Finite Group Databasebeta

← #32985016

Subgroups — #32985016

Order 18688.

570 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618327C211yesmaximal, characteristic
2#22610082C211yesmaximal, characteristic
3C4⋊C8×Dic73C211yesmaximal, characteristic
4C2×#17988334C211yesmaximal, characteristic
5C2×#17988333C211yesmaximal, characteristic
6C2×#17988332C211yesmaximal, characteristic
7C2×#332×C73C211yesmaximal, characteristic
8C2×#14556591C2211yescharacteristic
9C2×#14556589—22no—
10C2×C4⋊#10596831C2211yescharacteristic
11C2×C4⋊#10596831C2211yescharacteristic
12C2×#14556520—22no—
13C2×C8×Dic73—21no—
14#17988456—21no—
15#17988456—21no—
16#17988456C414yes—
17C42×Dic73C2211yescharacteristic
18#17988341—21no—
19#17988334—22no—
20#17988333—22no—
21#17988332—22no—
22C2×C4⋊Q8×C73C2211yescharacteristic
23C2×C4⋊C8×C73C2211yescharacteristic
24C2×C4⋊C8×C73C2211yescharacteristic
25#332×C73—22no—
26C22×Dic146—21no—
27C22×#10596831—21no—
28C22×#10596831—21no—
29#14556591—21no—
30#14556591—21no—
31#14556591—21no—
32#14556591—21no—
33#14556589—44no—
34#14556589—44no—
35C2×C4⋊Dic73—21no—
36C2×C4⋊Dic73C2×C412yes—
37C2×#11924007—24no—
38C2×#11924007—24no—
39C2×C4×Dic73C2×C412yes—
40C2×C4×Dic73D411yescharacteristic
41C2×C4×Dic73D412yes—
42C2×C4×Dic73D411yescharacteristic
43C4⋊#10596831—21no—
44C4⋊#10596831—21no—
45C4⋊#10596831—21no—
46C4⋊#10596831D412yes—
47#14556520—44no—
48C8×Dic73—42no—
49C22×Q8×C73—21no—
50C22×C8×C73—21no—
51C22×C8×C73—21no—
52C4⋊Q8×C73—21no—
53C4⋊Q8×C73—21no—
54C4⋊Q8×C73—21no—
55C4⋊Q8×C73—21no—
56C2×C4⋊C4×C73—21no—
57C2×C4⋊C4×C73C2×C412yes—
58C2×C42×C73C2311yescharacteristic
59C4⋊C8×C73—21no—
60C4⋊C8×C73—21no—
61C4⋊C8×C73—21no—
62C4⋊C8×C73D412yes—
63C2×Dic146—41no—
64C2×Dic146—41no—
65C2×Dic146—42no—
66C2×Dic146—42no—
67C22×Dic73—22no—
68C22×Dic73C22⋊C412yes—
69C22×Dic73C22⋊C412yes—
70C2×#10596831—22no—
71C2×#10596831—41no—
72C2×#10596831—41no—
73C2×#10596831—41no—
74C2×#10596831—42no—
75C4⋊Dic73—22no—
76C4⋊Dic73—22no—
77C4⋊Dic73—41no—
78C4⋊Dic73—41no—
79#11924007—48no—
80#11924007—48no—
81C4×Dic73—21no—
82C4×Dic73—21no—
83C4×Dic73—24no—
84C4×Dic73D814yes—
85C4×Dic73SD1614yes—
86C4×Dic73SD1612yes—
87C4×Dic73Q1612yes—
88C2×Q8×C73—41no—
89C2×Q8×C73—41no—
90C2×Q8×C73—42no—
91C2×Q8×C73—42no—
92C22×C4×C73—22no—
93C22×C4×C73C22×C411yescharacteristic
94C22×C4×C73C2×D411yescharacteristic
95C22×C4×C73C2×D411yescharacteristic
96C2×C8×C73—22no—
97C2×C8×C73—41no—
98C2×C8×C73—41no—
99C2×C8×C73—41no—
100C2×C8×C73—42no—
101C4⋊C4×C73—22no—
102C4⋊C4×C73—22no—
103C4⋊C4×C73—41no—
104C4⋊C4×C73—41no—
105C42×C73C2×D411yescharacteristic
106C42×C73C2×D411yescharacteristic
107C42×C73#4111yescharacteristic
108C42×C73#4111yescharacteristic
109C23×C73C2×C22⋊C411yescharacteristic
110Q8×C73—82no—
111Q8×C73—81no—
112Q8×C73—81no—
113C2×C4×C73—22no—
114C2×C4×C73—42no—
115C2×C4×C73—44no—
116C2×C4×C73C4×D411yescharacteristic
117C2×C4×C73C4×D411yescharacteristic
118C2×C4×C73#12111yescharacteristic
119C2×C4×C73#12111yescharacteristic
120C2×C4×C73#12411yescharacteristic
121C2×C4×C73#12711yescharacteristic
122C2×C4×C73C2×D812yes—
123C2×C4×C73C2×SD1611yescharacteristic
124C2×C4×C73C2×SD1612yes—
125C2×C4×C73C2×Q1611yescharacteristic
126C2×C4×C73#13711yescharacteristic
127C2×C4×C73#13711yescharacteristic
128C2×Dic73—22no—
129C2×Dic73—22no—
130C2×Dic73—42no—
131C2×Dic73—44no—
132C2×Dic73#10114yes—
133C2×Dic73#10214yes—
134C2×Dic73#10214yes—
135C2×Dic73#10314yes—
136Dic146—82no—
137Dic146—81no—
138Dic146—81no—
139C8×C73—42no—
140C8×C73—81no—
141#10596831—42no—
142#10596831—81no—
143C22×C73#39011yescharacteristic
144C22×C73C2×#10112yes—
145C22×C73C2×#10212yes—
146C22×C73C2×#10311yescharacteristic
147C22×C73#41911yescharacteristic
148C4×C73—21no—
149C4×C73—21no—
150C4×C73—82no—
151C4×C73#46111yescharacteristic
152C4×C73#46111yescharacteristic
153C4×C73#46211yescharacteristic
154C4×C73#46211yescharacteristic
155C4×C73#48612yes—
156C4×C73#49211yescharacteristic
157C4×C73#49311yescharacteristic
158Dic73—24no—
159Dic73—82no—
160Dic73#33218yescomplemented
161#9692—731nomaximal, Sylow
162C2×C73C2×#33212yes—
163C2×C73#154612yes—
164C2×C73#195711yescharacteristic
165C2×C73#196611yescharacteristic
166C2×C73#198111yescharacteristic
167#2868—731no—
168#1842—731no—
169C4×C4⋊C8—731no—
170C2×#332—731no—
171C2×#332—731no—
172C2×#332—731no—
173C2×#332D7311yescharacteristic
174C73#969211yescharacteristic, complemented, Sylow
175C2×C4⋊Q8—731no—
176C2×C4⋊Q8—1462no—
177C2×C4⋊Q8C2×D7311yescharacteristic
178C2×C4⋊C8—731no—
179C2×C4⋊C8—731no—
180C2×C4⋊C8—1462no—
181C2×C4⋊C8C2×D7311yescharacteristic
182C2×C4⋊C8C2×D7311yescharacteristic
183C2×C4×C8—1461no—
184#384—734no—
185#384—1461no—
186#384—1461no—
187C43—731no—
188#336—1461no—
189#332—22no—
190#332—1462no—
191#332—1462no—
192#332—1462no—
193C22×Q8—21no—
194C22×Q8—1461no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—1461no—
198C22×C8—1461no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—2924no—
204C4⋊Q8—2924no—
205C4⋊Q8—1461no—
206C4⋊Q8—1461no—
207C4⋊Q8—1461no—
208C4⋊Q8—1461no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—732no—
211C2×C4⋊C4—1464no—
212C2×C4⋊C4—1464no—
213C2×C4⋊C4—1461no—
214C2×C4⋊C4C4×D7312yes—
215C2×C42—732no—
216C2×C42—731no—
217C2×C42—732no—
218C2×C42—731no—
219C2×C42C22×D7311yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—2924no—
224C4⋊C8—732no—
225C4⋊C8—1461no—
226C4⋊C8—1461no—
227C4⋊C8—1461no—
228C4⋊C8C22⋊D7312yes—
229C4×C8—2922no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—42no—
233C2×Q8—42no—
234C2×Q8—2921no—
235C2×Q8—2921no—
236C2×Q8—2922no—
237C2×Q8—2922no—
238C22×C4—22no—
239C22×C4—732no—
240C22×C4—732no—
241C22×C4—1462no—
242C22×C4C2×C4×D7311yescharacteristic
243C22×C4D4×D7311yescharacteristic
244C22×C4D4×D7311yescharacteristic
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—42no—
250C2×C8—2921no—
251C2×C8—2921no—
252C2×C8—2921no—
253C2×C8—2922no—
254C2×C8—1462no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—2928no—
260C4⋊C4—2928no—
261C4⋊C4—2921no—
262C4⋊C4—2921no—
263C4⋊C4—1462no—
264C4⋊C4—1462no—
265C42—734no—
266C42—732no—
267C42—734no—
268C42—732no—
269C42—1464no—
270C42—1461no—
271C42—1461no—
272C42D4×D7311yescharacteristic
273C42C2×C22⋊D7311yescharacteristic
274C42#1192402711yescharacteristic
275C42#1192402811yescharacteristic
276C23C22⋊C4×D7311yescharacteristic
277Q8—82no—
278Q8—81no—
279Q8—81no—
280Q8—5842no—
281Q8—5841no—
282Q8—5841no—
283C2×C4—22no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—2922no—
287C2×C4—2924no—
288C2×C4—734no—
289C2×C4—734no—
290C2×C4—734no—
291C2×C4—734no—
292C2×C4—1462no—
293C2×C4—1462no—
294C2×C4#1455655111yescharacteristic
295C2×C4C4×C22⋊D7311yescharacteristic
296C2×C4#1455656311yescharacteristic
297C2×C4#1455656411yescharacteristic
298C2×C4#1455657711yescharacteristic
299C2×C4#1455658711yescharacteristic
300C2×C4D8×D7312yes—
301C2×C4SD16×D7312yes—
302C2×C4SD16×D7311yescharacteristic
303C2×C4Q16×D7311yescharacteristic
304C2×C4#1455662011yescharacteristic
305C2×C4#1455662311yescharacteristic
306C8—42no—
307C8—81no—
308C8—2922no—
309C8—5841no—
310C22#1798848711yescharacteristic
311C22#101×D7312yes—
312C22#102×D7312yes—
313C22#103×D7311yescharacteristic
314C22#1798859411yescharacteristic
315C4—21no—
316C4—21no—
317C4—82no—
318C4—5842no—
319C4—738no—
320C4—1464no—
321C4#1798879011yescharacteristic
322C4#1798879111yescharacteristic
323C4#1798879511yescharacteristic
324C4#1798879611yescharacteristic
325C4#1798893212yes—
326C4#1798895811yescharacteristic
327C4#1798896211yescharacteristic
328C2#332×D7312yes—
329C2#2260860112yes—
330C2#2261073511yescharacteristic
331C2#2261077311yescharacteristic
332C2#2261085211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D73
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC2×#332×C73C2
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C42×C73C23
hypercenterC2×#332D73
hypocenterC73#9692
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
160. Dic73#332semidirect
174. C73#9692semidirect

Maximal subgroups

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

subgroupindex
#226183272
#226100822
C4⋊C8×Dic732
C2×#179883342
C2×#179883332
C2×#179883322
C2×#332×C732
#969273