Finite Group Databasebeta

← #11787050

Subgroups — #11787050

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×#63815C211yesmaximal, characteristic
2#10592698C211yesmaximal, characteristic, complemented
3C3×#5002C211yesmaximal, characteristic
4C2×#63577C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70292—31nomaximal
9#68774—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3711—21no—
18#63815—22no—
19#63815—22no—
20C2×D3×C3⋊C8—21no—
21C4⋊(C3⋊(C3⋊C8))—21no—
22C4⋊(C3⋊(C3⋊C8))—21no—
23C3×#810C411yescharacteristic, complemented
24C3×#810C411yescharacteristic, complemented
25C3×#809C411yescharacteristic, complemented
26C3×#809C411yescharacteristic, complemented
27#63577—22no—
28#63569—22no—
29C2×#948—31no—
30C2×#907—31no—
31C3×#416—31no—
32C2×#837—31no—
33C2×#822—31no—
34C2×#819—31no—
35#5002D311yescharacteristic
36#4999—31no—
37#4999—31no—
38#4999—61no—
39C2×#805—31no—
40C3×#339—31no—
41#4550—31no—
42#4532D311yescharacteristic, complemented
43#4524—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
54C32×C4⋊C4C2×C411yescharacteristic
55C32×C4⋊C4C2×C411yescharacteristic
56C32×C22⋊C4—21no—
57C32×C42—21no—
58#3748—21no—
59#3748—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)D411yescharacteristic
64C2×C3⋊(C3⋊C8)D411yescharacteristic
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
74#3711—24no—
75D3×C3⋊C8—24no—
76#1866—91noSylow
77C2×C3×#41—31no—
78C2×#235C2×D311yescharacteristic
79C2×C3×M16—31no—
80C22×C3×C8—31no—
81C3×#117—21no—
82C3×#117C2×D311yescharacteristic
83C3×#117C2×D311yescharacteristic
84C2×C3×C42—31no—
85#948—62no—
86#948—62no—
87C2×C4×Dic3C2×D311yescharacteristic
88C2×#208—31no—
89C2×#208—31no—
90C2×#208—61no—
91C2×#208—61no—
92C2×#208C2×D311yescharacteristic
93C22×C3⋊C8—31no—
94C22×C3⋊C8—31no—
95C22×C3⋊C8—61no—
96C22×C3⋊C8—61no—
97C22×C3⋊C8C2×D311yescharacteristic
98#907—62no—
99#907—62no—
100C2×ΓL(1,𝔽25)—61no—
101C2×D3×C8—61no—
102C3×#103—31no—
103C3×#103—31no—
104C3×#102—31no—
105C3×#102—31no—
106#837—62no—
107#822—62no—
108#819—62no—
109#810Dic311yescharacteristic, complemented
110#810Dic311yescharacteristic, complemented
111#809Dic311yescharacteristic, complemented
112#809Dic311yescharacteristic, complemented
113#805—62no—
114C4⋊(C3⋊C8)—61no—
115C4⋊(C3⋊C8)—61no—
116C4⋊(C3⋊C8)—61no—
117C4⋊(C3⋊C8)—61no—
118C4⋊(C3⋊C8)—62no—
119C4⋊(C3⋊C8)—62no—
120C23×C32#4111yescharacteristic
121C22×C3×D3—21no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×Q811yescharacteristic
129C2×C32×C4#4111yescharacteristic
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—
142C3⋊(C3⋊C8)—21no—
143C3⋊(C3⋊C8)—21no—
144C3⋊(C3⋊C8)—41no—
145C3×C3⋊C8—21no—
146C3×C3⋊C8—21no—
147C3×C3⋊C8—22no—
148C2×#131—91no—
149C2×#108—91no—
150#424—91no—
151C2×#104—91no—
152#416—31no—
153#339—31no—
154#336—91no—
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#235D1212yes—
173C2×D12C2×Dic311yescharacteristic
174C2×C4×D3—21no—
175C2×Dic6C2×Dic311yescharacteristic
176C3×M16—32no—
177C3×M16—61no—
178C2×C3×C8—31no—
179C2×C3×C8—31no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4C4×D311yescharacteristic
186C3×C4⋊C4C4×D311yescharacteristic
187C3×C4⋊C4C2×Dic311yescharacteristic
188C3×C4⋊C4C2×Dic311yescharacteristic
189C3×C22⋊C4—22no—
190C3×C22⋊C4—21no—
191C3×C22⋊C4—21no—
192C3×C42—22no—
193C3×C42—21no—
194C3×C42—21no—
195C3×C42—61no—
196C3×C42—61no—
197C4×Dic3—21no—
198C4×Dic3—21no—
199#208—21no—
200#208—64no—
201#208—61no—
202#208—61no—
203#208—61no—
204#208—61no—
205#208—121no—
206#208—121no—
207#208D1212yes—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—31no—
212C2×C3⋊C8—31no—
213C2×C3⋊C8—31no—
214C2×C3⋊C8—31no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—64no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—62no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226C2×C3⋊C8—121no—
227C2×C3⋊C8C2×Dic311yescharacteristic
228C2×C3⋊C8C2×Dic311yescharacteristic
229ΓL(1,𝔽25)—64no—
230D3×C8—64no—
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×C4—41no—
240C32×C4—41no—
241C32×C4C2×C4⋊C411yescharacteristic
242C32×C4C4×D411yescharacteristic
243C32×C4#12011yescharacteristic
244C32×C4C22⋊Q811yescharacteristic
245C3×Dic3—22no—
246C3×Dic3—42no—
247C2×#41—31no—
248#131—182no—
249#131—182no—
250C2×M16—31no—
251C2×M16—91no—
252C2×M16—181no—
253C22×C8—31no—
254C22×C8—91no—
255C22×C8—181no—
256#117D3211yescharacteristic
257C2×C42—31no—
258#108—182no—
259C4⋊C8—181no—
260C4⋊C8—181no—
261#104—182no—
262#103—31no—
263#103—31no—
264#102—31no—
265#102—31no—
266C23×C3—21no—
267C23×C3—61no—
268C23×C3#23711yescharacteristic
269C23×C3#23711yescharacteristic
270C22×D3—21no—
271C3×Q8—32no—
272C3×Q8—61no—
273C3×D4—32no—
274C3×D4—62no—
275C3×D4—62no—
276C3×D4—61no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—61no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—121no—
294C2×C3×C4—121no—
295C2×C3×C4C2×Dic611yescharacteristic
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×D1211yescharacteristic
298C2×C3×C4C2×D1211yescharacteristic
299C2×C3×C4#23511yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4#23711yescharacteristic
305C2×C3×C4D3×Q811yescharacteristic
306C2×C3×C4C22×Dic311yescharacteristic
307#67—22no—
308#67—22no—
309C2×Dic3—21no—
310C2×Dic3—22no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313D12—21no—
314D12C4⋊Dic312yes—
315C4×D3—22no—
316C4×D3—22no—
317Dic6—21no—
318Dic6C4⋊Dic312yes—
319C3×C8—61no—
320C3×C8—61no—
321C3×C8—62no—
322C3⋊C8—22no—
323C3⋊C8—21no—
324C3⋊C8—21no—
325C3⋊C8—61no—
326C3⋊C8—61no—
327C3⋊C8—61no—
328C3⋊C8—61no—
329C3⋊C8—121no—
330C3⋊C8—121no—
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—61no—
352M16—184no—
353M16—181no—
354M16—181no—
355C2×C8—31no—
356C2×C8—31no—
357C2×C8—61no—
358C2×C8—61no—
359C2×C8—61no—
360C2×C8—91no—
361C2×C8—91no—
362C2×C8—184no—
363C2×C8—181no—
364C2×C8—181no—
365C2×C8—181no—
366C4⋊C4D3×Dic311yescharacteristic
367C4⋊C4D3×Dic311yescharacteristic
368C22⋊C4—21no—
369C42—21no—
370C42—61no—
371C42—61no—
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×C3#87811yescharacteristic
385C22×C3#67⋊C411yescharacteristic
386C22×C3#88311yescharacteristic
387C22×C3#88611yescharacteristic
388C22×C3#89711yescharacteristic
389C22×C3D4×Dic311yescharacteristic
390C2×D3—22no—
391C2×D3—41no—
392C2×D3—41no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—42no—
398C3×C4—42no—
399C3×C4—41no—
400C3×C4—41no—
401C3×C4—41no—
402C3×C4—41no—
403C3×C4—62no—
404C3×C4—122no—
405C3×C4C4×D1211yescharacteristic
406C3×C4#87811yescharacteristic
407C3×C4#88211yescharacteristic
408C3×C4#88211yescharacteristic
409C3×C4D3×C4⋊C411yescharacteristic
410C3×C4#89611yescharacteristic
411C3×C4C2×C4⋊Dic311yescharacteristic
412C3×C4D4×Dic311yescharacteristic
413Dic3—22no—
414Dic3—42no—
415C32#186611yescharacteristic, complemented, Sylow
416C23—61no—
417C23#380511yescharacteristic
418Q8—32no—
419Q8—61no—
420D4—32no—
421D4—62no—
422D4—62no—
423D4—61no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—61no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—62no—
430C2×C4—121no—
431C2×C4—121no—
432C2×C4D3×Dic611yescharacteristic
433C2×C4#379511yescharacteristic
434C2×C4D3×D1211yescharacteristic
435C2×C4D3×D1211yescharacteristic
436C2×C4C2×D3×Dic311yescharacteristic
437C2×C4#381111yescharacteristic
438C8—61no—
439C8—61no—
440C8—62no—
441C8—181no—
442C8—181no—
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#482311yescharacteristic
456C2×C3#482411yescharacteristic
457C2×C3#495011yescharacteristic
458C2×C3#519611yescharacteristic
459C2×C3#519711yescharacteristic
460D3—42no—
461C22—21no—
462C22—21no—
463C22—62no—
464C22—121no—
465C22—121no—
466C22#6389111yescharacteristic
467C22#6389311yescharacteristic
468C22#67⋊Dic311yescharacteristic
469C4—41no—
470C4—41no—
471C4—62no—
472C4—122no—
473C4D3×C4⋊Dic311yescharacteristic
474C4Dic3×D1211yescharacteristic
475C4#6389611yescharacteristic
476C4#6392311yescharacteristic
477C3—21no—
478C3#6877411yescharacteristic, complemented
479C3#7029211yescharacteristic, complemented
480C2—21no—
481C2—21no—
482C2—122no—
483C2#1059137911yescharacteristic
484C2#1059167511yescharacteristic
485C2#1059167611yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1866
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10592698C2semidirect
4. C2×#63577C2semidirect
6. C3×#4532C2semidirect
7. #10589155C2semidirect
23. C3×#810C4semidirect
24. C3×#810C4semidirect
25. C3×#809C4semidirect
26. C3×#809C4semidirect
42. #4532D3semidirect
109. #810Dic3semidirect
110. #810Dic3semidirect
111. #809Dic3semidirect
112. #809Dic3semidirect
415. C32#1866semidirect
478. C3#68774semidirect
479. C3#70292semidirect

Maximal subgroups

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

subgroupindex
C2×#638152
#105926982
C3×#50022
C2×#635772
C2×#635692
C3×#45322
#105891552
#702923
#687743