Finite Group Databasebeta

← #11922433

Subgroups — #11922433

Order 1152.

645 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 645 conjugacy classes of subgroups — too many to draw. Only its 59 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×#1010⋊C3C211yesmaximal, characteristic, complemented
2C2×C3×#985C211yesmaximal, characteristic, complemented
3#10593660C211yesmaximal, characteristic, complemented
4#10593217C212yesmaximal, complemented
5#10593210C212yesmaximal, complemented
6#85538—31nomaximal
7#83913—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#1010⋊C3—22no—
10C2×D3×SL(2,𝔽3)C2212yes—
11C3×#985—22no—
12C2×C3×GL(2,𝔽3)C2211yescharacteristic
13C2×C3×#226C2211yescharacteristic
14#63908—41nomaximal
15C3⋊#859C2212yes—
16C2×#1010D311yescharacteristic, complemented
17C2×2−1+4⋊C3—31no—
18C2×#985D311yescharacteristic, complemented
19C2×C3×#135—31no—
20#5833—31no—
21C2×#951—31no—
22#5426—31no—
23#5426—61no—
24#5421—32no—
25#5419—32no—
26#5232—31no—
27#5186—32no—
28#5173—32no—
29#5170—32no—
30#5158—32no—
31#5110—31no—
32C2×#816—31no—
33C2×C3×D12—41no—
34C2×C3×C4×D3—41no—
35C3×#41⋊C3D412yescomplemented
36C2×C3×SL(2,𝔽3)C2311yescharacteristic
37C2×#625—42no—
38D3×SL(2,𝔽3)—22no—
39C3×GL(2,𝔽3)—21no—
40C3×#226—21no—
41C4⋊(C3⋊Dic3)—41no—
42(C2×D3)⋊Dic3—42no—
43#3013—91noSylow
44C2×C3×#41—31no—
45C2×C3×#41C2×D311yescharacteristic
46#1010—22no—
47#1010—62no—
48C2×D3×Q8C2×D312yes—
49C2×#237—32no—
50C2×#235—31no—
51C22×Dic6—31no—
522−1+4⋊C3—62no—
53C2×#41⋊C3—21no—
54C2×#41⋊C3C2×D311yescharacteristic
55C22×SL(2,𝔽3)—32no—
56#985—22no—
57C2×GL(2,𝔽3)C2×D311yescharacteristic
58C2×#226C2×D311yescharacteristic
59C3×#135—62no—
60C3×#135—62no—
61C2×C3×Q16—31no—
62C2×C3×SD16—31no—
63C2×C3×SD16—31no—
64C2×C3×D8—31no—
65C22×C3×C8—31no—
66#951—64no—
67#946—32no—
68C2×#216—32no—
69#939—62no—
70#938—32no—
71#938—121no—
72C2×#214—32no—
73#930—61no—
74C2×C4⋊Dic3—31no—
75#924—61no—
76C2×#208—31no—
77#859—32no—
78#859—62no—
79#835—32no—
80#832—32no—
81(C2×D3)⋊C8—32no—
82(C2×D3)⋊C8—32no—
83#816—32no—
84#816—32no—
85C22×C3×D3—41no—
86C22×C3×D3—42no—
87C2×C32×C4—41no—
88C2×C3⋊Dic3—42no—
89C2×C3×Dic3—41no—
90C3×D12—82no—
91C3×C4×D3—82no—
92C3×SL(2,𝔽3)C2×D411yescharacteristic
93#625—84no—
94C2×2−1+4—31no—
95C2×#137—91no—
96C2×#135—31no—
97#537—91no—
98#452—92no—
99#451—92no—
100#449—92no—
101#448—92no—
102#417—91no—
103C2×#103—91no—
104#408—91no—
105C3×#41—32no—
106C3×#41—62no—
107C3×#41—62no—
108C3×#41#6712yescomplemented
109C2×C3×Q8—31no—
110C2×C3×Q8C22×D311yescharacteristic
111C2×C3×D4—31no—
112C2×C3×D4—31no—
113C2×C3×D4—61no—
114C2×C3×D4—121no—
115C22×C3×C4—31no—
116C22×C3×C4—61no—
117C2×#67—32no—
118C2×#67—62no—
119C2×#67—122no—
120C22×Dic3—61no—
121C22×Dic3—61no—
122D3×Q8—22no—
123D3×Q8—62no—
124#237—64no—
125#237—64no—
126#235—62no—
127#235—62no—
128C2×D12S411yescharacteristic
129C2×C4×D3—32no—
130C2×C4×D3—41no—
131C2×Dic6—32no—
132C2×Dic6—34no—
133C2×Dic6—31no—
134C2×Dic6—62no—
135#41⋊C3—22no—
136#41⋊C3#6712yescomplemented
137C2×SL(2,𝔽3)—21no—
138C2×SL(2,𝔽3)—62no—
139C2×SL(2,𝔽3)C22×D311yescharacteristic
140GL(2,𝔽3)—21no—
141#226—21no—
142C3×Q16—61no—
143C3×Q16—61no—
144C3×SD16—62no—
145C3×SD16—61no—
146C3×SD16—61no—
147C3×D8—62no—
148C2×C3×C8—31no—
149C2×C3×C8—31no—
150C2×C3×C8—62no—
151#217—62no—
152#217—122no—
153#216—64no—
154#214—64no—
155(C2×D3)⋊C4—62no—
156C4⋊Dic3—32no—
157C4⋊Dic3—61no—
158C4⋊Dic3—121no—
159C4⋊Dic3—241no—
160Dic3⋊C4—62no—
161#208—62no—
162C2×C3⋊C8—32no—
163C22×C32—41no—
164C2×C3×D3—42no—
165C2×C3×D3—82no—
166C2×C3×D3—82no—
167C2×C3×D3—82no—
168C2×C3×D3—81no—
169C2×C3×D3—81no—
170C32×C4—42no—
171C3⋊Dic3—82no—
172C3×Dic3—81no—
1732−1+4—62no—
1742−1+4—182no—
175C2×#41—31no—
176C2×#41—91no—
177C2×#41—92no—
178C2×#41D3211yescharacteristic
179C22×Q8—32no—
180C22×Q8—91no—
181#137—184no—
182#135—62no—
183#135—62no—
184C2×Q16—31no—
185C2×Q16—92no—
186C2×SD16—31no—
187C2×SD16—31no—
188C2×SD16—92no—
189C2×D8—31no—
190C2×M16—91no—
191C22×C8—31no—
192C22⋊Q8—92no—
193C22⋊Q8—181no—
194#121—92no—
195#121—181no—
196#121—182no—
197C2×C4⋊C4—91no—
198#103—92no—
199#103—92no—
200#103—92no—
201#102—92no—
202C22⋊C8—92no—
203C22⋊C8—92no—
204C23×C3—31no—
205C23×C3—61no—
206C23×C3—122no—
207C22×D3—41no—
208C22×D3C2×S412yes—
209C3×Q8—31no—
210C3×Q8—61no—
211C3×Q8—61no—
212C3×Q8C2×#6711yescharacteristic
213C3×D4—32no—
214C3×D4—61no—
215C3×D4—61no—
216C3×D4—61no—
217C3×D4—122no—
218C3×D4—242no—
219C2×C3×C4—31no—
220C2×C3×C4—32no—
221C2×C3×C4—32no—
222C2×C3×C4—41no—
223C2×C3×C4—61no—
224C2×C3×C4—81no—
225C2×C3×C4—122no—
226C2×C3×C4C2×S411yescharacteristic
227#67—64no—
228#67—242no—
229#67—244no—
230C2×Dic3—32no—
231C2×Dic3—41no—
232C2×Dic3—64no—
233C2×Dic3—62no—
234C2×Dic3—122no—
235C2×Dic3—242no—
236C2×Dic3—241no—
237D12—22no—
238C4×D3—62no—
239C4×D3—62no—
240C4×D3—82no—
241Dic6—34no—
242Dic6—62no—
243Dic6—62no—
244SL(2,𝔽3)—21no—
245SL(2,𝔽3)C2×#6711yescharacteristic
246C3×C8—61no—
247C3×C8—61no—
248C3⋊C8—62no—
249C2×C32—41no—
250C2×C32—41no—
251C2×C32—41no—
252C3×D3—82no—
253C3×D3—162no—
254#41—32no—
255#41—62no—
256#41—62no—
257#41—182no—
258#41—182no—
259#41—184no—
260#41—184no—
261#41#62512yescomplemented
262C2×Q8—31no—
263C2×Q8—62no—
264C2×Q8—92no—
265C2×Q8—94no—
266C2×Q8—91no—
267C2×Q8—182no—
268C2×Q8—182no—
269C2×Q8C2×D3211yescharacteristic
270C2×D4—31no—
271C2×D4—31no—
272C2×D4—31no—
273C2×D4—61no—
274C2×D4—92no—
275C2×D4—182no—
276C22×C4—31no—
277C22×C4—61no—
278C22×C4—92no—
279C22×C4—181no—
280C22×C4—181no—
281Q16—61no—
282Q16—61no—
283Q16—184no—
284SD16—62no—
285SD16—61no—
286SD16—61no—
287SD16—184no—
288D8—62no—
289M16—182no—
290C2×C8—31no—
291C2×C8—31no—
292C2×C8—62no—
293C2×C8—92no—
294C4⋊C4—92no—
295C4⋊C4—182no—
296C4⋊C4—181no—
297C22⋊C4—182no—
298C22⋊C4—182no—
299C22×C3—32no—
300C22×C3—41no—
301C22×C3—61no—
302C22×C3—61no—
303C22×C3—81no—
304C22×C3—121no—
305C22×C3—121no—
306C22×C3—121no—
307C22×C3—242no—
308C22×C3—242no—
309C22×C3—242no—
310C22×C3C22×S411yescharacteristic
311C2×D3—22no—
312C2×D3—22no—
313C2×D3—22no—
314C2×D3—42no—
315C2×D3—81no—
316C2×D3—81no—
317C3×C4—31no—
318C3×C4—31no—
319C3×C4—42no—
320C3×C4—82no—
321C3×C4—121no—
322C3×C4GL(2,ℤ/4)12yes—
323Dic3—62no—
324Dic3—81no—
325Dic3—122no—
326Dic3—242no—
327Dic3—482no—
328C32—41noSylow
329C23—31no—
330C23—32no—
331C23—61no—
332Q8—31no—
333Q8—61no—
334Q8—61no—
335Q8—94no—
336Q8—182no—
337Q8—182no—
338Q8C2×#62511yescharacteristic
339D4—32no—
340D4—61no—
341D4—61no—
342D4—61no—
343D4—62no—
344D4—122no—
345D4—184no—
346D4—722no—
347C2×C4—31no—
348C2×C4—32no—
349C2×C4—32no—
350C2×C4—61no—
351C2×C4—92no—
352C2×C4—122no—
353C2×C4—182no—
354C2×C4—182no—
355C2×C4—184no—
356C2×C4—182no—
357C2×C4—721no—
358C2×C4D3×S411yescharacteristic
359C8—61no—
360C8—61no—
361C8—182no—
362C2×C3—41no—
363C2×C3—41no—
364C2×C3—41no—
365C2×C3—62no—
366C2×C3—81no—
367C2×C3—81no—
368C2×C3—81no—
369C2×C3—241no—
370C2×C3—482no—
371C2×C3#592611yescharacteristic
372C2×C3#592711yescharacteristic
373C2×C3C2×GL(2,ℤ/4)11yescharacteristic
374D3—42no—
375D3—82no—
376C22—32no—
377C22—61no—
378C22—61no—
379C22—62no—
380C22—62no—
381C22—62no—
382C22—121no—
383C22—121no—
384C22—121no—
385C22C2×D3×S411yescharacteristic
386C4—31no—
387C4—31no—
388C4—121no—
389C4—182no—
390C4—362no—
391C4#6420912yes—
392C3—41no—
393C3—81no—
394C3#8553811yescharacteristic, complemented
395C2—62no—
396C2—122no—
397C2—241no—
398C2#1059645211yescharacteristic
399C2#1059645911yescharacteristic
400C2C2×#6420911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FittingC2×C3×#41C2×D3
socleC22×C3C22×S4
hypercenterC2×C4D3×S4
hypocenterC3×SL(2,𝔽3)C2×D4
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
1. C2×#1010⋊C3C2semidirect
2. C2×C3×#985C2semidirect
3. #10593660C2semidirect
4. #10593217C2semidirect
5. #10593210C2semidirect
16. C2×#1010D3semidirect
18. C2×#985D3semidirect
35. C3×#41⋊C3D4semidirect
108. C3×#41#67semidirect
136. #41⋊C3#67semidirect
261. #41#625semidirect
394. C3#85538semidirect

Maximal subgroups

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

subgroupindex
C2×#1010⋊C32
C2×C3×#9852
#105936602
#105932172
#105932102
#855383
#839133
#639084