Finite Group Databasebeta

← #11805931

Subgroups — #11805931

Order 1152.

1057 conjugacy classes of subgroups.

The subgroup lattice has 439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
3C3×#4935C211yesmaximal, characteristic
4#10591274C212yesmaximal
5Dic3×C4⋊Dic3C212yesmaximal
6#10591262C214yesmaximal
7#10591224C212yesmaximal
8#10591221C212yesmaximal
9#82462—31nomaximal
10#74325—31nomaximal
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4×C3⋊Dic3C2212yes—
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C3×C4×Dic6C418yescomplemented
23C2×Dic32C2214yes—
24#63658C2212yes—
25#63579C2214yes—
26#63579C2214yes—
27#63579C2214yes—
28C2×C3×C4×Q8—31no—
29C2×C4×Dic6D311yescharacteristic
30C3×#384—31no—
31#5229—32no—
32#4980—34no—
33#4978—34no—
34#4977—32no—
35Dic3×C4⋊C4—32no—
36Dic3×C4⋊C4—32no—
37Dic3×C4⋊C4—32no—
38#4973—32no—
39#4936—32no—
40#4935D311yescharacteristic
41C4×C4⋊Dic3—31no—
42C4×C4⋊Dic3—31no—
43C4×C4⋊Dic3—32no—
44C4×C4⋊Dic3—61no—
45C22×C32×C4C2311yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3C2312yes—
49C22×C3⋊Dic3C2312yes—
50C22×C3×Dic3C2314yes—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2312yes—
53C2×C3×Dic6—22no—
54C2×C3×Dic6—22no—
55C2×C3×Dic6C2×C414yes—
56C32×C42C2×C414yes—
57C4⋊(C3⋊Dic3)—22no—
58C4⋊(C3⋊Dic3)Q814yescomplemented
59C4×C3⋊Dic3—24no—
60C3×C4⋊Dic3—24no—
61C3×C4⋊Dic3—24no—
62C3×C4⋊Dic3—42no—
63C3×C4⋊Dic3C2×C414yes—
64C3×Dic3⋊C4C2×C418yes—
65C3×C4×Dic3C2×C418yes—
66Dic32—44no—
67#2355—91noSylow
68C22×C3×Q8—31no—
69C22×Dic6C2×D311yescharacteristic
70C3×C4×Q8—38no—
71C2×C3×C4⋊C4—32no—
72C2×C3×C4⋊C4—31no—
73C2×C3×C4⋊C4—32no—
74C2×C3×C4⋊C4—32no—
75C2×C3×C4⋊C4—32no—
76C2×C3×C42—21no—
77C2×C3×C42—32no—
78C2×C3×C42C2×D311yescharacteristic
79C2×C3×C42C2×D311yescharacteristic
80C2×C4⋊Dic3—31no—
81C2×C4⋊Dic3—31no—
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—61no—
85C2×C4⋊Dic3—61no—
86C2×C4⋊Dic3C2×D312yes—
87C2×C4⋊Dic3C2×D312yes—
88C2×C4⋊Dic3C2×D312yes—
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×Dic3⋊C4C2×D312yes—
91C2×C4×Dic3—32no—
92C2×C4×Dic3—32no—
93C2×C4×Dic3—34no—
94C2×C4×Dic3—34no—
95C2×C4×Dic3—62no—
96C2×C4×Dic3C2×D312yes—
97C4×Dic6Dic318yescomplemented
98C3⋊#95—32no—
99C3⋊#95—32no—
100C3⋊#95—34no—
101C3⋊#95—34no—
102C3⋊#95—34no—
103C3⋊#95—34no—
104C3⋊#95—34no—
105C3⋊#95—34no—
106C3⋊#95—62no—
107C23×C32C2411yescharacteristic
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4C22×C412yes—
111C2×C32×C4C22×C412yes—
112C2×C32×C4C22×C412yes—
113C2×C32×C4C2×Q812yes—
114C2×C32×C4#4112yes—
115C2×C32×C4#4112yes—
116C2×C32×C4#4112yes—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3C2×Q814yes—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3C22×C414yes—
131C2×C3×Dic3C22×C414yes—
132C3×Dic6—28no—
133C2×C4×Q8—31no—
134#391—92no—
135#387—94no—
136#384—31no—
137#382—92no—
138C4×C4⋊C4—92no—
139C4×C4⋊C4—92no—
140C4×C4⋊C4—91no—
141C2×C3×Q8—34no—
142C2×C3×Q8—62no—
143C2×C3×Q8—62no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—32no—
148C22×C3×C4—32no—
149C22×C3×C4—34no—
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—32no—
159C22×Dic3—32no—
160C22×Dic3—62no—
161C22×Dic3—62no—
162C22×Dic3C22×D314yes—
163C22×Dic3C22×D312yes—
164C22×Dic3C22×D312yes—
165C2×Dic6—22no—
166C2×Dic6—22no—
167C2×Dic6C2×Dic314yes—
168C3×C4⋊C4—38no—
169C3×C4⋊C4—34no—
170C3×C4⋊C4—64no—
171C3×C4⋊C4—64no—
172C3×C4⋊C4—122no—
173C3×C42—24no—
174C3×C42—38no—
175C3×C42C4×D314yes—
176C3×C42C2×Dic314yes—
177C4⋊Dic3—24no—
178C4⋊Dic3—24no—
179C4⋊Dic3—34no—
180C4⋊Dic3—34no—
181C4⋊Dic3—42no—
182C4⋊Dic3—64no—
183C4⋊Dic3—64no—
184C4⋊Dic3—62no—
185C4⋊Dic3—62no—
186C4⋊Dic3C2×Dic314yes—
187Dic3⋊C4C2×Dic318yes—
188C4×Dic3—64no—
189C4×Dic3—64no—
190C4×Dic3—124no—
191C4×Dic3—124no—
192C4×Dic3—124no—
193C4×Dic3C2×Dic318yes—
194C22×C32C23×C411yescharacteristic
195C22×C32C22×Q811yescharacteristic
196C22×C32C2×#4111yescharacteristic
197C22×C32C2×#4111yescharacteristic
198C22×C32C2×#4111yescharacteristic
199C22×C32H(5,𝔽2)11yescharacteristic
200C22×C322−1+411yescharacteristic
201C32×C4—22no—
202C32×C4#11714yes—
203C32×C4C4×Q814yes—
204C3⋊Dic3—24no—
205C3⋊Dic3—42no—
206C3×Dic3—24no—
207C3×Dic3—24no—
208C3×Dic3—44no—
209C22×Q8—31no—
210C4×Q8—38no—
211C2×C4⋊C4—31no—
212C2×C4⋊C4—32no—
213C2×C4⋊C4—32no—
214C2×C4⋊C4—32no—
215C2×C4⋊C4—32no—
216C2×C4⋊C4—91no—
217C2×C4⋊C4—91no—
218C2×C42—32no—
219C2×C42—92no—
220C2×C42—94no—
221C2×C42D3211yescharacteristic
222#95—94no—
223#95—94no—
224#95—94no—
225#95—92no—
226C23×C3—21no—
227C23×C3C23×D311yescharacteristic
228C23×C3C23×D311yescharacteristic
229C3×Q8—68no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—34no—
242C2×C3×C4—34no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4—62no—
248C2×C3×C4—62no—
249C2×C3×C4—64no—
250C2×C3×C4—64no—
251C2×C3×C4—64no—
252C2×C3×C4C2×C4×D312yes—
253C2×C3×C4C2×C4×D312yes—
254C2×C3×C4C2×C4×D312yes—
255C2×C3×C4#23512yes—
256C2×C3×C4#23512yes—
257C2×C3×C4#23712yes—
258C2×C3×C4#23712yes—
259C2×C3×C4D3×Q812yes—
260C2×C3×C4D3×Q812yes—
261C2×C3×C4#23912yes—
262C2×C3×C4#23912yes—
263C2×C3×C4C22×Dic312yes—
264C2×C3×C4C22×Dic312yes—
265C2×C3×C4C22×Dic312yes—
266C2×Dic3—22no—
267C2×Dic3—22no—
268C2×Dic3—22no—
269C2×Dic3—22no—
270C2×Dic3—24no—
271C2×Dic3—24no—
272C2×Dic3—24no—
273C2×Dic3—34no—
274C2×Dic3—34no—
275C2×Dic3—64no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—64no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—122no—
288C2×Dic3—122no—
289C2×Dic3—122no—
290C2×Dic3—122no—
291C2×Dic3C22×Dic314yes—
292C2×Dic3C22×Dic314yes—
293Dic6—28no—
294C2×C32C2×#11711yescharacteristic
295C2×C32C2×C4×Q811yescharacteristic
296C2×C32#52011yescharacteristic
297C2×C32#55411yescharacteristic
298C2×C32#55611yescharacteristic
299C2×C32#55711yescharacteristic
300C2×C32#55911yescharacteristic
301C2×Q8—34no—
302C2×Q8—62no—
303C2×Q8—62no—
304C22×C4—32no—
305C22×C4—32no—
306C22×C4—34no—
307C22×C4—92no—
308C22×C4—92no—
309C22×C4C2×D3211yescharacteristic
310C22×C4C2×D3211yescharacteristic
311C22×C4C2×D3211yescharacteristic
312C4⋊C4—38no—
313C4⋊C4—34no—
314C4⋊C4—64no—
315C4⋊C4—64no—
316C4⋊C4—94no—
317C4⋊C4—122no—
318C4⋊C4—182no—
319C42—38no—
320C42—184no—
321C42—364no—
322C42D3×Dic314yes—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3C22×C4×D311yescharacteristic
331C22×C3C2×#23511yescharacteristic
332C22×C3C2×#23511yescharacteristic
333C22×C3C2×#23711yescharacteristic
334C22×C3C2×#23711yescharacteristic
335C22×C3#100411yescharacteristic
336C22×C3C2×D3×Q811yescharacteristic
337C22×C3C2×D3×Q811yescharacteristic
338C22×C3C2×#23911yescharacteristic
339C22×C3C2×#23911yescharacteristic
340C22×C3#100711yescharacteristic
341C22×C3#100911yescharacteristic
342C22×C3#101011yescharacteristic
343C22×C3C23×Dic311yescharacteristic
344C3×C4—22no—
345C3×C4—22no—
346C3×C4—24no—
347C3×C4—24no—
348C3×C4—42no—
349C3×C4—64no—
350C3×C4—64no—
351C3×C4—124no—
352C3×C4#88714yes—
353C3×C4#89214yes—
354C3×C4#92614yes—
355C3×C4Q8×Dic314yes—
356Dic3—24no—
357Dic3—24no—
358Dic3—44no—
359Dic3—64no—
360Dic3—64no—
361Dic3—124no—
362Dic3—124no—
363Dic3—122no—
364Dic3—122no—
365C32#235511yescharacteristic, complemented, Sylow
366C23C22×D3211yescharacteristic
367Q8—68no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—34no—
371C2×C4—34no—
372C2×C4—62no—
373C2×C4—62no—
374C2×C4—62no—
375C2×C4—62no—
376C2×C4—64no—
377C2×C4—64no—
378C2×C4—64no—
379C2×C4—94no—
380C2×C4—182no—
381C2×C4—182no—
382C2×C4—182no—
383C2×C4—182no—
384C2×C4—182no—
385C2×C4#379512yes—
386C2×C4#379612yes—
387C2×C4#379712yes—
388C2×C4#379912yes—
389C2×C4C2×D3×Dic312yes—
390C2×C4C2×D3×Dic312yes—
391C2×C4C2×D3×Dic312yes—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3C2×#88711yescharacteristic
400C2×C3C2×#89211yescharacteristic
401C2×C3#550411yescharacteristic
402C2×C3#556711yescharacteristic
403C2×C3#557911yescharacteristic
404C2×C3#558411yescharacteristic
405C2×C3#558511yescharacteristic
406C2×C3#571311yescharacteristic
407C2×C3#572111yescharacteristic
408C2×C3#573011yescharacteristic
409C2×C3#573211yescharacteristic
410C2×C3C2×#92611yescharacteristic
411C2×C3C2×Q8×Dic311yescharacteristic
412C2×C3#582711yescharacteristic
413C22C2×#379511yescharacteristic
414C22C2×#379611yescharacteristic
415C22#6429711yescharacteristic
416C22C2×#379711yescharacteristic
417C22C2×#379911yescharacteristic
418C22#6430711yescharacteristic
419C22C22×D3×Dic311yescharacteristic
420C4—22no—
421C4—64no—
422C4—64no—
423C4—124no—
424C4—184no—
425C4—362no—
426C4#6384114yes—
427C4#6384314yes—
428C3—21no—
429C3#7432511yescharacteristic, complemented
430C3#8246211yescharacteristic, complemented
431C2#1059386411yescharacteristic
432C2#1059386511yescharacteristic
433C2#1059395111yescharacteristic
434C2#1059395811yescharacteristic
435C2C2×#6384111yescharacteristic
436C2C2×#6384311yescharacteristic
437C2#1059498611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2355
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
22. C3×C4×Dic6C4semidirect
58. C4⋊(C3⋊Dic3)Q8semidirect
97. C4×Dic6Dic3semidirect
365. C32#2355semidirect
429. C3#74325semidirect
430. C3#82462semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
C4×C4⋊(C3⋊Dic3)2
C3×#49352
#105912742
Dic3×C4⋊Dic32
#105912622
#105912242
#105912212
#824623
#743253