Finite Group Databasebeta

← #11887670

Subgroups — #11887670

Order 1152.

830 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5579C211yesmaximal, characteristic
2Dic6×D12C211yesmaximal, characteristic
3#10592730C211yesmaximal, characteristic, complemented
4C3×C4×#216C211yesmaximal, characteristic, complemented
5#10591653C212yesmaximal, complemented
6#10591596C212yesmaximal, complemented
7D3×#810C212yesmaximal, complemented
8#10590427C212yesmaximal, complemented
9C3⋊C8×D12C211yesmaximal, characteristic
10#10590310C211yesmaximal, characteristic, complemented
11#10590288C211yesmaximal, characteristic, complemented
12#83640—31nomaximal
13#79735—31nomaximal
14C2×D3×Dic6C2212yes—
15C32×C4×Q8C2211yescharacteristic
16C2×#3756C2212yes—
17#64078C2211yescharacteristic
18C3×#946C2212yes—
19C2×C3×#216C2211yescharacteristic
20C3×#896—22no—
21C3×D3×C4⋊C4C2212yes—
22C3×C4×D12—21no—
23C3×C4×D12C2211yescharacteristic
24C3×#870—21no—
25C3×#869C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27#63918—21no—
28#63893—22no—
29Dic3×D12—21no—
30#63857C2212yes—
31C2×D3×C3⋊C8C2212yes—
32#63637C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#835C2211yescharacteristic
35C3×#810C2211yescharacteristic
36C3×#807C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38#63576C2212yes—
39#63567C2212yes—
40#63567C2212yes—
41#63565C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43C3×#554—31no—
44#5579D311yescharacteristic
45Q8×D12—31no—
46D4×Dic6—31no—
47C3×C4×Q16—31no—
48#5186—32no—
49#5093—31no—
50#5091—31no—
51#5051—32no—
52#5050—32no—
53#5031—31no—
54#5031—31no—
55#5031—61no—
56C4×#216D311yescharacteristic, complemented
57#5021—31no—
58D4×C3⋊C8—31no—
59#4970—32no—
60C2×#810—32no—
61#4884—32no—
62#4813—32no—
63D3×#103—32no—
64C8×D12—31no—
65#4681—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634C2312yes—
68C2×C3×D12D411yescharacteristic
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6C2311yescharacteristic
73C2×#627—22no—
74C2×D3×Dic3—22no—
75D3×Dic6—24no—
76D3×Dic6—42no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C42—21no—
80C32×C42C2311yescharacteristic
81#3756—42no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)—21no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#216—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4D412yes—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—21no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98Dic3⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100D3×C3⋊C8—42no—
101#3299—91noSylow
102C2×D3×Q8—32no—
103C22×Dic6—32no—
104C2×C3×Q16—31no—
105C3×C4⋊Q8—31no—
106C3×#125—61no—
107C3×C22⋊Q8—32no—
108C3×C22⋊Q8—62no—
109C3×C4×Q8—21no—
110C3×C4×Q8—31no—
111C3×C4×Q8C2×D311yescharacteristic
112C3×C4×Q8C2×D311yescharacteristic
113C3×C4×D4—31no—
114C3×C4×D4—61no—
115C2×C3×C4⋊C4—32no—
116#946C2×D312yes—
117C2×#216—32no—
118C2×#216—32no—
119C2×#216—62no—
120C2×#216C2×D311yescharacteristic
121D4×Dic3—61no—
122#924—32no—
123C22×C3⋊C8—32no—
124C2×D3×C8—32no—
125#897—32no—
126#897—62no—
127#896—22no—
128D3×C4⋊C4C2×D312yes—
129#888—61no—
130#878—62no—
131C4×D12—21no—
132C4×D12—61no—
133C4×D12C2×D311yescharacteristic
134#870—21no—
135#869—31no—
136#869—31no—
137#869—61no—
138#869—61no—
139#869C2×D311yescharacteristic
140C4×Dic6C2×D311yescharacteristic
141C3×#107—31no—
142C3×#103—31no—
143C3×#103—31no—
144C3×C4×C8—31no—
145#835—32no—
146#835C2×D311yescharacteristic
147#830—32no—
148(C2×D3)⋊C8—32no—
149#816—32no—
150#816—32no—
151#810—32no—
152#810—32no—
153#810—32no—
154#810—32no—
155#810—32no—
156#810—62no—
157#810C2×D311yescharacteristic
158#807—32no—
159#807—32no—
160#807C2×D311yescharacteristic
161C4⋊(C3⋊C8)—31no—
162C4⋊(C3⋊C8)—31no—
163C4⋊(C3⋊C8)—61no—
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3×D3C2×D412yes—
166C32×Q8—21no—
167C32×Q8—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—22no—
174#634—22no—
175#634—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C3×D12Q1614yescomplemented
181C3×C4×D3—22no—
182C3×C4×D3—22no—
183C3×C4×D3—82no—
184C3×Dic6—21no—
185C3×Dic6—81no—
186C3×Dic6#4112yes—
187#627—44no—
188D3×Dic3—44no—
189C3⋊(C3⋊C8)—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192#554—31no—
193D4×Q8—91no—
194#487—91no—
195#484—92no—
196#477—91no—
197#467—92no—
198#462—91no—
199#451—92no—
200C4×Q16—31no—
201C8×D4—91no—
202C2×#103—92no—
203C2×C3×Q8—21no—
204C2×C3×Q8—31no—
205C2×C3×Q8—61no—
206C2×C3×Q8C22×D311yescharacteristic
207C2×C3×Q8C22×D311yescharacteristic
208C2×C3×D4—31no—
209C22×C3×C4—32no—
210C22×C3×C4—62no—
211C22×Dic3—62no—
212D3×Q8—64no—
213D3×Q8—122no—
214C2×D12#6711yescharacteristic
215C2×C4×D3—22no—
216C2×C4×D3—62no—
217C2×C4×D3C22×D312yes—
218C2×Dic6—21no—
219C2×Dic6—32no—
220C2×Dic6—32no—
221C2×Dic6—62no—
222C2×Dic6—64no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—122no—
226C2×Dic6C22×D311yescharacteristic
227C3×Q16—62no—
228C2×C3×C8—31no—
229C2×C3×C8—31no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—41no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—62no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4C22×D311yescharacteristic
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C22⋊C4—32no—
244C3×C22⋊C4—62no—
245C3×C42—21no—
246C3×C42—21no—
247C3×C42—21no—
248C3×C42—41no—
249C3×C42—61no—
250C3×C42C22×D311yescharacteristic
251C3×C42C22×D311yescharacteristic
252#217—62no—
253#216—22no—
254#216—122no—
255#216—122no—
256#216—124no—
257(C2×D3)⋊C4—22no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4#6712yes—
260C4⋊Dic3—21no—
261C4⋊Dic3—61no—
262C4⋊Dic3—61no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3—62no—
266C4⋊Dic3—121no—
267C4⋊Dic3—121no—
268C4⋊Dic3#6711yescharacteristic
269C4⋊Dic3C22×D311yescharacteristic
270C4⋊Dic3C22×D312yes—
271Dic3⋊C4—21no—
272Dic3⋊C4—22no—
273Dic3⋊C4—22no—
274Dic3⋊C4—62no—
275C4×Dic3—21no—
276C2×C3⋊C8—32no—
277C2×C3⋊C8—32no—
278C2×C3⋊C8—62no—
279C2×C3⋊C8—122no—
280C2×C3⋊C8C22×D311yescharacteristic
281C2×C3⋊C8C22×D311yescharacteristic
282D3×C8—122no—
283C22×C32C22×D411yescharacteristic
284C2×C3×D3—22no—
285C2×C3×D3—22no—
286C2×C3×D3C2×Q1614yes—
287C32×C4—21no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4C2×Q1612yes—
291C32×C4C2×#4111yescharacteristic
292C32×C4H(5,𝔽2)11yescharacteristic
293C3⋊Dic3—42no—
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C22×Q8—92no—
299C2×Q16—31no—
300C2×Q16—92no—
301C22×C8—92no—
302C4⋊Q8—31no—
303C4⋊Q8—91no—
304C4⋊Q8—181no—
305#125—61no—
306C22⋊Q8—32no—
307C22⋊Q8—62no—
308C22⋊Q8—92no—
309C22⋊Q8—182no—
310C4×Q8—31no—
311C4×Q8D3211yescharacteristic
312C4×D4—31no—
313C4×D4—61no—
314C4×D4—181no—
315C2×C4⋊C4—32no—
316#107—31no—
317#107—92no—
318C4⋊C8—91no—
319#103—31no—
320#103—31no—
321#103—92no—
322#103—92no—
323#103—92no—
324#103—92no—
325C22⋊C8—92no—
326C4×C8—31no—
327C23×C3—32no—
328C22×D3C2×#6712yes—
329C3×Q8—22no—
330C3×Q8—21no—
331C3×Q8—21no—
332C3×Q8—21no—
333C3×Q8—21no—
334C3×Q8—32no—
335C3×Q8—41no—
336C3×Q8—61no—
337C3×Q8—241no—
338C3×D4—34no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—32no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—61no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—61no—
354C2×C3×C4—242no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—22no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—122no—
367C2×Dic3—124no—
368C2×Dic3C2×#6712yes—
369D12#21614yescomplemented
370C4×D3—22no—
371C4×D3—22no—
372C4×D3—82no—
373C4×D3—124no—
374Dic6—21no—
375Dic6—62no—
376Dic6—62no—
377Dic6—62no—
378Dic6—62no—
379Dic6—81no—
380Dic6—122no—
381Dic6—122no—
382Dic6—124no—
383Dic6—124no—
384Dic6#23512yes—
385C3×C8—61no—
386C3×C8—61no—
387C3⋊C8—21no—
388C3⋊C8—21no—
389C3⋊C8—62no—
390C3⋊C8—62no—
391C3⋊C8—122no—
392C2×C32#54611yescharacteristic
393C2×C32C22×Q1611yescharacteristic
394C2×C32#57711yescharacteristic
395C3×D3—24no—
396C2×Q8—31no—
397C2×Q8—61no—
398C2×Q8—92no—
399C2×Q8—182no—
400C2×Q8—184no—
401C2×Q8—362no—
402C2×Q8C2×D3211yescharacteristic
403C2×D4—31no—
404C22×C4—32no—
405C22×C4—62no—
406C22×C4—182no—
407Q16—62no—
408Q16—362no—
409C2×C8—31no—
410C2×C8—31no—
411C2×C8—92no—
412C2×C8—362no—
413C4⋊C4—21no—
414C4⋊C4—31no—
415C4⋊C4—31no—
416C4⋊C4—32no—
417C4⋊C4—62no—
418C4⋊C4—62no—
419C4⋊C4—61no—
420C4⋊C4—61no—
421C4⋊C4—182no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4C2×D3211yescharacteristic
425C22⋊C4—32no—
426C22⋊C4—62no—
427C22⋊C4—182no—
428C42—21no—
429C42—61no—
430C42C2×D3211yescharacteristic
431C22×C3—21no—
432C22×C3—34no—
433C22×C3—62no—
434C22×C3—62no—
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C22×#6711yescharacteristic
437C2×D3—22no—
438C2×D3—22no—
439C2×D3C2×#21614yes—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—22no—
445C3×C4—41no—
446C3×C4—42no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4—41no—
450C3×C4—41no—
451C3×C4—62no—
452C3×C4—62no—
453C3×C4—81no—
454C3×C4—122no—
455C3×C4—121no—
456C3×C4D3×Q1612yes—
457C3×C4C2×#21612yes—
458C3×C4C2×#23511yescharacteristic
459C3×C4D3×#4111yescharacteristic
460C3×C4#100911yescharacteristic
461C3×C4#100911yescharacteristic
462Dic3—22no—
463Dic3—22no—
464Dic3—41no—
465Dic3—42no—
466Dic3—122no—
467Dic3—122no—
468Dic3—242no—
469C32#329911yescharacteristic, complemented, Sylow
470C23—32no—
471Q8—21no—
472Q8—21no—
473Q8—32no—
474Q8—61no—
475Q8—182no—
476Q8—182no—
477Q8—241no—
478Q8—364no—
479D4—34no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—32no—
483C2×C4—61no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—182no—
489C2×C4—242no—
490C2×C4—364no—
491C2×C4D3×#6711yescharacteristic
492C2×C4D3×#6711yescharacteristic
493C2×C4C22×D3211yescharacteristic
494C8—61no—
495C8—61no—
496C8—182no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—64no—
501C2×C3#555011yescharacteristic
502C2×C3C2×D3×Q1611yescharacteristic
503C2×C3#577011yescharacteristic
504C2×C3C22×#21611yescharacteristic
505C2×C3#582911yescharacteristic
506C2×C3#583611yescharacteristic
507D3—24no—
508C22—34no—
509C22—62no—
510C22—62no—
511C22C2×D3×#6711yescharacteristic
512C4—21no—
513C4—41no—
514C4—41no—
515C4—62no—
516C4—62no—
517C4—122no—
518C4—121no—
519C4—362no—
520C4D3×#21612yes—
521C4D3×#23511yescharacteristic
522C4#6430811yescharacteristic
523C3—21no—
524C3#7973511yescharacteristic, complemented
525C3#8364011yescharacteristic, complemented
526C2—64no—
527C2#1059506711yescharacteristic
528C2C2×D3×#21611yescharacteristic
529C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC4×Q8D32
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #10592730C2semidirect
4. C3×C4×#216C2semidirect
5. #10591653C2semidirect
6. #10591596C2semidirect
7. D3×#810C2semidirect
8. #10590427C2semidirect
10. #10590310C2semidirect
11. #10590288C2semidirect
56. C4×#216D3semidirect
180. C3×D12Q16semidirect
369. D12#216semidirect
469. C32#3299semidirect
524. C3#79735semidirect
525. C3#83640semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
Dic6×D122
#105927302
C3×C4×#2162
#105916532
#105915962
D3×#8102
#105904272
C3⋊C8×D122
#105903102
#105902882
#836403
#797353