Finite Group Databasebeta

← #11808856

Subgroups — #11808856

Order 1152.

1157 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic
2C2×C4×#627C211yesmaximal, characteristic
3C3×C4×Dic3⋊C4C212yesmaximal
4#10591397C211yesmaximal, characteristic
5#10591356C211yesmaximal, characteristic
6#10591354C212yesmaximal
7#10591340C212yesmaximal
8C4×Dic3⋊Dic3C212yesmaximal
9#10591222C211yesmaximal, characteristic
10#10591215C211yesmaximal, characteristic
11#10591195C211yesmaximal, characteristic
12#73669—32nomaximal
13C22×#634C2211yescharacteristic
14C22×#627C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3750C2211yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C4×#634—24no—
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×#3724C2211yescharacteristic
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C4×#627—24no—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33#63579C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2211yescharacteristic
37#63579C2211yescharacteristic
38C2×C4×Dic6—32no—
39C2×C4×Dic6—32no—
40C2×C4×Dic6—61no—
41C3×C4×C4⋊C4—32no—
42#4982—32no—
43#4982—32no—
44#4979—32no—
45#4979—32no—
46C4×C4⋊Dic3—32no—
47#4932—32no—
48C4×Dic3⋊C4—32no—
49C4×Dic3⋊C4D312yes—
50#4657—32no—
51#4657—32no—
52#4656—32no—
53#4656—32no—
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C2×#634—22no—
62C2×#634—22no—
63C2×#634—22no—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C2×#627—22no—
69C2×#627—24no—
70C32×C42—22no—
71C4⋊(C3⋊Dic3)—22no—
72#3750—22no—
73#3750—22no—
74C4×C3⋊Dic3—22no—
75C4×C3⋊Dic3D414yes—
76C3×Dic3⋊C4—24no—
77C3×Dic3⋊C4—24no—
78C3×C4×Dic3—24no—
79C3×C4×Dic3Q818yescomplemented
80#3724—22no—
81Dic3⋊Dic3—24no—
82Dic3⋊Dic3—24no—
83Dic3⋊Dic3—24no—
84#2399—91noSylow
85C22×Dic6—32no—
86C22×Dic6—32no—
87C22×Dic6—61no—
88C2×C3×C4⋊C4—32no—
89C2×C3×C4⋊C4—32no—
90C2×C3×C42—21no—
91C2×C3×C42—32no—
92C2×C3×C42—32no—
93C2×C3×C42C2×D312yes—
94C2×C4⋊Dic3—32no—
95C2×C4⋊Dic3—32no—
96C2×C4⋊Dic3—32no—
97C2×C4⋊Dic3—32no—
98C2×C4⋊Dic3—61no—
99C2×Dic3⋊C4—32no—
100C2×Dic3⋊C4—32no—
101C2×Dic3⋊C4—32no—
102C2×Dic3⋊C4—32no—
103C2×Dic3⋊C4—32no—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—61no—
106C2×Dic3⋊C4—61no—
107C2×Dic3⋊C4C2×D312yes—
108C2×Dic3⋊C4C2×D312yes—
109C2×C4×Dic3—32no—
110C2×C4×Dic3—32no—
111C2×C4×Dic3—61no—
112C2×C4×Dic3—61no—
113C2×C4×Dic3C2×D312yes—
114C2×C4×Dic3C2×D312yes—
115C4×Dic6—68no—
116C4×Dic6—68no—
117C4×Dic6—68no—
118C3×#95—32no—
119C3×#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C3⋊#95C2×D312yes—
129C3⋊#95C2×D312yes—
130C23×C32C2411yescharacteristic
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—22no—
135C2×C32×C4C2×D412yes—
136C2×C32×C4C2×Q814yes—
137C2×C32×C4#4112yes—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3C2×D412yes—
146C2×C3⋊Dic3C2×D412yes—
147C2×C3⋊Dic3#4112yes—
148#634—28no—
149C2×C3×Dic3—22no—
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×Dic3C2×Q814yes—
159C2×C3×Dic3C2×Q814yes—
160C2×C3×Dic3#4114yes—
161#627—28no—
162C2×C4×Q8—91no—
163C2×C4×Q8—91no—
164#398—91no—
165#398—92no—
166#398—91no—
167#395—91no—
168#395—92no—
169#395—91no—
170C4×C4⋊C4—32no—
171C4×C4⋊C4—92no—
172#376—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—64no—
196C2×Dic6—64no—
197C2×Dic6—64no—
198C2×Dic6—64no—
199C2×Dic6—64no—
200C2×Dic6—64no—
201C2×Dic6—64no—
202C2×Dic6—64no—
203C2×Dic6—64no—
204C3×C4⋊C4—64no—
205C3×C4⋊C4—64no—
206C3×C42—24no—
207C3×C42—24no—
208C3×C42—38no—
209C3×C42—64no—
210C4⋊Dic3—64no—
211C4⋊Dic3—64no—
212C4⋊Dic3—64no—
213C4⋊Dic3—64no—
214C4⋊Dic3—64no—
215Dic3⋊C4—24no—
216Dic3⋊C4—24no—
217Dic3⋊C4—64no—
218Dic3⋊C4—64no—
219Dic3⋊C4—64no—
220Dic3⋊C4—64no—
221Dic3⋊C4—64no—
222Dic3⋊C4—64no—
223Dic3⋊C4—64no—
224Dic3⋊C4—64no—
225C4×Dic3—24no—
226C4×Dic3—38no—
227C4×Dic3—64no—
228C4×Dic3—64no—
229C4×Dic3—64no—
230C4×Dic3Dic618yescomplemented
231C22×C32C22×D411yescharacteristic
232C22×C32C22×Q812yes—
233C22×C32C2×#4111yescharacteristic
234C22×C32C2×#4112yes—
235C22×C32C2×#4111yescharacteristic
236C32×C4—22no—
237C32×C4—41no—
238C32×C4C4⋊Q814yes—
239C3⋊Dic3—22no—
240C3⋊Dic3—22no—
241C3⋊Dic3—22no—
242C3⋊Dic3—41no—
243C3×Dic3—24no—
244C3×Dic3—24no—
245C3×Dic3—24no—
246C3×Dic3—42no—
247C22×Q8—91no—
248C22×Q8—91no—
249C4×Q8—184no—
250C4×Q8—184no—
251C2×C4⋊C4—32no—
252C2×C4⋊C4—32no—
253C2×C4⋊C4—92no—
254C2×C4⋊C4—91no—
255C2×C4⋊C4—92no—
256C2×C4⋊C4—92no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—91no—
259C2×C4⋊C4—91no—
260C2×C42—32no—
261C2×C42—32no—
262C2×C42—91no—
263C2×C42—91no—
264C2×C42D3211yescharacteristic
265#95—32no—
266#95—32no—
267#95—91no—
268#95—92no—
269#95—91no—
270#95—92no—
271#95—92no—
272C23×C3—21no—
273C23×C3C23×D312yes—
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—24no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—34no—
286C2×C3×C4—34no—
287C2×C3×C4—34no—
288C2×C3×C4—42no—
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×Dic614yes—
299C2×C3×C4#23514yes—
300C2×C3×C4D3×D414yes—
301C2×C3×C4D3×Q814yes—
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—34no—
312C2×Dic3—34no—
313C2×Dic3—34no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
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—122no—
332C2×Dic3—122no—
333C2×Dic3C2×Dic614yes—
334C2×Dic3C2×Dic614yes—
335C2×Dic3#23514yes—
336Dic6—616no—
337Dic6—616no—
338Dic6—616no—
339C2×C32#52511yescharacteristic
340C2×C32#52511yescharacteristic
341C2×C32C2×C4⋊Q811yescharacteristic
342C2×C32#53312yes—
343C2×C32#53312yes—
344C2×Q8—182no—
345C2×Q8—182no—
346C2×Q8—184no—
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—64no—
361C4⋊C4—64no—
362C4⋊C4—182no—
363C4⋊C4—182no—
364C4⋊C4—182no—
365C4⋊C4—184no—
366C4⋊C4—182no—
367C4⋊C4—184no—
368C4⋊C4—184no—
369C42—22no—
370C42—38no—
371C42—64no—
372C42—94no—
373C42—182no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—22no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3C22×Dic612yes—
380C22×C3C2×#23512yes—
381C22×C3C2×#23512yes—
382C22×C3C2×D3×D412yes—
383C22×C3C2×D3×Q812yes—
384C22×C3D3×#4112yes—
385C22×C3D3×#4112yes—
386C3×C4—24no—
387C3×C4—24no—
388C3×C4—24no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—64no—
392C3×C4—64no—
393C3×C4—64no—
394C3×C4—122no—
395C3×C4#88818yes—
396Dic3—24no—
397Dic3—24no—
398Dic3—24no—
399Dic3—42no—
400Dic3—64no—
401Dic3—64no—
402Dic3—64no—
403Dic3—64no—
404Dic3—64no—
405Dic3—122no—
406Dic3—122no—
407Dic3—122no—
408C32#239911yescharacteristic, complemented, Sylow
409C23C22×D3211yescharacteristic
410Q8—188no—
411Q8—188no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—21no—
416C2×C4—34no—
417C2×C4—34no—
418C2×C4—34no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—92no—
429C2×C4—92no—
430C2×C4—92no—
431C2×C4—181no—
432C2×C4—181no—
433C2×C4—182no—
434C2×C4—181no—
435C2×C4—181no—
436C2×C4—182no—
437C2×C4—181no—
438C2×C4D3×Dic614yes—
439C2×C4#379812yes—
440C2×C4#381112yes—
441C2×C3—21no—
442C2×C3—22no—
443C2×C3—22no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3#547012yes—
447C2×C3C2×#88812yes—
448C2×C3#551712yes—
449C2×C3#554712yes—
450C2×C3#554712yes—
451C2×C3#557812yes—
452C2×C3#557812yes—
453C22C2×D3×Dic612yes—
454C22C2×#379811yescharacteristic
455C22D3×#23512yes—
456C22#6430611yescharacteristic
457C22C2×#381111yescharacteristic
458C4—22no—
459C4—41no—
460C4—64no—
461C4—64no—
462C4—64no—
463C4—122no—
464C4—182no—
465C4—182no—
466C4—182no—
467C4—361no—
468C4#6384014yes—
469C3—21no—
470C3#7366912yescomplemented
471C2#1059387312yes—
472C2#1059392612yes—
473C2C2×#6384011yescharacteristic
474C2#1059501611yescharacteristic
475C2#1059507611yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, prime radical, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#2399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
79. C3×C4×Dic3Q8semidirect
230. C4×Dic3Dic6semidirect
408. C32#2399semidirect
470. C3#73669semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C4×#6272
C3×C4×Dic3⋊C42
#105913972
#105913562
#105913542
#105913402
C4×Dic3⋊Dic32
#105912222
#105912152
#105911952
#736693