Finite Group Databasebeta

← #11794541

Subgroups — #11794541

Order 1152.

637 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63641C211yesmaximal, characteristic, complemented
2C2×C3×#821C211yesmaximal, characteristic
3#10591357C211yesmaximal, characteristic, complemented
4#10591323C211yesmaximal, characteristic
5C2×#63576C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic
7C3×#4551C211yesmaximal, characteristic, complemented
8#70194—31nomaximal
9#68901—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×Dic3⋊Dic3—21no—
18C2×(C2×D3)⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20#63641—22no—
21C3×#821—22no—
22#63579—21no—
23#63576—22no—
24#63562—22no—
25C2×C3×#102—31no—
26#5221—31no—
27C2×#832—31no—
28C2×#821D311yescharacteristic
29C2×Dic3⋊C8—31no—
30C2×Dic3⋊C8—31no—
31C2×Dic3⋊C8—61no—
32#4988—31no—
33#4984—31no—
34#4972—31no—
35C2×#809—31no—
36C2×#807—31no—
37C2×#807—31no—
38C3×#340—31no—
39#4551D311yescharacteristic, complemented
40C23×C3×D3—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3D411yescharacteristic
43C22×C3⋊Dic3D411yescharacteristic
44C22×C3×Dic3—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12Q812yes—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)D412yes—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3D412yes—
67Dic3⋊Dic3—42no—
68(C2×D3)⋊Dic3—42no—
69(C2×D3)⋊Dic3—42no—
70#2067—91noSylow
71C22×C3×D4—31no—
72C22×D12C2×D311yescharacteristic
73C22×C3×C8—21no—
74C22×C3×C8C2×D311yescharacteristic
75C22×C3×C8C2×D311yescharacteristic
76C2×C3×C4⋊C4—31no—
77C2×C3×C4⋊C4—31no—
78C2×C3×C4⋊C4—31no—
79C2×#217—61no—
80C2×#217—61no—
81C2×(C2×D3)⋊C4—61no—
82C2×(C2×D3)⋊C4—61no—
83C2×C4⋊Dic3—61no—
84C2×C4⋊Dic3C2×D311yescharacteristic
85C2×C4⋊Dic3C2×D311yescharacteristic
86C2×C4⋊Dic3C2×D311yescharacteristic
87C2×Dic3⋊C4—61no—
88C2×C4×Dic3—31no—
89C2×C4×Dic3—31no—
90C2×C4×Dic3—61no—
91C22×C3⋊C8—31no—
92C22×C3⋊C8—31no—
93C22×C3⋊C8—61no—
94C3×#102—62no—
95#832—62no—
96C3⋊#95—61no—
97C3⋊#95—61no—
98#821—22no—
99Dic3⋊C8—62no—
100Dic3⋊C8—62no—
101Dic3⋊C8—64no—
102#809—62no—
103#807—62no—
104#807—62no—
105C23×C32C2×D411yescharacteristic
106C22×C3×D3—22no—
107C22×C3×D3—41no—
108C22×C3×D3—41no—
109C22×C3×D3—41no—
110C22×C3×D3—41no—
111C22×C3×D3—41no—
112C22×C3×D3—41no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×Q811yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3D812yes—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C3×D12—22no—
135C3×D12—22no—
136C3×D12—41no—
137C3×D12—41no—
138C32×C8—41no—
139C3⋊(C3⋊C8)—22no—
140C2×#107—91no—
141C2×C4⋊C8—91no—
142C2×#102—31no—
143C2×#102—91no—
144#390—91no—
145#389—91no—
146#340—31no—
147C24×C3—61no—
148C23×D3—21no—
149C2×C3×D4—32no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C2×C3×D4—61no—
154C2×C3×D4—61no—
155C22×C3×C4—21no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×Dic3—21no—
162C22×Dic3—21no—
163C22×Dic3—21no—
164C22×Dic3—31no—
165C22×Dic3—31no—
166C22×Dic3—31no—
167C22×Dic3—31no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12Dic612yes—
176C2×C3×C8—22no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—41no—
184C2×C3×C8—41no—
185C3×C4⋊C4—32no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191#217—122no—
192#217—122no—
193(C2×D3)⋊C4—122no—
194(C2×D3)⋊C4—122no—
195C4⋊Dic3—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—122no—
201C4⋊Dic3#6712yes—
202Dic3⋊C4—122no—
203C4×Dic3—62no—
204C4×Dic3—62no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209C2×C3⋊C8—32no—
210C2×C3⋊C8—32no—
211C2×C3⋊C8—62no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—121no—
217C2×C3⋊C8—121no—
218C22×C32#12111yescharacteristic
219C22×C32#12111yescharacteristic
220C22×C32C22⋊Q811yescharacteristic
221C22×C32C2×D811yescharacteristic
222C22×C32#13511yescharacteristic
223C22×C32AGL(1,ℤ/8)11yescharacteristic
224C22×C32#13711yescharacteristic
225C2×C3×D3—42no—
226C2×C3×D3—42no—
227C2×C3×D3—42no—
228C2×C3×D3—81no—
229C2×C3×D3—81no—
230C2×C3×D3—81no—
231C2×C3×D3—81no—
232C32×C4#12111yescharacteristic
233C32×C4C22⋊Q811yescharacteristic
234C32×C4C22⋊Q811yescharacteristic
235C32×C4#12611yescharacteristic
236C3⋊Dic3—22no—
237C3⋊Dic3—41no—
238C3×Dic3—42no—
239C3×Dic3—81no—
240C3×Dic3—81no—
241C22×D4—31no—
242C22×C8—91no—
243C22×C8D3211yescharacteristic
244C2×C4⋊C4—31no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—31no—
247C2×C4⋊C4—181no—
248C2×C22⋊C4—181no—
249C2×C22⋊C4—181no—
250C2×C42—91no—
251#107—182no—
252C4⋊C8—182no—
253#102—62no—
254#102—182no—
255#95—181no—
256C23×C3—21no—
257C23×C3—62no—
258C23×C3—121no—
259C23×C3—121no—
260C23×C3—121no—
261C23×C3—121no—
262C23×C3—121no—
263C23×C3—121no—
264C23×C3D3×D411yescharacteristic
265C23×C3D3×D411yescharacteristic
266C22×D3—22no—
267C22×D3—41no—
268C22×D3—41no—
269C22×D3—41no—
270C22×D3—41no—
271C22×D3—41no—
272C22×D3—41no—
273C3×D4—62no—
274C3×D4—62no—
275C3×D4—121no—
276C3×D4—121no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—62no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4C2×Dic611yescharacteristic
293C2×C3×C4#23511yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4#23511yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4#23711yescharacteristic
302C2×C3×C4D3×Q811yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304C2×Dic3—22no—
305C2×Dic3—32no—
306C2×Dic3—32no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—62no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3—61no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331D12—22no—
332D12—22no—
333D12—41no—
334D12—41no—
335C3×C8—42no—
336C3×C8—41no—
337C3×C8—41no—
338C3⋊C8—62no—
339C3⋊C8—62no—
340C3⋊C8—122no—
341C2×C32#39611yescharacteristic
342C2×C32#45911yescharacteristic
343C2×C32#46411yescharacteristic
344C2×C32#46611yescharacteristic
345C2×C32#46811yescharacteristic
346C2×C32#47411yescharacteristic
347C2×C32#47811yescharacteristic
348C3×D3—82no—
349C24—61no—
350C2×D4—32no—
351C2×D4—61no—
352C2×D4—61no—
353C2×D4—61no—
354C2×D4—61no—
355C2×D4—61no—
356C22×C4—61no—
357C22×C4—61no—
358C22×C4—61no—
359C22×C4—91no—
360C22×C4—91no—
361C22×C4C2×D3211yescharacteristic
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—92no—
366C2×C8—181no—
367C2×C8—181no—
368C4⋊C4—32no—
369C4⋊C4—61no—
370C4⋊C4—61no—
371C4⋊C4—61no—
372C4⋊C4—61no—
373C4⋊C4—61no—
374C4⋊C4—362no—
375C22⋊C4—362no—
376C22⋊C4—362no—
377C42—181no—
378C42—181no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—122no—
387C22×C3—122no—
388C22×C3—122no—
389C22×C3—241no—
390C22×C3—241no—
391C22×C3—241no—
392C22×C3—241no—
393C22×C3#87811yescharacteristic
394C22×C3#88411yescharacteristic
395C22×C3#88411yescharacteristic
396C22×C3#88411yescharacteristic
397C22×C3#89611yescharacteristic
398C22×C3D3×D811yescharacteristic
399C22×C3D3×D811yescharacteristic
400C22×C3#91111yescharacteristic
401C22×C3#91411yescharacteristic
402C22×C3#91511yescharacteristic
403C22×C3#91611yescharacteristic
404C22×C3#91611yescharacteristic
405C22×C3#91811yescharacteristic
406C22×C3#93911yescharacteristic
407C2×D3—42no—
408C2×D3—42no—
409C2×D3—42no—
410C2×D3—81no—
411C2×D3—81no—
412C2×D3—81no—
413C2×D3—81no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—122no—
419C3×C4—241no—
420C3×C4—241no—
421C3×C4#87611yescharacteristic
422C3×C4#87811yescharacteristic
423C3×C4#87911yescharacteristic
424C3×C4#88411yescharacteristic
425C3×C4#89611yescharacteristic
426C3×C4#89611yescharacteristic
427C3×C4#92411yescharacteristic
428C3×C4#93811yescharacteristic
429Dic3—42no—
430Dic3—64no—
431Dic3—62no—
432Dic3—62no—
433Dic3—81no—
434Dic3—81no—
435Dic3—122no—
436Dic3—121no—
437Dic3—121no—
438C32#206711yescharacteristic, complemented, Sylow
439C23—62no—
440C23—121no—
441C23—121no—
442C23—121no—
443C23—121no—
444C23—121no—
445C23—121no—
446C23#380211yescharacteristic
447D4—62no—
448D4—62no—
449D4—121no—
450D4—121no—
451C2×C4—62no—
452C2×C4—92no—
453C2×C4—121no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4—121no—
457C2×C4—121no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—181no—
462C2×C4—181no—
463C2×C4—181no—
464C2×C4—181no—
465C2×C4—181no—
466C2×C4D3×Dic611yescharacteristic
467C2×C4#379511yescharacteristic
468C2×C4#379811yescharacteristic
469C2×C4#380411yescharacteristic
470C2×C4D3×#6711yescharacteristic
471C2×C4#381111yescharacteristic
472C8—41no—
473C8—182no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—242no—
482C2×C3#467611yescharacteristic
483C2×C3#475911yescharacteristic
484C2×C3#476311yescharacteristic
485C2×C3#477511yescharacteristic
486C2×C3#477511yescharacteristic
487C2×C3#478011yescharacteristic
488C2×C3#478611yescharacteristic
489C2×C3#479811yescharacteristic
490C2×C3#481211yescharacteristic
491C2×C3#487111yescharacteristic
492C2×C3#489011yescharacteristic
493C2×C3#494811yescharacteristic
494C2×C3#515011yescharacteristic
495C2×C3#516611yescharacteristic
496D3—82no—
497C22—122no—
498C22—122no—
499C22—122no—
500C22—241no—
501C22—241no—
502C22—241no—
503C22—241no—
504C22#6379711yescharacteristic
505C22#6379811yescharacteristic
506C22#6380911yescharacteristic
507C22#6381111yescharacteristic
508C22#6388511yescharacteristic
509C22#6389911yescharacteristic
510C22#6391211yescharacteristic
511C4—122no—
512C4—182no—
513C4—241no—
514C4—241no—
515C4—361no—
516C4#6385111yescharacteristic
517C4#6385911yescharacteristic
518C4#6389611yescharacteristic
519C4#6395811yescharacteristic
520C3—21no—
521C3#6890111yescharacteristic, complemented
522C3#7019411yescharacteristic, complemented
523C2—242no—
524C2#1059074911yescharacteristic
525C2#1059077811yescharacteristic
526C2#1059078211yescharacteristic
527C2#1059079611yescharacteristic
528C2#1059083911yescharacteristic
529C2#1059084211yescharacteristic
530C2#1059130911yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32#2067
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#63641C2semidirect
3. #10591357C2semidirect
5. C2×#63576C2semidirect
7. C3×#4551C2semidirect
39. #4551D3semidirect
438. C32#2067semidirect
521. C3#68901semidirect
522. C3#70194semidirect

Maximal subgroups

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

subgroupindex
C2×#636412
C2×C3×#8212
#105913572
#105913232
C2×#635762
C2×#635622
C3×#45512
#701943
#689013