Finite Group Databasebeta

← #11922348

Subgroups — #11922348

Order 1152.

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

normal subgroups only

This group has 431 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
1Dic3×#41⋊C3C211yesmaximal, characteristic
2#10593658C211yesmaximal, characteristic
3C3×#5424C211yesmaximal, characteristic
4#10593212C211yesmaximal, characteristic, complemented
5#10593202C211yesmaximal, characteristic, complemented
6#10593199C211yesmaximal, characteristic, complemented
7#10593196C211yesmaximal, characteristic, complemented
8#85334—31nomaximal
9#78822—31nomaximal
10C2×C3×#41⋊C3C2211yescharacteristic
11C4×#627—41nomaximal
12Dic3×SL(2,𝔽3)C2211yescharacteristic
13Dic3×SL(2,𝔽3)C2211yescharacteristic
14C3⋊#859C2211yescharacteristic
15C3⋊#859C2211yescharacteristic
16C3×#859C2211yescharacteristic
17C3×#859C2211yescharacteristic
18Dic3×#41D311yescharacteristic
19#5517—31no—
20C4×#41⋊C3—31no—
21#5424—31no—
22#5424—61no—
23#5424D311yescharacteristic
24#5391—31no—
25#5389—31no—
26#5389—31no—
27#5386—31no—
28C3×#416—31no—
29#5233—31no—
30#5106—31no—
31C2×Dic3⋊C8—31no—
32#4998—31no—
33#4799—31no—
34#4796—31no—
35#4793—31no—
36#4791—31no—
37#4766—31no—
38#4763—31no—
39#4761—31no—
40#4759—31no—
41C3×#41⋊C3Q812yescomplemented
42C2×C3×SL(2,𝔽3)C2311yescharacteristic
43C2×#627—41no—
44C4×C3⋊Dic3—41no—
45C3×C4×Dic3—41no—
46C3×C4×Dic3—41no—
47#3724—41no—
48Dic3⋊Dic3—41no—
49Dic3⋊Dic3—41no—
50#3076—91noSylow
51C2×C3×#41C2×D311yescharacteristic
52C2×#41⋊C3—21no—
53C2×#41⋊C3C2×D311yescharacteristic
54C22×C3×C8—31no—
55C3×#117—31no—
56Q8×Dic3C2×D311yescharacteristic
57Q8×Dic3C2×D311yescharacteristic
58D4×Dic3—31no—
59D4×Dic3—31no—
60#926—31no—
61#926—31no—
62C2×C4×Dic3—31no—
63C22×C3⋊C8—31no—
64#890—31no—
65#890—31no—
66#888—31no—
67#888—31no—
68#878—61no—
69#878—61no—
70C4×Dic6—61no—
71C4×Dic6—61no—
72C4×Dic6—121no—
73C4×SL(2,𝔽3)—31no—
74C4×SL(2,𝔽3)—31no—
75#859—31no—
76#859—31no—
77#859—61no—
78#859—61no—
79#859C2×D311yescharacteristic
80#859C2×D311yescharacteristic
81C3×#103—31no—
82C3×#103—31no—
83C3×#102—31no—
84C3×#102—31no—
85#835—31no—
86#835—31no—
87#832—31no—
88#832—31no—
89#818—31no—
90#818—31no—
91#817—31no—
92#817—31no—
93Dic3⋊C8—31no—
94Dic3⋊C8—31no—
95Dic3⋊C8—31no—
96Dic3⋊C8—31no—
97#808—31no—
98#808—31no—
99#807—31no—
100#807—31no—
101C2×C32×C4—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3×Dic3—41no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3—41no—
107C2×C3×Dic3—41no—
108C3×SL(2,𝔽3)C2×Q811yescharacteristic
109#627—44no—
110#533—91no—
111C4×#41—31no—
112#479—91no—
113#479—91no—
114#478—91no—
115#478—91no—
116#477—91no—
117#476—91no—
118#475—91no—
119#474—91no—
120#427—91no—
121#427—91no—
122C2×C4⋊C8—91no—
123#416—31no—
124#416—91no—
125C3×#41—32no—
126C3×#41Dic612yescomplemented
127C2×C3×Q8C22×D311yescharacteristic
128C2×C3×D4—31no—
129C22×C3×C4—31no—
130C22×Dic3—31no—
131C22×Dic3—31no—
132C2×Dic6—61no—
133C2×Dic6—61no—
134C2×Dic6—121no—
135#41⋊C3—22no—
136#41⋊C3Dic612yescomplemented
137C2×SL(2,𝔽3)—21no—
138C2×SL(2,𝔽3)C22×D311yescharacteristic
139C2×C3×C8—31no—
140C2×C3×C8—31no—
141C2×C3×C8—62no—
142C3×C4⋊C4—31no—
143C3×C4⋊C4—31no—
144C3×C22⋊C4—61no—
145C3×C42—61no—
146C3×C42—121no—
147#217—61no—
148#217—61no—
149C4⋊Dic3—31no—
150C4⋊Dic3—31no—
151C4⋊Dic3—31no—
152C4⋊Dic3—31no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—121no—
156Dic3⋊C4—61no—
157Dic3⋊C4—61no—
158Dic3⋊C4—61no—
159Dic3⋊C4—61no—
160Dic3⋊C4—121no—
161Dic3⋊C4—121no—
162C4×Dic3—31no—
163C4×Dic3—31no—
164C4×Dic3—31no—
165C4×Dic3—41no—
166C4×Dic3—61no—
167C4×Dic3—121no—
168C4×Dic3—241no—
169C4×Dic3S411yescharacteristic
170C2×C3⋊C8—31no—
171C2×C3⋊C8—31no—
172C2×C3⋊C8—62no—
173C22×C32—41no—
174C32×C4—42no—
175C3⋊Dic3—42no—
176C3⋊Dic3—81no—
177C3×Dic3—42no—
178C3×Dic3—42no—
179C3×Dic3—81no—
180C3×Dic3—81no—
181C2×#41D3211yescharacteristic
182C22×C8—31no—
183C22×C8—91no—
184C4⋊Q8—91no—
185C4⋊Q8—91no—
186#125—91no—
187#125—91no—
188C22⋊Q8—181no—
189C22⋊Q8—181no—
190C4×Q8—31no—
191C4×Q8—31no—
192C4×Q8—181no—
193C4×Q8—181no—
194C4×D4—91no—
195C4×D4—91no—
196#117—31no—
197#117—91no—
198#117—91no—
199C2×C42—91no—
200#107—91no—
201#107—91no—
202#107—91no—
203#107—91no—
204#106—91no—
205#106—91no—
206#106—91no—
207#106—91no—
208C4⋊C8—91no—
209C4⋊C8—91no—
210C4⋊C8—91no—
211C4⋊C8—91no—
212#103—31no—
213#103—31no—
214#103—91no—
215#103—91no—
216#102—31no—
217#102—31no—
218#102—91no—
219#102—91no—
220C23×C3—31no—
221C3×Q8—31no—
222C3×Q8C2×Dic611yescharacteristic
223C3×D4—32no—
224C3×D4—61no—
225C2×C3×C4—31no—
226C2×C3×C4—32no—
227C2×C3×C4—32no—
228C2×C3×C4—41no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—81no—
232C2×C3×C4—121no—
233C2×C3×C4—121no—
234C2×C3×C4C2×S411yescharacteristic
235C2×Dic3—31no—
236C2×Dic3—31no—
237C2×Dic3—41no—
238C2×Dic3—41no—
239C2×Dic3—62no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—121no—
243C2×Dic3—121no—
244C2×Dic3—121no—
245C2×Dic3—241no—
246C2×Dic3—241no—
247C2×Dic3C2×S411yescharacteristic
248C2×Dic3C2×S411yescharacteristic
249Dic6—124no—
250Dic6—122no—
251Dic6—122no—
252SL(2,𝔽3)—21no—
253SL(2,𝔽3)C2×Dic611yescharacteristic
254C3×C8—61no—
255C3×C8—61no—
256C3⋊C8—61no—
257C3⋊C8—61no—
258C2×C32—41no—
259C2×C32—41no—
260C2×C32—41no—
261#41—32no—
262#41#62712yescomplemented
263C2×Q8—181no—
264C2×Q8—181no—
265C2×Q8C2×D3211yescharacteristic
266C2×D4—31no—
267C22×C4—31no—
268C22×C4—91no—
269C22×C4—91no—
270C2×C8—31no—
271C2×C8—31no—
272C2×C8—62no—
273C2×C8—91no—
274C2×C8—91no—
275C2×C8—182no—
276C4⋊C4—31no—
277C4⋊C4—31no—
278C4⋊C4—91no—
279C4⋊C4—91no—
280C4⋊C4—91no—
281C4⋊C4—91no—
282C4⋊C4—181no—
283C4⋊C4—181no—
284C4⋊C4—181no—
285C4⋊C4—181no—
286C4⋊C4—181no—
287C4⋊C4—181no—
288C22⋊C4—61no—
289C22⋊C4—181no—
290C22⋊C4—181no—
291C42—31no—
292C42—61no—
293C42—91no—
294C42—91no—
295C42—91no—
296C42—181no—
297C22×C3—32no—
298C22×C3—41no—
299C22×C3—61no—
300C22×C3—61no—
301C22×C3—81no—
302C22×C3C22×S411yescharacteristic
303C3×C4—31no—
304C3×C4—31no—
305C3×C4—42no—
306C3×C4—82no—
307C3×C4—122no—
308C3×C4—121no—
309C3×C4—121no—
310C3×C4—241no—
311C3×C4A4⋊Q812yes—
312Dic3—21no—
313Dic3—42no—
314Dic3—61no—
315Dic3—61no—
316Dic3—81no—
317Dic3—122no—
318Dic3—121no—
319Dic3—121no—
320Dic3—241no—
321Dic3—242no—
322Dic3—242no—
323Dic3#98512yes—
324C32—41noSylow
325C23—31no—
326Q8—31no—
327Q8—362no—
328Q8—362no—
329Q8C2×#62711yescharacteristic
330D4—32no—
331D4—61no—
332C2×C4—31no—
333C2×C4—31no—
334C2×C4—32no—
335C2×C4—32no—
336C2×C4—31no—
337C2×C4—61no—
338C2×C4—61no—
339C2×C4—91no—
340C2×C4—91no—
341C2×C4—182no—
342C2×C4—181no—
343C2×C4—181no—
344C2×C4—361no—
345C2×C4D3×S411yescharacteristic
346C8—61no—
347C8—61no—
348C8—181no—
349C8—181no—
350C2×C3—41no—
351C2×C3—41no—
352C2×C3—41no—
353C2×C3—62no—
354C2×C3—81no—
355C2×C3—81no—
356C2×C3—81no—
357C2×C3C2×A4⋊Q811yescharacteristic
358C2×C3C2×#98511yescharacteristic
359C2×C3#592311yescharacteristic
360C22—32no—
361C22—61no—
362C22—61no—
363C22C2×D3×S411yescharacteristic
364C4—32no—
365C4—31no—
366C4—31no—
367C4—61no—
368C4—121no—
369C4—121no—
370C4—181no—
371C4—181no—
372C4—361no—
373C4—361no—
374C4#6420412yes—
375C3—41no—
376C3—81no—
377C3#8533411yescharacteristic, complemented
378C2—62no—
379C2#1059645411yescharacteristic
380C2D3×#98511yescharacteristic
381C2C2×#6420411yescharacteristic
subgroupG/H
center, hypercenterC2×C4D3×S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FrattiniC22C2×D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3C22×S4
prime radicalC2×C3×#41⋊C3C22
hypocenterC3×SL(2,𝔽3)C2×Q8
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #10593212C2semidirect
5. #10593202C2semidirect
6. #10593199C2semidirect
7. #10593196C2semidirect
41. C3×#41⋊C3Q8semidirect
126. C3×#41Dic6semidirect
136. #41⋊C3Dic6semidirect
262. #41#627semidirect
377. C3#85334semidirect

Maximal subgroups

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

subgroupindex
Dic3×#41⋊C32
#105936582
C3×#54242
#105932122
#105932022
#105931992
#105931962
#853343
#788223
C4×#6274