Finite Group Databasebeta

← #11774655

Subgroups — #11774655

Order 1152.

567 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3795C211yesmaximal, characteristic
2C3×#4837C211yesmaximal, characteristic, complemented
3C4×#3711C211yesmaximal, characteristic, complemented
4#10589350C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#70497—31nomaximal
9#68174—31nomaximal
10C2×#3795C411yescharacteristic
11C4×#634C2211yescharacteristic
12C2×C3×ΓL(1,𝔽25)—21no—
13C3×C4×D12C2211yescharacteristic
14C3×C42×D3C2211yescharacteristic
15C4×#625—21no—
16Dic3×D12C411yescharacteristic
17#63879—21no—
18#63877—21no—
19C4×D3×Dic3—21no—
20#63844C411yescharacteristic
21#63841C411yescharacteristic
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×#237—31no—
30C4×#235—31no—
31C3×#423—31no—
32C4×#208—31no—
33#4837D311yescharacteristic, complemented
34C4×ΓL(1,𝔽25)—31no—
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4484—31no—
38#4484—31no—
39#4484—31no—
40#4484—61no—
41#4483—31no—
42#4483D311yescharacteristic, complemented
43#4456—31no—
44C2×#634C2×C411yescharacteristic
45C2×C3×D12C2×C411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3C2×C411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×C4×D3D411yescharacteristic
50C2×#625—21no—
51C2×D3×Dic3—21no—
52C2×D3×Dic3—21no—
53#3795—22no—
54#3795—22no—
55C2×C32×C8—21no—
56C32×C42C2311yescharacteristic
57C4⋊(C3⋊Dic3)C2×C411yescharacteristic
58#3750—21no—
59C4×C3⋊Dic3—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3C2×C411yescharacteristic
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—
69#3724—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72Dic32—21no—
73Dic32—21no—
74#3711—24no—
75#1489—91noSylow
76C2×#237—31no—
77C2×#235—31no—
78C2×C3×M16—61no—
79C3×C4×D4—31no—
80C2×C3×C42—31no—
81D4×Dic3—31no—
82C4×#67—61no—
83C4×#67—61no—
84C4×#67—61no—
85#926—31no—
86C2×C4×Dic3—61no—
87C2×#208—61no—
88C2×ΓL(1,𝔽25)—21no—
89C2×ΓL(1,𝔽25)—61no—
90#892—31no—
91#887—31no—
92#67⋊C4—61no—
93#877—61no—
94C4×D12—31no—
95C4×D12C2×D311yescharacteristic
96#872—61no—
97C42×D3—61no—
98C42×D3C2×D311yescharacteristic
99C4×Dic6—31no—
100C4×Dic6—31no—
101C4×Dic6—31no—
102C4×Dic6—61no—
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—
123C2×C3⋊Dic3—21no—
124#634—21no—
125#634M1612yescomplemented
126C2×C3×Dic3—21no—
127C2×C3×Dic3C22⋊C411yescharacteristic
128C2×C3×Dic3C22⋊C411yescharacteristic
129C2×C3×Dic3C22⋊C411yescharacteristic
130C3×D12—21no—
131C3×D12M1612yescomplemented
132C3×C4×D3—21no—
133C3×C4×D3—21no—
134C3×C4×D3—21no—
135C3×C4×D3—21no—
136C3×C4×D3—22no—
137C3×C4×D3—41no—
138C3×C4×D3—41no—
139#625—24no—
140D3×Dic3—24no—
141D3×Dic3—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—91no—
150Q8⋊C8—91no—
151D4⋊C8—31no—
152D4⋊C8—91no—
153C2×C3×D4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—61no—
158C2×#67—61no—
159C2×#67—61no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162#237—62no—
163#237—62no—
164#235—62no—
165#235—62no—
166C2×D12C4×D311yescharacteristic
167C2×C4×D3—21no—
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×C4×D3C4×D311yescharacteristic
171C2×C4×D3D1211yescharacteristic
172C2×C4×D3#6711yescharacteristic
173C2×Dic6—31no—
174C2×Dic6—31no—
175C2×Dic6—61no—
176C3×M16—122no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8—41no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C3×C4⋊C4—31no—
183C3×C22⋊C4—61no—
184C3×C42—21no—
185C3×C42—31no—
186C3×C42—31no—
187C3×C42—31no—
188C3×C42C22×D311yescharacteristic
189C3×C42C22×D311yescharacteristic
190#217—61no—
191#217—61no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—61no—
195C4⋊Dic3—31no—
196C4⋊Dic3—31no—
197C4⋊Dic3—61no—
198C4⋊Dic3C4×D311yescharacteristic
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—121no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—121no—
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—21no—
225C2×C3×D3—21no—
226C2×C3×D3—21no—
227C2×C3×D3—41no—
228C2×C3×D3—41no—
229C32×C4—21no—
230C32×C4C2×M1611yescharacteristic
231C32×C4C2×M1611yescharacteristic
232C32×C4AGL(1,ℤ/8)11yescharacteristic
233C32×C4#13711yescharacteristic
234C3⋊Dic3—22no—
235C3⋊Dic3—41no—
236C3×Dic3—21no—
237C3×Dic3—21no—
238C3×Dic3—41no—
239C3×Dic3#10412yes—
240C2×#41—91no—
241C2×M16—61no—
242C2×M16—181no—
243C4×Q8—91no—
244C4×Q8—91no—
245C4×D4—31no—
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—
260C23×C3—61no—
261C22×D3—21no—
262C22×D3(C2×D3)⋊C411yescharacteristic
263C3×D4—32no—
264C3×D4—61no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—31no—
269C2×C3×C4—31no—
270C2×C3×C4—31no—
271C2×C3×C4—62no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—121no—
278C2×C3×C4—121no—
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—
286#67—64no—
287C2×Dic3—21no—
288C2×Dic3—64no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293C2×Dic3—121no—
294C2×Dic3—121no—
295C2×Dic3—122no—
296C2×Dic3(C2×D3)⋊C411yescharacteristic
297C2×Dic3(C2×D3)⋊C411yescharacteristic
298C2×Dic3(C2×D3)⋊C411yescharacteristic
299D12—21no—
300D12ΓL(1,𝔽25)12yescomplemented
301C4×D3—21no—
302C4×D3—21no—
303C4×D3—21no—
304C4×D3—21no—
305C4×D3—22no—
306C4×D3—41no—
307C4×D3—41no—
308C4×D3—64no—
309C4×D3—122no—
310Dic6—32no—
311Dic6—32no—
312Dic6—62no—
313Dic6—61no—
314Dic6—61no—
315Dic6—121no—
316C3×C8—41no—
317C3×C8—41no—
318C3×C8—62no—
319C3×C8—81no—
320C3×C8—121no—
321C3⋊C8—22no—
322C3⋊C8—41no—
323C3⋊C8—62no—
324C3⋊C8—62no—
325C3⋊C8—122no—
326C2×C32#40711yescharacteristic
327C2×C32#41711yescharacteristic
328C2×C32C2×#10411yescharacteristic
329C3×D3—41no—
330C3×D3—42no—
331#41—182no—
332#41—182no—
333C2×Q8—91no—
334C2×D4—31no—
335C2×D4—181no—
336C22×C4—31no—
337C22×C4—31no—
338C22×C4—31no—
339C22×C4—61no—
340C22×C4—181no—
341C22×C4—181no—
342M16—122no—
343M16—184no—
344C2×C8—21no—
345C2×C8—61no—
346C2×C8—61no—
347C2×C8—181no—
348C4⋊C4—31no—
349C4⋊C4—91no—
350C4⋊C4—181no—
351C4⋊C4—181no—
352C22⋊C4—61no—
353C22⋊C4—181no—
354C22⋊C4—181no—
355C42—31no—
356C42—31no—
357C42—31no—
358C42—181no—
359C42—181no—
360C42—181no—
361C42C2×D3211yescharacteristic
362C22×C3—21no—
363C22×C3—62no—
364C22×C3—61no—
365C22×C3—61no—
366C22×C3—61no—
367C22×C3—121no—
368C22×C3—121no—
369C22×C3D3×C22⋊C411yescharacteristic
370C22×C3C2×(C2×D3)⋊C411yescharacteristic
371C2×D3—21no—
372C2×D3—21no—
373C2×D3—21no—
374C2×D3—22no—
375C2×D3—41no—
376C2×D3—41no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—32no—
384C3×C4—41no—
385C3×C4—61no—
386C3×C4—61no—
387C3×C4—121no—
388C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
389C3×C4D3×M1611yescharacteristic
390C3×C4D3×M1611yescharacteristic
391C3×C4D3×M1611yescharacteristic
392C3×C4#91111yescharacteristic
393C3×C4#91511yescharacteristic
394C3×C4#93211yescharacteristic
395C3×C4#94211yescharacteristic
396Dic3—21no—
397Dic3—21no—
398Dic3—41no—
399Dic3—62no—
400Dic3—62no—
401Dic3—122no—
402Dic3—121no—
403Dic3—121no—
404Dic3—241no—
405Dic3#82512yes—
406C32#148911yescharacteristic, complemented, Sylow
407C23—31no—
408C23—61no—
409Q8—92no—
410Q8—181no—
411D4—32no—
412D4—61no—
413D4—184no—
414C2×C4—31no—
415C2×C4—31no—
416C2×C4—31no—
417C2×C4—62no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—121no—
424C2×C4—121no—
425C2×C4—184no—
426C2×C4—181no—
427C2×C4—181no—
428C2×C4—362no—
429C2×C4C4×D3211yescharacteristic
430C2×C4D3×D1211yescharacteristic
431C2×C4D3×#6711yescharacteristic
432C8—41no—
433C8—62no—
434C8—121no—
435C8—182no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—121no—
440C2×C3—122no—
441C2×C3#472611yescharacteristic
442C2×C3#477111yescharacteristic
443C2×C3D3×#10411yescharacteristic
444C2×C3#496611yescharacteristic
445C2×C3#512611yescharacteristic
446C2×C3C2×#82511yescharacteristic
447D3—42no—
448D3—41no—
449C22—61no—
450C22—61no—
451C22—61no—
452C22—62no—
453C22—121no—
454C22—121no—
455C22D3×(C2×D3)⋊C411yescharacteristic
456C4—21no—
457C4—32no—
458C4—61no—
459C4—61no—
460C4—121no—
461C4—182no—
462C4—361no—
463C4D3×ΓL(1,𝔽25)11yescharacteristic
464C4#6379111yescharacteristic
465C4#6393211yescharacteristic
466C4#6394611yescharacteristic
467C3—21no—
468C3#6817411yescharacteristic, complemented
469C3#7049711yescharacteristic, complemented
470C2—121no—
471C2—122no—
472C2#1059060711yescharacteristic
473C2#1059093611yescharacteristic
474C2D3×#82511yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3795C4
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. #10589350C2semidirect
5. C3×#4483C2semidirect
6. #10589085C2semidirect
7. #10589080C2semidirect
33. #4837D3semidirect
42. #4483D3semidirect
125. #634M16semidirect
131. C3×D12M16semidirect
300. D12ΓL(1,𝔽25)semidirect
406. C32#1489semidirect
468. C3#68174semidirect
469. C3#70497semidirect

Maximal subgroups

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

subgroupindex
C4×#37952
C3×#48372
C4×#37112
#105893502
C3×#44832
#105890852
#105890802
#704973
#681743