Finite Group Databasebeta

← #11792549

Subgroups — #11792549

Order 1152.

1422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic
2C22×#3754C211yesmaximal, characteristic, complemented
3C22×#3744C211yesmaximal, characteristic, complemented
4C2×C32×#102C211yesmaximal, characteristic, complemented
5#10592672C211yesmaximal, characteristic, complemented
6C2×#63636C211yesmaximal, characteristic, complemented
7#10589416C211yesmaximal, characteristic, complemented
8#70210—34nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×#638—22no—
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15#64149—22no—
16#64149—22no—
17C2×#3754—22no—
18C2×#3754—22no—
19C2×#3754—22no—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C2×#3744—22no—
23C2×#3744—22no—
24C2×#3744—22no—
25C32×#102—22no—
26#63658—22no—
27#63636—22no—
28C2×#940—34no—
29C22×#214—34no—
30C22×#204—34no—
31C2×C3×#102D314yescomplemented
32#4973—34no—
33C2×#809—34no—
34#4550—34no—
35C24×C32—21no—
36C23×C3⋊D3—21no—
37C2×C32×D4—21no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4D412yes—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—28no—
46C2×#638—44no—
47C2×#638—44no—
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3D412yes—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)D412yes—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634—21no—
61C2×#634D412yescomplemented
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8D412yescomplemented
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67#3754—28no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)D412yescomplemented
73#3744—28no—
74#2014—91noSylow
75C22×C3×D4C2×D314yes—
76C22×#67—68no—
77C22×D12—34no—
78C22×Dic6—34no—
79C22×C3×C8C2×D314yes—
80C2×C3×C4⋊C4C2×D314yes—
81#940—68no—
82#940—68no—
83C2×#214—68no—
84C2×#214—68no—
85C2×#214—68no—
86C2×C4×Dic3—34no—
87C22×C3⋊C8—34no—
88C2×#204—68no—
89C2×#204—68no—
90C2×#204—68no—
91C3×#102—28no—
92C3⋊#95—68no—
93#809—68no—
94C23×C32—22no—
95C23×C32—41no—
96C23×C32—41no—
97C23×C32—42no—
98C23×C32—42no—
99C23×C32C2×D411yescharacteristic
100C22×C3⋊D3—22no—
101C22×C3⋊D3—41no—
102C22×C3⋊D3—41no—
103C22×C3⋊D3—42no—
104C22×C3⋊D3—42no—
105C32×D4—22no—
106C32×D4—22no—
107C32×D4—41no—
108C32×D4—41no—
109C2×C32×C4—41no—
110C2×C32×C4—42no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117#638—416no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3SD1614yescomplemented
124C4⋊(C3⋊D3)—22no—
125C4⋊(C3⋊D3)—22no—
126C4⋊(C3⋊D3)—41no—
127C4⋊(C3⋊D3)—41no—
128#634—22no—
129#634—22no—
130#634—41no—
131#634—41no—
132C32×C8—22no—
133C3⋊(C3⋊C8)—22no—
134C22×SD16—91no—
135C22×SD16—91no—
136C2×#127—91no—
137C2×#102—91no—
138C2×#102C3⋊D311yescharacteristic, complemented
139#391—91no—
140#336—91no—
141C24×C3—24no—
142C23×D3—64no—
143C2×C3×D4—24no—
144C2×C3×D4—24no—
145C2×C3×D4—24no—
146C2×C3×D4—24no—
147C2×C3×D4—24no—
148C2×C3×D4D1218yes—
149C22×C3×C4—24no—
150C22×C3×C4C22×D314yes—
151C2×#67—632no—
152C2×#67—1216no—
153C2×#67—1216no—
154C22×Dic3—38no—
155C22×Dic3—64no—
156C2×D12—38no—
157C2×D12—64no—
158C2×D12—64no—
159C2×D12—64no—
160C2×D12—64no—
161C2×D12—64no—
162C2×Dic6—38no—
163C2×Dic6—64no—
164C2×Dic6—64no—
165C2×Dic6—64no—
166C2×Dic6—64no—
167C2×Dic6—64no—
168C2×C3×C8—24no—
169C2×C3×C8—24no—
170C2×C3×C8#6718yescomplemented
171C3×C4⋊C4—24no—
172C3×C4⋊C4—24no—
173#214—632no—
174C4×Dic3—64no—
175C4×Dic3—64no—
176C2×C3⋊C8—38no—
177C2×C3⋊C8—64no—
178C2×C3⋊C8—64no—
179#204—632no—
180C22×C32—42no—
181C22×C32—44no—
182C22×C32—82no—
183C22×C32—81no—
184C22×C32—81no—
185C22×C32#12011yescharacteristic
186C22×C32#12111yescharacteristic
187C22×C32#12711yescharacteristic
188C22×C32C2×SD1612yes—
189C22×C32AGL(1,ℤ/8)12yes—
190C2×C3⋊D3—42no—
191C2×C3⋊D3—44no—
192C2×C3⋊D3—82no—
193C2×C3⋊D3—81no—
194C2×C3⋊D3—81no—
195C32×C4—81no—
196C32×C4#12011yescharacteristic
197C32×C4#12011yescharacteristic
198C32×C4#12111yescharacteristic
199C32×C4#12111yescharacteristic
200C3⋊Dic3—24no—
201C3⋊Dic3—42no—
202C22×Q8—91no—
203C22×D4—91no—
204C22×D4—182no—
205C22×D4C2×C3⋊D311yescharacteristic
206C2×SD16—182no—
207C2×SD16—182no—
208C2×SD16—182no—
209C2×SD16—182no—
210C2×SD16—182no—
211C2×SD16—182no—
212C22×C8—91no—
213C22×C8C2×C3⋊D311yescharacteristic
214#127—182no—
215#127—182no—
216C2×C4⋊C4C2×C3⋊D311yescharacteristic
217C2×C42—91no—
218#102—22no—
219#102—182no—
220#95—182no—
221C23×C3—28no—
222C23×C3—44no—
223C23×C3—48no—
224C23×C3—48no—
225C23×C3—44no—
226C23×C3D3×D414yes—
227C22×D3—68no—
228C22×D3—124no—
229C22×D3—128no—
230C22×D3—128no—
231C22×D3—124no—
232C3×D4—28no—
233C3×D4—28no—
234C3×D4—44no—
235C3×D4—44no—
236C2×C3×C4—48no—
237C2×C3×C4—44no—
238C2×C3×C4C2×D1214yes—
239C2×C3×C4#23514yes—
240C2×C3×C4D3×D414yes—
241C2×C3×C4D3×D414yes—
242C2×C3×C4D3×D414yes—
243C2×C3×C4C2×#6714yes—
244#67—1264no—
245C2×Dic3—316no—
246C2×Dic3—68no—
247C2×Dic3—68no—
248C2×Dic3—68no—
249C2×Dic3—124no—
250C2×Dic3—124no—
251D12—68no—
252D12—68no—
253D12—124no—
254D12—124no—
255Dic6—68no—
256Dic6—68no—
257Dic6—124no—
258Dic6—124no—
259C3×C8—28no—
260C3⋊C8—68no—
261C2×C32—82no—
262C2×C32#39211yescharacteristic
263C2×C32#45012yes—
264C2×C32#46012yes—
265C2×C32#49211yescharacteristic
266C2×C32#49611yescharacteristic
267C3⋊D3—82no—
268C24—21no—
269C24—181no—
270C2×Q8—92no—
271C2×Q8—181no—
272C2×Q8—181no—
273C2×Q8—181no—
274C2×Q8—181no—
275C2×Q8—181no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—92no—
282C2×D4—188no—
283C2×D4—181no—
284C2×D4—181no—
285C2×D4—181no—
286C2×D4—181no—
287C2×D4—181no—
288C2×D4—364no—
289C2×D4—364no—
290C2×D4C4⋊(C3⋊D3)12yes—
291C22×C4—21no—
292C22×C4—92no—
293C22×C4—181no—
294C22×C4C22×C3⋊D311yescharacteristic
295SD16—188no—
296SD16—188no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—92no—
300C2×C8—181no—
301C2×C8—181no—
302C2×C8#63812yescomplemented
303C4⋊C4—21no—
304C4⋊C4—21no—
305C42—181no—
306C42—181no—
307C22×C3—48no—
308C22×C3—416no—
309C22×C3—84no—
310C22×C3—84no—
311C22×C3—88no—
312C22×C3#88214yes—
313C22×C3#88414yes—
314C22×C3#91118yes—
315C22×C3D3×SD1618yes—
316C22×C3#94014yes—
317C2×D3—128no—
318C2×D3—1216no—
319C2×D3—244no—
320C2×D3—244no—
321C2×D3—248no—
322C3×C4—84no—
323C3×C4#88214yes—
324C3×C4#88414yes—
325C3×C4#93014yes—
326C3×C4#93714yes—
327Dic3—616no—
328Dic3—128no—
329C32#201411yescharacteristic, complemented, Sylow
330C23—22no—
331C23—41no—
332C23—42no—
333C23—42no—
334C23—41no—
335C23—182no—
336C23—361no—
337C23—362no—
338C23—362no—
339C23—361no—
340C23D4×C3⋊D311yescharacteristic
341Q8—182no—
342Q8—182no—
343Q8—361no—
344Q8—361no—
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349D4—182no—
350D4—182no—
351D4—3616no—
352D4—361no—
353D4—361no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—94no—
357C2×C4—182no—
358C2×C4—182no—
359C2×C4—182no—
360C2×C4—361no—
361C2×C4—361no—
362C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
363C2×C4#382811yescharacteristic
364C2×C4D4×C3⋊D311yescharacteristic
365C2×C4D4×C3⋊D311yescharacteristic
366C2×C4D4×C3⋊D311yescharacteristic
367C2×C4C2×#63811yescharacteristic
368C8—22no—
369C8—182no—
370C2×C3—88no—
371C2×C3#476218yes—
372C2×C3#477618yes—
373C2×C3#496014yes—
374C2×C3#515414yes—
375C2×C3#517514yes—
376D3—248no—
377C22—42no—
378C22—44no—
379C22—81no—
380C22—81no—
381C22—82no—
382C22—362no—
383C22—364no—
384C22—721no—
385C22—721no—
386C22—722no—
387C22#6409111yescharacteristic
388C22#6409311yescharacteristic
389C22#6412012yes—
390C22SD16×C3⋊D312yes—
391C22#6414911yescharacteristic
392C4—81no—
393C4—184no—
394C4—362no—
395C4#6409111yescharacteristic
396C4#6409311yescharacteristic
397C4#6413911yescharacteristic
398C4#6414611yescharacteristic
399C3#7021014yescomplemented
400C2—82no—
401C2—722no—
402C2#1059246112yes—
403C2#1059247512yes—
404C2#1059265911yescharacteristic
405C2#1059285311yescharacteristic
406C2#1059287411yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC2×#64149C2
hypercenterC2×#102C3⋊D3
hypocenterC32#2014
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C22×#3754C2semidirect
3. C22×#3744C2semidirect
4. C2×C32×#102C2semidirect
5. #10592672C2semidirect
6. C2×#63636C2semidirect
7. #10589416C2semidirect
31. C2×C3×#102D3semidirect
61. C2×#634D4semidirect
64. C2×C32×C8D4semidirect
72. C2×C3⋊(C3⋊C8)D4semidirect
123. C2×C3⋊Dic3SD16semidirect
138. C2×#102C3⋊D3semidirect
170. C2×C3×C8#67semidirect
302. C2×C8#638semidirect
329. C32#2014semidirect
399. C3#70210semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
C22×#37542
C22×#37442
C2×C32×#1022
#105926722
C2×#636362
#105894162
#702103