Finite Group Databasebeta

← #11808863

Subgroups — #11808863

Order 1152.

1083 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic
2C2×#63837C211yesmaximal, characteristic
3#10592682C211yesmaximal, characteristic
4C3×#4983C211yesmaximal, characteristic
5#10591346C211yesmaximal, characteristic
6#10591344C211yesmaximal, characteristic
7#10591339C212yesmaximal
8#10591243C212yesmaximal
9Dic3×Dic3⋊C4C212yesmaximal
10#10591239C211yesmaximal, characteristic
11#10591195C212yesmaximal
12#82467—31nomaximal
13#77740—31nomaximal
14C22×C3×Dic6C2211yescharacteristic
15C22×#627C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3750C2212yes—
18C2×#3750C2211yescharacteristic
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2211yescharacteristic
22C2×C3×C4×Dic3C2212yes—
23C2×C3×C4×Dic3C2211yescharacteristic
24C3×#887—24no—
25C2×#3724C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×Dic32C2211yescharacteristic
29C2×Dic32C2211yescharacteristic
30C2×Dic32C2212yes—
31#63837—24no—
32#63658C2211yescharacteristic
33#63658C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4×Q8—31no—
40C2×#887—31no—
41C2×#887D311yescharacteristic
42C2×C4×Dic6—31no—
43C3×#398—31no—
44#5230—31no—
45#5230—31no—
46#4983—31no—
47#4983—31no—
48#4983—61no—
49#4983D311yescharacteristic
50#4981—32no—
51#4979—31no—
52#4979—32no—
53#4979—32no—
54Dic3×C4⋊C4—32no—
55#4932—31no—
56C4×Dic3⋊C4—32no—
57C4×Dic3⋊C4—32no—
58#4657—32no—
59#4656—31no—
60#4649—32no—
61#4648—31no—
62C22×C32×C4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3×Dic3C2311yescharacteristic
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×Dic6—22no—
74C2×C3×Dic6—24no—
75C2×#627—22no—
76C2×#627—22no—
77C2×#627—22no—
78C32×C4⋊C4—22no—
79#3750—22no—
80#3750—24no—
81C3×Dic3⋊C4—22no—
82C3×Dic3⋊C4—24no—
83C3×Dic3⋊C4—24no—
84C3×C4×Dic3—24no—
85C3×C4×Dic3D414yes—
86#3724—24no—
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3—24no—
89Dic32—22no—
90Dic32—22no—
91Dic32Q818yescomplemented
92#2399—91noSylow
93C22×C3×Q8—31no—
94C22×Dic6—31no—
95C22×Dic6—31no—
96C22×Dic6C2×D311yescharacteristic
97C3×C4×Q8—64no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4C2×D311yescharacteristic
103C2×C3×C4⋊C4C2×D311yescharacteristic
104C2×C3×C42—31no—
105C2×C3×C42—32no—
106C2×C4⋊Dic3—32no—
107C2×C4⋊Dic3—31no—
108C2×Dic3⋊C4—32no—
109C2×Dic3⋊C4—31no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—31no—
112C2×Dic3⋊C4—32no—
113C2×Dic3⋊C4—31no—
114C2×Dic3⋊C4—32no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—61no—
117C2×Dic3⋊C4—62no—
118C2×Dic3⋊C4C2×D312yes—
119C2×Dic3⋊C4C2×D312yes—
120C2×Dic3⋊C4C2×D311yescharacteristic
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—31no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3C2×D312yes—
128C2×C4×Dic3C2×D311yescharacteristic
129#887—24no—
130#887—64no—
131C4×Dic6—64no—
132C3×#95—31no—
133C3×#95—32no—
134C3⋊#95—31no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—31no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—61no—
145C3⋊#95—62no—
146C3⋊#95C2×D312yes—
147C3⋊#95C2×D311yescharacteristic
148C23×C32C2411yescharacteristic
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4C2×D412yes—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3C2×Q814yes—
161C2×C3⋊Dic3#4112yes—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3C2×D412yes—
173C2×C3×Dic3C2×D412yes—
174C2×C3×Dic3C2×Q814yes—
175C2×C3×Dic3C2×Q814yes—
176C2×C3×Dic3#4114yes—
177C2×C3×Dic3#4112yes—
178C3×Dic6—28no—
179#627—28no—
180C2×C4×Q8—31no—
181C2×C4×Q8—91no—
182#398—31no—
183#398—92no—
184#398—91no—
185#395—91no—
186#395—92no—
187#395—91no—
188C4×C4⋊C4—92no—
189C4×C4⋊C4—92no—
190#376—91no—
191C2×C3×Q8—64no—
192C2×C3×Q8—62no—
193C22×C3×C4—21no—
194C22×C3×C4—22no—
195C22×C3×C4—31no—
196C22×C3×C4—32no—
197C22×C3×C4—31no—
198C22×C3×C4—32no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4C22×D312yes—
202C22×C3×C4C22×D312yes—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—62no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C22×Dic3C22×D311yescharacteristic
215C22×Dic3C22×D312yes—
216C22×Dic3C22×D311yescharacteristic
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D311yescharacteristic
219C22×Dic3C22×D311yescharacteristic
220C2×Dic6—22no—
221C2×Dic6—24no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—62no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—42no—
231C3×C4⋊C4—64no—
232C3×C4⋊C4—64no—
233C3×C4⋊C4—62no—
234C3×C42—34no—
235C3×C42—64no—
236C4⋊Dic3—62no—
237C4⋊Dic3—64no—
238Dic3⋊C4—22no—
239Dic3⋊C4—24no—
240Dic3⋊C4—24no—
241Dic3⋊C4—64no—
242Dic3⋊C4—64no—
243Dic3⋊C4—64no—
244Dic3⋊C4—64no—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247Dic3⋊C4—64no—
248Dic3⋊C4—62no—
249Dic3⋊C4—124no—
250Dic3⋊C4—122no—
251C4×Dic3—24no—
252C4×Dic3—38no—
253C4×Dic3—38no—
254C4×Dic3—62no—
255C4×Dic3—62no—
256C4×Dic3—62no—
257C4×Dic3—62no—
258C4×Dic3#6714yes—
259C22×C32C22×D411yescharacteristic
260C22×C32C22×Q812yes—
261C22×C32C2×#4112yes—
262C22×C32C2×#4111yescharacteristic
263C22×C32C2×#4111yescharacteristic
264C32×C4—22no—
265C32×C4—42no—
266C3⋊Dic3—22no—
267C3⋊Dic3—24no—
268C3⋊Dic3—41no—
269C3×Dic3—22no—
270C3×Dic3—22no—
271C3×Dic3—24no—
272C3×Dic3—24no—
273C3×Dic3—41no—
274C3×Dic3C4⋊Q814yes—
275C22×Q8—31no—
276C22×Q8—91no—
277C4×Q8—64no—
278C4×Q8—184no—
279C2×C4⋊C4—32no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—32no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—92no—
284C2×C4⋊C4—92no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—92no—
287C2×C4⋊C4D3211yescharacteristic
288C2×C42—31no—
289C2×C42—32no—
290C2×C42—92no—
291C2×C42—91no—
292C2×C42—91no—
293#95—31no—
294#95—32no—
295#95—92no—
296#95—92no—
297#95—92no—
298#95—91no—
299#95—92no—
300C23×C3—21no—
301C23×C3C23×D311yescharacteristic
302C23×C3C23×D311yescharacteristic
303C3×Q8—68no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—32no—
314C2×C3×C4—34no—
315C2×C3×C4—32no—
316C2×C3×C4—34no—
317C2×C3×C4—34no—
318C2×C3×C4—32no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—61no—
326C2×C3×C4—62no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—62no—
330C2×C3×C4—61no—
331C2×C3×C4—62no—
332C2×C3×C4—61no—
333C2×C3×C4D3×D412yes—
334C2×C3×C4C2×#6712yes—
335C2×Dic3—22no—
336C2×Dic3—21no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—22no—
343C2×Dic3—21no—
344C2×Dic3—22no—
345C2×Dic3—34no—
346C2×Dic3—34no—
347C2×Dic3—32no—
348C2×Dic3—32no—
349C2×Dic3—64no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—62no—
360C2×Dic3—61no—
361C2×Dic3—62no—
362C2×Dic3—61no—
363C2×Dic3—122no—
364C2×Dic3—121no—
365C2×Dic3—122no—
366C2×Dic3—121no—
367C2×Dic3—121no—
368C2×Dic3—122no—
369C2×Dic3#23514yes—
370C2×Dic3#23712yes—
371C2×Dic3D3×Q814yes—
372C2×Dic3D3×Q814yes—
373C2×Dic3C2×#6712yes—
374C2×Dic3C2×#6712yes—
375Dic6—28no—
376Dic6—68no—
377Dic6—68no—
378C2×C32#52511yescharacteristic
379C2×C32#52511yescharacteristic
380C2×C32C2×C4⋊Q811yescharacteristic
381C2×C32#53312yes—
382C2×C32#53312yes—
383C2×Q8—64no—
384C2×Q8—62no—
385C2×Q8—182no—
386C2×Q8—182no—
387C2×Q8—182no—
388C22×C4—31no—
389C22×C4—32no—
390C22×C4—31no—
391C22×C4—32no—
392C22×C4—31no—
393C22×C4—31no—
394C22×C4—92no—
395C22×C4—91no—
396C22×C4—91no—
397C22×C4C2×D3212yes—
398C22×C4C2×D3211yescharacteristic
399C4⋊C4—22no—
400C4⋊C4—64no—
401C4⋊C4—64no—
402C4⋊C4—62no—
403C4⋊C4—184no—
404C4⋊C4—182no—
405C4⋊C4—184no—
406C4⋊C4—184no—
407C4⋊C4—182no—
408C42—34no—
409C42—64no—
410C42—98no—
411C42—182no—
412C42—182no—
413C22×C3—22no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—21no—
418C22×C3C2×#23512yes—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C2×#23711yescharacteristic
421C22×C3C2×D3×Q812yes—
422C22×C3C2×D3×Q812yes—
423C22×C3D3×#4112yes—
424C22×C3D3×#4111yescharacteristic
425C22×C3D3×#4111yescharacteristic
426C22×C3D3×#4111yescharacteristic
427C22×C3C22×#6711yescharacteristic
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—34no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—42no—
434C3×C4—64no—
435C3×C4—62no—
436C3×C4—64no—
437C3×C4—62no—
438C3×C4—82no—
439C3×C4—121no—
440Dic3—24no—
441Dic3—22no—
442Dic3—22no—
443Dic3—24no—
444Dic3—41no—
445Dic3—64no—
446Dic3—62no—
447Dic3—64no—
448Dic3—62no—
449Dic3—124no—
450Dic3—122no—
451Dic3—121no—
452Dic3—121no—
453Dic3—241no—
454Dic3#94414yes—
455C32#239911yescharacteristic, complemented, Sylow
456C23C22×D3211yescharacteristic
457Q8—68no—
458Q8—188no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—34no—
464C2×C4—32no—
465C2×C4—34no—
466C2×C4—32no—
467C2×C4—34no—
468C2×C4—32no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—61no—
477C2×C4—62no—
478C2×C4—61no—
479C2×C4—92no—
480C2×C4—94no—
481C2×C4—182no—
482C2×C4—181no—
483C2×C4—182no—
484C2×C4—181no—
485C2×C4—182no—
486C2×C4—181no—
487C2×C4D3×#6712yes—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—21no—
493C2×C3#557812yes—
494C2×C3#557812yes—
495C2×C3#560611yescharacteristic
496C2×C3#562212yes—
497C2×C3#565611yescharacteristic
498C2×C3#568812yes—
499C2×C3D3×C4⋊Q811yescharacteristic
500C2×C3#579111yescharacteristic
501C2×C3C2×#94411yescharacteristic
502C2×C3#582811yescharacteristic
503C22D3×#23512yes—
504C22D3×#23711yescharacteristic
505C22#6431211yescharacteristic
506C22D32×Q812yes—
507C22C2×D3×#6711yescharacteristic
508C4—22no—
509C4—34no—
510C4—42no—
511C4—64no—
512C4—64no—
513C4—62no—
514C4—62no—
515C4—121no—
516C4—184no—
517C4—182no—
518C4—361no—
519C3—21no—
520C3#7774011yescharacteristic, complemented
521C3#8246711yescharacteristic, complemented
522C2#1059438612yes—
523C2#1059439812yes—
524C2#1059489611yescharacteristic
525C2#1059530111yescharacteristic
526C2D3×#94411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, prime radical, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
91. Dic32Q8semidirect
455. C32#2399semidirect
520. C3#77740semidirect
521. C3#82467semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8872
C2×#638372
#105926822
C3×#49832
#105913462
#105913442
#105913392
#105912432
Dic3×Dic3⋊C42
#105912392
#105911952
#824673
#777403