Finite Group Databasebeta

← #11787045

Subgroups — #11787045

Order 1152.

597 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C211yesmaximal, characteristic
2#10592801C211yesmaximal, characteristic, complemented
3C2×#63577C211yesmaximal, characteristic, complemented
4C2×#63569C211yesmaximal, characteristic
5#10591084C211yesmaximal, characteristic
6C3×#4550C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#72017—31nomaximal
9#68694—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#901—22no—
18C3×#901—22no—
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21#63641—21no—
22#63641—21no—
23#63577—22no—
24#63569—22no—
25#63566C411yescharacteristic, complemented
26#63566C411yescharacteristic, complemented
27#63563C411yescharacteristic, complemented
28#63563C411yescharacteristic, complemented
29C2×C3×#131—31no—
30C2×#901D311yescharacteristic
31C2×#837—31no—
32#5233—31no—
33C2×#822—31no—
34#5113—31no—
35C2×#819—31no—
36#5102—31no—
37#5102—31no—
38#5102—61no—
39C2×#805—31no—
40C3×#336—31no—
41#4555—31no—
42#4550D311yescharacteristic, complemented
43#4523—31no—
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67—21no—
46C22×C3×Dic3—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235D412yes—
50C3×#235Q812yes—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6C2×C411yescharacteristic
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C2×C32×C8D411yescharacteristic
57C2×C32×C8D411yescharacteristic
58#3757—21no—
59C4⋊(C3⋊Dic3)C2×C411yescharacteristic
60C4⋊(C3⋊Dic3)C2×C411yescharacteristic
61C4×C3⋊Dic3—21no—
62#3748—21no—
63#3748—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—21no—
67C3×#208—21no—
68C3×#208D412yes—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8C2×C411yescharacteristic
73C2×C3×C3⋊C8C2×C411yescharacteristic
74C3×ΓL(1,𝔽25)—24no—
75C3×D3×C8—24no—
76#1866—91noSylow
77C2×C3×#41—31no—
78C2×#235C2×D311yescharacteristic
79C3×#131—62no—
80C3×#131—62no—
81C2×C3×M16—31no—
82C2×C3×M16—61no—
83C22×C3×C8—21no—
84C22×C3×C8—31no—
85C22×C3×C8—61no—
86C22×C3×C8C2×D311yescharacteristic
87C22×C3×C8C2×D311yescharacteristic
88C2×C3×C42—31no—
89#926—31no—
90#926—31no—
91#926—61no—
92C2×C4×Dic3C2×D311yescharacteristic
93C2×#208—31no—
94C2×#208—31no—
95C2×#208—61no—
96C2×#208C2×D311yescharacteristic
97C22×C3⋊C8C2×D311yescharacteristic
98#901—22no—
99#901—22no—
100C2×ΓL(1,𝔽25)—21no—
101C2×D3×C8—21no—
102#837—62no—
103#835—31no—
104#835—31no—
105#832—31no—
106#832—31no—
107#822—62no—
108#821—31no—
109#821—31no—
110#819—62no—
111#816—31no—
112#816—31no—
113Dic3⋊C8—62no—
114Dic3⋊C8—62no—
115Dic3⋊C8—61no—
116Dic3⋊C8—61no—
117Dic3⋊C8—61no—
118Dic3⋊C8—61no—
119#805—62no—
120C23×C32#4111yescharacteristic
121C22×C3×D3—21no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×Q811yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C3×#67—22no—
131C3×#67—22no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C3×D12—21no—
137C3×D12C4⋊C412yes—
138C3×C4×D3—22no—
139C3×C4×D3—22no—
140C3×Dic6—21no—
141C3×Dic6C4⋊C412yes—
142C32×C8—21no—
143C32×C8—21no—
144C3⋊(C3⋊C8)—41no—
145C3×C3⋊C8—21no—
146C3×C3⋊C8—21no—
147C3×C3⋊C8—22no—
148C2×#131—31no—
149C2×#108—91no—
150#424—91no—
151C2×#104—91no—
152#416—91no—
153#339—91no—
154#336—31no—
155C3×#41—32no—
156C3×#41—32no—
157C3×#41—61no—
158C3×#41—61no—
159C2×C3×Q8—31no—
160C2×C3×D4—31no—
161C2×C3×D4—61no—
162C22×C3×C4—21no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C2×#67—21no—
168C22×Dic3—21no—
169#235—21no—
170#235—21no—
171#235Dic612yes—
172#235#6712yes—
173C2×D12C4×D311yescharacteristic
174C2×C4×D3—21no—
175C2×Dic6C4×D311yescharacteristic
176C3×M16—32no—
177C3×M16—64no—
178C3×M16—61no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—31no—
186C2×C3×C8—31no—
187C2×C3×C8—41no—
188C2×C3×C8—41no—
189C2×C3×C8—64no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192C2×C3×C8—61no—
193C2×C3×C8D1211yescharacteristic
194C2×C3×C8D1211yescharacteristic
195C2×C3×C8#6711yescharacteristic
196C2×C3×C8#6711yescharacteristic
197C3×C42—61no—
198C3×C42—61no—
199#217—62no—
200#217—61no—
201#217—61no—
202C4⋊Dic3—31no—
203C4⋊Dic3—31no—
204C4⋊Dic3—31no—
205C4⋊Dic3—31no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4×Dic3—21no—
209C4×Dic3—21no—
210C4×Dic3—62no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213#208—21no—
214#208—61no—
215#208—61no—
216#208—61no—
217#208—61no—
218#208—121no—
219#208—121no—
220#208#6712yes—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—62no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8C4×D311yescharacteristic
228C2×C3⋊C8C4×D311yescharacteristic
229ΓL(1,𝔽25)—24no—
230D3×C8—24no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32C4×D411yescharacteristic
234C22×C32C22⋊Q811yescharacteristic
235C22×C32#12311yescharacteristic
236C2×C3×D3—22no—
237C2×C3×D3—41no—
238C2×C3×D3—41no—
239C32×C4C2×C4⋊C411yescharacteristic
240C32×C4C4×D411yescharacteristic
241C32×C4#12011yescharacteristic
242C32×C4C22⋊Q811yescharacteristic
243C3⋊Dic3—41no—
244C3⋊Dic3—41no—
245C3×Dic3—22no—
246C3×Dic3—42no—
247C2×#41—31no—
248#131—62no—
249#131—62no—
250C2×M16—31no—
251C2×M16—61no—
252C2×M16—91no—
253C22×C8—31no—
254C22×C8—61no—
255C22×C8D3211yescharacteristic
256#117—91no—
257C2×C42—31no—
258#108—182no—
259C4⋊C8—181no—
260C4⋊C8—181no—
261#104—182no—
262#103—91no—
263#103—91no—
264#102—91no—
265#102—91no—
266C23×C3—21no—
267C23×C3—61no—
268C23×C3#23511yescharacteristic
269C23×C3#23511yescharacteristic
270C22×D3—21no—
271C3×Q8—32no—
272C3×Q8—61no—
273C3×D4—32no—
274C3×D4—62no—
275C3×D4—62no—
276C3×D4—61no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—61no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4C2×Dic611yescharacteristic
290C2×C3×C4C2×C4×D311yescharacteristic
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C2×D1211yescharacteristic
293C2×C3×C4#23511yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4#23711yescharacteristic
297C2×C3×C4D3×Q811yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301#67—22no—
302#67—22no—
303C2×Dic3—21no—
304C2×Dic3—22no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313D12—21no—
314D12Dic3⋊C412yes—
315C4×D3—22no—
316C4×D3—22no—
317Dic6—21no—
318Dic6Dic3⋊C412yes—
319C3×C8—21no—
320C3×C8—21no—
321C3×C8—21no—
322C3×C8—21no—
323C3×C8—41no—
324C3×C8—41no—
325C3×C8—62no—
326C3×C8—61no—
327C3×C8—61no—
328C3⋊C8—21no—
329C3⋊C8—21no—
330C3⋊C8—22no—
331C3⋊C8—122no—
332C3⋊C8—121no—
333C3⋊C8—121no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32#38511yescharacteristic
337C2×C32#44311yescharacteristic
338C2×C32#44411yescharacteristic
339C3×D3—42no—
340#41—32no—
341#41—32no—
342#41—61no—
343#41—61no—
344C2×Q8—31no—
345C2×D4—31no—
346C2×D4—61no—
347C22×C4—61no—
348C22×C4—61no—
349C22×C4C2×D3211yescharacteristic
350M16—32no—
351M16—64no—
352M16—61no—
353M16—181no—
354M16—181no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—31no—
358C2×C8—31no—
359C2×C8—64no—
360C2×C8—61no—
361C2×C8—61no—
362C2×C8—61no—
363C2×C8—181no—
364C2×C8#62611yescharacteristic
365C2×C8#62611yescharacteristic
366C4⋊C4—91no—
367C4⋊C4—91no—
368C22⋊C4—181no—
369C42—61no—
370C42—61no—
371C42—181no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—62no—
382C22×C3—121no—
383C22×C3—121no—
384C22×C3C4×D1211yescharacteristic
385C22×C3#88311yescharacteristic
386C22×C3#89611yescharacteristic
387C22×C3#92411yescharacteristic
388C22×C3C4×#6711yescharacteristic
389C22×C3#92911yescharacteristic
390C2×D3—22no—
391C2×D3—41no—
392C2×D3—41no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—62no—
398C3×C4—122no—
399C3×C4#67⋊C411yescharacteristic
400C3×C4#88211yescharacteristic
401C3×C4D3×C4⋊C411yescharacteristic
402C3×C4#89711yescharacteristic
403C3×C4C2×Dic3⋊C411yescharacteristic
404C3×C4#92411yescharacteristic
405C3×C4C4×#6711yescharacteristic
406C3×C4#95311yescharacteristic
407Dic3—22no—
408Dic3—42no—
409Dic3—122no—
410Dic3—122no—
411Dic3—121no—
412Dic3—121no—
413Dic3—121no—
414Dic3—121no—
415C32#186611yescharacteristic, complemented, Sylow
416C23—61no—
417C23#379811yescharacteristic
418Q8—32no—
419Q8—61no—
420D4—32no—
421D4—62no—
422D4—62no—
423D4—61no—
424C2×C4—61no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—121no—
429C2×C4—121no—
430C2×C4—181no—
431C2×C4—181no—
432C2×C4D3×Dic611yescharacteristic
433C2×C4#379511yescharacteristic
434C2×C4C4×D3211yescharacteristic
435C2×C4C2×#62611yescharacteristic
436C2×C4D3×#6711yescharacteristic
437C2×C4D3×#6711yescharacteristic
438C8—21no—
439C8—21no—
440C8—61no—
441C8—61no—
442C8—62no—
443C8—361no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—41no—
452C2×C3—41no—
453C2×C3—122no—
454C2×C3#466811yescharacteristic
455C2×C3#470011yescharacteristic
456C2×C3#471711yescharacteristic
457C2×C3#514411yescharacteristic
458C2×C3#514511yescharacteristic
459C2×C3#521011yescharacteristic
460D3—42no—
461C22—21no—
462C22—21no—
463C22—62no—
464C22—121no—
465C22—121no—
466C22#6385111yescharacteristic
467C22C4×#62611yescharacteristic
468C22#6390511yescharacteristic
469C4—62no—
470C4—122no—
471C4—361no—
472C4—361no—
473C4#6385711yescharacteristic
474C4D3×Dic3⋊C411yescharacteristic
475C4#6387911yescharacteristic
476C4#6397711yescharacteristic
477C3—21no—
478C3#6869411yescharacteristic, complemented
479C3#7201711yescharacteristic, complemented
480C2—21no—
481C2—21no—
482C2—122no—
483C2#1059092311yescharacteristic
484C2#1059092411yescharacteristic
485C2#1059127811yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1866
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10592801C2semidirect
3. C2×#63577C2semidirect
6. C3×#4550C2semidirect
7. #10589162C2semidirect
25. #63566C4semidirect
26. #63566C4semidirect
27. #63563C4semidirect
28. #63563C4semidirect
42. #4550D3semidirect
415. C32#1866semidirect
478. C3#68694semidirect
479. C3#72017semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9012
#105928012
C2×#635772
C2×#635692
#105910842
C3×#45502
#105891622
#720173
#686943