Finite Group Databasebeta

← C3×#85499 #11922783

Subgroups — C3×#85499 #11922783

Order 1152.

638 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 76 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×Q8×A4C211yesmaximal, characteristic, complemented
2C3×#5912C211yesmaximal, characteristic
3C3×#5417C212yesmaximal, complemented
4C3×#5416C212yesmaximal, complemented
5C3×#5409C211yesmaximal, characteristic, complemented
6#85499C311yesmaximal, characteristic, direct product factor
7C3×#3004—31nomaximal
8C3×Q8×A4—21no—
9C3×Q8×A4C2212yes—
10C2×C3×C4×A4—21no—
11C2×C3×C4×A4C2211yescharacteristic
12C3×GL(2,ℤ/4)—21no—
13C3×C4⋊S4C2211yescharacteristic
14C3×C4×S4—21no—
15C3×A4⋊Q8C2211yescharacteristic
16C3×#942—41nomaximal
17C3×A4⋊C8C2212yes—
18C23×C3×Q8D311yescharacteristic, complemented
19C2×Q8×A4—21no—
20C2×Q8×A4C2×C311yescharacteristic, complemented
21#5912C2×C311yescharacteristic
22C2×C3×#137—31no—
23C2×C3×#137—31no—
24C3×#525—31no—
25#5417C2×C312yescomplemented
26#5416C2×C312yescomplemented
27#5409C2×C311yescharacteristic, complemented
28C3×#451—32no—
29C3×#451—32no—
30C3×#448—32no—
31C3×#448—32no—
32C3×#419—31no—
33C3×#419—31no—
34C3×#407—31no—
35C22×C3×A4D411yescharacteristic
36C2×C3×S4—21no—
37C2×C32×Q8—41no—
38C3×#235—41no—
39C3×C4×A4—22no—
40C3×C4×A4D411yescharacteristic
41C3×C4×A4C2311yescharacteristic
42C3×SL(2,ℤ/4)—21no—
43C3×#216—42no—
44C3×#215—42no—
45C3×#208—41no—
46#3004—31noSylow
47C2×C3×#41—31no—
48C22×C3×Q8—21no—
49C22×C3×Q8—31no—
50C22×C3×Q8—31no—
51C22×C3×Q8—32no—
52C22×C3×Q8—61no—
53C22×C3×Q8—61no—
54C22×C3×Q8C2×D312yes—
55C23×C3×C4—21no—
56C23×C3×C4C2×D311yescharacteristic
57Q8×A4—22no—
58Q8×A4—21no—
59Q8×A4—22no—
60Q8×A4C22×C312yes—
61C2×C4×A4—22no—
62C2×C4×A4—21no—
63C2×C4×A4—21no—
64C2×C4×A4C22×C311yescharacteristic
65GL(2,ℤ/4)—21no—
66C4⋊S4C22×C311yescharacteristic
67C4×S4—21no—
68A4⋊Q8C22×C311yescharacteristic
69C3×#137—62no—
70C3×#137—62no—
71C3×#137—62no—
72C3×#137—61no—
73C3×#137—61no—
74C2×C3×Q16—32no—
75C2×C3×Q16—32no—
76C2×C3×SD16—32no—
77C2×C3×SD16—32no—
78C2×C3×M16—31no—
79C2×C3×M16—31no—
80C3×#123—61no—
81C3×C22⋊Q8—31no—
82C3×C22⋊Q8—31no—
83C3×#121—31no—
84C3×#121—31no—
85C3×#120—61no—
86C3×C4×D4—61no—
87C3×C4×D4—61no—
88C3×#117—31no—
89#942—41no—
90A4⋊C8C22×C312yes—
91C3×#103—32no—
92C3×#103—32no—
93C3×#103—32no—
94C3×#103—32no—
95C3×C22⋊C8—32no—
96C3×C22⋊C8—32no—
97C2×C3×A4—21no—
98C2×C3×A4C2×D411yescharacteristic
99C3×S4—41no—
100C32×Q8—42no—
101C32×Q8—81no—
102C2×C32×C4—41no—
103C2×C32×C4—81no—
104C3×#67—81no—
105C3×D12—41no—
106C3×C4×D3—81no—
107C3×Dic6—41no—
108C3×C3⋊C8—42no—
109C23×Q8C3×D311yescharacteristic, complemented
110C2×#137—31no—
111C2×#137—31no—
112#525—31no—
113#451—32no—
114#451—32no—
115#448—32no—
116#448—32no—
117#419—31no—
118#419—31no—
119#407—31no—
120C24×C3#6711yescharacteristic
121C22×A4—21no—
122C22×A4C3×D411yescharacteristic
123C2×S4—21no—
124C3×#41—61no—
125C3×#41—61no—
126C3×#41—61no—
127C3×#41—61no—
128C2×C3×Q8—32no—
129C2×C3×Q8—32no—
130C2×C3×Q8—32no—
131C2×C3×Q8—32no—
132C2×C3×Q8—32no—
133C2×C3×Q8—31no—
134C2×C3×Q8—31no—
135C2×C3×Q8—41no—
136C2×C3×Q8—61no—
137C2×C3×Q8—61no—
138C2×C3×Q8—61no—
139C2×C3×Q8—62no—
140C2×C3×Q8—61no—
141C2×C3×Q8—61no—
142C2×C3×Q8—62no—
143C2×C3×Q8—64no—
144C2×C3×Q8—81no—
145C2×C3×Q8S411yescharacteristic, complemented
146C2×C3×D4—31no—
147C2×C3×D4—61no—
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C22×C3×C4—22no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—61no—
156C22×C3×C4—61no—
157C22×C3×C4—62no—
158C22×C3×C4—61no—
159C22×C3×C4#6711yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161#235—41no—
162C4×A4—24no—
163C4×A4—22no—
164C4×A4—21no—
165C4×A4—21no—
166C4×A4C3×D411yescharacteristic
167C4×A4C23×C311yescharacteristic
168SL(2,ℤ/4)—21no—
169C3×Q16—64no—
170C3×Q16—62no—
171C3×Q16—62no—
172C3×SD16—64no—
173C3×SD16—62no—
174C3×SD16—62no—
175C3×M16—61no—
176C3×M16—61no—
177C3×M16—61no—
178C3×M16—61no—
179C2×C3×C8—32no—
180C2×C3×C8—32no—
181C3×C4⋊C4—31no—
182C3×C4⋊C4—31no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C42—61no—
191#216—42no—
192#215—42no—
193#208—41no—
194C22×C32—41no—
195C2×C3×D3—81no—
196C3×A4#13711yescharacteristic, complemented
197C32×C4—41no—
198C32×C4—41no—
199C32×C4—82no—
200C3×Dic3—81no—
201C2×#41—31no—
202C22×Q8—21no—
203C22×Q8—31no—
204C22×Q8—31no—
205C22×Q8—32no—
206C22×Q8—61no—
207C22×Q8—61no—
208C22×Q8C2×C3×D312yes—
209C23×C4—21no—
210C23×C4C2×C3×D311yescharacteristic
211#137—62no—
212#137—62no—
213#137—62no—
214#137—61no—
215#137—61no—
216C2×Q16—32no—
217C2×Q16—32no—
218C2×SD16—32no—
219C2×SD16—32no—
220C2×M16—31no—
221C2×M16—31no—
222#123—61no—
223C22⋊Q8—31no—
224C22⋊Q8—31no—
225#121—31no—
226#121—31no—
227#120—61no—
228C4×D4—61no—
229C4×D4—61no—
230#117—31no—
231#103—32no—
232#103—32no—
233#103—32no—
234#103—32no—
235C22⋊C8—32no—
236C22⋊C8—32no—
237C23×C3—21no—
238C23×C3—31no—
239C23×C3—31no—
240C23×C3—61no—
241C23×C3—61no—
242C23×C3C2×#6711yescharacteristic
243C2×A4—22no—
244C2×A4—21no—
245C2×A4—21no—
246C2×A4C2×C3×D411yescharacteristic
247S4—41no—
248C3×Q8—21no—
249C3×Q8—34no—
250C3×Q8—32no—
251C3×Q8—42no—
252C3×Q8—62no—
253C3×Q8—62no—
254C3×Q8—62no—
255C3×Q8—61no—
256C3×Q8—61no—
257C3×Q8—61no—
258C3×Q8—81no—
259C3×Q8—82no—
260C3×Q8—82no—
261C3×Q8C2×S412yes—
262C3×D4—61no—
263C3×D4—61no—
264C3×D4—121no—
265C3×D4—122no—
266C3×D4—121no—
267C3×D4—121no—
268C3×D4—121no—
269C2×C3×C4—21no—
270C2×C3×C4—31no—
271C2×C3×C4—31no—
272C2×C3×C4—31no—
273C2×C3×C4—31no—
274C2×C3×C4—31no—
275C2×C3×C4—31no—
276C2×C3×C4—31no—
277C2×C3×C4—41no—
278C2×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4—61no—
281C2×C3×C4—62no—
282C2×C3×C4—61no—
283C2×C3×C4—62no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—81no—
288C2×C3×C4—82no—
289C2×C3×C4—81no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4C2×S411yescharacteristic
293#67—81no—
294D12—41no—
295C4×D3—81no—
296Dic6—41no—
297C3×C8—62no—
298C3×C8—62no—
299C3⋊C8—42no—
300C2×C32—41no—
301C2×C32—81no—
302C3×D3—161no—
303C24C3×#6711yescharacteristic
304#41—61no—
305#41—61no—
306#41—61no—
307#41—61no—
308C2×Q8—32no—
309C2×Q8—32no—
310C2×Q8—32no—
311C2×Q8—32no—
312C2×Q8—32no—
313C2×Q8—31no—
314C2×Q8—31no—
315C2×Q8—61no—
316C2×Q8—61no—
317C2×Q8—61no—
318C2×Q8—62no—
319C2×Q8—61no—
320C2×Q8—61no—
321C2×Q8—62no—
322C2×Q8—64no—
323C2×Q8C3×S411yescharacteristic, complemented
324C2×D4—31no—
325C2×D4—61no—
326C2×D4—61no—
327C2×D4—61no—
328C22×C4—22no—
329C22×C4—31no—
330C22×C4—31no—
331C22×C4—31no—
332C22×C4—31no—
333C22×C4—61no—
334C22×C4—61no—
335C22×C4—62no—
336C22×C4—61no—
337C22×C4C3×#6711yescharacteristic
338C22×C4C22×C3×D311yescharacteristic
339Q16—64no—
340Q16—62no—
341Q16—62no—
342SD16—64no—
343SD16—62no—
344SD16—62no—
345M16—61no—
346M16—61no—
347M16—61no—
348M16—61no—
349C2×C8—32no—
350C2×C8—32no—
351C4⋊C4—31no—
352C4⋊C4—31no—
353C4⋊C4—61no—
354C4⋊C4—61no—
355C22⋊C4—61no—
356C22⋊C4—61no—
357C22⋊C4—61no—
358C22⋊C4—61no—
359C22⋊C4—61no—
360C42—61no—
361C22×C3—31no—
362C22×C3—31no—
363C22×C3—32no—
364C22×C3—31no—
365C22×C3—41no—
366C22×C3—61no—
367C22×C3—61no—
368C22×C3—61no—
369C22×C3—81no—
370C22×C3—121no—
371C22×C3—121no—
372C22×C3—121no—
373C22×C3#94211yescharacteristic, complemented
374C22×C3GL(2,ℤ/4)11yescharacteristic
375C2×D3—81no—
376A4—21no—
377A4C3×#13711yescharacteristic, complemented
378C3×C4—22no—
379C3×C4—31no—
380C3×C4—31no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—62no—
384C3×C4—82no—
385C3×C4—84no—
386C3×C4—81no—
387C3×C4—81no—
388C3×C4—121no—
389C3×C4—121no—
390C3×C4—121no—
391C3×C4GL(2,ℤ/4)11yescharacteristic
392C3×C4C22×S411yescharacteristic
393Dic3—81no—
394C32—41noSylow
395C23—21no—
396C23—31no—
397C23—31no—
398C23—61no—
399C23—61no—
400C23C2×C3×#6711yescharacteristic
401Q8—21no—
402Q8—34no—
403Q8—32no—
404Q8—62no—
405Q8—62no—
406Q8—62no—
407Q8—61no—
408Q8—61no—
409Q8—61no—
410Q8C2×C3×S412yes—
411D4—61no—
412D4—61no—
413D4—121no—
414D4—121no—
415D4—122no—
416D4—121no—
417D4—121no—
418C2×C4—21no—
419C2×C4—31no—
420C2×C4—31no—
421C2×C4—31no—
422C2×C4—31no—
423C2×C4—31no—
424C2×C4—31no—
425C2×C4—31no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—61no—
429C2×C4—62no—
430C2×C4—61no—
431C2×C4—62no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—121no—
436C2×C4—121no—
437C2×C4C2×C3×S411yescharacteristic
438C8—62no—
439C8—62no—
440C2×C3—21no—
441C2×C3—31no—
442C2×C3—31no—
443C2×C3—41no—
444C2×C3—61no—
445C2×C3—81no—
446C2×C3—82no—
447C2×C3—81no—
448C2×C3—241no—
449C2×C3C2×GL(2,ℤ/4)11yescharacteristic
450D3—161no—
451C22—31no—
452C22—31no—
453C22—32no—
454C22—31no—
455C22—61no—
456C22—61no—
457C22—61no—
458C22—121no—
459C22—121no—
460C22—121no—
461C22C3×#94211yescharacteristic, complemented
462C22C3×GL(2,ℤ/4)11yescharacteristic
463C4—22no—
464C4—31no—
465C4—31no—
466C4—62no—
467C4—121no—
468C4—121no—
469C4—121no—
470C4C3×GL(2,ℤ/4)11yescharacteristic
471C4C22×C3×S411yescharacteristic
472C3—41no—
473C3—81no—
474C3#8549911yescharacteristic, direct product factor
475C2—21no—
476C2—31no—
477C2—31no—
478C2—61no—
479C2—241no—
480C2C2×C3×GL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC2×C3C2×GL(2,ℤ/4)
commutator, cosocleC4×A4C23×C3
FrattiniC4C22×C3×S4
FittingC23×C3×Q8D3
socleC23×C3C2×#67
prime radicalC3×#5912C2
hypercenterC2×C3×Q8S4
hypocenterA4C3×#137
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×A4C2semidirect
3. C3×#5417C2semidirect
4. C3×#5416C2semidirect
5. C3×#5409C2semidirect
6. #85499C3direct (N × H)
18. C23×C3×Q8D3semidirect
20. C2×Q8×A4C2×C3semidirect
25. #5417C2×C3semidirect
26. #5416C2×C3semidirect
27. #5409C2×C3semidirect
109. C23×Q8C3×D3semidirect
145. C2×C3×Q8S4semidirect
196. C3×A4#137semidirect
323. C2×Q8C3×S4semidirect
373. C22×C3#942semidirect
377. A4C3×#137semidirect
461. C22C3×#942semidirect
474. C3#85499direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×Q8×A42
C3×#59122
C3×#54172
C3×#54162
C3×#54092
#854993
C3×#30043
C3×#9424