Finite Group Databasebeta

← #11774623

Subgroups — #11774623

Order 1152.

647 conjugacy classes of subgroups.

The subgroup lattice has 475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic
2C3×#4926C211yesmaximal, characteristic, complemented
3C3×#4925C211yesmaximal, characteristic, complemented
4#10589085C212yesmaximal, complemented
5#10589082C212yesmaximal, complemented
6#70798—31nomaximal
7#70763—31nomaximal
8C2×#3828C411yescharacteristic
9C2×C32×C42C2211yescharacteristic
10C4×#638—21no—
11C4×#638—21no—
12#64135C411yescharacteristic
13C4×C4⋊(C3⋊D3)C411yescharacteristic
14C4×C4⋊(C3⋊D3)C2211yescharacteristic
15#64081—21no—
16C42×C3⋊D3—21no—
17C4×#634C411yescharacteristic
18C4×#634C2211yescharacteristic
19C3×#830—21no—
20C3×#830—21no—
21C3×C4⋊(C3⋊C8)—21no—
22C3×C4⋊(C3⋊C8)C2212yes—
23C3×#803—21no—
24C3×C4×C3⋊C8C2212yes—
25C4×#235—31no—
26C4×#235—31no—
27C4×#235—61no—
28C3×#432—31no—
29C3×#431—31no—
30#4926D311yescharacteristic, complemented
31#4925D311yescharacteristic, complemented
32#4484—32no—
33#4483—32no—
34#4459—32no—
35#4456—32no—
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C2×#638—21no—
40#3828—22no—
41#3828—22no—
42C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—21no—
46C2×#634C2×C411yescharacteristic
47C32×C42C2×C411yescharacteristic
48C32×C42D411yescharacteristic
49C32×C42D411yescharacteristic
50C32×C42C2311yescharacteristic
51#3757—21no—
52#3752—21no—
53#3752—21no—
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55C4⋊(C3⋊Dic3)C2×C411yescharacteristic
56#3750—21no—
57#3750—21no—
58C4×C3⋊Dic3—21no—
59C4×C3⋊Dic3—21no—
60C4×C3⋊Dic3—21no—
61C2×C3×C3⋊C8—22no—
62C2×C3×C3⋊C8—22no—
63#1488—91noSylow
64C2×#235—31no—
65C2×#235—31no—
66C2×#235—61no—
67C2×C3×C42—21no—
68C2×C3×C42C2×D311yescharacteristic
69C2×C3×C42C2×D311yescharacteristic
70C4×#67—62no—
71C4×#67—62no—
72C4×#67—61no—
73C4×#67—61no—
74C4×#67—61no—
75C4×#67—61no—
76#926—31no—
77#926—31no—
78#926—61no—
79C4×D12—31no—
80C4×D12—31no—
81C4×D12—31no—
82C4×D12—31no—
83C4×D12—61no—
84C4×D12—61no—
85#872—62no—
86#872—61no—
87#872—61no—
88C42×D3—62no—
89C42×D3—61no—
90C42×D3—61no—
91C4×Dic6—31no—
92C4×Dic6—31no—
93C4×Dic6—31no—
94C4×Dic6—31no—
95C4×Dic6—61no—
96C4×Dic6—61no—
97C3×C4⋊C8—32no—
98C3×C4⋊C8—61no—
99C3×C22⋊C8—61no—
100C3×C22⋊C8—61no—
101C3×#97—61no—
102C3×C4×C8—32no—
103#830—21no—
104#830—21no—
105C4⋊(C3⋊C8)—21no—
106C4⋊(C3⋊C8)C2×D312yes—
107#803—21no—
108C4×C3⋊C8C2×D312yes—
109C23×C32C22⋊C411yescharacteristic
110C22×C3⋊D3—21no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4—22no—
114C2×C32×C4—41no—
115C2×C32×C4C22⋊C411yescharacteristic
116C2×C32×C4C22⋊C411yescharacteristic
117C2×C32×C4C22⋊C411yescharacteristic
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121#638—24no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C4⋊(C3⋊D3)—21no—
126C4⋊(C3⋊D3)M1612yes—
127C4×C3⋊D3—24no—
128C4×C3⋊D3—42no—
129C4×C3⋊D3—42no—
130#634—21no—
131#634M1612yes—
132C3×C3⋊C8—42no—
133C3×C3⋊C8—42no—
134C4×#41—91no—
135#432—31no—
136#431—31no—
137Q8⋊C8—92no—
138D4⋊C8—92no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4C4×D311yescharacteristic
143C22×C3×C4C4×D311yescharacteristic
144C22×C3×C4D1211yescharacteristic
145C22×C3×C4D1211yescharacteristic
146C22×C3×C4#6711yescharacteristic
147C22×C3×C4#6711yescharacteristic
148C2×#67—62no—
149C2×#67—61no—
150C2×#67—61no—
151#235—62no—
152#235—62no—
153#235—62no—
154#235—62no—
155#235—64no—
156#235—64no—
157C2×D12—31no—
158C2×D12—31no—
159C2×D12—61no—
160C2×C4×D3—62no—
161C2×C4×D3—61no—
162C2×C4×D3—61no—
163C2×C4×D3—62no—
164C2×C4×D3—62no—
165C2×C4×D3—61no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×Dic6—31no—
170C2×Dic6—31no—
171C2×Dic6—61no—
172C2×C3×C8—62no—
173C2×C3×C8—62no—
174C3×C42—21no—
175C3×C42—21no—
176C3×C42—21no—
177C3×C42—21no—
178C3×C42C4×D311yescharacteristic
179C3×C42C4×D311yescharacteristic
180C3×C42D1211yescharacteristic
181C3×C42D1211yescharacteristic
182C3×C42#6711yescharacteristic
183C3×C42#6711yescharacteristic
184C3×C42C22×D311yescharacteristic
185C3×C42C22×D311yescharacteristic
186#217—62no—
187#217—61no—
188#217—61no—
189(C2×D3)⋊C4—62no—
190(C2×D3)⋊C4—62no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—61no—
195C4⋊Dic3—31no—
196C4⋊Dic3—31no—
197C4⋊Dic3—31no—
198C4⋊Dic3—31no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201Dic3⋊C4—62no—
202Dic3⋊C4—62no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207C4×Dic3—62no—
208C4×Dic3—62no—
209C4×Dic3—62no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C2×C3⋊C8—22no—
217C2×C3⋊C8—22no—
218C22×C32—21no—
219C22×C32—21no—
220C22×C32—21no—
221C22×C32C2×C22⋊C411yescharacteristic
222C2×C3⋊D3—22no—
223C2×C3⋊D3—41no—
224C2×C3⋊D3—41no—
225C32×C4—21no—
226C32×C4—21no—
227C32×C4—21no—
228C32×C4—21no—
229C32×C4C2×M1611yescharacteristic
230C32×C4C2×M1611yescharacteristic
231C32×C4#13512yes—
232C3⋊Dic3—22no—
233C3⋊Dic3—41no—
234C3⋊Dic3—41no—
235C2×#41—91no—
236C4×Q8—91no—
237C4×Q8—91no—
238C4×D4—91no—
239C4×D4—91no—
240C4×D4—181no—
241C4×D4—181no—
242#117—91no—
243#117—181no—
244C2×C42—181no—
245C2×C42D3211yescharacteristic
246C4⋊C8—32no—
247C4⋊C8—61no—
248C22⋊C8—61no—
249C22⋊C8—61no—
250#97—61no—
251C4×C8—32no—
252C23×C3—21no—
253C23×C3(C2×D3)⋊C411yescharacteristic
254C23×C3(C2×D3)⋊C411yescharacteristic
255C22×D3—62no—
256C22×D3—61no—
257C22×D3—61no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—22no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—42no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—42no—
276C2×C3×C4(C2×D3)⋊C411yescharacteristic
277C2×C3×C4(C2×D3)⋊C411yescharacteristic
278C2×C3×C4(C2×D3)⋊C411yescharacteristic
279C2×C3×C4(C2×D3)⋊C411yescharacteristic
280C2×C3×C4(C2×D3)⋊C411yescharacteristic
281C2×C3×C4(C2×D3)⋊C411yescharacteristic
282C2×C3×C4C2×C4×D311yescharacteristic
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4C2×D1211yescharacteristic
285C2×C3×C4C2×D1211yescharacteristic
286C2×C3×C4C2×#6711yescharacteristic
287C2×C3×C4C2×#6711yescharacteristic
288#67—68no—
289#67—64no—
290#67—64no—
291C2×Dic3—62no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—62no—
295C2×Dic3—62no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—61no—
300D12—32no—
301D12—32no—
302D12—62no—
303D12—62no—
304D12—61no—
305D12—61no—
306C4×D3—68no—
307C4×D3—64no—
308C4×D3—64no—
309C4×D3—124no—
310C4×D3—122no—
311C4×D3—122no—
312C4×D3—124no—
313C4×D3—122no—
314C4×D3—122no—
315Dic6—32no—
316Dic6—32no—
317Dic6—62no—
318Dic6—62no—
319Dic6—61no—
320Dic6—61no—
321C3×C8—122no—
322C3×C8—122no—
323C3⋊C8—42no—
324C3⋊C8—42no—
325C2×C32—41no—
326C2×C32#40711yescharacteristic
327C2×C32#41611yescharacteristic
328C2×C32#42111yescharacteristic
329C3⋊D3—42no—
330#41—182no—
331#41—182no—
332C2×Q8—91no—
333C2×D4—91no—
334C2×D4—181no—
335C22×C4—181no—
336C22×C4—181no—
337C22×C4—181no—
338C22×C4#62411yescharacteristic
339C22×C4#62611yescharacteristic
340C22×C4#62611yescharacteristic
341C2×C8—62no—
342C2×C8—62no—
343C4⋊C4—91no—
344C4⋊C4—91no—
345C4⋊C4—181no—
346C4⋊C4—181no—
347C22⋊C4—181no—
348C22⋊C4—181no—
349C22⋊C4—181no—
350C42—181no—
351C42—181no—
352C42—181no—
353C42#62411yescharacteristic
354C42#62611yescharacteristic
355C42#62611yescharacteristic
356C42C2×D3211yescharacteristic
357C22×C3—22no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3C2×(C2×D3)⋊C411yescharacteristic
368C22×C3C2×(C2×D3)⋊C411yescharacteristic
369C2×D3—64no—
370C2×D3—62no—
371C2×D3—62no—
372C2×D3—122no—
373C2×D3—122no—
374C2×D3—121no—
375C2×D3—121no—
376C2×D3—121no—
377C2×D3—121no—
378C3×C4—22no—
379C3×C4—22no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—22no—
391C3×C4—41no—
392C3×C4—41no—
393C3×C4#90412yes—
394C3×C4D3×M1611yescharacteristic
395C3×C4D3×M1611yescharacteristic
396C3×C4D3×M1611yescharacteristic
397C3×C4D3×M1611yescharacteristic
398C3×C4#95012yes—
399Dic3—64no—
400Dic3—62no—
401Dic3—62no—
402Dic3—122no—
403Dic3—122no—
404Dic3—121no—
405Dic3—121no—
406Dic3—121no—
407Dic3—121no—
408C32#148811yescharacteristic, complemented, Sylow
409C23—181no—
410C23#372211yescharacteristic
411Q8—92no—
412Q8—181no—
413D4—92no—
414D4—184no—
415D4—181no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—184no—
421C2×C4—181no—
422C2×C4—181no—
423C2×C4—181no—
424C2×C4—362no—
425C2×C4—362no—
426C2×C4#372211yescharacteristic
427C2×C4#372211yescharacteristic
428C2×C4#372211yescharacteristic
429C2×C4C2×#62411yescharacteristic
430C2×C4C2×#62611yescharacteristic
431C2×C4C2×#62611yescharacteristic
432C8—122no—
433C8—122no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—42no—
438C2×C3—41no—
439C2×C3—41no—
440C2×C3#500211yescharacteristic
441C2×C3#500511yescharacteristic
442C2×C3#511311yescharacteristic
443C2×C3#512611yescharacteristic
444C2×C3#512611yescharacteristic
445C2×C3#513911yescharacteristic
446D3—124no—
447D3—122no—
448D3—122no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—182no—
453C22—361no—
454C22—361no—
455C22C2×#372211yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—182no—
461C4—361no—
462C4—361no—
463C4#6381811yescharacteristic
464C4#6381811yescharacteristic
465C4#6382912yes—
466C3—21no—
467C3#7076311yescharacteristic, complemented
468C3#7079811yescharacteristic, complemented
469C2—41no—
470C2—362no—
471C2#1059107411yescharacteristic
472C2#1059110511yescharacteristic
473C2#1059111311yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3828C4
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4926C2semidirect
3. C3×#4925C2semidirect
4. #10589085C2semidirect
5. #10589082C2semidirect
30. #4926D3semidirect
31. #4925D3semidirect
408. C32#1488semidirect
467. C3#70763semidirect
468. C3#70798semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C3×#49262
C3×#49252
#105890852
#105890822
#707983
#707633