Finite Group Databasebeta

← C3×#85381 #11922668

Subgroups — C3×#85381 #11922668

Order 1152.

477 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 477 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C3×#548⋊C3C211yesmaximal, characteristic, complemented
2C3×#5427C211yesmaximal, characteristic, complemented
3C3×#5424C211yesmaximal, characteristic, complemented
4C3×#5421C211yesmaximal, characteristic, complemented
5C2×C3×#859C211yesmaximal, characteristic, complemented
6C3×C4×GL(2,𝔽3)C211yesmaximal, characteristic, complemented
7C3×#5389C211yesmaximal, characteristic, complemented
8#85381C311yesmaximal, characteristic, direct product factor
9C3×#3301—31nomaximal
10C2×C3×#41⋊C3C2211yescharacteristic
11C22×C3×SL(2,𝔽3)C2211yescharacteristic
12C2×C3×GL(2,𝔽3)C2211yescharacteristic
13C3×#67⋊C4—41nomaximal
14C3×C4×SL(2,𝔽3)C2211yescharacteristic
15C3×#859C2211yescharacteristic
16C3×#859C2211yescharacteristic
17C3×#859C2211yescharacteristic
18C3×#553—31no—
19C3×#548D311yescharacteristic, complemented
20#548⋊C3—21no—
21#548⋊C3C2×C311yescharacteristic, complemented
22#5427C2×C311yescharacteristic, complemented
23#5424C2×C311yescharacteristic, complemented
24#5421C2×C311yescharacteristic, complemented
25C2×#859C2×C311yescharacteristic, complemented
26C4×GL(2,𝔽3)C2×C311yescharacteristic, complemented
27#5389C2×C311yescharacteristic, complemented
28C3×#488—31no—
29C3×#485—31no—
30C3×#481—31no—
31C3×#479—31no—
32C3×#466—31no—
33C3×#465—31no—
34C3×#463—31no—
35C3×#449—31no—
36C3×#448—31no—
37C3×C4×SD16—31no—
38C3×C8×D4—31no—
39C3×#416—31no—
40C2×C3×#103—31no—
41C2×C3×#67—41no—
42C22×C3×Dic3—41no—
43C2×C3×C4×D3—41no—
44C3×#41⋊C3—21no—
45C2×C3×SL(2,𝔽3)—21no—
46C2×C3×SL(2,𝔽3)C2311yescharacteristic
47C3×GL(2,𝔽3)—21no—
48C32×C22⋊C4—41no—
49C3×(C2×D3)⋊C4—41no—
50C3×Dic3⋊C4—41no—
51C3×C4×Dic3—41no—
52#3301—31noSylow
53C2×C3×#41C2×D311yescharacteristic
54C22×C3×Q8C2×D311yescharacteristic
55C2×#41⋊C3—21no—
56C2×#41⋊C3C22×C311yescharacteristic
57C22×SL(2,𝔽3)—21no—
58C22×SL(2,𝔽3)C22×C311yescharacteristic
59C2×GL(2,𝔽3)C22×C311yescharacteristic
60C2×C3×SD16—31no—
61C2×C3×SD16—31no—
62C2×C3×D8—31no—
63C22×C3×C8—31no—
64C22×C3×C8—31no—
65C3×#126—61no—
66C3×#125—31no—
67C3×#124—31no—
68C3×#123—61no—
69C3×C22⋊Q8—31no—
70C3×#121—31no—
71C3×#121—31no—
72C3×#121—31no—
73C3×#121—61no—
74C3×C4×Q8C2×D311yescharacteristic
75C3×C4×D4—31no—
76C3×C4×D4—31no—
77C3×C4×D4—61no—
78C3×#117—31no—
79C2×C3×C4⋊C4—31no—
80#67⋊C4—41no—
81C4×SL(2,𝔽3)—21no—
82C4×SL(2,𝔽3)C22×C311yescharacteristic
83#859C22×C311yescharacteristic
84#859C22×C311yescharacteristic
85#859C22×C311yescharacteristic
86C3×#107—31no—
87C3×#106—31no—
88C3×#106—31no—
89C3×C4⋊C8—31no—
90C3×#103—31no—
91C3×#103—31no—
92C3×#103—31no—
93C3×#103—31no—
94C3×#103—31no—
95C3×#103—31no—
96C3×#102—31no—
97C3×#102—31no—
98C3×#102—31no—
99C3×#102—31no—
100C3×C22⋊C8—31no—
101C3×C22⋊C8—31no—
102C3×C4×C8—31no—
103C23×C32—41no—
104C22×C3×D3—41no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C3×#67—44no—
108C2×C3×Dic3—41no—
109C2×C3×Dic3—41no—
110C2×C3×Dic3—41no—
111C2×C3×Dic3—82no—
112C3×C4×D3—82no—
113C3×SL(2,𝔽3)#4111yescharacteristic
114#553—31no—
115#548C3×D311yescharacteristic, complemented
116#488—31no—
117#485—31no—
118#481—31no—
119#479—31no—
120#466—31no—
121#465—31no—
122#463—31no—
123#449—31no—
124#448—31no—
125C4×SD16—31no—
126C8×D4—31no—
127#416—31no—
128C2×#103—31no—
129C3×#41—21no—
130C3×#41—61no—
131C2×C3×Q8—21no—
132C2×C3×Q8—31no—
133C2×C3×Q8—61no—
134C2×C3×Q8C22×D311yescharacteristic
135C2×C3×D4—31no—
136C2×C3×D4—31no—
137C2×C3×D4—31no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C22×C3×C4—31no—
141C22×C3×C4—31no—
142C22×C3×C4—61no—
143C22×C3×C4—61no—
144C2×#67—41no—
145C22×Dic3—41no—
146C2×C4×D3—41no—
147#41⋊C3—21no—
148#41⋊C3—41no—
149C2×SL(2,𝔽3)—21no—
150C2×SL(2,𝔽3)—21no—
151C2×SL(2,𝔽3)—41no—
152C2×SL(2,𝔽3)C23×C311yescharacteristic
153GL(2,𝔽3)—21no—
154C3×SD16—61no—
155C3×SD16—61no—
156C3×SD16—121no—
157C3×D8—121no—
158C2×C3×C8—31no—
159C2×C3×C8—31no—
160C2×C3×C8—31no—
161C2×C3×C8—31no—
162C2×C3×C8—121no—
163C2×C3×C8—121no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C22⋊C4—31no—
173C3×C22⋊C4—41no—
174C3×C22⋊C4—61no—
175C3×C22⋊C4—61no—
176C3×C22⋊C4—61no—
177C3×C22⋊C4—61no—
178C3×C22⋊C4—61no—
179C3×C22⋊C4—81no—
180C3×C22⋊C4S411yescharacteristic
181C3×C42—31no—
182C3×C42—61no—
183(C2×D3)⋊C4—41no—
184Dic3⋊C4—41no—
185C4×Dic3—41no—
186C22×C32—42no—
187C22×C32—41no—
188C22×C32—81no—
189C22×C32—81no—
190C2×C3×D3—42no—
191C2×C3×D3—81no—
192C2×C3×D3—81no—
193C32×C4—81no—
194C32×C4—81no—
195C3×Dic3—42no—
196C3×Dic3—42no—
197C3×Dic3—81no—
198C2×#41C2×C3×D311yescharacteristic
199C22×Q8C2×C3×D311yescharacteristic
200C2×SD16—31no—
201C2×SD16—31no—
202C2×D8—31no—
203C22×C8—31no—
204C22×C8—31no—
205#126—61no—
206#125—31no—
207#124—31no—
208#123—61no—
209C22⋊Q8—31no—
210#121—31no—
211#121—31no—
212#121—31no—
213#121—61no—
214C4×Q8C2×C3×D311yescharacteristic
215C4×D4—31no—
216C4×D4—31no—
217C4×D4—61no—
218#117—31no—
219C2×C4⋊C4—31no—
220#107—31no—
221#106—31no—
222#106—31no—
223C4⋊C8—31no—
224#103—31no—
225#103—31no—
226#103—31no—
227#103—31no—
228#103—31no—
229#103—31no—
230#102—31no—
231#102—31no—
232#102—31no—
233#102—31no—
234C22⋊C8—31no—
235C22⋊C8—31no—
236C4×C8—31no—
237C23×C3—31no—
238C23×C3—41no—
239C23×C3—61no—
240C23×C3—81no—
241C23×C3C2×S411yescharacteristic
242C22×D3—41no—
243C3×Q8—31no—
244C3×Q8—61no—
245C3×Q8—61no—
246C3×Q8#23711yescharacteristic
247C3×D4—61no—
248C3×D4—61no—
249C3×D4—61no—
250C3×D4—61no—
251C3×D4—62no—
252C3×D4—122no—
253C3×D4—241no—
254C2×C3×C4—31no—
255C2×C3×C4—31no—
256C2×C3×C4—31no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—81no—
267C2×C3×C4—81no—
268C2×C3×C4—241no—
269C2×C3×C4—241no—
270C2×C3×C4C2×S411yescharacteristic
271C2×C3×C4C2×S411yescharacteristic
272#67—44no—
273C2×Dic3—41no—
274C2×Dic3—41no—
275C2×Dic3—41no—
276C2×Dic3—82no—
277C4×D3—82no—
278SL(2,𝔽3)—21no—
279SL(2,𝔽3)C3×#4111yescharacteristic
280C3×C8—61no—
281C3×C8—61no—
282C3×C8—61no—
283C3×C8—61no—
284C2×C32—41no—
285C2×C32—41no—
286C2×C32—41no—
287C2×C32—82no—
288C3×D3—82no—
289#41—21no—
290#41—61no—
291C2×Q8—21no—
292C2×Q8—31no—
293C2×Q8—61no—
294C2×Q8C22×C3×D311yescharacteristic
295C2×D4—31no—
296C2×D4—31no—
297C2×D4—31no—
298C2×D4—61no—
299C2×D4—61no—
300C22×C4—31no—
301C22×C4—31no—
302C22×C4—61no—
303C22×C4—61no—
304SD16—61no—
305SD16—61no—
306SD16—121no—
307D8—121no—
308C2×C8—31no—
309C2×C8—31no—
310C2×C8—31no—
311C2×C8—31no—
312C2×C8—121no—
313C2×C8—121no—
314C4⋊C4—31no—
315C4⋊C4—31no—
316C4⋊C4—31no—
317C4⋊C4—31no—
318C4⋊C4—31no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C22⋊C4—31no—
323C22⋊C4—61no—
324C22⋊C4—61no—
325C22⋊C4—61no—
326C22⋊C4—61no—
327C22⋊C4—61no—
328C22⋊C4C3×S411yescharacteristic
329C42—31no—
330C42—61no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—41no—
334C22×C3—42no—
335C22×C3—61no—
336C22×C3—61no—
337C22×C3—61no—
338C22×C3—81no—
339C22×C3—81no—
340C22×C3—81no—
341C22×C3—82no—
342C22×C3—121no—
343C22×C3—121no—
344C22×C3—121no—
345C22×C3—161no—
346C22×C3—161no—
347C22×C3#98512yes—
348C22×C3C22×S411yescharacteristic
349C2×D3—42no—
350C2×D3—81no—
351C2×D3—81no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—31no—
355C3×C4—31no—
356C3×C4—61no—
357C3×C4—61no—
358C3×C4—81no—
359C3×C4—81no—
360C3×C4—121no—
361C3×C4—121no—
362C3×C4—121no—
363C3×C4—161no—
364C3×C4—161no—
365Dic3—42no—
366Dic3—42no—
367Dic3—81no—
368C32—41noSylow
369C23—31no—
370C23—61no—
371C23C2×C3×S411yescharacteristic
372Q8—31no—
373Q8—61no—
374Q8—61no—
375Q8C3×#23711yescharacteristic
376D4—61no—
377D4—61no—
378D4—61no—
379D4—61no—
380D4—62no—
381D4—122no—
382D4—241no—
383C2×C4—31no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—61no—
387C2×C4—61no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—241no—
394C2×C4—241no—
395C2×C4C2×C3×S411yescharacteristic
396C2×C4C2×C3×S411yescharacteristic
397C8—61no—
398C8—61no—
399C8—61no—
400C8—61no—
401C2×C3—22no—
402C2×C3—41no—
403C2×C3—41no—
404C2×C3—41no—
405C2×C3—82no—
406C2×C3—81no—
407C2×C3—81no—
408C2×C3—81no—
409C2×C3—121no—
410C2×C3—162no—
411C2×C3—241no—
412C2×C3#591411yescharacteristic
413C2×C3C2×#98511yescharacteristic
414C2×C3#592611yescharacteristic
415D3—82no—
416C22—21no—
417C22—21no—
418C22—61no—
419C22—61no—
420C22—61no—
421C22—121no—
422C22—121no—
423C22—121no—
424C22C3×#98512yes—
425C22C22×C3×S411yescharacteristic
426C4—21no—
427C4—21no—
428C4—31no—
429C4—31no—
430C4—61no—
431C4—61no—
432C4—121no—
433C4—121no—
434C4—121no—
435C3—41no—
436C3—81no—
437C3#8538111yescharacteristic, direct product factor
438C2—22no—
439C2—121no—
440C2—241no—
441C2C3×#591411yescharacteristic
442C2C2×C3×#98511yescharacteristic
443C2C3×#592611yescharacteristic
subgroupG/H
center, socleC22×C3C22×S4
commutator, cosocleC2×SL(2,𝔽3)C23×C3
FrattiniC22C22×C3×S4
FittingC3×#548D3
hypercenterC3×C22⋊C4S4
hypocenterSL(2,𝔽3)C3×#41
LCSG ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3)
UCSC1 ◁ C22×C3 ◁ C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#548⋊C3C2semidirect
2. C3×#5427C2semidirect
3. C3×#5424C2semidirect
4. C3×#5421C2semidirect
5. C2×C3×#859C2semidirect
6. C3×C4×GL(2,𝔽3)C2semidirect
7. C3×#5389C2semidirect
8. #85381C3direct (N × H)
19. C3×#548D3semidirect
21. #548⋊C3C2×C3semidirect
22. #5427C2×C3semidirect
23. #5424C2×C3semidirect
24. #5421C2×C3semidirect
25. C2×#859C2×C3semidirect
26. C4×GL(2,𝔽3)C2×C3semidirect
27. #5389C2×C3semidirect
115. #548C3×D3semidirect
437. C3#85381direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#548⋊C32
C3×#54272
C3×#54242
C3×#54212
C2×C3×#8592
C3×C4×GL(2,𝔽3)2
C3×#53892
#853813
C3×#33013
C3×#67⋊C44