Finite Group Databasebeta

← #32974095

Subgroups — #32974095

Order 18688.

504 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556570C211yesmaximal, characteristic
2#22609999C211yesmaximal, characteristic
3#22607756C212yesmaximal, complemented
4#22607755C212yesmaximal, complemented
5C73×#1797C211yesmaximal, characteristic
6C2×#14556570C411yescharacteristic
7C2×C4×Dic146C411yescharacteristic
8C2×C22⋊#10596831—21no—
9#17988493C2211yescharacteristic
10#17988485C2211yescharacteristic
11#17988471—21no—
12#17988460—21no—
13#17988447C411yescharacteristic
14C4×#11924007—21no—
15C4×C4⋊Dic73C411yescharacteristic
16C4×C22⋊Dic73—21no—
17#17988342—21no—
18#17988342C2212yes—
19C22×C42×C73C2211yescharacteristic
20C2×C4⋊C8×C73—21no—
21C2×C22⋊C8×C73—21no—
22#336×C73C2212yes—
23C22×Dic146C2×C411yescharacteristic
24C22×#10596831—22no—
25#14556570—22no—
26#14556570C814yescomplemented
27C4×Dic146—42no—
28C2×C4⋊Dic73C2×C411yescharacteristic
29C2×C4⋊Dic73C2×C411yescharacteristic
30C2×C4⋊Dic73C2×C411yescharacteristic
31C2×#11924007—21no—
32C2×#11924007—21no—
33C2×#11924007—21no—
34C2×C22⋊Dic73—21no—
35C2×C22⋊Dic73—21no—
36C2×C4×Dic73—21no—
37C2×C4×Dic73—21no—
38C22⋊#10596831—42no—
39#14556498—21no—
40#14556498—21no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44C23×C4×C73C2×C411yescharacteristic
45C23×C4×C73D411yescharacteristic
46C23×C4×C73D411yescharacteristic
47C22×C8×C73—22no—
48C2×C42×C73—42no—
49C2×C42×C73C2×C411yescharacteristic
50C2×C42×C73D411yescharacteristic
51C2×C42×C73D411yescharacteristic
52C2×C42×C73C2311yescharacteristic
53C4⋊C8×C73—42no—
54C22⋊C8×C73—42no—
55C2×Dic146—21no—
56C2×Dic146—41no—
57C2×Dic146—41no—
58C2×Dic146C2×C812yes—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C2×#10596831—42no—
64C2×#10596831—42no—
65C2×#10596831—42no—
66C4⋊Dic73—21no—
67C4⋊Dic73—41no—
68C4⋊Dic73—41no—
69C4⋊Dic73C2×C812yes—
70#11924007—24no—
71#11924007—42no—
72#11924007—41no—
73#11924007—41no—
74C22⋊Dic73—24no—
75C22⋊Dic73—42no—
76C4×Dic73—42no—
77C4×Dic73—42no—
78C24×C73C22⋊C411yescharacteristic
79C22×C4×C73—22no—
80C22×C4×C73—21no—
81C22×C4×C73—21no—
82C22×C4×C73—22no—
83C22×C4×C73—41no—
84C22×C4×C73—41no—
85C22×C4×C73—41no—
86C22×C4×C73—41no—
87C22×C4×C73—41no—
88C22×C4×C73C22⋊C411yescharacteristic
89C22×C4×C73C22⋊C411yescharacteristic
90C22×C4×C73C22⋊C411yescharacteristic
91C22×C4×C73C2×C812yes—
92C22×C4×C73M1612yes—
93C22×C4×C73C22×C411yescharacteristic
94C22×C4×C73C2×D411yescharacteristic
95C22×C4×C73C2×D411yescharacteristic
96C2×C8×C73—42no—
97C2×C8×C73—42no—
98C2×C8×C73—42no—
99C42×C73—22no—
100C42×C73—22no—
101C42×C73—41no—
102C42×C73—41no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73C22⋊C812yes—
110C23×C73C2×C22⋊C411yescharacteristic
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—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—42no—
125C2×C4×C73—42no—
126C2×C4×C73—44no—
127C2×C4×C73—42no—
128C2×C4×C73—42no—
129C2×C4×C73C22⋊C812yes—
130C2×C4×C73#9912yes—
131C2×C4×C73C22×C811yescharacteristic
132C2×C4×C73C2×M1611yescharacteristic
133C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C73#13711yescharacteristic
135C2×C4×C73#13712yes—
136C2×Dic73—22no—
137C2×Dic73—22no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73—41no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145C2×Dic73—41no—
146C2×Dic73—41no—
147C2×Dic73—41no—
148Dic146—42no—
149Dic146—42no—
150C8×C73—82no—
151#10596831—82no—
152C22×C73—22no—
153C22×C73—22no—
154C22×C73—22no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73C2×C22⋊C811yescharacteristic
160C22×C73C2×#9911yescharacteristic
161C22×C73#41311yescharacteristic
162C22×C73#41711yescharacteristic
163C22×C73#41911yescharacteristic
164C22×C73#42111yescharacteristic
165C22×C73#42111yescharacteristic
166C4×C73—21no—
167C4×C73—21no—
168C4×C73—22no—
169C4×C73—22no—
170C4×C73—22no—
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—41no—
174Dic73—42no—
175Dic73—42no—
176Dic73—81no—
177Dic73—81no—
178#7600—731nomaximal, Sylow
179C2×C73—42no—
180C2×C73#145911yescharacteristic
181C2×C73#147711yescharacteristic
182C2×C73#147911yescharacteristic
183C2×C73#151111yescharacteristic
184C2×C73#151311yescharacteristic
185C2×C73#153511yescharacteristic
186C2×C73#155911yescharacteristic
187C4×C22⋊Q8—731no—
188#1817—731no—
189#1797D7311yescharacteristic
190#1272—732no—
191#1271—732no—
192C73#760011yescharacteristic, complemented, Sylow
193C2×C22⋊Q8—731no—
194C2×C4×Q8—731no—
195C22×C42C2×D7311yescharacteristic
196C2×C4⋊C8—21no—
197C2×C22⋊C8—21no—
198C2×C22⋊C8—1461no—
199#391—731no—
200#389—731no—
201#387—1461no—
202#385—1461no—
203#380—731no—
204C4×C4⋊C4—731no—
205C4×C4⋊C4—1461no—
206C4×C22⋊C4—1461no—
207#336—732no—
208#336—1461no—
209#336C2×D7312yes—
210C22×Q8—731no—
211C23×C4C4×D7311yescharacteristic
212C23×C4D29211yescharacteristic
213C23×C4C22⋊D7311yescharacteristic
214C22×C8—22no—
215C22×C8—1462no—
216C22⋊Q8—734no—
217C22⋊Q8—1462no—
218C4×Q8—2922no—
219C2×C4⋊C4—731no—
220C2×C4⋊C4—731no—
221C2×C4⋊C4—731no—
222C2×C4⋊C4—1461no—
223C2×C4⋊C4—1461no—
224C2×C4⋊C4—1461no—
225C2×C22⋊C4—1461no—
226C2×C22⋊C4—1461no—
227C2×C42—42no—
228C2×C42—1461no—
229C2×C42—1461no—
230C2×C42C4×D7311yescharacteristic
231C2×C42D29211yescharacteristic
232C2×C42C22⋊D7311yescharacteristic
233C2×C42C22×D7311yescharacteristic
234C4⋊C8—42no—
235C22⋊C8—42no—
236C22⋊C8—2922no—
237#95—1461no—
238#95—1461no—
239#95—1461no—
240#95—1461no—
241#95—1461no—
242C24#1192400511yescharacteristic
243C2×Q8—2921no—
244C2×Q8—2921no—
245C2×Q8—732no—
246C2×Q8—1461no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—1461no—
257C22×C4—1461no—
258C22×C4—1461no—
259C22×C4—1461no—
260C22×C4#1192400511yescharacteristic
261C22×C4#1192400511yescharacteristic
262C22×C4#1192400511yescharacteristic
263C22×C4C8×D7312yes—
264C22×C4#1192401112yes—
265C22×C4C2×C4×D7311yescharacteristic
266C22×C4C2×C22⋊D7311yescharacteristic
267C22×C4C2×D29211yescharacteristic
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—2922no—
272C2×C8—2922no—
273C2×C8—2922no—
274C4⋊C4—2921no—
275C4⋊C4—2921no—
276C4⋊C4—2922no—
277C4⋊C4—2921no—
278C4⋊C4—2921no—
279C4⋊C4—732no—
280C4⋊C4—1464no—
281C4⋊C4—1461no—
282C22⋊C4—2922no—
283C22⋊C4—1464no—
284C42—22no—
285C42—22no—
286C42—41no—
287C42—41no—
288C42—2922no—
289C42—2922no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23#1455650312yes—
297C23C2×#1192400511yescharacteristic
298Q8—2922no—
299Q8—2922no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—44no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—2921no—
319C2×C4—2921no—
320C2×C4—2921no—
321C2×C4—2921no—
322C2×C4—2921no—
323C2×C4—2921no—
324C2×C4—2921no—
325C2×C4—2921no—
326C2×C4—2921no—
327C2×C4—2921no—
328C2×C4—1462no—
329C2×C4—1462no—
330C2×C4#1455650312yes—
331C2×C4#1455650512yes—
332C2×C4C2×C8×D7311yescharacteristic
333C2×C4C2×#1192401111yescharacteristic
334C2×C4#1455661711yescharacteristic
335C2×C4#1455662211yescharacteristic
336C2×C4#1455662412yes—
337C8—82no—
338C8—5842no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22C2×#1455650311yescharacteristic
347C22C2×#1455650511yescharacteristic
348C22#1798856911yescharacteristic
349C22#1798858611yescharacteristic
350C22#1798859711yescharacteristic
351C22#1798860311yescharacteristic
352C22#1798860511yescharacteristic
353C4—22no—
354C4—22no—
355C4—21no—
356C4—21no—
357C4—22no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—2922no—
362C4—2922no—
363C4—5841no—
364C4—5841no—
365C2—42no—
366C2#2260824711yescharacteristic
367C2#2260831611yescharacteristic
368C2#2260832711yescharacteristic
369C2#2260846511yescharacteristic
370C2#2260847211yescharacteristic
371C2#2260856311yescharacteristic
372C2#2260865911yescharacteristic
subgroupG/H
centerC23C2×#11924005
commutatorC2×C4×C73C22×C8
FrattiniC2×C42C22×D73
FittingC73×#1797C2
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C42×C73C23
hypercenter#1797D73
hypocenterC73#7600
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #22607756C2semidirect
4. #22607755C2semidirect
26. #14556570C8semidirect
192. C73#7600semidirect

Maximal subgroups

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

subgroupindex
C4×#145565702
#226099992
#226077562
#226077552
C73×#17972
#760073