Finite Group Databasebeta

← #11783460

Subgroups — #11783460

Order 1152.

702 conjugacy classes of subgroups.

The subgroup lattice has 481 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64283C211yesmaximal, characteristic
2#10594969C211yesmaximal, characteristic
3C2×#63818C211yesmaximal, characteristic
4#10590054C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3792—21no—
7#64283—21no—
8#64283—21no—
9#64283C412yescomplemented
10#64283C2212yes—
11C2×#3788C412yescomplemented
12C2×#3787—21no—
13C3×#926—21no—
14C2×C3×#208—21no—
15#63974C412yes—
16#63957—21no—
17#63900—21no—
18C4×#624—21no—
19#63874C2212yes—
20#63849C412yes—
21C2×#3712—21no—
22#63818—21no—
23#63818—21no—
24#63818C412yescomplemented
25#63818C2212yes—
26C2×#3710C412yescomplemented
27C2×D3×M16—61no—
28D3×#117—61no—
29C23×C3⋊D3C2×C411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C3⋊Dic3D411yescharacteristic
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3C2×C411yescharacteristic
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C2×C4×C3⋊D3C2×C411yescharacteristic
36C2×C4×C3⋊D3C2×C411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3Q811yescharacteristic
42C2×C4×C3⋊D3Q811yescharacteristic
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×#624—22no—
45#3792—22no—
46#3792—22no—
47C2×#622—22no—
48#3788—22no—
49#3788C2×C414yescomplemented
50#3787—22no—
51#3787—22no—
52C3×#217—22no—
53C3×C4⋊Dic3—22no—
54C3×C4×Dic3—22no—
55C3×#208—22no—
56C3×#208—22no—
57C2×C3×C3⋊C8—22no—
58#3724—22no—
59#3722C2×C414yes—
60Dic32—22no—
61#3712—22no—
62#3712—22no—
63#3710—22no—
64#3710C2×C414yescomplemented
65C2×#344—91nomaximal, Sylow
66C22×C4×D3—61no—
67C22×C4×D3—61no—
68C2×C3×M16—61no—
69C3×#117—61no—
70#926—21no—
71C2×#208—21no—
72D3×M16—62no—
73D3×M16—62no—
74D3×M16—62no—
75D3×M16—62no—
76C2×ΓL(1,𝔽25)—62no—
77C2×D3×C8—62no—
78#892—62no—
79D3×C4⋊C4—62no—
80D3×C22⋊C4—62no—
81#877—62no—
82#872—62no—
83C42×D3—62no—
84C23×C32C22⋊C411yescharacteristic
85C22×C3⋊D3—42no—
86C22×C3⋊D3C4211yescharacteristic
87C22×C3⋊D3C4211yescharacteristic
88C22×C3⋊D3C22⋊C411yescharacteristic
89C22×C3⋊D3C4⋊C411yescharacteristic
90C22×C3⋊D3C4⋊C411yescharacteristic
91C22×C3⋊D3C22×C411yescharacteristic
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4C4⋊C411yescharacteristic
96C2×C32×C4C4⋊C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C3⋊Dic3C22⋊C411yescharacteristic
99C2×C3⋊Dic3C22⋊C411yescharacteristic
100C2×C3⋊Dic3C22⋊C411yescharacteristic
101C2×C3⋊Dic3C4⋊C411yescharacteristic
102C2×C3⋊Dic3C4⋊C411yescharacteristic
103C2×C3⋊Dic3C2×D411yescharacteristic
104C4×C3⋊D3C4211yescharacteristic
105C4×C3⋊D3C4211yescharacteristic
106C4×C3⋊D3C22⋊C411yescharacteristic
107C4×C3⋊D3C22⋊C411yescharacteristic
108C4×C3⋊D3C22⋊C411yescharacteristic
109C4×C3⋊D3C22⋊C411yescharacteristic
110C4×C3⋊D3C4⋊C411yescharacteristic
111C4×C3⋊D3C4⋊C411yescharacteristic
112C4×C3⋊D3C4⋊C411yescharacteristic
113C4×C3⋊D3C4⋊C411yescharacteristic
114C4×C3⋊D3C4⋊C411yescharacteristic
115C4×C3⋊D3C4⋊C411yescharacteristic
116C4×C3⋊D3C22×C411yescharacteristic
117C4×C3⋊D3C22×C411yescharacteristic
118C4×C3⋊D3C2×D411yescharacteristic
119C4×C3⋊D3C2×Q811yescharacteristic
120C2×C3×Dic3—24no—
121#624—44no—
122#622—24no—
123C3×C3⋊C8—24no—
124C22×M16—91no—
125C22×M16—91no—
126C2×#117—91no—
127#344—94no—
128C23×D3—61no—
129C23×D3—61no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×Dic3—61no—
133C22×Dic3—61no—
134C2×C4×D3—61no—
135C2×C4×D3—61no—
136C2×C4×D3—61no—
137C2×C4×D3—61no—
138C2×C4×D3—61no—
139C2×C4×D3—61no—
140C2×C4×D3—61no—
141C2×C4×D3—61no—
142C2×C4×D3—61no—
143C2×C4×D3—61no—
144C2×C4×D3—61no—
145C2×C4×D3—61no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×C4×D3—61no—
149C2×C4×D3—61no—
150C2×C4×D3—61no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×C4×D3—61no—
155C2×C4×D3—61no—
156C2×C4×D3—61no—
157C2×C4×D3—61no—
158C2×C4×D3—64no—
159C3×M16—62no—
160C3×M16—62no—
161C2×C3×C8—62no—
162C3×C4⋊C4—62no—
163C3×C22⋊C4—62no—
164C3×C42—62no—
165#217—22no—
166(C2×D3)⋊C4—64no—
167C4⋊Dic3—22no—
168Dic3⋊C4—64no—
169C4×Dic3—22no—
170C4×Dic3—64no—
171#208—22no—
172#208—22no—
173C2×C3⋊C8—22no—
174ΓL(1,𝔽25)—64no—
175ΓL(1,𝔽25)—64no—
176D3×C8—64no—
177D3×C8—64no—
178C22×C32—41no—
179C22×C32#9511yescharacteristic
180C22×C32#9511yescharacteristic
181C22×C32C2×C22⋊C411yescharacteristic
182C2×C3⋊D3—22no—
183C2×C3⋊D3—22no—
184C2×C3⋊D3—22no—
185C2×C3⋊D3—41no—
186C2×C3⋊D3—41no—
187C2×C3⋊D3—41no—
188C2×C3⋊D3#9511yescharacteristic
189C2×C3⋊D3#9511yescharacteristic
190C2×C3⋊D3C2×C4211yescharacteristic
191C2×C3⋊D3C2×C4⋊C411yescharacteristic
192C32×C4#9511yescharacteristic
193C32×C4#9511yescharacteristic
194C32×C4C2×C22⋊C411yescharacteristic
195C32×C4C2×C4⋊C411yescharacteristic
196C3⋊Dic3#9511yescharacteristic
197C3⋊Dic3#9511yescharacteristic
198C3⋊Dic3C2×C22⋊C411yescharacteristic
199C3⋊Dic3C2×C4⋊C411yescharacteristic
200C3×Dic3—44no—
201C23×C4—91no—
202C2×M16—61no—
203C2×M16—92no—
204C2×M16—92no—
205C2×M16—92no—
206C2×M16—92no—
207C2×M16—92no—
208C2×M16—181no—
209C2×M16—181no—
210C2×M16—181no—
211C2×M16—181no—
212C2×M16—181no—
213C2×M16—181no—
214C22×C8—92no—
215C22×C8—181no—
216#117—61no—
217#117—92no—
218#117—92no—
219#117—181no—
220C2×C4⋊C4—181no—
221C2×C22⋊C4—92no—
222C2×C42—181no—
223C23×C3—21no—
224C23×C3—21no—
225C22×D3—61no—
226C22×D3—61no—
227C22×D3—61no—
228C22×D3—61no—
229C22×D3—61no—
230C22×D3—61no—
231C22×D3—61no—
232C22×D3—61no—
233C22×D3—61no—
234C22×D3—61no—
235C22×D3—61no—
236C22×D3—61no—
237C22×D3—124no—
238C22×D3—124no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—64no—
252C2×Dic3—24no—
253C2×Dic3—61no—
254C2×Dic3—61no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C4×D3—61no—
266C4×D3—61no—
267C4×D3—61no—
268C4×D3—61no—
269C4×D3—61no—
270C4×D3—61no—
271C4×D3—61no—
272C4×D3—61no—
273C4×D3—61no—
274C4×D3—61no—
275C4×D3—61no—
276C4×D3—61no—
277C4×D3—61no—
278C4×D3—61no—
279C4×D3—61no—
280C4×D3—61no—
281C4×D3—61no—
282C4×D3—61no—
283C4×D3—61no—
284C4×D3—61no—
285C4×D3—61no—
286C4×D3—61no—
287C4×D3—61no—
288C4×D3—61no—
289C4×D3—61no—
290C4×D3—61no—
291C4×D3—61no—
292C4×D3—61no—
293C4×D3—61no—
294C4×D3—61no—
295C4×D3—61no—
296C4×D3—61no—
297C4×D3—128no—
298C3×C8—64no—
299C3⋊C8—24no—
300C2×C32—21no—
301C2×C32—21no—
302C2×C32—21no—
303C2×C32C2×#9511yescharacteristic
304C3⋊D3—21no—
305C3⋊D3—21no—
306C3⋊D3—21no—
307C3⋊D3#34412yescomplemented
308C24—91no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4—91no—
312C22×C4—91no—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—91no—
316C22×C4—91no—
317C22×C4—91no—
318C22×C4—91no—
319C22×C4—91no—
320C22×C4—91no—
321C22×C4—91no—
322C22×C4—182no—
323C22×C4GO+(4,𝔽2)11yescharacteristic
324M16—62no—
325M16—62no—
326M16—94no—
327M16—182no—
328M16—182no—
329M16—182no—
330M16—182no—
331M16—182no—
332C2×C8—62no—
333C2×C8—94no—
334C2×C8—182no—
335C2×C8—182no—
336C2×C8—182no—
337C2×C8—182no—
338C4⋊C4—62no—
339C4⋊C4—182no—
340C22⋊C4—62no—
341C22⋊C4—94no—
342C42—62no—
343C42—182no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—42no—
351C22×C3—42no—
352C2×D3—61no—
353C2×D3—61no—
354C2×D3—61no—
355C2×D3—61no—
356C2×D3—61no—
357C2×D3—61no—
358C2×D3—61no—
359C2×D3—61no—
360C2×D3—64no—
361C2×D3—64no—
362C2×D3—122no—
363C2×D3—122no—
364C2×D3—122no—
365C2×D3—122no—
366C2×D3—122no—
367C2×D3—122no—
368C2×D3—122no—
369C2×D3—122no—
370C2×D3—122no—
371C2×D3—122no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—124no—
381Dic3—44no—
382Dic3—61no—
383Dic3—61no—
384Dic3—61no—
385Dic3—61no—
386Dic3—61no—
387Dic3—61no—
388Dic3—61no—
389Dic3—61no—
390C32C2×#34411yescharacteristic, complemented, Sylow
391C23—91no—
392C23—91no—
393C23—91no—
394C23—91no—
395C23—91no—
396C23—91no—
397C23—362no—
398C23D32⋊C411yescharacteristic
399C2×C4—64no—
400C2×C4—91no—
401C2×C4—91no—
402C2×C4—91no—
403C2×C4—91no—
404C2×C4—91no—
405C2×C4—91no—
406C2×C4—91no—
407C2×C4—91no—
408C2×C4—91no—
409C2×C4—91no—
410C2×C4—91no—
411C2×C4—91no—
412C2×C4—91no—
413C2×C4—91no—
414C2×C4—91no—
415C2×C4—91no—
416C2×C4—91no—
417C2×C4—91no—
418C2×C4—91no—
419C2×C4—91no—
420C2×C4—91no—
421C2×C4—91no—
422C2×C4—364no—
423C2×C4D32⋊C411yescharacteristic
424C2×C4D32⋊C411yescharacteristic
425C2×C4D32⋊C411yescharacteristic
426C2×C4#377311yescharacteristic
427C2×C4#377311yescharacteristic
428C2×C4C2×GO+(4,𝔽2)11yescharacteristic
429C8—64no—
430C8—184no—
431C2×C3—22no—
432C2×C3—22no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—41no—
436C2×C3—41no—
437C2×C3—41no—
438C2×C3—41no—
439D3—62no—
440D3—62no—
441D3—62no—
442D3—62no—
443D3—121no—
444D3—121no—
445D3—121no—
446D3—121no—
447C22—41no—
448C22—91no—
449C22—91no—
450C22—91no—
451C22—91no—
452C22—182no—
453C22—182no—
454C22—182no—
455C22—361no—
456C22—361no—
457C22—361no—
458C22#6373711yescharacteristic
459C22#6373711yescharacteristic
460C22C2×D32⋊C411yescharacteristic
461C4—91no—
462C4—91no—
463C4—91no—
464C4—91no—
465C4—124no—
466C4#6373711yescharacteristic
467C4#6373711yescharacteristic
468C4C2×D32⋊C411yescharacteristic
469C4C2×#377311yescharacteristic
470C3—21no—
471C3—21no—
472C2—21no—
473C2—21no—
474C2—21no—
475C2—92no—
476C2—181no—
477C2—181no—
478C2—181no—
479C2C2×#6373711yescharacteristic
subgroupG/H
centerC4C2×D32⋊C4
commutatorC2×C3⋊D3C2×C42
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32C2×#95
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#344
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590054C2semidirect
9. #64283C4semidirect
11. C2×#3788C4semidirect
24. #63818C4semidirect
26. C2×#3710C4semidirect
49. #3788C2×C4semidirect
64. #3710C2×C4semidirect
307. C3⋊D3#344semidirect
390. C32C2×#344semidirect

Maximal subgroups

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

subgroupindex
C2×#642832
#105949692
C2×#638182
#105900542
C2×#3449