Finite Group Databasebeta

← #11868014

Subgroups — #11868014

Order 1152.

1356 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#131C211yesmaximal, characteristic, complemented
2#10596293C212yesmaximal, complemented
3C2×#64113C211yesmaximal, characteristic, complemented
4#10592842C212yesmaximal, complemented
5#10592841C212yesmaximal, complemented
6#10592840C214yesmaximal, complemented
7#10592831C212yesmaximal, complemented
8C2×#63646C211yesmaximal, characteristic, complemented
9#83805—34nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×#3828C2212yes—
12C32×#131—21no—
13C32×#131—21no—
14C32×#131C2212yes—
15C32×#131C2212yes—
16C2×C32×M16—21no—
17C2×C32×M16C2211yescharacteristic
18C22×C32×C8—21no—
19C22×C32×C8C2211yescharacteristic
20#64160C2214yes—
21#64159—24no—
22#64158C2214yes—
23#64151—22no—
24#64141—22no—
25C2×#3748C2212yes—
26C2×#3746C2211yescharacteristic, complemented
27#64113—21no—
28#64113—21no—
29#64113—21no—
30#64113—21no—
31C2×#3745C2211yescharacteristic, complemented
32C2×#3744C2212yescomplemented
33#63651C2214yescomplemented
34#63650C2214yescomplemented
35#63646C2212yescomplemented
36#63646C2212yescomplemented
37C2×C3×#131D314yescomplemented
38#5822—38no—
39C2×#904—34no—
40#5143—38no—
41#5142—38no—
42#5141—316no—
43#5132—38no—
44C2×#819—34no—
45C32×#41—21no—
46C32×#41—21no—
47C32×#41D412yes—
48C32×#41C2312yes—
49C2×C32×Q8D411yescharacteristic
50C2×C32×D4—21no—
51C2×C32×D4D411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C2×#638—22no—
55#3828—22no—
56#3828—22no—
57#3828—22no—
58#3828—22no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C4×C3⋊D3—22no—
61C2×#634C2312yes—
62C32×M16—21no—
63C32×M16—22no—
64C32×M16—22no—
65C32×M16C2312yes—
66C2×C32×C8—21no—
67C2×C32×C8—22no—
68C2×C32×C8—22no—
69C2×C32×C8D411yescharacteristic
70C2×C32×C8D411yescharacteristic
71C2×C32×C8D411yescharacteristic
72C2×C32×C8D411yescharacteristic
73C2×C32×C8C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75#3756—24no—
76#3755—24no—
77#3754—24no—
78#3753—24no—
79#3748—22no—
80#3748C2314yes—
81C2×C3⋊(C3⋊C8)—22no—
82#3746—21no—
83#3746—21no—
84#3745—21no—
85#3745—21no—
86#3744—22no—
87#3744—22no—
88#3067—91noSylow
89C2×C3×#41C2×D314yes—
90C2×#235—38no—
91C3×#131—24no—
92C3×#131—24no—
93C3×#131C2×D318yes—
94C3×#131C2×D318yes—
95C2×C3×M16—24no—
96C2×C3×M16C2×D314yes—
97C22×C3×C8—24no—
98C22×C3×C8C2×D314yes—
99#951—316no—
100#950—616no—
101#949—316no—
102#942—68no—
103#932—68no—
104C2×#208—38no—
105C2×Dic12—34no—
106#904—64no—
107#904—64no—
108#904—64no—
109#904—64no—
110C2×D24—34no—
111C2×#204—38no—
112#824—316no—
113#823—316no—
114#819—38no—
115#819—38no—
116C23×C32—21no—
117C23×C32#4111yescharacteristic
118C22×C3⋊D3—22no—
119C32×Q8—21no—
120C32×Q8C2×D412yes—
121C32×D4—22no—
122C32×D4—22no—
123C32×D4—21no—
124C32×D4C2×D412yes—
125C2×C32×C4—21no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4C2411yescharacteristic
134#638—42no—
135#638—42no—
136C2×C3⋊Dic3—22no—
137C4⋊(C3⋊D3)—22no—
138C4⋊(C3⋊D3)—22no—
139C4×C3⋊D3—42no—
140C4×C3⋊D3—42no—
141#634—22no—
142#634—22no—
143C32×C8—22no—
144C32×C8C2×D411yescharacteristic
145C32×C8C2×D411yescharacteristic
146C32×C8C2×D411yescharacteristic
147C32×C8C2×D411yescharacteristic
148C3⋊(C3⋊C8)—24no—
149#575—92no—
150C2×#135—91no—
151C2×#131C3⋊D311yescharacteristic, complemented
152#473—92no—
153#472—92no—
154#471—94no—
155C2×#108—91no—
156#413—92no—
157C3×#41—24no—
158C3×#41—24no—
159C3×#41D1218yes—
160C3×#41C22×D318yes—
161C2×C3×Q8D1214yes—
162C2×C3×D4—24no—
163C2×C3×D4D1214yes—
164C22×C3×C4—24no—
165C22×C3×C4C22×D314yes—
166C2×#67—68no—
167#235—68no—
168#235—68no—
169#235—68no—
170#235—68no—
171C2×D12—38no—
172C2×C4×D3—68no—
173C2×Dic6—38no—
174C3×M16—24no—
175C3×M16—28no—
176C3×M16—28no—
177C3×M16C22×D318yes—
178C2×C3×C8—24no—
179C2×C3×C8—28no—
180C2×C3×C8—28no—
181C2×C3×C8#6714yes—
182C2×C3×C8#6714yes—
183C2×C3×C8#6714yes—
184C2×C3×C8#6714yes—
185C2×C3×C8C22×D314yes—
186C2×C3×C8C22×D314yes—
187#216—616no—
188#215—616no—
189#214—616no—
190#213—616no—
191#208—316no—
192#208—68no—
193C2×C3⋊C8—68no—
194Dic12—64no—
195Dic12—64no—
196D24—64no—
197D24—64no—
198#204—68no—
199#204—68no—
200C22×C32—22no—
201C22×C32—41no—
202C22×C32—42no—
203C22×C32#12111yescharacteristic
204C22×C32#12111yescharacteristic
205C22×C32C2×#4111yescharacteristic
206C2×C3⋊D3—42no—
207C2×C3⋊D3—82no—
208C32×C4—22no—
209C32×C4#12111yescharacteristic
210C32×C4#12111yescharacteristic
211C32×C4C22×D411yescharacteristic
212C32×C4C22×D411yescharacteristic
213C3⋊Dic3—42no—
214C2×#41—92no—
215C2×#41C2×C3⋊D311yescharacteristic
216#137—94no—
217#137—182no—
218AGL(1,ℤ/8)—94no—
219AGL(1,ℤ/8)—182no—
220#135—184no—
221#135—181no—
222#135—181no—
223#135—181no—
224#135—181no—
225C2×Q16—91no—
226C2×SD16—92no—
227C2×D8—91no—
228#131—21no—
229#131—21no—
230#131C2×C3⋊D312yes—
231#131C2×C3⋊D312yes—
232C2×M16—21no—
233C2×M16—92no—
234C2×M16C2×C3⋊D311yescharacteristic
235C22×C8—21no—
236C22×C8C2×C3⋊D311yescharacteristic
237#108—92no—
238#108—92no—
239#101—94no—
240#100—94no—
241C23×C3—24no—
242C23×C3#23514yes—
243C22×D3—68no—
244C3×Q8—24no—
245C3×Q8C2×D1218yes—
246C3×D4—28no—
247C3×D4—28no—
248C3×D4—24no—
249C3×D4C2×D1218yes—
250C2×C3×C4—24no—
251C2×C3×C4—28no—
252C2×C3×C4—28no—
253C2×C3×C4C2×D1214yes—
254C2×C3×C4C2×D1214yes—
255C2×C3×C4#23514yes—
256C2×C3×C4C2×#6714yes—
257C2×C3×C4C2×#6714yes—
258C2×C3×C4C23×D314yes—
259#67—128no—
260#67—128no—
261C2×Dic3—68no—
262D12—68no—
263D12—68no—
264C4×D3—128no—
265C4×D3—128no—
266Dic6—68no—
267Dic6—68no—
268C3×C8—28no—
269C3×C8C2×#6714yes—
270C3×C8C2×#6714yes—
271C3×C8C2×#6714yes—
272C3×C8C2×#6714yes—
273C3⋊C8—616no—
274C2×C32—21no—
275C2×C32—21no—
276C2×C32—21no—
277C2×C32—42no—
278C2×C32C2×#12111yescharacteristic
279C3⋊D3—82no—
280#41—21no—
281#41—21no—
282#41—182no—
283#41—182no—
284#41—182no—
285#41—182no—
286#41C4⋊(C3⋊D3)12yes—
287#41C22×C3⋊D312yes—
288C2×Q8—92no—
289C2×Q8C4⋊(C3⋊D3)11yescharacteristic
290C2×D4—21no—
291C2×D4—92no—
292C2×D4—182no—
293C2×D4C4⋊(C3⋊D3)11yescharacteristic
294C22×C4—21no—
295C22×C4—182no—
296C22×C4C22×C3⋊D311yescharacteristic
297Q16—184no—
298Q16—181no—
299Q16—181no—
300SD16—184no—
301SD16—184no—
302SD16—182no—
303SD16—182no—
304D8—184no—
305D8—181no—
306D8—181no—
307M16—21no—
308M16—22no—
309M16—22no—
310M16—94no—
311M16—182no—
312M16C22×C3⋊D312yes—
313C2×C8—21no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—182no—
317C2×C8#63811yescharacteristic
318C2×C8#63811yescharacteristic
319C2×C8#63811yescharacteristic
320C2×C8#63811yescharacteristic
321C2×C8C22×C3⋊D311yescharacteristic
322C2×C8C22×C3⋊D311yescharacteristic
323C22×C3—28no—
324C22×C3—44no—
325C22×C3—48no—
326C22×C3#93014yes—
327C22×C3#93014yes—
328C22×C3C2×#23514yes—
329C2×D3—128no—
330C2×D3—248no—
331C3×C4—28no—
332C3×C4#93014yes—
333C3×C4#93014yes—
334C3×C4C22×D1214yes—
335C3×C4C22×#6714yes—
336Dic3—128no—
337C32#306711yescharacteristic, complemented, Sylow
338C23—21no—
339C23—182no—
340C23#382811yescharacteristic
341Q8—21no—
342Q8—182no—
343Q8—182no—
344Q8C2×C4⋊(C3⋊D3)12yes—
345D4—22no—
346D4—22no—
347D4—21no—
348D4—182no—
349D4—182no—
350D4—362no—
351D4—362no—
352D4C2×C4⋊(C3⋊D3)12yes—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—182no—
357C2×C4—362no—
358C2×C4—362no—
359C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
360C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
361C2×C4#382811yescharacteristic
362C2×C4C2×#63811yescharacteristic
363C2×C4C2×#63811yescharacteristic
364C2×C4C23×C3⋊D311yescharacteristic
365C8—22no—
366C8—184no—
367C8C2×#63811yescharacteristic
368C8C2×#63811yescharacteristic
369C8C2×#63811yescharacteristic
370C8C2×#63811yescharacteristic
371C2×C3—24no—
372C2×C3—24no—
373C2×C3—24no—
374C2×C3—48no—
375C2×C3C2×#93014yes—
376D3—248no—
377C22—22no—
378C22—41no—
379C22—42no—
380C22—362no—
381C22—722no—
382C22#6413911yescharacteristic
383C22#6413911yescharacteristic
384C22C2×#382811yescharacteristic
385C4—22no—
386C4—362no—
387C4#6413911yescharacteristic
388C4#6413911yescharacteristic
389C4C22×C4⋊(C3⋊D3)11yescharacteristic
390C4C22×#63811yescharacteristic
391C3#8380514yescomplemented
392C2—21no—
393C2—21no—
394C2—21no—
395C2—42no—
396C2—722no—
397C2C2×#6413911yescharacteristic
subgroupG/H
centerC4#64139
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#131C2
socleC2×C32C2×#121
hypercenterC2×#131C3⋊D3
hypocenterC32#3067
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C2×C32×#131C2semidirect
2. #10596293C2semidirect
3. C2×#64113C2semidirect
4. #10592842C2semidirect
5. #10592841C2semidirect
6. #10592840C2semidirect
7. #10592831C2semidirect
8. C2×#63646C2semidirect
26. C2×#3746C22semidirect
31. C2×#3745C22semidirect
32. C2×#3744C22semidirect
33. #63651C22semidirect
34. #63650C22semidirect
35. #63646C22semidirect
36. #63646C22semidirect
37. C2×C3×#131D3semidirect
151. C2×#131C3⋊D3semidirect
337. C32#3067semidirect
391. C3#83805semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1312
#105962932
C2×#641132
#105928422
#105928412
#105928402
#105928312
C2×#636462
#838053