Finite Group Databasebeta

← #11898337

Subgroups — #11898337

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#556C211yesmaximal, characteristic, complemented
2#10596055C211yesmaximal, characteristic, complemented
3#10592791C211yesmaximal, characteristic, complemented
4#10592782C211yesmaximal, characteristic, complemented
5#10592758C212yesmaximal
6#10592753C212yesmaximal, complemented
7C4×#3756C212yesmaximal, complemented
8#10592727C212yesmaximal, complemented
9Q8×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10592718C211yesmaximal, characteristic, complemented
11C4×#3753C211yesmaximal, characteristic
12#83670—34nomaximal
13C32×C4⋊Q8C2211yescharacteristic
14C32×#126—22no—
15C32×#124C2212yes—
16C32×C22⋊Q8—21no—
17C32×C4×Q8C2212yes—
18C32×C4×Q8C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C32×#117—21no—
21#64155—21no—
22C2×#3756C2212yes—
23C2×#3756C2212yes—
24C2×#3755C2212yes—
25C2×#3754C2212yes—
26C2×#3753C2211yescharacteristic
27#64107—22no—
28#64101—21no—
29#64084C2212yes—
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31#64078C2211yescharacteristic
32C4×#634C2212yes—
33#63662C2212yes—
34#63659C2211yescharacteristic
35#63637C2212yes—
36#63636C2211yescharacteristic
37#63634C2211yescharacteristic
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C4⋊(C3⋊(C3⋊C8))C2212yes—
40C4×C3⋊(C3⋊C8)C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2212yes—
42C3×#556D314yescomplemented
43#5584—34no—
44#5092—34no—
45#5083—34no—
46#5059—38no—
47#5054—38no—
48C4×#216—38no—
49#5028—38no—
50Q8×C3⋊C8—34no—
51#5019—34no—
52C4×#213—34no—
53C2×C32×Q8D411yescharacteristic
54C2×C32×Q8C2312yes—
55C2×C32×D4C2311yescharacteristic
56C22×C32×C4—21no—
57C2×C4⋊(C3⋊D3)C2311yescharacteristic
58C2×C4×C3⋊D3—21no—
59C2×#634C2312yes—
60C32×C4⋊C4—21no—
61C32×C4⋊C4—22no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4D411yescharacteristic
64C32×C4⋊C4D412yes—
65C32×C4⋊C4C2311yescharacteristic
66C32×C22⋊C4—22no—
67C32×C22⋊C4—21no—
68C32×C22⋊C4—22no—
69C32×C42—22no—
70C32×C42C2312yes—
71C32×C42C2311yescharacteristic
72#3756—24no—
73#3756—42no—
74#3755—42no—
75#3754—42no—
76#3753—22no—
77#3752—21no—
78#3752—22no—
79#3752—22no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—22no—
84C4×C3⋊Dic3—22no—
85C2×C3⋊(C3⋊C8)C2312yes—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88#3393—91noSylow
89C3×C4⋊Q8C2×D314yes—
90C3×#126—28no—
91C3×#124C2×D318yes—
92C3×C22⋊Q8—24no—
93C3×C4×Q8C2×D318yes—
94C3×C4×Q8C2×D314yes—
95C3×C4×D4C2×D314yes—
96C3×#117—24no—
97#946—64no—
98C2×#216—38no—
99C2×#216—38no—
100C2×#215—38no—
101C2×#214—38no—
102C2×#213—34no—
103#898—68no—
104#892—64no—
105#875—38no—
106C4×D12—34no—
107#869—34no—
108C4×Dic6—38no—
109#835—38no—
110#832—34no—
111#810—38no—
112#809—34no—
113#807—34no—
114C4⋊(C3⋊C8)—34no—
115C4⋊(C3⋊C8)—38no—
116C4×C3⋊C8—34no—
117C4×C3⋊C8—38no—
118C23×C32—21no—
119C22×C3⋊D3—21no—
120C32×Q8—22no—
121C32×Q8—22no—
122C32×Q8—22no—
123C32×D4—21no—
124C32×D4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—22no—
127C2×C32×C4—42no—
128C2×C32×C4C2×D412yes—
129C2×C32×C4C2×D412yes—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2411yescharacteristic
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—22no—
135C4⋊(C3⋊D3)—21no—
136C4⋊(C3⋊D3)—21no—
137C4×C3⋊D3—42no—
138#634—22no—
139#634—22no—
140C3⋊(C3⋊C8)—22no—
141C3⋊(C3⋊C8)—21no—
142C3⋊(C3⋊C8)#4112yes—
143#556—91no—
144#556C3⋊D311yescharacteristic, complemented
145#495—92no—
146#494—91no—
147#464—92no—
148#464—92no—
149#461—91no—
150#461—91no—
151C8×Q8—91no—
152C4×Q16—92no—
153C4×D8—91no—
154C2×C3×Q8#6714yes—
155C2×C3×Q8C22×D318yes—
156C2×C3×D4C22×D314yes—
157C22×C3×C4—24no—
158C2×D12—34no—
159C2×C4×D3—64no—
160C2×Dic6—38no—
161C3×C4⋊C4—24no—
162C3×C4⋊C4—28no—
163C3×C4⋊C4—24no—
164C3×C4⋊C4#6714yes—
165C3×C4⋊C4#6718yes—
166C3×C4⋊C4C22×D314yes—
167C3×C22⋊C4—28no—
168C3×C22⋊C4—24no—
169C3×C22⋊C4—28no—
170C3×C42—28no—
171C3×C42C22×D318yes—
172C3×C42C22×D314yes—
173#216—616no—
174#216—128no—
175#215—128no—
176#214—128no—
177#213—68no—
178(C2×D3)⋊C4—64no—
179(C2×D3)⋊C4—68no—
180(C2×D3)⋊C4—68no—
181C4⋊Dic3—34no—
182C4⋊Dic3—64no—
183C4⋊Dic3—64no—
184Dic3⋊C4—68no—
185C4×Dic3—68no—
186C2×C3⋊C8—34no—
187C2×C3⋊C8—34no—
188C2×C3⋊C8—38no—
189C22×C32—41no—
190C22×C32—41no—
191C22×C32—41no—
192C22×C32C22×D411yescharacteristic
193C2×C3⋊D3—41no—
194C2×C3⋊D3—41no—
195C2×C3⋊D3—41no—
196C32×C4—22no—
197C32×C4—22no—
198C32×C4—21no—
199C32×C4—42no—
200C32×C4—41no—
201C32×C4#13512yes—
202C32×C4C2×#4111yescharacteristic
203C32×C4H(5,𝔽2)11yescharacteristic
204C3⋊Dic3—42no—
205C3⋊Dic3—41no—
206C2×Q16—92no—
207C2×Q16—92no—
208C2×SD16—92no—
209C2×SD16—92no—
210C2×D8—91no—
211C4⋊Q8—91no—
212C4⋊Q8C2×C3⋊D311yescharacteristic
213#126—22no—
214#126—182no—
215#124—92no—
216#124C2×C3⋊D312yes—
217C22⋊Q8—21no—
218C22⋊Q8—181no—
219C4×Q8—92no—
220C4×Q8C2×C3⋊D312yes—
221C4×Q8C2×C3⋊D311yescharacteristic
222C4×D4—91no—
223C4×D4C2×C3⋊D311yescharacteristic
224#117—21no—
225#117—181no—
226#107—91no—
227C4⋊C8—91no—
228C4⋊C8—92no—
229#103—92no—
230#103—92no—
231#102—91no—
232#102—91no—
233C4×C8—91no—
234C4×C8—92no—
235C23×C3—24no—
236C22×D3—64no—
237C3×Q8—28no—
238C3×Q8—28no—
239C3×Q8—28no—
240C3×D4—24no—
241C3×D4—24no—
242C2×C3×C4—24no—
243C2×C3×C4—28no—
244C2×C3×C4—48no—
245C2×C3×C4C2×#6718yes—
246C2×C3×C4C2×#6718yes—
247C2×C3×C4C2×#6714yes—
248C2×C3×C4C2×#6714yes—
249C2×C3×C4C23×D314yes—
250C2×Dic3—64no—
251C2×Dic3—68no—
252D12—64no—
253D12—64no—
254C4×D3—128no—
255Dic6—68no—
256Dic6—68no—
257C3⋊C8—38no—
258C3⋊C8—68no—
259C3⋊C8—64no—
260C2×C32—81no—
261C2×C32#55011yescharacteristic
262C2×C32C2×#13511yescharacteristic
263C2×C32#57811yescharacteristic
264C3⋊D3—81no—
265C2×Q8—92no—
266C2×Q8#63811yescharacteristic
267C2×Q8C22×C3⋊D312yes—
268C2×D4—91no—
269C2×D4C22×C3⋊D311yescharacteristic
270C22×C4—21no—
271C22×C4—181no—
272Q16—184no—
273Q16—362no—
274SD16—362no—
275SD16—362no—
276D8—182no—
277C2×C8—91no—
278C2×C8—91no—
279C2×C8—92no—
280C4⋊C4—21no—
281C4⋊C4—22no—
282C4⋊C4—21no—
283C4⋊C4—91no—
284C4⋊C4—181no—
285C4⋊C4—182no—
286C4⋊C4—181no—
287C4⋊C4#63811yescharacteristic
288C4⋊C4#63812yes—
289C4⋊C4C22×C3⋊D311yescharacteristic
290C22⋊C4—22no—
291C22⋊C4—21no—
292C22⋊C4—22no—
293C22⋊C4—182no—
294C22⋊C4—181no—
295C22⋊C4—182no—
296C42—22no—
297C42—182no—
298C42C22×C3⋊D311yescharacteristic
299C42C22×C3⋊D312yes—
300C22×C3—44no—
301C22×C3—44no—
302C22×C3—44no—
303C22×C3C22×#6714yes—
304C2×D3—124no—
305C2×D3—124no—
306C2×D3—124no—
307C3×C4—28no—
308C3×C4—28no—
309C3×C4—24no—
310C3×C4—44no—
311C3×C4—48no—
312C3×C4#95018yes—
313C3×C4D3×#4114yes—
314C3×C4#100914yes—
315Dic3—124no—
316Dic3—128no—
317C32#339311yescharacteristic, complemented, Sylow
318C23—21no—
319C23—181no—
320Q8—22no—
321Q8—22no—
322Q8—22no—
323Q8—182no—
324Q8—182no—
325D4—21no—
326D4—21no—
327D4—181no—
328D4—181no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—42no—
332C2×C4—181no—
333C2×C4—182no—
334C2×C4—362no—
335C2×C4C2×#63812yes—
336C2×C4C2×#63811yescharacteristic
337C2×C4C2×#63812yes—
338C2×C4C2×#63811yescharacteristic
339C2×C4C23×C3⋊D311yescharacteristic
340C8—92no—
341C8—182no—
342C8—181no—
343C2×C3—84no—
344C2×C3C2×#95014yes—
345C2×C3#583414yes—
346C2×C3#583814yes—
347D3—244no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—361no—
352C22—361no—
353C22—361no—
354C22C22×#63811yescharacteristic
355C4—22no—
356C4—22no—
357C4—21no—
358C4—41no—
359C4—42no—
360C4—361no—
361C4—362no—
362C4#6415912yes—
363C4#41×C3⋊D311yescharacteristic
364C4#6436611yescharacteristic
365C3#8367014yescomplemented
366C2—81no—
367C2—721no—
368C2C2×#6415911yescharacteristic
369C2#1059630511yescharacteristic
370C2#1059630911yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#556C2
socleC22×C32C22×D4
prime radicalC2×#3753C22
hypercenter#556C3⋊D3
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C32×#556C2semidirect
2. #10596055C2semidirect
3. #10592791C2semidirect
4. #10592782C2semidirect
6. #10592753C2semidirect
7. C4×#3756C2semidirect
8. #10592727C2semidirect
9. Q8×C3⋊(C3⋊C8)C2semidirect
10. #10592718C2semidirect
42. C3×#556D3semidirect
144. #556C3⋊D3semidirect
317. C32#3393semidirect
365. C3#83670semidirect

Maximal subgroups

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

subgroupindex
C32×#5562
#105960552
#105927912
#105927822
#105927582
#105927532
C4×#37562
#105927272
Q8×C3⋊(C3⋊C8)2
#105927182
C4×#37532
#836703