Finite Group Databasebeta

← #11787040

Subgroups — #11787040

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#10592812C211yesmaximal, characteristic
3C2×C3×#819C211yesmaximal, characteristic, complemented
4#10591119C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic
6C3×#4550C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70722—31nomaximal
9#68694—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12#64135C2211yescharacteristic
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#63648C411yescharacteristic, complemented
22#63648C411yescharacteristic, complemented
23#63643C411yescharacteristic, complemented
24#63643C411yescharacteristic, complemented
25C3×#819—22no—
26#63572—21no—
27#63572—21no—
28#63570—22no—
29C2×#907—31no—
30C2×#901—31no—
31C2×C3×#108—31no—
32C2×#825—31no—
33#5119—31no—
34#5113—31no—
35#5113—31no—
36#5113—61no—
37C2×#819D311yescharacteristic, complemented
38#5102—31no—
39C2×#805—31no—
40C3×#336—31no—
41#4555—31no—
42#4550D311yescharacteristic, complemented
43#4523—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—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C2×C32×C8C2×C411yescharacteristic
57C2×C32×C8C2×C411yescharacteristic
58#3757—21no—
59C4⋊(C3⋊Dic3)C2×C411yescharacteristic
60C4⋊(C3⋊Dic3)C2×C411yescharacteristic
61C4×C3⋊Dic3—21no—
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—21no—
83C22×C3×C8—31no—
84C22×C3×C8C2×D311yescharacteristic
85C22×C3×C8C2×D311yescharacteristic
86C2×C3×C42—31no—
87#926—31no—
88#926—31no—
89#926—61no—
90C2×C4×Dic3C2×D311yescharacteristic
91C2×#208C2×D311yescharacteristic
92C2×#208C2×D311yescharacteristic
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×#108—62no—
103#825—62no—
104#821—31no—
105#821—31no—
106#821—31no—
107#821—31no—
108#821—61no—
109#821—61no—
110#819—22no—
111#816—31no—
112#816—31no—
113#816—31no—
114#816—31no—
115#816—61no—
116#816—61no—
117Dic3⋊C8—61no—
118Dic3⋊C8—61no—
119Dic3⋊C8—61no—
120Dic3⋊C8—61no—
121#805—62no—
122C23×C32#4111yescharacteristic
123C22×C3⋊D3—21no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×Q811yescharacteristic
129C2×C32×C4#4111yescharacteristic
130#638—22no—
131#638—22no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
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—
144C32×C8—21no—
145C32×C8—21no—
146C3×C3⋊C8—21no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—21no—
149C3×C3⋊C8—41no—
150C2×#131—91no—
151C2×#108—31no—
152#424—91no—
153C2×#104—91no—
154#416—91no—
155#339—91no—
156#336—31no—
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—21no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8—31no—
197C2×C3×C8—31no—
198C2×C3×C8—41no—
199C2×C3×C8—41no—
200C2×C3×C8—61no—
201C2×C3×C8—61no—
202C2×C3×C8—61no—
203C2×C3×C8—61no—
204C2×C3×C8C4×D311yescharacteristic
205C2×C3×C8C4×D311yescharacteristic
206C2×C3×C8C4×D311yescharacteristic
207C2×C3×C8C4×D311yescharacteristic
208C3×C42—61no—
209C3×C42—61no—
210#217—61no—
211#217—61no—
212#217—121no—
213C4⋊Dic3—31no—
214C4⋊Dic3—31no—
215C4⋊Dic3—31no—
216C4⋊Dic3—31no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4×Dic3—21no—
220C4×Dic3—21no—
221C4×Dic3—61no—
222C4×Dic3—61no—
223C4×Dic3—121no—
224#208—21no—
225#208—21no—
226#208—21no—
227#208#6712yes—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8D1211yescharacteristic
233C2×C3⋊C8D1211yescharacteristic
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×C4C2×C4⋊C411yescharacteristic
247C32×C4C4×D411yescharacteristic
248C32×C4#12011yescharacteristic
249C32×C4C22⋊Q811yescharacteristic
250C3⋊Dic3—22no—
251C3⋊Dic3—41no—
252C3⋊Dic3—41no—
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—181no—
262C22×C8D3211yescharacteristic
263#117—91no—
264C2×C42—31no—
265#108—62no—
266C4⋊C8—181no—
267C4⋊C8—181no—
268#104—182no—
269#103—91no—
270#103—91no—
271#102—91no—
272#102—91no—
273C23×C3—21no—
274C23×C3#23511yescharacteristic
275C23×C3#23911yescharacteristic
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—62no—
286C2×C3×C4—121no—
287C2×C3×C4—121no—
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4C2×D1211yescharacteristic
291C2×C3×C4#23511yescharacteristic
292C2×C3×C4D3×D411yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4#23711yescharacteristic
297C2×C3×C4D3×Q811yescharacteristic
298C2×C3×C4D3×Q811yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300#67—62no—
301#67—62no—
302#67—62no—
303#67—62no—
304#67—122no—
305#67—122no—
306C2×Dic3—22no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—121no—
316C2×Dic3—121no—
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—21no—
337C3×C8—21no—
338C3×C8—21no—
339C3×C8—21no—
340C3×C8—41no—
341C3×C8—41no—
342C3×C8—62no—
343C3×C8—61no—
344C3×C8—61no—
345C3×C8—121no—
346C3⋊C8—21no—
347C3⋊C8—21no—
348C3⋊C8—22no—
349C3⋊C8—41no—
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—21no—
372C2×C8—21no—
373C2×C8—31no—
374C2×C8—31no—
375C2×C8—61no—
376C2×C8—61no—
377C2×C8—61no—
378C2×C8—61no—
379C2×C8—184no—
380C2×C8#62411yescharacteristic
381C2×C8#62411yescharacteristic
382C4⋊C4—91no—
383C4⋊C4—91no—
384C22⋊C4—181no—
385C42—61no—
386C42—61no—
387C42—181no—
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×C3C4×D1211yescharacteristic
398C22×C3#88311yescharacteristic
399C22×C3#89311yescharacteristic
400C22×C3#89411yescharacteristic
401C22×C3#89611yescharacteristic
402C22×C3#94611yescharacteristic
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—122no—
417C3×C4#67⋊C411yescharacteristic
418C3×C4#88211yescharacteristic
419C3×C4D3×C4⋊C411yescharacteristic
420C3×C4D3×C4⋊C411yescharacteristic
421C3×C4#89611yescharacteristic
422C3×C4#89711yescharacteristic
423C3×C4C4×#6711yescharacteristic
424C3×C4#93711yescharacteristic
425Dic3—42no—
426Dic3—62no—
427Dic3—62no—
428Dic3—122no—
429Dic3—121no—
430Dic3—121no—
431Dic3—121no—
432Dic3—121no—
433Dic3—241no—
434Dic3—241no—
435C32#186611yescharacteristic, complemented, Sylow
436C23—181no—
437C23#379911yescharacteristic
438Q8—92no—
439Q8—181no—
440D4—92no—
441D4—182no—
442D4—182no—
443D4—181no—
444C2×C4—62no—
445C2×C4—121no—
446C2×C4—121no—
447C2×C4—181no—
448C2×C4—182no—
449C2×C4—182no—
450C2×C4—181no—
451C2×C4—181no—
452C2×C4#379711yescharacteristic
453C2×C4D3×D1211yescharacteristic
454C2×C4#380211yescharacteristic
455C2×C4#380411yescharacteristic
456C2×C4C2×#62411yescharacteristic
457C2×C4D3×#6711yescharacteristic
458C8—21no—
459C8—21no—
460C8—61no—
461C8—61no—
462C8—62no—
463C8—121no—
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#470011yescharacteristic
475C2×C3#471711yescharacteristic
476C2×C3#489411yescharacteristic
477C2×C3#489511yescharacteristic
478C2×C3#498911yescharacteristic
479D3—122no—
480D3—122no—
481D3—242no—
482C22—21no—
483C22—21no—
484C22—182no—
485C22—361no—
486C22—361no—
487C22#6385411yescharacteristic
488C22#6388811yescharacteristic
489C22#6389411yescharacteristic
490C4—122no—
491C4—182no—
492C4—361no—
493C4—361no—
494C4#6389511yescharacteristic
495C4#6390011yescharacteristic
496C4#6392211yescharacteristic
497C4#6395211yescharacteristic
498C3—21no—
499C3#6869411yescharacteristic, complemented
500C3#7072211yescharacteristic, complemented
501C2—21no—
502C2—21no—
503C2—362no—
504C2#1059091711yescharacteristic
505C2#1059091811yescharacteristic
506C2#1059137811yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32C4×D4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1866
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#819C2semidirect
4. #10591119C2semidirect
6. C3×#4550C2semidirect
7. #10589162C2semidirect
21. #63648C4semidirect
22. #63648C4semidirect
23. #63643C4semidirect
24. #63643C4semidirect
37. C2×#819D3semidirect
42. #4550D3semidirect
435. C32#1866semidirect
499. C3#68694semidirect
500. C3#70722semidirect

Maximal subgroups

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

subgroupindex
C2×#638172
#105928122
C2×C3×#8192
#105911192
C2×#635702
C3×#45502
#105891622
#707223
#686943