Finite Group Databasebeta

← #11805577

Subgroups — #11805577

Order 1152.

1233 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#627C211yesmaximal, characteristic
2C2×#63838C211yesmaximal, characteristic
3C2×#63838C211yesmaximal, characteristic
4#10592348C211yesmaximal, characteristic
5C3×#4647C212yesmaximal
6#10591359C211yesmaximal, characteristic
7#10591337C211yesmaximal, characteristic
8#10591328C211yesmaximal, characteristic
9#10591265C212yesmaximal
10#10591244C212yesmaximal
11#10591243C212yesmaximal
12#75981—32nomaximal
13C22×#627C2211yescharacteristic
14C2×#3750C2211yescharacteristic
15C2×#3750C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×C4×Dic3C2212yes—
24C2×#3724C2212yes—
25C2×#3724C2211yescharacteristic
26C2×#3724C2211yescharacteristic
27C2×#3724C2211yescharacteristic
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2212yes—
32C4×#627—24no—
33#63838—24no—
34#63838C418yescomplemented
35C32×#95C2211yescharacteristic
36#63658C2211yescharacteristic
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39C2×#887—32no—
40C2×#887—32no—
41C2×C4×Dic6—32no—
42C3×#389—32no—
43#4984—32no—
44#4976—32no—
45#4976—32no—
46#4975—32no—
47#4975—32no—
48#4975—32no—
49C4×Dic3⋊C4—32no—
50#4649—32no—
51#4649—32no—
52#4649—61no—
53#4647—32no—
54#4647D312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C2×#627C2×C414yes—
67C2×#627D414yes—
68C2×#627Q814yes—
69#3750—22no—
70#3750Q814yescomplemented
71C4×C3⋊Dic3—22no—
72C4×C3⋊Dic3—22no—
73C4×C3⋊Dic3C2×C414yes—
74C3×C4⋊Dic3—42no—
75C3×Dic3⋊C4—24no—
76C3×Dic3⋊C4—42no—
77C3×Dic3⋊C4C2×C418yes—
78C3×C4×Dic3—24no—
79#3724—22no—
80#3724—22no—
81#3724—24no—
82#3724C2×C414yes—
83Dic3⋊Dic3—24no—
84Dic3⋊Dic3—42no—
85Dic32—24no—
86Dic32C2×C418yes—
87Q8×C4⋊C4—91noSylow
88C22×Dic6—32no—
89C2×C3×C4⋊C4—32no—
90C2×C3×C4⋊C4—32no—
91C2×C3×C4⋊C4—32no—
92C2×C3×C4⋊C4—32no—
93C2×C3×C42—32no—
94C2×C4⋊Dic3—32no—
95C2×C4⋊Dic3—32no—
96C2×C4⋊Dic3C2×D312yes—
97C2×Dic3⋊C4—32no—
98C2×Dic3⋊C4—32no—
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—32no—
106C2×Dic3⋊C4—61no—
107C2×Dic3⋊C4—61no—
108C2×Dic3⋊C4C2×D312yes—
109C2×Dic3⋊C4C2×D312yes—
110C2×Dic3⋊C4C2×D312yes—
111C2×C4×Dic3—32no—
112C2×C4×Dic3—32no—
113C2×C4×Dic3—32no—
114C2×C4×Dic3—32no—
115C2×C4×Dic3—32no—
116C2×C4×Dic3—32no—
117C2×C4×Dic3—32no—
118C2×C4×Dic3—61no—
119C2×C4×Dic3—61no—
120C2×C4×Dic3—61no—
121C2×C4×Dic3C2×D312yes—
122#887—316no—
123#887—68no—
124C4×Dic6—68no—
125C3×#95—21no—
126C3×#95—32no—
127C3×#95C2×D312yes—
128C3⋊#95—32no—
129C3⋊#95—32no—
130C3⋊#95—32no—
131C3⋊#95—61no—
132C3⋊#95C2×D312yes—
133C23×C32C2411yescharacteristic
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4C22×C412yes—
142C2×C32×C4C2×Q812yes—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3C22×C412yes—
149C2×C3⋊Dic3C22×C412yes—
150C2×C3⋊Dic3C2×D412yes—
151C2×C3⋊Dic3C2×Q812yes—
152C2×C3⋊Dic3C2×Q812yes—
153C2×C3⋊Dic3C2×Q812yes—
154C2×C3⋊Dic3#4112yes—
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×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3C22×C414yes—
164C2×C3×Dic3C22×C414yes—
165C2×C3×Dic3C2×D414yes—
166C2×C3×Dic3C2×Q814yes—
167#627C4⋊C4116yescomplemented
168C2×C4×Q8—91no—
169C2×C4×Q8—91no—
170C2×C4×Q8—91no—
171#389—32no—
172#389—91no—
173#389—91no—
174#389—92no—
175#384—92no—
176#384—91no—
177C4×C4⋊C4—92no—
178C4×C4⋊C4—91no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—32no—
183C22×C3×C4—32no—
184C22×C3×C4—32no—
185C22×C3×C4—32no—
186C22×C3×C4C22×D312yes—
187C22×C3×C4C22×D312yes—
188C22×C3×C4C22×D312yes—
189C22×Dic3—32no—
190C22×Dic3—32no—
191C22×Dic3—32no—
192C22×Dic3—32no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C22×Dic3—61no—
197C22×Dic3C22×D312yes—
198C22×Dic3C22×D312yes—
199C22×Dic3C22×D312yes—
200C22×Dic3C22×D312yes—
201C2×Dic6—38no—
202C2×Dic6—38no—
203C2×Dic6—38no—
204C3×C4⋊C4—38no—
205C3×C4⋊C4—64no—
206C3×C4⋊C4—122no—
207C3×C4⋊C4—122no—
208C3×C42—64no—
209C4⋊Dic3—42no—
210C4⋊Dic3—64no—
211C4⋊Dic3—122no—
212Dic3⋊C4—24no—
213Dic3⋊C4—38no—
214Dic3⋊C4—38no—
215Dic3⋊C4—42no—
216Dic3⋊C4—64no—
217Dic3⋊C4—64no—
218Dic3⋊C4—64no—
219Dic3⋊C4—64no—
220Dic3⋊C4—64no—
221Dic3⋊C4—64no—
222Dic3⋊C4—64no—
223Dic3⋊C4—64no—
224Dic3⋊C4—122no—
225Dic3⋊C4C4×D318yes—
226C4×Dic3—24no—
227C4×Dic3—38no—
228C4×Dic3—38no—
229C4×Dic3—38no—
230C4×Dic3—64no—
231C4×Dic3—64no—
232C4×Dic3—64no—
233C4×Dic3—64no—
234C4×Dic3—64no—
235C4×Dic3—122no—
236C4×Dic3—122no—
237C22×C32C23×C411yescharacteristic
238C22×C32C22×D411yescharacteristic
239C22×C32C22×Q811yescharacteristic
240C22×C32C22×Q811yescharacteristic
241C22×C32C2×#4111yescharacteristic
242C22×C32H(5,𝔽2)11yescharacteristic
243C22×C322−1+411yescharacteristic
244C32×C4—22no—
245C32×C4—22no—
246C32×C4—41no—
247C3⋊Dic3—22no—
248C3⋊Dic3—41no—
249C3⋊Dic3C2×C4⋊C414yes—
250C3⋊Dic3C4×Q814yescomplemented
251C3×Dic3—24no—
252C3×Dic3—42no—
253C3×Dic3—42no—
254C3×Dic3C2×C4⋊C418yes—
255C22×Q8—91no—
256C4×Q8—98no—
257C4×Q8—184no—
258C4×Q8—184no—
259C2×C4⋊C4—32no—
260C2×C4⋊C4—32no—
261C2×C4⋊C4—32no—
262C2×C4⋊C4—32no—
263C2×C4⋊C4—91no—
264C2×C4⋊C4—91no—
265C2×C4⋊C4—91no—
266C2×C4⋊C4—91no—
267C2×C4⋊C4—92no—
268C2×C4⋊C4—92no—
269C2×C4⋊C4—91no—
270C2×C4⋊C4—92no—
271C2×C42—32no—
272C2×C42—92no—
273C2×C42—91no—
274C2×C42—92no—
275C2×C42—91no—
276C2×C42—91no—
277#95—32no—
278#95—92no—
279#95—91no—
280#95D3211yescharacteristic
281C23×C3—21no—
282C23×C3C23×D312yes—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—34no—
294C2×C3×C4—34no—
295C2×C3×C4—34no—
296C2×C3×C4—34no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4C2×C4×D314yes—
312C2×C3×C4D3×Q814yes—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—22no—
321C2×Dic3—34no—
322C2×Dic3—34no—
323C2×Dic3—34no—
324C2×Dic3—34no—
325C2×Dic3—34no—
326C2×Dic3—34no—
327C2×Dic3—34no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—121no—
342C2×Dic3—121no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3C2×C4×D314yes—
346C2×Dic3C2×C4×D314yes—
347C2×Dic3D3×D414yes—
348C2×Dic3D3×Q814yes—
349Dic6—332no—
350C2×C32C22×C4⋊C411yescharacteristic
351C2×C32C2×C4×Q811yescharacteristic
352C2×C32#52011yescharacteristic
353C2×C32D4×Q811yescharacteristic
354C2×C32#55011yescharacteristic
355C2×C32#55711yescharacteristic
356C2×C32Q8211yescharacteristic
357C2×Q8—94no—
358C2×Q8—94no—
359C2×Q8—94no—
360C22×C4—32no—
361C22×C4—32no—
362C22×C4—32no—
363C22×C4—32no—
364C22×C4—91no—
365C22×C4—91no—
366C22×C4—91no—
367C22×C4—91no—
368C22×C4C2×D3211yescharacteristic
369C22×C4C2×D3211yescharacteristic
370C22×C4C2×D3211yescharacteristic
371C4⋊C4—38no—
372C4⋊C4—64no—
373C4⋊C4—94no—
374C4⋊C4—94no—
375C4⋊C4—122no—
376C4⋊C4—122no—
377C4⋊C4—182no—
378C4⋊C4—184no—
379C4⋊C4—182no—
380C4⋊C4—182no—
381C4⋊C4—184no—
382C4⋊C4—362no—
383C42—64no—
384C42—98no—
385C42—94no—
386C42—182no—
387C42—182no—
388C42—184no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3C22×C4×D312yes—
397C22×C3C2×D3×D412yes—
398C22×C3#100412yes—
399C22×C3C2×D3×Q812yes—
400C22×C3C2×D3×Q812yes—
401C22×C3D3×#4112yes—
402C22×C3#101012yes—
403C3×C4—24no—
404C3×C4—24no—
405C3×C4—38no—
406C3×C4—42no—
407C3×C4—42no—
408C3×C4—42no—
409C3×C4—42no—
410C3×C4—64no—
411C3×C4—122no—
412C3×C4—122no—
413Dic3—24no—
414Dic3—38no—
415Dic3—38no—
416Dic3—42no—
417Dic3—42no—
418Dic3—64no—
419Dic3—64no—
420Dic3—64no—
421Dic3—122no—
422Dic3—122no—
423Dic3—122no—
424Dic3D3×C4⋊C418yes—
425C32Q8×C4⋊C411yescharacteristic, complemented, Sylow
426C23C22×D3211yescharacteristic
427Q8—916no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—34no—
436C2×C4—34no—
437C2×C4—34no—
438C2×C4—34no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—62no—
447C2×C4—92no—
448C2×C4—92no—
449C2×C4—92no—
450C2×C4—92no—
451C2×C4—92no—
452C2×C4—92no—
453C2×C4—92no—
454C2×C4—181no—
455C2×C4—181no—
456C2×C4—181no—
457C2×C4—181no—
458C2×C4—181no—
459C2×C4#379712yes—
460C2×C4C4×D3212yes—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3C2×D3×C4⋊C412yes—
469C2×C3#554612yes—
470C2×C3C4×D3×Q812yes—
471C2×C3#559912yes—
472C2×C3#563212yes—
473C2×C3#568512yes—
474C2×C3#572212yes—
475C22C2×#379711yescharacteristic
476C22C2×C4×D3211yescharacteristic
477C22#6430611yescharacteristic
478C22#6430911yescharacteristic
479C22D32×D411yescharacteristic
480C22#6431311yescharacteristic
481C22D32×Q811yescharacteristic
482C4—22no—
483C4—22no—
484C4—38no—
485C4—41no—
486C4—64no—
487C4—94no—
488C4—94no—
489C4—122no—
490C4—122no—
491C4—182no—
492C4—361no—
493C3—21no—
494C3#7598112yescomplemented
495C2C4×#379711yescharacteristic
496C2#1059405111yescharacteristic
497C2#1059407211yescharacteristic
498C2#1059419011yescharacteristic
499C2#1059431311yescharacteristic
500C2#1059459711yescharacteristic
501C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, prime radical, cosocleC23×C32C24
hypercenter#95D32
hypocenterC32Q8×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
34. #63838C4semidirect
70. #3750Q8semidirect
167. #627C4⋊C4semidirect
250. C3⋊Dic3C4×Q8semidirect
425. C32Q8×C4⋊C4semidirect
494. C3#75981semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
C2×#638382
#105923482
C3×#46472
#105913592
#105913372
#105913282
#105912652
#105912442
#105912432
#759813