Finite Group Databasebeta

← #11792579

Subgroups — #11792579

Order 1152.

1170 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
1C22×#3756C211yesmaximal, characteristic, complemented
2C22×#3755C211yesmaximal, characteristic
3C2×#64084C211yesmaximal, characteristic
4C32×#391C211yesmaximal, characteristic, complemented
5C2×#63637C211yesmaximal, characteristic, complemented
6C2×#63636C211yesmaximal, characteristic
7#10589390C211yesmaximal, characteristic, complemented
8#69689—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×#3756—22no—
15C2×#3756—22no—
16C2×#3756—22no—
17C2×#3755—22no—
18C2×#3755—22no—
19C2×#3755—22no—
20C2×#3752—22no—
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23#64084—22no—
24#64084—22no—
25C32×#95—22no—
26#63637—22no—
27#63636—22no—
28C22×#216—34no—
29C22×#215—34no—
30C2×#875—34no—
31C3×#391D314yescomplemented
32C2×#810—34no—
33C2×#809—34no—
34#4524—34no—
35C23×C3⋊D3—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8—21no—
38C2×C32×Q8—21no—
39C2×C32×Q8—21no—
40C2×C32×Q8—21no—
41C2×C32×Q8D412yes—
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4D412yes—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)D412yes—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634D412yes—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C42—21no—
62C32×C42—21no—
63#3756—28no—
64#3755—28no—
65#3752—28no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)D412yes—
71C2×C3⋊(C3⋊C8)D412yes—
72#2015—91noSylow
73C22×C3×Q8C2×D314yes—
74C22×D12—34no—
75C22×Dic6—34no—
76C2×C3×C4⋊C4C2×D314yes—
77C2×C3×C42C2×D314yes—
78C2×#216—68no—
79C2×#216—68no—
80C2×#216—68no—
81C2×#215—68no—
82C2×#215—68no—
83C2×#215—68no—
84C2×(C2×D3)⋊C4—68no—
85C22×C3⋊C8—34no—
86C22×C3⋊C8—34no—
87#875—68no—
88#875—68no—
89C3×#95—28no—
90#810—68no—
91#809—68no—
92C23×C32C2×D411yescharacteristic
93C22×C3⋊D3—22no—
94C22×C3⋊D3—41no—
95C22×C3⋊D3—41no—
96C22×C3⋊D3—42no—
97C22×C3⋊D3—42no—
98C32×Q8—22no—
99C32×Q8—22no—
100C32×Q8—41no—
101C32×Q8—41no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4—22no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4—42no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—41no—
118C2×C3⋊Dic3—41no—
119C4⋊(C3⋊D3)—22no—
120C4⋊(C3⋊D3)—22no—
121C4⋊(C3⋊D3)—41no—
122C4⋊(C3⋊D3)—41no—
123#634—22no—
124#634—22no—
125#634—41no—
126#634—41no—
127C3⋊(C3⋊C8)—22no—
128C3⋊(C3⋊C8)—22no—
129C22×Q16—91no—
130C22×SD16—91no—
131C2×#124—91no—
132C2×#103—91no—
133C2×#102—91no—
134#391C3⋊D311yescharacteristic, complemented
135#336—91no—
136C23×D3—64no—
137C2×C3×Q8—24no—
138C2×C3×Q8—24no—
139C2×C3×Q8—24no—
140C2×C3×Q8—24no—
141C2×C3×Q8—24no—
142C2×C3×Q8D1218yes—
143C22×C3×C4—24no—
144C22×C3×C4—24no—
145C22×C3×C4#6718yes—
146C22×C3×C4C22×D314yes—
147C22×Dic3—64no—
148C2×D12—38no—
149C2×D12—64no—
150C2×D12—64no—
151C2×D12—64no—
152C2×D12—64no—
153C2×D12—64no—
154C2×Dic6—38no—
155C2×Dic6—64no—
156C2×Dic6—64no—
157C2×Dic6—64no—
158C2×Dic6—64no—
159C2×Dic6—64no—
160C3×C4⋊C4—24no—
161C3×C4⋊C4—24no—
162C3×C42—24no—
163C3×C42—24no—
164#216—632no—
165#215—632no—
166(C2×D3)⋊C4—632no—
167C2×C3⋊C8—38no—
168C2×C3⋊C8—38no—
169C2×C3⋊C8—64no—
170C2×C3⋊C8—64no—
171C2×C3⋊C8—64no—
172C2×C3⋊C8—64no—
173C22×C32#12011yescharacteristic
174C22×C32#12111yescharacteristic
175C22×C32#12711yescharacteristic
176C22×C32#13512yes—
177C22×C32#13712yes—
178C2×C3⋊D3—42no—
179C2×C3⋊D3—44no—
180C2×C3⋊D3—82no—
181C2×C3⋊D3—81no—
182C2×C3⋊D3—81no—
183C32×C4—42no—
184C32×C4—42no—
185C32×C4—81no—
186C32×C4#12011yescharacteristic
187C32×C4#12011yescharacteristic
188C32×C4#12111yescharacteristic
189C32×C4#12111yescharacteristic
190C3⋊Dic3—42no—
191C22×Q8—91no—
192C22×Q8C2×C3⋊D311yescharacteristic
193C22×D4—91no—
194C2×Q16—182no—
195C2×Q16—182no—
196C2×Q16—182no—
197C2×SD16—182no—
198C2×SD16—182no—
199C2×SD16—182no—
200C22×C8—91no—
201C22×C8—91no—
202#124—182no—
203#124—182no—
204C2×C4⋊C4C2×C3⋊D311yescharacteristic
205C2×C22⋊C4—182no—
206C2×C42C2×C3⋊D311yescharacteristic
207#103—182no—
208#102—182no—
209#95—22no—
210C23×C3C2×#6714yes—
211C22×D3—68no—
212C22×D3—124no—
213C22×D3—124no—
214C22×D3—128no—
215C22×D3—128no—
216C3×Q8—28no—
217C3×Q8—28no—
218C3×Q8—44no—
219C3×Q8—44no—
220C2×C3×C4—28no—
221C2×C3×C4—28no—
222C2×C3×C4—28no—
223C2×C3×C4—28no—
224C2×C3×C4—44no—
225C2×C3×C4—44no—
226C2×C3×C4—44no—
227C2×C3×C4—48no—
228C2×C3×C4C2×D1214yes—
229C2×C3×C4#23514yes—
230C2×C3×C4D3×D414yes—
231C2×C3×C4D3×D414yes—
232C2×C3×C4D3×D414yes—
233C2×C3×C4D3×D414yes—
234C2×Dic3—68no—
235C2×Dic3—124no—
236C2×Dic3—124no—
237D12—68no—
238D12—68no—
239D12—124no—
240D12—124no—
241Dic6—68no—
242Dic6—68no—
243Dic6—124no—
244Dic6—124no—
245C3⋊C8—68no—
246C3⋊C8—68no—
247C2×C32#39211yescharacteristic
248C2×C32#45212yes—
249C2×C32#46412yes—
250C2×C32#49511yescharacteristic
251C2×C32#49711yescharacteristic
252C3⋊D3—82no—
253C24—181no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—92no—
260C2×Q8—181no—
261C2×Q8—181no—
262C2×Q8—181no—
263C2×Q8—181no—
264C2×Q8—181no—
265C2×Q8C4⋊(C3⋊D3)12yes—
266C2×D4—92no—
267C2×D4—181no—
268C2×D4—181no—
269C2×D4—181no—
270C2×D4—181no—
271C2×D4—181no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—181no—
275C22×C4#63812yes—
276C22×C4C22×C3⋊D311yescharacteristic
277Q16—188no—
278SD16—188no—
279C2×C8—92no—
280C2×C8—92no—
281C2×C8—181no—
282C2×C8—181no—
283C2×C8—181no—
284C2×C8—181no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C22⋊C4—188no—
288C42—21no—
289C42—21no—
290C22×C3#93014yes—
291C22×C3#93714yes—
292C22×C3#94014yes—
293C22×C3#94218yes—
294C22×C3#95018yes—
295C2×D3—128no—
296C2×D3—1216no—
297C2×D3—248no—
298C2×D3—244no—
299C2×D3—244no—
300C3×C4—48no—
301C3×C4—48no—
302C3×C4—84no—
303C3×C4#88214yes—
304C3×C4#88214yes—
305C3×C4#88414yes—
306C3×C4#88414yes—
307Dic3—128no—
308C32#201511yescharacteristic, complemented, Sylow
309C23—182no—
310C23—361no—
311C23—361no—
312C23—362no—
313C23—362no—
314C23C2×#63811yescharacteristic
315Q8—22no—
316Q8—22no—
317Q8—41no—
318Q8—41no—
319Q8—182no—
320Q8—182no—
321Q8—361no—
322Q8—361no—
323D4—182no—
324D4—182no—
325D4—361no—
326D4—361no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—182no—
336C2×C4—361no—
337C2×C4—361no—
338C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
339C2×C4#382811yescharacteristic
340C2×C4D4×C3⋊D311yescharacteristic
341C2×C4D4×C3⋊D311yescharacteristic
342C2×C4D4×C3⋊D311yescharacteristic
343C2×C4D4×C3⋊D311yescharacteristic
344C8—182no—
345C8—182no—
346C2×C3#496014yes—
347C2×C3#502818yes—
348C2×C3#504718yes—
349C2×C3#505914yes—
350C2×C3#508614yes—
351D3—248no—
352C22—362no—
353C22—364no—
354C22—721no—
355C22—722no—
356C22—721no—
357C22#6413911yescharacteristic
358C22#6414611yescharacteristic
359C22#6414911yescharacteristic
360C22#6415112yes—
361C22#6415912yes—
362C4—42no—
363C4—42no—
364C4—81no—
365C4—362no—
366C4#6409111yescharacteristic
367C4#6409111yescharacteristic
368C4#6409311yescharacteristic
369C4#6409311yescharacteristic
370C3#6968914yescomplemented
371C2—722no—
372C2#1059265911yescharacteristic
373C2#1059272712yes—
374C2#1059274612yes—
375C2#1059275811yescharacteristic
376C2#1059278511yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#391C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#391C3⋊D3
hypocenterC32#2015
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C22×#3756C2semidirect
4. C32×#391C2semidirect
5. C2×#63637C2semidirect
7. #10589390C2semidirect
31. C3×#391D3semidirect
134. #391C3⋊D3semidirect
308. C32#2015semidirect
370. C3#69689semidirect

Maximal subgroups

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

subgroupindex
C22×#37562
C22×#37552
C2×#640842
C32×#3912
C2×#636372
C2×#636362
#105893902
#696893