Finite Group Databasebeta

← #11791140

Subgroups — #11791140

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×#63637C211yesmaximal, characteristic, complemented
3C3×#4988C211yesmaximal, characteristic
4C2×C3×#807C211yesmaximal, characteristic, complemented
5#10591213C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic
7C2×#63554C211yesmaximal, characteristic, complemented
8#70629—31nomaximal
9#69649—31nomaximal
10C22×#634C2211yescharacteristic
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×#3716—22no—
19C2×#3716—22no—
20C2×#3716C414yescomplemented
21#63637—22no—
22C3×#807—22no—
23#63579—22no—
24#63562—22no—
25#63554—22no—
26C22×#214—31no—
27C22×#204—31no—
28C2×C3×#107—31no—
29C3×#390—31no—
30C2×#832—31no—
31C2×#815—31no—
32#4988D311yescharacteristic
33#4973—31no—
34C2×#810—31no—
35C2×#810—31no—
36C2×#810—61no—
37C2×#809—31no—
38C2×#807D311yescharacteristic, complemented
39#4929—31no—
40C2×#803—31no—
41C23×C3×D3—21no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
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—
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#3716—28no—
73#1973—91noSylow
74C22×C3×D4—31no—
75C22×D12C2×D311yescharacteristic
76C22×Dic6—31no—
77C22×Dic6—31no—
78C22×Dic6—61no—
79C22×C3×C8—31no—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4C2×D311yescharacteristic
83C2×C3×C4⋊C4C2×D311yescharacteristic
84C2×C3×C22⋊C4—62no—
85C2×C3×C42—31no—
86C2×#214—34no—
87C2×#214—62no—
88C2×#214—62no—
89C2×(C2×D3)⋊C4—22no—
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4×Dic3C2×D311yescharacteristic
92C22×C3⋊C8—31no—
93C22×C3⋊C8—31no—
94C22×C3⋊C8—61no—
95C22×C3⋊C8C2×D311yescharacteristic
96C2×#204—34no—
97C2×#204—62no—
98C2×#204—62no—
99C3×#107—62no—
100#832—62no—
101C3⋊#95—62no—
102C3⋊#95—62no—
103#815—62no—
104#810—62no—
105#810—62no—
106#810—64no—
107#809—62no—
108#807—22no—
109#803—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×C4—41no—
117C2×C32×C4—42no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
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—
140C3⋊(C3⋊C8)—22no—
141C3×C3⋊C8C22⋊C414yescomplemented
142C22×SD16—91no—
143C2×#107—31no—
144C2×#103—91no—
145C2×#102—91no—
146C2×#97—91no—
147#391—91no—
148#390—31no—
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—21no—
159C22×C3×C4—21no—
160C22×C3×C4—32no—
161C22×C3×C4—41no—
162C22×C3×C4—61no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C22×Dic3—21no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168C22×Dic3—121no—
169C22×Dic3#6712yes—
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—32no—
195C2×C3×C8—32no—
196C2×C3×C8—32no—
197C3×C4⋊C4—22no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—41no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205C3×C22⋊C4—124no—
206C3×C42—61no—
207C3×C42—61no—
208#214—68no—
209(C2×D3)⋊C4—44no—
210C4⋊Dic3—21no—
211C4⋊Dic3—21no—
212C4×Dic3—21no—
213C4×Dic3—21no—
214C2×C3⋊C8—32no—
215C2×C3⋊C8—32no—
216C2×C3⋊C8—62no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—121no—
222C2×C3⋊C8—121no—
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×C4—81no—
238C32×C4C2×C22⋊C411yescharacteristic
239C32×C4C4×D411yescharacteristic
240C32×C4#12111yescharacteristic
241C32×C4#12411yescharacteristic
242C3⋊Dic3—42no—
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×C8—91no—
252C2×C4⋊C4—31no—
253C2×C4⋊C4D3211yescharacteristic
254C2×C22⋊C4—62no—
255C2×C42—31no—
256#107—62no—
257#103—182no—
258#102—182no—
259#97—182no—
260#95—182no—
261C23×C3—21no—
262C23×C3—62no—
263C23×C3—121no—
264C23×C3—122no—
265C23×C3—122no—
266C23×C3—121no—
267C23×C3D3×D411yescharacteristic
268C23×C3C2×#6711yescharacteristic
269C22×D3—22no—
270C22×D3—42no—
271C22×D3—41no—
272C22×D3—41no—
273C22×D3—42no—
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—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—82no—
293C2×C3×C4—122no—
294C2×C3×C4—121no—
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×D1211yescharacteristic
298C2×C3×C4#23511yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4#23711yescharacteristic
304C2×C3×C4#23911yescharacteristic
305C2×C3×C4#23911yescharacteristic
306C2×C3×C4C2×#6711yescharacteristic
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—42no—
311C2×Dic3—41no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—122no—
315C2×Dic3—122no—
316C2×Dic3—122no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3—121no—
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—34no—
338C3⋊C8—62no—
339C3⋊C8—62no—
340C3⋊C8—122no—
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—21no—
362C22×C4—32no—
363C22×C4—61no—
364C22×C4—181no—
365C22×C4C2×D3211yescharacteristic
366SD16—188no—
367C2×C8—32no—
368C2×C8—32no—
369C2×C8—32no—
370C2×C8—92no—
371C2×C8—181no—
372C2×C8—181no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C22⋊C4—124no—
378C42—61no—
379C42—61no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—124no—
386C22×C3—122no—
387C22×C3—242no—
388C22×C3—241no—
389C22×C3—241no—
390C22×C3#89311yescharacteristic
391C22×C3#89511yescharacteristic
392C22×C3#91112yes—
393C22×C3#91812yes—
394C22×C3C4×#6711yescharacteristic
395C22×C3#93212yes—
396C22×C3#93911yescharacteristic
397C22×C3#94011yescharacteristic
398C22×C3#94011yescharacteristic
399C22×C3#95112yes—
400C2×D3—42no—
401C2×D3—44no—
402C2×D3—82no—
403C2×D3—81no—
404C2×D3—81no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—82no—
410C3×C4—81no—
411C3×C4—81no—
412C3×C4—122no—
413C3×C4—241no—
414C3×C4D3×C22⋊C411yescharacteristic
415C3×C4#67⋊C411yescharacteristic
416C3×C4#88411yescharacteristic
417C3×C4#88511yescharacteristic
418C3×C4#89311yescharacteristic
419C3×C4#89511yescharacteristic
420C3×C4C2×(C2×D3)⋊C411yescharacteristic
421C3×C4#94711yescharacteristic
422Dic3—42no—
423Dic3—81no—
424Dic3—124no—
425Dic3—122no—
426Dic3—122no—
427C32#197311yescharacteristic, complemented, Sylow
428C23—62no—
429C23—121no—
430C23—122no—
431C23—122no—
432C23—121no—
433C23D3×#6711yescharacteristic
434Q8—182no—
435Q8—182no—
436Q8—361no—
437Q8—361no—
438D4—62no—
439D4—62no—
440D4—121no—
441D4—121no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—62no—
447C2×C4—122no—
448C2×C4—121no—
449C2×C4—182no—
450C2×C4—361no—
451C2×C4—361no—
452C2×C4#379611yescharacteristic
453C2×C4#379911yescharacteristic
454C2×C4C4×D3211yescharacteristic
455C2×C4D3×D1211yescharacteristic
456C2×C4D3×#6711yescharacteristic
457C2×C4#381111yescharacteristic
458C8—34no—
459C8—182no—
460C2×C3—22no—
461C2×C3—22no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—242no—
466C2×C3#488612yes—
467C2×C3#488912yes—
468C2×C3#495711yescharacteristic
469C2×C3#498811yescharacteristic
470C2×C3#501812yes—
471C2×C3#504212yes—
472C2×C3#506011yescharacteristic
473C2×C3#507411yescharacteristic
474C2×C3#515411yescharacteristic
475C2×C3#519011yescharacteristic
476D3—82no—
477C22—124no—
478C22—122no—
479C22—242no—
480C22—241no—
481C22—241no—
482C22#6388611yescharacteristic
483C22#6390411yescharacteristic
484C22#6393212yes—
485C22#6394312yes—
486C22#6397911yescharacteristic
487C4—81no—
488C4—122no—
489C4—241no—
490C4—362no—
491C4#6388111yescharacteristic
492C4#6390711yescharacteristic
493C4#6391011yescharacteristic
494C4D3×(C2×D3)⋊C411yescharacteristic
495C3—21no—
496C3#6964911yescharacteristic, complemented
497C3#7062911yescharacteristic, complemented
498C2—242no—
499C2#1059058812yes—
500C2#1059059012yes—
501C2#1059138411yescharacteristic
502C2#1059146911yescharacteristic
503C2#1059162711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1973
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×#63637C2semidirect
4. C2×C3×#807C2semidirect
5. #10591213C2semidirect
7. C2×#63554C2semidirect
20. C2×#3716C4semidirect
38. C2×#807D3semidirect
141. C3×C3⋊C8C22⋊C4semidirect
341. C3⋊C8(C2×D3)⋊C4semidirect
427. C32#1973semidirect
496. C3#69649semidirect
497. C3#70629semidirect

Maximal subgroups

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

subgroupindex
C22×#37162
C2×#636372
C3×#49882
C2×C3×#8072
#105912132
C2×#635622
C2×#635542
#706293
#696493