Finite Group Databasebeta

← #34003796

Subgroups — #34003796

Order 18688.

528 conjugacy classes of subgroups.

The subgroup lattice has 344 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
5#22612502C211yesmaximal, characteristic
6C2×#14556658C2212yes—
7C2×#14556658C2212yes—
8C2×#14556646—21no—
9C2×C4×#10596833—21no—
10#17989453—21no—
11#17989453—21no—
12#17989446C418yescomplemented
13C2×#14556590C2211yescharacteristic
14C2×#14556556—21no—
15#17988491—21no—
16#17988485C411yescharacteristic
17#17988482—21no—
18#17988456C2211yescharacteristic
19C4⋊C4×Dic73C411yescharacteristic
20C4⋊C4×Dic73C411yescharacteristic
21#17988438—21no—
22C42×Dic73C2211yescharacteristic
23#389×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—
35#14556556—44no—
36C2×C4⋊Dic73C2×C411yescharacteristic
37C2×C4⋊Dic73C2×C411yescharacteristic
38C2×#11924007—21no—
39C2×#11924007—21no—
40C2×#11924007—21no—
41C2×#11924007—21no—
42C2×C4×Dic73—21no—
43C2×C4×Dic73—21no—
44C2×C4×Dic73C2×C411yescharacteristic
45C2×C4×Dic73D411yescharacteristic
46C2×C4×Dic73D411yescharacteristic
47C2×C4×Dic73D411yescharacteristic
48C2×C4×Dic73D411yescharacteristic
49C2×C4×Dic73C2311yescharacteristic
50#14556498—21no—
51#14556498—21no—
52#14556498—21no—
53C2×C4⋊C4×C73—21no—
54C2×C4⋊C4×C73C2×C411yescharacteristic
55C2×C4⋊C4×C73C2×C411yescharacteristic
56C2×C42×C73C2×C411yescharacteristic
57#95×C73—21no—
58C2×#10596833—24no—
59C2×#10596833—24no—
60C2×#10596833—42no—
61C2×#10596833—42no—
62C2×#10596833—42no—
63C2×#10596833—42no—
64C2×Dic146—24no—
65C2×Dic146—42no—
66C2×Dic146—41no—
67C2×Dic146—41no—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C22×Dic73C22⋊C411yescharacteristic
71C22×Dic73C22⋊C411yescharacteristic
72C22×Dic73C2×D411yescharacteristic
73C22×Dic73C2×D411yescharacteristic
74C4⋊Dic73—21no—
75C4⋊Dic73—41no—
76C4⋊Dic73C4212yes—
77#11924007—24no—
78#11924007—42no—
79#11924007—42no—
80#11924007—42no—
81C4×Dic73—22no—
82C4×Dic73—22no—
83C4×Dic73—22no—
84C4×Dic73—21no—
85C4×Dic73—21no—
86C4×Dic73—42no—
87C4×Dic73—42no—
88C4×Dic73SD1612yes—
89C4×Dic73Q1612yes—
90C4×Dic73C22×C412yes—
91C4×Dic73#4112yes—
92C22×C4×C73—21no—
93C22×C4×C73—21no—
94C22×C4×C73C22⋊C411yescharacteristic
95C22×C4×C73C22⋊C411yescharacteristic
96C22×C4×C73C22×C411yescharacteristic
97C4⋊C4×C73—21no—
98C4⋊C4×C73—41no—
99C4⋊C4×C73—42no—
100C4⋊C4×C73C4212yes—
101C42×C73—41no—
102C23×C73C2×C22⋊C411yescharacteristic
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—22no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—41no—
116C2×C4×C73#10312yes—
117C2×C4×C73C2×C4211yescharacteristic
118C2×C4×C73#11711yescharacteristic
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—22no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126C2×Dic73—41no—
127C2×Dic73—41no—
128C2×Dic73—41no—
129C2×Dic73#10112yes—
130C2×Dic73#10312yes—
131C2×Dic73C4×D412yes—
132C2×Dic73C4×D412yes—
133C2×Dic73C2×SD1611yescharacteristic
134C2×Dic73C2×Q1611yescharacteristic
135C2×Dic73#13512yes—
136C2×Dic73AGL(1,ℤ/8)12yes—
137C2×Dic73AGL(1,ℤ/8)11yescharacteristic
138C2×Dic73#13711yescharacteristic
139Dic146—44no—
140Dic146—44no—
141#10596833—44no—
142#10596833—44no—
143C22×C73C4×C22⋊C411yescharacteristic
144C22×C73C2×#10111yescharacteristic
145C22×C73#41311yescharacteristic
146C22×C73C2×#10311yescharacteristic
147C22×C73#41611yescharacteristic
148C22×C73#41711yescharacteristic
149C22×C73#41811yescharacteristic
150C4×C73—22no—
151C4×C73—21no—
152C4×C73—21no—
153C4×C73—41no—
154C4×C73—42no—
155C4×C73—81no—
156Dic73—22no—
157Dic73—22no—
158Dic73—42no—
159Dic73—81no—
160Dic73C4×SD1612yes—
161Dic73C4×Q1612yes—
162Dic73#44012yes—
163Dic73#44212yes—
164#8237—731nomaximal, Sylow
165C2×C73#154911yescharacteristic
166C2×C73#155011yescharacteristic
167C2×C73#155211yescharacteristic
168C2×C73#155311yescharacteristic
169C2×C73C4×#10111yescharacteristic
170C2×C73C4×#10311yescharacteristic
171C2×C73#176211yescharacteristic
172C4×C4⋊Q8—731no—
173#1767—731no—
174C4×C4⋊C8—731no—
175C2×#332—732no—
176#1296—732no—
177C73#823711yescharacteristic, complemented, Sylow
178C2×C4⋊Q8—731no—
179C2×C4×Q8—1461no—
180C2×C4⋊C8—732no—
181C2×C4⋊C8—732no—
182C2×#97—1461no—
183C2×C4×C8—1461no—
184#391—1461no—
185#389—731no—
186#389—1461no—
187#389#6440811yescharacteristic
188#384—731no—
189C4×C4⋊C4—731no—
190C4×C4⋊C4—731no—
191C4×C4⋊C4—1461no—
192C43—731no—
193#336—1461no—
194#336—1461no—
195#332—738no—
196C22×Q8—1461no—
197C22×C8—1462no—
198C22×C8—1462no—
199C4⋊Q8—734no—
200C4⋊Q8—1462no—
201C4×Q8—2924no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—731no—
204C2×C4⋊C4—731no—
205C2×C4⋊C4—1461no—
206C2×C4⋊C4—1461no—
207C2×C4⋊C4—1461no—
208C2×C4⋊C4—1461no—
209C2×C4⋊C4C2×#6440811yescharacteristic
210C2×C4⋊C4C2×#6440811yescharacteristic
211C2×C42—731no—
212C2×C42—731no—
213C2×C42—731no—
214C2×C42—731no—
215C2×C42—731no—
216C2×C42—731no—
217C2×C42—1461no—
218C2×C42—1461no—
219C2×C42C2×#6440811yescharacteristic
220C4⋊C8—734no—
221C4⋊C8—734no—
222C4⋊C8—1462no—
223C4⋊C8—1462no—
224#97—2922no—
225C4×C8—2922no—
226#95—21no—
227#95—1461no—
228#95—1461no—
229#95—1461no—
230C2×Q8—2922no—
231C2×Q8—2921no—
232C2×Q8—2921no—
233C2×Q8—1464no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—731no—
237C22×C4—731no—
238C22×C4—731no—
239C22×C4—731no—
240C22×C4—1461no—
241C22×C4—1461no—
242C22×C4C22⋊#6440811yescharacteristic
243C22×C4C22⋊#6440811yescharacteristic
244C22×C4C22×#6440811yescharacteristic
245C2×C8—2922no—
246C2×C8—2922no—
247C2×C8—2922no—
248C2×C8—2922no—
249C2×C8—1464no—
250C2×C8—1464no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—2921no—
255C4⋊C4—2922no—
256C4⋊C4—2922no—
257C4⋊C4—2922no—
258C4⋊C4—732no—
259C4⋊C4—1464no—
260C4⋊C4—1461no—
261C4⋊C4C4×#6440812yes—
262C42—41no—
263C42—2922no—
264C42—2922no—
265C42—732no—
266C42—732no—
267C42—732no—
268C42—732no—
269C42—1461no—
270C42—1462no—
271C42—1461no—
272C42—1462no—
273C42—1462no—
274C23C2×C22⋊#6440811yescharacteristic
275Q8—2924no—
276Q8—2924no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—2921no—
291C2×C4—2921no—
292C2×C4—2921no—
293C2×C4—2921no—
294C2×C4—2921no—
295C2×C4—732no—
296C2×C4—732no—
297C2×C4—731no—
298C2×C4—731no—
299C2×C4—732no—
300C2×C4—731no—
301C2×C4—731no—
302C2×C4—732no—
303C2×C4—732no—
304C2×C4—732no—
305C2×C4—1462no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1461no—
310C2×C4#1455665412yes—
311C2×C4C2×C4×#6440811yescharacteristic
312C2×C4#1455667011yescharacteristic
313C8—2924no—
314C8—2924no—
315C22C4×C22⋊#6440811yescharacteristic
316C22D73⋊#10111yescharacteristic
317C22#1798957411yescharacteristic
318C22C2×#1455665411yescharacteristic
319C22#1798957711yescharacteristic
320C22#1798957811yescharacteristic
321C22#1798957911yescharacteristic
322C4—21no—
323C4—21no—
324C4—22no—
325C4—42no—
326C4—41no—
327C4—81no—
328C4—2922no—
329C4—5841no—
330C4—732no—
331C4—732no—
332C4—732no—
333C4—732no—
334C4—1462no—
335C4—1462no—
336C2#2262544711yescharacteristic
337C2#2262544911yescharacteristic
338C2#2262545311yescharacteristic
339C2#2262545511yescharacteristic
340C2#2262568411yescharacteristic
341C2C4×#1455665411yescharacteristic
342C2#2262570111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C2×C42
FrattiniC22×C4C22×#64408
Fitting#389×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#389#64408
hypocenterC73#8237
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
12. #17989446C4semidirect
177. C73#8237semidirect

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
#226125022
#823773