Finite Group Databasebeta

← #11807827

Subgroups — #11807827

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63982C211yesmaximal, characteristic
2#10592641C211yesmaximal, characteristic
3C3×#4944C212yesmaximal
4#10591701C212yesmaximal
5#10591697C211yesmaximal, characteristic
6#10591333C212yesmaximal, complemented
7#10591330C212yesmaximal, complemented
8#10591251C212yesmaximal, complemented
9#10591235C212yesmaximal, complemented
10#75491—32nomaximal
11C23×C3⋊Dic3C2211yescharacteristic
12C22×#627C2211yescharacteristic
13C2×C32×C22⋊C4C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C2×#3750C2212yes—
16C2×C3×#217C2212yes—
17C2×C3×#217C2212yes—
18C2×C3×Dic3⋊C4C2212yes—
19C2×C3×C4×Dic3C2212yes—
20#63982C418yescomplemented
21C2×#3724C2211yescharacteristic
22C2×Dic3⋊Dic3C2212yes—
23C2×Dic3⋊Dic3C2212yes—
24C2×Dic32C2212yes—
25#63658C2212yes—
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2212yes—
28#63579C2212yes—
29#63579C2212yes—
30#63579C2211yescharacteristic
31#63579C2212yes—
32#63579C2211yescharacteristic
33C2×#878—32no—
34C3×#388—32no—
35#4976—32no—
36#4973—32no—
37#4951—32no—
38#4944—32no—
39#4944D312yes—
40#4943—32no—
41#4942—32no—
42#4942—61no—
43#4933—32no—
44#4928—32no—
45#4655—32no—
46#4654—32no—
47#4652—32no—
48#4646—32no—
49C24×C32C2311yescharacteristic
50C22×C32×C4C2312yes—
51C22×C3⋊Dic3—42no—
52C22×C3⋊Dic3C2×C414yes—
53C22×C3⋊Dic3C2312yes—
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C2×#627—42no—
61C2×#627C2×C414yes—
62C32×C22⋊C4—41no—
63#3757—41no—
64#3750—42no—
65C3×#217—42no—
66C3×#217C2×C418yes—
67C3×Dic3⋊C4—42no—
68C3×C4×Dic3—42no—
69#3724C2×C414yes—
70Dic3⋊Dic3—42no—
71Dic3⋊Dic3C2×C418yes—
72Dic32—42no—
73#2378—91noSylow
74C23×Dic3—32no—
75C23×Dic3—61no—
76C22×Dic6—32no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C22⋊C4—21no—
79C2×C3×C22⋊C4—32no—
80C2×C3×C22⋊C4—32no—
81C2×C3×C22⋊C4C2×D312yes—
82C2×C3×C42—32no—
83C2×#217—32no—
84C2×#217—61no—
85C2×#217C2×D312yes—
86C2×#217C2×D312yes—
87C2×C4⋊Dic3—32no—
88C2×C4⋊Dic3—32no—
89C2×Dic3⋊C4—32no—
90C2×Dic3⋊C4—32no—
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4—32no—
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—62no—
95C2×Dic3⋊C4C2×D312yes—
96C2×C4×Dic3—32no—
97C2×C4×Dic3—32no—
98C2×C4×Dic3C2×D312yes—
99#878—316no—
100C3×#95—32no—
101C3×#95—32no—
102C3⋊#95—32no—
103C3⋊#95—32no—
104C3⋊#95—32no—
105C3⋊#95—32no—
106C3⋊#95—32no—
107C3⋊#95—32no—
108C3⋊#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—62no—
113C3⋊#95C2×D312yes—
114C3⋊#95C2×D312yes—
115C23×C32—21no—
116C23×C32—21no—
117C23×C32—22no—
118C23×C32—22no—
119C23×C32C22×C412yes—
120C23×C32C2411yescharacteristic
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—44no—
130C2×C3⋊Dic3C22×C412yes—
131C2×C3⋊Dic3C22×C412yes—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3C22×C414yes—
143C2×C3×Dic3C22×C414yes—
144#627—44no—
145C2×C22⋊Q8—91no—
146#391—92no—
147#389—92no—
148#388—32no—
149#388—92no—
150#387—92no—
151#387—92no—
152#381—91no—
153#380—91no—
154C24×C3—21no—
155C24×C3C22×D312yes—
156C22×C3×C4—22no—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4—32no—
160C22×C3×C4—32no—
161C22×C3×C4C22×D312yes—
162C22×C3×C4C22×D312yes—
163C22×Dic3—32no—
164C22×Dic3—32no—
165C22×Dic3—38no—
166C22×Dic3—32no—
167C22×Dic3—32no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—64no—
171C22×Dic3—62no—
172C22×Dic3—122no—
173C22×Dic3—122no—
174C22×Dic3—124no—
175C22×Dic3C22×D312yes—
176C22×Dic3C22×D312yes—
177C22×Dic3C22×D312yes—
178C22×Dic3C22×D312yes—
179C2×Dic6—38no—
180C2×Dic6—122no—
181C2×Dic6—122no—
182C3×C4⋊C4—122no—
183C3×C22⋊C4—38no—
184C3×C22⋊C4—42no—
185C3×C22⋊C4—42no—
186C3×C22⋊C4—122no—
187C3×C42—122no—
188#217—42no—
189#217—122no—
190#217—122no—
191#217C4×D318yes—
192C4⋊Dic3—38no—
193C4⋊Dic3—122no—
194Dic3⋊C4—38no—
195Dic3⋊C4—38no—
196Dic3⋊C4—42no—
197Dic3⋊C4—122no—
198Dic3⋊C4—122no—
199Dic3⋊C4—122no—
200Dic3⋊C4—124no—
201C4×Dic3—42no—
202C4×Dic3—122no—
203C4×Dic3—122no—
204C22×C32—22no—
205C22×C32—22no—
206C22×C32—22no—
207C22×C32—42no—
208C22×C32—42no—
209C22×C32C23×C411yescharacteristic
210C22×C32H(5,𝔽2)11yescharacteristic
211C22×C32H(5,𝔽2)12yes—
212C22×C322−1+412yes—
213C22×C322−1+411yescharacteristic
214C32×C4—42no—
215C3⋊Dic3—22no—
216C3⋊Dic3—22no—
217C3⋊Dic3—42no—
218C3×Dic3—24no—
219C3×Dic3—24no—
220C3×Dic3—42no—
221C3×Dic3—42no—
222C22×Q8—91no—
223C23×C4—91no—
224C22⋊Q8—98no—
225C2×C4⋊C4—32no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4—92no—
228C2×C4⋊C4—92no—
229C2×C4⋊C4—92no—
230C2×C22⋊C4—32no—
231C2×C22⋊C4—32no—
232C2×C22⋊C4—91no—
233C2×C22⋊C4D3211yescharacteristic
234C2×C42—32no—
235C2×C42—92no—
236#95—32no—
237#95—32no—
238#95—91no—
239#95—92no—
240#95—91no—
241#95—92no—
242#95—92no—
243#95—92no—
244C23×C3—22no—
245C23×C3—22no—
246C23×C3—22no—
247C23×C3—22no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—22no—
251C23×C3—22no—
252C23×C3—21no—
253C23×C3—22no—
254C23×C3—42no—
255C23×C3—42no—
256C23×C3C2×C4×D314yes—
257C23×C3C23×D312yes—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—34no—
265C2×C3×C4—34no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—62no—
270C2×C3×C4—62no—
271C2×C3×C4—62no—
272C2×C3×C4—62no—
273C2×C3×C4—62no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4—62no—
278C2×C3×C4—62no—
279C2×Dic3—22no—
280C2×Dic3—22no—
281C2×Dic3—22no—
282C2×Dic3—22no—
283C2×Dic3—22no—
284C2×Dic3—22no—
285C2×Dic3—22no—
286C2×Dic3—22no—
287C2×Dic3—22no—
288C2×Dic3—22no—
289C2×Dic3—34no—
290C2×Dic3—34no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—64no—
294C2×Dic3—62no—
295C2×Dic3—62no—
296C2×Dic3—62no—
297C2×Dic3—62no—
298C2×Dic3—62no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—122no—
305C2×Dic3—122no—
306C2×Dic3—122no—
307C2×Dic3—122no—
308C2×Dic3—128no—
309C2×Dic3—128no—
310C2×Dic3C2×C4×D314yes—
311C2×Dic3C2×C4×D314yes—
312Dic6—128no—
313C2×C32—42no—
314C2×C32#51811yescharacteristic
315C2×C32#51911yescharacteristic
316C2×C32#52011yescharacteristic
317C2×C32#56212yes—
318C2×C32#56312yes—
319C24C2×D3211yescharacteristic
320C2×Q8—94no—
321C2×Q8—362no—
322C22×C4—32no—
323C22×C4—32no—
324C22×C4—32no—
325C22×C4—32no—
326C22×C4—91no—
327C22×C4—91no—
328C22×C4—94no—
329C22×C4—92no—
330C22×C4—362no—
331C22×C4C2×D3212yes—
332C4⋊C4—94no—
333C4⋊C4—98no—
334C4⋊C4—122no—
335C4⋊C4—362no—
336C4⋊C4—362no—
337C22⋊C4—38no—
338C22⋊C4—41no—
339C22⋊C4—122no—
340C22⋊C4—361no—
341C42—122no—
342C42—362no—
343C22×C3—24no—
344C22×C3—24no—
345C22×C3—24no—
346C22×C3—24no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—21no—
352C22×C3—42no—
353C22×C3—42no—
354C22×C3—44no—
355C22×C3—44no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—42no—
359C22×C3—42no—
360C22×C3C22×C4×D312yes—
361C22×C3#100412yes—
362C22×C3#100412yes—
363C22×C3#100912yes—
364C22×C3#101012yes—
365C22×C3#101012yes—
366C22×C3#101012yes—
367C3×C4—42no—
368C3×C4—42no—
369C3×C4—64no—
370C3×C4—64no—
371C3×C4—82no—
372C3×C4—122no—
373C3×C4—122no—
374Dic3—24no—
375Dic3—24no—
376Dic3—42no—
377Dic3—42no—
378Dic3—64no—
379Dic3—64no—
380Dic3—64no—
381Dic3—122no—
382Dic3—122no—
383Dic3—122no—
384Dic3—242no—
385C32#237811yescharacteristic, complemented, Sylow
386C23—21no—
387C23—22no—
388C23—22no—
389C23—21no—
390C23C4×D3212yes—
391C23C22×D3211yescharacteristic
392Q8—364no—
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—92no—
409C2×C4—92no—
410C2×C4—182no—
411C2×C4—182no—
412C2×C4—182no—
413C2×C4—182no—
414C2×C4—182no—
415C2×C4—364no—
416C2×C3—21no—
417C2×C3—22no—
418C2×C3—22no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—44no—
422C2×C3—44no—
423C2×C3#551612yes—
424C2×C3#554512yes—
425C2×C3#554612yes—
426C2×C3#562112yes—
427C2×C3#566712yes—
428C2×C3#567212yes—
429C2×C3#571212yes—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—42no—
434C22—42no—
435C22#6429811yescharacteristic
436C22C2×C4×D3211yescharacteristic
437C22#6430912yes—
438C22#6431412yes—
439C22#6433011yescharacteristic
440C4—42no—
441C4—64no—
442C4—64no—
443C4—122no—
444C4—122no—
445C4—182no—
446C4—182no—
447C4—362no—
448C3—21no—
449C3#7549112yescomplemented
450C2—42no—
451C2#1059417612yes—
452C2#1059424511yescharacteristic
453C2#1059425611yescharacteristic
454C2#1059487611yescharacteristic
455C2#1059526312yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2378
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. #10591333C2semidirect
7. #10591330C2semidirect
8. #10591251C2semidirect
9. #10591235C2semidirect
20. #63982C4semidirect
385. C32#2378semidirect
449. C3#75491semidirect

Maximal subgroups

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

subgroupindex
C2×#639822
#105926412
C3×#49442
#105917012
#105916972
#105913332
#105913302
#105912512
#105912352
#754913