Finite Group Databasebeta

← C3×#85374 #11922667

Subgroups — C3×#85374 #11922667

Order 1152.

575 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 575 conjugacy classes of subgroups — too many to draw. Only its 72 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
2C22×C3×#226C211yesmaximal, characteristic, complemented
3C3×#548⋊C3C211yesmaximal, characteristic, complemented
4C3×#5425C211yesmaximal, characteristic, complemented
5C3×#5421C211yesmaximal, characteristic, complemented
6C3×#5395C211yesmaximal, characteristic, complemented
7C3×C4×#226C211yesmaximal, characteristic, complemented
8#85374C311yesmaximal, characteristic, direct product factor
9C3×#3285—31nomaximal
10C2×C3×#41⋊C3C2211yescharacteristic
11C22×C3×SL(2,𝔽3)C2211yescharacteristic
12C3×#985—22no—
13C2×C3×GL(2,𝔽3)C2211yescharacteristic
14C2×C3×#226—22no—
15C2×C3×#226C2211yescharacteristic
16C2×C3×#226C2211yescharacteristic
17C3×#67⋊C4—41nomaximal
18C3×C4×SL(2,𝔽3)C2211yescharacteristic
19C3×#859C2211yescharacteristic
20C2×#985C2×C311yescharacteristic, complemented
21C22×#226C2×C311yescharacteristic, complemented
22C2×C3×#135—31no—
23C22×C3×Q16—31no—
24C3×#548—31no—
25C3×#548D311yescharacteristic, complemented
26#548⋊C3—21no—
27#548⋊C3C2×C311yescharacteristic, complemented
28#5425C2×C311yescharacteristic, complemented
29#5421C2×C311yescharacteristic, complemented
30#5395C2×C311yescharacteristic, complemented
31C4×#226C2×C311yescharacteristic, complemented
32C3×#495—31no—
33C3×#467—31no—
34C3×#466—31no—
35C3×#464—31no—
36C3×#464—31no—
37C3×#452—31no—
38C3×#452—31no—
39C3×#448—31no—
40C3×#448—31no—
41C3×C4×Q16—31no—
42C3×C8×D4—31no—
43C2×C3×#67—41no—
44C22×C3×Dic3—41no—
45C2×C3×C4×D3—41no—
46C3×#41⋊C3—21no—
47C2×C3×SL(2,𝔽3)—21no—
48C2×C3×SL(2,𝔽3)C2311yescharacteristic
49C3×GL(2,𝔽3)—21no—
50C3×#226—21no—
51C3×#226D412yescomplemented
52C32×C22⋊C4—41no—
53C3×(C2×D3)⋊C4—41no—
54C3×Dic3⋊C4—41no—
55C3×C4×Dic3—41no—
56#3285—31noSylow
57C2×C3×#41—31no—
58C2×C3×#41C2×D311yescharacteristic
59C22×C3×Q8—31no—
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—
66C2×GL(2,𝔽3)C22×C311yescharacteristic
67C2×#226—22no—
68C2×#226C22×C311yescharacteristic
69C2×#226C22×C311yescharacteristic
70C3×#135—62no—
71C3×#135—62no—
72C2×C3×Q16—31no—
73C2×C3×Q16—31no—
74C2×C3×Q16—31no—
75C2×C3×Q16—31no—
76C2×C3×Q16—62no—
77C2×C3×Q16—62no—
78C2×C3×SD16—31no—
79C2×C3×SD16—31no—
80C2×C3×SD16—31no—
81C2×C3×SD16—31no—
82C2×C3×D8—31no—
83C22×C3×C8—31no—
84C22×C3×C8—31no—
85C3×#124—31no—
86C3×#124—31no—
87C3×#124—61no—
88C3×C22⋊Q8—31no—
89C3×C22⋊Q8—31no—
90C3×C22⋊Q8—61no—
91C3×#121—31no—
92C3×#121—31no—
93C3×#121—61no—
94C3×C4×Q8—31no—
95C3×C4×Q8C2×D311yescharacteristic
96C3×C4×D4—31no—
97C3×C4×D4—61no—
98#67⋊C4—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×C4×C8—31no—
113C23×C32—41no—
114C22×C3×D3—41no—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C3×#67—44no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—41no—
120C2×C3×Dic3—41no—
121C2×C3×Dic3—82no—
122C3×C4×D3—82no—
123C3×SL(2,𝔽3)C2×D411yescharacteristic
124C2×#135—31no—
125C22×Q16—31no—
126#548—31no—
127#548C3×D311yescharacteristic, complemented
128#495—31no—
129#467—31no—
130#466—31no—
131#464—31no—
132#464—31no—
133#452—31no—
134#452—31no—
135#448—31no—
136#448—31no—
137C4×Q16—31no—
138C8×D4—31no—
139C3×#41—21no—
140C3×#41—61no—
141C3×#41—62no—
142C3×#41—121no—
143C2×C3×Q8—21no—
144C2×C3×Q8—31no—
145C2×C3×Q8—31no—
146C2×C3×Q8—31no—
147C2×C3×Q8—61no—
148C2×C3×Q8—61no—
149C2×C3×Q8—62no—
150C2×C3×Q8—121no—
151C2×C3×Q8C22×D311yescharacteristic
152C2×C3×D4—31no—
153C2×C3×D4—31no—
154C2×C3×D4—31no—
155C2×C3×D4—61no—
156C2×C3×D4—61no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C2×#67—41no—
162C22×Dic3—41no—
163C2×C4×D3—41no—
164#41⋊C3—21no—
165#41⋊C3—41no—
166C2×SL(2,𝔽3)—21no—
167C2×SL(2,𝔽3)—21no—
168C2×SL(2,𝔽3)—41no—
169C2×SL(2,𝔽3)C23×C311yescharacteristic
170GL(2,𝔽3)—21no—
171#226—21no—
172#226C3×D412yescomplemented
173C3×Q16—32no—
174C3×Q16—32no—
175C3×Q16—62no—
176C3×Q16—61no—
177C3×Q16—62no—
178C3×Q16—61no—
179C3×SD16—62no—
180C3×SD16—61no—
181C3×SD16—61no—
182C3×SD16—121no—
183C3×SD16—121no—
184C3×D8—62no—
185C2×C3×C8—31no—
186C2×C3×C8—31no—
187C2×C3×C8—31no—
188C2×C3×C8—31no—
189C2×C3×C8—62no—
190C2×C3×C8—62no—
191C3×C4⋊C4—31no—
192C3×C4⋊C4—31no—
193C3×C4⋊C4—31no—
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—61no—
203C3×C22⋊C4—81no—
204C3×C22⋊C4S411yescharacteristic
205C3×C42—31no—
206C3×C42—61no—
207(C2×D3)⋊C4—41no—
208Dic3⋊C4—41no—
209C4×Dic3—41no—
210C22×C32—42no—
211C22×C32—41no—
212C22×C32—81no—
213C22×C32—81no—
214C2×C3×D3—42no—
215C2×C3×D3—81no—
216C2×C3×D3—81no—
217C32×C4—81no—
218C32×C4—81no—
219C3×Dic3—42no—
220C3×Dic3—42no—
221C3×Dic3—81no—
222C2×#41—31no—
223C2×#41C2×C3×D311yescharacteristic
224C22×Q8—31no—
225C22×Q8C2×C3×D311yescharacteristic
226#135—62no—
227#135—62no—
228C2×Q16—31no—
229C2×Q16—31no—
230C2×Q16—31no—
231C2×Q16—31no—
232C2×Q16—62no—
233C2×Q16—62no—
234C2×SD16—31no—
235C2×SD16—31no—
236C2×SD16—31no—
237C2×SD16—31no—
238C2×D8—31no—
239C22×C8—31no—
240C22×C8—31no—
241#124—31no—
242#124—31no—
243#124—61no—
244C22⋊Q8—31no—
245C22⋊Q8—31no—
246C22⋊Q8—61no—
247#121—31no—
248#121—31no—
249#121—61no—
250C4×Q8—31no—
251C4×Q8C2×C3×D311yescharacteristic
252C4×D4—31no—
253C4×D4—61no—
254#107—31no—
255C4⋊C8—31no—
256#103—31no—
257#103—31no—
258#103—31no—
259#103—31no—
260#102—31no—
261#102—31no—
262C22⋊C8—31no—
263C22⋊C8—31no—
264C4×C8—31no—
265C23×C3—31no—
266C23×C3—41no—
267C23×C3—61no—
268C23×C3—81no—
269C23×C3C2×S411yescharacteristic
270C22×D3—41no—
271C3×Q8—31no—
272C3×Q8—32no—
273C3×Q8—61no—
274C3×Q8—61no—
275C3×Q8—61no—
276C3×Q8—61no—
277C3×Q8—61no—
278C3×Q8—122no—
279C3×Q8D3×D411yescharacteristic
280C3×D4—61no—
281C3×D4—61no—
282C3×D4—61no—
283C3×D4—61no—
284C3×D4—62no—
285C3×D4—122no—
286C3×D4—122no—
287C2×C3×C4—31no—
288C2×C3×C4—31no—
289C2×C3×C4—31no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—81no—
300C2×C3×C4—81no—
301C2×C3×C4—122no—
302C2×C3×C4—122no—
303C2×C3×C4C2×S411yescharacteristic
304C2×C3×C4C2×S411yescharacteristic
305#67—44no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—82no—
310C4×D3—82no—
311SL(2,𝔽3)—21no—
312SL(2,𝔽3)C2×C3×D411yescharacteristic
313C3×C8—32no—
314C3×C8—61no—
315C3×C8—61no—
316C3×C8—61no—
317C2×C32—41no—
318C2×C32—41no—
319C2×C32—41no—
320C2×C32—82no—
321C3×D3—82no—
322#41—21no—
323#41—61no—
324#41—62no—
325#41—121no—
326C2×Q8—21no—
327C2×Q8—31no—
328C2×Q8—31no—
329C2×Q8—31no—
330C2×Q8—61no—
331C2×Q8—61no—
332C2×Q8—62no—
333C2×Q8—121no—
334C2×Q8C22×C3×D311yescharacteristic
335C2×D4—31no—
336C2×D4—31no—
337C2×D4—31no—
338C2×D4—61no—
339C2×D4—61no—
340C22×C4—31no—
341C22×C4—31no—
342C22×C4—61no—
343C22×C4—61no—
344Q16—32no—
345Q16—32no—
346Q16—62no—
347Q16—61no—
348Q16—62no—
349Q16—61no—
350SD16—62no—
351SD16—61no—
352SD16—61no—
353SD16—121no—
354SD16—121no—
355D8—62no—
356C2×C8—31no—
357C2×C8—31no—
358C2×C8—31no—
359C2×C8—31no—
360C2×C8—62no—
361C2×C8—62no—
362C4⋊C4—31no—
363C4⋊C4—31no—
364C4⋊C4—31no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C22⋊C4—31no—
368C22⋊C4—61no—
369C22⋊C4—61no—
370C22⋊C4—61no—
371C22⋊C4—61no—
372C22⋊C4—61no—
373C22⋊C4C3×S411yescharacteristic
374C42—31no—
375C42—61no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—41no—
379C22×C3—42no—
380C22×C3—61no—
381C22×C3—61no—
382C22×C3—61no—
383C22×C3—81no—
384C22×C3—81no—
385C22×C3—81no—
386C22×C3—82no—
387C22×C3—121no—
388C22×C3—121no—
389C22×C3—121no—
390C22×C3—161no—
391C22×C3—161no—
392C22×C3#98512yescomplemented
393C22×C3C22×S411yescharacteristic
394C2×D3—42no—
395C2×D3—81no—
396C2×D3—81no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—31no—
400C3×C4—31no—
401C3×C4—61no—
402C3×C4—62no—
403C3×C4—61no—
404C3×C4—81no—
405C3×C4—81no—
406C3×C4—121no—
407C3×C4—121no—
408C3×C4—161no—
409C3×C4—161no—
410Dic3—42no—
411Dic3—42no—
412Dic3—81no—
413C32—41noSylow
414C23—31no—
415C23—61no—
416C23C2×C3×S411yescharacteristic
417Q8—31no—
418Q8—32no—
419Q8—61no—
420Q8—61no—
421Q8—61no—
422Q8—61no—
423Q8—61no—
424Q8—122no—
425Q8C3×D3×D411yescharacteristic
426D4—61no—
427D4—61no—
428D4—61no—
429D4—61no—
430D4—62no—
431D4—122no—
432D4—122no—
433C2×C4—31no—
434C2×C4—31no—
435C2×C4—31no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—61no—
442C2×C4—61no—
443C2×C4—122no—
444C2×C4—122no—
445C2×C4C2×C3×S411yescharacteristic
446C2×C4C2×C3×S411yescharacteristic
447C8—32no—
448C8—61no—
449C8—61no—
450C8—61no—
451C2×C3—22no—
452C2×C3—41no—
453C2×C3—41no—
454C2×C3—41no—
455C2×C3—82no—
456C2×C3—81no—
457C2×C3—81no—
458C2×C3—81no—
459C2×C3—121no—
460C2×C3—162no—
461C2×C3—241no—
462C2×C3D4×S411yescharacteristic
463C2×C3C2×#98511yescharacteristic
464C2×C3#592711yescharacteristic
465D3—82no—
466C22—21no—
467C22—21no—
468C22—61no—
469C22—61no—
470C22—61no—
471C22—121no—
472C22—121no—
473C22—121no—
474C22C3×#98512yescomplemented
475C22C22×C3×S411yescharacteristic
476C4—21no—
477C4—21no—
478C4—31no—
479C4—31no—
480C4—61no—
481C4—62no—
482C4—61no—
483C4—121no—
484C4—121no—
485C3—41no—
486C3—81no—
487C3#8537411yescharacteristic, direct product factor
488C2—22no—
489C2—121no—
490C2—241no—
491C2C3×D4×S411yescharacteristic
492C2C2×C3×#98511yescharacteristic
493C2C3×#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. C22×C3×#226C2semidirect
3. C3×#548⋊C3C2semidirect
4. C3×#5425C2semidirect
5. C3×#5421C2semidirect
6. C3×#5395C2semidirect
7. C3×C4×#226C2semidirect
8. #85374C3direct (N × H)
20. C2×#985C2×C3semidirect
21. C22×#226C2×C3semidirect
25. C3×#548D3semidirect
27. #548⋊C3C2×C3semidirect
28. #5425C2×C3semidirect
29. #5421C2×C3semidirect
30. #5395C2×C3semidirect
31. C4×#226C2×C3semidirect
51. C3×#226D4semidirect
127. #548C3×D3semidirect
172. #226C3×D4semidirect
392. C22×C3#985semidirect
474. C22C3×#985semidirect
487. C3#85374direct (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
C22×C3×#2262
C3×#548⋊C32
C3×#54252
C3×#54212
C3×#53952
C3×C4×#2262
#853743
C3×#32853
C3×#67⋊C44