Finite Group Databasebeta

← #11774654

Subgroups — #11774654

Order 1152.

595 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3796C211yesmaximal, characteristic
2#10592536C211yesmaximal, characteristic, complemented
3C4×#3712C211yesmaximal, characteristic, complemented
4C3×#4484C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#68238—31nomaximal
9#68174—31nomaximal
10C2×#3796C411yescharacteristic
11C2×#3743—21no—
12C42×C3⋊D3C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15C4×#626—21no—
16#63898C411yescharacteristic
17#63881—21no—
18#63878—21no—
19C4×D3×Dic3—21no—
20#63849C411yescharacteristic
21#63843C411yescharacteristic
22C2×#3712—21no—
23C32×C4⋊C8C2211yescharacteristic
24#63641—21no—
25C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×C4×C3⋊C8C2211yescharacteristic
28#63555—21no—
29C4×#239—31no—
30C4×#237—31no—
31#4837—31no—
32#4837—31no—
33#4837—61no—
34C4×ΓL(1,𝔽25)—31no—
35C4×ΓL(1,𝔽25)—31no—
36C3×Q8⋊C8—31no—
37C3×D4⋊C8—31no—
38#4535—31no—
39D4⋊(C3⋊C8)—31no—
40#4484D311yescharacteristic, complemented
41#4483D311yescharacteristic, complemented
42#4459—31no—
43#4456—31no—
44C2×C4×C3⋊D3C2×C411yescharacteristic
45C2×C4×C3⋊D3D411yescharacteristic
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C3×D12C2×C411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×Dic6C2×C411yescharacteristic
50C2×#626—21no—
51C2×D3×Dic3—21no—
52C2×D3×Dic3—21no—
53#3796—22no—
54#3796—22no—
55C2×C32×C8—21no—
56C32×C42C2311yescharacteristic
57C4×C3⋊Dic3C2×C411yescharacteristic
58C4×C3⋊Dic3D411yescharacteristic
59C4×C3⋊Dic3D411yescharacteristic
60C2×C3⋊(C3⋊C8)—21no—
61#3743—42no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3C2×C411yescharacteristic
64C3×C4⋊Dic3C2×C411yescharacteristic
65C3×Dic3⋊C4—21no—
66C3×C4×Dic3—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69Dic3⋊Dic3—21no—
70#3722—21no—
71(C2×D3)⋊Dic3—21no—
72Dic32—21no—
73Dic32—21no—
74#3712—24no—
75#1489—91noSylow
76C2×#239—31no—
77C2×#237—31no—
78C3×C4×Q8—31no—
79C3×C4×D4—31no—
80Q8×Dic3—31no—
81D4×Dic3—31no—
82C4×#67—61no—
83C2×C4×Dic3—61no—
84C2×ΓL(1,𝔽25)—61no—
85C2×ΓL(1,𝔽25)—61no—
86C2×ΓL(1,𝔽25)—61no—
87C2×ΓL(1,𝔽25)—61no—
88C2×ΓL(1,𝔽25)—62no—
89#893—31no—
90#893—61no—
91#892—31no—
92#892—31no—
93#892—61no—
94#887—31no—
95#67⋊C4—61no—
96#877—61no—
97C4×D12—61no—
98C4×D12C2×D311yescharacteristic
99C42×D3—31no—
100C42×D3—31no—
101C42×D3—61no—
102C42×D3—61no—
103C4×Dic6C2×D311yescharacteristic
104C3×C4⋊C8—21no—
105C3×C4⋊C8C2×D311yescharacteristic
106C3×C4⋊C8C2×D311yescharacteristic
107C3×C4×C8—31no—
108C3×C4×C8—31no—
109#815—61no—
110#815—61no—
111Dic3⋊C8—61no—
112Dic3⋊C8—61no—
113Dic3⋊C8—62no—
114C4⋊(C3⋊C8)—31no—
115C4⋊(C3⋊C8)—31no—
116C4⋊(C3⋊C8)—61no—
117C4×C3⋊C8C2×D311yescharacteristic
118C4×C3⋊C8C2×D311yescharacteristic
119C22×C3⋊D3C22⋊C411yescharacteristic
120C22×C3×D3—21no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3C22⋊C411yescharacteristic
125C2×C3⋊Dic3C22⋊C411yescharacteristic
126C2×C3⋊Dic3C22⋊C411yescharacteristic
127C4×C3⋊D3—21no—
128C4×C3⋊D3—21no—
129C4×C3⋊D3—21no—
130C4×C3⋊D3—21no—
131C4×C3⋊D3—22no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C3×D12—21no—
136C3×D12M1612yescomplemented
137C3×C4×D3—41no—
138C3×C4×D3—41no—
139C3×Dic6—21no—
140C3×Dic6M1612yescomplemented
141#626—24no—
142D3×Dic3—24no—
143D3×Dic3—42no—
144C32×C8—41no—
145C3⋊(C3⋊C8)—41no—
146C3×C3⋊C8—22no—
147C3×C3⋊C8—22no—
148C4×#41—91no—
149#423—91no—
150C4×M16—91no—
151Q8⋊C8—31no—
152Q8⋊C8—91no—
153D4⋊C8—31no—
154D4⋊C8—91no—
155C2×C3×Q8—31no—
156C2×C3×D4—31no—
157C22×C3×C4—61no—
158C2×#67—61no—
159C22×Dic3—61no—
160C22×Dic3—61no—
161#239—62no—
162#239—62no—
163#237—62no—
164#237—62no—
165C2×D12—61no—
166C2×D12C4×D311yescharacteristic
167C2×C4×D3—21no—
168C2×C4×D3—31no—
169C2×C4×D3—31no—
170C2×C4×D3—31no—
171C2×C4×D3—31no—
172C2×C4×D3—31no—
173C2×C4×D3—31no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×C4×D3—61no—
177C2×C4×D3—61no—
178C2×C4×D3—61no—
179C2×Dic6C4×D311yescharacteristic
180C2×C3×C8—22no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—61no—
184C2×C3×C8—61no—
185C3×C4⋊C4—31no—
186C3×C4⋊C4—31no—
187C3×C4⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C42—21no—
190C3×C42—61no—
191C3×C42C22×D311yescharacteristic
192C3×C42C22×D311yescharacteristic
193#217—61no—
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—61no—
198C4⋊Dic3—61no—
199C4⋊Dic3C4×D311yescharacteristic
200C4⋊Dic3C4×D311yescharacteristic
201Dic3⋊C4—21no—
202Dic3⋊C4—61no—
203C4×Dic3—21no—
204C4×Dic3—31no—
205C4×Dic3—31no—
206C4×Dic3—31no—
207C4×Dic3—31no—
208C4×Dic3—31no—
209C4×Dic3—31no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—62no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—61no—
222ΓL(1,𝔽25)—64no—
223ΓL(1,𝔽25)—64no—
224ΓL(1,𝔽25)—124no—
225ΓL(1,𝔽25)—122no—
226ΓL(1,𝔽25)—122no—
227C22×C32C2×C22⋊C411yescharacteristic
228C2×C3⋊D3—21no—
229C2×C3⋊D3—21no—
230C2×C3⋊D3—21no—
231C2×C3×D3—22no—
232C2×C3×D3—41no—
233C2×C3×D3—41no—
234C32×C4—21no—
235C32×C4C2×M1611yescharacteristic
236C32×C4C2×M1611yescharacteristic
237C32×C4AGL(1,ℤ/8)11yescharacteristic
238C32×C4#13711yescharacteristic
239C3⋊Dic3—21no—
240C3⋊Dic3—21no—
241C3⋊Dic3#10412yes—
242C3×Dic3—22no—
243C3×Dic3—41no—
244C3×Dic3—41no—
245C2×#41—91no—
246C2×M16—181no—
247C2×M16—181no—
248C4×Q8—31no—
249C4×Q8—91no—
250C4×D4—31no—
251C4×D4—91no—
252C4×D4—181no—
253C4×D4—181no—
254#117—91no—
255#117—181no—
256C2×C42—91no—
257C2×C42—181no—
258C4⋊C8—91no—
259C4⋊C8—181no—
260C4⋊C8D3211yescharacteristic
261#97—181no—
262C4×C8—31no—
263C4×C8—31no—
264C23×C3—61no—
265C22×D3—21no—
266C22×D3—31no—
267C22×D3—31no—
268C22×D3—61no—
269C3×Q8—32no—
270C3×Q8—61no—
271C3×D4—32no—
272C3×D4—61no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—121no—
280C2×C3×C4—121no—
281C2×C3×C4C2×C4×D311yescharacteristic
282C2×C3×C4C2×C4×D311yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287#67—64no—
288C2×Dic3—21no—
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—31no—
292C2×Dic3—31no—
293C2×Dic3—31no—
294C2×Dic3—31no—
295C2×Dic3—31no—
296C2×Dic3—31no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—61no—
300C2×Dic3—64no—
301C2×Dic3—122no—
302D12—21no—
303D12—64no—
304D12ΓL(1,𝔽25)12yescomplemented
305C4×D3—41no—
306C4×D3—41no—
307C4×D3—62no—
308C4×D3—62no—
309C4×D3—62no—
310C4×D3—62no—
311C4×D3—64no—
312C4×D3—61no—
313C4×D3—61no—
314C4×D3—61no—
315C4×D3—61no—
316C4×D3—61no—
317C4×D3—61no—
318C4×D3—61no—
319C4×D3—61no—
320C4×D3—122no—
321C4×D3—121no—
322C4×D3—121no—
323C4×D3—122no—
324Dic6—21no—
325Dic6ΓL(1,𝔽25)12yescomplemented
326C3×C8—42no—
327C3×C8—41no—
328C3×C8—41no—
329C3×C8—62no—
330C3×C8—62no—
331C3⋊C8—22no—
332C3⋊C8—22no—
333C3⋊C8—122no—
334C3⋊C8—121no—
335C3⋊C8—121no—
336C2×C32#40711yescharacteristic
337C2×C32#41711yescharacteristic
338C2×C32C2×#10411yescharacteristic
339C3⋊D3—41no—
340C3×D3—42no—
341#41—182no—
342#41—182no—
343C2×Q8—31no—
344C2×D4—31no—
345C2×D4—181no—
346C22×C4—61no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—91no—
350C22×C4—181no—
351C22×C4—181no—
352M16—184no—
353M16—362no—
354C2×C8—21no—
355C2×C8—61no—
356C2×C8—61no—
357C2×C8—181no—
358C4⋊C4—31no—
359C4⋊C4—31no—
360C4⋊C4—61no—
361C4⋊C4—181no—
362C22⋊C4—61no—
363C22⋊C4—181no—
364C22⋊C4—181no—
365C42—61no—
366C42—91no—
367C42—91no—
368C42—91no—
369C42—181no—
370C42—181no—
371C42C2×D3211yescharacteristic
372C22×C3—21no—
373C22×C3—62no—
374C22×C3—121no—
375C22×C3—121no—
376C22×C3D3×C22⋊C411yescharacteristic
377C22×C3D3×C22⋊C411yescharacteristic
378C2×D3—22no—
379C2×D3—41no—
380C2×D3—41no—
381C2×D3—62no—
382C2×D3—61no—
383C2×D3—61no—
384C2×D3—61no—
385C2×D3—61no—
386C2×D3—61no—
387C2×D3—61no—
388C2×D3—121no—
389C2×D3—121no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—41no—
397C3×C4—62no—
398C3×C4—121no—
399C3×C4—121no—
400C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
401C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
402C3×C4D3×M1611yescharacteristic
403C3×C4D3×M1611yescharacteristic
404C3×C4#91111yescharacteristic
405C3×C4#91411yescharacteristic
406C3×C4#91511yescharacteristic
407C3×C4#91811yescharacteristic
408Dic3—22no—
409Dic3—32no—
410Dic3—32no—
411Dic3—41no—
412Dic3—41no—
413Dic3—62no—
414Dic3—62no—
415Dic3—61no—
416Dic3—61no—
417Dic3—61no—
418Dic3—61no—
419Dic3—121no—
420C32#148911yescharacteristic, complemented, Sylow
421C23—61no—
422C23—91no—
423Q8—32no—
424Q8—61no—
425D4—32no—
426D4—61no—
427D4—184no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—91no—
432C2×C4—91no—
433C2×C4—91no—
434C2×C4—121no—
435C2×C4—121no—
436C2×C4—182no—
437C2×C4—184no—
438C2×C4—181no—
439C2×C4—181no—
440C2×C4—181no—
441C2×C4—181no—
442C2×C4—362no—
443C2×C4C4×D3211yescharacteristic
444C2×C4#380211yescharacteristic
445C2×C4#381111yescharacteristic
446C8—41no—
447C8—62no—
448C8—62no—
449C8—361no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—122no—
454C2×C3#472611yescharacteristic
455C2×C3#472611yescharacteristic
456C2×C3#477111yescharacteristic
457C2×C3#480311yescharacteristic
458C2×C3D3×#10411yescharacteristic
459C2×C3D3×#10411yescharacteristic
460D3—42no—
461D3—122no—
462D3—121no—
463D3—121no—
464C22—62no—
465C22—121no—
466C22—121no—
467C22—181no—
468C22—181no—
469C22—181no—
470C22#6392111yescharacteristic
471C4—21no—
472C4—62no—
473C4—92no—
474C4—121no—
475C4—121no—
476C4—181no—
477C4—181no—
478C4D3×ΓL(1,𝔽25)11yescharacteristic
479C4D3×ΓL(1,𝔽25)11yescharacteristic
480C4#6393711yescharacteristic
481C4#6395111yescharacteristic
482C3—21no—
483C3#6817411yescharacteristic, complemented
484C3#6823811yescharacteristic, complemented
485C2—122no—
486C2—361no—
487C2#1059061211yescharacteristic
488C2#1059093711yescharacteristic
489C2#1059100811yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3796C4
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. #10592536C2semidirect
3. C4×#3712C2semidirect
4. C3×#4484C2semidirect
5. C3×#4483C2semidirect
6. #10589084C2semidirect
7. #10589081C2semidirect
40. #4484D3semidirect
41. #4483D3semidirect
136. C3×D12M16semidirect
140. C3×Dic6M16semidirect
304. D12ΓL(1,𝔽25)semidirect
325. Dic6ΓL(1,𝔽25)semidirect
420. C32#1489semidirect
483. C3#68174semidirect
484. C3#68238semidirect

Maximal subgroups

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

subgroupindex
C4×#37962
#105925362
C4×#37122
C3×#44842
C3×#44832
#105890842
#105890812
#682383
#681743