Finite Group Databasebeta

← #11807891

Subgroups — #11807891

Order 1152.

1183 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63953C211yesmaximal, characteristic
2#10592657C211yesmaximal, characteristic
3C3×#4944C212yesmaximal, complemented
4#10591722C211yesmaximal, characteristic
5#10591719C212yesmaximal, complemented
6#10591375C212yesmaximal, complemented
7#10591289C212yesmaximal, complemented
8#10591245C212yesmaximal, complemented
9#10591191C212yesmaximal, complemented
10#75493—32nomaximal
11C22×#638C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C22×#627C2211yescharacteristic
14C22×#624C2211yescharacteristic
15C2×C32×C22⋊C4C2211yescharacteristic
16C2×#3752C2212yes—
17C2×C3×#217C2212yes—
18C2×C3×#217C2212yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×Dic3⋊Dic3C2212yes—
22C2×Dic3⋊Dic3C2212yes—
23C2×#3722C2211yescharacteristic
24C2×#3722C2212yes—
25C2×Dic32C2211yescharacteristic
26#63953C418yescomplemented
27#63658C2212yes—
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30#63579C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33C2×#885—32no—
34C3×#388—32no—
35#4990—32no—
36#4977—32no—
37#4958—32no—
38#4958—61no—
39#4956—32no—
40#4950—32no—
41#4946—32no—
42#4944D312yescomplemented
43#4940—32no—
44#4929—32no—
45#4668—32no—
46#4668—32no—
47#4650—32no—
48#4646—32no—
49C24×C32C2311yescharacteristic
50C23×C3⋊D3C2311yescharacteristic
51C22×C32×C4C2312yes—
52C2×#638—41no—
53C2×#638—41no—
54C2×#638C2×C414yes—
55C22×C3⋊Dic3—42no—
56C22×C3⋊Dic3—41no—
57C22×C3⋊Dic3C2312yes—
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C2×#627—41no—
64C2×#627—41no—
65C2×#627C2×C414yescomplemented
66C2×#624—41no—
67C2×#624—42no—
68C32×C22⋊C4—41no—
69#3752—42no—
70C3×#217—42no—
71C3×#217C2×C418yescomplemented
72C3×Dic3⋊C4—42no—
73C3×C4×Dic3—42no—
74Dic3⋊Dic3—42no—
75Dic3⋊Dic3—42no—
76#3722—41no—
77#3722C2×C418yescomplemented
78Dic32C2×C414yescomplemented
79#2379—91noSylow
80C22×#67—32no—
81C22×#67—61no—
82C23×Dic3—32no—
83C23×Dic3—61no—
84C22×C4×D3—32no—
85C22×Dic6—32no—
86C2×C3×C4⋊C4—32no—
87C2×C3×C22⋊C4—21no—
88C2×C3×C22⋊C4—32no—
89C2×C3×C22⋊C4—32no—
90C2×C3×C22⋊C4C2×D312yes—
91C2×C3×C42—32no—
92C2×#217C2×D312yes—
93C2×#217C2×D312yes—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4—32no—
97C2×(C2×D3)⋊C4—32no—
98C2×(C2×D3)⋊C4—32no—
99C2×(C2×D3)⋊C4—62no—
100C2×C4⋊Dic3—32no—
101C2×C4⋊Dic3—32no—
102C2×Dic3⋊C4—32no—
103C2×Dic3⋊C4—32no—
104C2×Dic3⋊C4C2×D312yes—
105C2×C4×Dic3—32no—
106C2×C4×Dic3C2×D312yes—
107#885—316no—
108C3×#95—32no—
109C3×#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C3⋊#95—32no—
114C3⋊#95—32no—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—62no—
119C3⋊#95C2×D312yes—
120C3⋊#95C2×D312yes—
121C23×C32—21no—
122C23×C32—21no—
123C23×C32—22no—
124C23×C32—22no—
125C23×C32C22×C412yes—
126C23×C32C2411yescharacteristic
127C22×C3⋊D3—21no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—21no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3C22×C412yes—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135#638—44no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—44no—
142C2×C3⋊Dic3C22×C412yes—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3C22×C414yes—
154C2×C3×Dic3C22×C414yes—
155#627—44no—
156#624—44no—
157C2×#124—91no—
158#391—92no—
159#388—32no—
160#388—92no—
161#386—91no—
162#386—91no—
163#385—92no—
164#385—92no—
165#382—92no—
166C24×C3—21no—
167C24×C3C22×D312yes—
168C23×D3—32no—
169C23×D3—61no—
170C22×C3×C4—22no—
171C22×C3×C4—32no—
172C22×C3×C4—32no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4C22×D312yes—
176C22×C3×C4C22×D312yes—
177C2×#67—38no—
178C2×#67—64no—
179C2×#67—122no—
180C2×#67—122no—
181C2×#67—122no—
182C2×#67—122no—
183C22×Dic3—32no—
184C22×Dic3—32no—
185C22×Dic3—32no—
186C22×Dic3—61no—
187C22×Dic3—62no—
188C22×Dic3—122no—
189C22×Dic3—122no—
190C22×Dic3—122no—
191C22×Dic3—124no—
192C22×Dic3—122no—
193C22×Dic3C22×D312yes—
194C22×Dic3C22×D312yes—
195C22×Dic3C22×D312yes—
196C22×Dic3C22×D312yes—
197C2×C4×D3—122no—
198C2×C4×D3—122no—
199C2×C4×D3—122no—
200C2×Dic6—38no—
201C2×Dic6—122no—
202C2×Dic6—122no—
203C3×C4⋊C4—122no—
204C3×C22⋊C4—38no—
205C3×C22⋊C4—42no—
206C3×C22⋊C4—42no—
207C3×C22⋊C4—122no—
208C3×C42—122no—
209#217—42no—
210#217C4×D318yescomplemented
211(C2×D3)⋊C4—38no—
212(C2×D3)⋊C4—38no—
213(C2×D3)⋊C4—122no—
214(C2×D3)⋊C4—122no—
215(C2×D3)⋊C4—122no—
216(C2×D3)⋊C4—124no—
217C4⋊Dic3—122no—
218C4⋊Dic3—122no—
219Dic3⋊C4—42no—
220Dic3⋊C4—122no—
221Dic3⋊C4—122no—
222C4×Dic3—38no—
223C4×Dic3—42no—
224C22×C32—22no—
225C22×C32—24no—
226C22×C32—41no—
227C22×C32—42no—
228C22×C32—41no—
229C22×C32C23×C411yescharacteristic
230C22×C32H(5,𝔽2)11yescharacteristic
231C22×C32H(5,𝔽2)12yes—
232C22×C32H(5,𝔽2)11yescharacteristic
233C22×C322−1+412yes—
234C2×C3⋊D3—22no—
235C2×C3⋊D3—24no—
236C2×C3⋊D3—41no—
237C2×C3⋊D3—42no—
238C2×C3⋊D3—41no—
239C32×C4—42no—
240C3⋊Dic3—22no—
241C3⋊Dic3—42no—
242C3×Dic3—24no—
243C3×Dic3—24no—
244C3×Dic3—42no—
245C3×Dic3—42no—
246C22×Q8—91no—
247C22×D4—91no—
248C23×C4—91no—
249C23×C4—91no—
250#124—98no—
251C2×C4⋊C4—32no—
252C2×C4⋊C4—92no—
253C2×C4⋊C4—92no—
254C2×C22⋊C4—32no—
255C2×C22⋊C4—32no—
256C2×C22⋊C4—92no—
257C2×C22⋊C4—91no—
258C2×C22⋊C4—92no—
259C2×C22⋊C4D3211yescharacteristic
260C2×C42—32no—
261C2×C42—91no—
262#95—32no—
263#95—32no—
264#95—92no—
265#95—92no—
266#95—92no—
267#95—92no—
268C23×C3—22no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3—21no—
277C23×C3—22no—
278C23×C3—42no—
279C23×C3—42no—
280C23×C3C2×C4×D314yes—
281C23×C3C23×D312yes—
282C22×D3—34no—
283C22×D3—62no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—122no—
291C22×D3—121no—
292C22×D3—121no—
293C22×D3—122no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—34no—
301C2×C3×C4—34no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—42no—
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×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315#67—128no—
316#67—128no—
317C2×Dic3—22no—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—34no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—64no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—122no—
339C2×Dic3—122no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—128no—
343C2×Dic3—128no—
344C2×Dic3C2×C4×D314yes—
345C2×Dic3C2×C4×D314yes—
346C4×D3—128no—
347Dic6—128no—
348C2×C32—42no—
349C2×C32#51811yescharacteristic
350C2×C32#52012yes—
351C2×C32H(3,𝔽4)11yescharacteristic
352C2×C32#56212yes—
353C2×C32#56311yescharacteristic
354C3⋊D3—42no—
355C24—91no—
356C24C2×D3211yescharacteristic
357C2×Q8—94no—
358C2×Q8—361no—
359C2×Q8—361no—
360C2×D4—94no—
361C2×D4—361no—
362C2×D4—361no—
363C22×C4—32no—
364C22×C4—32no—
365C22×C4—32no—
366C22×C4—32no—
367C22×C4—91no—
368C22×C4—92no—
369C22×C4—361no—
370C22×C4—362no—
371C22×C4—361no—
372C22×C4—362no—
373C22×C4C2×D3212yes—
374C4⋊C4—122no—
375C4⋊C4—362no—
376C4⋊C4—362no—
377C22⋊C4—38no—
378C22⋊C4—41no—
379C22⋊C4—98no—
380C22⋊C4—122no—
381C22⋊C4—362no—
382C22⋊C4—361no—
383C42—94no—
384C42—122no—
385C22×C3—24no—
386C22×C3—24no—
387C22×C3—24no—
388C22×C3—24no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—21no—
394C22×C3—44no—
395C22×C3—42no—
396C22×C3—44no—
397C22×C3—42no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3—42no—
401C22×C3—42no—
402C22×C3C22×C4×D312yes—
403C22×C3#100412yes—
404C22×C3#100412yes—
405C22×C3#100912yes—
406C22×C3#100912yes—
407C22×C3#101012yes—
408C22×C3#101012yes—
409C2×D3—64no—
410C2×D3—64no—
411C2×D3—64no—
412C2×D3—122no—
413C2×D3—124no—
414C2×D3—122no—
415C2×D3—122no—
416C2×D3—122no—
417C2×D3—122no—
418C2×D3—241no—
419C2×D3—242no—
420C2×D3—241no—
421C3×C4—42no—
422C3×C4—42no—
423C3×C4—64no—
424C3×C4—64no—
425C3×C4—82no—
426C3×C4—122no—
427C3×C4—122no—
428Dic3—24no—
429Dic3—24no—
430Dic3—42no—
431Dic3—42no—
432Dic3—64no—
433Dic3—122no—
434Dic3—124no—
435Dic3—122no—
436Dic3—122no—
437C32#237911yescharacteristic, complemented, Sylow
438C23—21no—
439C23—22no—
440C23—22no—
441C23—21no—
442C23—92no—
443C23—181no—
444C23—182no—
445C23—182no—
446C23—181no—
447C23C4×D3212yes—
448C23C22×D3211yescharacteristic
449Q8—364no—
450D4—364no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—34no—
455C2×C4—34no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—92no—
467C2×C4—181no—
468C2×C4—181no—
469C2×C4—182no—
470C2×C4—182no—
471C2×C4—182no—
472C2×C4—364no—
473C2×C4—364no—
474C2×C3—22no—
475C2×C3—21no—
476C2×C3—22no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—44no—
480C2×C3—44no—
481C2×C3#552312yes—
482C2×C3#554512yes—
483C2×C3#554612yes—
484C2×C3#562112yes—
485C2×C3#566712yes—
486C2×C3#568312yes—
487C2×C3#571212yes—
488D3—124no—
489D3—242no—
490C22—24no—
491C22—22no—
492C22—41no—
493C22—42no—
494C22—41no—
495C22—184no—
496C22—182no—
497C22—361no—
498C22—362no—
499C22—361no—
500C22C2×C4×D3211yescharacteristic
501C22#6430811yescharacteristic
502C22#6430912yes—
503C22#6431412yes—
504C22#6433011yescharacteristic
505C4—42no—
506C4—64no—
507C4—64no—
508C4—122no—
509C4—122no—
510C4—182no—
511C4—362no—
512C3—21no—
513C3#7549312yescomplemented
514C2—42no—
515C2—362no—
516C2#1059403611yescharacteristic
517C2#1059404912yes—
518C2#1059431111yescharacteristic
519C2#1059505811yescharacteristic
520C2#1059526312yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2379
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4944C2semidirect
5. #10591719C2semidirect
6. #10591375C2semidirect
7. #10591289C2semidirect
8. #10591245C2semidirect
9. #10591191C2semidirect
26. #63953C4semidirect
42. #4944D3semidirect
65. C2×#627C2×C4semidirect
71. C3×#217C2×C4semidirect
77. #3722C2×C4semidirect
78. Dic32C2×C4semidirect
210. #217C4×D3semidirect
437. C32#2379semidirect
513. C3#75493semidirect

Maximal subgroups

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

subgroupindex
C2×#639532
#105926572
C3×#49442
#105917222
#105917192
#105913752
#105912892
#105912452
#105911912
#754933