Finite Group Databasebeta

← #32974460

Subgroups — #32974460

Order 18688.

464 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618298C211yesmaximal, characteristic
2#22609784C211yesmaximal, characteristic, complemented
3#22607753C212yesmaximal, complemented
4#22607751C212yesmaximal
5C4×C4⋊C8×C73C211yesmaximal, characteristic, complemented
6C2×#14556585—21no—
7C2×C4⋊#10596831—21no—
8C2×#14556502—21no—
9#17988489C411yescharacteristic
10#17988489C411yescharacteristic
11#17988489C2211yescharacteristic
12#17988485C411yescharacteristic
13#17988485C411yescharacteristic
14#17988485C2211yescharacteristic
15#17988478—21no—
16#17988478—21no—
17#17988478—21no—
18#17988342C2212yes—
19C2×C4⋊C8×C73—21no—
20C2×C4×C8×C73—21no—
21C43×C73C2211yescharacteristic
22#336×C73C2212yes—
23C22×D292C2×C411yescharacteristic
24C22×#10596831—22no—
25#14556585—42no—
26#14556585—42no—
27C2×C4⋊Dic73C2×C411yescharacteristic
28C2×C4⋊Dic73C2×C411yescharacteristic
29C2×C4⋊Dic73C2×C411yescharacteristic
30C2×#11924007—21no—
31C2×#11924007—21no—
32C2×#11924007—21no—
33C2×#11924005—21no—
34C2×#11924005—21no—
35C2×#11924005—21no—
36C2×#11924005—21no—
37C2×#11924005—21no—
38C2×#11924005—21no—
39C4⋊#10596831—24no—
40#14556502—42no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44C22×C8×C73—22no—
45C2×C42×C73C2×C411yescharacteristic
46C2×C42×C73C2×C411yescharacteristic
47C2×C42×C73D411yescharacteristic
48C2×C42×C73D411yescharacteristic
49C2×C42×C73D411yescharacteristic
50C2×C42×C73D411yescharacteristic
51C2×C42×C73C2311yescharacteristic
52C4⋊C8×C73—24no—
53C4×C8×C73—42no—
54C23×D73—21no—
55C2×D292—22no—
56C2×D292—41no—
57C2×D292—41no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C2×#10596831—24no—
62C2×#10596831—42no—
63C2×#10596831—42no—
64C4⋊Dic73—22no—
65C4⋊Dic73—41no—
66C4⋊Dic73—41no—
67#11924007—42no—
68#11924007—42no—
69#11924007—41no—
70#11924007—41no—
71#11924005—42no—
72#11924005—42no—
73#11924005—42no—
74#11924005—42no—
75#11924005—41no—
76#11924005—41no—
77#11924005—41no—
78#11924005—41no—
79C22×C4×C73C22⋊C411yescharacteristic
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22⋊C411yescharacteristic
82C22×C4×C73C22⋊C411yescharacteristic
83C22×C4×C73C22×C411yescharacteristic
84C22×C4×C73C2×D411yescharacteristic
85C22×C4×C73C2×D411yescharacteristic
86C2×C8×C73—24no—
87C2×C8×C73—42no—
88C2×C8×C73—42no—
89C42×C73—22no—
90C42×C73—22no—
91C42×C73—22no—
92C42×C73—21no—
93C42×C73—21no—
94C42×C73—41no—
95C42×C73—41no—
96C42×C73D812yes—
97C42×C73SD1612yes—
98C23×C73C2×C22⋊C411yescharacteristic
99C22×D73—41no—
100C22×D73—41no—
101C22×D73—41no—
102C22×D73—41no—
103C22×D73—41no—
104C22×D73—41no—
105C22×D73—41no—
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—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73#10212yes—
121C2×C4×C73#10212yes—
122C2×C4×C73#10412yes—
123C2×C4×C73#10412yes—
124C2×C4×C73#13112yes—
125C2×C4×C73C2×D811yescharacteristic
126C2×C4×C73C2×SD1611yescharacteristic
127C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C73#13711yescharacteristic
129C2×Dic73—41no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138D292—82no—
139C8×C73—44no—
140#10596831—44no—
141C22×C73#40811yescharacteristic
142C22×C73#41011yescharacteristic
143C22×C73#41311yescharacteristic
144C22×C73C2×#10211yescharacteristic
145C22×C73#41711yescharacteristic
146C22×C73C2×#10411yescharacteristic
147C22×C73C2×#10411yescharacteristic
148C2×D73—81no—
149C2×D73—81no—
150C2×D73—81no—
151C2×D73—81no—
152C2×D73—81no—
153C2×D73—81no—
154C2×D73—81no—
155C4×C73—22no—
156C4×C73—22no—
157C4×C73—22no—
158C4×C73—22no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—21no—
162C4×C73—21no—
163C4×C73—22no—
164Dic73—81no—
165Dic73—81no—
166Dic73—81no—
167#7686—731nomaximal, Sylow
168C2×C73#147311yescharacteristic
169C2×C73#148311yescharacteristic
170C2×C73#149211yescharacteristic
171C2×C73#150211yescharacteristic
172C2×C73#150911yescharacteristic
173C2×C73#152411yescharacteristic
174C2×C73#154711yescharacteristic
175D73—161no—
176#2860—731no—
177#1767—731no—
178C4×C4⋊C8D7311yescharacteristic, complemented
179#1271—732no—
180#1270—732no—
181C73#768611yescharacteristic, complemented, Sylow
182C2×#126—1461no—
183C2×C4⋊C8—21no—
184C2×C4⋊C8—1461no—
185C2×#97—1461no—
186C2×C4×C8—21no—
187#390—731no—
188#390—731no—
189#390—731no—
190#389—731no—
191#389—731no—
192#389—731no—
193#388—1461no—
194#388—1461no—
195#388—1461no—
196C43C2×D7311yescharacteristic
197#336—732no—
198#336C2×D7312yes—
199C22×D4—731no—
200C22×C8—22no—
201C22×C8—1462no—
202#126—2922no—
203#126—2922no—
204C2×C4⋊C4—731no—
205C2×C4⋊C4—731no—
206C2×C4⋊C4—731no—
207C2×C4⋊C4—1461no—
208C2×C4⋊C4—1461no—
209C2×C4⋊C4—1461no—
210C2×C22⋊C4—1461no—
211C2×C22⋊C4—1461no—
212C2×C22⋊C4—1461no—
213C2×C22⋊C4—1461no—
214C2×C22⋊C4—1461no—
215C2×C22⋊C4—1461no—
216C2×C42C4×D7311yescharacteristic
217C2×C42C4×D7311yescharacteristic
218C2×C42D29211yescharacteristic
219C2×C42D29211yescharacteristic
220C2×C42C22⋊D7311yescharacteristic
221C2×C42C22⋊D7311yescharacteristic
222C2×C42C22×D7311yescharacteristic
223C4⋊C8—24no—
224C4⋊C8—1464no—
225#97—2922no—
226C4×C8—42no—
227#95—1461no—
228#95—1461no—
229#95—1461no—
230C24—1461no—
231C2×D4—2921no—
232C2×D4—2921no—
233C2×D4—1462no—
234C22×C4—1461no—
235C22×C4—1461no—
236C22×C4—1461no—
237C22×C4#1192400511yescharacteristic
238C22×C4#1192400511yescharacteristic
239C22×C4#1192400511yescharacteristic
240C22×C4#1192400511yescharacteristic
241C22×C4C2×C4×D7311yescharacteristic
242C22×C4C2×C22⋊D7311yescharacteristic
243C22×C4C2×D29211yescharacteristic
244C2×C8—24no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—2922no—
248C2×C8—2922no—
249C2×C8—1464no—
250C4⋊C4—2921no—
251C4⋊C4—2921no—
252C4⋊C4—2922no—
253C4⋊C4—2922no—
254C4⋊C4—2921no—
255C4⋊C4—2921no—
256C4⋊C4—1462no—
257C22⋊C4—2922no—
258C22⋊C4—2922no—
259C22⋊C4—2922no—
260C22⋊C4—2922no—
261C22⋊C4—2921no—
262C22⋊C4—2921no—
263C22⋊C4—2921no—
264C22⋊C4—2921no—
265C42—22no—
266C42—22no—
267C42—22no—
268C42—21no—
269C42—21no—
270C42—41no—
271C42—41no—
272C42D58412yes—
273C42#1192401712yes—
274C23—2921no—
275C23—2921no—
276C23—2921no—
277C23—2921no—
278C23—2921no—
279C23—2921no—
280C23—2921no—
281C23C2×#1192400511yescharacteristic
282D4—5842no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—2921no—
298C2×C4—2921no—
299C2×C4—2921no—
300C2×C4—2921no—
301C2×C4—2921no—
302C2×C4—2921no—
303C2×C4—2921no—
304C2×C4—2921no—
305C2×C4—2921no—
306C2×C4#1455651312yes—
307C2×C4#1455651312yes—
308C2×C4#1455651712yes—
309C2×C4#1455651912yes—
310C2×C4#1455659712yes—
311C2×C4C2×D58411yescharacteristic
312C2×C4C2×#1192401711yescharacteristic
313C2×C4#1455661711yescharacteristic
314C2×C4#1455662211yescharacteristic
315C8—44no—
316C8—2924no—
317C22—5841no—
318C22—5841no—
319C22—5841no—
320C22—5841no—
321C22—5841no—
322C22—5841no—
323C22—5841no—
324C22#1798855311yescharacteristic
325C22#1798856011yescharacteristic
326C22#1798856911yescharacteristic
327C22C2×#1455651311yescharacteristic
328C22#1798858611yescharacteristic
329C22C2×#1455651711yescharacteristic
330C22C2×#1455651911yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—22no—
336C4—22no—
337C4—22no—
338C4—22no—
339C4—22no—
340C4—5841no—
341C4—5841no—
342C4—5841no—
343C2—11681no—
344C2#2260829811yescharacteristic
345C2#2260834211yescharacteristic
346C2#2260838311yescharacteristic
347C2#2260842711yescharacteristic
348C2#2260845411yescharacteristic
349C2#2260852011yescharacteristic
350C2#2260860611yescharacteristic
subgroupG/H
centerC23C2×#11924005
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC4×C4⋊C8×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC22×D292C2×C4
cosocleC2×C42×C73C23
hypercenterC4×C4⋊C8D73
hypocenterC73#7686
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #22609784C2semidirect
3. #22607753C2semidirect
5. C4×C4⋊C8×C73C2semidirect
178. C4×C4⋊C8D73semidirect
181. C73#7686semidirect

Maximal subgroups

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

subgroupindex
#226182982
#226097842
#226077532
#226077512
C4×C4⋊C8×C732
#768673