Finite Group Databasebeta

← #11805567

Subgroups — #11805567

Order 1152.

1285 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic
2C2×#63844C212yesmaximal
3C3×#4935C211yesmaximal, characteristic
4C3×C4×C4⋊Dic3C211yesmaximal, characteristic
5#10591359C212yesmaximal
6#10591274C212yesmaximal
7#10591264C214yesmaximal
8#10591212C212yesmaximal
9#74323—31nomaximal
10C4⋊C4×Dic6—31nomaximal
11C22×#634C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750C2212yes—
15C2×C4×C3⋊Dic3C2212yes—
16C4×#634C418yescomplemented
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×C4⋊Dic3C2212yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2212yes—
23C2×#3724C2214yes—
24C2×#3724C2214yes—
25C2×Dic32C2214yes—
26#63844—28no—
27C3×C3⋊#95C2212yes—
28#63579C2214yes—
29C2×#887—32no—
30C2×C4×Dic6—31no—
31C2×C4×Dic6—31no—
32C2×C4×Dic6—32no—
33C2×C4×Dic6—61no—
34C3×#384—31no—
35C3×C4×C4⋊C4—31no—
36#4976—34no—
37#4975—32no—
38#4975—32no—
39Dic3×C4⋊C4—32no—
40Dic3×C4⋊C4—32no—
41#4972—32no—
42#4935D311yescharacteristic
43C4×C4⋊Dic3D311yescharacteristic
44#4928—32no—
45#4647—34no—
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2312yes—
50C22×C3⋊Dic3C2312yes—
51C2×#634C2×C414yes—
52C2×#634D414yes—
53C2×#634Q814yes—
54C22×C3×Dic3C2312yes—
55C22×C3×Dic3C2314yes—
56C22×C3×Dic3C2312yes—
57C32×C42C2×C414yes—
58C4⋊(C3⋊Dic3)C2×C414yes—
59#3750C2×C418yes—
60C4×C3⋊Dic3C2×C418yes—
61C3×C4⋊Dic3—24no—
62C3×C4⋊Dic3—22no—
63C3×C4⋊Dic3—24no—
64C3×C4⋊Dic3—42no—
65C3×C4⋊Dic3Q814yescomplemented
66C3×C4×Dic3—24no—
67#3724—28no—
68#3724—44no—
69Dic32—28no—
70Q8×C4⋊C4—91noSylow
71C22×Dic6—31no—
72C22×Dic6—31no—
73C22×Dic6—61no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4—32no—
76C2×C3×C4⋊C4—32no—
77C2×C3×C4⋊C4—31no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C42—21no—
80C2×C3×C42—32no—
81C2×C3×C42C2×D311yescharacteristic
82C2×C3×C42C2×D311yescharacteristic
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—61no—
86C2×C4⋊Dic3C2×D312yes—
87C2×C4⋊Dic3C2×D311yescharacteristic
88C2×C4⋊Dic3C2×D312yes—
89C2×C4⋊Dic3C2×D312yes—
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4—32no—
93C2×Dic3⋊C4—34no—
94C2×Dic3⋊C4—34no—
95C2×Dic3⋊C4—34no—
96C2×Dic3⋊C4—34no—
97C2×Dic3⋊C4—62no—
98C2×C4×Dic3—32no—
99C2×C4×Dic3—32no—
100C2×C4×Dic3—34no—
101C2×C4×Dic3—34no—
102C2×C4×Dic3—62no—
103C2×C4×Dic3C2×D312yes—
104#887—68no—
105C4×Dic6—38no—
106C4×Dic6—38no—
107C4×Dic6—68no—
108C4×Dic6—68no—
109C3×#95—32no—
110C3⋊#95—34no—
111C3⋊#95—34no—
112C3⋊#95C2×D312yes—
113C23×C32C2411yescharacteristic
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4C22×C412yes—
117C2×C32×C4C22×C412yes—
118C2×C32×C4C22×C412yes—
119C2×C32×C4C2×D412yes—
120C2×C32×C4C2×Q812yes—
121C2×C32×C4C2×Q812yes—
122C2×C32×C4#4112yes—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3C22×C414yes—
126C2×C3⋊Dic3C22×C414yes—
127C2×C3⋊Dic3C2×D414yes—
128C2×C3⋊Dic3C2×Q814yes—
129#634C4⋊C4116yescomplemented
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—24no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—24no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—24no—
138C2×C3×Dic3C2×Q814yes—
139C2×C4×Q8—92no—
140C2×C4×Q8—91no—
141#389—94no—
142#389—92no—
143#384—31no—
144#384—92no—
145C4×C4⋊C4—31no—
146C4×C4⋊C4—92no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—32no—
151C22×C3×C4—34no—
152C22×C3×C4—32no—
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×Dic3—32no—
160C22×Dic3—32no—
161C22×Dic3—32no—
162C22×Dic3—32no—
163C22×Dic3—62no—
164C22×Dic3—62no—
165C22×Dic3C22×D314yes—
166C22×Dic3C22×D312yes—
167C22×Dic3C22×D312yes—
168C2×Dic6—34no—
169C2×Dic6—34no—
170C2×Dic6—34no—
171C2×Dic6—34no—
172C2×Dic6—34no—
173C2×Dic6—34no—
174C2×Dic6—64no—
175C2×Dic6—64no—
176C2×Dic6—64no—
177C3×C4⋊C4—34no—
178C3×C4⋊C4—64no—
179C3×C4⋊C4—64no—
180C3×C4⋊C4—62no—
181C3×C4⋊C4—122no—
182C3×C42—24no—
183C3×C42—64no—
184C3×C42C4×D314yes—
185C3×C42C4×D314yes—
186C4⋊Dic3—22no—
187C4⋊Dic3—24no—
188C4⋊Dic3—24no—
189C4⋊Dic3—34no—
190C4⋊Dic3—34no—
191C4⋊Dic3—42no—
192C4⋊Dic3—64no—
193C4⋊Dic3Dic614yescomplemented
194Dic3⋊C4—38no—
195Dic3⋊C4—38no—
196Dic3⋊C4—68no—
197Dic3⋊C4—68no—
198Dic3⋊C4—68no—
199Dic3⋊C4—124no—
200Dic3⋊C4—124no—
201C4×Dic3—24no—
202C4×Dic3—38no—
203C4×Dic3—38no—
204C4×Dic3—68no—
205C4×Dic3—68no—
206C4×Dic3—68no—
207C22×C32C23×C411yescharacteristic
208C22×C32C22×D411yescharacteristic
209C22×C32C22×Q811yescharacteristic
210C22×C32C22×Q811yescharacteristic
211C22×C32C2×#4111yescharacteristic
212C22×C32H(5,𝔽2)11yescharacteristic
213C22×C322−1+411yescharacteristic
214C32×C4—22no—
215C32×C4C2×C4⋊C414yes—
216C32×C4C4×Q814yescomplemented
217C3⋊Dic3—24no—
218C3⋊Dic3C2×C4⋊C418yes—
219C3×Dic3—24no—
220C3×Dic3—44no—
221C3×Dic3—42no—
222C22×Q8—91no—
223C4×Q8—98no—
224C4×Q8—188no—
225C2×C4⋊C4—31no—
226C2×C4⋊C4—32no—
227C2×C4⋊C4—31no—
228C2×C4⋊C4—32no—
229C2×C4⋊C4—32no—
230C2×C4⋊C4—92no—
231C2×C4⋊C4—91no—
232C2×C4⋊C4—94no—
233C2×C4⋊C4—94no—
234C2×C42—32no—
235C2×C42—92no—
236C2×C42—94no—
237C2×C42D3211yescharacteristic
238#95—32no—
239#95—94no—
240C23×C3—21no—
241C23×C3C23×D311yescharacteristic
242C23×C3C23×D311yescharacteristic
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—22no—
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—34no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—62no—
258C2×C3×C4—62no—
259C2×C3×C4—64no—
260C2×C3×C4—64no—
261C2×C3×C4—62no—
262C2×C3×C4—62no—
263C2×C3×C4—62no—
264C2×C3×C4—64no—
265C2×C3×C4C2×Dic612yes—
266C2×C3×C4C2×C4×D312yes—
267C2×C3×C4C2×C4×D312yes—
268C2×C3×C4C2×C4×D312yes—
269C2×C3×C4C2×C4×D312yes—
270C2×C3×C4C2×C4×D312yes—
271C2×C3×C4C2×C4×D312yes—
272C2×C3×C4#23512yes—
273C2×C3×C4D3×D412yes—
274C2×C3×C4D3×D412yes—
275C2×C3×C4#23712yes—
276C2×C3×C4D3×Q812yes—
277C2×C3×C4D3×Q812yes—
278C2×C3×C4D3×Q812yes—
279C2×Dic3—22no—
280C2×Dic3—22no—
281C2×Dic3—22no—
282C2×Dic3—22no—
283C2×Dic3—24no—
284C2×Dic3—24no—
285C2×Dic3—24no—
286C2×Dic3—22no—
287C2×Dic3—34no—
288C2×Dic3—34no—
289C2×Dic3—34no—
290C2×Dic3—34no—
291C2×Dic3—34no—
292C2×Dic3—34no—
293C2×Dic3—34no—
294C2×Dic3—34no—
295C2×Dic3—64no—
296C2×Dic3—64no—
297C2×Dic3—64no—
298C2×Dic3—64no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—122no—
304C2×Dic3—122no—
305C2×Dic3C2×Dic614yes—
306Dic6—316no—
307Dic6—316no—
308Dic6—616no—
309C2×C32C22×C4⋊C411yescharacteristic
310C2×C32C2×C4×Q811yescharacteristic
311C2×C32#52011yescharacteristic
312C2×C32D4×Q811yescharacteristic
313C2×C32#55011yescharacteristic
314C2×C32#55711yescharacteristic
315C2×C32Q8211yescharacteristic
316C2×Q8—94no—
317C2×Q8—94no—
318C2×Q8—94no—
319C22×C4—32no—
320C22×C4—32no—
321C22×C4—34no—
322C22×C4—92no—
323C22×C4—92no—
324C22×C4C2×D3211yescharacteristic
325C22×C4C2×D3211yescharacteristic
326C22×C4C2×D3211yescharacteristic
327C4⋊C4—34no—
328C4⋊C4—62no—
329C4⋊C4—64no—
330C4⋊C4—64no—
331C4⋊C4—98no—
332C4⋊C4—94no—
333C4⋊C4—122no—
334C4⋊C4—188no—
335C4⋊C4—364no—
336C42—64no—
337C42—98no—
338C42—188no—
339C42#62414yes—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3C22×Dic611yescharacteristic
348C22×C3C22×C4×D311yescharacteristic
349C22×C3C22×C4×D311yescharacteristic
350C22×C3C2×#23511yescharacteristic
351C22×C3C2×D3×D411yescharacteristic
352C22×C3C2×D3×D411yescharacteristic
353C22×C3C2×#23711yescharacteristic
354C22×C3#100411yescharacteristic
355C22×C3C2×D3×Q811yescharacteristic
356C22×C3C2×D3×Q811yescharacteristic
357C22×C3C2×D3×Q811yescharacteristic
358C22×C3#100711yescharacteristic
359C22×C3#100911yescharacteristic
360C22×C3#101011yescharacteristic
361C3×C4—22no—
362C3×C4—22no—
363C3×C4—24no—
364C3×C4—24no—
365C3×C4—42no—
366C3×C4—64no—
367C3×C4—122no—
368C3×C4—124no—
369C3×C4C4×Dic614yescomplemented
370C3×C4#88714yescomplemented
371C3×C4D3×C4⋊C414yes—
372C3×C4D3×C4⋊C414yes—
373Dic3—24no—
374Dic3—38no—
375Dic3—38no—
376Dic3—44no—
377Dic3—42no—
378Dic3—68no—
379Dic3—64no—
380Dic3—64no—
381Dic3—124no—
382C32Q8×C4⋊C411yescharacteristic, complemented, Sylow
383C23C22×D3211yescharacteristic
384Q8—916no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—34no—
388C2×C4—62no—
389C2×C4—62no—
390C2×C4—62no—
391C2×C4—64no—
392C2×C4—62no—
393C2×C4—64no—
394C2×C4—64no—
395C2×C4—62no—
396C2×C4—94no—
397C2×C4—94no—
398C2×C4—94no—
399C2×C4—94no—
400C2×C4—182no—
401C2×C4—182no—
402C2×C4D3×Dic612yes—
403C2×C4#379512yes—
404C2×C4#379712yes—
405C2×C4#380212yes—
406C2×C4C2×#62412yes—
407C2×C4C2×#62412yes—
408C2×C4C2×#62412yes—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3C2×C4×Dic611yescharacteristic
417C2×C3C2×#88711yescharacteristic
418C2×C3C2×D3×C4⋊C411yescharacteristic
419C2×C3C2×D3×C4⋊C411yescharacteristic
420C2×C3#550411yescharacteristic
421C2×C3#552311yescharacteristic
422C2×C3D4×Dic611yescharacteristic
423C2×C3#555311yescharacteristic
424C2×C3Q8×Dic611yescharacteristic
425C2×C3#556711yescharacteristic
426C2×C3#571811yescharacteristic
427C2×C3#572111yescharacteristic
428C2×C3#572211yescharacteristic
429C2×C3#572711yescharacteristic
430C22C2×D3×Dic611yescharacteristic
431C22C2×#379511yescharacteristic
432C22#6429711yescharacteristic
433C22C2×#379711yescharacteristic
434C22C2×#380211yescharacteristic
435C22#6430711yescharacteristic
436C22C22×#62411yescharacteristic
437C4—22no—
438C4—64no—
439C4—98no—
440C4—122no—
441C4—124no—
442C4—184no—
443C4#6384414yescomplemented
444C4#6390014yes—
445C3—21no—
446C3C4⋊C4×Dic611yescharacteristic, complemented
447C3#7432311yescharacteristic, complemented
448C2#1059385611yescharacteristic
449C2#1059386411yescharacteristic
450C2#1059390411yescharacteristic
451C2#1059390611yescharacteristic
452C2C2×#6384411yescharacteristic
453C2C2×#6390011yescharacteristic
454C2#1059499011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32Q8×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
16. C4×#634C4semidirect
65. C3×C4⋊Dic3Q8semidirect
129. #634C4⋊C4semidirect
193. C4⋊Dic3Dic6semidirect
216. C32×C4C4×Q8semidirect
369. C3×C4C4×Dic6semidirect
370. C3×C4#887semidirect
382. C32Q8×C4⋊C4semidirect
443. C4#63844semidirect
446. C3C4⋊C4×Dic6semidirect
447. C3#74323semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×#638442
C3×#49352
C3×C4×C4⋊Dic32
#105913592
#105912742
#105912642
#105912122
#743233
C4⋊C4×Dic63