Finite Group Databasebeta

← #11785183

Subgroups — #11785183

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#832C212yesmaximal
3#10591359C211yesmaximal, characteristic, complemented
4C2×#63572C211yesmaximal, characteristic, complemented
5#10589164C212yesmaximal, complemented
6#70153—32nomaximal
7C22×C32×D4C2211yescharacteristic
8C23×C3⋊Dic3—21no—
9C2×#3757—21no—
10D4×C3⋊Dic3—22no—
11D4×C3⋊Dic3C414yescomplemented
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×#3724—21no—
17C2×#3724—21no—
18C3×#832—24no—
19#63572—22no—
20C2×D4×Dic3—32no—
21C2×D4×Dic3—61no—
22C2×C3×#102—32no—
23C2×#832D312yes—
24C2×Dic3⋊C8—32no—
25#4975—32no—
26#4551—32no—
27#4529—32no—
28C24×C32—21no—
29C2×C32×D4—21no—
30C2×C32×D4—21no—
31C2×C32×D4—21no—
32C2×C32×D4C2×C412yes—
33C2×C32×D4D412yes—
34C2×C32×D4Q812yes—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—24no—
38C22×C3⋊Dic3—42no—
39C22×C3⋊Dic3—42no—
40C22×C3⋊Dic3D411yescharacteristic
41C22×C3⋊Dic3D411yescharacteristic
42C22×C3×Dic3—22no—
43#3757—24no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)C2×C412yes—
46C4×C3⋊Dic3C2×C412yes—
47C4×C3⋊Dic3D412yes—
48C3×C4⋊Dic3—22no—
49C3×C4⋊Dic3—22no—
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8—22no—
53#3724—42no—
54#3724—42no—
55#1802—91noSylow
56C22×C3×D4—21no—
57C22×C3×D4C2×D312yes—
58C23×Dic3—62no—
59C23×Dic3—62no—
60C22×C3×C8—32no—
61C2×C3×C4⋊C4—32no—
62C2×#217—62no—
63C2×#217—62no—
64D4×Dic3—38no—
65D4×Dic3—64no—
66D4×Dic3—64no—
67D4×Dic3—64no—
68C2×C4⋊Dic3—32no—
69C2×C4⋊Dic3—61no—
70C2×C4⋊Dic3C2×D312yes—
71C2×Dic3⋊C4—62no—
72C2×Dic3⋊C4—62no—
73C2×C4×Dic3—32no—
74C2×C4×Dic3—61no—
75C22×C3⋊C8C2×D312yes—
76C3×#102—64no—
77#832—24no—
78Dic3⋊C8—64no—
79C23×C32—22no—
80C23×C32—22no—
81C23×C32—22no—
82C23×C32—41no—
83C23×C32—41no—
84C23×C32—41no—
85C23×C32—41no—
86C23×C32C2×D411yescharacteristic
87C32×D4—22no—
88C32×D4—22no—
89C32×D4—22no—
90C32×D4C4⋊C414yescomplemented
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×Q811yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—48no—
103C2×C3⋊Dic3C22⋊C412yes—
104C2×C3⋊Dic3C22⋊C412yes—
105C2×C3⋊Dic3D812yes—
106C2×C3⋊Dic3SD1612yes—
107C2×C3×Dic3—42no—
108C2×C3×Dic3—42no—
109C2×C3×Dic3—42no—
110C3×C3⋊C8—42no—
111C2×C4×D4—91no—
112C2×C4⋊C8—91no—
113C2×#102—32no—
114#384—91no—
115#340—92no—
116C24×C3—22no—
117C24×C3—22no—
118C2×C3×D4—22no—
119C2×C3×D4—22no—
120C2×C3×D4—22no—
121C2×C3×D4—22no—
122C2×C3×D4—22no—
123C2×C3×D4—22no—
124C2×C3×D4—22no—
125C2×C3×D4—22no—
126C2×C3×D4—22no—
127C2×C3×D4Dic614yes—
128C2×C3×D4C4×D314yes—
129C2×C3×D4#6714yes—
130C22×C3×C4—21no—
131C22×C3×C4—62no—
132C22×C3×C4C22×D312yes—
133C22×Dic3—22no—
134C22×Dic3—32no—
135C22×Dic3—32no—
136C22×Dic3—61no—
137C22×Dic3—61no—
138C22×Dic3—68no—
139C22×Dic3—62no—
140C22×Dic3—68no—
141C22×Dic3—62no—
142C22×Dic3—124no—
143C22×Dic3—124no—
144C22×Dic3—124no—
145C22×Dic3—124no—
146C2×C3×C8—62no—
147C2×C3×C8—62no—
148C2×C3×C8—62no—
149C3×C4⋊C4—62no—
150C3×C4⋊C4—62no—
151#217—68no—
152#217—68no—
153C4⋊Dic3—22no—
154C4⋊Dic3—22no—
155C4⋊Dic3—34no—
156C4⋊Dic3—62no—
157C4⋊Dic3—62no—
158C4⋊Dic3—62no—
159Dic3⋊C4—124no—
160Dic3⋊C4—124no—
161C4×Dic3—34no—
162C4×Dic3—34no—
163C4×Dic3—62no—
164C4×Dic3—62no—
165C2×C3⋊C8—22no—
166C2×C3⋊C8—22no—
167C2×C3⋊C8—22no—
168C22×C32—24no—
169C22×C32—42no—
170C22×C32—42no—
171C22×C32—42no—
172C22×C32—42no—
173C22×C32—42no—
174C22×C32—42no—
175C22×C32C2×C22⋊C411yescharacteristic
176C22×C32#12111yescharacteristic
177C22×C32C22⋊Q811yescharacteristic
178C22×C32C2×D811yescharacteristic
179C22×C32C2×SD1611yescharacteristic
180C22×C32AGL(1,ℤ/8)11yescharacteristic
181C22×C32#13711yescharacteristic
182C32×C4C2×C4⋊C411yescharacteristic
183C32×C4#11711yescharacteristic
184C32×C4#12111yescharacteristic
185C32×C4C22⋊Q811yescharacteristic
186C3⋊Dic3—22no—
187C3⋊Dic3—42no—
188C3⋊Dic3#10214yescomplemented
189C3×Dic3—82no—
190C22×D4D3211yescharacteristic
191C23×C4—181no—
192C22×C8—32no—
193C4×D4—94no—
194C4×D4—182no—
195C2×C4⋊C4—32no—
196C2×C4⋊C4—91no—
197C2×C4⋊C4—181no—
198C2×C4⋊C4—181no—
199C2×C22⋊C4—181no—
200C2×C42—91no—
201C4⋊C8—182no—
202#102—64no—
203C23×C3—24no—
204C23×C3—24no—
205C23×C3—24no—
206C23×C3—24no—
207C23×C3—24no—
208C23×C3—24no—
209C23×C3—21no—
210C23×C3—42no—
211C23×C3—42no—
212C23×C3—42no—
213C23×C3—42no—
214C23×C3—42no—
215C23×C3—42no—
216C23×C3—42no—
217C23×C3—42no—
218C23×C3D3×D412yes—
219C3×D4—24no—
220C3×D4—24no—
221C3×D4—24no—
222C3×D4—24no—
223C3×D4—24no—
224C3×D4—24no—
225C3×D4—24no—
226C3×D4Dic3⋊C418yescomplemented
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—122no—
234C2×C3×C4—122no—
235C2×C3×C4—122no—
236C2×C3×C4C2×Dic612yes—
237C2×C3×C4C2×C4×D312yes—
238C2×C3×C4D3×D412yes—
239C2×C3×C4#23712yes—
240C2×C3×C4#23712yes—
241C2×C3×C4C2×#6712yes—
242C2×Dic3—34no—
243C2×Dic3—34no—
244C2×Dic3—34no—
245C2×Dic3—34no—
246C2×Dic3—42no—
247C2×Dic3—42no—
248C2×Dic3—42no—
249C2×Dic3—62no—
250C2×Dic3—62no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—64no—
256C2×Dic3—64no—
257C2×Dic3—121no—
258C2×Dic3—121no—
259C2×Dic3—1216no—
260C2×Dic3—1216no—
261C2×Dic3—122no—
262C2×Dic3—122no—
263C2×Dic3—122no—
264C2×Dic3—122no—
265C3×C8—122no—
266C3⋊C8—42no—
267C2×C32—44no—
268C2×C32#38011yescharacteristic
269C2×C32C2×#10211yescharacteristic
270C2×C32#41711yescharacteristic
271C2×C32#45911yescharacteristic
272C2×C32#46111yescharacteristic
273C2×C32#47411yescharacteristic
274C2×C32#47611yescharacteristic
275C24—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4#62412yes—
280C2×D4#62512yes—
281C2×D4#62712yes—
282C22×C4—62no—
283C22×C4—91no—
284C22×C4—91no—
285C22×C4—184no—
286C22×C4—181no—
287C22×C4—362no—
288C22×C4—362no—
289C22×C4C2×D3211yescharacteristic
290C2×C8—62no—
291C2×C8—62no—
292C2×C8—62no—
293C4⋊C4—62no—
294C4⋊C4—62no—
295C4⋊C4—92no—
296C4⋊C4—181no—
297C4⋊C4—362no—
298C4⋊C4—362no—
299C22⋊C4—184no—
300C42—92no—
301C42—92no—
302C22×C3—28no—
303C22×C3—28no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—44no—
312C22×C3—44no—
313C22×C3—44no—
314C22×C3—44no—
315C22×C3—44no—
316C22×C3—44no—
317C22×C3—44no—
318C22×C3—44no—
319C22×C3—44no—
320C22×C3—44no—
321C22×C3—44no—
322C22×C3—44no—
323C22×C3#87812yes—
324C22×C3D3×C22⋊C412yes—
325C22×C3D3×D812yes—
326C22×C3#91112yes—
327C22×C3D3×SD1612yes—
328C22×C3#91512yes—
329C22×C3#93912yes—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—242no—
335C3×C4#87712yes—
336C3×C4#87812yes—
337C3×C4C2×Dic3⋊C412yes—
338C3×C4#93912yes—
339Dic3—38no—
340Dic3—64no—
341Dic3—64no—
342Dic3—82no—
343Dic3—122no—
344Dic3—124no—
345Dic3—124no—
346C32#180211yescharacteristic, complemented, Sylow
347C23—22no—
348C23—22no—
349C23—22no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23#381111yescharacteristic
355D4—22no—
356D4—22no—
357D4—22no—
358D4#372414yescomplemented
359C2×C4—92no—
360C2×C4—92no—
361C2×C4—92no—
362C2×C4—92no—
363C2×C4—122no—
364C2×C4—122no—
365C2×C4—122no—
366C2×C4—181no—
367C2×C4—181no—
368C2×C4—182no—
369C2×C4—368no—
370C2×C4—361no—
371C2×C4—361no—
372C2×C4#380511yescharacteristic
373C2×C4#380511yescharacteristic
374C2×C4C2×#62411yescharacteristic
375C2×C4C2×#62511yescharacteristic
376C2×C4C2×#62711yescharacteristic
377C2×C4#381111yescharacteristic
378C8—122no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—48no—
387C2×C3—48no—
388C2×C3#475912yes—
389C2×C3#476112yes—
390C2×C3D3×#10212yes—
391C2×C3#477112yes—
392C2×C3#494212yes—
393C2×C3#515012yes—
394C2×C3#516212yes—
395C22—24no—
396C22—42no—
397C22—42no—
398C22—42no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22#6392611yescharacteristic
403C22#6392711yescharacteristic
404C22#6393011yescharacteristic
405C22#6393111yescharacteristic
406C22#6397411yescharacteristic
407C22#6398011yescharacteristic
408C22#6398211yescharacteristic
409C4—94no—
410C4—182no—
411C4—242no—
412C4—362no—
413C4#6395711yescharacteristic
414C4C2×#372411yescharacteristic
415C4#6398011yescharacteristic
416C4#6398211yescharacteristic
417C3—21no—
418C3#7015312yescomplemented
419C2—44no—
420C2#1059141611yescharacteristic
421C2#1059141811yescharacteristic
422C2#1059148611yescharacteristic
423C2#1059149411yescharacteristic
424C2#1059149511yescharacteristic
425C2#1059149711yescharacteristic
426C2#1059172011yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1802
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. #10591359C2semidirect
4. C2×#63572C2semidirect
5. #10589164C2semidirect
11. D4×C3⋊Dic3C4semidirect
90. C32×D4C4⋊C4semidirect
188. C3⋊Dic3#102semidirect
226. C3×D4Dic3⋊C4semidirect
346. C32#1802semidirect
358. D4#3724semidirect
418. C3#70153semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#8322
#105913592
C2×#635722
#105891642
#701533