Finite Group Databasebeta

← #11857637

Subgroups — #11857637

Order 1152.

1646 conjugacy classes of subgroups.

The subgroup lattice has 493 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic
2C2×#64283C212yesmaximal, complemented
3#10593836C212yesmaximal, complemented
4#10593825C212yesmaximal, complemented
5#10593824C214yesmaximal, complemented
6#10593808C214yesmaximal, complemented
7C2×C32×#41C411yescharacteristic
8#41×C3⋊D3—22no—
9#41×C3⋊D3—22no—
10#41×C3⋊D3—22no—
11#41×C3⋊D3—22no—
12C2×#3832C411yescharacteristic
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×#3830C411yescharacteristic
15C2×#3830C2212yes—
16C2×D4×C3⋊D3C412yes—
17C2×D4×C3⋊D3C2211yescharacteristic
18C2×#3828C411yescharacteristic
19C2×#3828C2212yes—
20C22×C4×C3⋊D3C412yes—
21C22×C4×C3⋊D3C2211yescharacteristic
22C2×#3792C2214yescomplemented
23#64283—22no—
24#64283—22no—
25#64283C2214yes—
26#64283C2214yescomplemented
27C2×#3788—22no—
28C2×#3787—22no—
29#63788C2218yescomplemented
30#63780C2218yescomplemented
31C2×D3×#41—62no—
32C23×C3⋊D3C2×C412yes—
33C23×C3⋊D3C2×C411yescharacteristic
34C32×#41—22no—
35C32×#41—22no—
36C2×C32×Q8C2×C411yescharacteristic
37C2×C32×D4C2×C412yes—
38C2×C32×D4C2×C411yescharacteristic
39C22×C32×C4C2×C412yes—
40C22×C32×C4C2×C411yescharacteristic
41C2×#638C2×C412yes—
42C2×#638C2×C412yes—
43C2×#638C2312yes—
44C22×C3⋊Dic3C2×C412yes—
45C22×C3⋊Dic3C2311yescharacteristic
46#3832—22no—
47#3832—22no—
48Q8×C3⋊D3—22no—
49Q8×C3⋊D3—22no—
50#3830—24no—
51#3830—24no—
52#3830—22no—
53#3830—22no—
54D4×C3⋊D3—24no—
55D4×C3⋊D3—24no—
56D4×C3⋊D3—22no—
57D4×C3⋊D3—22no—
58#3828—22no—
59#3828—22no—
60#3828—24no—
61#3828—24no—
62C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
63C2×C4⋊(C3⋊D3)C2×C412yes—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3C2×C412yes—
69C2×C4×C3⋊D3C2×C412yes—
70C2×C4×C3⋊D3C2×C412yes—
71C2×C4×C3⋊D3C2×C411yescharacteristic
72C2×C4×C3⋊D3C2×C411yescharacteristic
73C2×C4×C3⋊D3D412yes—
74C2×C4×C3⋊D3D412yes—
75C2×C4×C3⋊D3D412yes—
76C2×C4×C3⋊D3D412yes—
77C2×C4×C3⋊D3C2311yescharacteristic
78C2×C4×C3⋊D3C2311yescharacteristic
79C2×#634C2×C411yescharacteristic
80C2×#634C2312yes—
81#3792—24no—
82#3792C2318yes—
83C2×#622—24no—
84#3788—24no—
85#3788—24no—
86#3787—24no—
87#3787—24no—
88C2×#413—91nomaximal, Sylow
89C2×C3×#41—22no—
90D3×#41—68no—
91D3×#41—68no—
92D3×#41—68no—
93D3×#41—68no—
94C2×#239—62no—
95C2×D3×Q8—62no—
96C2×#237—62no—
97C2×#237—64no—
98C2×D3×D4—64no—
99C2×D3×D4—62no—
100C2×#235—62no—
101C2×#235—64no—
102C22×C4×D3—64no—
103C22×C4×D3—62no—
104C23×C32C22×C412yes—
105C23×C32C22×C411yescharacteristic
106C22×C3⋊D3—22no—
107C22×C3⋊D3—22no—
108C22×C3⋊D3—42no—
109C22×C3⋊D3—44no—
110C22×C3⋊D3C22⋊C412yes—
111C22×C3⋊D3C22⋊C412yes—
112C22×C3⋊D3C22×C411yescharacteristic
113C22×C3⋊D3C22×C412yes—
114C22×C3⋊D3C22×C411yescharacteristic
115C32×Q8—22no—
116C32×D4—24no—
117C32×D4—22no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4C22⋊C412yes—
121C2×C32×C4C22⋊C412yes—
122C2×C32×C4C22×C412yes—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C22×C411yescharacteristic
125#638—24no—
126#638—24no—
127#638—24no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3C22×C412yes—
131C2×C3⋊Dic3C22×C411yescharacteristic
132C2×C3⋊Dic3C2×D412yes—
133C2×C3⋊Dic3C2×D412yes—
134C2×C3⋊Dic3C2411yescharacteristic
135C4⋊(C3⋊D3)—24no—
136C4⋊(C3⋊D3)—22no—
137C4×C3⋊D3—22no—
138C4×C3⋊D3—22no—
139C4×C3⋊D3—22no—
140C4×C3⋊D3—22no—
141C4×C3⋊D3—22no—
142C4×C3⋊D3—22no—
143C4×C3⋊D3C22⋊C411yescharacteristic
144C4×C3⋊D3C22⋊C411yescharacteristic
145C4×C3⋊D3C22⋊C411yescharacteristic
146C4×C3⋊D3C22⋊C411yescharacteristic
147C4×C3⋊D3C22⋊C412yes—
148C4×C3⋊D3C22⋊C412yes—
149C4×C3⋊D3C2×D412yes—
150C4×C3⋊D3C2×D412yes—
151C4×C3⋊D3C2×D412yes—
152C4×C3⋊D3C2×D412yes—
153#634—22no—
154#634—24no—
155#622—28no—
156C22×#41—91no—
157C22×M16—92no—
158#413—94no—
159#413—94no—
160C2×#101—92no—
161C2×#100—92no—
162C23×D3—62no—
163C23×D3—64no—
164C3×#41—28no—
165C3×#41—28no—
166C2×C3×Q8—22no—
167C2×C3×D4—24no—
168C2×C3×D4—22no—
169C22×C3×C4—24no—
170C22×C3×C4—22no—
171C2×#67—64no—
172C2×#67—64no—
173C2×#67—64no—
174C22×Dic3—64no—
175C22×Dic3—62no—
176#239—68no—
177#239—68no—
178D3×Q8—68no—
179D3×Q8—68no—
180#237—68no—
181#237—68no—
182#237—616no—
183#237—616no—
184D3×D4—68no—
185D3×D4—68no—
186D3×D4—616no—
187D3×D4—616no—
188#235—616no—
189#235—616no—
190#235—68no—
191#235—68no—
192C2×D12—62no—
193C2×D12—64no—
194C2×C4×D3—62no—
195C2×C4×D3—64no—
196C2×C4×D3—62no—
197C2×C4×D3—64no—
198C2×C4×D3—62no—
199C2×C4×D3—62no—
200C2×C4×D3—64no—
201C2×C4×D3—64no—
202C2×C4×D3—64no—
203C2×C4×D3—64no—
204C2×C4×D3—64no—
205C2×C4×D3—68no—
206C2×C4×D3—68no—
207C2×C4×D3—68no—
208C2×C4×D3—68no—
209C2×Dic6—62no—
210C2×Dic6—64no—
211C22×C32—22no—
212C22×C32—41no—
213C22×C32—42no—
214C22×C32C2×C22⋊C412yes—
215C22×C32C23×C411yescharacteristic
216C2×C3⋊D3—22no—
217C2×C3⋊D3—22no—
218C2×C3⋊D3—24no—
219C2×C3⋊D3—42no—
220C2×C3⋊D3—41no—
221C2×C3⋊D3—44no—
222C2×C3⋊D3—44no—
223C2×C3⋊D3—42no—
224C2×C3⋊D3C2×C22⋊C411yescharacteristic
225C2×C3⋊D3C2×C22⋊C412yes—
226C2×C3⋊D3C2×C22⋊C411yescharacteristic
227C32×C4—22no—
228C32×C4C2×C22⋊C412yes—
229C32×C4C2×C22⋊C411yescharacteristic
230C32×C4C2×C22⋊C411yescharacteristic
231C3⋊Dic3—22no—
232C3⋊Dic3C2×C22⋊C411yescharacteristic
233C3⋊Dic3C2×C22⋊C411yescharacteristic
234C3⋊Dic3C22×D412yes—
235C2×#41—91no—
236C2×#41—92no—
237C2×#41—91no—
238C2×#41—92no—
239C2×#41—91no—
240C2×#41—182no—
241C2×#41—182no—
242C2×#41—182no—
243C2×#41—182no—
244C2×#41#15711yescharacteristic
245C22×Q8—91no—
246C22×D4—91no—
247C22×D4—92no—
248C23×C4—91no—
249C23×C4—92no—
250C2×M16—94no—
251C2×M16—94no—
252C2×M16—94no—
253C2×M16—182no—
254C2×M16—182no—
255C2×M16—182no—
256C22×C8—182no—
257#101—98no—
258#100—98no—
259C23×C3—24no—
260C23×C3—22no—
261C22×D3—62no—
262C22×D3—64no—
263C22×D3—64no—
264C22×D3—62no—
265C22×D3—64no—
266C22×D3—68no—
267C22×D3—68no—
268C22×D3—128no—
269C22×D3—1216no—
270C3×Q8—28no—
271C3×D4—216no—
272C3×D4—28no—
273C2×C3×C4—28no—
274C2×C3×C4—28no—
275C2×C3×C4—24no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—24no—
279C2×C3×C4—24no—
280#67—616no—
281#67—616no—
282#67—616no—
283C2×Dic3—64no—
284C2×Dic3—62no—
285C2×Dic3—64no—
286C2×Dic3—64no—
287C2×Dic3—62no—
288C2×Dic3—68no—
289C2×Dic3—68no—
290D12—616no—
291D12—68no—
292C4×D3—62no—
293C4×D3—62no—
294C4×D3—62no—
295C4×D3—62no—
296C4×D3—64no—
297C4×D3—64no—
298C4×D3—64no—
299C4×D3—64no—
300C4×D3—64no—
301C4×D3—64no—
302C4×D3—68no—
303C4×D3—68no—
304C4×D3—68no—
305C4×D3—68no—
306C4×D3—68no—
307C4×D3—68no—
308Dic6—616no—
309Dic6—68no—
310C2×C32—21no—
311C2×C32—22no—
312C2×C32—42no—
313C2×C32C22×C22⋊C411yescharacteristic
314C3⋊D3—21no—
315C3⋊D3—22no—
316C3⋊D3—42no—
317C3⋊D3#41312yescomplemented
318C24—91no—
319C24—92no—
320#41—22no—
321#41—22no—
322#41—184no—
323#41—184no—
324#41—184no—
325#41—184no—
326#41—182no—
327#41—182no—
328#41—182no—
329#41—182no—
330#41—182no—
331#41—182no—
332C2×Q8—92no—
333C2×Q8—91no—
334C2×Q8—182no—
335C2×Q8—182no—
336C2×Q8C2×#15711yescharacteristic
337C2×D4—92no—
338C2×D4—92no—
339C2×D4—92no—
340C2×D4—92no—
341C2×D4—91no—
342C2×D4—182no—
343C2×D4—182no—
344C2×D4—184no—
345C2×D4—184no—
346C2×D4C2×#15712yes—
347C2×D4C2×#15711yescharacteristic
348C22×C4—91no—
349C22×C4—91no—
350C22×C4—91no—
351C22×C4—91no—
352C22×C4—91no—
353C22×C4—92no—
354C22×C4—92no—
355C22×C4—92no—
356C22×C4—92no—
357C22×C4—92no—
358C22×C4—92no—
359C22×C4—92no—
360C22×C4—92no—
361C22×C4—182no—
362C22×C4—182no—
363C22×C4—182no—
364C22×C4—182no—
365C22×C4C2×#15712yes—
366C22×C4C2×#15711yescharacteristic
367M16—98no—
368M16—184no—
369M16—184no—
370M16—184no—
371C2×C8—184no—
372C2×C8—184no—
373C2×C8—184no—
374C22×C3—28no—
375C22×C3—24no—
376C22×C3—22no—
377C22×C3—44no—
378C22×C3—48no—
379C2×D3—62no—
380C2×D3—62no—
381C2×D3—64no—
382C2×D3—68no—
383C2×D3—68no—
384C2×D3—128no—
385C2×D3—128no—
386C2×D3—1216no—
387C2×D3—1216no—
388C2×D3—124no—
389C2×D3—128no—
390C3×C4—28no—
391C3×C4—24no—
392C3×C4—22no—
393C3×C4—22no—
394Dic3—64no—
395Dic3—62no—
396Dic3—62no—
397Dic3—68no—
398C32C2×#41311yescharacteristic, complemented, Sylow
399C23—92no—
400C23—91no—
401C23—92no—
402C23—91no—
403C23—92no—
404C23—182no—
405C23—182no—
406C23—362no—
407C23—364no—
408C23C22×#15712yes—
409C23C22×#15711yescharacteristic
410Q8—22no—
411Q8—184no—
412Q8—182no—
413D4—24no—
414D4—22no—
415D4—184no—
416D4—184no—
417D4—184no—
418D4—184no—
419D4—182no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—92no—
423C2×C4—92no—
424C2×C4—91no—
425C2×C4—91no—
426C2×C4—92no—
427C2×C4—92no—
428C2×C4—92no—
429C2×C4—91no—
430C2×C4—91no—
431C2×C4—92no—
432C2×C4—92no—
433C2×C4—92no—
434C2×C4—91no—
435C2×C4—91no—
436C2×C4—92no—
437C2×C4—182no—
438C2×C4—182no—
439C2×C4—182no—
440C2×C4—182no—
441C2×C4—182no—
442C2×C4—182no—
443C2×C4—182no—
444C2×C4—182no—
445C2×C4C22⋊#15712yes—
446C2×C4C22⋊#15712yes—
447C2×C4C22×#15712yes—
448C2×C4C22×#15711yescharacteristic
449C2×C4C22×#15711yescharacteristic
450C8—188no—
451C2×C3—24no—
452C2×C3—22no—
453C2×C3—44no—
454C2×C3—48no—
455D3—64no—
456D3—64no—
457D3—124no—
458D3—128no—
459C22—22no—
460C22—41no—
461C22—42no—
462C22—91no—
463C22—91no—
464C22—92no—
465C22—182no—
466C22—184no—
467C22—182no—
468C22—361no—
469C22—362no—
470C22—362no—
471C22—364no—
472C22—364no—
473C22C2×C22⋊#15712yes—
474C22C23×#15711yescharacteristic
475C4—22no—
476C4—92no—
477C4—91no—
478C4—91no—
479C4—182no—
480C4C2×C22⋊#15711yescharacteristic
481C4C2×C22⋊#15712yes—
482C4C2×C22⋊#15711yescharacteristic
483C3—22no—
484C2—21no—
485C2—22no—
486C2—42no—
487C2—92no—
488C2—181no—
489C2—182no—
490C2—362no—
491C2C22×C22⋊#15711yescharacteristic
subgroupG/H
centerC4C2×C22⋊#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
FittingC2×C32×#41C4
socleC2×C32C22×C22⋊C4
prime radicalC2×#41×C3⋊D3C2
cosocleC2×C3⋊Dic3C24
hypercenterC2×#41#157
hypocenterC32C2×#413
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#64283C2semidirect
3. #10593836C2semidirect
4. #10593825C2semidirect
5. #10593824C2semidirect
6. #10593808C2semidirect
22. C2×#3792C22semidirect
26. #64283C22semidirect
29. #63788C22semidirect
30. #63780C22semidirect
317. C3⋊D3#413semidirect
398. C32C2×#413semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C2×#642832
#105938362
#105938252
#105938242
#105938082
C2×#4139