Finite Group Databasebeta

← D3×#4477 #11796459

Subgroups — D3×#4477 #11796459

Order 1152.

552 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 90 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
1D3×#947C211yesmaximal, characteristic
2C3×D3×#101C211yesmaximal, characteristic, complemented
3D3×#836C211yesmaximal, characteristic, complemented
4#10589343C211yesmaximal, characteristic, complemented
5C3×#4477C211yesmaximal, characteristic, complemented
6#10589183C211yesmaximal, characteristic, complemented
7#10589182C211yesmaximal, characteristic, complemented
8C2×#4477—31nomaximal
9D3×#355—31nomaximal
10C2×C3×D3×Q8C2211yescharacteristic
11C2×D3×D12C411yescharacteristic
12#64156C2211yescharacteristic
13C3×#947C2211yescharacteristic
14C3×D3×M16—21no—
15D3×(C2×D3)⋊C4—21no—
16D3×(C2×D3)⋊C4—21no—
17#63907—21no—
18#63907—21no—
19C4×D3×Dic3C411yescharacteristic
20#63864C411yescharacteristic
21#63863C411yescharacteristic
22D3×#208—21no—
23C32×#101C2211yescharacteristic, complemented
24#63663C2211yescharacteristic, complemented
25C3×#836C2211yescharacteristic, complemented
26C3×#836C2211yescharacteristic, complemented
27C3×#824—21no—
28#63560—21no—
29C2×#947—31no—
30D3×#124—31no—
31C2×C3×#101—31no—
32C2×#836—31no—
33D3×#101—31no—
34D3×#101D311yescharacteristic, complemented
35C3×#355—31no—
36#4542—31no—
37#4477—31no—
38#4477—31no—
39#4477—31no—
40#4477—31no—
41#4477—31no—
42#4477—61no—
43#4477D311yescharacteristic, direct product factor
44C22×D32—21no—
45C2×C32×Q8C2311yescharacteristic
46C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
47C3×D3×Q8—41no—
48C3×D3×Q8—41no—
49C2×C3×D12C2×C411yescharacteristic
50C2×C3×C4×D3C2×C411yescharacteristic
51C2×C3×C4×D3D411yescharacteristic
52C2×C3×C4×D3D411yescharacteristic
53C2×C3×Dic6C2×C411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×C3×Dic6D411yescharacteristic
56C2×#626—21no—
57C2×D3×Dic3—21no—
58D3×D12—41no—
59D3×D12—41no—
60C32×M16—21no—
61#3752—21no—
62#3752—21no—
63C4×C3⋊Dic3C2×C411yescharacteristic
64#3748—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×C4×Dic3C2×C411yescharacteristic
68C3×#208—21no—
69C3×#208—21no—
70C3×ΓL(1,𝔽25)—41no—
71C3×D3×C8—41no—
72#3722—21no—
73#3722—21no—
74(C2×D3)⋊Dic3—21no—
75(C2×D3)⋊Dic3—21no—
76Dic32—21no—
77#3711—41no—
78D3×C3⋊C8—41no—
79C2×#355—91noSylow
80C22×C3×Q8—31no—
81C2×D3×Q8C2×D311yescharacteristic
82C2×D3×D4—31no—
83C22×D12—31no—
84C2×C3×M16—61no—
85C3×#124—31no—
86#947—31no—
87#947—31no—
88#947—31no—
89#947—31no—
90#947—61no—
91#947—61no—
92#947—61no—
93#947C2×D311yescharacteristic
94#936—31no—
95C2×(C2×D3)⋊C4—61no—
96C2×(C2×D3)⋊C4—61no—
97C2×C4×Dic3—31no—
98C2×#208—61no—
99D3×M16—21no—
100D3×M16—61no—
101#885—61no—
102#885—61no—
103D3×C22⋊C4—61no—
104D3×C22⋊C4—61no—
105#875—31no—
106C42×D3—31no—
107C3×#101—21no—
108C3×#101—31no—
109C3×#101—31no—
110C3×#101—61no—
111C3×#101C2×D311yescharacteristic, complemented
112C3×#101C2×D311yescharacteristic, complemented
113#836—31no—
114#836—31no—
115#836—61no—
116#836—61no—
117#836C2×D311yescharacteristic, complemented
118#836C2×D311yescharacteristic, complemented
119#824—21no—
120#824—61no—
121C22×C3⋊D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3C22⋊C411yescharacteristic
124C2×D32—44no—
125C2×D32—41no—
126C2×D32—41no—
127C32×Q8—41no—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C3⋊Dic3—21no—
132C4⋊(C3⋊D3)—41no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3C22⋊C411yescharacteristic
135C2×C3×Dic3C22⋊C411yescharacteristic
136C2×C3×Dic3C22⋊C411yescharacteristic
137C3×D12—41no—
138C3×C4×D3—21no—
139C3×C4×D3—21no—
140C3×C4×D3—21no—
141C3×C4×D3—21no—
142C3×C4×D3—21no—
143C3×C4×D3—21no—
144C3×Dic6—41no—
145C3×Dic6—41no—
146C3×Dic6—41no—
147#626—42no—
148D3×Dic3—42no—
149C32×C8—41no—
150C3⋊(C3⋊C8)—41no—
151C3×C3⋊C8—41no—
152C3×C3⋊C8—41no—
153C2×#124—91no—
154C2×#101—31no—
155C2×#101—91no—
156#355—31no—
157#355—91no—
158#355—91no—
159#355—91no—
160C23×D3—61no—
161C23×D3—61no—
162C2×C3×Q8—21no—
163C2×C3×Q8—31no—
164C2×C3×Q8—31no—
165C2×C3×Q8—31no—
166C2×C3×Q8—121no—
167C2×C3×Q8—121no—
168C2×C3×Q8C22×D311yescharacteristic
169C2×C3×Q8C22×D311yescharacteristic
170C2×C3×D4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—31no—
173C22×C3×C4—31no—
174C2×#67—61no—
175C22×Dic3—61no—
176D3×Q8—41no—
177D3×Q8—41no—
178D3×D4—121no—
179D3×D4—121no—
180C2×D12—31no—
181C2×D12—31no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—121no—
185C2×D12—121no—
186C2×D12C4×D311yescharacteristic
187C2×C4×D3—61no—
188C2×C4×D3C4×D311yescharacteristic
189C2×C4×D3D1211yescharacteristic
190C2×C4×D3#6711yescharacteristic
191C2×Dic6C4×D311yescharacteristic
192C2×Dic6D1211yescharacteristic
193C2×Dic6#6711yescharacteristic
194C3×M16—21no—
195C3×M16—21no—
196C3×M16—41no—
197C3×M16—61no—
198C3×M16—61no—
199C3×M16—121no—
200C2×C3×C8—121no—
201C3×C22⋊C4—61no—
202C3×C22⋊C4—61no—
203C3×C42—31no—
204#217—61no—
205#217—61no—
206(C2×D3)⋊C4—21no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—121no—
219(C2×D3)⋊C4—121no—
220C4×Dic3—31no—
221C4×Dic3—31no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C4×Dic3C4×D311yescharacteristic
226#208—21no—
227#208—21no—
228#208—61no—
229#208—61no—
230#208—121no—
231#208—121no—
232C2×C3⋊C8—121no—
233ΓL(1,𝔽25)—41no—
234ΓL(1,𝔽25)—121no—
235D3×C8—41no—
236D3×C8—121no—
237C22×C32C2×C22⋊C411yescharacteristic
238C2×C3⋊D3—42no—
239C2×C3⋊D3—41no—
240C2×C3×D3—22no—
241C2×C3×D3—42no—
242C2×C3×D3—41no—
243C2×C3×D3#9911yescharacteristic
244C2×C3×D3#9911yescharacteristic
245D32—82no—
246D32—82no—
247C32×C4—21no—
248C32×C4—21no—
249C32×C4—21no—
250C3⋊Dic3—41no—
251C3×Dic3—21no—
252C3×Dic3—21no—
253C3×Dic3—21no—
254C3×Dic3—41no—
255C22×Q8—31no—
256C22×D4—91no—
257C2×M16—61no—
258C2×M16—181no—
259#124—31no—
260#124—91no—
261#124—91no—
262#124—91no—
263#124—181no—
264#124—181no—
265C2×C22⋊C4—181no—
266C2×C22⋊C4—181no—
267C2×C42—91no—
268#101—31no—
269#101—31no—
270#101—61no—
271#101—91no—
272#101—181no—
273#101D3211yescharacteristic, complemented
274C23×C3—31no—
275C23×C3—61no—
276C22×D3—21no—
277C22×D3—61no—
278C22×D3—61no—
279C22×D3—121no—
280C22×D3—124no—
281C22×D3—121no—
282C22×D3—121no—
283C22×D3—124no—
284C22×D3—121no—
285C22×D3—121no—
286C22×D3(C2×D3)⋊C411yescharacteristic
287C3×Q8—41no—
288C3×Q8—41no—
289C3×Q8—81no—
290C3×Q8—121no—
291C3×Q8—121no—
292C3×Q8—121no—
293C3×D4—121no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—31no—
298C2×C3×C4—31no—
299C2×C3×C4—31no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—61no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—61no—
306C2×C3×C4—61no—
307C2×C3×C4C2×C4×D311yescharacteristic
308C2×C3×C4C2×C4×D311yescharacteristic
309C2×C3×C4C2×D1211yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313#67—122no—
314C2×Dic3—21no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—121no—
318C2×Dic3—122no—
319C2×Dic3(C2×D3)⋊C411yescharacteristic
320C2×Dic3(C2×D3)⋊C411yescharacteristic
321C2×Dic3(C2×D3)⋊C411yescharacteristic
322D12—41no—
323D12—121no—
324D12—121no—
325D12—122no—
326D12—241no—
327C4×D3—21no—
328C4×D3—21no—
329C4×D3—21no—
330C4×D3—21no—
331C4×D3—21no—
332C4×D3—21no—
333C4×D3—122no—
334Dic6—41no—
335Dic6—41no—
336Dic6—41no—
337C3×C8—41no—
338C3×C8—41no—
339C3×C8—81no—
340C3×C8—121no—
341C3×C8—121no—
342C3⋊C8—41no—
343C3⋊C8—41no—
344C3⋊C8—121no—
345C3⋊C8—121no—
346C3⋊C8—241no—
347C2×C32—21no—
348C2×C32C2×#9911yescharacteristic
349C3⋊D3—81no—
350C3×D3—21no—
351C3×D3—81no—
352C3×D3#35512yescomplemented
353C24—181no—
354C2×Q8—31no—
355C2×Q8—31no—
356C2×Q8—31no—
357C2×Q8—121no—
358C2×Q8—121no—
359C2×Q8C2×D3211yescharacteristic
360C2×D4—31no—
361C2×D4—91no—
362C2×D4—181no—
363C2×D4—361no—
364C2×D4—361no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—181no—
369M16—21no—
370M16—61no—
371M16—61no—
372M16—121no—
373M16—181no—
374M16—361no—
375C2×C8—121no—
376C2×C8—361no—
377C22⋊C4—61no—
378C22⋊C4—61no—
379C22⋊C4—181no—
380C22⋊C4—181no—
381C22⋊C4—181no—
382C22⋊C4—181no—
383C22⋊C4—181no—
384C22⋊C4—181no—
385C42—31no—
386C42—91no—
387C42—181no—
388C22×C3—21no—
389C22×C3—31no—
390C22×C3—31no—
391C22×C3—62no—
392C22×C3—122no—
393C22×C3—121no—
394C22×C3D3×C22⋊C411yescharacteristic
395C22×C3C2×(C2×D3)⋊C411yescharacteristic
396C2×D3—22no—
397C2×D3—42no—
398C2×D3—41no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—121no—
402C2×D3—121no—
403C2×D3—241no—
404C2×D3—242no—
405C2×D3—242no—
406C2×D3—242no—
407C2×D3—242no—
408C2×D3—242no—
409C2×D3#80611yescharacteristic
410C2×D3#80611yescharacteristic
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—41no—
418C3×C4—41no—
419C3×C4—41no—
420C3×C4—61no—
421C3×C4—61no—
422C3×C4—61no—
423C3×C4—121no—
424Dic3—21no—
425Dic3—21no—
426Dic3—21no—
427Dic3—41no—
428Dic3—121no—
429Dic3—121no—
430Dic3—241no—
431C32C2×#35511yescharacteristic, complemented, Sylow
432C23—31no—
433C23—61no—
434C23—181no—
435C23—361no—
436C23—361no—
437C23—364no—
438Q8—41no—
439Q8—121no—
440Q8—121no—
441Q8—121no—
442D4—121no—
443D4—361no—
444D4—362no—
445C2×C4—31no—
446C2×C4—31no—
447C2×C4—31no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—181no—
456C2×C4—362no—
457C2×C4C4×D3211yescharacteristic
458C2×C4D3×D1211yescharacteristic
459C2×C4D3×#6711yescharacteristic
460C8—41no—
461C8—121no—
462C8—121no—
463C8—361no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—32no—
468C2×C3—41no—
469C2×C3—61no—
470C2×C3—241no—
471C2×C3D3×#9911yescharacteristic
472C2×C3C2×#80611yescharacteristic
473D3—21no—
474D3—81no—
475D3—241no—
476D3—241no—
477D3—481no—
478D3#447712yesdirect product factor
479C22—31no—
480C22—31no—
481C22—62no—
482C22—122no—
483C22—121no—
484C22—362no—
485C22—361no—
486C22—722no—
487C22—722no—
488C22D3×(C2×D3)⋊C411yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—61no—
493C4—61no—
494C4—61no—
495C4—121no—
496C4—361no—
497C3—21no—
498C3D3×#35511yescharacteristic, complemented
499C3C2×#447711yescharacteristic, complemented
500C2—21no—
501C2—32no—
502C2—61no—
503C2—241no—
504C2—721no—
505C2D3×#80611yescharacteristic
subgroupG/H
centerC2D3×#806
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C2×D32
FittingC32×#101C22
socleC2×C32C2×#99
prime radicalC2×D3×D12C4
cosocleC2×C32×Q8C23
hypercenter#101D32
hypocenterC32C2×#355
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
2. C3×D3×#101C2semidirect
3. D3×#836C2semidirect
4. #10589343C2semidirect
5. C3×#4477C2semidirect
6. #10589183C2semidirect
7. #10589182C2semidirect
23. C32×#101C22semidirect
24. #63663C22semidirect
25. C3×#836C22semidirect
26. C3×#836C22semidirect
34. D3×#101D3semidirect
43. #4477D3direct (N × H)
111. C3×#101C2×D3semidirect
112. C3×#101C2×D3semidirect
117. #836C2×D3semidirect
118. #836C2×D3semidirect
273. #101D32semidirect
352. C3×D3#355semidirect
431. C32C2×#355semidirect
478. D3#4477direct (N × H)
498. C3D3×#355semidirect
499. C3C2×#4477semidirect

Maximal subgroups

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

subgroupindex
D3×#9472
C3×D3×#1012
D3×#8362
#105893432
C3×#44772
#105891832
#105891822
C2×#44773
D3×#3553