Finite Group Databasebeta

← #11791142

Subgroups — #11791142

Order 1152.

809 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3717C211yesmaximal, characteristic
2#10592687C211yesmaximal, characteristic
3C2×C3×#810C211yesmaximal, characteristic, complemented
4C2×C3×#807C211yesmaximal, characteristic, complemented
5#10591221C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7C2×#63555C211yesmaximal, characteristic, complemented
8#70629—31nomaximal
9#70260—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3752—22no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3717—22no—
19C2×#3717—22no—
20C2×#3717C414yescomplemented
21C3×#810—22no—
22C3×#807—22no—
23#63579—22no—
24#63564—22no—
25#63555—22no—
26C22×#215—31no—
27C22×#204—31no—
28C2×C3×#107—31no—
29C2×C3×#103—31no—
30#5229—31no—
31C2×#821—31no—
32C2×#815—31no—
33C2×#815—31no—
34#4988—31no—
35#4988—31no—
36#4988—61no—
37#4973—31no—
38C2×#810D311yescharacteristic, complemented
39C2×#809—31no—
40C2×#807D311yescharacteristic, complemented
41C23×C3⋊D3—21no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3D412yes—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)C2×C412yes—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6C2×C412yes—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61#3752—44no—
62C4×C3⋊Dic3—21no—
63C4×C3⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8C2×C412yes—
69C2×C3×C3⋊C8D412yes—
70C2×C3×C3⋊C8D412yes—
71C2×C3×C3⋊C8D412yes—
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—31no—
80C22×C3×C8—31no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4C2×D311yescharacteristic
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×#215—34no—
86C2×#215—62no—
87C2×#215—62no—
88C2×(C2×D3)⋊C4—62no—
89C2×(C2×D3)⋊C4—62no—
90C2×(C2×D3)⋊C4—64no—
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×C4×Dic3—31no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—61no—
95C22×C3⋊C8C2×D311yescharacteristic
96C22×C3⋊C8C2×D311yescharacteristic
97C2×#204—34no—
98C2×#204—62no—
99C2×#204—62no—
100C3×#107—62no—
101C3×#103—62no—
102C3⋊#95—62no—
103C3⋊#95—62no—
104#821—62no—
105#815—62no—
106#815—62no—
107#810—22no—
108#809—62no—
109#807—22no—
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—22no—
126C2×C3⋊Dic3—22no—
127C4⋊(C3⋊D3)—22no—
128C4⋊(C3⋊D3)—22no—
129C4⋊(C3⋊D3)—41no—
130C4⋊(C3⋊D3)—41no—
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—
140C3×C3⋊C8—22no—
141C3×C3⋊C8C22⋊C414yescomplemented
142C22×SD16—91no—
143C2×#107—31no—
144C2×#103—31no—
145C2×#102—91no—
146C2×#97—91no—
147#391—91no—
148#390—91no—
149C23×D3—62no—
150C23×D3—61no—
151C23×D3—61no—
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—22no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—21no—
168C22×Dic3—32no—
169C22×Dic3—32no—
170C22×Dic3—62no—
171C2×D12—32no—
172C2×D12—32no—
173C2×D12—62no—
174C2×D12—61no—
175C2×D12—61no—
176C2×D12—61no—
177C2×D12—61no—
178C2×D12—61no—
179C2×D12—61no—
180C2×D12—61no—
181C2×D12—61no—
182C2×D12—62no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—121no—
186C2×D12—121no—
187C2×D12—121no—
188C2×D12—121no—
189C2×Dic6—21no—
190C2×Dic6—21no—
191C2×Dic6—21no—
192C2×Dic6—21no—
193C2×Dic6—21no—
194C2×Dic6C4×D312yes—
195C2×C3×C8—32no—
196C2×C3×C8—32no—
197C2×C3×C8—32no—
198C2×C3×C8—32no—
199C2×C3×C8—61no—
200C2×C3×C8—61no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—41no—
206C3×C4⋊C4—41no—
207C3×C4⋊C4—61no—
208C3×C4⋊C4—61no—
209#215—68no—
210(C2×D3)⋊C4—128no—
211(C2×D3)⋊C4—124no—
212(C2×D3)⋊C4—124no—
213C4⋊Dic3—21no—
214C4⋊Dic3—21no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217C4×Dic3—61no—
218C4×Dic3—61no—
219C4×Dic3—121no—
220C4×Dic3—121no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8C4×D312yes—
224C2×C3⋊C8D1212yes—
225C2×C3⋊C8#6712yes—
226C2×C3⋊C8#6712yes—
227#204—68no—
228C22×C32C4×D411yescharacteristic
229C22×C32#12111yescharacteristic
230C22×C32#12711yescharacteristic
231C22×C32AGL(1,ℤ/8)12yes—
232C22×C32#13712yes—
233C2×C3⋊D3—42no—
234C2×C3⋊D3—44no—
235C2×C3⋊D3—82no—
236C2×C3⋊D3—81no—
237C2×C3⋊D3—81no—
238C32×C4—81no—
239C32×C4C2×C22⋊C411yescharacteristic
240C32×C4C4×D411yescharacteristic
241C32×C4#12111yescharacteristic
242C32×C4#12411yescharacteristic
243C3⋊Dic3—42no—
244C3×Dic3—42no—
245C3×Dic3—81no—
246C22×Q8—31no—
247C22×D4—91no—
248C2×SD16—94no—
249C2×SD16—182no—
250C2×SD16—182no—
251C22×C8—31no—
252C22×C8—31no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4D3211yescharacteristic
255C2×C22⋊C4—182no—
256C2×C42—91no—
257#107—62no—
258#103—62no—
259#102—182no—
260#97—182no—
261#95—182no—
262C23×C3—21no—
263C23×C3D3×D411yescharacteristic
264C23×C3D3×D411yescharacteristic
265C22×D3—64no—
266C22×D3—62no—
267C22×D3—62no—
268C22×D3—124no—
269C22×D3—122no—
270C22×D3—122no—
271C22×D3—124no—
272C22×D3—121no—
273C22×D3—121no—
274C22×D3—122no—
275C22×D3—122no—
276C22×D3—122no—
277C22×D3—122no—
278C22×D3—121no—
279C22×D3—121no—
280C3×Q8—62no—
281C3×Q8—62no—
282C3×Q8—121no—
283C3×Q8—121no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—44no—
291C2×C3×C4—42no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—62no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—122no—
300C2×C3×C4—121no—
301C2×C3×C4C2×C4×D311yescharacteristic
302C2×C3×C4C2×C4×D311yescharacteristic
303C2×C3×C4C2×D1211yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4#23711yescharacteristic
309C2×C3×C4#23911yescharacteristic
310C2×C3×C4#23911yescharacteristic
311C2×C3×C4C2×#6711yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313C2×Dic3—22no—
314C2×Dic3—41no—
315C2×Dic3—41no—
316C2×Dic3—42no—
317C2×Dic3—41no—
318C2×Dic3—64no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—122no—
326C2×Dic3—122no—
327D12—62no—
328D12—62no—
329D12—62no—
330D12—62no—
331D12—122no—
332D12—122no—
333D12—122no—
334D12—122no—
335D12—121no—
336D12—121no—
337D12—121no—
338D12—121no—
339Dic6—22no—
340Dic6—22no—
341Dic6—41no—
342Dic6—41no—
343C3×C8—34no—
344C3×C8—62no—
345C3⋊C8—22no—
346C3⋊C8(C2×D3)⋊C414yescomplemented
347C2×C32#39011yescharacteristic
348C2×C32#44012yes—
349C2×C32#46812yes—
350C2×C32#49611yescharacteristic
351C2×C32#49711yescharacteristic
352C3⋊D3—82no—
353C24—181no—
354C2×Q8—32no—
355C2×Q8—61no—
356C2×Q8—61no—
357C2×Q8—61no—
358C2×Q8—61no—
359C2×Q8—61no—
360C2×D4—92no—
361C2×D4—181no—
362C2×D4—181no—
363C2×D4—181no—
364C2×D4—181no—
365C2×D4—181no—
366C22×C4—21no—
367C22×C4—61no—
368C22×C4—61no—
369C22×C4—92no—
370C22×C4C2×D3211yescharacteristic
371SD16—188no—
372C2×C8—32no—
373C2×C8—32no—
374C2×C8—32no—
375C2×C8—32no—
376C2×C8—61no—
377C2×C8—61no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C22⋊C4—364no—
383C42—181no—
384C42—181no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—22no—
388C22×C3—22no—
389C22×C3—21no—
390C22×C3#67⋊C411yescharacteristic
391C22×C3#88411yescharacteristic
392C22×C3#89311yescharacteristic
393C22×C3#89511yescharacteristic
394C22×C3#91112yes—
395C22×C3#91412yes—
396C22×C3#91812yes—
397C22×C3#91812yes—
398C22×C3#94011yescharacteristic
399C22×C3#94011yescharacteristic
400C2×D3—124no—
401C2×D3—128no—
402C2×D3—124no—
403C2×D3—122no—
404C2×D3—122no—
405C2×D3—124no—
406C2×D3—244no—
407C2×D3—242no—
408C2×D3—242no—
409C2×D3—242no—
410C2×D3—241no—
411C2×D3—241no—
412C2×D3—241no—
413C2×D3—241no—
414C2×D3—242no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—82no—
420C3×C4—81no—
421C3×C4—81no—
422C3×C4—122no—
423C3×C4—241no—
424C3×C4D3×C22⋊C411yescharacteristic
425C3×C4#88511yescharacteristic
426C3×C4#89311yescharacteristic
427C3×C4#89511yescharacteristic
428C3×C4C2×(C2×D3)⋊C411yescharacteristic
429C3×C4C4×#6711yescharacteristic
430C3×C4#93911yescharacteristic
431C3×C4#94711yescharacteristic
432Dic3—42no—
433Dic3—81no—
434Dic3—124no—
435Dic3—122no—
436Dic3—122no—
437C32#197311yescharacteristic, complemented, Sylow
438C23—182no—
439C23—361no—
440C23—362no—
441C23—362no—
442C23—361no—
443C23#381111yescharacteristic
444Q8—62no—
445Q8—62no—
446Q8—121no—
447Q8—121no—
448D4—182no—
449D4—182no—
450D4—361no—
451D4—361no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—62no—
455C2×C4—121no—
456C2×C4—121no—
457C2×C4—122no—
458C2×C4—121no—
459C2×C4—182no—
460C2×C4—182no—
461C2×C4—182no—
462C2×C4#379611yescharacteristic
463C2×C4#379911yescharacteristic
464C2×C4C4×D3211yescharacteristic
465C2×C4D3×D1211yescharacteristic
466C2×C4D3×#6711yescharacteristic
467C2×C4D3×#6711yescharacteristic
468C8—34no—
469C8—62no—
470C2×C3—22no—
471C2×C3—22no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3#481212yes—
476C2×C3#481712yes—
477C2×C3#488612yes—
478C2×C3#488912yes—
479C2×C3#495711yescharacteristic
480C2×C3#498811yescharacteristic
481C2×C3#515411yescharacteristic
482C2×C3#517611yescharacteristic
483C2×C3#519011yescharacteristic
484C2×C3#519011yescharacteristic
485D3—244no—
486D3—242no—
487D3—242no—
488C22—364no—
489C22—362no—
490C22—722no—
491C22—721no—
492C22—721no—
493C22#6388111yescharacteristic
494C22#6391011yescharacteristic
495C22#6393712yes—
496C22#6394512yes—
497C22#6397911yescharacteristic
498C4—81no—
499C4—122no—
500C4—241no—
501C4—362no—
502C4#6388611yescharacteristic
503C4#6390411yescharacteristic
504C4#6390711yescharacteristic
505C4D3×(C2×D3)⋊C411yescharacteristic
506C3—21no—
507C3#7026011yescharacteristic, complemented
508C3#7062911yescharacteristic, complemented
509C2—722no—
510C2#1059048412yes—
511C2#1059052212yes—
512C2#1059138411yescharacteristic
513C2#1059147511yescharacteristic
514C2#1059162911yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
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
3. C2×C3×#810C2semidirect
4. C2×C3×#807C2semidirect
5. #10591221C2semidirect
7. C2×#63555C2semidirect
20. C2×#3717C4semidirect
38. C2×#810D3semidirect
40. C2×#807D3semidirect
141. C3×C3⋊C8C22⋊C4semidirect
346. C3⋊C8(C2×D3)⋊C4semidirect
437. C32#1973semidirect
507. C3#70260semidirect
508. C3#70629semidirect

Maximal subgroups

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

subgroupindex
C22×#37172
#105926872
C2×C3×#8102
C2×C3×#8072
#105912212
C2×#635642
C2×#635552
#706293
#702603