Finite Group Databasebeta

← C3⋊D3×#440 #11860030

Subgroups — C3⋊D3×#440 #11860030

Order 1152.

1632 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×C3⋊D3C211yesmaximal, characteristic
2C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
3C4×D4×C3⋊D3C211yesmaximal, characteristic
4C32×#440C211yesmaximal, characteristic, complemented
5#10592863C211yesmaximal, characteristic, complemented
6#10592725C211yesmaximal, characteristic, complemented
7#10592717C211yesmaximal, characteristic, complemented
8#10592588C211yesmaximal, characteristic, complemented
9C3⋊D3×#107C211yesmaximal, characteristic, complemented
10#10592516C211yesmaximal, characteristic, complemented
11C3⋊D3×#103C211yesmaximal, characteristic, complemented
12C3⋊D3×#102C211yesmaximal, characteristic
13#10592456C211yesmaximal, characteristic, complemented
14#10592409C211yesmaximal, characteristic, complemented
15C3⋊D3×#97C211yesmaximal, characteristic, complemented
16D3×#440—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C2×D4×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3—21no—
20C2×C32×SD16C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25D4×C3⋊Dic3C2211yescharacteristic
26C2×#3754C2211yescharacteristic
27C4×#638—21no—
28SD16×C3⋊D3C418yescomplemented
29C2×#3744C2211yescharacteristic
30C2×C8×C3⋊D3C2211yescharacteristic
31C2×C8×C3⋊D3C2211yescharacteristic
32#64102C2211yescharacteristic
33C4⋊C4×C3⋊D3—21no—
34C4⋊C4×C3⋊D3C2211yescharacteristic
35C4⋊C4×C3⋊D3C2211yescharacteristic
36#64096—21no—
37#64096C2211yescharacteristic, complemented
38#64090—21no—
39C22⋊C4×C3⋊D3—21no—
40C4×C4⋊(C3⋊D3)C2211yescharacteristic
41C42×C3⋊D3—21no—
42C42×C3⋊D3C2211yescharacteristic
43C4×#634—21no—
44C4×#634C2211yescharacteristic, complemented
45C32×#107C2211yescharacteristic, complemented
46C32×#103C2211yescharacteristic, complemented
47C32×#102C2211yescharacteristic
48C32×#97C2211yescharacteristic, complemented
49#63662C2211yescharacteristic, complemented
50#63659C2211yescharacteristic
51#63648C2211yescharacteristic
52#63645C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63642C2211yescharacteristic, complemented
55#63642C2211yescharacteristic, complemented
56#63637C2211yescharacteristic, complemented
57#63636C2211yescharacteristic
58#63634C2211yescharacteristic, complemented
59#63634C2211yescharacteristic, complemented
60#63630C2211yescharacteristic, complemented
61C2×D3×SD16—34no—
62C4×D3×Q8—34no—
63C4×D3×D4—34no—
64C3×#440D314yescomplemented
65#5164—34no—
66#5026—34no—
67#5018—34no—
68#4889—34no—
69D3×#107—34no—
70#4817—34no—
71D3×#103—34no—
72D3×#102—34no—
73#4757—34no—
74#4710—34no—
75D3×#97—34no—
76C23×C3⋊D3—21no—
77C2×C32×Q8C2311yescharacteristic
78C2×C32×D4C2311yescharacteristic
79C22×C32×C4—21no—
80C2×#638—21no—
81C22×C3⋊Dic3—21no—
82Q8×C3⋊D3—22no—
83Q8×C3⋊D3C2×C414yescomplemented
84D4×C3⋊D3—22no—
85D4×C3⋊D3C2×C414yes—
86C2×C4⋊(C3⋊D3)C2311yescharacteristic
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3—44no—
93C2×C4×C3⋊D3D411yescharacteristic
94C2×C4×C3⋊D3D411yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×#634—21no—
97C2×#634C2311yescharacteristic
98C32×SD16C2×C414yescomplemented
99C2×C32×C8C2311yescharacteristic
100C2×C32×C8C2311yescharacteristic
101C32×C4⋊C4—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C32×C22⋊C4—21no—
105C32×C42—21no—
106C32×C42C2311yescharacteristic
107#3757—21no—
108#3755C2×C414yescomplemented
109#3754C2×C414yescomplemented
110#3752—21no—
111#3752—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3D411yescharacteristic
123C4×C3⋊Dic3D411yescharacteristic
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3744C2×C414yescomplemented
128C8×C3⋊D3—22no—
129C8×C3⋊D3C2×C414yescomplemented
130C2×#440—91noSylow
131C2×D3×Q8—34no—
132C2×D3×D4—34no—
133C22×C4×D3—64no—
134C2×C3×SD16C2×D314yes—
135C3×C4×Q8C2×D314yescomplemented
136C3×C4×D4C2×D314yes—
137Q8×Dic3—34no—
138C2×#215—34no—
139D4×Dic3—34no—
140C2×#214—34no—
141C4×#67—64no—
142D3×SD16—332no—
143C2×#204—34no—
144C2×D3×C8—34no—
145C2×D3×C8—34no—
146#893—34no—
147D3×C4⋊C4—34no—
148D3×C4⋊C4—34no—
149D3×C4⋊C4—64no—
150#887—34no—
151#887—64no—
152#67⋊C4—64no—
153D3×C22⋊C4—64no—
154C4×D12—34no—
155C42×D3—34no—
156C42×D3—64no—
157C4×Dic6—34no—
158C4×Dic6—64no—
159C3×#107C2×D314yescomplemented
160C3×#103C2×D314yescomplemented
161C3×#102C2×D314yes—
162C3×#97C2×D314yescomplemented
163#835—34no—
164#832—34no—
165#821—34no—
166#818—34no—
167#816—34no—
168#815—34no—
169#815—34no—
170#810—34no—
171#809—34no—
172#807—34no—
173#807—34no—
174#803—34no—
175C23×C32—21no—
176C22×C3⋊D3—21no—
177C22×C3⋊D3—24no—
178C22×C3⋊D3—42no—
179C22×C3⋊D3—42no—
180C22×C3⋊D3C2×D411yescharacteristic
181C32×Q8—21no—
182C32×Q8C22×C412yescomplemented
183C32×D4—21no—
184C32×D4C22×C412yes—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—42no—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2411yescharacteristic
192#638—24no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—42no—
197C2×C3⋊Dic3C2×D411yescharacteristic
198C2×C3⋊Dic3C2×D411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C4⋊(C3⋊D3)—21no—
201C4⋊(C3⋊D3)C22×C412yes—
202C4×C3⋊D3—24no—
203C4×C3⋊D3—22no—
204C4×C3⋊D3—22no—
205C4×C3⋊D3—42no—
206C4×C3⋊D3—42no—
207C4×C3⋊D3—42no—
208C4×C3⋊D3—42no—
209C4×C3⋊D3C22×C412yes—
210C4×C3⋊D3#4112yes—
211#634—21no—
212#634—24no—
213#634C22×C412yescomplemented
214C32×C8—21no—
215C32×C8C22×C412yescomplemented
216C3⋊(C3⋊C8)—21no—
217C3⋊(C3⋊C8)C22×C412yescomplemented
218C22×SD16—91no—
219C2×C4×Q8—91no—
220C2×C4×D4—91no—
221#440—91no—
222#440—91no—
223#440—91no—
224#440—91no—
225#440—91no—
226#440—91no—
227#440—91no—
228#440C3⋊D311yescharacteristic, direct product factor
229C2×#107—91no—
230C2×#103—91no—
231C2×#102—91no—
232C2×#97—91no—
233C23×D3—64no—
234C2×C3×Q8C22×D314yes—
235C2×C3×D4C22×D314yes—
236C22×C3×C4—24no—
237C2×#67—64no—
238C22×Dic3—64no—
239D3×Q8—316no—
240D3×Q8—68no—
241D3×D4—316no—
242D3×D4—68no—
243C2×D12—34no—
244C2×C4×D3—34no—
245C2×C4×D3—34no—
246C2×C4×D3—34no—
247C2×C4×D3—64no—
248C2×C4×D3—64no—
249C2×C4×D3—64no—
250C2×C4×D3—64no—
251C2×C4×D3—64no—
252C2×C4×D3—1216no—
253C2×Dic6—34no—
254C2×Dic6—64no—
255C3×SD16C4×D3116yescomplemented
256C2×C3×C8C22×D314yes—
257C2×C3×C8C22×D314yes—
258C3×C4⋊C4—24no—
259C3×C4⋊C4C22×D314yes—
260C3×C4⋊C4C22×D314yes—
261C3×C22⋊C4—24no—
262C3×C42—24no—
263C3×C42C22×D314yes—
264#217—64no—
265#215—316no—
266#214—316no—
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4—64no—
269C4⋊Dic3—34no—
270C4⋊Dic3—34no—
271C4⋊Dic3—64no—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274Dic3⋊C4—64no—
275Dic3⋊C4—64no—
276C4×Dic3—34no—
277C4×Dic3—34no—
278C4×Dic3—34no—
279C4×Dic3—64no—
280C4×Dic3—64no—
281C4×Dic3—64no—
282C2×C3⋊C8—34no—
283C2×C3⋊C8—34no—
284#204—316no—
285D3×C8—316no—
286D3×C8—68no—
287C22×C32—22no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32C22×D411yescharacteristic
291C2×C3⋊D3—22no—
292C2×C3⋊D3—41no—
293C2×C3⋊D3—41no—
294C2×C3⋊D3—48no—
295C2×C3⋊D3C4×D412yes—
296C2×C3⋊D3AGL(1,ℤ/8)12yes—
297C2×C3⋊D3#13712yes—
298C32×C4—22no—
299C32×C4—21no—
300C32×C4—21no—
301C32×C4—41no—
302C32×C4—41no—
303C32×C4C23×C411yescharacteristic
304C32×C4C2×#4111yescharacteristic
305C3⋊Dic3—22no—
306C3⋊Dic3—21no—
307C3⋊Dic3—21no—
308C3⋊Dic3—41no—
309C3⋊Dic3—41no—
310C3⋊Dic3C4×D412yes—
311C22×Q8—91no—
312C22×D4—91no—
313C23×C4—181no—
314C2×SD16—91no—
315C2×SD16—91no—
316C2×SD16—98no—
317C2×SD16—91no—
318C2×SD16C2×C3⋊D311yescharacteristic
319C22×C8—91no—
320C22×C8—91no—
321C4×Q8—91no—
322C4×Q8—91no—
323C4×Q8—91no—
324C4×Q8—181no—
325C4×Q8—181no—
326C4×Q8C2×C3⋊D311yescharacteristic, complemented
327C4×D4—91no—
328C4×D4—91no—
329C4×D4—91no—
330C4×D4—181no—
331C4×D4—181no—
332C4×D4C2×C3⋊D311yescharacteristic
333C2×C4⋊C4—91no—
334C2×C4⋊C4—91no—
335C2×C4⋊C4—181no—
336C2×C22⋊C4—181no—
337C2×C42—91no—
338C2×C42—181no—
339#107—91no—
340#107—91no—
341#107—91no—
342#107C2×C3⋊D311yescharacteristic, complemented
343#103—91no—
344#103—91no—
345#103—91no—
346#103C2×C3⋊D311yescharacteristic, complemented
347#102—91no—
348#102—91no—
349#102—91no—
350#102C2×C3⋊D311yescharacteristic
351#97—91no—
352#97—91no—
353#97—91no—
354#97C2×C3⋊D311yescharacteristic, complemented
355C23×C3—24no—
356C22×D3—34no—
357C22×D3—616no—
358C22×D3—64no—
359C22×D3—128no—
360C22×D3—128no—
361C3×Q8—24no—
362C3×Q8C2×C4×D318yescomplemented
363C3×D4—24no—
364C3×D4C2×C4×D318yes—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—48no—
369C2×C3×C4D3×D414yes—
370C2×C3×C4D3×D414yes—
371C2×C3×C4C23×D314yes—
372#67—616no—
373C2×Dic3—34no—
374C2×Dic3—34no—
375C2×Dic3—34no—
376C2×Dic3—64no—
377C2×Dic3—64no—
378C2×Dic3—64no—
379C2×Dic3—128no—
380D12—38no—
381D12—64no—
382C4×D3—38no—
383C4×D3—38no—
384C4×D3—68no—
385C4×D3—68no—
386C4×D3—616no—
387C4×D3—128no—
388C4×D3—128no—
389C4×D3—128no—
390C4×D3—128no—
391Dic6—38no—
392Dic6—616no—
393Dic6—64no—
394C3×C8—24no—
395C3×C8C2×C4×D318yescomplemented
396C3⋊C8—38no—
397C3⋊C8—64no—
398C2×C32—42no—
399C2×C32C2×C4×D411yescharacteristic
400C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
401C2×C32C2×#13711yescharacteristic
402C3⋊D3—42no—
403C3⋊D3#44014yesdirect product factor
404C24—181no—
405C2×Q8—94no—
406C2×Q8—91no—
407C2×Q8—181no—
408C2×Q8—182no—
409C2×Q8C22×C3⋊D311yescharacteristic
410C2×D4—94no—
411C2×D4—91no—
412C2×D4—182no—
413C2×D4—181no—
414C2×D4C22×C3⋊D311yescharacteristic
415C22×C4—21no—
416C22×C4—91no—
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—181no—
420C22×C4—181no—
421C22×C4—181no—
422C22×C4—181no—
423C22×C4—181no—
424C22×C4—181no—
425C22×C4—364no—
426SD16—94no—
427SD16—94no—
428SD16—94no—
429SD16C4×C3⋊D314yescomplemented
430C2×C8—91no—
431C2×C8—94no—
432C2×C8—91no—
433C2×C8—182no—
434C2×C8C22×C3⋊D311yescharacteristic
435C2×C8C22×C3⋊D311yescharacteristic
436C4⋊C4—21no—
437C4⋊C4—91no—
438C4⋊C4—91no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C4⋊C4—181no—
442C4⋊C4—181no—
443C4⋊C4—181no—
444C4⋊C4C22×C3⋊D311yescharacteristic
445C4⋊C4C22×C3⋊D311yescharacteristic
446C22⋊C4—21no—
447C22⋊C4—181no—
448C22⋊C4—181no—
449C22⋊C4—181no—
450C42—21no—
451C42—91no—
452C42—91no—
453C42—91no—
454C42—181no—
455C42—181no—
456C42—181no—
457C42C22×C3⋊D311yescharacteristic
458C22×C3—28no—
459C22×C3—44no—
460C22×C3—44no—
461C22×C3C2×D3×D414yes—
462C2×D3—38no—
463C2×D3—38no—
464C2×D3—38no—
465C2×D3—68no—
466C2×D3—1232no—
467C2×D3—124no—
468C2×D3—124no—
469C3×C4—24no—
470C3×C4—24no—
471C3×C4—28no—
472C3×C4—44no—
473C3×C4—44no—
474C3×C4C22×C4×D314yes—
475C3×C4D3×#4114yes—
476Dic3—38no—
477Dic3—64no—
478Dic3—64no—
479Dic3—68no—
480Dic3—124no—
481Dic3—124no—
482C32C2×#44011yescharacteristic, complemented, Sylow
483C23—21no—
484C23—91no—
485C23—184no—
486C23—181no—
487C23—362no—
488C23—362no—
489Q8—21no—
490Q8—92no—
491Q8—184no—
492Q8—181no—
493Q8C2×C4×C3⋊D312yescomplemented
494D4—21no—
495D4—92no—
496D4—184no—
497D4—181no—
498D4C2×C4×C3⋊D312yes—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—42no—
503C2×C4—91no—
504C2×C4—92no—
505C2×C4—92no—
506C2×C4—91no—
507C2×C4—91no—
508C2×C4—182no—
509C2×C4—182no—
510C2×C4—184no—
511C2×C4—181no—
512C2×C4—181no—
513C2×C4—181no—
514C2×C4—362no—
515C2×C4—362no—
516C2×C4—362no—
517C2×C4—362no—
518C2×C4—362no—
519C2×C4D4×C3⋊D311yescharacteristic
520C2×C4D4×C3⋊D311yescharacteristic
521C2×C4C23×C3⋊D311yescharacteristic
522C8—21no—
523C8—92no—
524C8—181no—
525C8C2×C4×C3⋊D312yescomplemented
526C2×C3—48no—
527C2×C3C4×D3×D414yes—
528C2×C3D3×AGL(1,ℤ/8)14yes—
529C2×C3D3×#13714yes—
530D3—316no—
531D3—128no—
532C22—22no—
533C22—41no—
534C22—41no—
535C22—92no—
536C22—92no—
537C22—92no—
538C22—182no—
539C22—368no—
540C22—361no—
541C22—361no—
542C22C2×D4×C3⋊D311yescharacteristic
543C4—21no—
544C4—21no—
545C4—22no—
546C4—41no—
547C4—41no—
548C4—92no—
549C4—181no—
550C4—181no—
551C4—182no—
552C4—361no—
553C4—361no—
554C4C22×C4×C3⋊D311yescharacteristic
555C4#41×C3⋊D311yescharacteristic
556C3D3×#44014yescomplemented
557C2—42no—
558C2—94no—
559C2—362no—
560C2C4×D4×C3⋊D311yescharacteristic
561C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
562C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
cosocleC2×C32×C4C24
hypercenter#440C3⋊D3
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×C3⋊D3C2semidirect
4. C32×#440C2semidirect
5. #10592863C2semidirect
6. #10592725C2semidirect
7. #10592717C2semidirect
8. #10592588C2semidirect
9. C3⋊D3×#107C2semidirect
10. #10592516C2semidirect
11. C3⋊D3×#103C2semidirect
13. #10592456C2semidirect
14. #10592409C2semidirect
15. C3⋊D3×#97C2semidirect
21. C32×C4×Q8C22semidirect
23. Q8×C3⋊Dic3C22semidirect
28. SD16×C3⋊D3C4semidirect
37. #64096C22semidirect
44. C4×#634C22semidirect
45. C32×#107C22semidirect
46. C32×#103C22semidirect
48. C32×#97C22semidirect
49. #63662C22semidirect
52. #63645C22semidirect
53. #63643C22semidirect
54. #63642C22semidirect
55. #63642C22semidirect
56. #63637C22semidirect
58. #63634C22semidirect
59. #63634C22semidirect
60. #63630C22semidirect
64. C3×#440D3semidirect
83. Q8×C3⋊D3C2×C4semidirect
98. C32×SD16C2×C4semidirect
108. #3755C2×C4semidirect
109. #3754C2×C4semidirect
127. #3744C2×C4semidirect
129. C8×C3⋊D3C2×C4semidirect
135. C3×C4×Q8C2×D3semidirect
159. C3×#107C2×D3semidirect
160. C3×#103C2×D3semidirect
162. C3×#97C2×D3semidirect
182. C32×Q8C22×C4semidirect
213. #634C22×C4semidirect
215. C32×C8C22×C4semidirect
217. C3⋊(C3⋊C8)C22×C4semidirect
228. #440C3⋊D3direct (N × H)
255. C3×SD16C4×D3semidirect
326. C4×Q8C2×C3⋊D3semidirect
342. #107C2×C3⋊D3semidirect
346. #103C2×C3⋊D3semidirect
354. #97C2×C3⋊D3semidirect
362. C3×Q8C2×C4×D3semidirect
395. C3×C8C2×C4×D3semidirect
403. C3⋊D3#440direct (N × H)
429. SD16C4×C3⋊D3semidirect
482. C32C2×#440semidirect
493. Q8C2×C4×C3⋊D3semidirect
525. C8C2×C4×C3⋊D3semidirect
556. C3D3×#440semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×C3⋊D32
C4×Q8×C3⋊D32
C4×D4×C3⋊D32
C32×#4402
#105928632
#105927252
#105927172
#105925882
C3⋊D3×#1072
#105925162
C3⋊D3×#1032
C3⋊D3×#1022
#105924562
#105924092
C3⋊D3×#972
D3×#4403