Finite Group Databasebeta

← #11775158

Subgroups — #11775158

Order 1152.

589 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594910C211yesmaximal, characteristic
2C3×#4719C211yesmaximal, characteristic, complemented
3#10591239C211yesmaximal, characteristic, complemented
4#10589336C211yesmaximal, characteristic, complemented
5C3×#4470C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic, complemented
8#70832—31nomaximal
9#68278—31nomaximal
10C2×#3804—21no—
11#64139C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C2×C3×C4×Dic3C2211yescharacteristic
14#63978—21no—
15C2×Dic32—21no—
16#63918C411yescharacteristic, complemented
17#63911C411yescharacteristic, complemented
18#63894C411yescharacteristic, complemented
19Dic3×D12C411yescharacteristic, complemented
20#63880—21no—
21#63852—21no—
22C32×C22⋊C8C2211yescharacteristic
23#63658C2211yescharacteristic
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#815—21no—
27C3×Dic3⋊C8—21no—
28#63579—21no—
29#5596—31no—
30#5477—31no—
31C3×#432—31no—
32#4932—31no—
33#4719D311yescharacteristic, complemented
34#4648—31no—
35C3×#327—31no—
36#4537—31no—
37#4470—31no—
38#4470—31no—
39#4470—31no—
40#4470—31no—
41#4470—61no—
42#4470D311yescharacteristic, complemented
43#4451—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C2×C3×D12C2×C411yescharacteristic
53C2×#627—21no—
54C2×#626—21no—
55C2×#626—21no—
56C2×#624—21no—
57#3804—42no—
58#3804—42no—
59C2×D3×Dic3—21no—
60C2×C32×C8—21no—
61#3752—21no—
62C4⋊(C3⋊Dic3)C2×C411yescharacteristic
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3C2×C411yescharacteristic
65C3×C4×Dic3C2×C411yescharacteristic
66C3×C4×Dic3C2×C411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C2×C3×C3⋊C8—21no—
70Dic3⋊Dic3—21no—
71#3722—21no—
72(C2×D3)⋊Dic3—21no—
73Dic32—24no—
74#1505—91noSylow
75C2×#237—61no—
76C2×#235—61no—
77C3×#121—31no—
78C2×C3×C42—31no—
79#940—31no—
80#939—61no—
81D4×Dic3—31no—
82#930—31no—
83#930—31no—
84#930—61no—
85#930—61no—
86#930C2×D311yescharacteristic
87C2×C4×Dic3—61no—
88C2×C4×Dic3—61no—
89C2×C4×Dic3C2×D311yescharacteristic
90#893—31no—
91#888—31no—
92#885—61no—
93#67⋊C4—61no—
94#875—61no—
95#874—31no—
96C4×D12—31no—
97C4×D12—31no—
98C4×D12—61no—
99#869—31no—
100C3×C4⋊C8—61no—
101C3×C22⋊C8—21no—
102C3×C22⋊C8—31no—
103C3×C22⋊C8C2×D311yescharacteristic
104C3×C22⋊C8C2×D311yescharacteristic
105C3×#97—61no—
106C3×#95—31no—
107C3⋊#95—31no—
108C3⋊#95—31no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95C2×D311yescharacteristic
113#830C2×D311yescharacteristic
114#815—21no—
115Dic3⋊C8—21no—
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3—21no—
118C22×C3×D3—21no—
119C2×C32×C4—41no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122#638—41no—
123#638—41no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C4⋊(C3⋊D3)—41no—
129C3×#67—41no—
130C3×#67—41no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3C22⋊C411yescharacteristic
139C2×C3×Dic3C22⋊C411yescharacteristic
140C2×C3×Dic3C22⋊C411yescharacteristic
141C2×C3×Dic3C22⋊C411yescharacteristic
142C3×D12—41no—
143#627—42no—
144#626—42no—
145#626—42no—
146#624—42no—
147D3×Dic3—42no—
148C32×C8—41no—
149C3×C3⋊C8—41no—
150#532—91no—
151#432—31no—
152#376—91no—
153#327—31no—
154#327—91no—
155#327—91no—
156#327—91no—
157C2×C3×D4—31no—
158C2×C3×D4—61no—
159C22×C3×C4—21no—
160C22×C3×C4—31no—
161C22×C3×C4—31no—
162C22×C3×C4—61no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—21no—
166C2×#67—61no—
167C2×#67—61no—
168C2×#67—61no—
169C2×#67—61no—
170C2×#67—121no—
171C22×Dic3—21no—
172C22×Dic3—61no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—121no—
176C22×Dic3D1211yescharacteristic
177C22×Dic3D1211yescharacteristic
178#237—122no—
179#237—122no—
180#235—122no—
181#235—122no—
182C2×D12—31no—
183C2×D12—31no—
184C2×D12—61no—
185C2×D12—61no—
186C2×D12—61no—
187C2×D12C4×D311yescharacteristic
188C2×C4×D3—61no—
189C2×C4×D3—61no—
190C2×C4×D3—61no—
191C2×Dic6—61no—
192C2×Dic6—61no—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—41no—
196C2×C3×C8—61no—
197C3×C4⋊C4—31no—
198C3×C22⋊C4—61no—
199C3×C42—31no—
200C3×C42—31no—
201C3×C42—31no—
202C3×C42—31no—
203#217—61no—
204(C2×D3)⋊C4—21no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—121no—
211C4⋊Dic3—31no—
212C4⋊Dic3—31no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3C4×D311yescharacteristic
216Dic3⋊C4—61no—
217C4×Dic3—64no—
218C4×Dic3—64no—
219C4×Dic3C4×D311yescharacteristic
220C4×Dic3C4×D311yescharacteristic
221C4×Dic3#6711yescharacteristic
222C4×Dic3#6711yescharacteristic
223C2×C3⋊C8—21no—
224C22×C32—21no—
225C22×C32—21no—
226C22×C32C2×C22⋊C411yescharacteristic
227C22×C32AGL(1,ℤ/8)11yescharacteristic
228C22×C32AGL(1,ℤ/8)11yescharacteristic
229C2×C3⋊D3—41no—
230C2×C3⋊D3—41no—
231C2×C3⋊D3—41no—
232C2×C3×D3—41no—
233C2×C3×D3—41no—
234C2×C3×D3—41no—
235C32×C4—21no—
236C32×C4—21no—
237C3⋊Dic3—42no—
238C3⋊Dic3—41no—
239C3×Dic3—21no—
240C3×Dic3—21no—
241C3×Dic3—21no—
242C3×Dic3—42no—
243C3×Dic3—41no—
244C3×Dic3#10412yes—
245C2×#41—181no—
246C4⋊Q8—91no—
247#127—91no—
248#124—181no—
249#121—31no—
250#121—91no—
251#121—181no—
252C4×D4—91no—
253C4×D4—91no—
254C4×D4—181no—
255C2×C42—31no—
256C2×C42—181no—
257C4⋊C8—61no—
258C22⋊C8—31no—
259C22⋊C8D3211yescharacteristic
260#97—61no—
261#95—31no—
262#95—91no—
263#95—181no—
264C23×C3—21no—
265C23×C3—61no—
266C23×C3C2×D1211yescharacteristic
267C23×C3D3×D411yescharacteristic
268C22×D3—21no—
269C22×D3—61no—
270C22×D3—61no—
271C22×D3—121no—
272C3×D4—121no—
273C3×D4—121no—
274C3×D4—121no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—31no—
278C2×C3×C4—31no—
279C2×C3×C4—31no—
280C2×C3×C4—31no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—62no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—62no—
287C2×C3×C4—61no—
288C2×C3×C4—81no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295#67—41no—
296#67—41no—
297#67—122no—
298#67—121no—
299#67—121no—
300#67—121no—
301#67—121no—
302#67—122no—
303#67—241no—
304#67—241no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—21no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—121no—
317C2×Dic3—122no—
318C2×Dic3—122no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—241no—
324C2×Dic3—241no—
325C2×Dic3(C2×D3)⋊C411yescharacteristic
326C2×Dic3(C2×D3)⋊C411yescharacteristic
327C2×Dic3(C2×D3)⋊C411yescharacteristic
328C2×Dic3(C2×D3)⋊C411yescharacteristic
329D12—41no—
330D12—121no—
331D12—121no—
332D12—122no—
333D12—122no—
334D12—241no—
335C4×D3—122no—
336C4×D3—122no—
337C4×D3—122no—
338Dic6—122no—
339Dic6—122no—
340C3×C8—41no—
341C3×C8—41no—
342C3×C8—81no—
343C3×C8—121no—
344C3⋊C8—41no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32#41011yescharacteristic
348C2×C32#41811yescharacteristic
349C2×C32C2×#10411yescharacteristic
350C3⋊D3—81no—
351C3×D3—81no—
352#41—362no—
353#41—362no—
354C2×Q8—181no—
355C2×D4—31no—
356C2×D4—61no—
357C2×D4—91no—
358C2×D4—181no—
359C2×D4—181no—
360C2×D4—181no—
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—61no—
364C22×C4—181no—
365C22×C4—181no—
366C22×C4—181no—
367C22×C4C2×D3211yescharacteristic
368C2×C8—21no—
369C2×C8—61no—
370C4⋊C4—31no—
371C4⋊C4—91no—
372C4⋊C4—181no—
373C22⋊C4—61no—
374C22⋊C4—181no—
375C22⋊C4—181no—
376C22⋊C4—181no—
377C42—31no—
378C42—31no—
379C42—31no—
380C42—31no—
381C42—184no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—121no—
392C22×C3—121no—
393C22×C3—121no—
394C22×C3D3×C22⋊C411yescharacteristic
395C22×C3#90811yescharacteristic
396C22×C3#90811yescharacteristic
397C22×C3#91111yescharacteristic
398C22×C3#91411yescharacteristic
399C22×C3C2×(C2×D3)⋊C411yescharacteristic
400C2×D3—41no—
401C2×D3—41no—
402C2×D3—41no—
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—241no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—32no—
417C3×C4—41no—
418C3×C4—41no—
419C3×C4—61no—
420C3×C4—61no—
421C3×C4—61no—
422C3×C4—122no—
423C3×C4—121no—
424Dic3—21no—
425Dic3—21no—
426Dic3—21no—
427Dic3—42no—
428Dic3—41no—
429Dic3—122no—
430Dic3—122no—
431Dic3—121no—
432Dic3—121no—
433Dic3—241no—
434Dic3—242no—
435Dic3#82512yes—
436C32#150511yescharacteristic, complemented, Sylow
437C23—61no—
438C23—181no—
439C23D3×D1211yescharacteristic
440Q8—362no—
441D4—121no—
442D4—121no—
443D4—121no—
444D4—361no—
445D4—362no—
446D4—362no—
447D4—361no—
448D4—361no—
449C2×C4—31no—
450C2×C4—31no—
451C2×C4—31no—
452C2×C4—31no—
453C2×C4—41no—
454C2×C4—62no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—62no—
458C2×C4—61no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—182no—
462C2×C4—181no—
463C2×C4—362no—
464C2×C4—362no—
465C2×C4—361no—
466C2×C4—361no—
467C2×C4C4×D3211yescharacteristic
468C2×C4D3×#6711yescharacteristic
469C8—41no—
470C8—121no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—41no—
479C2×C3—41no—
480C2×C3—241no—
481C2×C3#474011yescharacteristic
482C2×C3#477011yescharacteristic
483C2×C3D3×#10411yescharacteristic
484C2×C3#500611yescharacteristic
485C2×C3#513111yescharacteristic
486C2×C3C2×#82511yescharacteristic
487D3—81no—
488D3—241no—
489D3—241no—
490D3—481no—
491C22—21no—
492C22—21no—
493C22—121no—
494C22—121no—
495C22—121no—
496C22—361no—
497C22—361no—
498C22—361no—
499C22#6379411yescharacteristic
500C22#6379511yescharacteristic
501C22D3×(C2×D3)⋊C411yescharacteristic
502C4—21no—
503C4—21no—
504C4—32no—
505C4—61no—
506C4—61no—
507C4—61no—
508C4—122no—
509C4—121no—
510C4—362no—
511C4—361no—
512C3—21no—
513C3#6827811yescharacteristic, complemented
514C3#7083211yescharacteristic, complemented
515C2—21no—
516C2—21no—
517C2—241no—
518C2—721no—
519C2#1059040511yescharacteristic
520C2#1059093911yescharacteristic
521C2D3×#82511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10594910C2
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1505
LCSG ▷ C2×C32×C4 ▷ C22×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. #10591239C2semidirect
4. #10589336C2semidirect
5. C3×#4470C2semidirect
6. #10589151C2semidirect
7. #10589150C2semidirect
16. #63918C4semidirect
17. #63911C4semidirect
18. #63894C4semidirect
19. Dic3×D12C4semidirect
33. #4719D3semidirect
42. #4470D3semidirect
436. C32#1505semidirect
513. C3#68278semidirect
514. C3#70832semidirect

Maximal subgroups

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

subgroupindex
#105949102
C3×#47192
#105912392
#105893362
C3×#44702
#105891512
#105891502
#708323
#682783