Finite Group Databasebeta

← #11807785

Subgroups — #11807785

Order 1152.

1261 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63912C211yesmaximal, characteristic
2#10592363C211yesmaximal, characteristic, complemented
3C3×#4668C212yesmaximal, complemented
4#10591384C212yesmaximal, complemented
5#10591382C212yesmaximal, complemented
6#10591381C212yesmaximal, complemented
7#10591325C211yesmaximal, characteristic, complemented
8#10591307C212yesmaximal, complemented
9#10591255C212yesmaximal, complemented
10#74401—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×C4×D3C2212yes—
13C22×#626C2212yes—
14C22×#625C2211yescharacteristic
15C2×#3752C2212yes—
16C2×C3×(C2×D3)⋊C4C2212yes—
17C2×C3×(C2×D3)⋊C4C2212yes—
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×#3724C2211yescharacteristic
21C2×#3722C2211yescharacteristic
22C2×#3722C2211yescharacteristic
23C2×(C2×D3)⋊Dic3C2212yes—
24C2×(C2×D3)⋊Dic3C2212yes—
25C2×Dic32C2212yes—
26#63912C418yescomplemented
27C32×#95C2211yescharacteristic
28#63658C2212yes—
29#63658C2211yescharacteristic
30C3×C3⋊#95C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33C2×#884—32no—
34C3×#385—32no—
35#5213—32no—
36#5213—32no—
37#4990—32no—
38#4988—32no—
39#4987—32no—
40#4978—32no—
41#4957—32no—
42#4956—32no—
43#4951—32no—
44#4668D312yescomplemented
45#4665—32no—
46#4664—32no—
47#4664—61no—
48#4652—32no—
49C23×C3⋊D3C2311yescharacteristic
50C23×C3×D3C2312yes—
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3C2312yes—
54C22×C3⋊Dic3C2311yescharacteristic
55C2×C4×C3⋊D3—42no—
56C2×C4×C3⋊D3C2×C414yescomplemented
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C2×C3×C4×D3—42no—
61C2×C3×C4×D3—42no—
62C2×C3×C4×D3—42no—
63C2×#626—42no—
64C2×#626—42no—
65C2×#626C2×C418yescomplemented
66C2×#625—42no—
67C2×#625C2×C414yes—
68#3752—42no—
69C3×(C2×D3)⋊C4—42no—
70C3×(C2×D3)⋊C4C2×C418yescomplemented
71C3×C4⋊Dic3—42no—
72C3×Dic3⋊C4—42no—
73#3724C2×C414yescomplemented
74#3722—41no—
75#3722—41no—
76(C2×D3)⋊Dic3—42no—
77(C2×D3)⋊Dic3—42no—
78Dic32—42no—
79#2377—91noSylow
80C23×C3×C4—32no—
81C22×#67—32no—
82C22×#67—32no—
83C22×D12—32no—
84C22×C4×D3—32no—
85C22×C4×D3—61no—
86C22×C4×D3C2×D312yes—
87C2×C3×C4⋊C4—32no—
88C2×C3×C4⋊C4—32no—
89C2×C3×C22⋊C4—32no—
90C2×C3×C22⋊C4—32no—
91C2×#217—32no—
92C2×#217—32no—
93C2×(C2×D3)⋊C4—32no—
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×(C2×D3)⋊C4C2×D312yes—
101C2×(C2×D3)⋊C4C2×D312yes—
102C2×C4⋊Dic3C2×D312yes—
103C2×Dic3⋊C4—32no—
104C2×Dic3⋊C4C2×D312yes—
105C2×C4×Dic3—32no—
106C2×C4×Dic3—32no—
107#884—316no—
108C3×#95—21no—
109C3×#95—32no—
110C3×#95C2×D312yes—
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⋊#95—61no—
120C3⋊#95C2×D312yes—
121C23×C32C2411yescharacteristic
122C22×C3⋊D3—22no—
123C22×C3⋊D3—21no—
124C22×C3⋊D3—22no—
125C22×C3⋊D3—21no—
126C22×C3⋊D3C22×C412yes—
127C22×C3×D3—22no—
128C22×C3×D3—22no—
129C22×C3×D3—22no—
130C22×C3×D3—22no—
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3C22×C414yes—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4C22×C412yes—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3C22×C412yes—
144C4×C3⋊D3—44no—
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—
154C3×C4×D3—48no—
155#626—48no—
156#625—44no—
157C2×#121—91no—
158#390—92no—
159#388—92no—
160#387—92no—
161#386—92no—
162#386—92no—
163#385—32no—
164#381—91no—
165#380—91no—
166C24×C3—32no—
167C23×D3—32no—
168C23×D3—61no—
169C23×D3C22×D312yes—
170C22×C3×C4—21no—
171C22×C3×C4—22no—
172C22×C3×C4—32no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4—122no—
176C22×C3×C4—122no—
177C22×C3×C4—122no—
178C22×C3×C4C22×D312yes—
179C22×C3×C4C22×D312yes—
180C22×C3×C4C22×D312yes—
181C2×#67—38no—
182C2×#67—38no—
183C2×#67—122no—
184C2×#67—122no—
185C2×#67—122no—
186C2×#67—122no—
187C22×Dic3—32no—
188C22×Dic3—32no—
189C22×Dic3—32no—
190C22×Dic3—61no—
191C22×Dic3—62no—
192C22×Dic3C22×D312yes—
193C22×Dic3C22×D312yes—
194C22×Dic3C22×D312yes—
195C2×D12—38no—
196C2×D12—122no—
197C2×D12—122no—
198C2×C4×D3—38no—
199C2×C4×D3—42no—
200C2×C4×D3—42no—
201C2×C4×D3—42no—
202C2×C4×D3—64no—
203C2×C4×D3—122no—
204C2×C4×D3—122no—
205C2×C4×D3—124no—
206C3×C4⋊C4—122no—
207C3×C4⋊C4—122no—
208C3×C22⋊C4—38no—
209C3×C22⋊C4—122no—
210#217—122no—
211#217—122no—
212(C2×D3)⋊C4—42no—
213(C2×D3)⋊C4—122no—
214(C2×D3)⋊C4—122no—
215(C2×D3)⋊C4—122no—
216(C2×D3)⋊C4—122no—
217(C2×D3)⋊C4—122no—
218(C2×D3)⋊C4—122no—
219(C2×D3)⋊C4—124no—
220(C2×D3)⋊C4C4×D318yescomplemented
221C4⋊Dic3—42no—
222Dic3⋊C4—38no—
223Dic3⋊C4—42no—
224C4×Dic3—122no—
225C4×Dic3—122no—
226C22×C32C23×C411yescharacteristic
227C22×C32H(5,𝔽2)11yescharacteristic
228C22×C32H(5,𝔽2)12yes—
229C22×C32H(5,𝔽2)12yes—
230C22×C322−1+411yescharacteristic
231C2×C3⋊D3—22no—
232C2×C3⋊D3—22no—
233C2×C3⋊D3—22no—
234C2×C3⋊D3—42no—
235C2×C3⋊D3—42no—
236C2×C3×D3—24no—
237C2×C3×D3—24no—
238C2×C3×D3—24no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C2×C3×D3—42no—
242C2×C3×D3—42no—
243C32×C4—22no—
244C32×C4—42no—
245C3⋊Dic3—22no—
246C3⋊Dic3—42no—
247C3×Dic3—24no—
248C3×Dic3—42no—
249C3×Dic3—42no—
250C22×D4—92no—
251C22×D4—91no—
252C23×C4—32no—
253C23×C4—91no—
254#121—98no—
255C2×C4⋊C4—32no—
256C2×C4⋊C4—32no—
257C2×C4⋊C4—91no—
258C2×C22⋊C4—32no—
259C2×C22⋊C4—32no—
260C2×C22⋊C4—91no—
261C2×C22⋊C4—91no—
262C2×C22⋊C4—92no—
263C2×C22⋊C4—92no—
264C2×C22⋊C4—92no—
265C2×C42—92no—
266#95—32no—
267#95—92no—
268#95—92no—
269#95—92no—
270#95—91no—
271#95D3211yescharacteristic
272C23×C3—21no—
273C23×C3—34no—
274C23×C3—62no—
275C23×C3—62no—
276C23×C3—62no—
277C23×C3—62no—
278C23×C3—62no—
279C23×C3—62no—
280C23×C3C23×D312yes—
281C22×D3—22no—
282C22×D3—22no—
283C22×D3—22no—
284C22×D3—22no—
285C22×D3—22no—
286C22×D3—22no—
287C22×D3—34no—
288C22×D3—62no—
289C22×D3—64no—
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—62no—
293C22×D3—62no—
294C22×D3—62no—
295C22×D3—62no—
296C22×D3—122no—
297C22×D3—121no—
298C22×D3—121no—
299C22×D3C2×C4×D314yes—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—34no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—128no—
323C2×C3×C4C2×C4×D314yes—
324#67—128no—
325#67—128no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—34no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348C2×Dic3C2×C4×D314yes—
349D12—128no—
350C4×D3—48no—
351C4×D3—128no—
352C4×D3—128no—
353C2×C32#51811yescharacteristic
354C2×C32#51811yescharacteristic
355C2×C32#52011yescharacteristic
356C2×C32#56012yes—
357C2×C32#56212yes—
358C3⋊D3—42no—
359C3×D3—44no—
360C24—32no—
361C24—91no—
362C2×D4—98no—
363C2×D4—94no—
364C2×D4—362no—
365C2×D4—362no—
366C2×D4—362no—
367C22×C4—32no—
368C22×C4—32no—
369C22×C4—32no—
370C22×C4—91no—
371C22×C4—94no—
372C22×C4—92no—
373C22×C4—122no—
374C22×C4—122no—
375C22×C4—122no—
376C22×C4—362no—
377C22×C4C2×D3212yes—
378C22×C4C2×D3211yescharacteristic
379C4⋊C4—94no—
380C4⋊C4—122no—
381C4⋊C4—122no—
382C22⋊C4—38no—
383C22⋊C4—122no—
384C22⋊C4—362no—
385C22⋊C4—361no—
386C22⋊C4—361no—
387C22⋊C4—362no—
388C22⋊C4—362no—
389C42—362no—
390C22×C3—21no—
391C22×C3—22no—
392C22×C3—21no—
393C22×C3—22no—
394C22×C3—21no—
395C22×C3—64no—
396C22×C3—64no—
397C22×C3—64no—
398C22×C3—122no—
399C22×C3—122no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3C22×C4×D312yes—
403C22×C3#100412yes—
404C22×C3#100412yes—
405C22×C3#100412yes—
406C22×C3#100712yes—
407C22×C3#100912yes—
408C22×C3#100912yes—
409C2×D3—24no—
410C2×D3—24no—
411C2×D3—24no—
412C2×D3—42no—
413C2×D3—42no—
414C2×D3—42no—
415C2×D3—42no—
416C2×D3—64no—
417C2×D3—64no—
418C2×D3—64no—
419C2×D3—64no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—124no—
423C2×D3—124no—
424C2×D3—122no—
425C2×D3—122no—
426C2×D3—122no—
427C2×D3—122no—
428C3×C4—24no—
429C3×C4—42no—
430C3×C4—42no—
431C3×C4—42no—
432C3×C4—64no—
433C3×C4—82no—
434C3×C4—122no—
435C3×C4—122no—
436Dic3—24no—
437Dic3—42no—
438Dic3—42no—
439Dic3—64no—
440Dic3—122no—
441Dic3—122no—
442Dic3—122no—
443Dic3—242no—
444C32#237711yescharacteristic, complemented, Sylow
445C23—34no—
446C23—62no—
447C23—62no—
448C23—62no—
449C23—62no—
450C23—62no—
451C23—62no—
452C23—92no—
453C23—182no—
454C23—181no—
455C23—182no—
456C23—181no—
457C23C22×D3211yescharacteristic
458D4—368no—
459D4—364no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—34no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—92no—
474C2×C4—128no—
475C2×C4—182no—
476C2×C4—182no—
477C2×C4—182no—
478C2×C4—182no—
479C2×C4—364no—
480C2×C4C4×D3212yes—
481C2×C3—22no—
482C2×C3—22no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—124no—
487C2×C3#550412yes—
488C2×C3#554512yes—
489C2×C3#554512yes—
490C2×C3#559512yes—
491C2×C3#564712yes—
492C2×C3#564712yes—
493C2×C3#566612yes—
494D3—44no—
495D3—124no—
496D3—124no—
497C22—64no—
498C22—64no—
499C22—64no—
500C22—122no—
501C22—122no—
502C22—122no—
503C22—122no—
504C22—182no—
505C22—182no—
506C22—182no—
507C22—362no—
508C22—362no—
509C22C2×C4×D3211yescharacteristic
510C22#6430712yes—
511C22#6431311yescharacteristic
512C22#6431412yes—
513C22#6431611yescharacteristic
514C4—22no—
515C4—42no—
516C4—64no—
517C4—122no—
518C4—122no—
519C4—182no—
520C4—362no—
521C3—21no—
522C3#7440112yescomplemented
523C2—124no—
524C2—362no—
525C2#1059399611yescharacteristic
526C2#1059423312yes—
527C2#1059425611yescharacteristic
528C2#1059450911yescharacteristic
529C2#1059458812yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63912C2
hypercenter#95D32
hypocenterC32#2377
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592363C2semidirect
3. C3×#4668C2semidirect
4. #10591384C2semidirect
5. #10591382C2semidirect
6. #10591381C2semidirect
7. #10591325C2semidirect
8. #10591307C2semidirect
9. #10591255C2semidirect
26. #63912C4semidirect
44. #4668D3semidirect
56. C2×C4×C3⋊D3C2×C4semidirect
65. C2×#626C2×C4semidirect
70. C3×(C2×D3)⋊C4C2×C4semidirect
73. #3724C2×C4semidirect
220. (C2×D3)⋊C4C4×D3semidirect
444. C32#2377semidirect
522. C3#74401semidirect

Maximal subgroups

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

subgroupindex
C2×#639122
#105923632
C3×#46682
#105913842
#105913822
#105913812
#105913252
#105913072
#105912552
#744013