Finite Group Databasebeta

← #80431

Subgroups — #80431

Order 384.

472 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#916C211yesmaximal, characteristic
2C2×#915C211yesmaximal, characteristic, complemented
3#5724C211yesmaximal, characteristic, complemented
4#5546C211yesmaximal, characteristic, complemented
5C3×#461C211yesmaximal, characteristic, complemented
6#5165C211yesmaximal, characteristic, complemented
7#5162C211yesmaximal, characteristic, complemented
8#5090C211yesmaximal, characteristic, complemented
9#5016C211yesmaximal, characteristic, complemented
10#4845C211yesmaximal, characteristic, complemented
11#4839C211yesmaximal, characteristic, complemented
12#4803C211yesmaximal, characteristic, complemented
13D3×#103C211yesmaximal, characteristic, complemented
14#4798C211yesmaximal, characteristic, complemented
15#4795C211yesmaximal, characteristic, complemented
16#3046—31nomaximal, Sylow
17C2×#239C2211yescharacteristic
18C2×D3×Q8C2211yescharacteristic
19C2×#237C2211yescharacteristic
20C2×C3×SD16C2211yescharacteristic
21C2×C3×SD16C2211yescharacteristic
22C3×C4⋊Q8C2211yescharacteristic
23C3×C4×D4C2211yescharacteristic
24#947C2211yescharacteristic
25#944C2211yescharacteristic
26C2×#216C2211yescharacteristic
27C2×#216C2211yescharacteristic
28D4×Dic3C2211yescharacteristic
29C2×#214C2211yescharacteristic
30C2×#213C2211yescharacteristic
31C4×#67—21no—
32C2×Dic3⋊C4—21no—
33#916—24no—
34#915—24no—
35C2×Dic12C2211yescharacteristic
36C2×#204C2211yescharacteristic
37C2×ΓL(1,𝔽25)C2211yescharacteristic
38C2×D3×C8C2211yescharacteristic
39#896—21no—
40#896—21no—
41#894—21no—
42#894—21no—
43D3×C4⋊C4C2211yescharacteristic
44#887C2211yescharacteristic
45#67⋊C4—21no—
46#877—21no—
47#875C2211yescharacteristic
48#872C2211yescharacteristic
49C4×Dic6C2211yescharacteristic
50C3×C4⋊C8C2211yescharacteristic
51C3×#103C2211yescharacteristic
52C3×#103C2211yescharacteristic
53#835C2211yescharacteristic
54#835C2211yescharacteristic
55#821C2211yescharacteristic
56#816C2211yescharacteristic
57Dic3⋊C8C2211yescharacteristic
58Dic3⋊C8C2211yescharacteristic
59#810C2211yescharacteristic
60#809C2211yescharacteristic
61C4⋊(C3⋊C8)C2211yescharacteristic
62C2×#137—31no—
63C2×#135—31no—
64#536—31no—
65#520—31no—
66#464—31no—
67#464—31no—
68#463—31no—
69#463—31no—
70#462—31no—
71#462—31no—
72#461—31no—
73#461D311yescharacteristic, complemented
74#424—31no—
75#417—31no—
76C2×#103—31no—
77C2×C3×Q8C2311yescharacteristic
78C2×C3×Q8C2311yescharacteristic
79C2×C3×D4C2311yescharacteristic
80C22×C3×C4—21no—
81C2×#67—21no—
82C22×Dic3—21no—
83C22×Dic3—21no—
84#239—22no—
85#239—22no—
86D3×Q8—22no—
87D3×Q8—22no—
88#237—22no—
89#237D414yes—
90C2×D12—21no—
91C2×D12C2311yescharacteristic
92C2×C4×D3—21no—
93C2×C4×D3—21no—
94C2×C4×D3—21no—
95C2×C4×D3C2311yescharacteristic
96C2×Dic6—21no—
97C2×Dic6C2311yescharacteristic
98C2×Dic6C2311yescharacteristic
99C3×SD16—22no—
100C3×SD16—22no—
101C2×C3×C8C2311yescharacteristic
102C2×C3×C8C2311yescharacteristic
103C3×C4⋊C4—21no—
104C3×C4⋊C4—21no—
105C3×C4⋊C4C2311yescharacteristic
106C3×C22⋊C4—21no—
107C3×C42C2311yescharacteristic
108#217—21no—
109#216—22no—
110#216—22no—
111#214—22no—
112#213—22no—
113(C2×D3)⋊C4—21no—
114(C2×D3)⋊C4—21no—
115(C2×D3)⋊C4—21no—
116(C2×D3)⋊C4—21no—
117(C2×D3)⋊C4D411yescharacteristic
118(C2×D3)⋊C4D411yescharacteristic
119C4⋊Dic3C2311yescharacteristic
120Dic3⋊C4—21no—
121Dic3⋊C4—21no—
122Dic3⋊C4—21no—
123Dic3⋊C4—21no—
124Dic3⋊C4—21no—
125Dic3⋊C4D411yescharacteristic
126Dic3⋊C4D411yescharacteristic
127C4×Dic3—21no—
128C4×Dic3—21no—
129C4×Dic3C2311yescharacteristic
130C2×C3⋊C8C2311yescharacteristic
131C2×C3⋊C8C2311yescharacteristic
132Dic12—22no—
133#204—22no—
134ΓL(1,𝔽25)—22no—
135D3×C8—22no—
136C2×#41—31no—
137C2×#41—31no—
138C22×Q8—31no—
139#137—64no—
140#135—64no—
141C2×Q16—31no—
142C2×Q16—31no—
143C2×Q16—31no—
144C2×SD16—31no—
145C2×SD16—31no—
146C2×SD16C2×D311yescharacteristic
147C2×SD16C2×D311yescharacteristic
148C2×D8—31no—
149C2×M16—31no—
150C22×C8—31no—
151C4⋊Q8—31no—
152C4⋊Q8C2×D311yescharacteristic
153#124—31no—
154#124—31no—
155#123—61no—
156#123—61no—
157C22⋊Q8—61no—
158C22⋊Q8—61no—
159C4×Q8—31no—
160C4×Q8—31no—
161C4×D4—31no—
162C4×D4—61no—
163C4×D4—61no—
164C4×D4C2×D311yescharacteristic
165#117—31no—
166#117—61no—
167C2×C4⋊C4—31no—
168C2×C4⋊C4—61no—
169C4⋊C8—31no—
170C4⋊C8—31no—
171C4⋊C8—31no—
172C4⋊C8C2×D311yescharacteristic
173#103—31no—
174#103—31no—
175#103—31no—
176#103—31no—
177#103C2×D311yescharacteristic
178#103C2×D311yescharacteristic
179#102—31no—
180#102—31no—
181C23×C3—21no—
182C22×D3—21no—
183C22×D3C2×D411yescharacteristic
184C3×Q8—21no—
185C3×Q8—21no—
186C3×Q8—21no—
187C3×Q8—21no—
188C3×D4—21no—
189C3×D4C2×D412yes—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—81no—
194C2×C3×C4C2×D411yescharacteristic
195C2×C3×C4C2×D411yescharacteristic
196C2×C3×C4C2411yescharacteristic
197#67—24no—
198C2×Dic3—21no—
199C2×Dic3—24no—
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—81no—
203C2×Dic3C2×D411yescharacteristic
204C2×Dic3C2×D411yescharacteristic
205C2×Dic3C2×D411yescharacteristic
206D12—21no—
207D12—21no—
208D12—42no—
209C4×D3—42no—
210C4×D3—42no—
211C4×D3—81no—
212C4×D3C2×D412yes—
213C4×D3#4112yes—
214Dic6—21no—
215Dic6—21no—
216Dic6—21no—
217Dic6—42no—
218Dic6C2×D412yes—
219C3×C8—21no—
220C3×C8—21no—
221C3⋊C8—21no—
222C3⋊C8—21no—
223#41—34no—
224#41—62no—
225#41—62no—
226#41—62no—
227C2×Q8—31no—
228C2×Q8—31no—
229C2×Q8—61no—
230C2×Q8—62no—
231C2×Q8—62no—
232C2×Q8C22×D311yescharacteristic
233C2×Q8C22×D311yescharacteristic
234C2×D4—31no—
235C2×D4—61no—
236C2×D4—61no—
237C2×D4C22×D311yescharacteristic
238C22×C4—21no—
239C22×C4—31no—
240C22×C4—61no—
241C22×C4—61no—
242C22×C4—61no—
243C22×C4—61no—
244C22×C4—61no—
245Q16—62no—
246Q16—62no—
247Q16—62no—
248SD16—22no—
249SD16—22no—
250SD16—62no—
251SD16—62no—
252D8—62no—
253M16—62no—
254C2×C8—31no—
255C2×C8—31no—
256C2×C8—62no—
257C2×C8C22×D311yescharacteristic
258C2×C8C22×D311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—31no—
262C4⋊C4—31no—
263C4⋊C4—31no—
264C4⋊C4—61no—
265C4⋊C4—61no—
266C4⋊C4—61no—
267C4⋊C4—61no—
268C4⋊C4—61no—
269C4⋊C4C22×D311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—31no—
272C22⋊C4—31no—
273C22⋊C4—61no—
274C22⋊C4—61no—
275C22⋊C4—61no—
276C22⋊C4—61no—
277C22⋊C4—61no—
278C42—31no—
279C42—61no—
280C42—61no—
281C42C22×D311yescharacteristic
282C22×C3—22no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3C22×D411yescharacteristic
286C2×D3—21no—
287C2×D3—21no—
288C2×D3—41no—
289C2×D3—41no—
290C2×D3—41no—
291C2×D3#12112yes—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—41no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4C22×D411yescharacteristic
298C3×C4C2×#4111yescharacteristic
299Dic3—22no—
300Dic3—21no—
301Dic3—21no—
302Dic3—41no—
303Dic3—41no—
304Dic3#12112yes—
305C23—21no—
306C23—31no—
307C23—61no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—32no—
313Q8—61no—
314Q8—61no—
315Q8—61no—
316Q8—122no—
317D4—21no—
318D4—64no—
319D4—61no—
320D4—61no—
321D4—122no—
322D4D3×D412yes—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—31no—
327C2×C4—32no—
328C2×C4—32no—
329C2×C4—31no—
330C2×C4—31no—
331C2×C4—64no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—61no—
335C2×C4—81no—
336C2×C4—122no—
337C2×C4—122no—
338C2×C4—241no—
339C2×C4—241no—
340C2×C4D3×D411yescharacteristic
341C2×C4D3×D411yescharacteristic
342C2×C4C23×D311yescharacteristic
343C8—21no—
344C8—21no—
345C8—61no—
346C8—61no—
347C2×C3—42no—
348C2×C3C2×#12111yescharacteristic
349C2×C3#57711yescharacteristic
350C2×C3#57811yescharacteristic
351D3—22no—
352D3—81no—
353C22—22no—
354C22—32no—
355C22—41no—
356C22—41no—
357C22—61no—
358C22—61no—
359C22—121no—
360C22—121no—
361C22—121no—
362C22C2×D3×D411yescharacteristic
363C4—21no—
364C4—21no—
365C4—32no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—61no—
370C4—61no—
371C4—62no—
372C4—121no—
373C4—121no—
374C4C2×D3×D411yescharacteristic
375C4D3×#4111yescharacteristic
376C3#304611yescharacteristic, complemented, Sylow
377C2—42no—
378C2—62no—
379C2—241no—
380C2D3×#12111yescharacteristic
381C2#576211yescharacteristic
382C2#577911yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#461C2
socleC22×C3C22×D4
prime radicalC2×#916C2
hypercenter#461D3
hypocenterC3#3046
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. C2×#915C2semidirect
3. #5724C2semidirect
4. #5546C2semidirect
5. C3×#461C2semidirect
6. #5165C2semidirect
7. #5162C2semidirect
8. #5090C2semidirect
9. #5016C2semidirect
10. #4845C2semidirect
11. #4839C2semidirect
12. #4803C2semidirect
13. D3×#103C2semidirect
14. #4798C2semidirect
15. #4795C2semidirect
73. #461D3semidirect
376. C3#3046semidirect

Maximal subgroups

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

subgroupindex
C2×#9162
C2×#9152
#57242
#55462
C3×#4612
#51652
#51622
#50902
#50162
#48452
#48392
#48032
D3×#1032
#47982
#47952
#30463