Finite Group Databasebeta

← #11784742

Subgroups — #11784742

Order 1152.

1285 conjugacy classes of subgroups.

The subgroup lattice has 413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic
2C2×#63647C211yesmaximal, characteristic
3C2×C3×#816C212yesmaximal, complemented
4#10591325C211yesmaximal, characteristic
5C2×#63565C212yesmaximal, complemented
6#70266—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×C3×Dic6C2212yes—
9C22×#627—21no—
10C22×#624—21no—
11C2×#3797—22no—
12C2×#3797—24no—
13C2×#3797—24no—
14C2×#3797C414yescomplemented
15C22×C32×C8C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×C4⋊Dic3C2212yes—
18C2×#3722—21no—
19#63647—22no—
20C3×#816—24no—
21#63579—21no—
22#63565—24no—
23C22×D3×Q8—32no—
24C2×C3×#103—32no—
25C2×#835—32no—
26C2×(C2×D3)⋊C8—32no—
27C2×(C2×D3)⋊C8—61no—
28C2×#816D312yescomplemented
29#4987—32no—
30C2×#810—32no—
31C23×C3⋊D3D411yescharacteristic
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3—22no—
36C2×C4×C3⋊D3C2×C412yes—
37C2×C4×C3⋊D3D412yes—
38C22×C3×Dic3—22no—
39C22×C3×Dic3—22no—
40C2×C3×Dic6—22no—
41C2×C3×Dic6—22no—
42C2×C3×Dic6—22no—
43C2×C3×Dic6C2×C414yes—
44C2×C3×Dic6D414yes—
45C2×C3×Dic6D414yes—
46C2×#627—28no—
47C2×#627—24no—
48C2×#624—28no—
49C2×#624—24no—
50#3797—28no—
51#3797—28no—
52#3797—216no—
53C2×C32×C8—21no—
54C2×C32×C8—22no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—22no—
57C3×C4⋊Dic3—22no—
58C3×C4⋊Dic3—22no—
59#3722—42no—
60#1787—91noSylow
61C22×C3×Q8—32no—
62C2×D3×Q8—38no—
63C2×D3×Q8—64no—
64C2×D3×Q8—64no—
65C2×D3×Q8—64no—
66C2×D3×Q8—64no—
67C2×D3×Q8—64no—
68C22×C4×D3—32no—
69C22×C4×D3—61no—
70C22×C4×D3—62no—
71C22×Dic6—62no—
72C22×Dic6C2×D312yes—
73C22×C3×C8—21no—
74C22×C3×C8C2×D312yes—
75C2×C3×C4⋊C4—32no—
76C2×(C2×D3)⋊C4—62no—
77C2×C4⋊Dic3C2×D312yes—
78C22×C3⋊C8—32no—
79C22×C3⋊C8—61no—
80C3×#103—64no—
81#835—64no—
82C3⋊#95—62no—
83(C2×D3)⋊C8—64no—
84(C2×D3)⋊C8—64no—
85#816—24no—
86#810—64no—
87C23×C32C2×D411yescharacteristic
88C22×C3⋊D3—22no—
89C22×C3⋊D3—22no—
90C22×C3⋊D3C22⋊C412yes—
91C22×C3⋊D3SD1612yes—
92C22×C3⋊D3Q1612yes—
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D412yes—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D412yes—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3C22⋊C412yes—
99C4×C3⋊D3—24no—
100C4×C3⋊D3—22no—
101C4×C3⋊D3—22no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—42no—
106C2×C3×Dic3—42no—
107C2×C3×Dic3—42no—
108C3×Dic6—24no—
109C3×Dic6—24no—
110C3×Dic6—24no—
111C3×Dic6C22⋊C418yescomplemented
112#627—216no—
113#624—216no—
114C32×C8—41no—
115C3⋊(C3⋊C8)—41no—
116C23×Q8—91no—
117C2×#103—32no—
118C2×#103—92no—
119C2×C22⋊C8—91no—
120#380—91no—
121C23×D3—32no—
122C23×D3—61no—
123C2×C3×Q8—34no—
124C2×C3×Q8—34no—
125C2×C3×Q8—34no—
126C2×C3×Q8—62no—
127C2×C3×Q8—62no—
128C2×C3×Q8—62no—
129C22×C3×C4—21no—
130C22×C3×C4—62no—
131C22×C3×C4—62no—
132C22×C3×C4C22×D312yes—
133C22×Dic3—22no—
134C22×Dic3—22no—
135C22×Dic3—32no—
136C22×Dic3—61no—
137D3×Q8—616no—
138D3×Q8—616no—
139D3×Q8—616no—
140D3×Q8—616no—
141C2×C4×D3—34no—
142C2×C4×D3—34no—
143C2×C4×D3—62no—
144C2×C4×D3—62no—
145C2×C4×D3—68no—
146C2×C4×D3—68no—
147C2×C4×D3—68no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×C4×D3—122no—
153C2×C4×D3—122no—
154C2×Dic6—22no—
155C2×Dic6—22no—
156C2×Dic6—22no—
157C2×Dic6—68no—
158C2×Dic6—68no—
159C2×Dic6—68no—
160C2×Dic6C4×D314yes—
161C2×Dic6D1214yes—
162C2×Dic6#6714yes—
163C2×C3×C8—22no—
164C2×C3×C8—22no—
165C2×C3×C8—22no—
166C2×C3×C8—22no—
167C2×C3×C8—42no—
168C3×C4⋊C4—62no—
169C3×C4⋊C4—62no—
170(C2×D3)⋊C4—124no—
171C4⋊Dic3—22no—
172C4⋊Dic3—22no—
173C2×C3⋊C8—62no—
174C2×C3⋊C8—62no—
175C2×C3⋊C8—62no—
176C2×C3⋊C8—62no—
177C2×C3⋊C8—122no—
178C22×C32C2×C22⋊C411yescharacteristic
179C22×C32#12012yes—
180C22×C32C2×SD1611yescharacteristic
181C22×C32C2×Q1611yescharacteristic
182C22×C32#13712yes—
183C2×C3⋊D3—22no—
184C2×C3⋊D3—22no—
185C2×C3⋊D3—24no—
186C2×C3⋊D3—24no—
187C2×C3⋊D3#10314yescomplemented
188C32×C4C2×C22⋊C412yes—
189C32×C4#12011yescharacteristic
190C32×C4#12011yescharacteristic
191C3⋊Dic3—22no—
192C3×Dic3—28no—
193C3×Dic3—82no—
194C22×Q8—32no—
195C22×Q8—94no—
196C22×Q8—181no—
197C22×Q8—182no—
198C22×Q8—184no—
199C22×Q8—184no—
200C23×C4—91no—
201C23×C4—181no—
202C22×C8—91no—
203C22×C8D3211yescharacteristic
204C2×C4⋊C4—32no—
205C2×C22⋊C4—181no—
206#103—64no—
207#103—184no—
208C22⋊C8—182no—
209#95—181no—
210C23×C3—21no—
211C23×C3D3×D412yes—
212C22×D3—34no—
213C22×D3—34no—
214C22×D3—34no—
215C22×D3—62no—
216C22×D3—62no—
217C22×D3—62no—
218C22×D3—62no—
219C22×D3—62no—
220C22×D3—62no—
221C22×D3—62no—
222C22×D3—122no—
223C22×D3—122no—
224C3×Q8—38no—
225C3×Q8—64no—
226C3×Q8—64no—
227C3×Q8—64no—
228C2×C3×C4—21no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—21no—
232C2×C3×C4—64no—
233C2×C3×C4—64no—
234C2×C3×C4—64no—
235C2×C3×C4—122no—
236C2×C3×C4—122no—
237C2×C3×C4—122no—
238C2×C3×C4C2×C4×D312yes—
239C2×C3×C4C2×D1212yes—
240C2×C3×C4D3×D412yes—
241C2×C3×C4D3×D412yes—
242C2×C3×C4D3×D412yes—
243C2×C3×C4C2×#6712yes—
244C2×Dic3—24no—
245C2×Dic3—24no—
246C2×Dic3—24no—
247C2×Dic3—34no—
248C2×Dic3—42no—
249C2×Dic3—42no—
250C2×Dic3—42no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3—122no—
255C4×D3—632no—
256C4×D3—64no—
257C4×D3—64no—
258C4×D3—64no—
259C4×D3—64no—
260C4×D3—124no—
261C4×D3—122no—
262C4×D3—122no—
263Dic6—24no—
264Dic6—24no—
265Dic6—24no—
266Dic6—632no—
267Dic6(C2×D3)⋊C418yescomplemented
268C3×C8—42no—
269C3×C8—42no—
270C3⋊C8—122no—
271C3⋊C8—122no—
272C2×C32#37911yescharacteristic
273C2×C32C2×#10311yescharacteristic
274C2×C32#41911yescharacteristic
275C2×C32#44812yes—
276C2×C32#45112yes—
277C3⋊D3—24no—
278C24—91no—
279C2×Q8—34no—
280C2×Q8—34no—
281C2×Q8—34no—
282C2×Q8—62no—
283C2×Q8—62no—
284C2×Q8—62no—
285C2×Q8—184no—
286C2×Q8—188no—
287C2×Q8—1816no—
288C2×Q8—188no—
289C2×Q8—188no—
290C22×C4—62no—
291C22×C4—62no—
292C22×C4—91no—
293C22×C4—92no—
294C22×C4—92no—
295C22×C4—184no—
296C22×C4—188no—
297C22×C4—182no—
298C22×C4—182no—
299C22×C4C2×D3211yescharacteristic
300C2×C8—22no—
301C2×C8—21no—
302C2×C8—182no—
303C2×C8—181no—
304C4⋊C4—62no—
305C4⋊C4—62no—
306C22⋊C4—362no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—22no—
310C22×C3—21no—
311C22×C3—22no—
312C22×C3D3×C22⋊C412yes—
313C22×C3#88212yes—
314C22×C3D3×SD1612yes—
315C22×C3#91512yes—
316C22×C3D3×Q1612yes—
317C22×C3#91812yes—
318C22×C3#93712yes—
319C2×D3—38no—
320C2×D3—64no—
321C2×D3—64no—
322C2×D3—64no—
323C2×D3—64no—
324C2×D3—64no—
325C2×D3—64no—
326C2×D3—64no—
327C2×D3—122no—
328C2×D3—124no—
329C2×D3—122no—
330C2×D3—124no—
331C3×C4—22no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—68no—
335C3×C4—242no—
336C3×C4D3×C22⋊C412yes—
337C3×C4#88212yes—
338C3×C4C2×(C2×D3)⋊C412yes—
339C3×C4#93712yes—
340Dic3—28no—
341Dic3—64no—
342Dic3—82no—
343Dic3—122no—
344C32#178711yescharacteristic, complemented, Sylow
345C23—92no—
346C23—92no—
347C23—92no—
348C23—182no—
349C23—182no—
350C23#380211yescharacteristic
351Q8—38no—
352Q8—64no—
353Q8—64no—
354Q8—64no—
355Q8—1816no—
356C2×C4—64no—
357C2×C4—64no—
358C2×C4—64no—
359C2×C4—92no—
360C2×C4—122no—
361C2×C4—122no—
362C2×C4—122no—
363C2×C4—1816no—
364C2×C4—182no—
365C2×C4—184no—
366C2×C4—182no—
367C2×C4—182no—
368C2×C4C4×D3211yescharacteristic
369C2×C4D3×D1212yes—
370C2×C4D3×#6712yes—
371C2×C4#381111yescharacteristic
372C8—41no—
373C8—361no—
374C2×C3—22no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—22no—
379C2×C3D3×#10312yes—
380C2×C3#480212yes—
381C2×C3#480612yes—
382C2×C3#480912yes—
383C2×C3#495512yes—
384C2×C3#517012yes—
385C2×C3#518612yes—
386D3—68no—
387D3—124no—
388C22—94no—
389C22—184no—
390C22—182no—
391C22—182no—
392C22—184no—
393C22#6379611yescharacteristic
394C22#6380211yescharacteristic
395C22#6381112yes—
396C22#6392111yescharacteristic
397C22#6392212yes—
398C4—68no—
399C4—182no—
400C4—242no—
401C4D3×(C2×D3)⋊C412yes—
402C4#6392311yescharacteristic
403C4#6398311yescharacteristic
404C3—21no—
405C3#7026612yescomplemented
406C2—184no—
407C2#1059067211yescharacteristic
408C2#1059069111yescharacteristic
409C2#1059082412yes—
410C2#1059095012yes—
411C2#1059139911yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1787
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#816C2semidirect
5. C2×#63565C2semidirect
14. C2×#3797C4semidirect
28. C2×#816D3semidirect
111. C3×Dic6C22⋊C4semidirect
187. C2×C3⋊D3#103semidirect
267. Dic6(C2×D3)⋊C4semidirect
344. C32#1787semidirect
405. C3#70266semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
C2×#636472
C2×C3×#8162
#105913252
C2×#635652
#702663