Finite Group Databasebeta

← #11808368

Subgroups — #11808368

Order 1152.

2088 conjugacy classes of subgroups.

The subgroup lattice has 447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×D4×C3⋊Dic3C212yesmaximal, complemented
3C2×#64086C211yesmaximal, characteristic, complemented
4C32×#392C211yesmaximal, characteristic
5#10592921C212yesmaximal, complemented
6#10592921C211yesmaximal, characteristic, complemented
7#10592652C211yesmaximal, characteristic, complemented
8#10592647C212yesmaximal, complemented
9C22⋊C4×C3⋊Dic3C212yesmaximal, complemented
10#10592360C211yesmaximal, characteristic, complemented
11#10592348C211yesmaximal, characteristic, complemented
12#76666—34nomaximal
13C22×C32×D4C2212yes—
14C22×C32×D4C2211yescharacteristic
15C23×C3⋊Dic3C2212yes—
16C23×C3⋊Dic3C2211yescharacteristic
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×C32×C22⋊C4C2212yes—
19C2×#3757C2211yescharacteristic
20C2×#3757C2212yes—
21C2×#3757C2212yes—
22C2×#3757C2212yes—
23C2×#3757C2212yes—
24D4×C3⋊Dic3—28no—
25D4×C3⋊Dic3—24no—
26C2×C4⋊(C3⋊Dic3)C2212yes—
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×#3750C2212yes—
29C2×#3750C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×C4×C3⋊Dic3C2212yes—
32C2×C4×C3⋊Dic3C2211yescharacteristic
33C2×C4×C3⋊Dic3C2211yescharacteristic
34#64086—24no—
35C32×#95C2211yescharacteristic
36#63658C2211yescharacteristic
37#63658C2212yes—
38#63658C2212yes—
39C2×D4×Dic3—34no—
40C2×D4×Dic3—38no—
41C2×#877—34no—
42C3×#392D314yes—
43#5222—34no—
44#5222—38no—
45#4953—34no—
46#4948—38no—
47Dic3×C22⋊C4—38no—
48#4661—34no—
49#4649—34no—
50C24×C32C2311yescharacteristic
51C24×C32C2312yes—
52C2×C32×D4—24no—
53C2×C32×D4—24no—
54C2×C32×D4—24no—
55C2×C32×D4—22no—
56C2×C32×D4—24no—
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2312yes—
60C22×C3⋊Dic3—22no—
61C22×C3⋊Dic3—22no—
62C22×C3⋊Dic3—24no—
63C22×C3⋊Dic3—24no—
64C22×C3⋊Dic3—24no—
65C22×C3⋊Dic3D414yescomplemented
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C32×C22⋊C4—22no—
73C32×C22⋊C4—24no—
74#3757—24no—
75#3757—24no—
76#3757—22no—
77#3757—24no—
78#3757—24no—
79C4⋊(C3⋊Dic3)—22no—
80C4⋊(C3⋊Dic3)—24no—
81#3750—22no—
82#3750—24no—
83#3750—22no—
84C4×C3⋊Dic3—22no—
85C4×C3⋊Dic3—24no—
86C4×C3⋊Dic3D414yescomplemented
87#2392—91noSylow
88C22×C3×D4C2×D314yes—
89C22×C3×D4C2×D318yes—
90C23×Dic3—34no—
91C23×Dic3—38no—
92C2×C3×C22⋊C4C2×D318yes—
93C2×C3×C22⋊C4C2×D314yes—
94C2×#217—38no—
95C2×#217—38no—
96C2×#217—38no—
97C2×#217—38no—
98C2×#217—34no—
99D4×Dic3—616no—
100D4×Dic3—632no—
101C2×C4⋊Dic3—38no—
102C2×C4⋊Dic3—34no—
103C2×Dic3⋊C4—38no—
104C2×Dic3⋊C4—34no—
105C2×Dic3⋊C4—34no—
106C2×C4×Dic3—34no—
107C2×C4×Dic3—38no—
108C2×C4×Dic3—34no—
109#877—616no—
110C3×#95C2×D314yes—
111C3⋊#95—34no—
112C3⋊#95—38no—
113C3⋊#95—38no—
114C23×C32—21no—
115C23×C32—22no—
116C23×C32—22no—
117C23×C32—22no—
118C23×C32—21no—
119C23×C32—22no—
120C23×C32—22no—
121C23×C32—22no—
122C23×C32—22no—
123C23×C32—22no—
124C23×C32C2×D412yes—
125C23×C32#4114yes—
126C23×C32C2411yescharacteristic
127C32×D4—28no—
128C32×D4—216no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4—21no—
133C2×C32×C4—22no—
134C2×C32×C4C2×D412yes—
135C2×C32×C4#4114yes—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—28no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—48no—
149C2×C3⋊Dic3C2×D412yes—
150C2×C3⋊Dic3C2×D412yes—
151C2×C3⋊Dic3C2×D412yes—
152C2×C3⋊Dic3C2×D412yes—
153C2×C3⋊Dic3#4112yes—
154C2×C4×D4—91no—
155C2×C4×D4—92no—
156C2×#117—91no—
157#398—91no—
158#397—91no—
159#396—92no—
160#394—92no—
161#394—91no—
162#392C3⋊D311yescharacteristic
163C4×C4⋊C4—91no—
164C4×C22⋊C4—92no—
165C24×C3C22×D314yes—
166C24×C3C22×D318yes—
167C2×C3×D4—216no—
168C2×C3×D4—216no—
169C2×C3×D4—216no—
170C2×C3×D4—28no—
171C2×C3×D4—216no—
172C22×C3×C4C22×D314yes—
173C22×C3×C4C22×D314yes—
174C22×C3×C4C22×D318yes—
175C22×Dic3—34no—
176C22×Dic3—316no—
177C22×Dic3—34no—
178C22×Dic3—34no—
179C22×Dic3—34no—
180C22×Dic3—38no—
181C22×Dic3—38no—
182C22×Dic3—68no—
183C22×Dic3—68no—
184C22×Dic3—616no—
185C22×Dic3—616no—
186C22×Dic3—616no—
187C3×C22⋊C4—28no—
188C3×C22⋊C4—216no—
189#217—68no—
190#217—616no—
191#217—616no—
192#217—616no—
193#217—616no—
194C4⋊Dic3—616no—
195C4⋊Dic3—68no—
196Dic3⋊C4—68no—
197Dic3⋊C4—68no—
198Dic3⋊C4—616no—
199C4×Dic3—316no—
200C4×Dic3—68no—
201C4×Dic3—616no—
202C22×C32—22no—
203C22×C32—24no—
204C22×C32—24no—
205C22×C32—24no—
206C22×C32—24no—
207C22×C32—42no—
208C22×C32—41no—
209C22×C32—42no—
210C22×C32—42no—
211C22×C32—42no—
212C22×C32—41no—
213C22×C32—42no—
214C22×C32C22×D411yescharacteristic
215C22×C32C22×D411yescharacteristic
216C22×C32C2×#4112yes—
217C22×C32C2×#4112yes—
218C22×C32C2×#4111yescharacteristic
219C32×C4—22no—
220C32×C4—24no—
221C32×C4—41no—
222C3⋊Dic3—22no—
223C3⋊Dic3—22no—
224C3⋊Dic3—42no—
225C3⋊Dic3—41no—
226C3⋊Dic3—42no—
227C3⋊Dic3#12114yes—
228C22×D4C2×C3⋊D311yescharacteristic
229C22×D4C2×C3⋊D312yes—
230C23×C4—91no—
231C23×C4—92no—
232C4×D4—184no—
233C4×D4—188no—
234#117—184no—
235C2×C4⋊C4—91no—
236C2×C4⋊C4—91no—
237C2×C4⋊C4—92no—
238C2×C4⋊C4—91no—
239C2×C4⋊C4—92no—
240C2×C22⋊C4—91no—
241C2×C22⋊C4—92no—
242C2×C22⋊C4—92no—
243C2×C22⋊C4—92no—
244C2×C22⋊C4—92no—
245C2×C22⋊C4C2×C3⋊D311yescharacteristic
246C2×C22⋊C4C2×C3⋊D312yes—
247C2×C42—91no—
248C2×C42—91no—
249C2×C42—92no—
250#95—92no—
251#95—92no—
252#95—91no—
253#95C2×C3⋊D311yescharacteristic
254C23×C3—24no—
255C23×C3—28no—
256C23×C3—28no—
257C23×C3—28no—
258C23×C3—28no—
259C23×C3—28no—
260C23×C3—28no—
261C23×C3—28no—
262C23×C3—28no—
263C23×C3—24no—
264C23×C3D3×D418yes—
265C23×C3#237116yes—
266C23×C3C23×D314yes—
267C3×D4—232no—
268C3×D4—264no—
269C2×C3×C4—28no—
270C2×C3×C4—28no—
271C2×C3×C4—28no—
272C2×C3×C4—24no—
273C2×C3×C4—28no—
274C2×C3×C4D3×D418yes—
275C2×C3×C4#237116yes—
276C2×Dic3—38no—
277C2×Dic3—38no—
278C2×Dic3—38no—
279C2×Dic3—38no—
280C2×Dic3—38no—
281C2×Dic3—632no—
282C2×Dic3—64no—
283C2×Dic3—68no—
284C2×Dic3—64no—
285C2×Dic3—64no—
286C2×Dic3—68no—
287C2×Dic3—68no—
288C2×Dic3—68no—
289C2×Dic3—68no—
290C2×Dic3—68no—
291C2×Dic3—68no—
292C2×Dic3—68no—
293C2×Dic3—1232no—
294C2×C32—42no—
295C2×C32—44no—
296C2×C32C2×#12111yescharacteristic
297C2×C32#52511yescharacteristic
298C2×C32#52512yes—
299C2×C32#52912yes—
300C2×C32#53211yescharacteristic
301C24C22×C3⋊D311yescharacteristic
302C24C22×C3⋊D312yes—
303C2×D4—24no—
304C2×D4—24no—
305C2×D4—24no—
306C2×D4—22no—
307C2×D4—24no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4—94no—
312C22×C4—92no—
313C22×C4—91no—
314C22×C4—92no—
315C22×C4—182no—
316C22×C4—182no—
317C22×C4—184no—
318C22×C4—184no—
319C22×C4—184no—
320C22×C4C22×C3⋊D311yescharacteristic
321C22×C4C22×C3⋊D311yescharacteristic
322C22×C4C22×C3⋊D312yes—
323C4⋊C4—182no—
324C4⋊C4—184no—
325C4⋊C4—182no—
326C4⋊C4—182no—
327C4⋊C4—184no—
328C22⋊C4—22no—
329C22⋊C4—24no—
330C22⋊C4—182no—
331C22⋊C4—184no—
332C22⋊C4—184no—
333C22⋊C4—184no—
334C22⋊C4—184no—
335C42—94no—
336C42—182no—
337C42—184no—
338C22×C3—216no—
339C22×C3—216no—
340C22×C3—216no—
341C22×C3—216no—
342C22×C3—28no—
343C22×C3—44no—
344C22×C3—48no—
345C22×C3—44no—
346C22×C3—48no—
347C22×C3—48no—
348C22×C3—48no—
349C22×C3—48no—
350C22×C3C2×D3×D414yes—
351C22×C3C2×D3×D414yes—
352C22×C3C2×#23718yes—
353C22×C3C2×#23718yes—
354C22×C3D3×#4114yes—
355C3×C4—28no—
356C3×C4—216no—
357C3×C4—44no—
358Dic3—316no—
359Dic3—68no—
360Dic3—68no—
361Dic3—124no—
362Dic3—128no—
363Dic3—128no—
364C32#239211yescharacteristic, complemented, Sylow
365C23—21no—
366C23—22no—
367C23—22no—
368C23—22no—
369C23—22no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—21no—
375C23D4×C3⋊D312yes—
376C23#383014yes—
377C23C23×C3⋊D311yescharacteristic
378D4—28no—
379D4—216no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—92no—
386C2×C4—92no—
387C2×C4—92no—
388C2×C4—92no—
389C2×C4—92no—
390C2×C4—188no—
391C2×C4—181no—
392C2×C4—182no—
393C2×C4—181no—
394C2×C4—182no—
395C2×C4—181no—
396C2×C4—182no—
397C2×C4—182no—
398C2×C4—182no—
399C2×C4—182no—
400C2×C4—182no—
401C2×C4—182no—
402C2×C4—368no—
403C2×C4D4×C3⋊D312yes—
404C2×C4#383014yes—
405C2×C3—48no—
406C2×C3—416no—
407C2×C3#558614yes—
408C2×C3#558618yes—
409C2×C3#560018yes—
410C2×C3D3×#12114yes—
411C2×C3#571614yes—
412C22—24no—
413C22—24no—
414C22—24no—
415C22—24no—
416C22—22no—
417C22—41no—
418C22—42no—
419C22—41no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22C2×D4×C3⋊D311yescharacteristic
425C22C2×D4×C3⋊D311yescharacteristic
426C22C2×#383012yes—
427C22C2×#383012yes—
428C22#41×C3⋊D311yescharacteristic
429C4—22no—
430C4—24no—
431C4—41no—
432C4—94no—
433C4—182no—
434C4—182no—
435C4—362no—
436C4—361no—
437C4—362no—
438C3#7666614yescomplemented
439C2—42no—
440C2—44no—
441C2#1059605711yescharacteristic
442C2#1059605712yes—
443C2#1059607112yes—
444C2C3⋊D3×#12111yescharacteristic
445C2#1059618711yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
Fitting, prime radicalC32×#392C2
hypercenter#392C3⋊D3
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
2. C2×D4×C3⋊Dic3C2semidirect
3. C2×#64086C2semidirect
5. #10592921C2semidirect
6. #10592921C2semidirect
7. #10592652C2semidirect
8. #10592647C2semidirect
9. C22⋊C4×C3⋊Dic3C2semidirect
10. #10592360C2semidirect
11. #10592348C2semidirect
65. C22×C3⋊Dic3D4semidirect
86. C4×C3⋊Dic3D4semidirect
364. C32#2392semidirect
438. C3#76666semidirect

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×#640862
C32×#3922
#105929212
#105926522
#105926472
C22⋊C4×C3⋊Dic32
#105923602
#105923482
#766663