C2×C8—1461no—
276C2×C8D4×D7311yescharacteristic
277C2×C8D4×D7311yescharacteristic
278C2×C8C2×C22⋊D7311yescharacteristic
279C2×C8#1192402711yescharacteristic
280C2×C8#1192402811yescharacteristic
281C2×C8#1192402811yescharacteristic
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—2921no—
285C4⋊C4—2921no—
286C22⋊C4—5842no—
287C22⋊C4—5842no—
288C42—1461no—
289C42—1461no—
290C16—41no—
291C16—1462no—
292C23—2922no—
293C23—5841no—
294C23—5841no—
295C23—5841no—
296C23—5841no—
297C23—5841no—
298C23—5841no—
299C23D8×D7311yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—81no—
303Q8—81no—
304D4—2922no—
305D4—2922no—
306D4—5841no—
307D4—5841no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—5841no—
315C2×C4—5841no—
316C2×C4—5841no—
317C2×C4—732no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4#1455656311yescharacteristic
324C2×C4#1455656411yescharacteristic
325C2×C4#1455656411yescharacteristic
326C2×C4#1455661211yescharacteristic
327C2×C4#1455661511yescharacteristic
328C2×C4#1455661811yescharacteristic
329C8—2921no—
330C8#1455655911yescharacteristic
331C8#1455657311yescharacteristic
332C8#1455657411yescharacteristic
333C8#1455657711yescharacteristic
334C22—5842no—
335C22—5842no—
336C22—5842no—
337C22—11681no—
338C22—11681no—
339C22—11681no—
340C22—11681no—
341C22#1798878011yescharacteristic
342C22#1798878111yescharacteristic
343C22#1798882211yescharacteristic
344C22SD32×D7311yescharacteristic
345C22#1798902011yescharacteristic
346C22#1798902411yescharacteristic
347C22#1798902911yescharacteristic
348C4—82no—
349C4—161no—
350C4—2921no—
351C4—11681no—
352C4—1462no—
353C4#1798850211yescharacteristic
354C4#1798880111yescharacteristic
355C4#1798880411yescharacteristic
356C4#1798883911yescharacteristic
357C2—11682no—
358C2#2261124011yescharacteristic
359C2#2261196911yescharacteristic
360C2#2261197511yescharacteristic
361C2#2261198911yescharacteristic
362C2#2261199511yescharacteristic
363C2#2261203011yescharacteristic
364C2#2261204711yescharacteristic
subgroupG/H
centerC23D8×D73
commutator, cosocleC22×C8×C73C23
FrattiniC22×C8C22×D73
FittingC2×#358×C73C2
socleC23×C73C2×D8
prime radicalC22×D584C22
hypercenterC2×#358D73
hypocenterC73#13449
LCSG ▷ C22×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#17988405C2semidirect
5. #22610793C2semidirect
6. #22608022C2semidirect
7. C2×#358×C73C2semidirect
141. C2×Dic73SD32semidirect
185. C2×#358D73semidirect
190. C73#13449semidirect

Maximal subgroups

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

subgroupindex
C22×#145565342
C2×#179884052
C2×#179883892
#226107952
#226107932
#226080222
C2×#358×C732
#1344973