Finite Group Databasebeta

← #11791144

Subgroups — #11791144

Order 1152.

753 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3715C211yesmaximal, characteristic
2C2×#63642C211yesmaximal, characteristic, complemented
3C2×C3×#821C211yesmaximal, characteristic
4C2×C3×#816C211yesmaximal, characteristic, complemented
5#10591323C211yesmaximal, characteristic
6#10591221C211yesmaximal, characteristic, complemented
7C2×#63576C211yesmaximal, characteristic, complemented
8#70260—31nomaximal
9#70192—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×(C2×D3)⋊Dic3—22no—
18C2×#3715—22no—
19C2×#3715—22no—
20C2×#3715C414yescomplemented
21#63642—22no—
22C3×#821—22no—
23C3×#816—22no—
24#63579—22no—
25#63576—22no—
26C22×#215—31no—
27C22×#214—31no—
28C2×C3×#103—31no—
29C2×C3×#102—31no—
30#5229—31no—
31#5221—31no—
32C2×#821D311yescharacteristic
33C2×#816D311yescharacteristic, complemented
34C2×#815—31no—
35C2×#815—31no—
36C2×#815—61no—
37#4988—31no—
38#4973—31no—
39C2×#807—31no—
40C2×#807—31no—
41C23×C3×D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3D412yes—
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×D12C2×C412yes—
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—
64C2×C3⋊(C3⋊C8)C2×C412yes—
65C2×C3⋊(C3⋊C8)D412yes—
66C2×C3⋊(C3⋊C8)D412yes—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71(C2×D3)⋊Dic3—44no—
72#3715—28no—
73#1973—91noSylow
74C22×C3×Q8—31no—
75C22×C3×D4—31no—
76C22×D12C2×D311yescharacteristic
77C22×Dic6C2×D311yescharacteristic
78C22×C3×C8—21no—
79C22×C3×C8C2×D311yescharacteristic
80C22×C3×C8C2×D311yescharacteristic
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—31no—
83C2×#217—62no—
84C2×#215—34no—
85C2×#215—62no—
86C2×#215—62no—
87C2×#214—34no—
88C2×#214—62no—
89C2×#214—62no—
90C2×(C2×D3)⋊C4—62no—
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×C4⋊Dic3C2×D311yescharacteristic
93C2×C4×Dic3—31no—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—61no—
96C22×C3⋊C8—31no—
97C22×C3⋊C8—31no—
98C22×C3⋊C8—61no—
99C3×#103—62no—
100C3×#102—62no—
101C3⋊#95—62no—
102C3⋊#95—62no—
103#821—22no—
104#816—22no—
105#815—62no—
106#815—62no—
107#815—64no—
108#807—62no—
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—22no—
124C2×C3⋊Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—42no—
131C2×C3×Dic3—42no—
132C3×D12—22no—
133C3×D12—22no—
134C3×D12—41no—
135C3×D12—41no—
136C3×Dic6—22no—
137C3×Dic6—22no—
138C3×Dic6—41no—
139C3×Dic6—41no—
140C32×C8—22no—
141C3⋊(C3⋊C8)C22⋊C414yescomplemented
142C22×SD16—91no—
143C2×#107—91no—
144C2×#103—31no—
145C2×#102—31no—
146C2×#97—91no—
147#391—91no—
148#390—91no—
149C24×C3—61no—
150C23×D3—21no—
151C2×C3×Q8—32no—
152C2×C3×Q8—61no—
153C2×C3×Q8—61no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
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—61no—
165C22×C3×C4—61no—
166C22×C3×C4—61no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×Dic3—21no—
170C22×Dic3—21no—
171C22×Dic3—21no—
172C22×Dic3—32no—
173C22×Dic3—32no—
174C22×Dic3—62no—
175C2×D12—21no—
176C2×D12—21no—
177C2×D12—21no—
178C2×D12—21no—
179C2×D12—21no—
180C2×D12C4×D312yes—
181C2×Dic6—21no—
182C2×Dic6—21no—
183C2×Dic6—21no—
184C2×Dic6—21no—
185C2×Dic6—21no—
186C2×Dic6C4×D312yes—
187C2×C3×C8—22no—
188C2×C3×C8—22no—
189C2×C3×C8—21no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—22no—
194C2×C3×C8#6712yes—
195C2×C3×C8#6712yes—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200#217—124no—
201#215—68no—
202#214—68no—
203(C2×D3)⋊C4—124no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4×Dic3—62no—
209C4×Dic3—62no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C2×C3⋊C8—32no—
215C2×C3⋊C8—32no—
216C2×C3⋊C8—32no—
217C2×C3⋊C8—32no—
218C2×C3⋊C8—32no—
219C2×C3⋊C8—32no—
220C2×C3⋊C8—62no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—62no—
223C22×C32C4×D411yescharacteristic
224C22×C32#12111yescharacteristic
225C22×C32#12711yescharacteristic
226C22×C32AGL(1,ℤ/8)12yes—
227C22×C32#13712yes—
228C2×C3×D3—42no—
229C2×C3×D3—44no—
230C2×C3×D3—82no—
231C2×C3×D3—81no—
232C2×C3×D3—81no—
233C32×C4C2×C22⋊C411yescharacteristic
234C32×C4C4×D411yescharacteristic
235C32×C4#12111yescharacteristic
236C32×C4#12411yescharacteristic
237C3⋊Dic3—42no—
238C3×Dic3—42no—
239C3×Dic3—81no—
240C3×Dic3—81no—
241C22×Q8—31no—
242C22×D4—31no—
243C2×SD16—94no—
244C2×SD16—182no—
245C2×SD16—182no—
246C22×C8—91no—
247C22×C8D3211yescharacteristic
248C2×C4⋊C4—31no—
249C2×C4⋊C4—31no—
250C2×C22⋊C4—182no—
251C2×C42—91no—
252#107—182no—
253#103—62no—
254#102—62no—
255#97—182no—
256#95—182no—
257C23×C3—21no—
258C23×C3—62no—
259C23×C3—121no—
260C23×C3—122no—
261C23×C3—122no—
262C23×C3—121no—
263C23×C3D3×D411yescharacteristic
264C23×C3D3×D411yescharacteristic
265C22×D3—22no—
266C22×D3—41no—
267C22×D3—42no—
268C22×D3—42no—
269C22×D3—41no—
270C3×Q8—62no—
271C3×Q8—62no—
272C3×Q8—121no—
273C3×Q8—121no—
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—121no—
286C2×C3×C4—121no—
287C2×C3×C4—122no—
288C2×C3×C4—122no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4#23511yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23711yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303C2×Dic3—22no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—42no—
307C2×Dic3—42no—
308C2×Dic3—41no—
309C2×Dic3—41no—
310C2×Dic3—64no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—122no—
318C2×Dic3—122no—
319D12—22no—
320D12—22no—
321D12—41no—
322D12—41no—
323Dic6—22no—
324Dic6—22no—
325Dic6—41no—
326Dic6—41no—
327C3×C8—24no—
328C3×C8—22no—
329C3×C8—22no—
330C3⋊C8—34no—
331C3⋊C8—34no—
332C3⋊C8—64no—
333C2×C32#39011yescharacteristic
334C2×C32#44012yes—
335C2×C32#46812yes—
336C2×C32#49611yescharacteristic
337C2×C32#49711yescharacteristic
338C3×D3—82no—
339C24—61no—
340C2×Q8—32no—
341C2×Q8—61no—
342C2×Q8—61no—
343C2×Q8—61no—
344C2×Q8—61no—
345C2×Q8—61no—
346C2×D4—32no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C22×C4—61no—
353C22×C4—61no—
354C22×C4—61no—
355C22×C4—92no—
356C22×C4C2×D3211yescharacteristic
357SD16—188no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—92no—
361C2×C8—92no—
362C2×C8—92no—
363C2×C8#62512yes—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C22⋊C4—364no—
369C42—181no—
370C42—181no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—122no—
377C22×C3—124no—
378C22×C3—241no—
379C22×C3—241no—
380C22×C3—242no—
381C22×C3#67⋊C411yescharacteristic
382C22×C3#67⋊C411yescharacteristic
383C22×C3#88411yescharacteristic
384C22×C3#88411yescharacteristic
385C22×C3#91112yes—
386C22×C3#91412yes—
387C22×C3#91512yes—
388C22×C3#91812yes—
389C22×C3#94011yescharacteristic
390C22×C3#94011yescharacteristic
391C2×D3—42no—
392C2×D3—44no—
393C2×D3—81no—
394C2×D3—81no—
395C2×D3—82no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—122no—
401C3×C4—241no—
402C3×C4—241no—
403C3×C4D3×C22⋊C411yescharacteristic
404C3×C4D3×C22⋊C411yescharacteristic
405C3×C4#88511yescharacteristic
406C3×C4#88511yescharacteristic
407C3×C4C4×#6711yescharacteristic
408C3×C4C4×#6711yescharacteristic
409C3×C4#93911yescharacteristic
410C3×C4#93911yescharacteristic
411Dic3—42no—
412Dic3—81no—
413Dic3—81no—
414Dic3—124no—
415Dic3—122no—
416Dic3—122no—
417C32#197311yescharacteristic, complemented, Sylow
418C23—62no—
419C23—122no—
420C23—122no—
421C23—121no—
422C23—121no—
423C23#380211yescharacteristic
424Q8—62no—
425Q8—62no—
426Q8—121no—
427Q8—121no—
428D4—62no—
429D4—62no—
430D4—121no—
431D4—121no—
432C2×C4—62no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—122no—
436C2×C4—122no—
437C2×C4—121no—
438C2×C4—121no—
439C2×C4—182no—
440C2×C4—182no—
441C2×C4—182no—
442C2×C4#379811yescharacteristic
443C2×C4C4×D3211yescharacteristic
444C2×C4#380211yescharacteristic
445C2×C4#380511yescharacteristic
446C2×C4C2×#62511yescharacteristic
447C2×C4#381111yescharacteristic
448C8—22no—
449C8—94no—
450C2×C3—22no—
451C2×C3—22no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—242no—
456C2×C3#475712yes—
457C2×C3#478012yes—
458C2×C3#481212yes—
459C2×C3#481712yes—
460C2×C3#495711yescharacteristic
461C2×C3#495711yescharacteristic
462C2×C3#515411yescharacteristic
463C2×C3#516711yescharacteristic
464C2×C3#517611yescharacteristic
465C2×C3#519011yescharacteristic
466D3—82no—
467C22—124no—
468C22—122no—
469C22—242no—
470C22—241no—
471C22—241no—
472C22#6379812yes—
473C22#6381112yes—
474C22#6390211yescharacteristic
475C22#6391211yescharacteristic
476C22#6391411yescharacteristic
477C4—122no—
478C4—241no—
479C4—241no—
480C4—362no—
481C4C4×#62511yescharacteristic
482C4#6391511yescharacteristic
483C4#6392111yescharacteristic
484C4#6398011yescharacteristic
485C3—21no—
486C3#7019211yescharacteristic, complemented
487C3#7026011yescharacteristic, complemented
488C2—242no—
489C2#1059074312yes—
490C2#1059084212yes—
491C2#1059087011yescharacteristic
492C2#1059088711yescharacteristic
493C2#1059138511yescharacteristic
subgroupG/H
centerC23#3802
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×#63642C2semidirect
4. C2×C3×#816C2semidirect
6. #10591221C2semidirect
7. C2×#63576C2semidirect
20. C2×#3715C4semidirect
33. C2×#816D3semidirect
141. C3⋊(C3⋊C8)C22⋊C4semidirect
417. C32#1973semidirect
486. C3#70192semidirect
487. C3#70260semidirect

Maximal subgroups

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

subgroupindex
C22×#37152
C2×#636422
C2×C3×#8212
C2×C3×#8162
#105913232
#105912212
C2×#635762
#702603
#701923