Finite Group Databasebeta

← C3×#85383 #11922670

Subgroups — C3×#85383 #11922670

Order 1152.

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

normal subgroups only

This group has 555 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
1C2×C3×#985C211yesmaximal, characteristic, complemented
2C2×C3×#983C211yesmaximal, characteristic, complemented
3C3×#548⋊C3C211yesmaximal, characteristic, complemented
4C3×#5425C211yesmaximal, characteristic, complemented
5C3×#5419C211yesmaximal, characteristic, complemented
6C3×#5394C211yesmaximal, characteristic, complemented
7C3×C4⋊#226C211yesmaximal, characteristic, complemented
8#85383C311yesmaximal, characteristic, direct product factor
9C3×#3269—31nomaximal
10C2×C3×#41⋊C3C2211yescharacteristic
11C22×C3×SL(2,𝔽3)C2211yescharacteristic
12C3×#985—22no—
13C3×#983—22no—
14C2×C3×GL(2,𝔽3)C2211yescharacteristic
15C2×C3×#226C2211yescharacteristic
16C2×C3×#226C2211yescharacteristic
17C3×#883—41nomaximal
18C3×C4×SL(2,𝔽3)C2211yescharacteristic
19C3×#859C2211yescharacteristic
20C2×#985C2×C311yescharacteristic, complemented
21C2×#983C2×C311yescharacteristic, complemented
22C2×C3×#137—31no—
23C2×C3×#135—31no—
24C3×#548D311yescharacteristic, complemented
25C3×#547—31no—
26#548⋊C3—21no—
27#548⋊C3C2×C311yescharacteristic, complemented
28#5425C2×C311yescharacteristic, complemented
29#5419C2×C311yescharacteristic, complemented
30#5394C2×C311yescharacteristic, complemented
31C4⋊#226C2×C311yescharacteristic, complemented
32C3×#497—31no—
33C3×#468—31no—
34C3×#467—31no—
35C3×#463—31no—
36C3×#462—31no—
37C3×#452—31no—
38C3×#452—31no—
39C3×#451—31no—
40C3×#449—31no—
41C3×#440—31no—
42C3×#435—31no—
43C2×C3×#67—41no—
44C2×C3×C4×D3—41no—
45C3×#41⋊C3—21no—
46C2×C3×SL(2,𝔽3)—21no—
47C2×C3×SL(2,𝔽3)C2311yescharacteristic
48C3×GL(2,𝔽3)D412yescomplemented
49C3×#226—21no—
50C3×#226—21no—
51C32×C22⋊C4—41no—
52C3×#217—41no—
53C3×(C2×D3)⋊C4—41no—
54C3×C4⋊Dic3—41no—
55C3×Dic3⋊C4—41no—
56#3269—31noSylow
57C2×C3×#41—31no—
58C2×C3×#41—31no—
59C2×C3×#41C2×D311yescharacteristic
60C22×C3×Q8C2×D311yescharacteristic
61C2×#41⋊C3—21no—
62C2×#41⋊C3C22×C311yescharacteristic
63C22×SL(2,𝔽3)—21no—
64C22×SL(2,𝔽3)C22×C311yescharacteristic
65#985—22no—
66#983—22no—
67C2×GL(2,𝔽3)C22×C311yescharacteristic
68C2×#226C22×C311yescharacteristic
69C2×#226C22×C311yescharacteristic
70C3×#137—62no—
71C3×#137—62no—
72C3×#135—62no—
73C3×#135—62no—
74C2×C3×Q16—31no—
75C2×C3×Q16—31no—
76C2×C3×Q16—31no—
77C2×C3×Q16—31no—
78C2×C3×SD16—31no—
79C2×C3×SD16—31no—
80C2×C3×SD16—31no—
81C2×C3×SD16—31no—
82C2×C3×D8—31no—
83C2×C3×M16—31no—
84C22×C3×C8—31no—
85C3×C4⋊Q8—31no—
86C3×#124—31no—
87C3×#123—61no—
88C3×#123—61no—
89C3×C22⋊Q8—31no—
90C3×C22⋊Q8—31no—
91C3×C22⋊Q8—31no—
92C3×#121—31no—
93C3×#121—61no—
94C3×C4×Q8C2×D311yescharacteristic
95C3×C4×D4—31no—
96C3×C4×D4—31no—
97C2×C3×C4⋊C4—61no—
98#883—41no—
99C4×SL(2,𝔽3)—21no—
100C4×SL(2,𝔽3)C22×C311yescharacteristic
101#859C22×C311yescharacteristic
102C3×#107—31no—
103C3×C4⋊C8—31no—
104C3×#103—31no—
105C3×#103—31no—
106C3×#103—31no—
107C3×#103—31no—
108C3×#102—31no—
109C3×#102—31no—
110C3×C22⋊C8—31no—
111C3×C22⋊C8—31no—
112C3×#97—31no—
113C23×C32—41no—
114C22×C3×D3—41no—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C3×#67—82no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—41no—
120C2×C3×Dic3—41no—
121C3×C4×D3—82no—
122C3×SL(2,𝔽3)C2×D411yescharacteristic
123C2×#137—31no—
124C2×#135—31no—
125#548C3×D311yescharacteristic, complemented
126#547—31no—
127#497—31no—
128#468—31no—
129#467—31no—
130#463—31no—
131#462—31no—
132#452—31no—
133#452—31no—
134#451—31no—
135#449—31no—
136#440—31no—
137#435—31no—
138C3×#41—21no—
139C3×#41—61no—
140C3×#41—62no—
141C3×#41—62no—
142C3×#41—121no—
143C3×#41—121no—
144C2×C3×Q8—21no—
145C2×C3×Q8—31no—
146C2×C3×Q8—31no—
147C2×C3×Q8—31no—
148C2×C3×Q8—61no—
149C2×C3×Q8C22×D311yescharacteristic
150C2×C3×D4—31no—
151C2×C3×D4—31no—
152C2×C3×D4—31no—
153C2×C3×D4—61no—
154C2×C3×D4—61no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C2×#67—41no—
161C2×C4×D3—41no—
162#41⋊C3—21no—
163#41⋊C3—41no—
164C2×SL(2,𝔽3)—21no—
165C2×SL(2,𝔽3)—21no—
166C2×SL(2,𝔽3)—41no—
167C2×SL(2,𝔽3)C23×C311yescharacteristic
168GL(2,𝔽3)C3×D412yescomplemented
169#226—21no—
170#226—21no—
171C3×Q16—62no—
172C3×Q16—61no—
173C3×Q16—61no—
174C3×Q16—61no—
175C3×Q16—61no—
176C3×Q16—121no—
177C3×SD16—32no—
178C3×SD16—32no—
179C3×SD16—62no—
180C3×SD16—62no—
181C3×SD16—121no—
182C3×D8—62no—
183C3×M16—62no—
184C2×C3×C8—31no—
185C2×C3×C8—31no—
186C2×C3×C8—31no—
187C2×C3×C8—31no—
188C2×C3×C8—62no—
189C3×C4⋊C4—31no—
190C3×C4⋊C4—31no—
191C3×C4⋊C4—31no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C22⋊C4—31no—
197C3×C22⋊C4—41no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C22⋊C4—61no—
202C3×C22⋊C4—81no—
203C3×C22⋊C4S411yescharacteristic
204C3×C42—31no—
205#217—41no—
206(C2×D3)⋊C4—41no—
207C4⋊Dic3—41no—
208Dic3⋊C4—41no—
209C22×C32—41no—
210C22×C32—81no—
211C22×C32—81no—
212C22×C32—81no—
213C2×C3×D3—42no—
214C2×C3×D3—81no—
215C2×C3×D3—81no—
216C32×C4—81no—
217C32×C4—81no—
218C3×Dic3—81no—
219C3×Dic3—81no—
220C3×Dic3—81no—
221C2×#41—31no—
222C2×#41—31no—
223C2×#41C2×C3×D311yescharacteristic
224C22×Q8C2×C3×D311yescharacteristic
225#137—62no—
226#137—62no—
227#135—62no—
228#135—62no—
229C2×Q16—31no—
230C2×Q16—31no—
231C2×Q16—31no—
232C2×Q16—31no—
233C2×SD16—31no—
234C2×SD16—31no—
235C2×SD16—31no—
236C2×SD16—31no—
237C2×D8—31no—
238C2×M16—31no—
239C22×C8—31no—
240C4⋊Q8—31no—
241#124—31no—
242#123—61no—
243#123—61no—
244C22⋊Q8—31no—
245C22⋊Q8—31no—
246C22⋊Q8—31no—
247#121—31no—
248#121—61no—
249C4×Q8C2×C3×D311yescharacteristic
250C4×D4—31no—
251C4×D4—31no—
252C2×C4⋊C4—61no—
253#107—31no—
254C4⋊C8—31no—
255#103—31no—
256#103—31no—
257#103—31no—
258#103—31no—
259#102—31no—
260#102—31no—
261C22⋊C8—31no—
262C22⋊C8—31no—
263#97—31no—
264C23×C3—31no—
265C23×C3—41no—
266C23×C3—61no—
267C23×C3—81no—
268C23×C3C2×S411yescharacteristic
269C22×D3—41no—
270C3×Q8—31no—
271C3×Q8—61no—
272C3×Q8—61no—
273C3×Q8—61no—
274C3×Q8—61no—
275C3×Q8—61no—
276C3×Q8—61no—
277C3×Q8D3×D411yescharacteristic
278C3×D4—32no—
279C3×D4—61no—
280C3×D4—61no—
281C3×D4—61no—
282C3×D4—121no—
283C3×D4—122no—
284C3×D4—122no—
285C2×C3×C4—31no—
286C2×C3×C4—31no—
287C2×C3×C4—31no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—61no—
297C2×C3×C4—81no—
298C2×C3×C4—81no—
299C2×C3×C4—122no—
300C2×C3×C4—122no—
301C2×C3×C4—122no—
302C2×C3×C4C2×S411yescharacteristic
303C2×C3×C4C2×S411yescharacteristic
304#67—82no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C4×D3—82no—
309SL(2,𝔽3)—21no—
310SL(2,𝔽3)C2×C3×D411yescharacteristic
311C3×C8—32no—
312C3×C8—61no—
313C3×C8—61no—
314C3×C8—61no—
315C2×C32—41no—
316C2×C32—41no—
317C2×C32—41no—
318C2×C32—161no—
319C3×D3—82no—
320#41—21no—
321#41—61no—
322#41—62no—
323#41—62no—
324#41—121no—
325#41—121no—
326C2×Q8—21no—
327C2×Q8—31no—
328C2×Q8—31no—
329C2×Q8—31no—
330C2×Q8—61no—
331C2×Q8C22×C3×D311yescharacteristic
332C2×D4—31no—
333C2×D4—31no—
334C2×D4—31no—
335C2×D4—61no—
336C2×D4—61no—
337C22×C4—31no—
338C22×C4—31no—
339C22×C4—61no—
340C22×C4—61no—
341C22×C4—61no—
342Q16—62no—
343Q16—61no—
344Q16—61no—
345Q16—61no—
346Q16—61no—
347Q16—121no—
348SD16—32no—
349SD16—32no—
350SD16—62no—
351SD16—62no—
352SD16—121no—
353D8—62no—
354M16—62no—
355C2×C8—31no—
356C2×C8—31no—
357C2×C8—31no—
358C2×C8—31no—
359C2×C8—62no—
360C4⋊C4—31no—
361C4⋊C4—31no—
362C4⋊C4—31no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C22⋊C4—31no—
368C22⋊C4—61no—
369C22⋊C4—61no—
370C22⋊C4—61no—
371C22⋊C4—61no—
372C22⋊C4C3×S411yescharacteristic
373C42—31no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—41no—
378C22×C3—61no—
379C22×C3—62no—
380C22×C3—61no—
381C22×C3—61no—
382C22×C3—81no—
383C22×C3—81no—
384C22×C3—81no—
385C22×C3—82no—
386C22×C3—81no—
387C22×C3—121no—
388C22×C3—121no—
389C22×C3—161no—
390C22×C3—161no—
391C22×C3C22×S411yescharacteristic
392C2×D3—42no—
393C2×D3—81no—
394C2×D3—81no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—31no—
398C3×C4—31no—
399C3×C4—61no—
400C3×C4—61no—
401C3×C4—81no—
402C3×C4—81no—
403C3×C4—121no—
404C3×C4—121no—
405C3×C4—121no—
406C3×C4—161no—
407C3×C4—161no—
408Dic3—81no—
409Dic3—81no—
410Dic3—81no—
411C32—41noSylow
412C23—31no—
413C23—61no—
414C23C2×C3×S411yescharacteristic
415Q8—31no—
416Q8—61no—
417Q8—61no—
418Q8—61no—
419Q8—61no—
420Q8—61no—
421Q8—61no—
422Q8C3×D3×D411yescharacteristic
423D4—32no—
424D4—61no—
425D4—61no—
426D4—61no—
427D4—121no—
428D4—122no—
429D4—122no—
430C2×C4—31no—
431C2×C4—31no—
432C2×C4—31no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—61no—
440C2×C4—122no—
441C2×C4—122no—
442C2×C4—122no—
443C2×C4C2×C3×S411yescharacteristic
444C2×C4C2×C3×S411yescharacteristic
445C8—32no—
446C8—61no—
447C8—61no—
448C8—61no—
449C2×C3—41no—
450C2×C3—41no—
451C2×C3—41no—
452C2×C3—41no—
453C2×C3—81no—
454C2×C3—81no—
455C2×C3—81no—
456C2×C3—121no—
457C2×C3—122no—
458C2×C3—161no—
459C2×C3—162no—
460C2×C3D4×S411yescharacteristic
461C2×C3#592311yescharacteristic
462C2×C3#592711yescharacteristic
463D3—82no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—61no—
468C22—62no—
469C22—61no—
470C22—61no—
471C22—121no—
472C22—121no—
473C22C22×C3×S411yescharacteristic
474C4—21no—
475C4—21no—
476C4—31no—
477C4—31no—
478C4—61no—
479C4—61no—
480C4—121no—
481C4—121no—
482C4—121no—
483C3—41no—
484C3—81no—
485C3#8538311yescharacteristic, direct product factor
486C2—41no—
487C2—121no—
488C2—122no—
489C2C3×D4×S411yescharacteristic
490C2C3×#592311yescharacteristic
491C2C3×#592711yescharacteristic
subgroupG/H
center, socleC22×C3C22×S4
commutator, cosocleC2×SL(2,𝔽3)C23×C3
FrattiniC22C22×C3×S4
FittingC3×#548D3
hypercenterC3×C22⋊C4S4
hypocenterSL(2,𝔽3)C2×C3×D4
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. C2×C3×#985C2semidirect
2. C2×C3×#983C2semidirect
3. C3×#548⋊C3C2semidirect
4. C3×#5425C2semidirect
5. C3×#5419C2semidirect
6. C3×#5394C2semidirect
7. C3×C4⋊#226C2semidirect
8. #85383C3direct (N × H)
20. C2×#985C2×C3semidirect
21. C2×#983C2×C3semidirect
24. C3×#548D3semidirect
27. #548⋊C3C2×C3semidirect
28. #5425C2×C3semidirect
29. #5419C2×C3semidirect
30. #5394C2×C3semidirect
31. C4⋊#226C2×C3semidirect
48. C3×GL(2,𝔽3)D4semidirect
125. #548C3×D3semidirect
168. GL(2,𝔽3)C3×D4semidirect
485. C3#85383direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9852
C2×C3×#9832
C3×#548⋊C32
C3×#54252
C3×#54192
C3×#53942
C3×C4⋊#2262
#853833
C3×#32693
C3×#8834