Finite Group Databasebeta

← #79498

Subgroups — #79498

Order 384.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#909C211yesmaximal, characteristic, complemented
2C2×#904C211yesmaximal, characteristic, complemented
3#5552C211yesmaximal, characteristic, complemented
4#5551C211yesmaximal, characteristic, complemented
5C3×#435C211yesmaximal, characteristic, complemented
6#5134C211yesmaximal, characteristic, complemented
7#5116C211yesmaximal, characteristic, complemented
8#4849C211yesmaximal, characteristic, complemented
9#4844C211yesmaximal, characteristic, complemented
10#4739C211yesmaximal, characteristic, complemented
11#4734C211yesmaximal, characteristic, complemented
12#4733C211yesmaximal, characteristic, complemented
13#4733C211yesmaximal, characteristic, complemented
14#4715C211yesmaximal, characteristic, complemented
15#4710C211yesmaximal, characteristic, complemented
16#3269—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C2×#235C2211yescharacteristic
19C2×#235C2211yescharacteristic
20C22×Dic6C2211yescharacteristic
21C2×C3×M16C2211yescharacteristic
22C22×C3×C8C2211yescharacteristic
23C3×C4×D4C2211yescharacteristic
24#939—21no—
25#938—21no—
26#930C2211yescharacteristic
27#924C2211yescharacteristic
28#924C2211yescharacteristic
29#924C2211yescharacteristic
30#909—24no—
31C2×Dic12C2211yescharacteristic
32C2×Dic12C2211yescharacteristic
33C2×Dic12C2211yescharacteristic
34C2×Dic12C2211yescharacteristic
35#904—24no—
36C2×D24C2211yescharacteristic
37C2×#204C2211yescharacteristic
38C2×#204C2211yescharacteristic
39C2×#204C2211yescharacteristic
40C2×#204C2211yescharacteristic
41#896—21no—
42D3×C4⋊C4—21no—
43#885—21no—
44#883—21no—
45#883—21no—
46#67⋊C4—21no—
47#875C2211yescharacteristic
48C4×D12C2211yescharacteristic
49#869C2211yescharacteristic
50C4×Dic6C2211yescharacteristic
51C3×C4⋊C8C2211yescharacteristic
52C3×C22⋊C8C2211yescharacteristic
53C3×C22⋊C8C2211yescharacteristic
54C3×#97C2211yescharacteristic
55#821C2211yescharacteristic
56#821C2211yescharacteristic
57#818C2211yescharacteristic
58#816C2211yescharacteristic
59#816C2211yescharacteristic
60#816C2211yescharacteristic
61#816C2211yescharacteristic
62C2×#137—31no—
63C2×#135—31no—
64#548—31no—
65#547—31no—
66#497—31no—
67#468—31no—
68#467—31no—
69#463—31no—
70#462—31no—
71#452—31no—
72#452—31no—
73#451—31no—
74#449—31no—
75#440—31no—
76#435D311yescharacteristic, complemented
77C2×C3×D4D411yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C2×#67—21no—
81C2×#67—21no—
82C2×#67—21no—
83C2×#67—21no—
84C22×Dic3—21no—
85#235—22no—
86#235—22no—
87#235—22no—
88#235—41no—
89#235—41no—
90#235—41no—
91C2×D12C2311yescharacteristic
92C2×D12C2311yescharacteristic
93C2×C4×D3—21no—
94C2×C4×D3—21no—
95C2×C4×D3—21no—
96C2×C4×D3—21no—
97C2×Dic6—22no—
98C2×Dic6—21no—
99C2×Dic6—41no—
100C2×Dic6C2311yescharacteristic
101C2×Dic6C2311yescharacteristic
102C2×Dic6C2311yescharacteristic
103C2×Dic6C2311yescharacteristic
104C3×M16—22no—
105C2×C3×C8—22no—
106C2×C3×C8C2311yescharacteristic
107C2×C3×C8C2311yescharacteristic
108C2×C3×C8C2311yescharacteristic
109C2×C3×C8C2311yescharacteristic
110C3×C4⋊C4D411yescharacteristic
111C3×C22⋊C4D411yescharacteristic
112C3×C22⋊C4D411yescharacteristic
113C3×C42C2311yescharacteristic
114#217—21no—
115#217—21no—
116#217—21no—
117(C2×D3)⋊C4—21no—
118(C2×D3)⋊C4—21no—
119(C2×D3)⋊C4—21no—
120(C2×D3)⋊C4—21no—
121C4⋊Dic3—21no—
122C4⋊Dic3—21no—
123C4⋊Dic3C2311yescharacteristic
124C4⋊Dic3C2311yescharacteristic
125Dic3⋊C4—21no—
126Dic3⋊C4—21no—
127Dic3⋊C4—21no—
128Dic3⋊C4—21no—
129C4×Dic3—21no—
130Dic12—22no—
131Dic12—22no—
132Dic12—22no—
133Dic12—41no—
134D24—22no—
135#204—22no—
136#204—22no—
137#204—41no—
138#204D414yescomplemented
139C2×#41—31no—
140C2×#41—31no—
141C2×#41—31no—
142C22×Q8—31no—
143#137—64no—
144#135—64no—
145C2×Q16—31no—
146C2×Q16—31no—
147C2×Q16—31no—
148C2×Q16—31no—
149C2×SD16—31no—
150C2×SD16—31no—
151C2×SD16—31no—
152C2×SD16—31no—
153C2×D8—31no—
154C2×M16C2×D311yescharacteristic
155C22×C8C2×D311yescharacteristic
156C4⋊Q8—31no—
157#124—31no—
158#124—61no—
159#123—61no—
160#123—61no—
161C22⋊Q8—31no—
162C22⋊Q8—31no—
163C22⋊Q8—31no—
164C22⋊Q8—61no—
165#121—31no—
166#121—61no—
167#121—61no—
168C4×Q8—31no—
169C4×D4—31no—
170C4×D4—61no—
171C4×D4C2×D311yescharacteristic
172C2×C4⋊C4—61no—
173#107—31no—
174C4⋊C8C2×D311yescharacteristic
175#103—31no—
176#103—31no—
177#103—31no—
178#103—31no—
179#102—31no—
180#102—31no—
181C22⋊C8C2×D311yescharacteristic
182C22⋊C8C2×D311yescharacteristic
183#97C2×D311yescharacteristic
184C23×C3C2×D411yescharacteristic
185C23×C3C2×D411yescharacteristic
186C22×D3—21no—
187C22×D3—21no—
188C3×D4—41no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4C2×D411yescharacteristic
194C2×C3×C4C2×D411yescharacteristic
195C2×C3×C4C2×D411yescharacteristic
196C2×C3×C4C2×D411yescharacteristic
197C2×C3×C4C2411yescharacteristic
198#67—42no—
199#67—42no—
200#67—42no—
201#67—42no—
202C2×Dic3—21no—
203C2×Dic3—21no—
204C2×Dic3—21no—
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3—21no—
208C2×Dic3—42no—
209D12—21no—
210D12—21no—
211D12—21no—
212D12C2×D412yes—
213C4×D3—42no—
214C4×D3—42no—
215C4×D3—42no—
216C4×D3—42no—
217Dic6—21no—
218Dic6—21no—
219Dic6—21no—
220Dic6—21no—
221Dic6—21no—
222Dic6—21no—
223Dic6—21no—
224Dic6—42no—
225Dic6C2×D412yes—
226C3×C8—21no—
227C3×C8—21no—
228C3×C8—21no—
229C3×C8C2×D412yes—
230#41—62no—
231#41—62no—
232#41—62no—
233#41—121no—
234#41—121no—
235#41—121no—
236C2×Q8—31no—
237C2×Q8—31no—
238C2×Q8—31no—
239C2×Q8—31no—
240C2×Q8—62no—
241C2×Q8—61no—
242C2×Q8—121no—
243C2×D4—31no—
244C2×D4—31no—
245C2×D4—61no—
246C2×D4—61no—
247C2×D4—61no—
248C2×D4—61no—
249C2×D4D1211yescharacteristic
250C22×C4—61no—
251C22×C4—61no—
252C22×C4—61no—
253C22×C4—61no—
254C22×C4—61no—
255C22×C4C22×D311yescharacteristic
256C22×C4C22×D311yescharacteristic
257Q16—62no—
258Q16—62no—
259Q16—62no—
260Q16—121no—
261SD16—34no—
262SD16—62no—
263SD16—62no—
264SD16—121no—
265D8—62no—
266M16—22no—
267C2×C8—22no—
268C2×C8C22×D311yescharacteristic
269C2×C8C22×D311yescharacteristic
270C2×C8C22×D311yescharacteristic
271C2×C8C22×D311yescharacteristic
272C4⋊C4—31no—
273C4⋊C4—31no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4D1211yescharacteristic
281C22⋊C4—61no—
282C22⋊C4—61no—
283C22⋊C4—61no—
284C22⋊C4—61no—
285C22⋊C4—61no—
286C22⋊C4—61no—
287C22⋊C4—61no—
288C22⋊C4D1211yescharacteristic
289C22⋊C4D1211yescharacteristic
290C42—61no—
291C42C22×D311yescharacteristic
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3C22×D411yescharacteristic
299C2×D3—22no—
300C2×D3—41no—
301C2×D3—41no—
302C2×D3—41no—
303C2×D3—41no—
304C2×D3—41no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4C22×D411yescharacteristic
310C3×C4H(5,𝔽2)11yescharacteristic
311Dic3—22no—
312Dic3—41no—
313Dic3—41no—
314Dic3—41no—
315Dic3—41no—
316Dic3—41no—
317C23—61no—
318C23—61no—
319C23C2×D1211yescharacteristic
320C23C2×D1211yescharacteristic
321Q8—32no—
322Q8—61no—
323Q8—61no—
324Q8—61no—
325Q8—61no—
326Q8—61no—
327Q8—61no—
328Q8—61no—
329Q8—122no—
330D4—32no—
331D4—41no—
332D4—61no—
333D4—61no—
334D4—61no—
335D4—122no—
336D4—122no—
337D4—122no—
338D4—122no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—61no—
344C2×C4—61no—
345C2×C4—61no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—122no—
350C2×C4—122no—
351C2×C4—122no—
352C2×C4—122no—
353C2×C4—122no—
354C2×C4C2×D1211yescharacteristic
355C2×C4C2×D1211yescharacteristic
356C2×C4C2×D1211yescharacteristic
357C2×C4C2×D1211yescharacteristic
358C2×C4C23×D311yescharacteristic
359C8—21no—
360C8—21no—
361C8—21no—
362C8D3×D412yes—
363C2×C3—41no—
364C2×C3—41no—
365C2×C3D4211yescharacteristic
366C2×C3#57511yescharacteristic
367C2×C3#57811yescharacteristic
368D3—42no—
369D3—81no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—62no—
377C22—121no—
378C22—121no—
379C22—121no—
380C22—121no—
381C22—121no—
382C22C22×D1211yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—62no—
388C4—121no—
389C4—121no—
390C4—121no—
391C4—121no—
392C4—121no—
393C4C2×D3×D411yescharacteristic
394C4#100911yescharacteristic
395C3#326911yescharacteristic, complemented, Sylow
396C2—41no—
397C2—41no—
398C2—122no—
399C2—241no—
400C2D4×D1211yescharacteristic
401C2#574811yescharacteristic
402C2#575311yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#435C2
socleC22×C3C22×D4
hypercenter#435D3
hypocenterC3#3269
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#909C2semidirect
2. C2×#904C2semidirect
3. #5552C2semidirect
4. #5551C2semidirect
5. C3×#435C2semidirect
6. #5134C2semidirect
7. #5116C2semidirect
8. #4849C2semidirect
9. #4844C2semidirect
10. #4739C2semidirect
11. #4734C2semidirect
12. #4733C2semidirect
13. #4733C2semidirect
14. #4715C2semidirect
15. #4710C2semidirect
76. #435D3semidirect
138. #204D4semidirect
395. C3#3269semidirect

Maximal subgroups

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

subgroupindex
C2×#9092
C2×#9042
#55522
#55512
C3×#4352
#51342
#51162
#48492
#48442
#47392
#47342
#47332
#47152
#47102
#32693