Finite Group Databasebeta

← #11807124

Subgroups — #11807124

Order 1152.

1085 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63840C211yesmaximal, characteristic
2#10592628C211yesmaximal, characteristic
3C3×C4×Dic3⋊C4C212yesmaximal
4#10591327C212yesmaximal
5#10591273C211yesmaximal, characteristic
6#10591268C212yesmaximal
7Dic3×Dic3⋊C4C212yesmaximal
8Dic3×Dic3⋊C4C212yesmaximal
9#10591191C212yesmaximal
10#73657—32nomaximal
11C22×#634C2211yescharacteristic
12C22×#627C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×Dic3⋊C4C2212yes—
16C2×C3×Dic3⋊C4C2212yes—
17C2×C3×C4×Dic3C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×#3724C2211yescharacteristic
20C2×Dic3⋊Dic3C2212yes—
21C2×Dic3⋊Dic3C2212yes—
22C2×Dic3⋊Dic3C2212yes—
23C2×Dic32C2212yes—
24C2×Dic32C2211yescharacteristic
25C2×Dic32C2211yescharacteristic
26#63840C418yescomplemented
27#63658C2212yes—
28#63658C2212yes—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33C2×#888—32no—
34C3×C4×C4⋊C4—32no—
35#4984—32no—
36Dic3×C4⋊C4—32no—
37Dic3×C4⋊C4—32no—
38C4×Dic3⋊C4—32no—
39C4×Dic3⋊C4—32no—
40C4×Dic3⋊C4D312yes—
41#4929—32no—
42#4929—32no—
43#4929—61no—
44#4928—32no—
45#4647—32no—
46#4647—32no—
47#4646—32no—
48#4646—32no—
49C22×C32×C4C2311yescharacteristic
50C22×C32×C4C2312yes—
51C22×C3⋊Dic3C2312yes—
52C22×C3⋊Dic3C2311yescharacteristic
53C22×C3⋊Dic3C2311yescharacteristic
54C2×#634—41no—
55C2×#634—41no—
56C2×#634C2×C414yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C2×#627—41no—
62C2×#627—41no—
63C2×#627C2×C414yes—
64C32×C42—41no—
65C4⋊(C3⋊Dic3)—41no—
66C3×Dic3⋊C4C2×C418yes—
67C3×Dic3⋊C4Q818yescomplemented
68C3×C4×Dic3—24no—
69C3×C4×Dic3—42no—
70#3724—41no—
71Dic3⋊Dic3—24no—
72Dic3⋊Dic3—42no—
73Dic3⋊Dic3C2×C418yes—
74Dic32—24no—
75Dic32—41no—
76Dic32C2×C414yes—
77#2369—91noSylow
78C22×Dic6—32no—
79C22×Dic6—32no—
80C22×Dic6—61no—
81C2×C3×C4⋊C4—32no—
82C2×C3×C4⋊C4—32no—
83C2×C3×C42—21no—
84C2×C3×C42—32no—
85C2×C3×C42—32no—
86C2×C3×C42C2×D312yes—
87C2×C4⋊Dic3—32no—
88C2×C4⋊Dic3—32no—
89C2×C4⋊Dic3—32no—
90C2×C4⋊Dic3—32no—
91C2×C4⋊Dic3—61no—
92C2×Dic3⋊C4—32no—
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—32no—
96C2×Dic3⋊C4C2×D312yes—
97C2×Dic3⋊C4C2×D312yes—
98C2×C4×Dic3—32no—
99C2×C4×Dic3—32no—
100C2×C4×Dic3—32no—
101C2×C4×Dic3—32no—
102C2×C4×Dic3C2×D312yes—
103C2×C4×Dic3C2×D312yes—
104#888—316no—
105C3×#95—32no—
106C3×#95—32no—
107C3⋊#95—32no—
108C3⋊#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C3⋊#95—32no—
114C3⋊#95—32no—
115C3⋊#95—62no—
116C3⋊#95—62no—
117C3⋊#95C2×D312yes—
118C3⋊#95C2×D312yes—
119C23×C32C2411yescharacteristic
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4C22×C412yes—
125C2×C32×C4C2×Q814yes—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3C22×C412yes—
134C2×C3⋊Dic3C22×C412yes—
135#634—44no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3C22×C414yes—
144C2×C3×Dic3C22×C414yes—
145C2×C3×Dic3C2×Q814yes—
146C2×C3×Dic3C2×Q814yes—
147C2×C3×Dic3#4114yes—
148#627—44no—
149C2×C4⋊Q8—91no—
150#391—91no—
151#391—92no—
152#391—91no—
153#389—92no—
154#389—92no—
155C4×C4⋊C4—32no—
156C4×C4⋊C4—92no—
157C4×C4⋊C4—92no—
158C22×C3×C4—21no—
159C22×C3×C4—22no—
160C22×C3×C4—32no—
161C22×C3×C4—32no—
162C22×C3×C4—32no—
163C22×C3×C4—32no—
164C22×C3×C4C22×D312yes—
165C22×C3×C4C22×D312yes—
166C22×C3×C4C22×D312yes—
167C22×Dic3—32no—
168C22×Dic3—32no—
169C22×Dic3—32no—
170C22×Dic3—32no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C22×Dic3—62no—
174C22×Dic3C22×D312yes—
175C22×Dic3C22×D312yes—
176C22×Dic3C22×D312yes—
177C22×Dic3C22×D312yes—
178C2×Dic6—38no—
179C2×Dic6—38no—
180C2×Dic6—64no—
181C2×Dic6—122no—
182C2×Dic6—122no—
183C2×Dic6—122no—
184C2×Dic6—122no—
185C2×Dic6—122no—
186C2×Dic6—122no—
187C3×C4⋊C4—38no—
188C3×C4⋊C4—38no—
189C3×C42—42no—
190C3×C42—42no—
191C3×C42—64no—
192C3×C42—122no—
193C4⋊Dic3—38no—
194C4⋊Dic3—64no—
195C4⋊Dic3—122no—
196C4⋊Dic3—122no—
197C4⋊Dic3—122no—
198Dic3⋊C4—38no—
199Dic3⋊C4—64no—
200Dic3⋊C4—122no—
201Dic3⋊C4—122no—
202Dic3⋊C4Dic618yescomplemented
203Dic3⋊C4C4×D318yes—
204C4×Dic3—24no—
205C4×Dic3—38no—
206C4×Dic3—42no—
207C4×Dic3—64no—
208C4×Dic3—64no—
209C4×Dic3—122no—
210C22×C32C23×C411yescharacteristic
211C22×C32C22×Q812yes—
212C22×C32C2×#4112yes—
213C22×C32H(5,𝔽2)11yescharacteristic
214C22×C32H(5,𝔽2)11yescharacteristic
215C32×C4—22no—
216C32×C4—24no—
217C3⋊Dic3—22no—
218C3⋊Dic3—22no—
219C3⋊Dic3—42no—
220C3×Dic3—24no—
221C3×Dic3—24no—
222C3×Dic3—42no—
223C3×Dic3C4×Q818yes—
224C22×Q8—91no—
225C22×Q8—91no—
226C4⋊Q8—98no—
227C2×C4⋊C4—32no—
228C2×C4⋊C4—32no—
229C2×C4⋊C4—92no—
230C2×C4⋊C4—92no—
231C2×C4⋊C4—91no—
232C2×C4⋊C4—92no—
233C2×C4⋊C4—91no—
234C2×C42—32no—
235C2×C42—32no—
236C2×C42—91no—
237C2×C42—92no—
238C2×C42—91no—
239C2×C42D3211yescharacteristic
240#95—32no—
241#95—32no—
242#95—92no—
243#95—92no—
244#95—92no—
245#95—92no—
246C23×C3—21no—
247C23×C3C23×D312yes—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—24no—
257C2×C3×C4—22no—
258C2×C3×C4—34no—
259C2×C3×C4—34no—
260C2×C3×C4—34no—
261C2×C3×C4—34no—
262C2×C3×C4—34no—
263C2×C3×C4—42no—
264C2×C3×C4—42no—
265C2×C3×C4—62no—
266C2×C3×C4—62no—
267C2×C3×C4—62no—
268C2×C3×C4—62no—
269C2×C3×C4—62no—
270C2×C3×C4—62no—
271C2×C3×C4—62no—
272C2×C3×C4C2×Dic614yes—
273C2×C3×C4C2×C4×D314yes—
274C2×C3×C4D3×Q814yes—
275C2×Dic3—22no—
276C2×Dic3—22no—
277C2×Dic3—22no—
278C2×Dic3—22no—
279C2×Dic3—22no—
280C2×Dic3—22no—
281C2×Dic3—22no—
282C2×Dic3—34no—
283C2×Dic3—34no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—62no—
295C2×Dic3—62no—
296C2×Dic3—121no—
297C2×Dic3—121no—
298C2×Dic3—121no—
299C2×Dic3—121no—
300C2×Dic3—122no—
301C2×Dic3—122no—
302C2×Dic3—122no—
303C2×Dic3C2×Dic614yes—
304C2×Dic3C2×Dic614yes—
305C2×Dic3C2×C4×D314yes—
306C2×Dic3C2×C4×D314yes—
307C2×Dic3#23514yes—
308Dic6—128no—
309Dic6—128no—
310Dic6—128no—
311C2×C32C2×C4×Q812yes—
312C2×C32#51811yescharacteristic
313C2×C32#55412yes—
314C2×C32#55511yescharacteristic
315C2×C32Q8211yescharacteristic
316C2×Q8—94no—
317C2×Q8—94no—
318C2×Q8—361no—
319C2×Q8—361no—
320C2×Q8—361no—
321C2×Q8—361no—
322C22×C4—32no—
323C22×C4—32no—
324C22×C4—32no—
325C22×C4—32no—
326C22×C4—91no—
327C22×C4—91no—
328C22×C4—92no—
329C22×C4C2×D3212yes—
330C22×C4C2×D3211yescharacteristic
331C4⋊C4—38no—
332C4⋊C4—38no—
333C4⋊C4—98no—
334C4⋊C4—184no—
335C4⋊C4—361no—
336C4⋊C4—361no—
337C4⋊C4—362no—
338C42—41no—
339C42—64no—
340C42—94no—
341C42—122no—
342C42—184no—
343C42—361no—
344C22×C3—22no—
345C22×C3—21no—
346C22×C3—22no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3C22×Dic612yes—
350C22×C3C22×C4×D312yes—
351C22×C3C2×#23512yes—
352C22×C3#100412yes—
353C22×C3C2×D3×Q812yes—
354C22×C3D3×#4112yes—
355C22×C3#100912yes—
356C3×C4—24no—
357C3×C4—24no—
358C3×C4—24no—
359C3×C4—24no—
360C3×C4—38no—
361C3×C4—44no—
362C3×C4—64no—
363C3×C4—64no—
364C3×C4—122no—
365Dic3—24no—
366Dic3—24no—
367Dic3—42no—
368Dic3—64no—
369Dic3—64no—
370Dic3—122no—
371Dic3—122no—
372Dic3—122no—
373Dic3—122no—
374Dic3—242no—
375Dic3C4×Dic618yes—
376C32#236911yescharacteristic, complemented, Sylow
377C23C22×D3211yescharacteristic
378Q8—364no—
379Q8—364no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—21no—
384C2×C4—34no—
385C2×C4—34no—
386C2×C4—34no—
387C2×C4—34no—
388C2×C4—34no—
389C2×C4—62no—
390C2×C4—62no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—62no—
394C2×C4—62no—
395C2×C4—62no—
396C2×C4—92no—
397C2×C4—92no—
398C2×C4—181no—
399C2×C4—181no—
400C2×C4—181no—
401C2×C4—181no—
402C2×C4—182no—
403C2×C4—182no—
404C2×C4—182no—
405C2×C4D3×Dic614yes—
406C2×C4C4×D3212yes—
407C2×C3—21no—
408C2×C3—22no—
409C2×C3—22no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3C2×C4×Dic612yes—
413C2×C3#551112yes—
414C2×C3#553212yes—
415C2×C3#553912yes—
416C2×C3#554512yes—
417C2×C3Q8×Dic612yes—
418C2×C3C4×D3×Q812yes—
419C22C2×D3×Dic612yes—
420C22C2×C4×D3211yescharacteristic
421C22D3×#23512yes—
422C22#6430811yescharacteristic
423C22#6433011yescharacteristic
424C4—24no—
425C4—22no—
426C4—38no—
427C4—64no—
428C4—64no—
429C4—122no—
430C4—182no—
431C4—182no—
432C4—362no—
433C3—21no—
434C3#7365712yescomplemented
435C2Dic6211yescharacteristic
436C2C4×D3×Dic612yes—
437C2#1059397711yescharacteristic
438C2#1059495112yes—
439C2#1059505811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2369
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
26. #63840C4semidirect
67. C3×Dic3⋊C4Q8semidirect
202. Dic3⋊C4Dic6semidirect
376. C32#2369semidirect
434. C3#73657semidirect

Maximal subgroups

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

subgroupindex
C2×#638402
#105926282
C3×C4×Dic3⋊C42
#105913272
#105912732
#105912682
Dic3×Dic3⋊C42
#105911912
#736573