Finite Group Databasebeta

← #11801806

Subgroups — #11801806

Order 1152.

1149 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×#64096C211yesmaximal, characteristic
2C3×#4980C212yesmaximal
3#10591274C211yesmaximal, characteristic
4#10591273C212yesmaximal
5#10591264C212yesmaximal
6#10591257C211yesmaximal, characteristic
7#10591257C211yesmaximal, characteristic
8#10591252C211yesmaximal, characteristic
9#10591252C211yesmaximal, characteristic
10C4×Dic32C211yesmaximal, characteristic
11#10591197C212yesmaximal
12#74938—32nomaximal
13C22×#634C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3750C2211yescharacteristic
16C2×#3750C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20#64096C418yescomplemented
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×C4×Dic3C2212yes—
23C2×#3724C2212yes—
24C2×#3724C2212yes—
25C2×Dic32C2211yescharacteristic
26C2×Dic32C2212yes—
27C2×Dic32C2211yescharacteristic
28C2×Dic32C2211yescharacteristic
29C2×Dic32C2211yescharacteristic
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37C2×#887—32no—
38C2×#887—61no—
39C3×#387—32no—
40#4980D312yes—
41#4976—32no—
42Dic3×C4⋊C4—32no—
43#4933—32no—
44C42×Dic3—32no—
45#4652—32no—
46#4649—32no—
47#4649—32no—
48#4648—32no—
49#4648—32no—
50#4647—32no—
51#4646—32no—
52#4646—32no—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3C2311yescharacteristic
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C2×#634—24no—
61C2×#634C2×C414yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C32×C4⋊C4C2×C414yes—
67#3750C2×C414yes—
68#3750C2×C414yes—
69C4×C3⋊Dic3C2×C414yes—
70C4×C3⋊Dic3C2×C414yes—
71C4×C3⋊Dic3C2×C414yes—
72C3×C4⋊Dic3—24no—
73C3×C4×Dic3—24no—
74#3724—24no—
75#3724—24no—
76Dic32—24no—
77Dic32—22no—
78Dic32—22no—
79Dic32—22no—
80Dic32Q814yescomplemented
81#2295—91noSylow
82C22×Dic6—32no—
83C22×Dic6—61no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—32no—
86C2×C3×C4⋊C4C2×D312yes—
87C2×C3×C42—32no—
88C2×C4⋊Dic3C2×D312yes—
89C2×Dic3⋊C4—32no—
90C2×Dic3⋊C4—32no—
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4—32no—
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—61no—
96C2×Dic3⋊C4—61no—
97C2×C4×Dic3—32no—
98C2×C4×Dic3—32no—
99C2×C4×Dic3—32no—
100C2×C4×Dic3—32no—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—32no—
104C2×C4×Dic3—32no—
105C2×C4×Dic3—32no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3C2×D312yes—
110#887—316no—
111#887—68no—
112C3×#95—32no—
113C3×#95—32no—
114C3×#95—32no—
115C3×#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95C2×D312yes—
123C3⋊#95C2×D312yes—
124C3⋊#95C2×D312yes—
125C3⋊#95C2×D312yes—
126C23×C32C2411yescharacteristic
127C2×C32×C4—22no—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4C22×C412yes—
131C2×C32×C4C22×C412yes—
132C2×C32×C4C22×C412yes—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3C22×C412yes—
136C2×C3⋊Dic3C22×C412yes—
137C2×C3⋊Dic3C22×C412yes—
138C2×C3⋊Dic3C22×C412yes—
139C2×C3⋊Dic3C2×Q812yes—
140C2×C3⋊Dic3#4114yes—
141C2×C3⋊Dic3#4112yes—
142#634—28no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3C2×Q814yes—
154C2×C3×Dic3#4114yes—
155C2×C4×Q8—91no—
156#391—92no—
157#389—92no—
158#387—32no—
159#387—92no—
160C4×C4⋊C4—91no—
161C4×C4⋊C4—91no—
162C4×C4⋊C4—91no—
163#376—91no—
164#376—91no—
165C43—91no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—32no—
170C22×C3×C4—32no—
171C22×C3×C4—32no—
172C22×C3×C4—32no—
173C22×C3×C4C22×D312yes—
174C22×C3×C4C22×D312yes—
175C22×C3×C4C22×D312yes—
176C22×Dic3—32no—
177C22×Dic3—32no—
178C22×Dic3—32no—
179C22×Dic3—32no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3C22×D312yes—
185C22×Dic3C22×D312yes—
186C22×Dic3C22×D312yes—
187C22×Dic3C22×D312yes—
188C2×Dic6—38no—
189C2×Dic6—64no—
190C2×Dic6—64no—
191C2×Dic6—64no—
192C2×Dic6—68no—
193C3×C4⋊C4—24no—
194C3×C4⋊C4—64no—
195C3×C4⋊C4C4×D318yes—
196C3×C42—64no—
197C4⋊Dic3—24no—
198Dic3⋊C4—38no—
199Dic3⋊C4—38no—
200Dic3⋊C4—64no—
201Dic3⋊C4—64no—
202Dic3⋊C4—64no—
203Dic3⋊C4—64no—
204Dic3⋊C4—64no—
205Dic3⋊C4—64no—
206C4×Dic3—24no—
207C4×Dic3—38no—
208C4×Dic3—38no—
209C4×Dic3—38no—
210C4×Dic3—38no—
211C4×Dic3—64no—
212C4×Dic3—64no—
213C4×Dic3—64no—
214C4×Dic3—64no—
215C4×Dic3—64no—
216C4×Dic3—64no—
217C4×Dic3—64no—
218C4×Dic3—64no—
219C22×C32C23×C411yescharacteristic
220C22×C32C22×Q811yescharacteristic
221C22×C32C2×#4112yes—
222C22×C32C2×#4112yes—
223C22×C32C2×#4111yescharacteristic
224C32×C4—22no—
225C32×C4—22no—
226C32×C4—22no—
227C3⋊Dic3—22no—
228C3⋊Dic3—22no—
229C3⋊Dic3#11714yes—
230C3⋊Dic3C4×Q814yes—
231C3×Dic3—24no—
232C3×Dic3—24no—
233C3×Dic3—42no—
234C3×Dic3—42no—
235C22×Q8—91no—
236C4×Q8—98no—
237C2×C4⋊C4—32no—
238C2×C4⋊C4—91no—
239C2×C4⋊C4—91no—
240C2×C4⋊C4—92no—
241C2×C4⋊C4—92no—
242C2×C4⋊C4D3211yescharacteristic
243C2×C42—32no—
244C2×C42—91no—
245C2×C42—91no—
246C2×C42—91no—
247C2×C42—91no—
248C2×C42—91no—
249C2×C42—92no—
250C2×C42—91no—
251C2×C42—91no—
252#95—32no—
253#95—32no—
254#95—32no—
255#95—32no—
256#95—92no—
257#95—92no—
258#95—92no—
259C23×C3—21no—
260C23×C3C23×D312yes—
261C2×C3×C4—24no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—34no—
272C2×C3×C4—34no—
273C2×C3×C4—42no—
274C2×C3×C4—42no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4—62no—
278C2×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4C2×C4×D314yes—
286C2×C3×C4C2×C4×D314yes—
287C2×C3×C4C2×C4×D314yes—
288C2×Dic3—22no—
289C2×Dic3—22no—
290C2×Dic3—22no—
291C2×Dic3—22no—
292C2×Dic3—22no—
293C2×Dic3—22no—
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—34no—
299C2×Dic3—34no—
300C2×Dic3—34no—
301C2×Dic3—34no—
302C2×Dic3—34no—
303C2×Dic3—34no—
304C2×Dic3—34no—
305C2×Dic3—34no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—64no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—64no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—122no—
319C2×Dic3#23714yes—
320C2×Dic3D3×Q814yes—
321Dic6—616no—
322Dic6—616no—
323C2×C32C2×#11711yescharacteristic
324C2×C32C2×C4×Q811yescharacteristic
325C2×C32C4×#4111yescharacteristic
326C2×C32#52912yes—
327C2×C32#53312yes—
328C2×Q8—94no—
329C2×Q8—184no—
330C22×C4—32no—
331C22×C4—32no—
332C22×C4—32no—
333C22×C4—32no—
334C22×C4—91no—
335C22×C4—91no—
336C22×C4—91no—
337C22×C4—91no—
338C22×C4C2×D3211yescharacteristic
339C22×C4C2×D3211yescharacteristic
340C22×C4C2×D3211yescharacteristic
341C4⋊C4—64no—
342C4⋊C4—94no—
343C4⋊C4—94no—
344C4⋊C4—184no—
345C4⋊C4—184no—
346C4⋊C4#62414yes—
347C42—64no—
348C42—94no—
349C42—94no—
350C42—94no—
351C42—94no—
352C42—184no—
353C42—182no—
354C42—182no—
355C42—182no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3C22×C4×D312yes—
362C22×C3C2×#23712yes—
363C22×C3C2×D3×Q812yes—
364C22×C3D3×#4112yes—
365C22×C3D3×#4112yes—
366C22×C3D3×#4112yes—
367C22×C3D3×#4112yes—
368C3×C4—24no—
369C3×C4—24no—
370C3×C4—24no—
371C3×C4—24no—
372C3×C4—42no—
373C3×C4—42no—
374C3×C4—64no—
375C3×C4—64no—
376C3×C4—122no—
377C3×C4—122no—
378Dic3—24no—
379Dic3—24no—
380Dic3—38no—
381Dic3—38no—
382Dic3—42no—
383Dic3—42no—
384Dic3—64no—
385Dic3—64no—
386Dic3—64no—
387Dic3—64no—
388Dic3—64no—
389Dic3—122no—
390C32#229511yescharacteristic, complemented, Sylow
391C23C22×D3211yescharacteristic
392Q8—188no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—34no—
397C2×C4—34no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—62no—
407C2×C4—62no—
408C2×C4—94no—
409C2×C4—92no—
410C2×C4—92no—
411C2×C4—92no—
412C2×C4—92no—
413C2×C4—92no—
414C2×C4—92no—
415C2×C4—182no—
416C2×C4—182no—
417C2×C4C2×#62412yes—
418C2×C4C2×#62412yes—
419C2×C4C2×#62412yes—
420C2×C3—21no—
421C2×C3—22no—
422C2×C3—21no—
423C2×C3—22no—
424C2×C3—21no—
425C2×C3D3×#11712yes—
426C2×C3C4×#23712yes—
427C2×C3C4×D3×Q812yes—
428C2×C3#562212yes—
429C2×C3#564912yes—
430C2×C3#568812yes—
431C2×C3#570612yes—
432C22#6430612yes—
433C22D3×#23712yes—
434C22D32×Q811yescharacteristic
435C22#6431911yescharacteristic
436C22C22×#62411yescharacteristic
437C4—22no—
438C4—22no—
439C4—22no—
440C4—64no—
441C4—64no—
442C4—94no—
443C4—94no—
444C4—122no—
445C4—122no—
446C4—182no—
447C4—182no—
448C3—21no—
449C3#7493812yescomplemented
450C2#1059438812yes—
451C2#1059443512yes—
452C2#1059496911yescharacteristic
453C2#1059519011yescharacteristic
454C2Q8×#62411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2295
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
20. #64096C4semidirect
80. Dic32Q8semidirect
390. C32#2295semidirect
449. C3#74938semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C3×#49802
#105912742
#105912732
#105912642
#105912572
#105912522
C4×Dic322
#105911972
#749383