Finite Group Databasebeta

← #34003792

Subgroups — #34003792

Order 18688.

528 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22625716C211yesmaximal, characteristic
2C4×#14556658C211yesmaximal, characteristic
3C2×#17989446C212yesmaximal
4#22624809C212yesmaximal
5C4×#14556590C211yesmaximal, characteristic
6C2×#14556658C2212yes—
7C2×#14556658C2212yes—
8C2×#14556646—21no—
9C2×C4×#10596833—21no—
10#17989453—21no—
11#17989453—21no—
12#17989446C418yescomplemented
13C2×#14556590C2211yescharacteristic
14C2×C4×Dic146—21no—
15#17988491—21no—
16#17988486C411yescharacteristic
17#17988484—21no—
18#17988483C411yescharacteristic
19#17988456C2211yescharacteristic
20C4×#11924007—21no—
21C4×C4⋊Dic73C411yescharacteristic
22C42×Dic73C2211yescharacteristic
23C4×C4⋊C4×C73C411yescharacteristic
24C22×#10596833—22no—
25C22×#10596833—22no—
26#14556658—22no—
27#14556658—22no—
28#14556658C2×C414yes—
29#14556658C2×C414yes—
30#14556646—42no—
31C4×#10596833—42no—
32C22×Dic146—21no—
33#14556590—22no—
34#14556590C2×C414yes—
35C4×Dic146—42no—
36C4×Dic146—42no—
37C2×C4⋊Dic73—21no—
38C2×C4⋊Dic73C2×C411yescharacteristic
39C2×C4⋊Dic73C2×C411yescharacteristic
40C2×#11924007—21no—
41C2×#11924007—21no—
42C2×#11924007—21no—
43C2×#11924007—21no—
44C2×C4×Dic73—21no—
45C2×C4×Dic73C2×C411yescharacteristic
46C2×C4×Dic73D411yescharacteristic
47C2×C4×Dic73D411yescharacteristic
48C2×C4×Dic73D411yescharacteristic
49C2×C4×Dic73D411yescharacteristic
50C2×C4×Dic73C2311yescharacteristic
51#14556498—21no—
52#14556498—21no—
53#14556498—21no—
54C2×C4⋊C4×C73C2×C411yescharacteristic
55C2×C4⋊C4×C73C2×C411yescharacteristic
56C2×C42×C73—21no—
57C2×C42×C73C2×C411yescharacteristic
58#95×C73—21no—
59C2×#10596833—24no—
60C2×#10596833—24no—
61C2×#10596833—42no—
62C2×#10596833—42no—
63C2×#10596833—42no—
64C2×#10596833—42no—
65C2×Dic146—24no—
66C2×Dic146—41no—
67C2×Dic146—41no—
68C2×Dic146—42no—
69C22×Dic73—21no—
70C22×Dic73—21no—
71C22×Dic73C22⋊C411yescharacteristic
72C22×Dic73C22⋊C411yescharacteristic
73C22×Dic73C2×D411yescharacteristic
74C22×Dic73C2×D411yescharacteristic
75C4⋊Dic73—21no—
76C4⋊Dic73—42no—
77C4⋊Dic73—41no—
78C4⋊Dic73C4212yes—
79#11924007—24no—
80#11924007—42no—
81#11924007—41no—
82#11924007—41no—
83#11924007—41no—
84#11924007—41no—
85C4×Dic73—22no—
86C4×Dic73—21no—
87C4×Dic73—21no—
88C4×Dic73—22no—
89C4×Dic73—41no—
90C4×Dic73—42no—
91C4×Dic73D812yes—
92C4×Dic73SD1612yes—
93C4×Dic73C22×C412yes—
94C4×Dic73#4112yes—
95C22×C4×C73—21no—
96C22×C4×C73—21no—
97C22×C4×C73C22⋊C411yescharacteristic
98C22×C4×C73C22⋊C411yescharacteristic
99C22×C4×C73C22×C411yescharacteristic
100C4⋊C4×C73—21no—
101C4⋊C4×C73—41no—
102C4⋊C4×C73C4212yes—
103C42×C73—22no—
104C42×C73—42no—
105C23×C73C2×C22⋊C411yescharacteristic
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—22no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—41no—
116C2×C4×C73—41no—
117C2×C4×C73—41no—
118C2×C4×C73#10112yes—
119C2×C4×C73#10212yes—
120C2×C4×C73C2×C4211yescharacteristic
121C2×C4×C73#11711yescharacteristic
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—22no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—41no—
129C2×Dic73—41no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73#10212yes—
134C2×Dic73C4×D412yes—
135C2×Dic73C4×D412yes—
136C2×Dic73C2×D811yescharacteristic
137C2×Dic73C2×SD1611yescharacteristic
138C2×Dic73#13512yes—
139C2×Dic73AGL(1,ℤ/8)11yescharacteristic
140C2×Dic73#13712yes—
141C2×Dic73#13711yescharacteristic
142Dic146—44no—
143Dic146—44no—
144#10596833—44no—
145#10596833—44no—
146C22×C73C4×C22⋊C411yescharacteristic
147C22×C73C2×#10111yescharacteristic
148C22×C73#41311yescharacteristic
149C22×C73C2×#10211yescharacteristic
150C22×C73#41611yescharacteristic
151C22×C73#41711yescharacteristic
152C22×C73#41911yescharacteristic
153C4×C73—22no—
154C4×C73—22no—
155C4×C73—21no—
156C4×C73—21no—
157C4×C73—42no—
158C4×C73—81no—
159Dic73—22no—
160Dic73—41no—
161Dic73—42no—
162Dic73—81no—
163Dic73C4×D812yes—
164Dic73C4×SD1612yes—
165Dic73#44012yes—
166Dic73#44112yes—
167#8236—731nomaximal, Sylow
168C2×C73#154611yescharacteristic
169C2×C73#154711yescharacteristic
170C2×C73#155211yescharacteristic
171C2×C73#155411yescharacteristic
172C2×C73C4×#10111yescharacteristic
173C2×C73C4×#10211yescharacteristic
174C2×C73#176311yescharacteristic
175C4×C4⋊Q8—731no—
176#1767—731no—
177C4×C4⋊C8—731no—
178C2×#332—732no—
179#1296—732no—
180C73#823611yescharacteristic, complemented, Sylow
181C2×C4⋊Q8—731no—
182C2×C4×Q8—1461no—
183C2×C4⋊C8—732no—
184C2×C4⋊C8—732no—
185C2×#97—1461no—
186C2×C4×C8—1461no—
187#391—1461no—
188#389—731no—
189#389—731no—
190#389—1461no—
191#384—731no—
192C4×C4⋊C4—731no—
193C4×C4⋊C4—1461no—
194C4×C4⋊C4#6440811yescharacteristic
195C43—731no—
196#336—1461no—
197#336—1461no—
198#332—738no—
199C22×Q8—1461no—
200C22×C8—1462no—
201C22×C8—1462no—
202C4⋊Q8—734no—
203C4⋊Q8—1462no—
204C4×Q8—2922no—
205C4×Q8—2922no—
206C2×C4⋊C4—731no—
207C2×C4⋊C4—731no—
208C2×C4⋊C4—1461no—
209C2×C4⋊C4—1461no—
210C2×C4⋊C4—1461no—
211C2×C4⋊C4—1461no—
212C2×C4⋊C4—1461no—
213C2×C4⋊C4C2×#6440811yescharacteristic
214C2×C4⋊C4C2×#6440811yescharacteristic
215C2×C42—21no—
216C2×C42—731no—
217C2×C42—731no—
218C2×C42—731no—
219C2×C42—731no—
220C2×C42—731no—
221C2×C42—731no—
222C2×C42—1461no—
223C2×C42C2×#6440811yescharacteristic
224C4⋊C8—734no—
225C4⋊C8—734no—
226C4⋊C8—1462no—
227C4⋊C8—1462no—
228#97—2922no—
229C4×C8—2922no—
230#95—21no—
231#95—1461no—
232#95—1461no—
233#95—1461no—
234C2×Q8—2921no—
235C2×Q8—2921no—
236C2×Q8—2922no—
237C2×Q8—1464no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—731no—
241C22×C4—731no—
242C22×C4—731no—
243C22×C4—731no—
244C22×C4—1461no—
245C22×C4—1461no—
246C22×C4C22⋊#6440811yescharacteristic
247C22×C4C22⋊#6440811yescharacteristic
248C22×C4C22×#6440811yescharacteristic
249C2×C8—2922no—
250C2×C8—2922no—
251C2×C8—2922no—
252C2×C8—2922no—
253C2×C8—1464no—
254C2×C8—1464no—
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—2921no—
258C4⋊C4—2921no—
259C4⋊C4—2921no—
260C4⋊C4—2922no—
261C4⋊C4—2921no—
262C4⋊C4—2921no—
263C4⋊C4—2922no—
264C4⋊C4—732no—
265C4⋊C4—1464no—
266C4⋊C4—1461no—
267C4⋊C4C4×#6440812yes—
268C42—22no—
269C42—42no—
270C42—2921no—
271C42—2922no—
272C42—732no—
273C42—732no—
274C42—732no—
275C42—732no—
276C42—1461no—
277C42—1462no—
278C42—1461no—
279C42—1462no—
280C23C2×C22⋊#6440811yescharacteristic
281Q8—2924no—
282Q8—2924no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—2921no—
296C2×C4—2921no—
297C2×C4—2921no—
298C2×C4—2921no—
299C2×C4—2921no—
300C2×C4—732no—
301C2×C4—732no—
302C2×C4—731no—
303C2×C4—731no—
304C2×C4—732no—
305C2×C4—731no—
306C2×C4—731no—
307C2×C4—732no—
308C2×C4—732no—
309C2×C4—1462no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4#1455665212yes—
316C2×C4#1455665312yes—
317C2×C4C2×C4×#6440811yescharacteristic
318C2×C4#1455667011yescharacteristic
319C8—2924no—
320C8—2924no—
321C22C4×C22⋊#6440811yescharacteristic
322C22C2×#1455665211yescharacteristic
323C22#1798957311yescharacteristic
324C22C2×#1455665311yescharacteristic
325C22#1798957711yescharacteristic
326C22#1798957811yescharacteristic
327C22#1798958011yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—22no—
332C4—42no—
333C4—81no—
334C4—2922no—
335C4—2921no—
336C4—5841no—
337C4—732no—
338C4—732no—
339C4—732no—
340C4—732no—
341C4—1462no—
342C2#2262544011yescharacteristic
343C2#2262544211yescharacteristic
344C2#2262545211yescharacteristic
345C2#2262545611yescharacteristic
346C2C4×#1455665211yescharacteristic
347C2C4×#1455665311yescharacteristic
348C2#2262570311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C2×C42
FrattiniC22×C4C22×#64408
FittingC4×C4⋊C4×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC4×C4⋊C4#64408
hypocenterC73#8236
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
12. #17989446C4semidirect
180. C73#8236semidirect

Maximal subgroups

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

subgroupindex
#226257162
C4×#145566582
C2×#179894462
#226248092
C4×#145565902
#823673