Finite Group Databasebeta

← #11803145

Subgroups — #11803145

Order 1152.

1293 conjugacy classes of subgroups.

The subgroup lattice has 445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#4932C211yesmaximal, characteristic, complemented
4#10591355C212yesmaximal, complemented
5#10591320C212yesmaximal
6#10591219C212yesmaximal, complemented
7#10591212C212yesmaximal, complemented
8#10591202C214yesmaximal, complemented
9#73761—31nomaximal
10#73415—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3C2212yes—
13C2×C32×C42C2211yescharacteristic
14C2×#3752C2212yes—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C418yescomplemented
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×#3724C2214yes—
21C2×#3722C2214yes—
22C2×#3722C2214yes—
23C3×C3⋊#95C2211yescharacteristic
24C3×C3⋊#95C2212yes—
25C3×C3⋊#95C2211yescharacteristic
26C3×C3⋊#95C2212yes—
27#63579C2214yes—
28C2×C4×D12—31no—
29C2×C4×D12—31no—
30C2×C4×D12—61no—
31C3×C4×C4⋊C4—31no—
32C3×#376—31no—
33#4988—32no—
34#4972—32no—
35#4940—34no—
36#4939—32no—
37C4×C4⋊Dic3D311yescharacteristic, complemented
38#4932D311yescharacteristic, complemented
39#4928—32no—
40#4669—34no—
41#4667—32no—
42#4667—32no—
43#4664—32no—
44#4664—32no—
45C23×C3⋊D3C2312yes—
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2312yes—
50C2×C4⋊(C3⋊D3)—24no—
51C2×C4⋊(C3⋊D3)C2×C414yes—
52C2×C4×C3⋊D3—44no—
53C2×C4×C3⋊D3C2×C418yes—
54C22×C3×Dic3C2314yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C32×C42C2×C414yes—
58#3752C2×C418yes—
59C4⋊(C3⋊Dic3)C2×C414yes—
60C3×C4⋊Dic3—24no—
61C3×C4×Dic3—24no—
62C3×C4×Dic3—42no—
63#3724—44no—
64#3722—44no—
65#3722—44no—
66#2319—91noSylow
67C22×D12—31no—
68C22×D12—31no—
69C22×D12—61no—
70C22×C4×D3—32no—
71C22×C4×D3—32no—
72C22×C4×D3—62no—
73C2×C3×C4⋊C4—32no—
74C2×C3×C42—21no—
75C2×C3×C42—32no—
76C2×C3×C42—32no—
77C2×C3×C42C2×D311yescharacteristic
78C2×C3×C42C2×D311yescharacteristic
79C2×(C2×D3)⋊C4—32no—
80C2×(C2×D3)⋊C4—32no—
81C2×(C2×D3)⋊C4—34no—
82C2×(C2×D3)⋊C4—34no—
83C2×(C2×D3)⋊C4—34no—
84C2×(C2×D3)⋊C4—34no—
85C2×(C2×D3)⋊C4—62no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—61no—
89C2×C4⋊Dic3C2×D312yes—
90C2×Dic3⋊C4—34no—
91C2×Dic3⋊C4—34no—
92C2×C4×Dic3C2×D312yes—
93C2×C4×Dic3C2×D312yes—
94C4×D12—38no—
95C4×D12—38no—
96C4×D12—68no—
97C3×#95—31no—
98C3×#95—32no—
99C3×#95—31no—
100C3×#95—32no—
101C3⋊#95—34no—
102C3⋊#95—34no—
103C3⋊#95C2×D311yescharacteristic
104C3⋊#95C2×D312yes—
105C3⋊#95C2×D311yescharacteristic
106C3⋊#95C2×D312yes—
107C23×C32C2411yescharacteristic
108C22×C3⋊D3—24no—
109C22×C3⋊D3—22no—
110C22×C3⋊D3—24no—
111C22×C3⋊D3—22no—
112C22×C3⋊D3C22×C414yes—
113C2×C32×C4—22no—
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4C22×C412yes—
117C2×C32×C4C22×C412yes—
118C2×C32×C4C22×C412yes—
119C2×C32×C4#4114yes—
120C2×C3⋊Dic3—24no—
121C2×C3⋊Dic3C22×C414yes—
122C4⋊(C3⋊D3)—28no—
123C4×C3⋊D3—48no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C4×D4—91no—
134#390—92no—
135#389—92no—
136#388—94no—
137#381—92no—
138#380—92no—
139C4×C4⋊C4—31no—
140#376—31no—
141C23×D3—32no—
142C23×D3—32no—
143C23×D3—62no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—32no—
148C22×C3×C4—34no—
149C22×C3×C4—32no—
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×Dic3—32no—
157C22×Dic3—32no—
158C22×Dic3—62no—
159C22×Dic3C22×D312yes—
160C22×Dic3C22×D314yes—
161C22×Dic3C22×D312yes—
162C2×D12—34no—
163C2×D12—34no—
164C2×D12—64no—
165C2×D12—68no—
166C2×D12—64no—
167C2×D12—64no—
168C2×C4×D3—38no—
169C2×C4×D3—38no—
170C2×C4×D3—68no—
171C2×C4×D3—124no—
172C2×C4×D3—124no—
173C2×C4×D3—128no—
174C3×C4⋊C4—64no—
175C3×C42—24no—
176C3×C42—64no—
177C3×C42—122no—
178C3×C42C4×D314yes—
179C3×C42C4×D314yes—
180(C2×D3)⋊C4—38no—
181(C2×D3)⋊C4—38no—
182(C2×D3)⋊C4—68no—
183(C2×D3)⋊C4—124no—
184(C2×D3)⋊C4—124no—
185(C2×D3)⋊C4—124no—
186(C2×D3)⋊C4—124no—
187C4⋊Dic3—24no—
188C4⋊Dic3—34no—
189C4⋊Dic3—34no—
190C4⋊Dic3—64no—
191Dic3⋊C4—124no—
192Dic3⋊C4—124no—
193C4×Dic3—24no—
194C4×Dic3—42no—
195C22×C32C23×C411yescharacteristic
196C22×C32C2×#4112yes—
197C22×C32H(5,𝔽2)11yescharacteristic
198C22×C32H(5,𝔽2)12yes—
199C22×C322−1+411yescharacteristic
200C2×C3⋊D3—24no—
201C2×C3⋊D3—24no—
202C2×C3⋊D3—24no—
203C2×C3⋊D3—44no—
204C2×C3⋊D3—44no—
205C32×C4—22no—
206C32×C4—22no—
207C32×C4#11714yes—
208C3⋊Dic3—24no—
209C3×Dic3—42no—
210C3×Dic3—44no—
211C3×Dic3—42no—
212C22×D4—91no—
213C23×C4—92no—
214C4×D4—98no—
215C2×C4⋊C4—32no—
216C2×C4⋊C4—91no—
217C2×C4⋊C4—94no—
218C2×C22⋊C4—92no—
219C2×C22⋊C4—94no—
220C2×C22⋊C4—94no—
221C2×C42—32no—
222C2×C42—32no—
223C2×C42D3211yescharacteristic
224#95—31no—
225#95—31no—
226#95—32no—
227#95—32no—
228#95—94no—
229C23×C3—21no—
230C23×C3C23×D311yescharacteristic
231C23×C3C23×D311yescharacteristic
232C22×D3—34no—
233C22×D3—34no—
234C22×D3—64no—
235C22×D3—68no—
236C22×D3—64no—
237C22×D3—64no—
238C22×D3—62no—
239C22×D3—62no—
240C22×D3—62no—
241C22×D3—64no—
242C22×D3—64no—
243C22×D3—62no—
244C22×D3—124no—
245C22×D3—122no—
246C22×D3—122no—
247C2×C3×C4—24no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—21no—
254C2×C3×C4—24no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—62no—
261C2×C3×C4—62no—
262C2×C3×C4—64no—
263C2×C3×C4—62no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4—64no—
267C2×C3×C4—62no—
268C2×C3×C4—64no—
269C2×C3×C4C2×C4×D312yes—
270C2×C3×C4C2×C4×D312yes—
271C2×C3×C4C2×C4×D312yes—
272C2×C3×C4C2×C4×D312yes—
273C2×C3×C4C2×C4×D312yes—
274C2×C3×C4C2×C4×D312yes—
275C2×C3×C4#23514yes—
276C2×C3×C4#23514yes—
277C2×Dic3—22no—
278C2×Dic3—22no—
279C2×Dic3—24no—
280C2×Dic3—24no—
281C2×Dic3—22no—
282C2×Dic3—24no—
283C2×Dic3—22no—
284C2×Dic3—22no—
285C2×Dic3—22no—
286C2×Dic3—34no—
287C2×Dic3—34no—
288C2×Dic3—64no—
289C2×Dic3—64no—
290C2×Dic3—64no—
291C2×Dic3—124no—
292D12—616no—
293D12—68no—
294D12—68no—
295C4×D3—128no—
296C4×D3—128no—
297C4×D3—1216no—
298C2×C32C2×#11711yescharacteristic
299C2×C32#51811yescharacteristic
300C2×C32#52011yescharacteristic
301C2×C32#54012yes—
302C2×C32#54212yes—
303C3⋊D3—44no—
304C24—92no—
305C2×D4—94no—
306C2×D4—184no—
307C22×C4—32no—
308C22×C4—32no—
309C22×C4—34no—
310C22×C4—92no—
311C22×C4—98no—
312C22×C4—364no—
313C22×C4C2×D3211yescharacteristic
314C22×C4C2×D3211yescharacteristic
315C22×C4C2×D3211yescharacteristic
316C4⋊C4—64no—
317C4⋊C4—94no—
318C4⋊C4—364no—
319C22⋊C4—98no—
320C22⋊C4—364no—
321C22⋊C4—364no—
322C42—64no—
323C42—122no—
324C42#62414yes—
325C22×C3—21no—
326C22×C3—22no—
327C22×C3—21no—
328C22×C3—22no—
329C22×C3—21no—
330C22×C3C22×C4×D311yescharacteristic
331C22×C3C22×C4×D311yescharacteristic
332C22×C3C2×#23512yes—
333C22×C3C2×#23512yes—
334C22×C3#100411yescharacteristic
335C22×C3#100711yescharacteristic
336C22×C3#100911yescharacteristic
337C22×C3#100912yes—
338C22×C3#100912yes—
339C22×C3#101011yescharacteristic
340C2×D3—68no—
341C2×D3—64no—
342C2×D3—64no—
343C2×D3—64no—
344C2×D3—64no—
345C2×D3—64no—
346C2×D3—64no—
347C2×D3—124no—
348C2×D3—124no—
349C2×D3—128no—
350C2×D3—128no—
351C2×D3—124no—
352C2×D3—124no—
353C2×D3—124no—
354C2×D3—124no—
355C3×C4—24no—
356C3×C4—22no—
357C3×C4—22no—
358C3×C4—22no—
359C3×C4—22no—
360C3×C4—24no—
361C3×C4—42no—
362C3×C4—124no—
363C3×C4—122no—
364C3×C4—122no—
365C3×C4#87214yes—
366C3×C4#87214yes—
367Dic3—42no—
368Dic3—42no—
369Dic3—44no—
370Dic3—64no—
371Dic3—64no—
372Dic3—124no—
373C32#231911yescharacteristic, complemented, Sylow
374C23—94no—
375C23—182no—
376C23—184no—
377C23—182no—
378C23—184no—
379C23C22×D3211yescharacteristic
380D4—188no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—62no—
385C2×C4—62no—
386C2×C4—62no—
387C2×C4—64no—
388C2×C4—64no—
389C2×C4—62no—
390C2×C4—62no—
391C2×C4—64no—
392C2×C4—62no—
393C2×C4—94no—
394C2×C4—184no—
395C2×C4—368no—
396C2×C4#379814yes—
397C2×C4C2×#62412yes—
398C2×C4C2×#62412yes—
399C2×C4C2×#62412yes—
400C2×C3—21no—
401C2×C3—22no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—22no—
405C2×C3C2×#87211yescharacteristic
406C2×C3C2×#87211yescharacteristic
407C2×C3#550411yescharacteristic
408C2×C3#552111yescharacteristic
409C2×C3#552111yescharacteristic
410C2×C3#552311yescharacteristic
411C2×C3#553412yes—
412C2×C3#553512yes—
413C2×C3#556212yes—
414C2×C3#558212yes—
415D3—128no—
416D3—124no—
417D3—124no—
418C22—184no—
419C22—184no—
420C22—184no—
421C22—364no—
422C22—364no—
423C22#6429711yescharacteristic
424C22C2×#379812yes—
425C22#6430711yescharacteristic
426C22#6430812yes—
427C22C22×#62411yescharacteristic
428C4—22no—
429C4—22no—
430C4—122no—
431C4—122no—
432C4—124no—
433C4—184no—
434C4#6387414yes—
435C3—21no—
436C3#7341511yescharacteristic, complemented
437C3#7376111yescharacteristic, complemented
438C2—364no—
439C2#1059387812yes—
440C2#1059398612yes—
441C2C2×#6387411yescharacteristic
442C2#1059499011yescharacteristic
443C2#1059499611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32#2319
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×C4⋊Dic3C2semidirect
3. C3×#4932C2semidirect
4. #10591355C2semidirect
6. #10591219C2semidirect
7. #10591212C2semidirect
8. #10591202C2semidirect
16. C4×C4⋊(C3⋊D3)C4semidirect
37. C4×C4⋊Dic3D3semidirect
38. #4932D3semidirect
373. C32#2319semidirect
436. C3#73415semidirect
437. C3#73761semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C3×C4×C4⋊Dic32
C3×#49322
#105913552
#105913202
#105912192
#105912122
#105912022
#737613
#734153