Finite Group Databasebeta

← #11791143

Subgroups — #11791143

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 505 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3716C211yesmaximal, characteristic
2C2×#63643C211yesmaximal, characteristic, complemented
3C2×C3×#821C211yesmaximal, characteristic
4C2×C3×#815C211yesmaximal, characteristic, complemented
5#10591318C211yesmaximal, characteristic
6#10591213C211yesmaximal, characteristic, complemented
7C2×#63575C211yesmaximal, characteristic, complemented
8#70192—31nomaximal
9#69826—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×(C2×D3)⋊Dic3—22no—
18C2×#3716—22no—
19C2×#3716—22no—
20C2×#3716C414yescomplemented
21#63643—22no—
22C3×#821—22no—
23C3×#815—22no—
24#63579—22no—
25#63575—22no—
26C22×#214—31no—
27C22×#204—31no—
28C2×C3×#102—31no—
29C2×C3×#97—31no—
30#5221—31no—
31C2×#821D311yescharacteristic
32C2×#818—31no—
33C2×#816—31no—
34C2×#816—31no—
35C2×#816—61no—
36C2×#815D311yescharacteristic, complemented
37#4973—31no—
38C2×#807—31no—
39#4939—31no—
40#4929—31no—
41C23×C3×D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634C2×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—
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8D412yes—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C2×C3×C3⋊C8C2×C412yes—
69C2×C3×C3⋊C8D412yes—
70C2×C3×C3⋊C8D412yes—
71(C2×D3)⋊Dic3—44no—
72#3716—28no—
73#1973—91noSylow
74C22×C3×D4—31no—
75C22×D12C2×D311yescharacteristic
76C22×Dic6—31no—
77C22×Dic6—31no—
78C22×Dic6—61no—
79C22×C3×C8—21no—
80C22×C3×C8—31no—
81C22×C3×C8C2×D311yescharacteristic
82C22×C3×C8C2×D311yescharacteristic
83C2×C3×C4⋊C4—31no—
84C2×C3×C42—31no—
85C2×#217—62no—
86C2×#214—34no—
87C2×#214—62no—
88C2×#214—62no—
89C2×(C2×D3)⋊C4—62no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—61no—
93C2×C4⋊Dic3C2×D311yescharacteristic
94C2×C4×Dic3C2×D311yescharacteristic
95C22×C3⋊C8C2×D311yescharacteristic
96C2×#204—34no—
97C2×#204—62no—
98C2×#204—62no—
99C3×#102—62no—
100C3×#97—62no—
101C3⋊#95—62no—
102C3⋊#95—62no—
103#821—22no—
104#818—62no—
105#816—64no—
106#816—62no—
107#816—62no—
108#815—22no—
109#807—62no—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—22no—
112C22×C3×D3—41no—
113C22×C3×D3—41no—
114C22×C3×D3—42no—
115C22×C3×D3—42no—
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—42no—
127#634—22no—
128#634—22no—
129#634—41no—
130#634—41no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—42no—
136C3×D12—22no—
137C3×D12—22no—
138C3×D12—41no—
139C3×D12—41no—
140C32×C8—22no—
141C3×C3⋊C8C22⋊C414yescomplemented
142C22×SD16—91no—
143C2×#107—91no—
144C2×#103—91no—
145C2×#102—31no—
146C2×#97—31no—
147#391—91no—
148#390—91no—
149C24×C3—61no—
150C23×D3—21no—
151C2×C3×D4—32no—
152C2×C3×D4—61no—
153C2×C3×D4—61no—
154C2×C3×D4—61no—
155C2×C3×D4—61no—
156C2×C3×D4—61no—
157C22×C3×C4—21no—
158C22×C3×C4—32no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C22×Dic3—21no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—121no—
168C22×Dic3—121no—
169C22×Dic3D1212yes—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12C4×D312yes—
176C2×Dic6—32no—
177C2×Dic6—32no—
178C2×Dic6—62no—
179C2×Dic6—62no—
180C2×Dic6—62no—
181C2×Dic6—61no—
182C2×Dic6—61no—
183C2×Dic6—61no—
184C2×Dic6—61no—
185C2×Dic6—61no—
186C2×Dic6—61no—
187C2×Dic6—61no—
188C2×Dic6—61no—
189C2×Dic6—61no—
190C2×Dic6—61no—
191C2×Dic6—121no—
192C2×Dic6—121no—
193C2×Dic6—121no—
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—22no—
199C2×C3×C8—32no—
200C2×C3×C8—32no—
201C2×C3×C8—32no—
202C2×C3×C8—41no—
203C2×C3×C8—41no—
204C2×C3×C8D1212yes—
205C2×C3×C8#6712yes—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C42—61no—
209C3×C42—61no—
210#217—124no—
211#214—68no—
212(C2×D3)⋊C4—124no—
213C4⋊Dic3—21no—
214C4⋊Dic3—21no—
215C4⋊Dic3—62no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3—61no—
220C4⋊Dic3—121no—
221C4×Dic3—21no—
222C4×Dic3—21no—
223C2×C3⋊C8C4×D312yes—
224C2×C3⋊C8D1212yes—
225C2×C3⋊C8#6712yes—
226#204—68no—
227C22×C32C4×D411yescharacteristic
228C22×C32#12111yescharacteristic
229C22×C32#12711yescharacteristic
230C22×C32AGL(1,ℤ/8)12yes—
231C22×C32#13712yes—
232C2×C3×D3—42no—
233C2×C3×D3—44no—
234C2×C3×D3—82no—
235C2×C3×D3—81no—
236C2×C3×D3—81no—
237C32×C4C2×C22⋊C411yescharacteristic
238C32×C4C4×D411yescharacteristic
239C32×C4#12111yescharacteristic
240C32×C4#12411yescharacteristic
241C3⋊Dic3—42no—
242C3⋊Dic3—81no—
243C3×Dic3—42no—
244C3×Dic3—81no—
245C22×Q8—91no—
246C22×D4—31no—
247C2×SD16—94no—
248C2×SD16—182no—
249C2×SD16—182no—
250C22×C8—31no—
251C22×C8D3211yescharacteristic
252C2×C4⋊C4—31no—
253C2×C4⋊C4—91no—
254C2×C22⋊C4—182no—
255C2×C42—31no—
256#107—182no—
257#103—182no—
258#102—62no—
259#97—62no—
260#95—182no—
261C23×C3—21no—
262C23×C3—62no—
263C23×C3—121no—
264C23×C3—122no—
265C23×C3—122no—
266C23×C3—121no—
267C23×C3C2×D1211yescharacteristic
268C23×C3D3×D411yescharacteristic
269C22×D3—22no—
270C22×D3—41no—
271C22×D3—42no—
272C22×D3—42no—
273C22×D3—41no—
274C3×D4—62no—
275C3×D4—62no—
276C3×D4—121no—
277C3×D4—121no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—121no—
288C2×C3×C4—122no—
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4C2×C4×D311yescharacteristic
291C2×C3×C4C2×D1211yescharacteristic
292C2×C3×C4C2×D1211yescharacteristic
293C2×C3×C4#23511yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4#23711yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—42no—
305C2×Dic3—41no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—122no—
309C2×Dic3—122no—
310C2×Dic3—122no—
311C2×Dic3—121no—
312C2×Dic3—121no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—122no—
316C2×Dic3—121no—
317C2×Dic3—122no—
318C2×Dic3—122no—
319C2×Dic3—121no—
320C2×Dic3—242no—
321D12—22no—
322D12—22no—
323D12—41no—
324D12—41no—
325Dic6—64no—
326Dic6—62no—
327Dic6—62no—
328Dic6—62no—
329Dic6—62no—
330Dic6—122no—
331Dic6—122no—
332Dic6—122no—
333Dic6—121no—
334Dic6—121no—
335Dic6—121no—
336Dic6—121no—
337C3×C8—22no—
338C3×C8—22no—
339C3×C8—34no—
340C3×C8—42no—
341C3⋊C8(C2×D3)⋊C414yescomplemented
342C2×C32#39011yescharacteristic
343C2×C32#44012yes—
344C2×C32#46812yes—
345C2×C32#49611yescharacteristic
346C2×C32#49711yescharacteristic
347C3×D3—82no—
348C24—61no—
349C2×Q8—92no—
350C2×Q8—181no—
351C2×Q8—181no—
352C2×Q8—181no—
353C2×Q8—181no—
354C2×Q8—181no—
355C2×D4—32no—
356C2×D4—61no—
357C2×D4—61no—
358C2×D4—61no—
359C2×D4—61no—
360C2×D4—61no—
361C22×C4—32no—
362C22×C4—61no—
363C22×C4—181no—
364C22×C4—181no—
365C22×C4C2×D3211yescharacteristic
366SD16—188no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—32no—
370C2×C8—32no—
371C2×C8—32no—
372C2×C8#62612yes—
373C4⋊C4—61no—
374C4⋊C4—61no—
375C4⋊C4—181no—
376C4⋊C4—181no—
377C22⋊C4—364no—
378C42—61no—
379C42—61no—
380C22×C3—22no—
381C22×C3—22no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—122no—
386C22×C3—124no—
387C22×C3—242no—
388C22×C3—241no—
389C22×C3—241no—
390C22×C3C4×D1211yescharacteristic
391C22×C3#87411yescharacteristic
392C22×C3#67⋊C411yescharacteristic
393C22×C3#88411yescharacteristic
394C22×C3#90812yes—
395C22×C3#90912yes—
396C22×C3#91112yes—
397C22×C3#91512yes—
398C22×C3#93011yescharacteristic
399C22×C3#94011yescharacteristic
400C2×D3—42no—
401C2×D3—44no—
402C2×D3—81no—
403C2×D3—81no—
404C2×D3—82no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—122no—
410C3×C4—241no—
411C3×C4C4×D1211yescharacteristic
412C3×C4#87511yescharacteristic
413C3×C4D3×C22⋊C411yescharacteristic
414C3×C4#88511yescharacteristic
415C3×C4C2×(C2×D3)⋊C411yescharacteristic
416C3×C4C4×#6711yescharacteristic
417C3×C4#93011yescharacteristic
418C3×C4#93911yescharacteristic
419Dic3—42no—
420Dic3—81no—
421Dic3—124no—
422Dic3—122no—
423Dic3—122no—
424Dic3—242no—
425Dic3—241no—
426Dic3—241no—
427C32#197311yescharacteristic, complemented, Sylow
428C23—62no—
429C23—122no—
430C23—122no—
431C23—121no—
432C23—121no—
433C23D3×D1211yescharacteristic
434Q8—182no—
435Q8—182no—
436Q8—361no—
437Q8—361no—
438D4—62no—
439D4—62no—
440D4—121no—
441D4—121no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—122no—
446C2×C4—121no—
447C2×C4—182no—
448C2×C4—361no—
449C2×C4—361no—
450C2×C4—362no—
451C2×C4—361no—
452C2×C4#379811yescharacteristic
453C2×C4C4×D3211yescharacteristic
454C2×C4D3×D1211yescharacteristic
455C2×C4#380411yescharacteristic
456C2×C4C2×#62611yescharacteristic
457C2×C4D3×#6711yescharacteristic
458C8—22no—
459C8—34no—
460C2×C3—22no—
461C2×C3—22no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—242no—
466C2×C3#471012yes—
467C2×C3#471211yescharacteristic
468C2×C3#471511yescharacteristic
469C2×C3#475712yes—
470C2×C3#478012yes—
471C2×C3#493911yescharacteristic
472C2×C3#495711yescharacteristic
473C2×C3#513412yes—
474C2×C3#515411yescharacteristic
475C2×C3#516711yescharacteristic
476D3—82no—
477C22—124no—
478C22—122no—
479C22—242no—
480C22—241no—
481C22—241no—
482C22#6379512yes—
483C22#6380012yes—
484C22#6388011yescharacteristic
485C22#6390611yescharacteristic
486C22#6391111yescharacteristic
487C4—122no—
488C4—241no—
489C4—362no—
490C4—721no—
491C4#6385211yescharacteristic
492C4C4×#62611yescharacteristic
493C4D3×(C2×D3)⋊C411yescharacteristic
494C4#6397811yescharacteristic
495C3—21no—
496C3#6982611yescharacteristic, complemented
497C3#7019211yescharacteristic, complemented
498C2—242no—
499C2#1059074712yes—
500C2#1059082812yes—
501C2#1059088311yescharacteristic
502C2#1059089711yescharacteristic
503C2#1059138311yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1973
LCSG ▷ C2×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
2. C2×#63643C2semidirect
4. C2×C3×#815C2semidirect
6. #10591213C2semidirect
7. C2×#63575C2semidirect
20. C2×#3716C4semidirect
36. C2×#815D3semidirect
141. C3×C3⋊C8C22⋊C4semidirect
341. C3⋊C8(C2×D3)⋊C4semidirect
427. C32#1973semidirect
496. C3#69826semidirect
497. C3#70192semidirect

Maximal subgroups

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

subgroupindex
C22×#37162
C2×#636432
C2×C3×#8212
C2×C3×#8152
#105913182
#105912132
C2×#635752
#701923
#698263