Finite Group Databasebeta

← D3×#5389 #11921679

Subgroups — D3×#5389 #11921679

Order 1152.

457 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 457 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C4×D3×SL(2,𝔽3)C211yesmaximal, characteristic
2#10593623C211yesmaximal, characteristic, complemented
3C3×#5389C211yesmaximal, characteristic, complemented
4D3×#859C211yesmaximal, characteristic
5D3×#859C211yesmaximal, characteristic
6#10593199C211yesmaximal, characteristic, complemented
7#10593196C211yesmaximal, characteristic, complemented
8C2×#5389—31nomaximal
9D3×#479—31nomaximal
10C2×D3×SL(2,𝔽3)C2211yescharacteristic
11C3×C4×SL(2,𝔽3)C2211yescharacteristic
12D3×Dic3⋊C4—41nomaximal
13Dic3×SL(2,𝔽3)C2211yescharacteristic
14C3⋊#859C2211yescharacteristic
15C3⋊#859C2211yescharacteristic
16C3×#859C2211yescharacteristic
17C3×#859C2211yescharacteristic
18D3×#125—31no—
19C4×D3×Q8D311yescharacteristic
20C2×C4×SL(2,𝔽3)—31no—
21C2×#859—31no—
22C2×#859—31no—
23#5389—31no—
24#5389—31no—
25#5389—31no—
26#5389—61no—
27#5389D311yescharacteristic, direct product factor
28C3×#479—31no—
29#5063—31no—
30#5022—31no—
31D3×#107—31no—
32#4877—31no—
33D3×#106—31no—
34#4857—31no—
35D3×C4⋊C8—31no—
36#4829—31no—
37D3×#103—31no—
38D3×#103—31no—
39#4799—31no—
40#4796—31no—
41C2×C3×C4×D3—41no—
42C2×C3×SL(2,𝔽3)C2311yescharacteristic
43C2×D3×Dic3—41no—
44C2×D3×Dic3—41no—
45D3×SL(2,𝔽3)Q812yes—
46#3750—41no—
47C3×Dic3⋊C4—41no—
48#3724—41no—
49Dic3⋊Dic3—41no—
50C2×#479—91noSylow
51C2×D3×Q8C2×D311yescharacteristic
52C22×SL(2,𝔽3)—31no—
53C3×#125—31no—
54C3×C4×Q8C2×D311yescharacteristic
55Q8×Dic3C2×D311yescharacteristic
56C2×Dic3⋊C4—121no—
57C2×D3×C8—31no—
58C2×D3×C8—31no—
59D3×C4⋊C4—31no—
60D3×C4⋊C4—31no—
61D3×C4⋊C4—31no—
62D3×C4⋊C4—61no—
63D3×C4⋊C4—61no—
64#890—31no—
65#890—31no—
66#889—61no—
67#889—61no—
68#887—31no—
69C42×D3—31no—
70#870—31no—
71C4×Dic6—31no—
72C4×SL(2,𝔽3)—21no—
73C4×SL(2,𝔽3)—31no—
74C4×SL(2,𝔽3)C2×D311yescharacteristic
75#859—31no—
76#859—31no—
77#859—61no—
78#859—61no—
79#859C2×D311yescharacteristic
80#859C2×D311yescharacteristic
81C3×#107—31no—
82C3×#106—31no—
83C3×C4⋊C8—31no—
84C3×#103—31no—
85C3×#103—31no—
86#835—31no—
87#835—31no—
88#818—31no—
89#817—31no—
90#816—31no—
91#816—31no—
92Dic3⋊C8—31no—
93Dic3⋊C8—31no—
94#810—31no—
95#810—31no—
96#808—31no—
97#808—31no—
98#807—31no—
99#807—31no—
100C4⋊(C3⋊C8)—31no—
101C22×C3×D3—41no—
102C2×C32×C4—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3—41no—
107C2×C3×Dic3—41no—
108C3×C4×D3—82no—
109C3×SL(2,𝔽3)C2×Q811yescharacteristic
110D3×Dic3—44no—
111D3×Dic3—82no—
112C2×#125—91no—
113C2×C4×Q8—31no—
114#479—31no—
115#479—91no—
116#479—91no—
117#479—91no—
118#479—91no—
119#479—91no—
120#479—91no—
121#479—91no—
122C2×#107—91no—
123C2×#106—91no—
124C2×C4⋊C8—91no—
125C2×#103—91no—
126C2×#103—91no—
127C2×C3×Q8C22×D311yescharacteristic
128C22×C3×C4—121no—
129C22×Dic3—121no—
130C22×Dic3—121no—
131D3×Q8—32no—
132D3×Q8Dic612yes—
133C2×C4×D3—31no—
134C2×C4×D3—31no—
135C2×C4×D3—61no—
136C2×C4×D3—61no—
137C2×C4×D3S411yescharacteristic
138C2×Dic6—31no—
139C2×SL(2,𝔽3)—21no—
140C2×SL(2,𝔽3)—32no—
141C2×SL(2,𝔽3)C22×D311yescharacteristic
142C2×C3×C8—31no—
143C2×C3×C8—31no—
144C3×C4⋊C4—31no—
145C3×C4⋊C4—31no—
146C3×C4⋊C4—31no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C42—31no—
150C4⋊Dic3—31no—
151C4⋊Dic3—31no—
152C4⋊Dic3—31no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155Dic3⋊C4—41no—
156Dic3⋊C4—61no—
157Dic3⋊C4—61no—
158Dic3⋊C4—61no—
159Dic3⋊C4—61no—
160Dic3⋊C4—61no—
161Dic3⋊C4—61no—
162Dic3⋊C4—61no—
163Dic3⋊C4—121no—
164Dic3⋊C4—121no—
165Dic3⋊C4—121no—
166Dic3⋊C4—241no—
167C4×Dic3—31no—
168C4×Dic3—31no—
169C4×Dic3—31no—
170C2×C3⋊C8—31no—
171C2×C3⋊C8—31no—
172D3×C8—62no—
173D3×C8—62no—
174C22×C32—41no—
175C2×C3×D3—42no—
176C2×C3×D3—42no—
177C2×C3×D3—42no—
178C32×C4—81no—
179C3⋊Dic3—42no—
180C3⋊Dic3—81no—
181C3×Dic3—42no—
182C3×Dic3—81no—
183C3×Dic3—81no—
184C22×Q8—31no—
185C22×C8—91no—
186C22×C8—91no—
187#125—31no—
188#125—91no—
189#125—91no—
190#125—91no—
191#125—181no—
192#125—181no—
193C4×Q8—31no—
194C4×Q8—91no—
195C4×Q8—91no—
196C4×Q8D3211yescharacteristic
197C2×C4⋊C4—91no—
198C2×C4⋊C4—91no—
199C2×C4⋊C4—91no—
200C2×C4⋊C4—181no—
201C2×C4⋊C4—181no—
202C2×C42—91no—
203#107—31no—
204#107—91no—
205#107—91no—
206#107—91no—
207#106—31no—
208#106—91no—
209#106—91no—
210#106—91no—
211C4⋊C8—31no—
212C4⋊C8—91no—
213C4⋊C8—91no—
214C4⋊C8—91no—
215#103—31no—
216#103—31no—
217#103—91no—
218#103—91no—
219#103—91no—
220#103—91no—
221#103—91no—
222#103—91no—
223C23×C3—121no—
224C22×D3C2×S411yescharacteristic
225C3×Q8—31no—
226C3×Q8C2×Dic611yescharacteristic
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—41no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4—81no—
233C2×C3×C4—121no—
234C2×C3×C4—242no—
235C2×C3×C4C2×S411yescharacteristic
236C2×Dic3—31no—
237C2×Dic3—31no—
238C2×Dic3—41no—
239C2×Dic3—41no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—121no—
243C2×Dic3—121no—
244C2×Dic3—124no—
245C2×Dic3—241no—
246C2×Dic3—241no—
247C2×Dic3—242no—
248C2×Dic3C2×S411yescharacteristic
249C4×D3—22no—
250C4×D3—32no—
251C4×D3—32no—
252C4×D3—62no—
253C4×D3—122no—
254C4×D3—122no—
255Dic6—32no—
256Dic6—61no—
257SL(2,𝔽3)—21no—
258SL(2,𝔽3)D3×Q811yescharacteristic
259C3×C8—61no—
260C3×C8—61no—
261C3⋊C8—61no—
262C3⋊C8—61no—
263C2×C32—41no—
264C2×C32—41no—
265C2×C32—41no—
266C3×D3—44no—
267C2×Q8—32no—
268C2×Q8—91no—
269C2×Q8—92no—
270C2×Q8C2×D3211yescharacteristic
271C22×C4—31no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4—181no—
275C22×C4—181no—
276C2×C8—31no—
277C2×C8—31no—
278C2×C8—91no—
279C2×C8—91no—
280C2×C8—182no—
281C2×C8—182no—
282C4⋊C4—31no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—61no—
286C4⋊C4—61no—
287C4⋊C4—91no—
288C4⋊C4—91no—
289C4⋊C4—91no—
290C4⋊C4—181no—
291C4⋊C4—181no—
292C4⋊C4—181no—
293C4⋊C4—181no—
294C4⋊C4—181no—
295C4⋊C4—181no—
296C4⋊C4—181no—
297C4⋊C4—181no—
298C4⋊C4—181no—
299C42—31no—
300C42—91no—
301C42—91no—
302C42—91no—
303C22×C3—41no—
304C22×C3—81no—
305C22×C3—122no—
306C22×C3—122no—
307C22×C3—122no—
308C22×C3C22×S411yescharacteristic
309C2×D3A4⋊Q812yes—
310C2×D3#98312yes—
311C2×D3#98512yes—
312C3×C4—21no—
313C3×C4—31no—
314C3×C4—31no—
315C3×C4—61no—
316C3×C4—81no—
317C3×C4—121no—
318C3×C4—121no—
319C3×C4—161no—
320C3×C4—241no—
321Dic3—21no—
322Dic3—32no—
323Dic3—42no—
324Dic3—61no—
325Dic3—81no—
326Dic3—122no—
327Dic3—121no—
328Dic3—121no—
329Dic3—241no—
330Dic3—242no—
331Dic3—481no—
332C32—41noSylow
333C23—31no—
334Q8—31no—
335Q8—92no—
336Q8—181no—
337Q8D3×Dic611yescharacteristic
338C2×C4—31no—
339C2×C4—31no—
340C2×C4—31no—
341C2×C4—62no—
342C2×C4—61no—
343C2×C4—61no—
344C2×C4—92no—
345C2×C4—92no—
346C2×C4—91no—
347C2×C4—91no—
348C2×C4—182no—
349C2×C4—181no—
350C2×C4—181no—
351C2×C4—362no—
352C2×C4—362no—
353C2×C4D3×S411yescharacteristic
354C8—61no—
355C8—61no—
356C8—181no—
357C8—181no—
358C2×C3—41no—
359C2×C3—41no—
360C2×C3—41no—
361C2×C3—81no—
362C2×C3—81no—
363C2×C3—81no—
364C2×C3—124no—
365C2×C3C2×A4⋊Q811yescharacteristic
366C2×C3C2×#98311yescharacteristic
367C2×C3C2×#98511yescharacteristic
368D3#538914yesdirect product factor
369C22—32no—
370C22—32no—
371C22—32no—
372C22C2×D3×S411yescharacteristic
373C4—21no—
374C4—31no—
375C4—31no—
376C4—61no—
377C4—61no—
378C4—92no—
379C4—121no—
380C4—121no—
381C4—181no—
382C4—361no—
383C4—361no—
384C3—41no—
385C3—81no—
386C3C2×#538911yescharacteristic, complemented
387C2—34no—
388C2D3×A4⋊Q811yescharacteristic
389C2D3×#98311yescharacteristic
390C2D3×#98511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FittingC3×C4×Q8C2×D3
socleC22×C3C22×S4
prime radicalC2×D3×SL(2,𝔽3)C22
hypercenterC2×C4D3×S4
hypocenterC3×SL(2,𝔽3)C2×Q8
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #10593623C2semidirect
3. C3×#5389C2semidirect
6. #10593199C2semidirect
7. #10593196C2semidirect
27. #5389D3direct (N × H)
368. D3#5389direct (N × H)
386. C3C2×#5389semidirect

Maximal subgroups

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

subgroupindex
C4×D3×SL(2,𝔽3)2
#105936232
C3×#53892
D3×#8592
#105931992
#105931962
C2×#53893
D3×#4793
D3×Dic3⋊C44