Finite Group Databasebeta

← #11787044

Subgroups — #11787044

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×#63815C211yesmaximal, characteristic
2C2×C3×#805C211yesmaximal, characteristic
3C2×#63578C211yesmaximal, characteristic, complemented
4#10591117C211yesmaximal, characteristic, complemented
5#10591083C211yesmaximal, characteristic
6#10589390C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8#70376—31nomaximal
9#68774—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3711—21no—
18#63815—22no—
19#63815—22no—
20C2×D3×C3⋊C8—21no—
21C3×#805—22no—
22#63578—22no—
23Dic3⋊(C3⋊C8)—21no—
24Dic3⋊(C3⋊C8)—21no—
25#63565C411yescharacteristic, complemented
26#63565C411yescharacteristic, complemented
27#63562C411yescharacteristic, complemented
28#63562C411yescharacteristic, complemented
29C2×#948—31no—
30C2×#907—31no—
31C2×C3×#104—31no—
32#5233—31no—
33C2×#822—31no—
34C2×#822—31no—
35#5119—31no—
36#5002—31no—
37#4999—31no—
38C2×#805D311yescharacteristic
39C3×#339—31no—
40#4524—31no—
41#4524—31no—
42#4524—61no—
43#4523D311yescharacteristic, complemented
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
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
54C32×C42—21no—
55C32×C42—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
61C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
62C2×C3⋊(C3⋊C8)D411yescharacteristic
63C2×C3⋊(C3⋊C8)D411yescharacteristic
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—
74#3711—24no—
75D3×C3⋊C8—24no—
76#1866—91noSylow
77C2×C3×#41—31no—
78C2×#235C2×D311yescharacteristic
79C2×C3×M16—31no—
80C2×C3×M16—31no—
81C3×#117—31no—
82C2×C3×C42—21no—
83C2×C3×C42C2×D311yescharacteristic
84C2×C3×C42C2×D311yescharacteristic
85#948—62no—
86#948—62no—
87#926C2×D311yescharacteristic
88C2×#208—61no—
89C2×#208C2×D311yescharacteristic
90C2×#208C2×D311yescharacteristic
91C22×C3⋊C8—31no—
92C22×C3⋊C8—31no—
93C22×C3⋊C8—31no—
94C22×C3⋊C8—31no—
95C22×C3⋊C8—61no—
96C22×C3⋊C8—61no—
97C22×C3⋊C8—61no—
98#907—62no—
99#907—62no—
100C2×ΓL(1,𝔽25)—61no—
101C2×D3×C8—61no—
102C3×#104—62no—
103#835—31no—
104#835—31no—
105#832—31no—
106#832—31no—
107#822—62no—
108#822—62no—
109Dic3⋊C8—61no—
110Dic3⋊C8—61no—
111#810—31no—
112#810—31no—
113#809—31no—
114#809—31no—
115#805—22no—
116C4⋊(C3⋊C8)—61no—
117C4⋊(C3⋊C8)—61no—
118C23×C32#4111yescharacteristic
119C22×C3×D3—21no—
120C2×C32×C4—22no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×Q811yescharacteristic
128C2×C32×C4#4111yescharacteristic
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—
140C3⋊(C3⋊C8)—21no—
141C3⋊(C3⋊C8)—21no—
142C3⋊(C3⋊C8)—21no—
143C3⋊(C3⋊C8)—21no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—41no—
146C2×#131—91no—
147C2×#108—91no—
148#424—91no—
149C2×#104—31no—
150#416—91no—
151#339—31no—
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—22no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—61no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C2×#67—21no—
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—61no—
177C3×M16—61no—
178C3×M16—61no—
179C2×C3×C8—61no—
180C2×C3×C8—61no—
181C3×C4⋊C4—31no—
182C3×C4⋊C4—31no—
183C3×C22⋊C4—61no—
184C3×C42—21no—
185C3×C42—21no—
186C3×C42—21no—
187C3×C42—21no—
188C3×C42—41no—
189C3×C42—41no—
190C3×C42—61no—
191#217—21no—
192C4⋊Dic3C4×D311yescharacteristic
193C4⋊Dic3C4×D311yescharacteristic
194C4×Dic3—21no—
195#208—21no—
196#208—21no—
197#208—21no—
198#208—64no—
199#208D1212yes—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—31no—
203C2×C3⋊C8—31no—
204C2×C3⋊C8—31no—
205C2×C3⋊C8—31no—
206C2×C3⋊C8—31no—
207C2×C3⋊C8—31no—
208C2×C3⋊C8—31no—
209C2×C3⋊C8—31no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—64no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—121no—
224C2×C3⋊C8—121no—
225C2×C3⋊C8—121no—
226C2×C3⋊C8—121no—
227ΓL(1,𝔽25)—64no—
228D3×C8—64no—
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×C4—42no—
238C32×C4C2×C4⋊C411yescharacteristic
239C32×C4C4×D411yescharacteristic
240C32×C4#12011yescharacteristic
241C32×C4C22⋊Q811yescharacteristic
242C3×Dic3—22no—
243C3×Dic3—41no—
244C3×Dic3—41no—
245C2×#41—31no—
246#131—182no—
247#131—182no—
248C2×M16—31no—
249C2×M16—31no—
250C2×M16—181no—
251C22×C8—91no—
252C22×C8—91no—
253C22×C8—181no—
254#117—31no—
255C2×C42D3211yescharacteristic
256#108—182no—
257C4⋊C8—181no—
258C4⋊C8—181no—
259#104—62no—
260#103—91no—
261#103—91no—
262#102—91no—
263#102—91no—
264C23×C3—21no—
265C23×C3—61no—
266C23×C3#23711yescharacteristic
267C23×C3#23711yescharacteristic
268C22×D3—21no—
269C3×Q8—32no—
270C3×Q8—61no—
271C3×D4—32no—
272C3×D4—62no—
273C3×D4—62no—
274C3×D4—61no—
275C2×C3×C4—24no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—61no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4C2×Dic611yescharacteristic
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×C4×D311yescharacteristic
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×C4C2×#6711yescharacteristic
307#67—22no—
308#67—22no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312D12—21no—
313D12Dic3⋊C412yes—
314C4×D3—22no—
315C4×D3—22no—
316Dic6—21no—
317Dic6Dic3⋊C412yes—
318C3×C8—62no—
319C3×C8—121no—
320C3⋊C8—22no—
321C3⋊C8—41no—
322C3⋊C8—61no—
323C3⋊C8—61no—
324C3⋊C8—61no—
325C3⋊C8—61no—
326C3⋊C8—61no—
327C3⋊C8—61no—
328C3⋊C8—61no—
329C3⋊C8—61no—
330C3⋊C8—121no—
331C3⋊C8—121no—
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—21no—
348C22×C4—61no—
349C22×C4C2×D3211yescharacteristic
350M16—32no—
351M16—61no—
352M16—61no—
353M16—61no—
354M16—184no—
355C2×C8—61no—
356C2×C8—61no—
357C2×C8—91no—
358C2×C8—91no—
359C2×C8—91no—
360C2×C8—91no—
361C2×C8—184no—
362C2×C8—181no—
363C2×C8—181no—
364C2×C8—181no—
365C2×C8—181no—
366C4⋊C4—31no—
367C4⋊C4—31no—
368C22⋊C4—61no—
369C42—21no—
370C42—21no—
371C42—61no—
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#87811yescharacteristic
385C22×C3#67⋊C411yescharacteristic
386C22×C3#67⋊C411yescharacteristic
387C22×C3#88311yescharacteristic
388C22×C3#89711yescharacteristic
389C22×C3#93511yescharacteristic
390C2×D3—22no—
391C2×D3—41no—
392C2×D3—41no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—44no—
398C3×C4—42no—
399C3×C4—42no—
400C3×C4—62no—
401C3×C4—121no—
402C3×C4—121no—
403C3×C4C4×D1211yescharacteristic
404C3×C4#87811yescharacteristic
405C3×C4#67⋊C411yescharacteristic
406C3×C4#88211yescharacteristic
407C3×C4D3×C4⋊C411yescharacteristic
408C3×C4#89611yescharacteristic
409C3×C4C2×Dic3⋊C411yescharacteristic
410C3×C4#93711yescharacteristic
411Dic3—22no—
412Dic3—41no—
413Dic3—41no—
414C32#186611yescharacteristic, complemented, Sylow
415C23—61no—
416C23#380511yescharacteristic
417Q8—32no—
418Q8—61no—
419D4—32no—
420D4—62no—
421D4—62no—
422D4—61no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—61no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4D3×Dic611yescharacteristic
432C2×C4C4×D3211yescharacteristic
433C2×C4D3×D1211yescharacteristic
434C2×C4#380211yescharacteristic
435C2×C4#380411yescharacteristic
436C2×C4D3×#6711yescharacteristic
437C8—62no—
438C8—121no—
439C8—181no—
440C8—181no—
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#466811yescharacteristic
454C2×C3#482311yescharacteristic
455C2×C3#482311yescharacteristic
456C2×C3#482411yescharacteristic
457C2×C3#482411yescharacteristic
458C2×C3#494611yescharacteristic
459D3—42no—
460C22—21no—
461C22—21no—
462C22—62no—
463C22—121no—
464C22—121no—
465C22#6389311yescharacteristic
466C22#6390211yescharacteristic
467C22#6396911yescharacteristic
468C4—42no—
469C4—62no—
470C4—121no—
471C4—121no—
472C4D3×Dic3⋊C411yescharacteristic
473C4#6388011yescharacteristic
474C4#6389911yescharacteristic
475C4#6392211yescharacteristic
476C3—21no—
477C3#6877411yescharacteristic, complemented
478C3#7037611yescharacteristic, complemented
479C2—21no—
480C2—21no—
481C2—122no—
482C2#1059038911yescharacteristic
483C2#1059039011yescharacteristic
484C2#1059137311yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1866
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×#63578C2semidirect
4. #10591117C2semidirect
6. #10589390C2semidirect
7. C3×#4523C2semidirect
25. #63565C4semidirect
26. #63565C4semidirect
27. #63562C4semidirect
28. #63562C4semidirect
43. #4523D3semidirect
414. C32#1866semidirect
477. C3#68774semidirect
478. C3#70376semidirect

Maximal subgroups

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

subgroupindex
C2×#638152
C2×C3×#8052
C2×#635782
#105911172
#105910832
#105893902
C3×#45232
#703763
#687743