Finite Group Databasebeta

← #11791101

Subgroups — #11791101

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3714C211yesmaximal, characteristic
2C2×#63636C211yesmaximal, characteristic, complemented
3C3×#4988C211yesmaximal, characteristic, complemented
4C2×C3×#808C211yesmaximal, characteristic, complemented
5#10591320C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7C2×#63554C211yesmaximal, characteristic, complemented
8#70576—31nomaximal
9#69648—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—22no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3722—22no—
19C2×#3714—22no—
20C2×#3714—22no—
21C2×#3714C414yescomplemented
22#63636—22no—
23C3×#808—22no—
24#63562—22no—
25#63554—22no—
26C22×#213—31no—
27C22×D24—31no—
28C2×C3×#106—31no—
29C3×#390—31no—
30C2×#832—31no—
31C2×#815—31no—
32#4988—31no—
33#4988D311yescharacteristic, complemented
34C2×#809—31no—
35C2×#809—31no—
36C2×#809—31no—
37C2×#809—61no—
38C2×#808D311yescharacteristic, complemented
39#4939—31no—
40C2×#803—31no—
41C23×C3⋊D3—21no—
42C23×C3×D3—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)C2×C412yes—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D412yes—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12C2×C412yes—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)D412yes—
64C3×(C2×D3)⋊C4—44no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C2×C3×C3⋊C8C2×C412yes—
70C2×C3×C3⋊C8D412yes—
71C2×C3×C3⋊C8D412yes—
72#3722—44no—
73#3714—28no—
74#1972—91noSylow
75C22×C3×D4—31no—
76C22×D12—31no—
77C22×D12—31no—
78C22×D12—61no—
79C22×D12C2×D311yescharacteristic
80C22×C3×C8—31no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4C2×D311yescharacteristic
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×C3×C22⋊C4—62no—
86C2×C3×C42—31no—
87C2×#213—34no—
88C2×#213—62no—
89C2×#213—62no—
90C2×(C2×D3)⋊C4—22no—
91C2×(C2×D3)⋊C4—62no—
92C2×(C2×D3)⋊C4—62no—
93C2×C4⋊Dic3C2×D311yescharacteristic
94C2×C4×Dic3C2×D311yescharacteristic
95C22×C3⋊C8—31no—
96C22×C3⋊C8—31no—
97C22×C3⋊C8—61no—
98C22×C3⋊C8C2×D311yescharacteristic
99C2×D24—34no—
100C2×D24—62no—
101C2×D24—62no—
102C3×#106—62no—
103#832—62no—
104#815—62no—
105#809—62no—
106#809—62no—
107#809—62no—
108#809—64no—
109#808—22no—
110#803—62no—
111C23×C32C2×D411yescharacteristic
112C22×C3⋊D3—22no—
113C22×C3⋊D3—41no—
114C22×C3⋊D3—41no—
115C22×C3⋊D3—42no—
116C22×C3⋊D3—42no—
117C22×C3×D3—22no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—42no—
121C22×C3×D3—42no—
122C2×C32×C4—41no—
123C2×C32×C4—42no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C4⋊(C3⋊D3)—22no—
131C4⋊(C3⋊D3)—22no—
132C4⋊(C3⋊D3)—41no—
133C4⋊(C3⋊D3)—41no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—42no—
139C3×D12—22no—
140C3×D12—22no—
141C3×D12—41no—
142C3×D12—41no—
143C3⋊(C3⋊C8)—22no—
144C3×C3⋊C8C22⋊C414yescomplemented
145C22×D8—91no—
146C2×#106—31no—
147C2×#102—91no—
148C2×#102—91no—
149C2×#97—91no—
150#390—31no—
151#390—91no—
152C24×C3—61no—
153C23×D3—21no—
154C23×D3—61no—
155C23×D3—61no—
156C23×D3—121no—
157C2×C3×D4—32no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—32no—
167C22×C3×C4—41no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—21no—
172C22×Dic3#6712yes—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12—21no—
176C2×D12—21no—
177C2×D12—21no—
178C2×D12—32no—
179C2×D12—32no—
180C2×D12—62no—
181C2×D12—62no—
182C2×D12—62no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—61no—
186C2×D12—61no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12—121no—
194C2×D12—121no—
195C2×D12—121no—
196C2×D12C4×D312yes—
197C2×C3×C8—32no—
198C2×C3×C8—32no—
199C2×C3×C8—32no—
200C3×C4⋊C4—22no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—41no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C22⋊C4—124no—
209C3×C42—61no—
210C3×C42—61no—
211#213—68no—
212(C2×D3)⋊C4—44no—
213(C2×D3)⋊C4—124no—
214(C2×D3)⋊C4—124no—
215C4⋊Dic3—21no—
216C4⋊Dic3—21no—
217C4×Dic3—21no—
218C4×Dic3—21no—
219C2×C3⋊C8—32no—
220C2×C3⋊C8—32no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—121no—
227C2×C3⋊C8—121no—
228C2×C3⋊C8C4×D312yes—
229C2×C3⋊C8D1212yes—
230C2×C3⋊C8#6712yes—
231D24—68no—
232C22×C32C4×D411yescharacteristic
233C22×C32#12111yescharacteristic
234C22×C32#12711yescharacteristic
235C22×C32AGL(1,ℤ/8)12yes—
236C22×C32AGL(1,ℤ/8)12yes—
237C2×C3⋊D3—42no—
238C2×C3⋊D3—44no—
239C2×C3⋊D3—82no—
240C2×C3⋊D3—81no—
241C2×C3⋊D3—81no—
242C2×C3×D3—42no—
243C2×C3×D3—44no—
244C2×C3×D3—82no—
245C2×C3×D3—81no—
246C2×C3×D3—81no—
247C32×C4—81no—
248C32×C4C2×C22⋊C411yescharacteristic
249C32×C4C4×D411yescharacteristic
250C32×C4#12111yescharacteristic
251C32×C4#12411yescharacteristic
252C3×Dic3—42no—
253C3×Dic3—81no—
254C22×D4—31no—
255C22×D4—91no—
256C2×D8—94no—
257C2×D8—182no—
258C2×D8—182no—
259C22×C8—31no—
260C22×C8—91no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4D3211yescharacteristic
263C2×C22⋊C4—62no—
264C2×C22⋊C4—182no—
265C2×C42—31no—
266#106—62no—
267#102—182no—
268#102—182no—
269#97—182no—
270C23×C3—21no—
271C23×C3—62no—
272C23×C3—121no—
273C23×C3—122no—
274C23×C3—122no—
275C23×C3—121no—
276C23×C3D3×D411yescharacteristic
277C23×C3C2×#6711yescharacteristic
278C22×D3—22no—
279C22×D3—42no—
280C22×D3—41no—
281C22×D3—41no—
282C22×D3—42no—
283C22×D3—62no—
284C22×D3—62no—
285C22×D3—122no—
286C22×D3—122no—
287C22×D3—122no—
288C22×D3—121no—
289C22×D3—122no—
290C22×D3—122no—
291C22×D3—122no—
292C22×D3—121no—
293C22×D3—121no—
294C22×D3—121no—
295C22×D3—122no—
296C22×D3—242no—
297C22×D3—242no—
298C3×D4—62no—
299C3×D4—62no—
300C3×D4—121no—
301C3×D4—121no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—82no—
317C2×C3×C4—121no—
318C2×C3×C4—122no—
319C2×C3×C4C2×C4×D311yescharacteristic
320C2×C3×C4C2×C4×D311yescharacteristic
321C2×C3×C4C2×D1211yescharacteristic
322C2×C3×C4#23511yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4#23711yescharacteristic
328C2×C3×C4#23911yescharacteristic
329C2×C3×C4#23911yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—42no—
335C2×Dic3—41no—
336D12—22no—
337D12—22no—
338D12—41no—
339D12—41no—
340D12—64no—
341D12—62no—
342D12—62no—
343D12—62no—
344D12—62no—
345D12—122no—
346D12—122no—
347D12—122no—
348D12—121no—
349D12—121no—
350D12—121no—
351D12—121no—
352C3×C8—34no—
353C3⋊C8—62no—
354C3⋊C8—62no—
355C3⋊C8—122no—
356C3⋊C8(C2×D3)⋊C414yescomplemented
357C2×C32#39011yescharacteristic
358C2×C32#44212yes—
359C2×C32#46912yes—
360C2×C32#49611yescharacteristic
361C2×C32#49611yescharacteristic
362C3⋊D3—82no—
363C3×D3—82no—
364C24—61no—
365C24—181no—
366C2×D4—32no—
367C2×D4—61no—
368C2×D4—61no—
369C2×D4—61no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—92no—
373C2×D4—181no—
374C2×D4—181no—
375C2×D4—181no—
376C2×D4—181no—
377C2×D4—181no—
378C22×C4—21no—
379C22×C4—32no—
380C22×C4—61no—
381C22×C4C2×D3211yescharacteristic
382D8—188no—
383C2×C8—32no—
384C2×C8—32no—
385C2×C8—32no—
386C2×C8—92no—
387C2×C8—181no—
388C2×C8—181no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—61no—
392C4⋊C4—61no—
393C22⋊C4—124no—
394C22⋊C4—364no—
395C42—61no—
396C42—61no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—21no—
402C22×C3—124no—
403C22×C3—122no—
404C22×C3—242no—
405C22×C3—241no—
406C22×C3—241no—
407C22×C3#89311yescharacteristic
408C22×C3#89511yescharacteristic
409C22×C3#91412yes—
410C22×C3#91412yes—
411C22×C3C4×#6711yescharacteristic
412C22×C3#93212yes—
413C22×C3#93911yescharacteristic
414C22×C3#94011yescharacteristic
415C22×C3#94011yescharacteristic
416C22×C3#94912yes—
417C2×D3—42no—
418C2×D3—44no—
419C2×D3—82no—
420C2×D3—81no—
421C2×D3—81no—
422C2×D3—124no—
423C2×D3—124no—
424C2×D3—122no—
425C2×D3—122no—
426C2×D3—124no—
427C2×D3—244no—
428C2×D3—244no—
429C2×D3—242no—
430C2×D3—242no—
431C2×D3—242no—
432C2×D3—241no—
433C2×D3—241no—
434C2×D3—242no—
435C2×D3—241no—
436C2×D3—241no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—82no—
442C3×C4—81no—
443C3×C4—81no—
444C3×C4—122no—
445C3×C4—241no—
446C3×C4D3×C22⋊C411yescharacteristic
447C3×C4#67⋊C411yescharacteristic
448C3×C4#88411yescharacteristic
449C3×C4#88511yescharacteristic
450C3×C4#89311yescharacteristic
451C3×C4#89511yescharacteristic
452C3×C4C2×(C2×D3)⋊C411yescharacteristic
453C3×C4#94711yescharacteristic
454Dic3—42no—
455Dic3—81no—
456C32#197211yescharacteristic, complemented, Sylow
457C23—62no—
458C23—121no—
459C23—122no—
460C23—122no—
461C23—121no—
462C23—182no—
463C23—361no—
464C23—362no—
465C23—362no—
466C23—361no—
467C23D3×#6711yescharacteristic
468D4—62no—
469D4—62no—
470D4—121no—
471D4—121no—
472D4—182no—
473D4—182no—
474D4—361no—
475D4—361no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—122no—
482C2×C4—121no—
483C2×C4#379611yescharacteristic
484C2×C4#379911yescharacteristic
485C2×C4C4×D3211yescharacteristic
486C2×C4D3×D1211yescharacteristic
487C2×C4D3×#6711yescharacteristic
488C2×C4#381111yescharacteristic
489C8—34no—
490C8—182no—
491C2×C3—22no—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—242no—
497C2×C3#486512yes—
498C2×C3#486912yes—
499C2×C3#495711yescharacteristic
500C2×C3#498811yescharacteristic
501C2×C3#501412yes—
502C2×C3#503912yes—
503C2×C3#505811yescharacteristic
504C2×C3#507411yescharacteristic
505C2×C3#517611yescharacteristic
506C2×C3#517611yescharacteristic
507D3—82no—
508D3—244no—
509D3—242no—
510D3—242no—
511C22—124no—
512C22—122no—
513C22—242no—
514C22—241no—
515C22—241no—
516C22—364no—
517C22—362no—
518C22—722no—
519C22—721no—
520C22—721no—
521C22#6388611yescharacteristic
522C22#6390411yescharacteristic
523C22#6393412yes—
524C22#6393912yes—
525C22#6397911yescharacteristic
526C4—81no—
527C4—122no—
528C4—241no—
529C4#6388111yescharacteristic
530C4#6390711yescharacteristic
531C4#6391011yescharacteristic
532C4D3×(C2×D3)⋊C411yescharacteristic
533C3—21no—
534C3#6964811yescharacteristic, complemented
535C3#7057611yescharacteristic, complemented
536C2—242no—
537C2—722no—
538C2#1059058612yes—
539C2#1059058912yes—
540C2#1059138411yescharacteristic
541C2#1059147211yescharacteristic
542C2#1059161911yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1972
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63636C2semidirect
3. C3×#4988C2semidirect
4. C2×C3×#808C2semidirect
5. #10591320C2semidirect
6. C2×#63562C2semidirect
7. C2×#63554C2semidirect
21. C2×#3714C4semidirect
33. #4988D3semidirect
38. C2×#808D3semidirect
144. C3×C3⋊C8C22⋊C4semidirect
356. C3⋊C8(C2×D3)⋊C4semidirect
456. C32#1972semidirect
534. C3#69648semidirect
535. C3#70576semidirect

Maximal subgroups

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

subgroupindex
C22×#37142
C2×#636362
C3×#49882
C2×C3×#8082
#105913202
C2×#635622
C2×#635542
#705763
#696483