Finite Group Databasebeta

← #11775057

Subgroups — #11775057

Order 1152.

613 conjugacy classes of subgroups.

The subgroup lattice has 527 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594910C211yesmaximal, characteristic
2C3×#4649C211yesmaximal, characteristic, complemented
3#10591053C211yesmaximal, characteristic, complemented
4#10589317C211yesmaximal, characteristic, complemented
5C3×#4451C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#69469—31nomaximal
9#68277—31nomaximal
10C2×#3804—21no—
11#64139C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C2×C3×Dic3⋊C4—21no—
14C2×C3×C4×Dic3—21no—
15C2×C3×C4×Dic3C2211yescharacteristic
16#63978—21no—
17#63918C411yescharacteristic, complemented
18#63911C411yescharacteristic, complemented
19#63894C411yescharacteristic, complemented
20Dic3×D12C411yescharacteristic, complemented
21#63880—21no—
22#63852—21no—
23C32×#95C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27Dic3⋊(C3⋊C8)—21no—
28Dic3×C3⋊C8—21no—
29#5596—31no—
30#5477—31no—
31C3×C4×C4⋊C4—31no—
32#4925—31no—
33#4718—31no—
34#4649D311yescharacteristic, complemented
35C3×#327—31no—
36#4537—31no—
37#4470—31no—
38#4451—31no—
39#4451—31no—
40#4451—31no—
41#4451—31no—
42#4451—61no—
43#4451D311yescharacteristic, complemented
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#638—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—
60#3752—21no—
61C4⋊(C3⋊Dic3)C2×C411yescharacteristic
62C2×C3⋊(C3⋊C8)—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3C2×C411yescharacteristic
65C3×Dic3⋊C4—24no—
66C3×C4×Dic3—42no—
67C3×C4×Dic3C2×C411yescharacteristic
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72Dic3⋊Dic3—21no—
73#3722—21no—
74(C2×D3)⋊Dic3—21no—
75#1502—91noSylow
76C2×#237—61no—
77C2×#235—61no—
78C3×#121—31no—
79C2×C3×C4⋊C4—61no—
80C2×C3×C42—31no—
81C2×C3×C42—61no—
82#940—31no—
83#939—61no—
84D4×Dic3—31no—
85#930—31no—
86#930—31no—
87#930—61no—
88#930—61no—
89#930C2×D311yescharacteristic
90C2×Dic3⋊C4—21no—
91C2×C4×Dic3—21no—
92C2×C4×Dic3C2×D311yescharacteristic
93#893—31no—
94#888—31no—
95#885—61no—
96#67⋊C4—61no—
97#875—61no—
98#874—31no—
99C4×D12—31no—
100C4×D12—31no—
101C4×D12—61no—
102#869—31no—
103C3×C22⋊C8—31no—
104C3×#95—21no—
105C3×#95—31no—
106C3×#95C2×D311yescharacteristic
107C3×#95C2×D311yescharacteristic
108C3⋊#95C2×D311yescharacteristic
109#830—31no—
110#830—31no—
111#830—61no—
112#830C2×D311yescharacteristic
113Dic3⋊C8—61no—
114C8×Dic3—61no—
115C4⋊(C3⋊C8)—61no—
116C4×C3⋊C8—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—21no—
119C22×C3×D3—21no—
120C2×C32×C4—22no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126#638—41no—
127#638—41no—
128C2×C3⋊Dic3—21no—
129C4⋊(C3⋊D3)—41no—
130C3×#67—41no—
131C3×#67—41no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3C22⋊C411yescharacteristic
138C2×C3×Dic3C22⋊C411yescharacteristic
139C2×C3×Dic3C22⋊C411yescharacteristic
140C2×C3×Dic3C22⋊C411yescharacteristic
141C2×C3×Dic3D812yes—
142C2×C3×Dic3SD1612yes—
143C3×D12—41no—
144#627—42no—
145#626—42no—
146#626—42no—
147#624—42no—
148D3×Dic3—42no—
149C3⋊(C3⋊C8)—41no—
150C3×C3⋊C8—41no—
151#532—91no—
152#431—91no—
153C4×C4⋊C4—31no—
154#327—31no—
155#327—91no—
156#327—91no—
157#327—91no—
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4—41no—
166C22×C3×C4—61no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C2×#67—21no—
170C2×#67—61no—
171C2×#67—61no—
172C2×#67—61no—
173C2×#67—61no—
174C2×#67—121no—
175C22×Dic3—21no—
176C22×Dic3—61no—
177C22×Dic3#6711yescharacteristic
178C22×Dic3#6711yescharacteristic
179#237—122no—
180#237—122no—
181#235—122no—
182#235—122no—
183C2×D12—31no—
184C2×D12—31no—
185C2×D12—61no—
186C2×D12—61no—
187C2×D12—61no—
188C2×D12C4×D311yescharacteristic
189C2×C4×D3—61no—
190C2×C4×D3—61no—
191C2×C4×D3—61no—
192C2×Dic6—61no—
193C2×Dic6—61no—
194C2×C3×C8—61no—
195C3×C4⋊C4—31no—
196C3×C4⋊C4—64no—
197C3×C22⋊C4—61no—
198C3×C42—31no—
199C3×C42—31no—
200C3×C42—31no—
201C3×C42—31no—
202C3×C42—122no—
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—24no—
217Dic3⋊C4—61no—
218C4×Dic3—42no—
219C4×Dic3C4×D311yescharacteristic
220C4×Dic3C4×D311yescharacteristic
221C4×Dic3D1211yescharacteristic
222C4×Dic3D1211yescharacteristic
223C2×C3⋊C8—21no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—121no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32C2×C22⋊C411yescharacteristic
230C22×C32C2×D811yescharacteristic
231C22×C32C2×SD1611yescharacteristic
232C2×C3⋊D3—41no—
233C2×C3⋊D3—41no—
234C2×C3⋊D3—41no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C2×C3×D3—41no—
238C32×C4—21no—
239C32×C4—21no—
240C32×C4—42no—
241C3⋊Dic3—41no—
242C3×Dic3—21no—
243C3×Dic3—42no—
244C3×Dic3—41no—
245C3×Dic3#10212yes—
246C3×Dic3#10212yes—
247C3×Dic3#10412yes—
248C2×#41—181no—
249C4⋊Q8—91no—
250#127—91no—
251#124—181no—
252#121—31no—
253#121—91no—
254#121—181no—
255C4×D4—91no—
256C4×D4—91no—
257C4×D4—181no—
258C2×C4⋊C4—61no—
259C2×C42—31no—
260C2×C42—61no—
261C4⋊C8—181no—
262C22⋊C8—31no—
263C22⋊C8—91no—
264C4×C8—181no—
265#95—31no—
266#95D3211yescharacteristic
267C23×C3—21no—
268C23×C3—61no—
269C23×C3D3×D411yescharacteristic
270C23×C3C2×#6711yescharacteristic
271C22×D3—21no—
272C22×D3—61no—
273C22×D3—61no—
274C22×D3—121no—
275C3×D4—121no—
276C3×D4—121no—
277C3×D4—121no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—31no—
283C2×C3×C4—31no—
284C2×C3×C4—31no—
285C2×C3×C4—32no—
286C2×C3×C4—32no—
287C2×C3×C4—31no—
288C2×C3×C4—42no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—61no—
298C2×C3×C4—81no—
299C2×C3×C4—81no—
300C2×C3×C4—81no—
301C2×C3×C4—121no—
302C2×C3×C4—121no—
303C2×C3×C4C2×C4×D311yescharacteristic
304C2×C3×C4C2×C4×D311yescharacteristic
305C2×C3×C4C2×D1211yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307#67—41no—
308#67—41no—
309#67—121no—
310#67—121no—
311#67—121no—
312#67—121no—
313#67—122no—
314#67—122no—
315#67—241no—
316#67—241no—
317C2×Dic3—22no—
318C2×Dic3—22no—
319C2×Dic3—21no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3—61no—
323C2×Dic3—61no—
324C2×Dic3—121no—
325C2×Dic3—122no—
326C2×Dic3(C2×D3)⋊C411yescharacteristic
327C2×Dic3(C2×D3)⋊C411yescharacteristic
328C2×Dic3(C2×D3)⋊C411yescharacteristic
329C2×Dic3(C2×D3)⋊C411yescharacteristic
330C2×Dic3#21312yes—
331C2×Dic3#21512yes—
332D12—41no—
333D12—121no—
334D12—121no—
335D12—122no—
336D12—122no—
337D12—241no—
338C4×D3—122no—
339C4×D3—122no—
340C4×D3—122no—
341Dic6—122no—
342Dic6—122no—
343C3×C8—121no—
344C3⋊C8—41no—
345C3⋊C8—121no—
346C3⋊C8—121no—
347C3⋊C8—241no—
348C2×C32—21no—
349C2×C32—21no—
350C2×C32#41011yescharacteristic
351C2×C32C2×#10211yescharacteristic
352C2×C32C2×#10411yescharacteristic
353C3⋊D3—81no—
354C3×D3—81no—
355#41—362no—
356#41—362no—
357C2×Q8—181no—
358C2×D4—31no—
359C2×D4—61no—
360C2×D4—91no—
361C2×D4—181no—
362C2×D4—181no—
363C2×D4—181no—
364C22×C4—21no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—61no—
368C22×C4—181no—
369C22×C4—181no—
370C22×C4C2×D3211yescharacteristic
371C2×C8—61no—
372C2×C8—181no—
373C4⋊C4—31no—
374C4⋊C4—64no—
375C4⋊C4—91no—
376C4⋊C4—181no—
377C22⋊C4—61no—
378C22⋊C4—181no—
379C22⋊C4—181no—
380C22⋊C4—181no—
381C42—31no—
382C42—31no—
383C42—31no—
384C42—31no—
385C42—122no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—41no—
394C22×C3—41no—
395C22×C3—121no—
396C22×C3—121no—
397C22×C3—121no—
398C22×C3D3×C22⋊C411yescharacteristic
399C22×C3D3×D811yescharacteristic
400C22×C3D3×SD1611yescharacteristic
401C22×C3C2×(C2×D3)⋊C411yescharacteristic
402C22×C3C2×#21311yescharacteristic
403C22×C3C2×#21511yescharacteristic
404C2×D3—41no—
405C2×D3—41no—
406C2×D3—41no—
407C2×D3—121no—
408C2×D3—121no—
409C2×D3—121no—
410C2×D3—121no—
411C2×D3—121no—
412C2×D3—121no—
413C2×D3—241no—
414C2×D3—241no—
415C2×D3—241no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—32no—
421C3×C4—32no—
422C3×C4—32no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4—42no—
426C3×C4—42no—
427C3×C4—61no—
428C3×C4—82no—
429C3×C4—122no—
430C3×C4—121no—
431Dic3—21no—
432Dic3—42no—
433Dic3—41no—
434Dic3—121no—
435Dic3—121no—
436Dic3—241no—
437Dic3#80512yes—
438Dic3#80912yes—
439Dic3#80912yes—
440C32#150211yescharacteristic, complemented, Sylow
441C23—61no—
442C23—181no—
443C23D3×#6711yescharacteristic
444Q8—362no—
445D4—121no—
446D4—121no—
447D4—121no—
448D4—361no—
449D4—362no—
450D4—362no—
451D4—361no—
452D4—361no—
453C2×C4—22no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—31no—
457C2×C4—32no—
458C2×C4—32no—
459C2×C4—31no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—61no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4—181no—
469C2×C4—362no—
470C2×C4—362no—
471C2×C4C4×D3211yescharacteristic
472C2×C4D3×D1211yescharacteristic
473C8—121no—
474C8—361no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—41no—
483C2×C3—41no—
484C2×C3—241no—
485C2×C3#474011yescharacteristic
486C2×C3D3×#10211yescharacteristic
487C2×C3D3×#10411yescharacteristic
488C2×C3C2×#80511yescharacteristic
489C2×C3C2×#80911yescharacteristic
490C2×C3#500611yescharacteristic
491D3—81no—
492D3—241no—
493D3—241no—
494D3—481no—
495C22—21no—
496C22—21no—
497C22—121no—
498C22—121no—
499C22—121no—
500C22—361no—
501C22—361no—
502C22—361no—
503C22D3×(C2×D3)⋊C411yescharacteristic
504C22D3×#21311yescharacteristic
505C22D3×#21511yescharacteristic
506C4—21no—
507C4—21no—
508C4—32no—
509C4—32no—
510C4—32no—
511C4—42no—
512C4—61no—
513C4—122no—
514C4—121no—
515C4—361no—
516C3—21no—
517C3#6827711yescharacteristic, complemented
518C3#6946911yescharacteristic, complemented
519C2—21no—
520C2—21no—
521C2—241no—
522C2—721no—
523C2D3×#80511yescharacteristic
524C2#1059040511yescharacteristic
525C2D3×#80911yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32C2×C22⋊C4
prime radical#10594910C2
cosocleC22×C32×C4C23
hypercenter#95D32
hypocenterC32#1502
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×#4649C2semidirect
3. #10591053C2semidirect
4. #10589317C2semidirect
5. C3×#4451C2semidirect
6. #10589151C2semidirect
7. #10589149C2semidirect
17. #63918C4semidirect
18. #63911C4semidirect
19. #63894C4semidirect
20. Dic3×D12C4semidirect
34. #4649D3semidirect
43. #4451D3semidirect
440. C32#1502semidirect
517. C3#68277semidirect
518. C3#69469semidirect

Maximal subgroups

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

subgroupindex
#105949102
C3×#46492
#105910532
#105893172
C3×#44512
#105891512
#105891492
#694693
#682773