Finite Group Databasebeta

← D3×#4874 #11874950

Subgroups — D3×#4874 #11874950

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#888C212yesmaximal
2#10592573C211yesmaximal, characteristic, complemented
3C3×D3×#107C211yesmaximal, characteristic
4C3×#4874C211yesmaximal, characteristic, complemented
5#10590902C211yesmaximal, characteristic, complemented
6#10590891C211yesmaximal, characteristic, complemented
7D3×#818C211yesmaximal, characteristic
8D3×C8×Dic3C211yesmaximal, characteristic
9D3×#807C212yesmaximal
10#10590415C212yesmaximal, complemented
11#10590411C212yesmaximal, complemented
12D3×#500—31nomaximal
13C2×#4874—31nomaximal
14C2×D3×Dic6—22no—
15#64097C2212yes—
16C2×C3×D3×C8C2211yescharacteristic
17C3×D3×C4⋊C4C2212yes—
18C3×#888C2212yes—
19#63919C2212yes—
20#63918C2212yes—
21D3×C4⋊Dic3C2212yes—
22D3×Dic3⋊C4—22no—
23C4×D3×Dic3C2211yescharacteristic
24#63840—22no—
25#63839—22no—
26C2×D3×C3⋊C8C2211yescharacteristic
27C32×#107C2211yescharacteristic
28#63645C2211yescharacteristic
29C8×C3⋊Dic3C2211yescharacteristic
30#63634C2212yes—
31C3×#818C2211yescharacteristic
32C3×#818C2211yescharacteristic
33C3×C8×Dic3C2211yescharacteristic
34C3×#807C2212yes—
35C3×#807C2212yes—
36#63576C2212yes—
37#63575C2212yes—
38#63575C2212yes—
39#63553C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41D3×C4⋊Q8—32no—
42C2×#888—32no—
43C3×#500—31no—
44C2×C3×#107—31no—
45C2×#818—31no—
46C2×C8×Dic3—31no—
47#5078—32no—
48C2×#807—32no—
49D3×#107—31no—
50D3×#107—32no—
51D3×#107D311yescharacteristic
52#4874—32no—
53#4874—31no—
54#4874—31no—
55#4874—31no—
56#4874—31no—
57#4874—31no—
58#4874—32no—
59#4874—32no—
60#4874—61no—
61#4874D311yescharacteristic, direct product factor
62C4×D3×C8—31no—
63#4682—31no—
64C2×#634—22no—
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3C2311yescharacteristic
67C2×C3×Dic6—22no—
68C2×#627—22no—
69C2×#627—22no—
70C2×D3×Dic3—22no—
71C2×D3×Dic3D411yescharacteristic
72C2×D3×Dic3D411yescharacteristic
73D3×Dic6—48no—
74C2×C32×C8C2311yescharacteristic
75C32×C4⋊C4C2312yes—
76C4⋊(C3⋊Dic3)C2312yes—
77#3750—22no—
78C4×C3⋊Dic3C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C3×C4⋊Dic3C2312yes—
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—22no—
83C3×Dic3⋊C4—22no—
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C3×D3×C8Q814yescomplemented
88#3724—22no—
89Dic3⋊Dic3—22no—
90Dic3⋊Dic3—22no—
91Dic32D411yescharacteristic
92Dic32D411yescharacteristic
93D3×C3⋊C8Q814yescomplemented
94C2×#500—91noSylow
95C2×D3×Q8—62no—
96C22×Dic6—62no—
97C22×C3×C8—31no—
98C3×C4⋊Q8—32no—
99C2×C3×C4⋊C4—32no—
100#944—62no—
101C2×C4⋊Dic3—32no—
102C2×Dic3⋊C4—62no—
103C2×C4×Dic3—31no—
104C22×C3⋊C8—31no—
105C2×D3×C8—31no—
106C2×D3×C8C2×D311yescharacteristic
107D3×C4⋊C4—32no—
108D3×C4⋊C4—62no—
109D3×C4⋊C4C2×D312yes—
110#888—32no—
111#888—32no—
112#888—32no—
113#888—32no—
114#888—32no—
115#888—62no—
116#888—62no—
117#888—62no—
118#888—62no—
119#888C2×D312yes—
120C42×D3—31no—
121#869—32no—
122C3×#107—21no—
123C3×#107—31no—
124C3×#107—31no—
125C3×#107—32no—
126C3×#107—32no—
127C3×#107C2×D311yescharacteristic
128C3×#107C2×D311yescharacteristic
129C3×C4×C8—31no—
130#818—31no—
131#818—31no—
132#818—32no—
133#818—32no—
134#818—61no—
135#818C2×D311yescharacteristic
136#818C2×D311yescharacteristic
137C8×Dic3—31no—
138C8×Dic3—31no—
139C8×Dic3—31no—
140C8×Dic3—31no—
141C8×Dic3—31no—
142C8×Dic3—61no—
143C8×Dic3C2×D311yescharacteristic
144#807—32no—
145#807—32no—
146#807—32no—
147#807—32no—
148#807—32no—
149#807—32no—
150#807—62no—
151#807C2×D312yes—
152#807C2×D312yes—
153C4×C3⋊C8—31no—
154C22×C3×D3C2×D411yescharacteristic
155C2×C32×C4—22no—
156C2×C32×C4C2411yescharacteristic
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3C2×D411yescharacteristic
159C2×C3⋊Dic3C2×D411yescharacteristic
160#634—44no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3C2×D411yescharacteristic
164C2×C3×Dic3C2×D411yescharacteristic
165C2×C3×Dic3C2×D411yescharacteristic
166C3×C4×D3—44no—
167C3×C4×D3C2×Q812yes—
168C3×C4×D3C2×Q812yes—
169C3×Dic6—44no—
170#627—44no—
171#627—44no—
172D3×Dic3—44no—
173D3×Dic3D814yes—
174D3×Dic3Q1614yes—
175C32×C8C2×Q812yescomplemented
176C3⋊(C3⋊C8)C2×Q812yescomplemented
177C3×C3⋊C8C2×Q812yescomplemented
178C3×C3⋊C8C2×Q812yescomplemented
179C2×C4⋊Q8—92no—
180#500—31no—
181#500—91no—
182#500—92no—
183#500—91no—
184#500—92no—
185#500—91no—
186C2×#107—31no—
187C2×#107—92no—
188C2×#107—91no—
189C2×C4×C8—91no—
190C2×C3×Q8—62no—
191C22×C3×C4—31no—
192C22×C3×C4—62no—
193C22×Dic3—31no—
194C22×Dic3—31no—
195C22×Dic3—62no—
196D3×Q8—128no—
197C2×C4×D3—22no—
198C2×C4×D3—31no—
199C2×C4×D3—31no—
200C2×C4×D3—62no—
201C2×C4×D3C22×D311yescharacteristic
202C2×Dic6—22no—
203C2×Dic6—62no—
204C2×Dic6—62no—
205C2×Dic6—62no—
206C2×Dic6—62no—
207C2×Dic6—62no—
208C2×Dic6—62no—
209C2×Dic6—122no—
210C2×Dic6—128no—
211C2×C3×C8—21no—
212C2×C3×C8—31no—
213C2×C3×C8—31no—
214C2×C3×C8—34no—
215C2×C3×C8C22×D311yescharacteristic
216C2×C3×C8C22×D311yescharacteristic
217C3×C4⋊C4—22no—
218C3×C4⋊C4—32no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—62no—
221C3×C4⋊C4—62no—
222C3×C4⋊C4C22×D312yes—
223C3×C4⋊C4C22×D312yes—
224C3×C42—31no—
225C4⋊Dic3—32no—
226C4⋊Dic3—32no—
227C4⋊Dic3—62no—
228C4⋊Dic3—62no—
229C4⋊Dic3—62no—
230C4⋊Dic3C22×D312yes—
231C4⋊Dic3C22×D312yes—
232Dic3⋊C4—22no—
233Dic3⋊C4—22no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239Dic3⋊C4—62no—
240Dic3⋊C4—122no—
241C4×Dic3—31no—
242C4×Dic3—31no—
243C4×Dic3—31no—
244C4×Dic3—31no—
245C4×Dic3—31no—
246C4×Dic3—31no—
247C4×Dic3—61no—
248C4×Dic3C22×D311yescharacteristic
249C2×C3⋊C8—31no—
250C2×C3⋊C8—31no—
251C2×C3⋊C8—34no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8C22×D311yescharacteristic
254C2×C3⋊C8C22×D311yescharacteristic
255D3×C8—34no—
256D3×C8Dic614yescomplemented
257C22×C32C22×D411yescharacteristic
258C2×C3×D3C4⋊Q812yes—
259C2×C3×D3C2×D812yes—
260C2×C3×D3C2×Q1612yes—
261C32×C4—42no—
262C32×C4C22×Q811yescharacteristic
263C32×C4C22×Q811yescharacteristic
264C3⋊Dic3—42no—
265C3⋊Dic3C2×D812yes—
266C3⋊Dic3C2×Q1612yes—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C3×Dic3C4⋊Q812yes—
270C3×Dic3C2×D812yes—
271C3×Dic3C2×Q1612yes—
272C22×Q8—182no—
273C22×C8—31no—
274C22×C8—91no—
275C4⋊Q8—32no—
276C4⋊Q8—92no—
277C4⋊Q8—92no—
278C4⋊Q8—92no—
279C4⋊Q8—182no—
280C4⋊Q8—182no—
281C2×C4⋊C4—32no—
282C2×C4⋊C4—92no—
283C2×C4⋊C4—182no—
284C2×C42—91no—
285#107—31no—
286#107—31no—
287#107—32no—
288#107—32no—
289#107—92no—
290#107—92no—
291#107—92no—
292#107—91no—
293#107—92no—
294#107D3211yescharacteristic
295C4×C8—31no—
296C4×C8—91no—
297C4×C8—91no—
298C4×C8—91no—
299C23×C3—31no—
300C22×D3D3×D411yescharacteristic
301C3×Q8—124no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—31no—
306C2×C3×C4—31no—
307C2×C3×C4—31no—
308C2×C3×C4—32no—
309C2×C3×C4—32no—
310C2×C3×C4—42no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—124no—
314C2×C3×C4C23×D311yescharacteristic
315C2×C3×C4C23×D311yescharacteristic
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—31no—
319C2×Dic3—31no—
320C2×Dic3—31no—
321C2×Dic3—31no—
322C2×Dic3—34no—
323C2×Dic3—34no—
324C2×Dic3—61no—
325C2×Dic3—61no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—122no—
329C2×Dic3—124no—
330C2×Dic3D3×D411yescharacteristic
331C2×Dic3D3×D411yescharacteristic
332C2×Dic3D3×D411yescharacteristic
333C4×D3—34no—
334C4×D3—34no—
335C4×D3—44no—
336C4×D3—124no—
337C4×D3C2×Dic612yes—
338C4×D3D3×Q812yes—
339Dic6—44no—
340Dic6—124no—
341Dic6—124no—
342Dic6—124no—
343Dic6—124no—
344Dic6—124no—
345Dic6—124no—
346Dic6—244no—
347C3×C8—22no—
348C3×C8—32no—
349C3×C8—32no—
350C3×C8C2×Dic612yescomplemented
351C3×C8D3×Q812yescomplemented
352C3⋊C8—32no—
353C3⋊C8—32no—
354C3⋊C8—62no—
355C3⋊C8C2×Dic612yescomplemented
356C3⋊C8D3×Q812yescomplemented
357C2×C32C2×C4⋊Q811yescharacteristic
358C2×C32C22×D811yescharacteristic
359C2×C32C22×Q1611yescharacteristic
360C3×D3#50014yescomplemented
361C2×Q8—62no—
362C2×Q8—182no—
363C2×Q8—182no—
364C2×Q8—182no—
365C2×Q8—368no—
366C22×C4—31no—
367C22×C4—62no—
368C22×C4—91no—
369C22×C4—91no—
370C22×C4—182no—
371C2×C8—31no—
372C2×C8—31no—
373C2×C8—34no—
374C2×C8—94no—
375C2×C8—91no—
376C2×C8C2×D3211yescharacteristic
377C4⋊C4—32no—
378C4⋊C4—32no—
379C4⋊C4—62no—
380C4⋊C4—62no—
381C4⋊C4—92no—
382C4⋊C4—182no—
383C4⋊C4—182no—
384C4⋊C4—182no—
385C4⋊C4—182no—
386C4⋊C4C2×D3212yes—
387C42—31no—
388C42—91no—
389C42—91no—
390C42—91no—
391C22×C3—21no—
392C22×C3—32no—
393C22×C3—32no—
394C22×C3—32no—
395C22×C3C2×D3×D411yescharacteristic
396C22×C3C2×D3×D411yescharacteristic
397C2×D3#88812yes—
398C2×D3D3×D812yes—
399C2×D3D3×Q1612yes—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—32no—
403C3×C4—32no—
404C3×C4—32no—
405C3×C4—42no—
406C3×C4—42no—
407C3×C4—82no—
408C3×C4—122no—
409C3×C4—122no—
410C3×C4C22×Dic611yescharacteristic
411C3×C4C2×D3×Q811yescharacteristic
412C3×C4C2×D3×Q811yescharacteristic
413C3×C4C2×D3×Q811yescharacteristic
414Dic3—32no—
415Dic3—32no—
416Dic3—32no—
417Dic3—32no—
418Dic3—42no—
419Dic3—42no—
420Dic3—62no—
421Dic3—62no—
422Dic3—122no—
423Dic3—122no—
424Dic3—242no—
425Dic3#88812yes—
426Dic3D3×D812yes—
427Dic3D3×Q1612yes—
428C32C2×#50011yescharacteristic, complemented, Sylow
429C23—31no—
430Q8—124no—
431Q8—364no—
432Q8—364no—
433Q8—364no—
434C2×C4—22no—
435C2×C4—31no—
436C2×C4—31no—
437C2×C4—31no—
438C2×C4—32no—
439C2×C4—32no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—94no—
443C2×C4—94no—
444C2×C4—91no—
445C2×C4—91no—
446C2×C4—124no—
447C2×C4—182no—
448C2×C4—364no—
449C2×C4C22×D3211yescharacteristic
450C8—32no—
451C8—32no—
452C8—92no—
453C8D3×Dic612yescomplemented
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—34no—
458C2×C3C2×#88811yescharacteristic
459C2×C3D3×C4⋊Q811yescharacteristic
460C2×C3C2×D3×D811yescharacteristic
461C2×C3C2×D3×D811yescharacteristic
462C2×C3C2×D3×Q1611yescharacteristic
463C2×C3C2×D3×Q1611yescharacteristic
464D3#487414yesdirect product factor
465C22—32no—
466C22—32no—
467C22—32no—
468C22D32×D411yescharacteristic
469C4—32no—
470C4—32no—
471C4—32no—
472C4—42no—
473C4—92no—
474C4—92no—
475C4—122no—
476C4—122no—
477C4—362no—
478C4C2×D3×Dic611yescharacteristic
479C4D32×Q811yescharacteristic
480C3—21no—
481C3C2×#487411yescharacteristic, complemented
482C3D3×#50011yescharacteristic, complemented
483C2—34no—
484C2D3×#88811yescharacteristic
485C2D32×D811yescharacteristic
486C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#107D32
hypocenterC32C2×#500
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10592573C2semidirect
4. C3×#4874C2semidirect
5. #10590902C2semidirect
6. #10590891C2semidirect
10. #10590415C2semidirect
11. #10590411C2semidirect
61. #4874D3direct (N × H)
87. C3×D3×C8Q8semidirect
93. D3×C3⋊C8Q8semidirect
175. C32×C8C2×Q8semidirect
176. C3⋊(C3⋊C8)C2×Q8semidirect
177. C3×C3⋊C8C2×Q8semidirect
178. C3×C3⋊C8C2×Q8semidirect
256. D3×C8Dic6semidirect
350. C3×C8C2×Dic6semidirect
351. C3×C8D3×Q8semidirect
355. C3⋊C8C2×Dic6semidirect
356. C3⋊C8D3×Q8semidirect
360. C3×D3#500semidirect
428. C32C2×#500semidirect
453. C8D3×Dic6semidirect
464. D3#4874direct (N × H)
481. C3C2×#4874semidirect
482. C3D3×#500semidirect

Maximal subgroups

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

subgroupindex
D3×#8882
#105925732
C3×D3×#1072
C3×#48742
#105909022
#105908912
D3×#8182
D3×C8×Dic32
D3×#8072
#105904152
#105904112
D3×#5003
C2×#48743