Finite Group Databasebeta

← #11787049

Subgroups — #11787049

Order 1152.

619 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63817C211yesmaximal, characteristic
2#10592701C211yesmaximal, characteristic
3C3×#4999C211yesmaximal, characteristic, complemented
4C2×#63578C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70545—31nomaximal
9#68774—31nomaximal
10C2×#3828C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×C4×Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3712—21no—
18#63817—22no—
19#63817—22no—
20C2×#3710—21no—
21#63637C411yescharacteristic, complemented
22#63637C411yescharacteristic, complemented
23#63636C411yescharacteristic, complemented
24#63636C411yescharacteristic, complemented
25C3×C4⋊(C3⋊C8)—21no—
26C3×C4⋊(C3⋊C8)—21no—
27#63578—22no—
28#63570—22no—
29C2×#907—31no—
30C2×#901—31no—
31C3×#424—31no—
32C2×#825—31no—
33C2×#822—31no—
34C2×#822—31no—
35#5002—31no—
36#5002—31no—
37#5002—61no—
38#4999D311yescharacteristic, complemented
39C2×#805—31no—
40C3×#339—31no—
41#4550—31no—
42#4532D311yescharacteristic, complemented
43#4524—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46#3828—21no—
47#3828—21no—
48#3828D412yes—
49#3828Q812yes—
50C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634C2×C411yescharacteristic
53C22×C3×Dic3—21no—
54C32×C4⋊C4C2×C411yescharacteristic
55C32×C4⋊C4C2×C411yescharacteristic
56C32×C22⋊C4—21no—
57C32×C42—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
61C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
62C3×C4×Dic3—21no—
63C3×C4×Dic3—21no—
64C3×#208—21no—
65C3×#208—21no—
66C3×#208—21no—
67C3×#208D412yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8D411yescharacteristic
73C2×C3×C3⋊C8D411yescharacteristic
74#3712—24no—
75#3710—24no—
76#1866—91noSylow
77C2×#235—31no—
78C2×#235—31no—
79C2×#235—61no—
80C2×C3×M16—31no—
81C2×C3×M16—31no—
82C22×C3×C8—31no—
83C3×#117—21no—
84C3×#117C2×D311yescharacteristic
85C3×#117C2×D311yescharacteristic
86C2×C3×C42—31no—
87C2×C4×Dic3C2×D311yescharacteristic
88C2×#208C2×D311yescharacteristic
89C2×#208C2×D311yescharacteristic
90C22×C3⋊C8—31no—
91C22×C3⋊C8—31no—
92C22×C3⋊C8—61no—
93C22×C3⋊C8C2×D311yescharacteristic
94#907—62no—
95#907—62no—
96#901—62no—
97#901—62no—
98C2×ΓL(1,𝔽25)—61no—
99C2×ΓL(1,𝔽25)—61no—
100C2×D3×C8—61no—
101C2×D3×C8—61no—
102C3×C4⋊C8—61no—
103C3×C4⋊C8—61no—
104#825—62no—
105#822—62no—
106#822—62no—
107#810—31no—
108#810—31no—
109#810—31no—
110#810—31no—
111#810—61no—
112#810—61no—
113#809—31no—
114#809—31no—
115#809—31no—
116#809—31no—
117#809—61no—
118#809—61no—
119#805—62no—
120C4⋊(C3⋊C8)—21no—
121C4⋊(C3⋊C8)—21no—
122C23×C32#4111yescharacteristic
123C22×C3⋊D3—21no—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×Q811yescharacteristic
131C2×C32×C4#4111yescharacteristic
132#638—22no—
133#638—22no—
134C2×C3⋊Dic3—21no—
135C4⋊(C3⋊D3)—21no—
136C4⋊(C3⋊D3)C4⋊C412yes—
137C4×C3⋊D3—22no—
138C4×C3⋊D3—22no—
139#634—21no—
140#634C4⋊C412yes—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C3⋊(C3⋊C8)—21no—
145C3⋊(C3⋊C8)—21no—
146C3×C3⋊C8—21no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—21no—
149C3×C3⋊C8—41no—
150C2×#131—91no—
151C2×#108—91no—
152#424—31no—
153C2×#104—91no—
154#416—91no—
155#339—31no—
156#336—91no—
157C22×C3×C4—21no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—61no—
162C2×#67—61no—
163C2×#67—121no—
164C22×Dic3—21no—
165#235—32no—
166#235—32no—
167#235—32no—
168#235—32no—
169#235—62no—
170#235—62no—
171#235—61no—
172#235—61no—
173#235—61no—
174#235—61no—
175#235—121no—
176#235—121no—
177C2×D12—31no—
178C2×D12—31no—
179C2×D12—61no—
180C2×C4×D3—61no—
181C2×C4×D3—61no—
182C2×C4×D3—121no—
183C2×Dic6—31no—
184C2×Dic6—31no—
185C2×Dic6—61no—
186C3×M16—32no—
187C3×M16—61no—
188C3×M16—61no—
189C3×M16—61no—
190C2×C3×C8—31no—
191C2×C3×C8—31no—
192C2×C3×C8—61no—
193C2×C3×C8—61no—
194C2×C3×C8—61no—
195C2×C3×C8—61no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4C4×D311yescharacteristic
199C3×C4⋊C4C4×D311yescharacteristic
200C3×C4⋊C4C4×D311yescharacteristic
201C3×C4⋊C4C4×D311yescharacteristic
202C3×C22⋊C4—21no—
203C3×C22⋊C4—21no—
204C3×C22⋊C4—41no—
205C3×C42—21no—
206C3×C42—21no—
207C3×C42—41no—
208C3×C42—61no—
209C3×C42—61no—
210C4×Dic3—21no—
211C4×Dic3—21no—
212#208—21no—
213#208—21no—
214#208—21no—
215#208D1212yes—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—31no—
221C2×C3⋊C8—31no—
222C2×C3⋊C8—31no—
223C2×C3⋊C8—31no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—121no—
231C2×C3⋊C8—121no—
232C2×C3⋊C8#6711yescharacteristic
233C2×C3⋊C8#6711yescharacteristic
234ΓL(1,𝔽25)—64no—
235ΓL(1,𝔽25)—64no—
236D3×C8—64no—
237D3×C8—64no—
238C22×C32—21no—
239C22×C32—21no—
240C22×C32C4×D411yescharacteristic
241C22×C32C22⋊Q811yescharacteristic
242C22×C32#12311yescharacteristic
243C2×C3⋊D3—22no—
244C2×C3⋊D3—41no—
245C2×C3⋊D3—41no—
246C32×C4—41no—
247C32×C4—41no—
248C32×C4C2×C4⋊C411yescharacteristic
249C32×C4C4×D411yescharacteristic
250C32×C4#12011yescharacteristic
251C32×C4C22⋊Q811yescharacteristic
252C3⋊Dic3—22no—
253C3×Dic3—42no—
254C2×#41—91no—
255#131—182no—
256#131—182no—
257C2×M16—31no—
258C2×M16—31no—
259C2×M16—181no—
260C22×C8—31no—
261C22×C8—91no—
262C22×C8—181no—
263#117D3211yescharacteristic
264C2×C42—31no—
265#108—182no—
266C4⋊C8—61no—
267C4⋊C8—61no—
268#104—182no—
269#103—91no—
270#103—91no—
271#102—91no—
272#102—91no—
273C23×C3—21no—
274C23×C3#23511yescharacteristic
275C23×C3#23711yescharacteristic
276C22×D3—61no—
277C22×D3—61no—
278C22×D3—121no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—62no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4C2×D1211yescharacteristic
297C2×C3×C4#23511yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×Q811yescharacteristic
303C2×C3×C4D3×Q811yescharacteristic
304C2×C3×C4#23911yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306#67—62no—
307#67—62no—
308#67—62no—
309#67—62no—
310#67—122no—
311#67—122no—
312C2×Dic3—22no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—121no—
318D12—32no—
319D12—32no—
320D12—62no—
321D12—61no—
322D12—61no—
323D12—121no—
324C4×D3—62no—
325C4×D3—62no—
326C4×D3—62no—
327C4×D3—62no—
328C4×D3—122no—
329C4×D3—122no—
330Dic6—32no—
331Dic6—32no—
332Dic6—62no—
333Dic6—61no—
334Dic6—61no—
335Dic6—121no—
336C3×C8—61no—
337C3×C8—61no—
338C3×C8—62no—
339C3×C8—121no—
340C3⋊C8—22no—
341C3⋊C8—21no—
342C3⋊C8—21no—
343C3⋊C8—41no—
344C3⋊C8—61no—
345C3⋊C8—61no—
346C3⋊C8—61no—
347C3⋊C8—61no—
348C3⋊C8—121no—
349C3⋊C8—121no—
350C2×C32—21no—
351C2×C32—21no—
352C2×C32#38511yescharacteristic
353C2×C32#44311yescharacteristic
354C2×C32#44411yescharacteristic
355C3⋊D3—42no—
356#41—92no—
357#41—92no—
358#41—181no—
359#41—181no—
360C2×Q8—91no—
361C2×D4—91no—
362C2×D4—181no—
363C22×C4—61no—
364C22×C4—181no—
365C22×C4C2×D3211yescharacteristic
366M16—32no—
367M16—61no—
368M16—61no—
369M16—61no—
370M16—184no—
371C2×C8—31no—
372C2×C8—31no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—61no—
376C2×C8—61no—
377C2×C8—91no—
378C2×C8—91no—
379C2×C8—184no—
380C2×C8—181no—
381C2×C8—181no—
382C4⋊C4#62411yescharacteristic
383C4⋊C4#62411yescharacteristic
384C22⋊C4—21no—
385C42—21no—
386C42—61no—
387C42—61no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3#67⋊C411yescharacteristic
398C22×C3#88311yescharacteristic
399C22×C3#89411yescharacteristic
400C22×C3#89611yescharacteristic
401C22×C3#89711yescharacteristic
402C22×C3C4×#6711yescharacteristic
403C2×D3—62no—
404C2×D3—62no—
405C2×D3—122no—
406C2×D3—121no—
407C2×D3—121no—
408C2×D3—121no—
409C2×D3—121no—
410C2×D3—241no—
411C2×D3—241no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—41no—
417C3×C4—41no—
418C3×C4—41no—
419C3×C4—41no—
420C3×C4—81no—
421C3×C4—81no—
422C3×C4—122no—
423C3×C4C4×D1211yescharacteristic
424C3×C4#88211yescharacteristic
425C3×C4D3×C4⋊C411yescharacteristic
426C3×C4D3×C4⋊C411yescharacteristic
427C3×C4#89311yescharacteristic
428C3×C4#89611yescharacteristic
429C3×C4#93711yescharacteristic
430C3×C4#94611yescharacteristic
431Dic3—42no—
432Dic3—62no—
433Dic3—62no—
434Dic3—122no—
435C32#186611yescharacteristic, complemented, Sylow
436C23—181no—
437C23#380411yescharacteristic
438Q8—92no—
439Q8—181no—
440D4—92no—
441D4—182no—
442D4—182no—
443D4—181no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—62no—
447C2×C4—121no—
448C2×C4—121no—
449C2×C4—181no—
450C2×C4—182no—
451C2×C4—182no—
452C2×C4#379711yescharacteristic
453C2×C4#379911yescharacteristic
454C2×C4D3×D1211yescharacteristic
455C2×C4#380211yescharacteristic
456C2×C4C2×#62411yescharacteristic
457C2×C4D3×#6711yescharacteristic
458C8—61no—
459C8—61no—
460C8—62no—
461C8—121no—
462C8—181no—
463C8—181no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—41no—
472C2×C3—41no—
473C2×C3#466811yescharacteristic
474C2×C3#482311yescharacteristic
475C2×C3#482411yescharacteristic
476C2×C3#498911yescharacteristic
477C2×C3#514411yescharacteristic
478C2×C3#514511yescharacteristic
479D3—122no—
480D3—122no—
481D3—242no—
482C22—21no—
483C22—21no—
484C22—182no—
485C22—361no—
486C22—361no—
487C22#6385411yescharacteristic
488C22#6389511yescharacteristic
489C22#6395211yescharacteristic
490C4—41no—
491C4—41no—
492C4—122no—
493C4—182no—
494C4#6388811yescharacteristic
495C4#6389411yescharacteristic
496C4#6390011yescharacteristic
497C4#6392211yescharacteristic
498C3—21no—
499C3#6877411yescharacteristic, complemented
500C3#7054511yescharacteristic, complemented
501C2—21no—
502C2—21no—
503C2—362no—
504C2#1059137811yescharacteristic
505C2#1059166211yescharacteristic
506C2#1059166311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C4×D4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1866
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. C3×#4999C2semidirect
4. C2×#63578C2semidirect
6. C3×#4532C2semidirect
7. #10589155C2semidirect
21. #63637C4semidirect
22. #63637C4semidirect
23. #63636C4semidirect
24. #63636C4semidirect
38. #4999D3semidirect
42. #4532D3semidirect
435. C32#1866semidirect
499. C3#68774semidirect
500. C3#70545semidirect

Maximal subgroups

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

subgroupindex
C2×#638172
#105927012
C3×#49992
C2×#635782
C2×#635702
C3×#45322
#105891552
#705453
#687743