Finite Group Databasebeta

← #11804896

Subgroups — #11804896

Order 1152.

2065 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic
2C2×#63844C212yesmaximal, complemented
3C3×#5229C212yesmaximal, complemented
4#10591355C212yesmaximal
5#10591325C211yesmaximal, characteristic
6C4×#3722C211yesmaximal, characteristic
7#10591273C214yesmaximal, complemented
8#10591260C212yesmaximal
9#76614—32nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×Q8×C3⋊D3—28no—
12C2×Q8×C3⋊D3C418yescomplemented
13C22×C4×C3⋊D3C2212yes—
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×#634C2212yes—
16C22×#634C2211yescharacteristic
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×#3724C2214yes—
20C2×#3722C2212yes—
21C2×#3722C2211yescharacteristic
22C2×#3722C2211yescharacteristic
23C2×Dic32C2214yes—
24#63844—28no—
25C3×C3⋊#95C2214yes—
26C3×C3⋊#95C2214yes—
27#63579C2212yes—
28#63579C2212yes—
29C22×D3×Q8—32no—
30C22×D3×Q8—61no—
31C2×#887—32no—
32C2×C4×Dic6—32no—
33C3×#391—32no—
34#5229D312yescomplemented
35#4987—32no—
36C4×(C2×D3)⋊C4—32no—
37#4667—34no—
38#4666—34no—
39#4646—34no—
40#4646—34no—
41C23×C3⋊D3C2311yescharacteristic
42C2×C32×Q8—24no—
43C2×C32×Q8C2×C414yes—
44C22×C32×C4C2312yes—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3C2311yescharacteristic
47C22×C3⋊Dic3C2312yes—
48Q8×C3⋊D3—232no—
49C2×C4×C3⋊D3—24no—
50C2×C4×C3⋊D3—28no—
51C2×C4×C3⋊D3C2×C414yes—
52C2×C4×C3⋊D3C2×C418yes—
53C2×#634—28no—
54C2×#634C2×C418yes—
55C2×#634C2×C414yes—
56C2×#634D418yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2314yes—
59C22×C3×Dic3C2312yes—
60C3×C4⋊Dic3—24no—
61C3×C4×Dic3—24no—
62#3724—28no—
63#3722—24no—
64#3722—22no—
65#3722Q814yescomplemented
66Dic32—28no—
67Q8×C22⋊C4—91noSylow
68C22×C3×Q8—21no—
69C22×C3×Q8C2×D312yes—
70C2×D3×Q8—316no—
71C2×D3×Q8—68no—
72C2×D3×Q8—68no—
73C2×D3×Q8—68no—
74C2×D3×Q8—616no—
75C22×C4×D3—34no—
76C22×C4×D3—32no—
77C22×C4×D3—62no—
78C22×C4×D3—61no—
79C22×Dic6—32no—
80C22×Dic6—34no—
81C22×Dic6—61no—
82C22×Dic6—62no—
83C2×C3×C4⋊C4—32no—
84C2×C3×C42—32no—
85C2×(C2×D3)⋊C4—32no—
86C2×(C2×D3)⋊C4—34no—
87C2×(C2×D3)⋊C4—32no—
88C2×C4⋊Dic3C2×D312yes—
89C2×Dic3⋊C4—34no—
90C2×Dic3⋊C4—34no—
91C2×C4×Dic3—34no—
92C2×C4×Dic3—34no—
93C2×C4×Dic3C2×D312yes—
94#887—68no—
95C4×Dic6—68no—
96C3×#95—34no—
97C3×#95—34no—
98C3⋊#95—32no—
99C3⋊#95—32no—
100C3⋊#95—34no—
101C3⋊#95C2×D314yes—
102C3⋊#95C2×D314yes—
103C23×C32C2411yescharacteristic
104C22×C3⋊D3—22no—
105C22×C3⋊D3—22no—
106C22×C3⋊D3C22×C412yes—
107C22×C3⋊D3C2×Q812yes—
108C22×C3⋊D3#4112yes—
109C32×Q8—28no—
110C2×C32×C4—24no—
111C2×C32×C4C22×C414yes—
112C2×C32×C4C22×C412yes—
113C2×C32×C4C2×D414yes—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3C22×C412yes—
116C2×C3⋊Dic3C22×C414yes—
117C2×C3⋊Dic3C2×D418yes—
118C4×C3⋊D3—28no—
119C4×C3⋊D3—216no—
120#634—216no—
121#634C22⋊C4116yescomplemented
122C2×C3×Dic3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3C2×Q814yescomplemented
131C23×Q8—91no—
132C2×C4×Q8—92no—
133#391—32no—
134#391—94no—
135#380—92no—
136#380—91no—
137C4×C22⋊C4—92no—
138C4×C22⋊C4—91no—
139C23×D3—32no—
140C23×D3—61no—
141C2×C3×Q8—28no—
142C2×C3×Q8—24no—
143C2×C3×Q8—24no—
144C2×C3×Q8—24no—
145C2×C3×Q8C4×D318yes—
146C22×C3×C4—22no—
147C22×C3×C4—21no—
148C22×C3×C4—32no—
149C22×C3×C4—34no—
150C22×C3×C4—32no—
151C22×C3×C4C22×D314yes—
152C22×C3×C4C22×D312yes—
153C22×Dic3—34no—
154C22×Dic3—32no—
155C22×Dic3—62no—
156C22×Dic3—61no—
157C22×Dic3C22×D314yes—
158C22×Dic3C22×D312yes—
159C22×Dic3C22×D312yes—
160D3×Q8—664no—
161D3×Q8—664no—
162C2×C4×D3—316no—
163C2×C4×D3—38no—
164C2×C4×D3—68no—
165C2×C4×D3—64no—
166C2×C4×D3—68no—
167C2×C4×D3—68no—
168C2×C4×D3—616no—
169C2×C4×D3—68no—
170C2×C4×D3—64no—
171C2×C4×D3—64no—
172C2×Dic6—38no—
173C2×Dic6—38no—
174C2×Dic6—38no—
175C2×Dic6—316no—
176C2×Dic6—64no—
177C2×Dic6—68no—
178C2×Dic6—68no—
179C2×Dic6—68no—
180C2×Dic6—68no—
181C2×Dic6—616no—
182C3×C4⋊C4—64no—
183C3×C42—64no—
184(C2×D3)⋊C4—38no—
185(C2×D3)⋊C4—68no—
186(C2×D3)⋊C4—64no—
187C4⋊Dic3—24no—
188Dic3⋊C4—68no—
189Dic3⋊C4—68no—
190C4×Dic3—24no—
191C4×Dic3—68no—
192C4×Dic3—68no—
193C22×C32C23×C411yescharacteristic
194C22×C32C22×D412yes—
195C22×C32C22×Q811yescharacteristic
196C22×C32C2×#4111yescharacteristic
197C22×C322−1+412yes—
198C2×C3⋊D3—22no—
199C2×C3⋊D3—22no—
200C2×C3⋊D3—24no—
201C2×C3⋊D3—24no—
202C2×C3⋊D3C4×Q814yescomplemented
203C32×C4—24no—
204C32×C4C2×C22⋊C414yes—
205C3⋊Dic3—22no—
206C3⋊Dic3C2×C22⋊C418yes—
207C3×Dic3—24no—
208C3×Dic3—42no—
209C3×Dic3—44no—
210C22×Q8—98no—
211C22×Q8—91no—
212C22×Q8—92no—
213C22×Q8—188no—
214C22×Q8D3211yescharacteristic
215C23×C4—92no—
216C23×C4—91no—
217C4×Q8—188no—
218C2×C4⋊C4—32no—
219C2×C4⋊C4—94no—
220C2×C22⋊C4—91no—
221C2×C22⋊C4—91no—
222C2×C22⋊C4—92no—
223C2×C42—32no—
224C2×C42—94no—
225#95—34no—
226#95—34no—
227#95—92no—
228#95—92no—
229C23×C3—21no—
230C23×C3C23×D312yes—
231C22×D3—34no—
232C22×D3—34no—
233C22×D3—34no—
234C22×D3—62no—
235C22×D3—62no—
236C22×D3—62no—
237C22×D3—64no—
238C22×D3—64no—
239C22×D3—62no—
240C22×D3—62no—
241C22×D3—62no—
242C22×D3—62no—
243C3×Q8—216no—
244C3×Q8—216no—
245C2×C3×C4—28no—
246C2×C3×C4—24no—
247C2×C3×C4—24no—
248C2×C3×C4—24no—
249C2×C3×C4—22no—
250C2×C3×C4—24no—
251C2×C3×C4—34no—
252C2×C3×C4—62no—
253C2×C3×C4—62no—
254C2×C3×C4—64no—
255C2×C3×C4—62no—
256C2×C3×C4—64no—
257C2×C3×C4—64no—
258C2×C3×C4—62no—
259C2×C3×C4—62no—
260C2×C3×C4C2×C4×D318yes—
261C2×C3×C4C2×C4×D314yes—
262C2×C3×C4D3×D414yes—
263C2×C3×C4D3×D414yes—
264C2×Dic3—22no—
265C2×Dic3—22no—
266C2×Dic3—22no—
267C2×Dic3—24no—
268C2×Dic3—22no—
269C2×Dic3—22no—
270C2×Dic3—24no—
271C2×Dic3—24no—
272C2×Dic3—38no—
273C2×Dic3—38no—
274C2×Dic3—38no—
275C2×Dic3—34no—
276C2×Dic3—64no—
277C2×Dic3—62no—
278C2×Dic3—68no—
279C2×Dic3—64no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3D3×Q814yescomplemented
283C4×D3—632no—
284C4×D3—632no—
285C4×D3—616no—
286C4×D3—616no—
287Dic6—332no—
288Dic6—616no—
289Dic6—632no—
290Dic6—632no—
291C2×C32C22×C22⋊C411yescharacteristic
292C2×C32C2×C4×Q811yescharacteristic
293C2×C32#51911yescharacteristic
294C2×C32#54812yes—
295C2×C32D4×Q812yes—
296C3⋊D3—24no—
297C24—91no—
298C2×Q8—24no—
299C2×Q8—94no—
300C2×Q8—98no—
301C2×Q8—98no—
302C2×Q8—188no—
303C2×Q8—1832no—
304C2×Q8#62414yes—
305C22×C4—32no—
306C22×C4—32no—
307C22×C4—34no—
308C22×C4—92no—
309C22×C4—91no—
310C22×C4—98no—
311C22×C4—94no—
312C22×C4—188no—
313C22×C4—184no—
314C22×C4C2×D3212yes—
315C22×C4C2×D3211yescharacteristic
316C4⋊C4—64no—
317C4⋊C4—188no—
318C22⋊C4—94no—
319C22⋊C4—182no—
320C22⋊C4—184no—
321C42—64no—
322C42—188no—
323C22×C3—22no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—22no—
328C22×C3C22×C4×D312yes—
329C22×C3C2×D3×D412yes—
330C22×C3C2×D3×D412yes—
331C22×C3C2×D3×Q812yes—
332C22×C3#100712yes—
333C22×C3D3×#4112yes—
334C22×C3#101012yes—
335C2×D3—38no—
336C2×D3—64no—
337C2×D3—64no—
338C2×D3—64no—
339C2×D3—68no—
340C2×D3—68no—
341C2×D3—64no—
342C2×D3—64no—
343C2×D3—64no—
344C2×D3—64no—
345C2×D3—64no—
346C2×D3—64no—
347C3×C4—28no—
348C3×C4—28no—
349C3×C4—24no—
350C3×C4—64no—
351C3×C4—124no—
352C3×C4—122no—
353C3×C4D3×C22⋊C418yes—
354Dic3—24no—
355Dic3—316no—
356Dic3—42no—
357Dic3—44no—
358Dic3—68no—
359Dic3—64no—
360Dic3—64no—
361C32Q8×C22⋊C411yescharacteristic, complemented, Sylow
362C23—92no—
363C23—92no—
364C23—92no—
365C23—182no—
366C23—182no—
367C23C22×D3211yescharacteristic
368Q8—28no—
369Q8—916no—
370Q8—1816no—
371C2×C4—24no—
372C2×C4—34no—
373C2×C4—62no—
374C2×C4—62no—
375C2×C4—62no—
376C2×C4—64no—
377C2×C4—62no—
378C2×C4—64no—
379C2×C4—62no—
380C2×C4—64no—
381C2×C4—94no—
382C2×C4—98no—
383C2×C4—92no—
384C2×C4—1816no—
385C2×C4—182no—
386C2×C4—188no—
387C2×C4C2×#62414yes—
388C2×C4C2×#62412yes—
389C2×C4#381114yes—
390C2×C3—21no—
391C2×C3—22no—
392C2×C3—22no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3C2×D3×C22⋊C412yes—
396C2×C3C4×D3×Q812yes—
397C2×C3#557212yes—
398C2×C3#563212yes—
399C2×C3#563312yes—
400C2×C3#567712yes—
401C2×C3#572712yes—
402D3—68no—
403D3—68no—
404C22—94no—
405C22—182no—
406C22—184no—
407C22—184no—
408C22—182no—
409C22#6431512yes—
410C22D32×Q811yescharacteristic
411C22#6431911yescharacteristic
412C22C22×#62411yescharacteristic
413C22C2×#381112yes—
414C4—24no—
415C4—64no—
416C4—98no—
417C4—122no—
418C4—124no—
419C4—182no—
420C4#6397414yes—
421C3—21no—
422C3#7661412yescomplemented
423C2—184no—
424C2#1059533911yescharacteristic
425C2#1059536112yes—
426C2#1059536212yes—
427C2Q8×#62411yescharacteristic
428C2C2×#6397411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×Q8C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC22×Q8D32
hypocenterC32Q8×C22⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#63844C2semidirect
3. C3×#5229C2semidirect
7. #10591273C2semidirect
12. C2×Q8×C3⋊D3C4semidirect
34. #5229D3semidirect
65. #3722Q8semidirect
121. #634C22⋊C4semidirect
130. C2×C3×Dic3C2×Q8semidirect
202. C2×C3⋊D3C4×Q8semidirect
282. C2×Dic3D3×Q8semidirect
361. C32Q8×C22⋊C4semidirect
422. C3#76614semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C2×#638442
C3×#52292
#105913552
#105913252
C4×#37222
#105912732
#105912602
#766143