Finite Group Databasebeta

← #11791145

Subgroups — #11791145

Order 1152.

781 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3717C211yesmaximal, characteristic
2C2×#63648C211yesmaximal, characteristic
3C2×C3×#816C211yesmaximal, characteristic, complemented
4C2×C3×#815C211yesmaximal, characteristic, complemented
5#10591320C211yesmaximal, characteristic
6#10591220C211yesmaximal, characteristic, complemented
7C2×#63575C211yesmaximal, characteristic, complemented
8#70260—31nomaximal
9#69826—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3722—22no—
18C2×#3717—22no—
19C2×#3717—22no—
20C2×#3717C414yescomplemented
21#63648—22no—
22C3×#816—22no—
23C3×#815—22no—
24#63579—22no—
25#63575—22no—
26C22×#215—31no—
27C22×#204—31no—
28C2×C3×#103—31no—
29C2×C3×#97—31no—
30#5229—31no—
31C2×#821—31no—
32C2×#821—31no—
33C2×#821—61no—
34C2×#818—31no—
35C2×#816D311yescharacteristic, complemented
36C2×#815D311yescharacteristic, complemented
37#4988—31no—
38C2×#807—31no—
39#4939—31no—
40#4929—31no—
41C23×C3⋊D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)C2×C412yes—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D412yes—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6C2×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#3722—44no—
72#3717—28no—
73#1973—91noSylow
74C22×C3×Q8—31no—
75C22×D12—31no—
76C22×D12—31no—
77C22×D12—61no—
78C22×Dic6C2×D311yescharacteristic
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×#215—34no—
86C2×#215—62no—
87C2×#215—62no—
88C2×(C2×D3)⋊C4—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×#103—62no—
100C3×#97—62no—
101C3⋊#95—62no—
102C3⋊#95—62no—
103#821—64no—
104#821—62no—
105#821—62no—
106#818—62no—
107#816—22no—
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—41no—
123C2×C3⋊Dic3—42no—
124C4⋊(C3⋊D3)—22no—
125C4⋊(C3⋊D3)—22no—
126C4⋊(C3⋊D3)—41no—
127C4⋊(C3⋊D3)—41no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—42no—
136C3×Dic6—22no—
137C3×Dic6—22no—
138C3×Dic6—41no—
139C3×Dic6—41no—
140C32×C8—22no—
141C3×C3⋊C8C22⋊C414yescomplemented
142C22×SD16—91no—
143C2×#107—91no—
144C2×#103—31no—
145C2×#102—91no—
146C2×#97—31no—
147#391—91no—
148#390—91no—
149C23×D3—61no—
150C23×D3—61no—
151C23×D3—121no—
152C2×C3×Q8—32no—
153C2×C3×Q8—61no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C2×C3×Q8—61no—
158C22×C3×C4—21no—
159C22×C3×C4—32no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168C22×Dic3—121no—
169C22×Dic3D1212yes—
170C2×D12—32no—
171C2×D12—32no—
172C2×D12—62no—
173C2×D12—62no—
174C2×D12—62no—
175C2×D12—61no—
176C2×D12—61no—
177C2×D12—61no—
178C2×D12—61no—
179C2×D12—61no—
180C2×D12—61no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—121no—
186C2×D12—121no—
187C2×D12—121no—
188C2×Dic6—21no—
189C2×Dic6—21no—
190C2×Dic6—21no—
191C2×Dic6—21no—
192C2×Dic6—21no—
193C2×Dic6C4×D312yes—
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#215—68no—
211(C2×D3)⋊C4—124no—
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—81no—
242C3×Dic3—42no—
243C3×Dic3—42no—
244C3×Dic3—81no—
245C22×Q8—31no—
246C22×D4—91no—
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—62no—
258#102—182no—
259#97—62no—
260#95—182no—
261C23×C3—21no—
262C23×C3C2×D1211yescharacteristic
263C23×C3D3×D411yescharacteristic
264C22×D3—62no—
265C22×D3—62no—
266C22×D3—122no—
267C22×D3—122no—
268C22×D3—122no—
269C22×D3—121no—
270C22×D3—121no—
271C22×D3—122no—
272C22×D3—122no—
273C22×D3—122no—
274C22×D3—122no—
275C22×D3—121no—
276C22×D3—121no—
277C22×D3—242no—
278C22×D3—242no—
279C3×Q8—62no—
280C3×Q8—62no—
281C3×Q8—121no—
282C3×Q8—121no—
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—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—121no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4—122no—
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4C2×C4×D311yescharacteristic
299C2×C3×C4C2×D1211yescharacteristic
300C2×C3×C4C2×D1211yescharacteristic
301C2×C3×C4#23511yescharacteristic
302C2×C3×C4#23511yescharacteristic
303C2×C3×C4#23511yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4#23711yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308C2×C3×C4C2×#6711yescharacteristic
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—42no—
316C2×Dic3—41no—
317C2×Dic3—122no—
318C2×Dic3—121no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321C2×Dic3—121no—
322C2×Dic3—242no—
323D12—64no—
324D12—62no—
325D12—62no—
326D12—62no—
327D12—62no—
328D12—122no—
329D12—122no—
330D12—122no—
331D12—121no—
332D12—121no—
333D12—121no—
334D12—121no—
335Dic6—22no—
336Dic6—22no—
337Dic6—41no—
338Dic6—41no—
339C3×C8—22no—
340C3×C8—22no—
341C3×C8—34no—
342C3×C8—42no—
343C3⋊C8(C2×D3)⋊C414yescomplemented
344C2×C32#39011yescharacteristic
345C2×C32#44012yes—
346C2×C32#46812yes—
347C2×C32#49611yescharacteristic
348C2×C32#49711yescharacteristic
349C3⋊D3—82no—
350C24—181no—
351C2×Q8—32no—
352C2×Q8—61no—
353C2×Q8—61no—
354C2×Q8—61no—
355C2×Q8—61no—
356C2×Q8—61no—
357C2×D4—92no—
358C2×D4—181no—
359C2×D4—181no—
360C2×D4—181no—
361C2×D4—181no—
362C2×D4—181no—
363C22×C4—32no—
364C22×C4—61no—
365C22×C4—61no—
366C22×C4—181no—
367C22×C4C2×D3211yescharacteristic
368SD16—188no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—32no—
372C2×C8—32no—
373C2×C8—32no—
374C2×C8#62612yes—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C4⋊C4—181no—
378C4⋊C4—181no—
379C22⋊C4—364no—
380C42—61no—
381C42—61no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3C4×D1211yescharacteristic
388C22×C3#87411yescharacteristic
389C22×C3#67⋊C411yescharacteristic
390C22×C3#88411yescharacteristic
391C22×C3#90812yes—
392C22×C3#90912yes—
393C22×C3#91412yes—
394C22×C3#91812yes—
395C22×C3#93011yescharacteristic
396C22×C3#94011yescharacteristic
397C2×D3—124no—
398C2×D3—122no—
399C2×D3—122no—
400C2×D3—124no—
401C2×D3—124no—
402C2×D3—244no—
403C2×D3—244no—
404C2×D3—242no—
405C2×D3—242no—
406C2×D3—242no—
407C2×D3—241no—
408C2×D3—241no—
409C2×D3—241no—
410C2×D3—241no—
411C2×D3—242no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—122no—
417C3×C4—122no—
418C3×C4—241no—
419C3×C4C4×D1211yescharacteristic
420C3×C4#87511yescharacteristic
421C3×C4D3×C22⋊C411yescharacteristic
422C3×C4#88511yescharacteristic
423C3×C4C2×(C2×D3)⋊C411yescharacteristic
424C3×C4C4×#6711yescharacteristic
425C3×C4#93011yescharacteristic
426C3×C4#93911yescharacteristic
427Dic3—42no—
428Dic3—42no—
429Dic3—81no—
430Dic3—242no—
431Dic3—241no—
432Dic3—241no—
433C32#197311yescharacteristic, complemented, Sylow
434C23—182no—
435C23—362no—
436C23—362no—
437C23—361no—
438C23—361no—
439C23D3×D1211yescharacteristic
440Q8—62no—
441Q8—62no—
442Q8—121no—
443Q8—121no—
444D4—182no—
445D4—182no—
446D4—361no—
447D4—361no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—121no—
453C2×C4—121no—
454C2×C4—122no—
455C2×C4—121no—
456C2×C4—362no—
457C2×C4—361no—
458C2×C4#379811yescharacteristic
459C2×C4C4×D3211yescharacteristic
460C2×C4D3×D1211yescharacteristic
461C2×C4#380411yescharacteristic
462C2×C4C2×#62611yescharacteristic
463C2×C4D3×#6711yescharacteristic
464C8—22no—
465C8—34no—
466C2×C3—22no—
467C2×C3—22no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3#471012yes—
472C2×C3#471211yescharacteristic
473C2×C3#471511yescharacteristic
474C2×C3#481212yes—
475C2×C3#481712yes—
476C2×C3#493911yescharacteristic
477C2×C3#495711yescharacteristic
478C2×C3#513412yes—
479C2×C3#517611yescharacteristic
480C2×C3#519011yescharacteristic
481D3—244no—
482D3—242no—
483D3—242no—
484C22—364no—
485C22—362no—
486C22—722no—
487C22—721no—
488C22—721no—
489C22#6379412yes—
490C22#6380112yes—
491C22#6388011yescharacteristic
492C22#6390611yescharacteristic
493C22#6391111yescharacteristic
494C4—122no—
495C4—122no—
496C4—241no—
497C4—721no—
498C4#6385211yescharacteristic
499C4C4×#62611yescharacteristic
500C4D3×(C2×D3)⋊C411yescharacteristic
501C4#6397811yescharacteristic
502C3—21no—
503C3#6982611yescharacteristic, complemented
504C3#7026011yescharacteristic, complemented
505C2—722no—
506C2#1059079512yes—
507C2#1059085012yes—
508C2#1059088111yescharacteristic
509C2#1059089911yescharacteristic
510C2#1059138311yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
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
3. C2×C3×#816C2semidirect
4. C2×C3×#815C2semidirect
6. #10591220C2semidirect
7. C2×#63575C2semidirect
20. C2×#3717C4semidirect
35. C2×#816D3semidirect
36. C2×#815D3semidirect
141. C3×C3⋊C8C22⋊C4semidirect
343. C3⋊C8(C2×D3)⋊C4semidirect
433. C32#1973semidirect
503. C3#69826semidirect
504. C3#70260semidirect

Maximal subgroups

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

subgroupindex
C22×#37172
C2×#636482
C2×C3×#8162
C2×C3×#8152
#105913202
#105912202
C2×#635752
#702603
#698263