Finite Group Databasebeta

← #11794051

Subgroups — #11794051

Order 1152.

972 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic
2C2×C32×C4⋊C8C211yesmaximal, characteristic, complemented
3C2×#63648C211yesmaximal, characteristic
4C2×#63643C211yesmaximal, characteristic, complemented
5#10592638C211yesmaximal, characteristic
6#10592628C211yesmaximal, characteristic, complemented
7#10589417C211yesmaximal, characteristic, complemented
8#70482—34nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×#3752—21no—
15C2×#3752—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3744—22no—
19C2×#3744—22no—
20C2×#3744—22no—
21C32×C4⋊C8—22no—
22#63658—21no—
23#63658—21no—
24#63648—22no—
25#63643—22no—
26C22×#204—34no—
27C2×C3×C4⋊C8D314yescomplemented
28C2×#821—34no—
29C2×#816—34no—
30#4939—34no—
31#4929—34no—
32#4551—34no—
33C23×C3⋊D3—21no—
34C22×C32×C4D411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4C2311yescharacteristic
37C22×C3⋊Dic3—21no—
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)D412yes—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634D412yes—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C2×C32×C8—21no—
57C2×C32×C8D412yes—
58C32×C42—21no—
59C32×C42—21no—
60#3752—42no—
61#3752—42no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66#3744—28no—
67#2055—91noSylow
68C22×D12—34no—
69C22×Dic6—34no—
70C22×C3×C8C2×D314yes—
71C22×C3×C8C2×D314yes—
72C2×C3×C42C2×D314yes—
73C2×(C2×D3)⋊C4—64no—
74C2×(C2×D3)⋊C4—64no—
75C2×C4⋊Dic3—34no—
76C2×C4⋊Dic3—34no—
77C2×#204—68no—
78C2×#204—68no—
79C2×#204—68no—
80C3×C4⋊C8—28no—
81C3⋊#95—64no—
82C3⋊#95—64no—
83#821—68no—
84#816—68no—
85C23×C32C2×D411yescharacteristic
86C22×C3⋊D3—22no—
87C22×C3⋊D3—41no—
88C22×C3⋊D3—41no—
89C22×C3⋊D3—41no—
90C22×C3⋊D3—41no—
91C22×C3⋊D3—41no—
92C22×C3⋊D3—41no—
93C2×C32×C4—21no—
94C2×C32×C4—21no—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4—21no—
98C2×C32×C4SD1612yescomplemented
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—41no—
107C2×C3⋊Dic3—41no—
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3—41no—
111C2×C3⋊Dic3—41no—
112C2×C3⋊Dic3—41no—
113C2×C3⋊Dic3—41no—
114C4⋊(C3⋊D3)—22no—
115C4⋊(C3⋊D3)—22no—
116C4⋊(C3⋊D3)—41no—
117C4⋊(C3⋊D3)—41no—
118#634—22no—
119#634—22no—
120#634—41no—
121#634—41no—
122C32×C8—22no—
123C32×C8—41no—
124C22×SD16—91no—
125C2×C4⋊C8C3⋊D311yescharacteristic, complemented
126C2×#103—91no—
127C2×#102—91no—
128#391—91no—
129#390—91no—
130#340—91no—
131C23×D3—64no—
132C22×C3×C4D1214yes—
133C22×C3×C4D1214yes—
134C22×C3×C4C22×D314yes—
135C22×Dic3—64no—
136C22×Dic3—64no—
137C22×Dic3—64no—
138C2×D12—38no—
139C2×D12—64no—
140C2×D12—64no—
141C2×D12—64no—
142C2×D12—64no—
143C2×D12—64no—
144C2×Dic6—38no—
145C2×Dic6—64no—
146C2×Dic6—64no—
147C2×Dic6—64no—
148C2×Dic6—64no—
149C2×Dic6—64no—
150C2×C3×C8—24no—
151C2×C3×C8—24no—
152C2×C3×C8—24no—
153C2×C3×C8—24no—
154C2×C3×C8—24no—
155C2×C3×C8#6718yes—
156C3×C42—24no—
157C3×C42—24no—
158(C2×D3)⋊C4—128no—
159(C2×D3)⋊C4—128no—
160C4⋊Dic3—64no—
161C4⋊Dic3—64no—
162C4⋊Dic3—64no—
163C4⋊Dic3—64no—
164#204—632no—
165C22×C32#12111yescharacteristic
166C22×C32#12111yescharacteristic
167C22×C32#12111yescharacteristic
168C22×C32C2×SD1611yescharacteristic
169C22×C32#13511yescharacteristic
170C22×C32AGL(1,ℤ/8)11yescharacteristic
171C22×C32#13711yescharacteristic
172C2×C3⋊D3—42no—
173C2×C3⋊D3—42no—
174C2×C3⋊D3—42no—
175C2×C3⋊D3—81no—
176C2×C3⋊D3—81no—
177C2×C3⋊D3—81no—
178C2×C3⋊D3—81no—
179C32×C4—22no—
180C32×C4—41no—
181C32×C4#12011yescharacteristic
182C32×C4#12311yescharacteristic
183C32×C4#12311yescharacteristic
184C32×C4#12411yescharacteristic
185C3⋊Dic3—42no—
186C3⋊Dic3—81no—
187C3⋊Dic3—81no—
188C22×Q8—91no—
189C22×D4—91no—
190C2×SD16—182no—
191C2×SD16—182no—
192C2×SD16—182no—
193C22×C8C2×C3⋊D311yescharacteristic
194C22×C8C2×C3⋊D311yescharacteristic
195C2×C4⋊C4—91no—
196C2×C4⋊C4—91no—
197C2×C22⋊C4—181no—
198C2×C22⋊C4—181no—
199C2×C42C2×C3⋊D311yescharacteristic
200C4⋊C8—22no—
201#103—182no—
202#102—182no—
203#95—181no—
204#95—181no—
205C23×C3C2×D1214yes—
206C22×D3—68no—
207C22×D3—124no—
208C22×D3—124no—
209C22×D3—124no—
210C22×D3—124no—
211C22×D3—124no—
212C22×D3—124no—
213C2×C3×C4—24no—
214C2×C3×C4—24no—
215C2×C3×C4—24no—
216C2×C3×C4—24no—
217C2×C3×C4—24no—
218C2×C3×C4#20418yescomplemented
219C2×C3×C4#23514yes—
220C2×C3×C4D3×D414yes—
221C2×C3×C4D3×D414yes—
222C2×C3×C4#23914yes—
223C2×C3×C4#23914yes—
224C2×C3×C4C2×#6714yes—
225C2×Dic3—68no—
226C2×Dic3—124no—
227C2×Dic3—124no—
228C2×Dic3—124no—
229C2×Dic3—124no—
230C2×Dic3—124no—
231C2×Dic3—124no—
232C2×Dic3—124no—
233C2×Dic3—124no—
234D12—68no—
235D12—68no—
236D12—124no—
237D12—124no—
238Dic6—68no—
239Dic6—68no—
240Dic6—124no—
241Dic6—124no—
242C3×C8—28no—
243C3×C8—44no—
244C2×C32#39411yescharacteristic
245C2×C32#46011yescharacteristic
246C2×C32#46111yescharacteristic
247C2×C32#46311yescharacteristic
248C2×C32#46411yescharacteristic
249C2×C32#46511yescharacteristic
250C2×C32#46811yescharacteristic
251C3⋊D3—82no—
252C24—181no—
253C2×Q8—92no—
254C2×Q8—181no—
255C2×Q8—181no—
256C2×Q8—181no—
257C2×Q8—181no—
258C2×Q8—181no—
259C2×D4—92no—
260C2×D4—181no—
261C2×D4—181no—
262C2×D4—181no—
263C2×D4—181no—
264C2×D4—181no—
265C22×C4—181no—
266C22×C4—181no—
267C22×C4—181no—
268C22×C4C4⋊(C3⋊D3)11yescharacteristic
269C22×C4C4⋊(C3⋊D3)11yescharacteristic
270C22×C4C22×C3⋊D311yescharacteristic
271SD16—188no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8#63812yes—
278C4⋊C4—181no—
279C4⋊C4—181no—
280C4⋊C4—181no—
281C4⋊C4—181no—
282C22⋊C4—362no—
283C22⋊C4—362no—
284C42—21no—
285C42—21no—
286C22×C3#89514yes—
287C22×C3#89514yes—
288C22×C3C2×#20414yes—
289C22×C3#90414yes—
290C22×C3#90814yes—
291C22×C3#90914yes—
292C22×C3#93014yes—
293C2×D3—128no—
294C2×D3—128no—
295C2×D3—128no—
296C2×D3—244no—
297C2×D3—244no—
298C2×D3—244no—
299C2×D3—244no—
300C3×C4—28no—
301C3×C4—44no—
302C3×C4#89414yes—
303C3×C4#89414yes—
304C3×C4#93714yes—
305C3×C4#94714yes—
306Dic3—128no—
307Dic3—244no—
308Dic3—244no—
309C32#205511yescharacteristic, complemented, Sylow
310C23—182no—
311C23—361no—
312C23—361no—
313C23—361no—
314C23—361no—
315C23—361no—
316C23—361no—
317C23C2×C4⋊(C3⋊D3)11yescharacteristic
318Q8—182no—
319Q8—182no—
320Q8—361no—
321Q8—361no—
322D4—182no—
323D4—182no—
324D4—361no—
325D4—361no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—182no—
332C2×C4—361no—
333C2×C4—361no—
334C2×C4—361no—
335C2×C4—361no—
336C2×C4—361no—
337C2×C4—361no—
338C2×C4—361no—
339C2×C4—361no—
340C2×C4#374412yescomplemented
341C2×C4#382811yescharacteristic
342C2×C4D4×C3⋊D311yescharacteristic
343C2×C4D4×C3⋊D311yescharacteristic
344C2×C4#383211yescharacteristic
345C2×C4#383211yescharacteristic
346C2×C4C2×#63811yescharacteristic
347C8—22no—
348C8—41no—
349C2×C3#484114yes—
350C2×C3#484414yes—
351C2×C3#484514yes—
352C2×C3#484814yes—
353C2×C3#499114yes—
354C2×C3#511414yes—
355C2×C3#513414yes—
356D3—248no—
357C22—362no—
358C22—362no—
359C22—362no—
360C22—721no—
361C22—721no—
362C22—721no—
363C22—721no—
364C22#6410411yescharacteristic
365C22#6410411yescharacteristic
366C22C2×#374411yescharacteristic
367C22#6411311yescharacteristic
368C22#6411711yescharacteristic
369C22#6411811yescharacteristic
370C22#6413911yescharacteristic
371C4—22no—
372C4—41no—
373C4—362no—
374C4—721no—
375C4—721no—
376C4#6410311yescharacteristic
377C4#6410311yescharacteristic
378C4#6414611yescharacteristic
379C4#6415611yescharacteristic
380C3#7048214yescomplemented
381C2—722no—
382C2#1059254011yescharacteristic
383C2#1059254311yescharacteristic
384C2#1059254411yescharacteristic
385C2#1059254711yescharacteristic
386C2#1059269011yescharacteristic
387C2#1059281311yescharacteristic
388C2#1059283311yescharacteristic
subgroupG/H
centerC23C2×C4⋊(C3⋊D3)
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×C4⋊C8C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C8C3⋊D3
hypocenterC32#2055
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C32×C4⋊C8C2semidirect
4. C2×#63643C2semidirect
6. #10592628C2semidirect
7. #10589417C2semidirect
27. C2×C3×C4⋊C8D3semidirect
98. C2×C32×C4SD16semidirect
125. C2×C4⋊C8C3⋊D3semidirect
218. C2×C3×C4#204semidirect
309. C32#2055semidirect
340. C2×C4#3744semidirect
380. C3#70482semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
C2×C32×C4⋊C82
C2×#636482
C2×#636432
#105926382
#105926282
#105894172
#704823