Finite Group Databasebeta

← #33003132

Subgroups — #33003132

Order 18688.

522 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989022C211yesmaximal, characteristic
2C2×#17988397C211yesmaximal, characteristic, complemented
3#22611646C211yesmaximal, characteristic, complemented
4#22610807C211yesmaximal, characteristic, complemented
5#22608036C211yesmaximal, characteristic, complemented
6#22608015C211yesmaximal, characteristic, complemented
7C73×#2943C211yesmaximal, characteristic, complemented
8C22×D584C2211yescharacteristic
9#17989022—22no—
10#17989022C414yescomplemented
11C2×#14556534—21no—
12C2×#14556532—21no—
13C2×#14556531C2211yescharacteristic
14C2×#14556531C2211yescharacteristic
15C2×#14556523C2211yescharacteristic
16C2×#14556513—21no—
17#17988489—21no—
18#17988397—22no—
19#17988387—22no—
20C2×#135×C73C2211yescharacteristic
21C4×#41×C73—21no—
22#442×C73—21no—
23#441×C73—21no—
24#440×C73—22no—
25#427×C73C2211yescharacteristic
26#416×C73—21no—
27C2×#97×C73C2211yescharacteristic
28C22×D292—21no—
29C2×D584—21no—
30C2×D584—21no—
31C2×D584—21no—
32C2×D584—21no—
33C2×D584—21no—
34C2×D584C2×C412yescomplemented
35C2×C4⋊Dic73—21no—
36C2×#11924005—42no—
37#14556534—24no—
38#14556532—24no—
39#14556531—21no—
40#14556531—21no—
41#14556531—21no—
42#14556531C2×C412yescomplemented
43C2×#11924003—21no—
44C2×#11924003—21no—
45#14556523—21no—
46#14556523—21no—
47#14556513—42no—
48C2×#41×C73—21no—
49#135×C73—21no—
50#135×C73—21no—
51#135×C73C2×C412yes—
52#135×C73D412yes—
53C2×Q16×C73D411yescharacteristic
54C2×SD16×C73—21no—
55C2×D8×C73D411yescharacteristic
56C22×C8×C73D411yescharacteristic
57C22×C8×C73C2311yescharacteristic
58C4×Q8×C73—22no—
59C4×D4×C73—22no—
60C4×D4×C73—42no—
61#117×C73—21no—
62#117×C73—41no—
63C2×C42×C73—41no—
64C2×C42×C73D411yescharacteristic
65#107×C73D412yes—
66#106×C73—21no—
67#103×C73—22no—
68#102×C73—22no—
69#97×C73—21no—
70#97×C73—21no—
71C23×D73—41no—
72C2×D292—22no—
73C2×D292—41no—
74C2×D292—41no—
75C2×D292—41no—
76C2×D292—41no—
77C2×D292—41no—
78C22×Dic73—41no—
79D584—22no—
80D584—22no—
81D584—41no—
82D584—41no—
83C4⋊Dic73—41no—
84C4⋊Dic73—41no—
85#11924005—84no—
86#11924003—22no—
87#11924003—41no—
88#41×C73—22no—
89#41×C73—22no—
90#41×C73—41no—
91#41×C73—41no—
92C2×Q8×C73—21no—
93C2×D4×C73—21no—
94C2×D4×C73—41no—
95C22×C4×C73—42no—
96C22×C4×C73—41no—
97C22×C4×C73D812yes—
98C22×C4×C73C2×D411yescharacteristic
99Q16×C73—21no—
100Q16×C73C22⋊C412yescomplemented
101SD16×C73—22no—
102SD16×C73—22no—
103D8×C73—21no—
104D8×C73C22⋊C412yescomplemented
105C2×C8×C73—21no—
106C2×C8×C73—21no—
107C2×C8×C73—21no—
108C2×C8×C73C22×C411yescharacteristic
109C2×C8×C73C2×D411yescharacteristic
110C2×C8×C73C2×D411yescharacteristic
111C2×C8×C73C2×D411yescharacteristic
112C2×C8×C73#4111yescharacteristic
113C2×C8×C73#4111yescharacteristic
114C4⋊C4×C73—22no—
115C4⋊C4×C73—42no—
116C22⋊C4×C73—42no—
117C22⋊C4×C73—41no—
118C42×C73—21no—
119C42×C73—21no—
120C42×C73—42no—
121C42×C73—41no—
122C23×C73—41no—
123C23×C73C2×D811yescharacteristic
124C22×D73—42no—
125C22×D73—82no—
126C22×D73—82no—
127C22×D73—81no—
128C22×D73—81no—
129Q8×C73—22no—
130Q8×C73—41no—
131D4×C73—22no—
132D4×C73—42no—
133D4×C73—42no—
134D4×C73—41no—
135C2×C4×C73—22no—
136C2×C4×C73—41no—
137C2×C4×C73—42no—
138C2×C4×C73—42no—
139C2×C4×C73—42no—
140C2×C4×C73—42no—
141C2×C4×C73—84no—
142C2×C4×C73C4×D411yescharacteristic
143C2×C4×C73#12011yescharacteristic
144C2×C4×C73#12111yescharacteristic
145C2×C4×C73#13511yescharacteristic
146C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
148C2×Dic73—82no—
149C2×Dic73—81no—
150D292—42no—
151D292—42no—
152D292—81no—
153D292—81no—
154C8×C73—41no—
155C8×C73C2×C22⋊C411yescharacteristic
156C8×C73C4×D411yescharacteristic
157C8×C73#12111yescharacteristic
158C8×C73#12311yescharacteristic
159C22×C73—22no—
160C22×C73—42no—
161C22×C73—82no—
162C22×C73C4×D811yescharacteristic
163C22×C73#44711yescharacteristic
164C22×C73#45911yescharacteristic
165C2×D73—84no—
166C2×D73—82no—
167C2×D73—161no—
168C2×D73—161no—
169C2×D73—162no—
170C4×C73—42no—
171C4×C73—42no—
172C4×C73—82no—
173C4×C73#38611yescharacteristic
174C4×C73#44211yescharacteristic
175C4×C73#44911yescharacteristic
176C4×C73#46311yescharacteristic
177Dic73—161no—
178#13025—731nomaximal, Sylow
179C2×C73—21no—
180C2×C73—21no—
181C2×C73—82no—
182C2×C73#187911yescharacteristic
183C2×C73#219012yes—
184D73—162no—
185C2×#509—731no—
186#2943D7311yescharacteristic, complemented
187C2×#360—731no—
188#2140—731no—
189#1972—731no—
190#1386—731no—
191#1377—731no—
192C73#1302511yescharacteristic, complemented, Sylow
193C2×#135C2×D7311yescharacteristic
194C22×D8—731no—
195C4×#41—21no—
196#509—734no—
197#509—1462no—
198C2×SD32—1461no—
199C2×D16—1461no—
200C2×M32—731no—
201C2×M32—731no—
202#442—21no—
203#441—21no—
204#440—22no—
205#427C2×D7311yescharacteristic
206C2×#106—731no—
207#416—21no—
208C2×#102—1461no—
209C2×#97C2×D7311yescharacteristic
210#390—1461no—
211#360—1462no—
212#357—1462no—
213C2×#41—21no—
214C22×D4—1461no—
215#135—21no—
216#135—21no—
217#135C4×D7312yes—
218#135D29212yes—
219C2×Q16C22⋊D7311yescharacteristic
220C2×SD16—21no—
221C2×D8—732no—
222C2×D8—1461no—
223C2×D8—1461no—
224C2×D8—1461no—
225C2×D8—1461no—
226C2×D8—1461no—
227C2×D8C22⋊D7311yescharacteristic
228C22×C8C22⋊D7311yescharacteristic
229C22×C8C22×D7311yescharacteristic
230C4×Q8—22no—
231C4×D4—22no—
232C4×D4—42no—
233#117—21no—
234#117—41no—
235C2×C4⋊C4—1461no—
236C2×C22⋊C4—2922no—
237C2×C42—41no—
238C2×C42C22⋊D7311yescharacteristic
239SD32—1464no—
240D16—1464no—
241M32—732no—
242M32—1461no—
243M32—1461no—
244M32—1461no—
245C2×C16—1461no—
246C2×C16—1461no—
247#107C22⋊D7312yes—
248#106—21no—
249#106—1461no—
250#106—1461no—
251#103—22no—
252#102—22no—
253#102—2922no—
254#97—21no—
255#97—21no—
256C24—2921no—
257#41—22no—
258#41—22no—
259#41—41no—
260#41—41no—
261C2×Q8—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—2921no—
265C2×D4—2921no—
266C2×D4—2921no—
267C2×D4—2921no—
268C2×D4—2921no—
269C2×D4—1462no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—2921no—
273C22×C4#1192401312yes—
274C22×C4C2×C22⋊D7311yescharacteristic
275Q16—21no—
276Q16#1192400512yescomplemented
277SD16—22no—
278SD16—22no—
279D8—21no—
280D8—2921no—
281D8—2921no—
282D8—1462no—
283D8—1462no—
284D8#1192400512yescomplemented
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8C2×C4×D7311yescharacteristic
289C2×C8C2×C22⋊D7311yescharacteristic
290C2×C8C2×C22⋊D7311yescharacteristic
291C2×C8C2×D29211yescharacteristic
292C2×C8#1192402811yescharacteristic
293C2×C8#1192402811yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—42no—
296C4⋊C4—2921no—
297C4⋊C4—2921no—
298C22⋊C4—42no—
299C22⋊C4—41no—
300C22⋊C4—5844no—
301C42—21no—
302C42—21no—
303C42—42no—
304C42—41no—
305C16—2921no—
306C16—1462no—
307C23—41no—
308C23—2922no—
309C23—5842no—
310C23—5842no—
311C23—5841no—
312C23—5841no—
313C23C2×#1192401311yescharacteristic
314Q8—22no—
315Q8—41no—
316D4—22no—
317D4—42no—
318D4—42no—
319D4—41no—
320D4—2922no—
321D4—2922no—
322D4—5841no—
323D4—5841no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—84no—
331C2×C4—5842no—
332C2×C4—5841no—
333C2×C4C4×C22⋊D7311yescharacteristic
334C2×C4#1455656011yescharacteristic
335C2×C4#1455656511yescharacteristic
336C2×C4#1455661111yescharacteristic
337C2×C4#1455661611yescharacteristic
338C2×C4#1455661711yescharacteristic
339C8—41no—
340C8C2×#1192400511yescharacteristic
341C8C4×C22⋊D7311yescharacteristic
342C8#1455656511yescharacteristic
343C8#1455657411yescharacteristic
344C22—22no—
345C22—42no—
346C22—82no—
347C22—5844no—
348C22—5842no—
349C22—11681no—
350C22—11681no—
351C22—11682no—
352C22C4×#1192401311yescharacteristic
353C22#1798872111yescharacteristic
354C22#1798878211yescharacteristic
355C4—42no—
356C4—42no—
357C4—82no—
358C4—11681no—
359C4#1798846611yescharacteristic
360C4#1798869711yescharacteristic
361C4#1798873211yescharacteristic
362C4#1798880211yescharacteristic
363C2—21no—
364C2—21no—
365C2—82no—
366C2—11682no—
367C2#2261027911yescharacteristic
368C2#2261187712yes—
subgroupG/H
centerC22#17988721
commutatorC2×C8×C73C22×C4
FrattiniC22×C8C22×D73
FittingC73×#2943C2
socleC22×C73#447
prime radicalC2×#17989022C2
cosocleC22×C8×C73C23
hypercenter#2943D73
hypocenterC73#13025
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #2943

Complements

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

NH ≅ G/Ntype
2. C2×#17988397C2semidirect
3. #22611646C2semidirect
4. #22610807C2semidirect
5. #22608036C2semidirect
6. #22608015C2semidirect
7. C73×#2943C2semidirect
10. #17989022C4semidirect
34. C2×D584C2×C4semidirect
42. #14556531C2×C4semidirect
100. Q16×C73C22⋊C4semidirect
104. D8×C73C22⋊C4semidirect
186. #2943D73semidirect
192. C73#13025semidirect
276. Q16#11924005semidirect
284. D8#11924005semidirect

Maximal subgroups

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

subgroupindex
C2×#179890222
C2×#179883972
#226116462
#226108072
#226080362
#226080152
C73×#29432
#1302573