Finite Group Databasebeta

← #11787047

Subgroups — #11787047

Order 1152.

599 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C211yesmaximal, characteristic
2C3×#5102C211yesmaximal, characteristic, complemented
3C2×#63578C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic
5#10591083C211yesmaximal, characteristic
6#10589416C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#72017—31nomaximal
9#70545—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#901—22no—
18C3×#901—22no—
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21C3×Dic3⋊C8—21no—
22C3×Dic3⋊C8—21no—
23#63578—22no—
24#63568—22no—
25#63565C411yescharacteristic, complemented
26#63565C411yescharacteristic, complemented
27#63562C411yescharacteristic, complemented
28#63562C411yescharacteristic, complemented
29C2×C3×#131—31no—
30C2×#901D311yescharacteristic
31C3×#424—31no—
32C2×#837—31no—
33#5233—31no—
34C2×#825—31no—
35C2×#822—31no—
36C2×#822—31no—
37#5102D311yescharacteristic, complemented
38#5002—31no—
39#4555—31no—
40#4550—31no—
41#4550—31no—
42#4550—61no—
43#4532—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×C3×#67—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
58C4×C3⋊Dic3—21no—
59C4×C3⋊Dic3—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
63C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
64C3×#217—21no—
65C3×C4⋊Dic3C2×C411yescharacteristic
66C3×C4⋊Dic3C2×C411yescharacteristic
67C3×C4×Dic3—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208D412yes—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
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—31no—
83C2×C3×M16—61no—
84C22×C3×C8—21no—
85C22×C3×C8—61no—
86C22×C3×C8C2×D311yescharacteristic
87C22×C3×C8C2×D311yescharacteristic
88C3×#117—31no—
89#926C2×D311yescharacteristic
90C2×C4×Dic3—31no—
91C2×C4×Dic3—31no—
92C2×C4×Dic3—61no—
93C2×#208C2×D311yescharacteristic
94C2×#208C2×D311yescharacteristic
95C22×C3⋊C8—31no—
96C22×C3⋊C8—31no—
97C22×C3⋊C8—61no—
98#901—22no—
99#901—22no—
100C2×ΓL(1,𝔽25)—21no—
101C2×D3×C8—21no—
102C3×C4⋊C8—61no—
103C3×C4⋊C8—61no—
104#837—62no—
105#835—31no—
106#835—31no—
107#832—31no—
108#832—31no—
109#825—62no—
110#822—62no—
111#822—62no—
112Dic3⋊C8—21no—
113Dic3⋊C8—21no—
114#810—31no—
115#810—31no—
116#809—31no—
117#809—31no—
118C23×C32#4111yescharacteristic
119C22×C3×D3—21no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×Q811yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C3×#67—22no—
130C3×#67—22no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C3×D12—21no—
135C3×D12C4⋊C412yes—
136C3×C4×D3—22no—
137C3×C4×D3—22no—
138C3×Dic6—21no—
139C3×Dic6C4⋊C412yes—
140C32×C8—21no—
141C32×C8—21no—
142C3⋊(C3⋊C8)—21no—
143C3⋊(C3⋊C8)—21no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—41no—
146C2×#131—31no—
147C2×#108—91no—
148#424—31no—
149C2×#104—91no—
150#416—91no—
151#339—91no—
152#336—91no—
153C3×#41—32no—
154C3×#41—32no—
155C3×#41—61no—
156C3×#41—61no—
157C2×C3×Q8—31no—
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C2×#67—21no—
165C22×Dic3—62no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168#235—21no—
169#235—21no—
170#235Dic612yes—
171#235#6712yes—
172C2×D12C4×D311yescharacteristic
173C2×C4×D3—21no—
174C2×Dic6C4×D311yescharacteristic
175C3×M16—32no—
176C3×M16—64no—
177C3×M16—61no—
178C3×M16—61no—
179C3×M16—61no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C2×C3×C8—41no—
187C2×C3×C8—41no—
188C2×C3×C8—64no—
189C2×C3×C8—61no—
190C2×C3×C8—61no—
191C2×C3×C8#6711yescharacteristic
192C2×C3×C8#6711yescharacteristic
193C2×C3×C8#6711yescharacteristic
194C2×C3×C8#6711yescharacteristic
195C3×C4⋊C4—31no—
196C3×C4⋊C4—31no—
197C3×C22⋊C4—61no—
198C3×C42—61no—
199#217—21no—
200C4⋊Dic3C4×D311yescharacteristic
201C4⋊Dic3C4×D311yescharacteristic
202C4×Dic3—21no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—121no—
208C4×Dic3—121no—
209#208—21no—
210#208—21no—
211#208—21no—
212#208#6712yes—
213C2×C3⋊C8—21no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—31no—
216C2×C3⋊C8—31no—
217C2×C3⋊C8—31no—
218C2×C3⋊C8—31no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226C2×C3⋊C8—121no—
227ΓL(1,𝔽25)—24no—
228D3×C8—24no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32C4×D411yescharacteristic
232C22×C32C22⋊Q811yescharacteristic
233C22×C32#12311yescharacteristic
234C2×C3×D3—22no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C32×C4C2×C4⋊C411yescharacteristic
238C32×C4C4×D411yescharacteristic
239C32×C4#12011yescharacteristic
240C32×C4C22⋊Q811yescharacteristic
241C3⋊Dic3—42no—
242C3×Dic3—22no—
243C3×Dic3—41no—
244C3×Dic3—41no—
245C2×#41—31no—
246#131—62no—
247#131—62no—
248C2×M16—31no—
249C2×M16—31no—
250C2×M16—61no—
251C22×C8—61no—
252C22×C8—91no—
253C22×C8D3211yescharacteristic
254#117—31no—
255C2×C42—91no—
256#108—182no—
257C4⋊C8—61no—
258C4⋊C8—61no—
259#104—182no—
260#103—91no—
261#103—91no—
262#102—91no—
263#102—91no—
264C23×C3—21no—
265C23×C3—61no—
266C23×C3#23511yescharacteristic
267C23×C3#23511yescharacteristic
268C22×D3—21no—
269C3×Q8—32no—
270C3×Q8—61no—
271C3×D4—32no—
272C3×D4—62no—
273C3×D4—62no—
274C3×D4—61no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—61no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4C2×Dic611yescharacteristic
287C2×C3×C4C2×C4×D311yescharacteristic
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4#23511yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4D3×Q811yescharacteristic
293C2×C3×C4#23911yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295C2×C3×C4C2×#6711yescharacteristic
296C2×C3×C4C2×#6711yescharacteristic
297C2×C3×C4C2×#6711yescharacteristic
298#67—22no—
299#67—22no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—21no—
303C2×Dic3—64no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—122no—
307C2×Dic3—122no—
308C2×Dic3—121no—
309C2×Dic3—121no—
310C2×Dic3—121no—
311C2×Dic3—121no—
312D12—21no—
313D12Dic3⋊C412yes—
314C4×D3—22no—
315C4×D3—22no—
316Dic6—21no—
317Dic6Dic3⋊C412yes—
318C3×C8—21no—
319C3×C8—21no—
320C3×C8—21no—
321C3×C8—21no—
322C3×C8—41no—
323C3×C8—41no—
324C3×C8—62no—
325C3×C8—121no—
326C3⋊C8—22no—
327C3⋊C8—41no—
328C3⋊C8—61no—
329C3⋊C8—61no—
330C3⋊C8—61no—
331C3⋊C8—61no—
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—181no—
349C22×C4C2×D3211yescharacteristic
350M16—32no—
351M16—64no—
352M16—61no—
353M16—61no—
354M16—61no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—64no—
358C2×C8—61no—
359C2×C8—61no—
360C2×C8—91no—
361C2×C8—91no—
362C2×C8—181no—
363C2×C8—181no—
364C2×C8#62511yescharacteristic
365C2×C8#62511yescharacteristic
366C4⋊C4—31no—
367C4⋊C4—31no—
368C22⋊C4—61no—
369C42—61no—
370C42—181no—
371C42—181no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—62no—
382C22×C3—121no—
383C22×C3—121no—
384C22×C3#89411yescharacteristic
385C22×C3#89611yescharacteristic
386C22×C3#92411yescharacteristic
387C22×C3C4×#6711yescharacteristic
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—121no—
399C3×C4—121no—
400C3×C4D3×C4⋊C411yescharacteristic
401C3×C4#89311yescharacteristic
402C3×C4C2×Dic3⋊C411yescharacteristic
403C3×C4#92411yescharacteristic
404C3×C4C4×#6711yescharacteristic
405C3×C4#93711yescharacteristic
406C3×C4#94611yescharacteristic
407C3×C4#95311yescharacteristic
408Dic3—22no—
409Dic3—41no—
410Dic3—41no—
411Dic3—124no—
412Dic3—122no—
413Dic3—122no—
414C32#186611yescharacteristic, complemented, Sylow
415C23—61no—
416C23#379811yescharacteristic
417Q8—32no—
418Q8—61no—
419D4—32no—
420D4—62no—
421D4—62no—
422D4—61no—
423C2×C4—61no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—182no—
429C2×C4—361no—
430C2×C4—361no—
431C2×C4D3×Dic611yescharacteristic
432C2×C4#379911yescharacteristic
433C2×C4C4×D3211yescharacteristic
434C2×C4C2×#62511yescharacteristic
435C2×C4D3×#6711yescharacteristic
436C2×C4D3×#6711yescharacteristic
437C8—21no—
438C8—21no—
439C8—62no—
440C8—121no—
441C8—181no—
442C8—181no—
443C2×C3—22no—
444C2×C3—22no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—122no—
453C2×C3#498911yescharacteristic
454C2×C3#514411yescharacteristic
455C2×C3#514411yescharacteristic
456C2×C3#514511yescharacteristic
457C2×C3#514511yescharacteristic
458C2×C3#521011yescharacteristic
459D3—42no—
460C22—21no—
461C22—21no—
462C22—62no—
463C22—121no—
464C22—121no—
465C22#6385011yescharacteristic
466C22#6385111yescharacteristic
467C22C4×#62511yescharacteristic
468C4—62no—
469C4—121no—
470C4—121no—
471C4—362no—
472C4#6385611yescharacteristic
473C4D3×Dic3⋊C411yescharacteristic
474C4#6390411yescharacteristic
475C4#6397611yescharacteristic
476C3—21no—
477C3#7054511yescharacteristic, complemented
478C3#7201711yescharacteristic, complemented
479C2—21no—
480C2—21no—
481C2—122no—
482C2#1059092111yescharacteristic
483C2#1059092211yescharacteristic
484C2#1059127711yescharacteristic
subgroupG/H
centerC2×C4C2×#625
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. C3×#5102C2semidirect
3. C2×#63578C2semidirect
6. #10589416C2semidirect
7. #10589160C2semidirect
25. #63565C4semidirect
26. #63565C4semidirect
27. #63562C4semidirect
28. #63562C4semidirect
37. #5102D3semidirect
414. C32#1866semidirect
477. C3#70545semidirect
478. 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
C3×#51022
C2×#635782
C2×#635682
#105910832
#105894162
#105891602
#720173
#705453