Finite Group Databasebeta

← #11888017

Subgroups — #11888017

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#547C211yesmaximal, characteristic
2#10596013C211yesmaximal, characteristic, complemented
3#10592938C212yesmaximal, complemented
4#10592932C212yesmaximal, complemented
5#10592789C211yesmaximal, characteristic, complemented
6#10592778C211yesmaximal, characteristic, complemented
7#10592750C212yesmaximal, complemented
8#10592744C212yesmaximal, complemented
9C4×#3754C211yesmaximal, characteristic, complemented
10D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
11#10592706C211yesmaximal, characteristic, complemented
12#83510—34nomaximal
13C2×C32×#41C2212yes—
14C32×C4⋊Q8C2211yescharacteristic
15C32×#123—22no—
16C32×C22⋊Q8C2212yes—
17C32×#121—21no—
18C32×C4×D4C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×C32×C4⋊C4—21no—
21C2×#3756C2212yes—
22#64145—21no—
23C2×#3754C2211yescharacteristic
24#64135C2212yes—
25#64133C2212yes—
26C22×C3⋊(C3⋊C8)C2212yes—
27#64096—21no—
28#64088—22no—
29#64078C2211yescharacteristic
30C4×#634C2211yescharacteristic
31#63662C2212yes—
32#63662C2212yes—
33#63662C2212yes—
34#63659C2211yescharacteristic
35#63659C2212yes—
36#63657C2212yes—
37#63637C2211yescharacteristic
38#63635C2211yescharacteristic
39#63634C2212yes—
40C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42C3×#547D314yes—
43#5542—34no—
44#5239—38no—
45#5233—38no—
46#5090—34no—
47#5079—34no—
48#5051—38no—
49#5045—38no—
50C4×#214—34no—
51D4×C3⋊C8—34no—
52#5007—34no—
53C32×#41—24no—
54C32×#41—42no—
55C2×C32×Q8C2312yes—
56C2×C32×D4—22no—
57C2×C32×D4D411yescharacteristic
58C2×C32×D4C2311yescharacteristic
59C22×C32×C4—22no—
60C22×C32×C4—21no—
61C22×C32×C4C2312yes—
62C2×#634—21no—
63C2×#634C2311yescharacteristic
64C32×C4⋊C4—21no—
65C32×C4⋊C4—22no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4D411yescharacteristic
68C32×C4⋊C4C2311yescharacteristic
69C32×C22⋊C4—22no—
70C32×C22⋊C4—21no—
71C32×C22⋊C4D412yes—
72C32×C42C2311yescharacteristic
73#3757—22no—
74#3757—22no—
75#3756—42no—
76#3754—22no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2312yes—
80#3750—21no—
81#3750—22no—
82C4×C3⋊Dic3—21no—
83C4×C3⋊Dic3—22no—
84C2×C3⋊(C3⋊C8)—42no—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2312yes—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88#3302—91noSylow
89C2×C3×#41C2×D318yes—
90C3×C4⋊Q8C2×D314yes—
91C3×#123—28no—
92C3×C22⋊Q8C2×D318yes—
93C3×#121—24no—
94C3×C4×D4C2×D314yes—
95C3×C4×D4C2×D314yes—
96C2×C3×C4⋊C4—24no—
97C2×#216—38no—
98#936—64no—
99C2×#214—34no—
100#926—38no—
101#924—38no—
102C22×C3⋊C8—38no—
103#887—64no—
104#879—68no—
105#869—34no—
106C4×Dic6—34no—
107#835—38no—
108#835—38no—
109#835—38no—
110#832—34no—
111#832—38no—
112#830—38no—
113#810—34no—
114#808—34no—
115#807—38no—
116C4⋊(C3⋊C8)—34no—
117C4×C3⋊C8—34no—
118C23×C32—21no—
119C23×C32C2×D412yes—
120C32×Q8—22no—
121C32×Q8—22no—
122C32×D4—22no—
123C32×D4—21no—
124C32×D4—44no—
125C32×D4#4112yes—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4—21no—
129C2×C32×C4—22no—
130C2×C32×C4—44no—
131C2×C32×C4—42no—
132C2×C32×C4C2×D412yes—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—22no—
139#634—21no—
140#634—21no—
141#634—42no—
142C3⋊(C3⋊C8)—21no—
143C3⋊(C3⋊C8)—21no—
144C3⋊(C3⋊C8)—22no—
145#556—91no—
146#547C3⋊D311yescharacteristic
147#487—91no—
148#485—92no—
149#474—91no—
150#467—92no—
151#462—91no—
152#452—92no—
153C4×SD16—91no—
154C8×D4—91no—
155#416—92no—
156C3×#41—216no—
157C3×#41—48no—
158C2×C3×Q8C22×D318yes—
159C2×C3×D4—28no—
160C2×C3×D4#6714yes—
161C2×C3×D4C22×D314yes—
162C22×C3×C4—24no—
163C22×C3×C4—28no—
164C22×C3×C4C22×D318yes—
165C2×Dic6—34no—
166C2×Dic6—64no—
167C3×C4⋊C4—24no—
168C3×C4⋊C4—28no—
169C3×C4⋊C4—24no—
170C3×C4⋊C4#6714yes—
171C3×C4⋊C4C22×D314yes—
172C3×C22⋊C4—28no—
173C3×C22⋊C4—24no—
174C3×C22⋊C4#6718yes—
175C3×C42C22×D314yes—
176#217—68no—
177#217—68no—
178#216—128no—
179#214—68no—
180C4⋊Dic3—38no—
181C4⋊Dic3—34no—
182C4⋊Dic3—64no—
183Dic3⋊C4—64no—
184Dic3⋊C4—68no—
185C4×Dic3—64no—
186C4×Dic3—68no—
187C2×C3⋊C8—34no—
188C2×C3⋊C8—34no—
189C2×C3⋊C8—38no—
190C2×C3⋊C8—128no—
191C22×C32—22no—
192C22×C32—22no—
193C22×C32—22no—
194C22×C32—22no—
195C22×C32—41no—
196C22×C32—41no—
197C22×C32C22×D411yescharacteristic
198C32×C4—22no—
199C32×C4—21no—
200C32×C4—42no—
201C32×C4—41no—
202C32×C4#13512yes—
203C32×C4C2×#4111yescharacteristic
204C32×C4H(5,𝔽2)11yescharacteristic
205C3⋊Dic3—41no—
206C3⋊Dic3—42no—
207C3⋊Dic3—41no—
208C2×#41C2×C3⋊D312yes—
209C2×Q16—92no—
210C2×SD16—91no—
211C22×C8—92no—
212C4⋊Q8—91no—
213C4⋊Q8C2×C3⋊D311yescharacteristic
214#126—182no—
215#124—181no—
216#123—22no—
217C22⋊Q8—92no—
218C22⋊Q8C2×C3⋊D312yes—
219#121—21no—
220C4×Q8—91no—
221C4×Q8—181no—
222C4×D4C2×C3⋊D311yescharacteristic
223C4×D4C2×C3⋊D311yescharacteristic
224#117—92no—
225C2×C4⋊C4—21no—
226#107—92no—
227#106—91no—
228C4⋊C8—91no—
229#103—92no—
230#103—92no—
231#103—92no—
232#103—91no—
233#102—91no—
234#102—92no—
235C22⋊C8—92no—
236C4×C8—91no—
237C23×C3—24no—
238C23×C3C2×#6718yes—
239C3×Q8—28no—
240C3×Q8—28no—
241C3×D4—28no—
242C3×D4—24no—
243C3×D4—416no—
244C3×D4#23718yes—
245C2×C3×C4—28no—
246C2×C3×C4—28no—
247C2×C3×C4—24no—
248C2×C3×C4—28no—
249C2×C3×C4—416no—
250C2×C3×C4—48no—
251C2×C3×C4C2×#6718yes—
252C2×C3×C4C2×#6714yes—
253C2×C3×C4C2×#6714yes—
254C2×C3×C4C23×D314yes—
255C2×Dic3—64no—
256C2×Dic3—64no—
257C2×Dic3—68no—
258Dic6—64no—
259Dic6—64no—
260Dic6—128no—
261C3⋊C8—64no—
262C3⋊C8—64no—
263C3⋊C8—68no—
264C2×C32—42no—
265C2×C32—42no—
266C2×C32#54611yescharacteristic
267C2×C32C2×#13511yescharacteristic
268C2×C32#57811yescharacteristic
269#41—24no—
270#41—42no—
271C2×Q8—91no—
272C2×Q8—181no—
273C2×Q8C22×C3⋊D312yes—
274C2×D4—22no—
275C2×D4#63811yescharacteristic
276C2×D4C22×C3⋊D311yescharacteristic
277C22×C4—21no—
278C22×C4—22no—
279C22×C4C22×C3⋊D312yes—
280Q16—362no—
281SD16—182no—
282C2×C8—91no—
283C2×C8—91no—
284C2×C8—92no—
285C2×C8—362no—
286C4⋊C4—21no—
287C4⋊C4—22no—
288C4⋊C4—21no—
289C4⋊C4—91no—
290C4⋊C4—92no—
291C4⋊C4—181no—
292C4⋊C4—182no—
293C4⋊C4—181no—
294C4⋊C4#63811yescharacteristic
295C4⋊C4C22×C3⋊D311yescharacteristic
296C22⋊C4—22no—
297C22⋊C4—21no—
298C22⋊C4—182no—
299C22⋊C4—182no—
300C22⋊C4#63812yes—
301C42—182no—
302C42—181no—
303C42C22×C3⋊D311yescharacteristic
304C22×C3—28no—
305C22×C3—28no—
306C22×C3—28no—
307C22×C3—28no—
308C22×C3—44no—
309C22×C3—44no—
310C22×C3C22×#6714yes—
311C3×C4—28no—
312C3×C4—24no—
313C3×C4—48no—
314C3×C4—44no—
315C3×C4#95018yes—
316C3×C4C2×#23714yes—
317C3×C4#100414yes—
318Dic3—124no—
319Dic3—128no—
320Dic3—124no—
321C32#330211yescharacteristic, complemented, Sylow
322C23—21no—
323C23C2×#63812yes—
324Q8—22no—
325Q8—22no—
326Q8—181no—
327Q8—181no—
328Q8—362no—
329D4—21no—
330D4—22no—
331D4—44no—
332D4#383012yes—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—181no—
340C2×C4—182no—
341C2×C4—181no—
342C2×C4C2×#63812yes—
343C2×C4C2×#63811yescharacteristic
344C2×C4C2×#63811yescharacteristic
345C2×C4C23×C3⋊D311yescharacteristic
346C8—181no—
347C8—181no—
348C8—182no—
349C2×C3—48no—
350C2×C3—48no—
351C2×C3#580614yes—
352C2×C3C2×#95014yes—
353C2×C3#583814yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22C22×#63811yescharacteristic
361C4—22no—
362C4—21no—
363C4—42no—
364C4—41no—
365C4—361no—
366C4—362no—
367C4—361no—
368C4#6415912yes—
369C4C2×#383011yescharacteristic
370C4#6436111yescharacteristic
371C3#8351014yescomplemented
372C2—42no—
373C2—42no—
374C2#1059627711yescharacteristic
375C2C2×#6415911yescharacteristic
376C2#1059630911yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
Fitting, prime radicalC32×#547C2
socleC22×C32C22×D4
hypercenter#547C3⋊D3
hypocenterC32#3302
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
2. #10596013C2semidirect
3. #10592938C2semidirect
4. #10592932C2semidirect
5. #10592789C2semidirect
6. #10592778C2semidirect
7. #10592750C2semidirect
8. #10592744C2semidirect
9. C4×#3754C2semidirect
10. D4×C3⋊(C3⋊C8)C2semidirect
11. #10592706C2semidirect
321. C32#3302semidirect
371. C3#83510semidirect

Maximal subgroups

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

subgroupindex
C32×#5472
#105960132
#105929382
#105929322
#105927892
#105927782
#105927502
#105927442
C4×#37542
D4×C3⋊(C3⋊C8)2
#105927062
#835103