Finite Group Databasebeta

← #11805948

Subgroups — #11805948

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic
2C3×#4980C212yesmaximal
3#10591360C211yesmaximal, characteristic
4#10591360C211yesmaximal, characteristic
5#10591359C211yesmaximal, characteristic
6C4×#3724C211yesmaximal, characteristic
7#10591273C212yesmaximal
8#10591263C212yesmaximal
9#10591257C211yesmaximal, characteristic
10#10591257C211yesmaximal, characteristic
11#10591243C212yesmaximal
12#74963—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×#3724C2211yescharacteristic
25C2×#3724C2211yescharacteristic
26C2×#3724C2211yescharacteristic
27C2×#3724C2211yescharacteristic
28C2×Dic32C2212yes—
29C2×Dic32C2212yes—
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#4978—32no—
42#4975—32no—
43C4×Dic3⋊C4—32no—
44C4×Dic3⋊C4—32no—
45#4655—32no—
46#4650—32no—
47#4650—32no—
48#4649—32no—
49#4649—32no—
50#4649—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—22no—
61C2×#634—22no—
62C2×#634C2×C414yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C32×C4⋊C4C2×C414yes—
68#3750C2×C414yes—
69#3750C2×C414yes—
70C4×C3⋊Dic3C2×C414yes—
71C4×C3⋊Dic3C2×C414yes—
72C4×C3⋊Dic3C2×C414yes—
73C3×C4⋊Dic3—42no—
74C3×C4×Dic3—42no—
75#3724—24no—
76#3724—22no—
77#3724—22no—
78#3724—22no—
79#3724Q814yescomplemented
80Dic32—24no—
81Dic32—42no—
82#2355—91noSylow
83C22×Dic6—32no—
84C22×Dic6—61no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—32no—
87C2×C3×C4⋊C4C2×D312yes—
88C2×C3×C42—32no—
89C2×C4⋊Dic3C2×D312yes—
90C2×Dic3⋊C4—32no—
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4—32no—
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—32no—
96C2×Dic3⋊C4—32no—
97C2×Dic3⋊C4—32no—
98C2×Dic3⋊C4—61no—
99C2×Dic3⋊C4—61no—
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—32no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3—61no—
110C2×C4×Dic3C2×D312yes—
111#887—316no—
112#887—68no—
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⋊#95—32no—
123C3⋊#95C2×D312yes—
124C3⋊#95C2×D312yes—
125C3⋊#95C2×D312yes—
126C3⋊#95C2×D312yes—
127C23×C32C2411yescharacteristic
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4C22×C412yes—
135C2×C32×C4C22×C412yes—
136C2×C32×C4C22×C412yes—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3C22×C412yes—
142C2×C3⋊Dic3C22×C412yes—
143C2×C3⋊Dic3C22×C412yes—
144C2×C3⋊Dic3C22×C412yes—
145C2×C3⋊Dic3C2×Q812yes—
146C2×C3⋊Dic3#4112yes—
147C2×C3⋊Dic3#4112yes—
148C2×C3⋊Dic3#4112yes—
149#634—28no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3C2×Q814yes—
162C2×C4×Q8—91no—
163#391—92no—
164#387—32no—
165#387—92no—
166#384—91no—
167#382—91no—
168#382—91no—
169C4×C4⋊C4—91no—
170C4×C4⋊C4—91no—
171C4×C4⋊C4—92no—
172C4×C4⋊C4—91no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—32no—
177C22×C3×C4—32no—
178C22×C3×C4—32no—
179C22×C3×C4—32no—
180C22×C3×C4C22×D312yes—
181C22×C3×C4C22×D312yes—
182C22×C3×C4C22×D312yes—
183C22×Dic3—32no—
184C22×Dic3—32no—
185C22×Dic3—32no—
186C22×Dic3—32no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3C22×D312yes—
192C22×Dic3C22×D312yes—
193C22×Dic3C22×D312yes—
194C22×Dic3C22×D312yes—
195C2×Dic6—38no—
196C2×Dic6—64no—
197C2×Dic6—64no—
198C2×Dic6—64no—
199C2×Dic6—64no—
200C2×Dic6—64no—
201C3×C4⋊C4—24no—
202C3×C4⋊C4—122no—
203C3×C4⋊C4C4×D318yes—
204C3×C42—122no—
205C4⋊Dic3—42no—
206Dic3⋊C4—38no—
207Dic3⋊C4—38no—
208Dic3⋊C4—38no—
209Dic3⋊C4—64no—
210Dic3⋊C4—64no—
211Dic3⋊C4—64no—
212Dic3⋊C4—64no—
213Dic3⋊C4—64no—
214Dic3⋊C4—64no—
215Dic3⋊C4—64no—
216C4×Dic3—38no—
217C4×Dic3—38no—
218C4×Dic3—38no—
219C4×Dic3—42no—
220C4×Dic3—64no—
221C4×Dic3—64no—
222C4×Dic3—64no—
223C4×Dic3—64no—
224C4×Dic3—64no—
225C4×Dic3—122no—
226C4×Dic3—122no—
227C22×C32C23×C411yescharacteristic
228C22×C32C22×Q811yescharacteristic
229C22×C32C2×#4111yescharacteristic
230C22×C32C2×#4111yescharacteristic
231C22×C32C2×#4111yescharacteristic
232C22×C32H(5,𝔽2)11yescharacteristic
233C22×C322−1+411yescharacteristic
234C32×C4—22no—
235C32×C4—22no—
236C32×C4—22no—
237C3⋊Dic3—22no—
238C3⋊Dic3—22no—
239C3⋊Dic3#11714yes—
240C3⋊Dic3C4×Q814yes—
241C3×Dic3—24no—
242C3×Dic3—42no—
243C3×Dic3—42no—
244C3×Dic3—42no—
245C22×Q8—91no—
246C4×Q8—98no—
247C2×C4⋊C4—32no—
248C2×C4⋊C4—91no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—91no—
251C2×C4⋊C4—91no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—91no—
254C2×C4⋊C4—92no—
255C2×C4⋊C4D3211yescharacteristic
256C2×C42—32no—
257C2×C42—91no—
258C2×C42—91no—
259C2×C42—91no—
260C2×C42—92no—
261C2×C42—92no—
262#95—32no—
263#95—32no—
264#95—32no—
265#95—32no—
266#95—92no—
267#95—92no—
268#95—92no—
269C23×C3—21no—
270C23×C3C23×D312yes—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—34no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4C2×C4×D314yes—
299C2×C3×C4C2×C4×D314yes—
300C2×C3×C4C2×C4×D314yes—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—34no—
313C2×Dic3—34no—
314C2×Dic3—34no—
315C2×Dic3—34no—
316C2×Dic3—34no—
317C2×Dic3—34no—
318C2×Dic3—34no—
319C2×Dic3—34no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3D3×Q814yes—
337Dic6—616no—
338Dic6—616no—
339C2×C32C2×#11711yescharacteristic
340C2×C32C2×C4×Q811yescharacteristic
341C2×C32#52011yescharacteristic
342C2×C32#55411yescharacteristic
343C2×C32#55611yescharacteristic
344C2×C32#55711yescharacteristic
345C2×C32#55911yescharacteristic
346C2×Q8—94no—
347C2×Q8—182no—
348C2×Q8—182no—
349C22×C4—32no—
350C22×C4—32no—
351C22×C4—32no—
352C22×C4—32no—
353C22×C4—91no—
354C22×C4—91no—
355C22×C4—91no—
356C22×C4—91no—
357C22×C4C2×D3211yescharacteristic
358C22×C4C2×D3211yescharacteristic
359C22×C4C2×D3211yescharacteristic
360C4⋊C4—94no—
361C4⋊C4—94no—
362C4⋊C4—94no—
363C4⋊C4—122no—
364C4⋊C4—184no—
365C4⋊C4—182no—
366C4⋊C4—182no—
367C4⋊C4—182no—
368C4⋊C4#62414yes—
369C42—94no—
370C42—94no—
371C42—94no—
372C42—122no—
373C42—184no—
374C42—362no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3C22×C4×D312yes—
383C22×C3#100412yes—
384C22×C3C2×D3×Q812yes—
385C22×C3D3×#4112yes—
386C22×C3D3×#4112yes—
387C22×C3D3×#4112yes—
388C22×C3#101012yes—
389C3×C4—24no—
390C3×C4—24no—
391C3×C4—24no—
392C3×C4—24no—
393C3×C4—42no—
394C3×C4—42no—
395C3×C4—64no—
396C3×C4—122no—
397C3×C4—122no—
398C3×C4—122no—
399Dic3—24no—
400Dic3—38no—
401Dic3—38no—
402Dic3—42no—
403Dic3—42no—
404Dic3—42no—
405Dic3—64no—
406Dic3—64no—
407Dic3—64no—
408Dic3—64no—
409Dic3—64no—
410Dic3—122no—
411C32#235511yescharacteristic, complemented, Sylow
412C23C22×D3211yescharacteristic
413Q8—188no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—34no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—62no—
432C2×C4—92no—
433C2×C4—92no—
434C2×C4—92no—
435C2×C4—92no—
436C2×C4—92no—
437C2×C4—92no—
438C2×C4—92no—
439C2×C4—92no—
440C2×C4—181no—
441C2×C4—181no—
442C2×C4—181no—
443C2×C4—181no—
444C2×C4C2×#62412yes—
445C2×C4C2×#62412yes—
446C2×C4C2×#62412yes—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3D3×#11712yes—
455C2×C3#554612yes—
456C2×C3C4×D3×Q812yes—
457C2×C3#563612yes—
458C2×C3#566412yes—
459C2×C3#568512yes—
460C2×C3#570212yes—
461C22#6430611yescharacteristic
462C22#6430611yescharacteristic
463C22#6430911yescharacteristic
464C22#6431311yescharacteristic
465C22D32×Q811yescharacteristic
466C22#6431911yescharacteristic
467C22C22×#62411yescharacteristic
468C4—22no—
469C4—22no—
470C4—22no—
471C4—64no—
472C4—94no—
473C4—94no—
474C4—122no—
475C4—122no—
476C4—122no—
477C4—182no—
478C4—182no—
479C3—21no—
480C3#7496312yescomplemented
481C2#1059447211yescharacteristic
482C2#1059453411yescharacteristic
483C2#1059457011yescharacteristic
484C2#1059459711yescharacteristic
485C2#1059496911yescharacteristic
486C2#1059521911yescharacteristic
487C2Q8×#62411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2355
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
79. #3724Q8semidirect
411. C32#2355semidirect
480. C3#74963semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C3×#49802
#105913602
#105913592
C4×#37242
#105912732
#105912632
#105912572
#105912432
#749633