Finite Group Databasebeta

← #80598

Subgroups — #80598

Order 384.

484 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#918C211yesmaximal, characteristic, complemented
2C2×#915C211yesmaximal, characteristic, complemented
3#5668C211yesmaximal, characteristic
4C4×D3×Q8C211yesmaximal, characteristic, complemented
5C3×#464C211yesmaximal, characteristic, complemented
6#5182C211yesmaximal, characteristic, complemented
7#5163C211yesmaximal, characteristic, complemented
8#5054C211yesmaximal, characteristic, complemented
9#5028C211yesmaximal, characteristic, complemented
10#4845C211yesmaximal, characteristic, complemented
11#4837C211yesmaximal, characteristic, complemented
12#4803C211yesmaximal, characteristic, complemented
13#4795C211yesmaximal, characteristic, complemented
14#4771C211yesmaximal, characteristic, complemented
15#4762C211yesmaximal, characteristic, complemented
16#3037—31nomaximal, Sylow
17C2×#239C2211yescharacteristic
18C2×D3×Q8C2211yescharacteristic
19C2×#237C2211yescharacteristic
20C2×C3×Q16C2211yescharacteristic
21C2×C3×SD16C2211yescharacteristic
22C3×#124C2211yescharacteristic
23C3×C4×Q8C2211yescharacteristic
24Q8×Dic3C2211yescharacteristic
25#944C2211yescharacteristic
26C2×#216C2211yescharacteristic
27C2×#216C2211yescharacteristic
28C2×#215C2211yescharacteristic
29#940C2211yescharacteristic
30C2×#214C2211yescharacteristic
31#918—24no—
32#915—24no—
33C2×Dic12C2211yescharacteristic
34C2×#204C2211yescharacteristic
35C2×ΓL(1,𝔽25)C2211yescharacteristic
36C2×ΓL(1,𝔽25)C2211yescharacteristic
37D3×C4⋊C4—21no—
38D3×C4⋊C4C2211yescharacteristic
39#887—21no—
40#887C2211yescharacteristic
41#884—21no—
42#884—21no—
43#67⋊C4—21no—
44#67⋊C4—21no—
45#875C2211yescharacteristic
46C42×D3—21no—
47C42×D3C2211yescharacteristic
48C4×Dic6—21no—
49C4×Dic6C2211yescharacteristic
50C3×C4⋊C8C2211yescharacteristic
51C3×#103C2211yescharacteristic
52C3×#102C2211yescharacteristic
53#835C2211yescharacteristic
54#832C2211yescharacteristic
55#821C2211yescharacteristic
56#816C2211yescharacteristic
57Dic3⋊C8C2211yescharacteristic
58Dic3⋊C8C2211yescharacteristic
59#810C2211yescharacteristic
60#809C2211yescharacteristic
61C4⋊(C3⋊C8)C2211yescharacteristic
62C2×#137—31no—
63C2×#137—31no—
64#532—31no—
65C2×C4×Q8—31no—
66#464—31no—
67#464—31no—
68#464—31no—
69#464D311yescharacteristic, complemented
70#462—31no—
71#462—31no—
72#460—31no—
73#460—31no—
74#423—31no—
75#417—31no—
76#417—31no—
77C2×C3×Q8C2311yescharacteristic
78C2×C3×Q8C2311yescharacteristic
79C2×C3×D4C2311yescharacteristic
80C2×#67—21no—
81C2×#67—21no—
82C2×#67—21no—
83C22×Dic3—21no—
84#239—22no—
85#239—22no—
86D3×Q8—22no—
87D3×Q8D414yescomplemented
88#237—22no—
89#237—22no—
90C2×D12—21no—
91C2×D12C2311yescharacteristic
92C2×C4×D3—21no—
93C2×C4×D3—21no—
94C2×C4×D3—21no—
95C2×C4×D3D411yescharacteristic
96C2×C4×D3D411yescharacteristic
97C2×C4×D3C2311yescharacteristic
98C2×Dic6—21no—
99C2×Dic6C2311yescharacteristic
100C2×Dic6C2311yescharacteristic
101C3×Q16—22no—
102C3×SD16—22no—
103C2×C3×C8C2311yescharacteristic
104C2×C3×C8C2311yescharacteristic
105C3×C4⋊C4—21no—
106C3×C4⋊C4C2311yescharacteristic
107C3×C22⋊C4—21no—
108C3×C22⋊C4—21no—
109C3×C42—21no—
110C3×C42C2311yescharacteristic
111#216—22no—
112#216—22no—
113#215—22no—
114#214—22no—
115(C2×D3)⋊C4—21no—
116(C2×D3)⋊C4—21no—
117C4⋊Dic3—21no—
118C4⋊Dic3C2311yescharacteristic
119Dic3⋊C4—21no—
120Dic3⋊C4—21no—
121Dic3⋊C4—21no—
122Dic3⋊C4—21no—
123Dic3⋊C4—21no—
124C4×Dic3—21no—
125C4×Dic3—21no—
126C4×Dic3—21no—
127C4×Dic3D411yescharacteristic
128C4×Dic3D411yescharacteristic
129C4×Dic3C2311yescharacteristic
130C2×C3⋊C8C2311yescharacteristic
131C2×C3⋊C8C2311yescharacteristic
132Dic12—22no—
133#204—22no—
134ΓL(1,𝔽25)—22no—
135ΓL(1,𝔽25)—22no—
136C2×#41—31no—
137C2×#41—31no—
138C22×Q8—31no—
139#137—64no—
140#137—64no—
141C2×Q16—31no—
142C2×Q16—31no—
143C2×Q16—31no—
144C2×Q16C2×D311yescharacteristic
145C2×SD16—31no—
146C2×SD16—31no—
147C2×SD16—31no—
148C2×SD16C2×D311yescharacteristic
149C2×M16—31no—
150C2×M16—31no—
151C4⋊Q8—31no—
152#127—31no—
153#124—31no—
154#124C2×D311yescharacteristic
155#121—61no—
156#121—61no—
157C4×Q8—31no—
158C4×Q8—31no—
159C4×Q8—31no—
160C4×Q8—61no—
161C4×Q8—61no—
162C4×Q8C2×D311yescharacteristic
163C4×D4—61no—
164C4×D4—61no—
165C2×C4⋊C4—31no—
166C2×C4⋊C4—61no—
167C2×C42—31no—
168C2×C42—61no—
169C4⋊C8—31no—
170C4⋊C8—31no—
171C4⋊C8—31no—
172C4⋊C8C2×D311yescharacteristic
173#103—31no—
174#103—31no—
175#103—31no—
176#103C2×D311yescharacteristic
177#102—31no—
178#102—31no—
179#102—31no—
180#102C2×D311yescharacteristic
181C23×C3—21no—
182C22×D3—21no—
183C22×D3C2×D411yescharacteristic
184C3×Q8—21no—
185C3×Q8—21no—
186C3×Q8—21no—
187C3×Q8C2×D412yes—
188C3×D4—21no—
189C3×D4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4C2×D411yescharacteristic
194C2×C3×C4C2×D411yescharacteristic
195C2×C3×C4C2411yescharacteristic
196#67—42no—
197#67—42no—
198#67—42no—
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—42no—
203C2×Dic3C2×D411yescharacteristic
204C2×Dic3C2×D411yescharacteristic
205C2×Dic3C2×D411yescharacteristic
206D12—21no—
207D12—21no—
208D12—42no—
209C4×D3—24no—
210C4×D3—22no—
211C4×D3—41no—
212C4×D3—42no—
213C4×D3—42no—
214C4×D3C2×D412yes—
215C4×D3#4112yes—
216Dic6—21no—
217Dic6—24no—
218Dic6—21no—
219Dic6—21no—
220Dic6C2×D412yes—
221C3×C8—21no—
222C3×C8—21no—
223C3⋊C8—21no—
224C3⋊C8—21no—
225#41—62no—
226#41—62no—
227#41—62no—
228#41—62no—
229C2×Q8—34no—
230C2×Q8—31no—
231C2×Q8—31no—
232C2×Q8—61no—
233C2×Q8—62no—
234C2×Q8C22×D311yescharacteristic
235C2×Q8C22×D311yescharacteristic
236C2×D4—31no—
237C2×D4—61no—
238C2×D4—61no—
239C2×D4—61no—
240C2×D4—61no—
241C2×D4C22×D311yescharacteristic
242C22×C4—31no—
243C22×C4—31no—
244C22×C4—31no—
245C22×C4—61no—
246C22×C4—61no—
247C22×C4—61no—
248C22×C4—61no—
249Q16—22no—
250Q16—62no—
251Q16—62no—
252Q16—62no—
253SD16—22no—
254SD16—62no—
255SD16—62no—
256SD16—62no—
257M16—62no—
258M16—62no—
259C2×C8—31no—
260C2×C8—31no—
261C2×C8C22×D311yescharacteristic
262C2×C8C22×D311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—31no—
265C4⋊C4—61no—
266C4⋊C4—61no—
267C4⋊C4—61no—
268C4⋊C4—61no—
269C4⋊C4—61no—
270C4⋊C4—61no—
271C4⋊C4C22×D311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—61no—
275C22⋊C4—61no—
276C42—21no—
277C42—31no—
278C42—31no—
279C42—31no—
280C42—61no—
281C42—61no—
282C42—61no—
283C42C22×D311yescharacteristic
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3C22×D411yescharacteristic
288C2×D3—21no—
289C2×D3—21no—
290C2×D3—41no—
291C2×D3—41no—
292C2×D3—41no—
293C2×D3#12112yes—
294C3×C4—22no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—41no—
298C3×C4—41no—
299C3×C4C22×D411yescharacteristic
300C3×C4C2×#4111yescharacteristic
301Dic3—22no—
302Dic3—21no—
303Dic3—41no—
304Dic3—41no—
305Dic3#12112yes—
306Dic3#13712yescomplemented
307C23—21no—
308C23—31no—
309C23—61no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—32no—
314Q8—64no—
315Q8—61no—
316Q8—61no—
317Q8—61no—
318Q8D3×D412yes—
319D4—21no—
320D4—21no—
321D4—61no—
322D4—61no—
323D4—122no—
324D4—122no—
325D4—122no—
326D4—122no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—31no—
331C2×C4—31no—
332C2×C4—32no—
333C2×C4—32no—
334C2×C4—31no—
335C2×C4—62no—
336C2×C4—64no—
337C2×C4—61no—
338C2×C4—61no—
339C2×C4—61no—
340C2×C4—121no—
341C2×C4—122no—
342C2×C4—122no—
343C2×C4—122no—
344C2×C4D3×D411yescharacteristic
345C2×C4D3×D411yescharacteristic
346C2×C4C23×D311yescharacteristic
347C8—21no—
348C8—21no—
349C8—61no—
350C8—61no—
351C2×C3—81no—
352C2×C3C2×#12111yescharacteristic
353C2×C3C2×#13711yescharacteristic
354C2×C3#57511yescharacteristic
355D3—22no—
356D3—81no—
357C22—32no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—61no—
362C22—61no—
363C22—121no—
364C22—121no—
365C22—121no—
366C22C2×D3×D411yescharacteristic
367C4—21no—
368C4—21no—
369C4—22no—
370C4—32no—
371C4—32no—
372C4—41no—
373C4—41no—
374C4—61no—
375C4—62no—
376C4—121no—
377C4—121no—
378C4C2×D3×D411yescharacteristic
379C4D3×#4111yescharacteristic
380C3#303711yescharacteristic, complemented, Sylow
381C2—62no—
382C2—81no—
383C2—241no—
384C2D3×#12111yescharacteristic
385C2#576811yescharacteristic
386C2D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#464C2
socleC22×C3C22×D4
prime radical#5668C2
hypercenter#464D3
hypocenterC3#3037
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#918C2semidirect
2. C2×#915C2semidirect
4. C4×D3×Q8C2semidirect
5. C3×#464C2semidirect
6. #5182C2semidirect
7. #5163C2semidirect
8. #5054C2semidirect
9. #5028C2semidirect
10. #4845C2semidirect
11. #4837C2semidirect
12. #4803C2semidirect
13. #4795C2semidirect
14. #4771C2semidirect
15. #4762C2semidirect
69. #464D3semidirect
87. D3×Q8D4semidirect
306. Dic3#137semidirect
380. C3#3037semidirect

Maximal subgroups

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

subgroupindex
C2×#9182
C2×#9152
#56682
C4×D3×Q82
C3×#4642
#51822
#51632
#50542
#50282
#48452
#48372
#48032
#47952
#47712
#47622
#30373