Finite Group Databasebeta

← #11774653

Subgroups — #11774653

Order 1152.

573 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
1C4×#3799C211yesmaximal, characteristic
2C3×#4837C211yesmaximal, characteristic, complemented
3C4×#3711C211yesmaximal, characteristic, complemented
4#10589349C211yesmaximal, characteristic, complemented
5C3×#4484C211yesmaximal, characteristic, complemented
6#10589083C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#70497—31nomaximal
9#68238—31nomaximal
10C2×#3799C411yescharacteristic
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C3×ΓL(1,𝔽25)—21no—
13C3×C42×D3C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63904—21no—
16C4×#626—21no—
17#63894C411yescharacteristic
18C4×#624—21no—
19Dic3×Dic6C411yescharacteristic
20#63841C411yescharacteristic
21#63836—21no—
22C2×#3711—21no—
23C32×C4⋊C8C2211yescharacteristic
24C4×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×Dic3⋊C8—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×C4×C3⋊C8C2211yescharacteristic
28#63554—21no—
29C4×#239—31no—
30C4×#235—31no—
31C3×#423—31no—
32C4×#208—31no—
33#4837D311yescharacteristic, complemented
34C4×ΓL(1,𝔽25)—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4484—31no—
38#4484D311yescharacteristic, complemented
39#4483—31no—
40#4483—31no—
41#4483—31no—
42#4483—61no—
43#4459—31no—
44C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
45C2×C4×C3⋊D3—21no—
46C2×C3×C4×D3C2×C411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×Dic6C2×C411yescharacteristic
50C2×#626—21no—
51C2×#624—21no—
52C2×#624—21no—
53#3799—22no—
54#3799—22no—
55C2×C32×C8—21no—
56C32×C42C2311yescharacteristic
57#3752—21no—
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic
59C2×C3⋊(C3⋊C8)—21no—
60C3×C4⋊Dic3C2×C411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C3×C4×Dic3C2×C411yescharacteristic
64C3×C4×Dic3D411yescharacteristic
65C3×C4×Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C3×ΓL(1,𝔽25)—42no—
69Dic3⋊Dic3—21no—
70#3722—21no—
71(C2×D3)⋊Dic3—21no—
72Dic32—21no—
73Dic32—21no—
74#3711—24no—
75#1489—91noSylow
76C2×#239—31no—
77C2×#235—31no—
78C2×C3×M16—61no—
79C3×C4×Q8—31no—
80C2×C3×C42—31no—
81Q8×Dic3—31no—
82C4×#67—61no—
83C4×#67—61no—
84#926—31no—
85C2×#208—61no—
86C2×ΓL(1,𝔽25)—21no—
87C2×ΓL(1,𝔽25)—61no—
88#893—31no—
89#893—61no—
90#892—31no—
91#892—61no—
92C4×D12—31no—
93C4×D12—31no—
94C4×D12—31no—
95C4×D12—61no—
96C4×D12—61no—
97#872—61no—
98C42×D3—61no—
99C42×D3—61no—
100C42×D3C2×D311yescharacteristic
101C4×Dic6—31no—
102C4×Dic6C2×D311yescharacteristic
103C3×C4⋊C8—21no—
104C3×C4⋊C8—31no—
105C3×C4⋊C8—61no—
106C3×C4⋊C8C2×D311yescharacteristic
107C3×C4⋊C8C2×D311yescharacteristic
108C3×C4×C8—31no—
109#815—61no—
110Dic3⋊C8—21no—
111C4⋊(C3⋊C8)C2×D311yescharacteristic
112#803—61no—
113C4×C3⋊C8—31no—
114C4×C3⋊C8—31no—
115C4×C3⋊C8—61no—
116C4×C3⋊C8C2×D311yescharacteristic
117C22×C3⋊D3—21no—
118C22×C3×D3C22⋊C411yescharacteristic
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3⋊Dic3—21no—
123C4⋊(C3⋊D3)—21no—
124C4⋊(C3⋊D3)M1612yescomplemented
125C4×C3⋊D3—41no—
126C4×C3⋊D3—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3C22⋊C411yescharacteristic
130C2×C3×Dic3C22⋊C411yescharacteristic
131C2×C3×Dic3C22⋊C411yescharacteristic
132C3×C4×D3—21no—
133C3×C4×D3—21no—
134C3×C4×D3—21no—
135C3×C4×D3—21no—
136C3×C4×D3—22no—
137C3×Dic6—21no—
138C3×Dic6M1612yescomplemented
139#626—24no—
140#624—24no—
141#624—42no—
142C32×C8—41no—
143C3⋊(C3⋊C8)—22no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—41no—
146C4×#41—91no—
147#423—31no—
148C4×M16—91no—
149Q8⋊C8—31no—
150Q8⋊C8—91no—
151D4⋊C8—91no—
152D4⋊C8—91no—
153C2×C3×Q8—31no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C2×#67—61no—
158#239—62no—
159#239—62no—
160#235—62no—
161#235—62no—
162C2×D12—31no—
163C2×D12—31no—
164C2×D12—61no—
165C2×D12—61no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×C4×D3—61no—
171C2×C4×D3—61no—
172C2×C4×D3—121no—
173C2×C4×D3C4×D311yescharacteristic
174C2×C4×D3D1211yescharacteristic
175C2×C4×D3#6711yescharacteristic
176C2×Dic6C4×D311yescharacteristic
177C3×M16—122no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—41no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C3×C4⋊C4—31no—
184C3×C4⋊C4—61no—
185C3×C42—21no—
186C3×C42—31no—
187C3×C42—31no—
188C3×C42—31no—
189C3×C42—61no—
190C3×C42C22×D311yescharacteristic
191C3×C42C22×D311yescharacteristic
192#217—61no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—61no—
198(C2×D3)⋊C4—121no—
199C4⋊Dic3—31no—
200C4⋊Dic3—31no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3C4×D311yescharacteristic
204Dic3⋊C4—21no—
205Dic3⋊C4—61no—
206C4×Dic3—21no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3C4×D311yescharacteristic
212C4×Dic3D1211yescharacteristic
213C4×Dic3#6711yescharacteristic
214#208—64no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—121no—
220ΓL(1,𝔽25)—42no—
221ΓL(1,𝔽25)—64no—
222C22×C32C2×C22⋊C411yescharacteristic
223C2×C3⋊D3—22no—
224C2×C3⋊D3—41no—
225C2×C3⋊D3—41no—
226C2×C3×D3—21no—
227C2×C3×D3—21no—
228C2×C3×D3—21no—
229C32×C4—21no—
230C32×C4C2×M1611yescharacteristic
231C32×C4C2×M1611yescharacteristic
232C32×C4AGL(1,ℤ/8)11yescharacteristic
233C32×C4#13711yescharacteristic
234C3⋊Dic3—41no—
235C3×Dic3—21no—
236C3×Dic3—22no—
237C3×Dic3—21no—
238C3×Dic3—41no—
239C3×Dic3#10412yes—
240C2×#41—91no—
241C2×M16—61no—
242C2×M16—181no—
243C4×Q8—31no—
244C4×Q8—91no—
245C4×D4—91no—
246C4×D4—91no—
247C4×D4—181no—
248C4×D4—181no—
249#117—91no—
250#117—181no—
251C2×C42—31no—
252C2×C42—181no—
253C4⋊C8—31no—
254C4⋊C8—61no—
255C4⋊C8D3211yescharacteristic
256#97—181no—
257C4×C8—31no—
258C4×C8—91no—
259C23×C3—31no—
260C22×D3—61no—
261C22×D3—61no—
262C22×D3—121no—
263C22×D3(C2×D3)⋊C411yescharacteristic
264C3×Q8—32no—
265C3×Q8—61no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—31no—
270C2×C3×C4—31no—
271C2×C3×C4—31no—
272C2×C3×C4—62no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4C2×C4×D311yescharacteristic
280C2×C3×C4C2×C4×D311yescharacteristic
281C2×C3×C4C2×D1211yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285#67—64no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—121no—
291C2×Dic3(C2×D3)⋊C411yescharacteristic
292C2×Dic3(C2×D3)⋊C411yescharacteristic
293C2×Dic3(C2×D3)⋊C411yescharacteristic
294D12—32no—
295D12—32no—
296D12—62no—
297D12—64no—
298D12—61no—
299D12—61no—
300D12—121no—
301C4×D3—21no—
302C4×D3—21no—
303C4×D3—21no—
304C4×D3—21no—
305C4×D3—22no—
306C4×D3—64no—
307C4×D3—64no—
308C4×D3—122no—
309C4×D3—121no—
310C4×D3—121no—
311C4×D3—121no—
312C4×D3—121no—
313C4×D3—122no—
314C4×D3—241no—
315C4×D3—241no—
316Dic6—21no—
317Dic6ΓL(1,𝔽25)12yescomplemented
318C3×C8—41no—
319C3×C8—41no—
320C3×C8—62no—
321C3×C8—81no—
322C3×C8—121no—
323C3⋊C8—22no—
324C3⋊C8—41no—
325C3⋊C8—62no—
326C3⋊C8—62no—
327C3⋊C8—122no—
328C2×C32#40711yescharacteristic
329C2×C32#41711yescharacteristic
330C2×C32C2×#10411yescharacteristic
331C3⋊D3—42no—
332C3×D3—41no—
333#41—182no—
334#41—182no—
335C2×Q8—31no—
336C2×D4—91no—
337C2×D4—181no—
338C22×C4—31no—
339C22×C4—31no—
340C22×C4—31no—
341C22×C4—181no—
342C22×C4—181no—
343C22×C4—181no—
344M16—122no—
345M16—184no—
346C2×C8—21no—
347C2×C8—61no—
348C2×C8—61no—
349C2×C8—181no—
350C4⋊C4—31no—
351C4⋊C4—61no—
352C4⋊C4—91no—
353C4⋊C4—181no—
354C22⋊C4—181no—
355C22⋊C4—181no—
356C22⋊C4—181no—
357C42—31no—
358C42—31no—
359C42—31no—
360C42—61no—
361C42—181no—
362C42—181no—
363C42C2×D3211yescharacteristic
364C22×C3—21no—
365C22×C3—61no—
366C22×C3—61no—
367C22×C3—61no—
368C22×C3D3×C22⋊C411yescharacteristic
369C22×C3C2×(C2×D3)⋊C411yescharacteristic
370C2×D3—21no—
371C2×D3—21no—
372C2×D3—21no—
373C2×D3—62no—
374C2×D3—62no—
375C2×D3—122no—
376C2×D3—121no—
377C2×D3—121no—
378C2×D3—121no—
379C2×D3—121no—
380C2×D3—241no—
381C2×D3—241no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—32no—
389C3×C4—41no—
390C3×C4—62no—
391C3×C4—61no—
392C3×C4—61no—
393C3×C4—121no—
394C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
395C3×C4D3×M1611yescharacteristic
396C3×C4D3×M1611yescharacteristic
397C3×C4D3×M1611yescharacteristic
398C3×C4#91411yescharacteristic
399C3×C4#91811yescharacteristic
400C3×C4#93211yescharacteristic
401C3×C4#94211yescharacteristic
402Dic3—21no—
403Dic3—21no—
404Dic3—22no—
405Dic3—41no—
406Dic3—121no—
407Dic3—121no—
408Dic3—241no—
409Dic3#82512yes—
410C32#148911yescharacteristic, complemented, Sylow
411C23—31no—
412C23—181no—
413Q8—32no—
414Q8—61no—
415D4—92no—
416D4—184no—
417D4—181no—
418C2×C4—31no—
419C2×C4—31no—
420C2×C4—31no—
421C2×C4—62no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—184no—
429C2×C4—181no—
430C2×C4—362no—
431C2×C4—361no—
432C2×C4—361no—
433C2×C4C4×D3211yescharacteristic
434C2×C4D3×D1211yescharacteristic
435C2×C4D3×#6711yescharacteristic
436C8—41no—
437C8—62no—
438C8—121no—
439C8—182no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—121no—
444C2×C3#472611yescharacteristic
445C2×C3#480311yescharacteristic
446C2×C3D3×#10411yescharacteristic
447C2×C3#496611yescharacteristic
448C2×C3#512611yescharacteristic
449C2×C3C2×#82511yescharacteristic
450D3—41no—
451D3—122no—
452D3—122no—
453D3—242no—
454C22—61no—
455C22—61no—
456C22—61no—
457C22—182no—
458C22—361no—
459C22—361no—
460C22D3×(C2×D3)⋊C411yescharacteristic
461C4—21no—
462C4—32no—
463C4—61no—
464C4—61no—
465C4—62no—
466C4—121no—
467C4—361no—
468C4D3×ΓL(1,𝔽25)11yescharacteristic
469C4#6379111yescharacteristic
470C4#6393411yescharacteristic
471C4#6394811yescharacteristic
472C3—21no—
473C3#6823811yescharacteristic, complemented
474C3#7049711yescharacteristic, complemented
475C2—121no—
476C2—362no—
477C2#1059060911yescharacteristic
478C2#1059093611yescharacteristic
479C2D3×#82511yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3799C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4837C2semidirect
3. C4×#3711C2semidirect
4. #10589349C2semidirect
5. C3×#4484C2semidirect
6. #10589083C2semidirect
7. #10589082C2semidirect
33. #4837D3semidirect
38. #4484D3semidirect
124. C4⋊(C3⋊D3)M16semidirect
138. C3×Dic6M16semidirect
317. Dic6ΓL(1,𝔽25)semidirect
410. C32#1489semidirect
473. C3#68238semidirect
474. C3#70497semidirect

Maximal subgroups

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

subgroupindex
C4×#37992
C3×#48372
C4×#37112
#105893492
C3×#44842
#105890832
#105890822
#704973
#682383