Finite Group Databasebeta

← D3×#568⋊C3 #11923316

Subgroups — D3×#568⋊C3 #11923316

Order 1152.

708 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#41⋊C3C211yesmaximal, characteristic
2C3×#568⋊C3C211yesmaximal, characteristic, complemented
3#5819⋊C3C211yesmaximal, characteristic, complemented
4#5750⋊C3C212yesmaximal, complemented
5D3×#131⋊C3C212yesmaximal, complemented
6D3×#568C311yesmaximal, characteristic, complemented
7C2×#568⋊C3—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9D3×#41⋊C3C411yescharacteristic
10D3×#41⋊C3C411yescharacteristic
11D3×#41⋊C3C2211yescharacteristic
12D3×#41⋊C3C2211yescharacteristic
13C2×D3×SL(2,𝔽3)C411yescharacteristic
14C2×C3⋊(#41⋊C3)C411yescharacteristic
15C3×D3×M16—41nomaximal
16C3×#131⋊C3C2212yescomplemented
17C3⋊(#131⋊C3)C2212yescomplemented
18C2×D3×#41C2×C311yescharacteristic
19C22×#41⋊C3—31no—
20C3×#568C2×C311yescharacteristic, complemented
21#5819C2×C311yescharacteristic, complemented
22#5750—32no—
23#5750C2×C312yescomplemented
24D3×#131—32no—
25D3×#131C2×C312yescomplemented
26#5745—31no—
27#5745—31no—
28C2×D3×M16—31no—
29C2×D3×M16—31no—
30#568⋊C3—21no—
31#568⋊C3—31no—
32#568⋊C3—32no—
33#568⋊C3D311yescharacteristic, direct product factor
34C2×#131⋊C3—32no—
35C2×C3×C4×D3—41no—
36C3×#41⋊C3C2×C411yescharacteristic
37C3×#41⋊C3C2311yescharacteristic
38C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
39D3×SL(2,𝔽3)C2×C411yescharacteristic
40D3×SL(2,𝔽3)C2×C411yescharacteristic
41C3⋊(#41⋊C3)C2×C411yescharacteristic
42C3⋊(#41⋊C3)C2×C411yescharacteristic
43C32×M16—41no—
44C3×#208—41no—
45C3×ΓL(1,𝔽25)—42no—
46C3×D3×C8—42no—
47C2×#568—31noSylow
48C2×C3×#41C22×C311yescharacteristic
49D3×#41—31no—
50D3×#41—31no—
51D3×#41—31no—
52D3×#41—31no—
53D3×#41C3×C411yescharacteristic
54D3×#41C3×C411yescharacteristic
55D3×#41C22×C311yescharacteristic
56D3×#41C22×C311yescharacteristic
57C2×#239C3×C411yescharacteristic
58C2×D3×Q8C3×C411yescharacteristic
59C2×#237—31no—
60C2×D3×D4—31no—
61C2×#235—31no—
62C22×C4×D3—31no—
63C2×#41⋊C3—21no—
64C2×#41⋊C3—31no—
65C2×#41⋊C3—31no—
66C2×#41⋊C3—31no—
67C2×#41⋊C3—31no—
68C2×#41⋊C3—31no—
69C2×#41⋊C3C2×D311yescharacteristic
70C22×SL(2,𝔽3)—31no—
71C3×#131—32no—
72C3×#131C22×C312yescomplemented
73C2×C3×M16—31no—
74C2×C3×M16—31no—
75C2×C3×M16—121no—
76#948—32no—
77#948C22×C312yescomplemented
78C2×#208—31no—
79C2×#208—31no—
80#907—34no—
81#907—32no—
82#907—32no—
83D3×M16—32no—
84D3×M16—31no—
85D3×M16—31no—
86D3×M16—31no—
87D3×M16—32no—
88D3×M16—32no—
89D3×M16—32no—
90D3×M16—32no—
91D3×M16A411yescharacteristic
92#901—34no—
93#901—32no—
94#901—32no—
95C2×ΓL(1,𝔽25)—32no—
96C2×ΓL(1,𝔽25)—32no—
97C2×D3×C8—32no—
98C2×D3×C8—32no—
99#131⋊C3—22no—
100#131⋊C3—32no—
101#131⋊C3C2×D312yescomplemented
102C22×C3×D3—41no—
103C2×C32×C4—41no—
104C2×C3×Dic3—41no—
105C3×C4×D3—41no—
106C3×C4×D3—41no—
107C3×C4×D3—41no—
108C3×C4×D3—41no—
109C3×SL(2,𝔽3)C22×C411yescharacteristic
110C32×C8—42no—
111C3×C3⋊C8—42no—
112C22×#41—31no—
113#568—31no—
114#568—32no—
115#568—91no—
116#568—91no—
117#568—92no—
118#568C3×D311yescharacteristic, complemented
119C2×#131—32no—
120C2×#131—92no—
121C22×M16—91no—
122C22×M16—91no—
123C23×D3—31no—
124C3×#41—31no—
125C3×#41—31no—
126C3×#41C2×C3×C411yescharacteristic
127C3×#41C23×C311yescharacteristic
128C2×C3×Q8C2×C3×C411yescharacteristic
129C2×C3×D4—31no—
130C22×C3×C4—31no—
131C22×C3×C4—121no—
132C2×#67—32no—
133C22×Dic3—31no—
134#239—31no—
135#239—31no—
136#239C2×C3×C411yescharacteristic
137#239C2×C3×C411yescharacteristic
138D3×Q8—31no—
139D3×Q8—31no—
140D3×Q8C2×C3×C411yescharacteristic
141D3×Q8C2×C3×C411yescharacteristic
142#237—32no—
143#237—32no—
144#237—31no—
145#237—31no—
146#237—31no—
147#237—31no—
148D3×D4—31no—
149D3×D4—31no—
150D3×D4—31no—
151D3×D4—31no—
152D3×D4—32no—
153D3×D4—32no—
154#235—32no—
155#235—32no—
156#235—31no—
157#235—31no—
158#235—31no—
159#235—31no—
160C2×D12—31no—
161C2×C4×D3—31no—
162C2×C4×D3—31no—
163C2×C4×D3—31no—
164C2×C4×D3—31no—
165C2×C4×D3—31no—
166C2×C4×D3—31no—
167C2×C4×D3—31no—
168C2×C4×D3—31no—
169C2×C4×D3—31no—
170C2×C4×D3—31no—
171C2×C4×D3—31no—
172C2×C4×D3C2×A411yescharacteristic
173C2×Dic6—31no—
174#41⋊C3—21no—
175#41⋊C3—21no—
176#41⋊C3—31no—
177#41⋊C3—31no—
178#41⋊C3C4×D311yescharacteristic
179#41⋊C3C22×D311yescharacteristic
180C2×SL(2,𝔽3)—21no—
181C2×SL(2,𝔽3)—31no—
182C2×SL(2,𝔽3)—31no—
183C2×SL(2,𝔽3)C4×D311yescharacteristic
184C3×M16—31no—
185C3×M16—32no—
186C3×M16—32no—
187C3×M16—41no—
188C3×M16—81no—
189C3×M16—122no—
190C3×M16—121no—
191C3×M16C2×A411yescharacteristic
192C2×C3×C8—32no—
193C2×C3×C8—32no—
194C2×C3×C8—122no—
195#208—31no—
196#208—32no—
197#208—32no—
198#208C2×A411yescharacteristic
199C2×C3⋊C8—32no—
200C2×C3⋊C8—32no—
201ΓL(1,𝔽25)—34no—
202ΓL(1,𝔽25)—32no—
203ΓL(1,𝔽25)—32no—
204ΓL(1,𝔽25)—32no—
205ΓL(1,𝔽25)C2×A412yes—
206D3×C8—34no—
207D3×C8—32no—
208D3×C8—32no—
209D3×C8—32no—
210D3×C8C2×A412yes—
211C22×C32—41no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C2×C3×D3—82no—
215C32×C4—41no—
216C32×C4—41no—
217C3×Dic3—41no—
218C3×Dic3—41no—
219C2×#41—31no—
220C2×#41—31no—
221C2×#41—31no—
222C2×#41—31no—
223C2×#41—31no—
224C2×#41—91no—
225C2×#41—91no—
226C2×#41—91no—
227C2×#41—91no—
228C2×#41—91no—
229C2×#41—91no—
230C2×#41C2×C3×D311yescharacteristic
231C22×Q8—31no—
232C22×D4—91no—
233C23×C4—91no—
234#131—32no—
235#131—32no—
236#131—94no—
237#131—92no—
238#131—92no—
239#131—94no—
240#131—92no—
241#131—92no—
242#131—92no—
243#131C2×C3×D312yescomplemented
244C2×M16—31no—
245C2×M16—31no—
246C2×M16—31no—
247C2×M16—92no—
248C2×M16—92no—
249C2×M16—92no—
250C2×M16—91no—
251C2×M16—92no—
252C2×M16—91no—
253C2×M16—91no—
254C2×M16—92no—
255C2×M16—92no—
256C2×M16—91no—
257C2×M16—91no—
258C2×M16—92no—
259C22×C8—92no—
260C22×C8—92no—
261C23×C3—31no—
262C23×C3—121no—
263C22×D3—31no—
264C22×D3—31no—
265C22×D3—31no—
266C22×D3—31no—
267C22×D3—31no—
268C22×D3—122no—
269C22×D3C4×A411yescharacteristic
270C3×Q8—31no—
271C3×Q8C22×C3×C411yescharacteristic
272C3×D4—31no—
273C3×D4—31no—
274C3×D4—32no—
275C2×C3×C4—31no—
276C2×C3×C4—31no—
277C2×C3×C4—31no—
278C2×C3×C4—31no—
279C2×C3×C4—31no—
280C2×C3×C4—41no—
281C2×C3×C4—81no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4C22×A411yescharacteristic
288#67—32no—
289#67—32no—
290#67—32no—
291#67—32no—
292C2×Dic3—31no—
293C2×Dic3—31no—
294C2×Dic3—31no—
295C2×Dic3—31no—
296C2×Dic3—31no—
297C2×Dic3C4×A411yescharacteristic
298D12—31no—
299D12—31no—
300D12—32no—
301C4×D3—31no—
302C4×D3—31no—
303C4×D3—31no—
304C4×D3—31no—
305C4×D3—31no—
306C4×D3—31no—
307C4×D3—31no—
308C4×D3—31no—
309C4×D3—31no—
310C4×D3—31no—
311C4×D3—31no—
312C4×D3—31no—
313C4×D3C4×A411yescharacteristic
314C4×D3C4×A411yescharacteristic
315C4×D3C22×A411yescharacteristic
316C4×D3C22×A411yescharacteristic
317Dic6—32no—
318Dic6—31no—
319Dic6—31no—
320SL(2,𝔽3)—21no—
321SL(2,𝔽3)C2×C4×D311yescharacteristic
322C3×C8—32no—
323C3×C8—42no—
324C3×C8—82no—
325C3×C8—122no—
326C3×C8C22×A412yes—
327C3⋊C8—32no—
328C3⋊C8C22×A412yes—
329C2×C32—41no—
330C2×C32—81no—
331C3×D3—42no—
332C3×D3—81no—
333C24—91no—
334#41—31no—
335#41—31no—
336#41—31no—
337#41—31no—
338#41—92no—
339#41—92no—
340#41—91no—
341#41—91no—
342#41—91no—
343#41—91no—
344#41—92no—
345#41—92no—
346#41—91no—
347#41—91no—
348#41—91no—
349#41—91no—
350#41—91no—
351#41—91no—
352#41C3×C4×D311yescharacteristic
353#41C22×C3×D311yescharacteristic
354C2×Q8—31no—
355C2×Q8—31no—
356C2×Q8—91no—
357C2×Q8—91no—
358C2×Q8—91no—
359C2×Q8C3×C4×D311yescharacteristic
360C2×D4—31no—
361C2×D4—91no—
362C2×D4—91no—
363C2×D4—91no—
364C2×D4—91no—
365C2×D4—91no—
366C2×D4—92no—
367C2×D4—92no—
368C2×D4—92no—
369C22×C4—31no—
370C22×C4—31no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—91no—
382C22×C4—91no—
383M16—31no—
384M16—31no—
385M16—32no—
386M16—32no—
387M16—32no—
388M16—92no—
389M16—92no—
390M16—92no—
391M16—94no—
392M16—91no—
393M16—92no—
394M16—92no—
395M16D3×A411yescharacteristic
396C2×C8—32no—
397C2×C8—32no—
398C2×C8—32no—
399C2×C8—92no—
400C2×C8—92no—
401C2×C8—92no—
402C2×C8—94no—
403C2×C8—92no—
404C2×C8—92no—
405C22×C3—31no—
406C22×C3—31no—
407C22×C3—41no—
408C22×C3—81no—
409C22×C3—121no—
410C22×C3—121no—
411C22×C3—121no—
412C22×C3—242no—
413C22×C3C2×C4×A411yescharacteristic
414C2×D3—22no—
415C2×D3—31no—
416C2×D3—31no—
417C2×D3—62no—
418C2×D3—62no—
419C2×D3—121no—
420C2×D3—121no—
421C2×D3—121no—
422C2×D3C2×C4×A411yescharacteristic
423C2×D3C2×C4×A411yescharacteristic
424C3×C4—31no—
425C3×C4—31no—
426C3×C4—41no—
427C3×C4—41no—
428C3×C4—81no—
429C3×C4—81no—
430C3×C4—121no—
431C3×C4—121no—
432C3×C4C2×C4×A411yescharacteristic
433C3×C4C23×A411yescharacteristic
434Dic3—31no—
435Dic3—31no—
436Dic3C2×C4×A411yescharacteristic
437Dic3C2×C4×A411yescharacteristic
438C32—41noSylow
439C23—31no—
440C23—31no—
441C23—91no—
442C23—91no—
443C23—91no—
444C23—91no—
445C23—91no—
446C23—362no—
447Q8—31no—
448Q8—91no—
449Q8—91no—
450Q8—92no—
451Q8C2×C3×C4×D311yescharacteristic
452D4—31no—
453D4—31no—
454D4—32no—
455D4—91no—
456D4—91no—
457D4—92no—
458D4—92no—
459D4—92no—
460D4—92no—
461D4—92no—
462C2×C4—31no—
463C2×C4—31no—
464C2×C4—31no—
465C2×C4—31no—
466C2×C4—31no—
467C2×C4—31no—
468C2×C4—31no—
469C2×C4—31no—
470C2×C4—31no—
471C2×C4—31no—
472C2×C4—91no—
473C2×C4—91no—
474C2×C4—91no—
475C2×C4—91no—
476C2×C4—91no—
477C2×C4—91no—
478C2×C4—91no—
479C2×C4—91no—
480C2×C4—91no—
481C2×C4—91no—
482C2×C4—91no—
483C2×C4—91no—
484C2×C4—91no—
485C2×C4—91no—
486C2×C4—91no—
487C2×C4—91no—
488C2×C4—91no—
489C2×C4C2×D3×A411yescharacteristic
490C8—32no—
491C8—32no—
492C8—92no—
493C8C2×D3×A412yes—
494C2×C3—21no—
495C2×C3—41no—
496C2×C3—61no—
497C2×C3—61no—
498C2×C3—81no—
499C2×C3—81no—
500C2×C3—122no—
501C2×C3—161no—
502C2×C3—241no—
503C2×C3C22×C4×A411yescharacteristic
504D3—21no—
505D3—61no—
506D3—61no—
507D3#568⋊C312yesdirect product factor
508C22—31no—
509C22—31no—
510C22—31no—
511C22—31no—
512C22—62no—
513C22—91no—
514C22—91no—
515C22—121no—
516C22—182no—
517C22—182no—
518C22—361no—
519C22—361no—
520C22—361no—
521C22C4×D3×A411yescharacteristic
522C4—31no—
523C4—31no—
524C4—31no—
525C4—31no—
526C4—91no—
527C4—91no—
528C4C4×D3×A411yescharacteristic
529C4C22×D3×A411yescharacteristic
530C3—41no—
531C3—81no—
532C3C2×#568⋊C311yescharacteristic, complemented
533C2—21no—
534C2—32no—
535C2—61no—
536C2—61no—
537C2—61no—
538C2—181no—
539C2—181no—
540C2C2×C4×D3×A411yescharacteristic
subgroupG/H
center, FrattiniC4C22×D3×A4
commutator, hypocenterC3×Q8C22×C3×C4
FittingC3×#568C2×C3
socleC2×C3C22×C4×A4
prime radicalC2×D3×#41⋊C3C2
cosocleC3×#41C23×C3
hypercenterM16D3×A4
LCSG ▷ C3×Q8
UCSC1 ◁ C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. C3×#568⋊C3C2semidirect
3. #5819⋊C3C2semidirect
4. #5750⋊C3C2semidirect
5. D3×#131⋊C3C2semidirect
6. D3×#568C3semidirect
16. C3×#131⋊C3C22semidirect
17. C3⋊(#131⋊C3)C22semidirect
20. C3×#568C2×C3semidirect
21. #5819C2×C3semidirect
23. #5750C2×C3semidirect
25. D3×#131C2×C3semidirect
33. #568⋊C3D3direct (N × H)
72. C3×#131C22×C3semidirect
77. #948C22×C3semidirect
101. #131⋊C3C2×D3semidirect
118. #568C3×D3semidirect
243. #131C2×C3×D3semidirect
507. D3#568⋊C3direct (N × H)
532. C3C2×#568⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#41⋊C32
C3×#568⋊C32
#5819⋊C32
#5750⋊C32
D3×#131⋊C32
D3×#5683
C2×#568⋊C33
C3×D3×M164