Finite Group Databasebeta

← #11774036

Subgroups — #11774036

Order 1152.

561 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63852C211yesmaximal, characteristic
2C3×#4719C211yesmaximal, characteristic, complemented
3#10591053C211yesmaximal, characteristic, complemented
4#10589334C211yesmaximal, characteristic, complemented
5C3×#4468C211yesmaximal, characteristic, complemented
6#10589146C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#70828—31nomaximal
9#68104—31nomaximal
10C22×#627C411yescharacteristic
11C22×#626C411yescharacteristic
12C2×#3752C2211yescharacteristic
13C2×C3×(C2×D3)⋊C4C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×#3722C411yescharacteristic
16C2×(C2×D3)⋊Dic3C411yescharacteristic
17#63852—21no—
18#63852—21no—
19#63852—21no—
20#63852—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#815—21no—
26C3×Dic3⋊C8—21no—
27Dic3⋊(C3⋊C8)—21no—
28Dic3×C3⋊C8—21no—
29C2×#885—31no—
30C2×#875—31no—
31C3×#432—31no—
32#4925—31no—
33#4719D311yescharacteristic, complemented
34#4718—31no—
35C3×#323—31no—
36#4525—31no—
37#4468—31no—
38#4468—31no—
39#4468—31no—
40#4468—31no—
41#4468—31no—
42#4468—61no—
43#4468D311yescharacteristic, complemented
44C23×C3⋊D3C2×C411yescharacteristic
45C23×C3×D3C2×C411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3C2×C411yescharacteristic
48C22×C3×Dic3C2×C411yescharacteristic
49C22×C3×Dic3C2×C411yescharacteristic
50C22×C3×Dic3C2×C411yescharacteristic
51C2×#627—21no—
52C2×#627—21no—
53C2×#627—42no—
54C2×#626—21no—
55C2×#626—21no—
56C2×#626—42no—
57C2×C32×C8—21no—
58#3752—21no—
59#3752—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4×Dic3D411yescharacteristic
64C3×C4×Dic3D411yescharacteristic
65C3×C4×Dic3D411yescharacteristic
66C3×C4×Dic3D411yescharacteristic
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69#3722—21no—
70#3722—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73#1469—91noSylow
74C22×#67—31no—
75C22×D12—31no—
76C22×Dic6—31no—
77C22×Dic6—31no—
78C2×C3×C22⋊C4—31no—
79C2×C3×C42—31no—
80C2×#217—31no—
81C2×(C2×D3)⋊C4—31no—
82C2×(C2×D3)⋊C4—31no—
83C2×(C2×D3)⋊C4—31no—
84C2×(C2×D3)⋊C4—31no—
85C2×(C2×D3)⋊C4—31no—
86C2×(C2×D3)⋊C4—61no—
87C2×(C2×D3)⋊C4C2×D311yescharacteristic
88C2×C4×Dic3C2×D311yescharacteristic
89#885—61no—
90#885—61no—
91#885—61no—
92#885—61no—
93#875—61no—
94#875—61no—
95#875—61no—
96#875—61no—
97C3×C4⋊C8—61no—
98C3×C22⋊C8—21no—
99C3×C22⋊C8—31no—
100C3×C22⋊C8—31no—
101C3×C22⋊C8C2×D311yescharacteristic
102C3×C22⋊C8C2×D311yescharacteristic
103C3×#97—61no—
104#830—31no—
105#830—31no—
106#830—61no—
107#830C2×D311yescharacteristic
108#830C2×D311yescharacteristic
109#815—21no—
110Dic3⋊C8—21no—
111Dic3⋊C8—61no—
112C8×Dic3—61no—
113C4⋊(C3⋊C8)—61no—
114C4×C3⋊C8—61no—
115C23×C32C22×C411yescharacteristic
116C22×C3⋊D3—21no—
117C22×C3⋊D3—21no—
118C22×C3⋊D3—21no—
119C22×C3⋊D3—41no—
120C22×C3⋊D3—41no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—41no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3C22⋊C411yescharacteristic
137C2×C3×Dic3C22⋊C411yescharacteristic
138C2×C3×Dic3C22⋊C411yescharacteristic
139C2×C3×Dic3C22⋊C411yescharacteristic
140#627—42no—
141#627—42no—
142#626—42no—
143#626—42no—
144C32×C8—41no—
145C3⋊(C3⋊C8)—41no—
146C3×C3⋊C8—41no—
147C3×C3⋊C8—41no—
148C2×#124—91no—
149#432—31no—
150#431—91no—
151#323—31no—
152#323—91no—
153#323—91no—
154#323—91no—
155C24×C3—31no—
156C23×D3—31no—
157C23×D3—31no—
158C23×D3—61no—
159C23×D3C4×D311yescharacteristic
160C22×C3×C4—21no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—31no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C2×#67—61no—
167C2×#67—61no—
168C2×#67—122no—
169C22×Dic3—31no—
170C22×Dic3—31no—
171C22×Dic3—61no—
172C22×Dic3C4×D311yescharacteristic
173C22×Dic3C4×D311yescharacteristic
174C22×Dic3C4×D311yescharacteristic
175C2×D12—61no—
176C2×D12—61no—
177C2×D12—122no—
178C2×Dic6—61no—
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×Dic6—61no—
182C2×Dic6—122no—
183C2×Dic6—122no—
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C2×C3×C8—41no—
187C2×C3×C8—61no—
188C2×C3×C8—61no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C42—31no—
192C3×C42—31no—
193C3×C42—31no—
194C3×C42—31no—
195#217—61no—
196#217—61no—
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—61no—
200(C2×D3)⋊C4—61no—
201(C2×D3)⋊C4—61no—
202(C2×D3)⋊C4—61no—
203(C2×D3)⋊C4—61no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—121no—
210(C2×D3)⋊C4—121no—
211C4×Dic3D1211yescharacteristic
212C4×Dic3D1211yescharacteristic
213C4×Dic3#6711yescharacteristic
214C4×Dic3#6711yescharacteristic
215C2×C3⋊C8—21no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—121no—
220C22×C32—21no—
221C22×C32—21no—
222C22×C32C2×C22⋊C411yescharacteristic
223C22×C32#13111yescharacteristic
224C22×C32#13111yescharacteristic
225C2×C3⋊D3—41no—
226C2×C3⋊D3—41no—
227C2×C3⋊D3—41no—
228C2×C3⋊D3—81no—
229C2×C3⋊D3—81no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C2×C3×D3—81no—
234C2×C3×D3—81no—
235C32×C4—21no—
236C32×C4—21no—
237C3⋊Dic3—41no—
238C3×Dic3—21no—
239C3×Dic3—21no—
240C3×Dic3—21no—
241C3×Dic3—41no—
242C3×Dic3#10012yes—
243C22×Q8—91no—
244C22×D4—91no—
245#124—181no—
246#124—181no—
247#124—181no—
248#124—181no—
249C2×C22⋊C4—31no—
250C2×C22⋊C4—91no—
251C2×C22⋊C4—91no—
252C2×C22⋊C4—91no—
253C2×C42—31no—
254C4⋊C8—61no—
255C4⋊C8—181no—
256C22⋊C8—31no—
257C22⋊C8—31no—
258C22⋊C8—91no—
259C22⋊C8D3211yescharacteristic
260#97—61no—
261C4×C8—181no—
262C23×C3—21no—
263C23×C3—61no—
264C23×C3—61no—
265C23×C3—61no—
266C23×C3—121no—
267C23×C3—121no—
268C23×C3C2×C4×D311yescharacteristic
269C23×C3C2×C4×D311yescharacteristic
270C22×D3—21no—
271C22×D3—21no—
272C22×D3—21no—
273C22×D3—41no—
274C22×D3—41no—
275C22×D3—61no—
276C22×D3—61no—
277C22×D3—62no—
278C22×D3—61no—
279C22×D3—61no—
280C22×D3—61no—
281C22×D3—61no—
282C22×D3—121no—
283C22×D3—121no—
284C22×D3—121no—
285C22×D3—121no—
286C22×D3—121no—
287C22×D3—121no—
288C22×D3—241no—
289C22×D3—241no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—31no—
293C2×C3×C4—31no—
294C2×C3×C4—31no—
295C2×C3×C4—31no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—62no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—81no—
303C2×C3×C4—121no—
304C2×C3×C4C2×D1211yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308#67—122no—
309#67—122no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312C2×Dic3—22no—
313C2×Dic3—21no—
314C2×Dic3—41no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3—241no—
321C2×Dic3(C2×D3)⋊C411yescharacteristic
322C2×Dic3(C2×D3)⋊C411yescharacteristic
323C2×Dic3(C2×D3)⋊C411yescharacteristic
324C2×Dic3(C2×D3)⋊C411yescharacteristic
325D12—122no—
326D12—122no—
327Dic6—122no—
328Dic6—122no—
329Dic6—122no—
330Dic6—122no—
331C3×C8—41no—
332C3×C8—41no—
333C3×C8—81no—
334C3×C8—121no—
335C3×C8—121no—
336C3⋊C8—41no—
337C3⋊C8—41no—
338C3⋊C8—121no—
339C3⋊C8—121no—
340C3⋊C8—241no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32#40811yescharacteristic
344C2×C32#41011yescharacteristic
345C2×C32C2×#10011yescharacteristic
346C3⋊D3—81no—
347C3×D3—81no—
348C24—31no—
349C24—91no—
350C2×Q8—181no—
351C2×Q8—181no—
352C2×Q8—362no—
353C2×D4—181no—
354C2×D4—181no—
355C2×D4—362no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4—31no—
359C22×C4—91no—
360C22×C4C2×D3211yescharacteristic
361C2×C8—21no—
362C2×C8—61no—
363C2×C8—61no—
364C2×C8—181no—
365C22⋊C4—61no—
366C22⋊C4—61no—
367C22⋊C4—181no—
368C22⋊C4—181no—
369C22⋊C4—181no—
370C22⋊C4—181no—
371C22⋊C4—181no—
372C22⋊C4—181no—
373C42—31no—
374C42—31no—
375C42—31no—
376C42—31no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—121no—
387C22×C3—121no—
388C22×C3—121no—
389C22×C3—241no—
390C22×C3—241no—
391C22×C3D3×C22⋊C411yescharacteristic
392C22×C3#90111yescharacteristic
393C22×C3#90711yescharacteristic
394C22×C3#90711yescharacteristic
395C22×C3#90711yescharacteristic
396C22×C3C2×(C2×D3)⋊C411yescharacteristic
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—41no—
400C2×D3—81no—
401C2×D3—81no—
402C2×D3—122no—
403C2×D3—121no—
404C2×D3—121no—
405C2×D3—121no—
406C2×D3—121no—
407C2×D3—121no—
408C2×D3—121no—
409C2×D3—241no—
410C2×D3—241no—
411C2×D3—242no—
412C2×D3—241no—
413C2×D3—241no—
414C2×D3—241no—
415C2×D3—241no—
416C2×D3—242no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—32no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—61no—
425C3×C4—61no—
426C3×C4—61no—
427C3×C4—121no—
428Dic3—21no—
429Dic3—21no—
430Dic3—21no—
431Dic3—41no—
432Dic3—121no—
433Dic3—121no—
434Dic3—241no—
435Dic3#82312yes—
436C32#146911yescharacteristic, complemented, Sylow
437C23—61no—
438C23—61no—
439C23—61no—
440C23—121no—
441C23—121no—
442C23—181no—
443C23—181no—
444C23—181no—
445C23—361no—
446C23—361no—
447C23C4×D3211yescharacteristic
448Q8—362no—
449Q8—362no—
450D4—362no—
451D4—362no—
452C2×C4—31no—
453C2×C4—31no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—41no—
457C2×C4—62no—
458C2×C4—61no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—121no—
462C2×C4—181no—
463C2×C4—361no—
464C2×C4D3×D1211yescharacteristic
465C2×C4D3×#6711yescharacteristic
466C8—41no—
467C8—121no—
468C8—121no—
469C8—361no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—41no—
478C2×C3—41no—
479C2×C3—241no—
480C2×C3#472711yescharacteristic
481C2×C3#474011yescharacteristic
482C2×C3D3×#10011yescharacteristic
483C2×C3#500611yescharacteristic
484C2×C3#512911yescharacteristic
485C2×C3C2×#82311yescharacteristic
486D3—81no—
487D3—242no—
488D3—241no—
489D3—241no—
490C22—21no—
491C22—21no—
492C22—121no—
493C22—121no—
494C22—121no—
495C22—241no—
496C22—241no—
497C22—361no—
498C22—361no—
499C22—361no—
500C22—721no—
501C22—721no—
502C22#6380411yescharacteristic
503C22#6380511yescharacteristic
504C22D3×(C2×D3)⋊C411yescharacteristic
505C4—21no—
506C4—21no—
507C4—32no—
508C4—61no—
509C4—61no—
510C4—61no—
511C4—121no—
512C4—361no—
513C3—21no—
514C3#6810411yescharacteristic, complemented
515C3#7082811yescharacteristic, complemented
516C2—21no—
517C2—21no—
518C2—241no—
519C2—721no—
520C2#1059040511yescharacteristic
521C2#1059095511yescharacteristic
522C2D3×#82311yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#626C4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1469
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4719C2semidirect
3. #10591053C2semidirect
4. #10589334C2semidirect
5. C3×#4468C2semidirect
6. #10589146C2semidirect
7. #10589145C2semidirect
33. #4719D3semidirect
43. #4468D3semidirect
436. C32#1469semidirect
514. C3#68104semidirect
515. C3#70828semidirect

Maximal subgroups

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

subgroupindex
C2×#638522
C3×#47192
#105910532
#105893342
C3×#44682
#105891462
#105891452
#708283
#681043