Finite Group Databasebeta

← C3×#71245 #11780628

Subgroups — C3×#71245 #11780628

Order 1152.

466 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 90 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×#5684C211yesmaximal, characteristic
2C32×#489C211yesmaximal, characteristic, complemented
3C3×#5086C211yesmaximal, characteristic, complemented
4C3×#5081C211yesmaximal, characteristic, complemented
5C3×#4540C211yesmaximal, characteristic, complemented
6C3×#4465C211yesmaximal, characteristic, complemented
7C3×#4464C211yesmaximal, characteristic, complemented
8C3×#1661—31nomaximal
9#71245C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×#124C2211yescharacteristic
12C3×#946—21no—
13C2×C3×#216—21no—
14C2×C3×#215—21no—
15C3×#939—21no—
16C3×#886—21no—
17C3×#884—21no—
18C3×#883—21no—
19C3×#878—21no—
20C3×#875C2211yescharacteristic
21C3×#870C2211yescharacteristic
22C32×#103—21no—
23C32×#102—21no—
24C32×#97C2211yescharacteristic
25C3×#808—21no—
26C3×#807—21no—
27C3×#803C2211yescharacteristic
28C3×#803C2211yescharacteristic
29C3×#562—31no—
30#5684C2×C311yescharacteristic
31C3×#501—31no—
32C3×#497—31no—
33C3×#489—21no—
34C3×#489D311yescharacteristic, complemented
35C3×#489C2×C311yescharacteristic, complemented
36#5086C2×C311yescharacteristic, complemented
37#5081C2×C311yescharacteristic, complemented
38C3×#330—31no—
39C3×#329—31no—
40C3×#329—31no—
41#4540C2×C311yescharacteristic, complemented
42#4465C2×C311yescharacteristic, complemented
43#4464C2×C311yescharacteristic, complemented
44C2×C32×Q8—21no—
45C2×C32×Q8D411yescharacteristic
46C2×C32×D4D411yescharacteristic
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3—21no—
52C2×C3×Dic6D411yescharacteristic
53C2×C32×C8—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C22⋊C4—21no—
57C32×C22⋊C4—21no—
58C32×C42C2311yescharacteristic
59C3×#217—21no—
60C3×#216—42no—
61C3×#215—42no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3D411yescharacteristic
67C3×C4⋊Dic3D411yescharacteristic
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#1661—31noSylow
74C2×C3×Q16—61no—
75C2×C3×SD16—61no—
76C3×C4⋊Q8—21no—
77C3×C4⋊Q8C2×D311yescharacteristic
78C3×C4⋊Q8C22×C311yescharacteristic
79C3×#125—31no—
80C3×#124—21no—
81C3×#124—31no—
82C3×#124C2×D311yescharacteristic
83C3×#124C22×C311yescharacteristic
84C3×#123—61no—
85C3×#123—61no—
86C3×C22⋊Q8—61no—
87C3×C22⋊Q8—61no—
88C3×#121—61no—
89C3×#121—61no—
90#946—21no—
91C2×#216—21no—
92C2×#215—21no—
93#939—21no—
94#886—21no—
95#884—21no—
96#883—21no—
97#878—21no—
98#875C22×C311yescharacteristic
99#870C22×C311yescharacteristic
100C3×#107—61no—
101C3×#106—61no—
102C3×#103—22no—
103C3×#103—21no—
104C3×#103—21no—
105C3×#102—22no—
106C3×#102—21no—
107C3×#102—21no—
108C3×#97—21no—
109C3×#97—31no—
110C3×#97—31no—
111C3×#97C2×D311yescharacteristic
112C3×#97C22×C311yescharacteristic
113#808—21no—
114#807—21no—
115#803C22×C311yescharacteristic
116#803C22×C311yescharacteristic
117C23×C32—21no—
118C22×C3×D3—21no—
119C32×Q8—41no—
120C32×Q8—41no—
121C32×Q8—41no—
122C32×D4—41no—
123C2×C32×C4—21no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C3×#67—81no—
129C3×#67—81no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—81no—
134C3×D12—41no—
135C3×C4×D3—81no—
136C3×Dic6—41no—
137C32×C8—41no—
138C3×C3⋊C8—22no—
139C3×C3⋊C8—22no—
140#562—31no—
141#501—31no—
142#497—31no—
143#489C3×D311yescharacteristic, complemented
144#330—31no—
145#329—31no—
146#329—31no—
147C2×C3×Q8—21no—
148C2×C3×Q8—21no—
149C2×C3×Q8—21no—
150C2×C3×Q8—31no—
151C2×C3×Q8—41no—
152C2×C3×Q8#6711yescharacteristic
153C2×C3×Q8C3×D411yescharacteristic
154C2×C3×D4—21no—
155C2×C3×D4—31no—
156C2×C3×D4—61no—
157C2×C3×D4—61no—
158C2×C3×D4#6711yescharacteristic
159C2×C3×D4C3×D411yescharacteristic
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C2×#67—21no—
163C2×#67—21no—
164C22×Dic3—21no—
165C2×D12C3×D411yescharacteristic
166C2×C4×D3—21no—
167C2×Dic6C3×D411yescharacteristic
168C3×Q16—122no—
169C3×SD16—122no—
170C2×C3×C8—22no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—31no—
181C3×C4⋊C4—31no—
182C3×C4⋊C4—41no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—21no—
190C3×C22⋊C4—21no—
191C3×C22⋊C4—41no—
192C3×C22⋊C4—41no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C42—21no—
198C3×C42C22×D311yescharacteristic
199C3×C42C23×C311yescharacteristic
200#217—21no—
201#216—42no—
202#215—42no—
203(C2×D3)⋊C4—21no—
204(C2×D3)⋊C4—21no—
205(C2×D3)⋊C4—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3C3×D411yescharacteristic
208C4⋊Dic3C3×D411yescharacteristic
209Dic3⋊C4—21no—
210Dic3⋊C4—21no—
211Dic3⋊C4—21no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—21no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32#12011yescharacteristic
218C2×C3×D3—41no—
219C2×C3×D3—41no—
220C2×C3×D3—41no—
221C32×C4—21no—
222C32×C4—21no—
223C32×C4—21no—
224C32×C4—41no—
225C32×C4—81no—
226C3×Dic3—41no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C2×Q16—61no—
230C2×SD16—61no—
231C4⋊Q8C2×C3×D311yescharacteristic
232#125—31no—
233#124—31no—
234#124C2×C3×D311yescharacteristic
235#123—61no—
236#123—61no—
237C22⋊Q8—61no—
238C22⋊Q8—61no—
239#121—61no—
240#121—61no—
241#107—61no—
242#106—61no—
243#103—21no—
244#102—21no—
245#97—31no—
246#97—31no—
247#97C2×C3×D311yescharacteristic
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—41no—
251C23×C3—61no—
252C22×D3—21no—
253C3×Q8—41no—
254C3×Q8—41no—
255C3×Q8—41no—
256C3×Q8—41no—
257C3×Q8—41no—
258C3×Q8—41no—
259C3×Q8—42no—
260C3×Q8—81no—
261C3×Q8—81no—
262C3×Q8—121no—
263C3×D4—41no—
264C3×D4—41no—
265C3×D4—42no—
266C3×D4—121no—
267C3×D4—241no—
268C3×D4—241no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—41no—
275C2×C3×C4—42no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—241no—
282C2×C3×C4—241no—
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286C2×C3×C4C2×C3×D411yescharacteristic
287C2×C3×C4C2×C3×D411yescharacteristic
288C2×C3×C4C2×C3×D411yescharacteristic
289#67—81no—
290#67—81no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—81no—
295D12—41no—
296C4×D3—81no—
297Dic6—41no—
298C3×C8—42no—
299C3×C8—41no—
300C3×C8—41no—
301C3×C8—62no—
302C3×C8—62no—
303C3⋊C8—22no—
304C3⋊C8—22no—
305C2×C32—81no—
306C2×C32#45311yescharacteristic
307C2×C32#45511yescharacteristic
308C2×C32#45611yescharacteristic
309C3×D3—81no—
310C2×Q8—21no—
311C2×Q8—31no—
312C2×Q8C3×#6711yescharacteristic
313C2×D4—31no—
314C2×D4—61no—
315C2×D4—61no—
316C2×D4C3×#6711yescharacteristic
317C22×C4—61no—
318C22×C4—61no—
319Q16—122no—
320SD16—122no—
321C2×C8—21no—
322C2×C8—61no—
323C2×C8—61no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—31no—
327C4⋊C4—31no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—61no—
335C22⋊C4—61no—
336C22⋊C4—61no—
337C22⋊C4—61no—
338C42C22×C3×D311yescharacteristic
339C22×C3—21no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—81no—
347C22×C3—81no—
348C22×C3—81no—
349C22×C3—121no—
350C22×C3—121no—
351C22×C3—121no—
352C22×C3#93711yescharacteristic
353C22×C3C3×#12011yescharacteristic
354C2×D3—41no—
355C2×D3—41no—
356C2×D3—41no—
357C3×C4—22no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—81no—
369C3×C4—82no—
370C3×C4—81no—
371C3×C4—81no—
372C3×C4—121no—
373C3×C4—121no—
374C3×C4—121no—
375Dic3—41no—
376Dic3—41no—
377Dic3—41no—
378C32#166111yescharacteristic, complemented, Sylow
379C23—21no—
380C23—61no—
381Q8—41no—
382Q8—41no—
383Q8—41no—
384Q8—121no—
385D4—41no—
386D4—121no—
387D4—241no—
388D4—241no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—241no—
395C2×C4—241no—
396C2×C4C3×D3×D411yescharacteristic
397C2×C4C3×D3×D411yescharacteristic
398C2×C4C2×C3×#6711yescharacteristic
399C8—41no—
400C8—62no—
401C8—62no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—81no—
406C2×C3—81no—
407C2×C3—161no—
408C2×C3—241no—
409C2×C3#506111yescharacteristic
410C2×C3#519811yescharacteristic
411C2×C3#520511yescharacteristic
412C2×C3C3×#45311yescharacteristic
413C2×C3C3×#45511yescharacteristic
414C2×C3C3×#45611yescharacteristic
415D3—81no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—121no—
420C22—121no—
421C22—121no—
422C22C3×#93711yescharacteristic
423C4—21no—
424C4—21no—
425C4—21no—
426C4—41no—
427C4—81no—
428C4—121no—
429C4—121no—
430C4—121no—
431C3—21no—
432C3#7124511yescharacteristic, direct product factor
433C3C3×#166111yescharacteristic, complemented
434C2—81no—
435C2—241no—
436C2C3×#506111yescharacteristic
437C2C3×#519811yescharacteristic
438C2C3×#520511yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#489C2
socleC22×C32#120
prime radicalC3×#5684C2
hypercenterC3×#489D3
hypocenterC3C3×#1661
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#489

Complements

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

NH ≅ G/Ntype
2. C32×#489C2semidirect
3. C3×#5086C2semidirect
4. C3×#5081C2semidirect
5. C3×#4540C2semidirect
6. C3×#4465C2semidirect
7. C3×#4464C2semidirect
9. #71245C3direct (N × H)
34. C3×#489D3semidirect
35. C3×#489C2×C3semidirect
36. #5086C2×C3semidirect
37. #5081C2×C3semidirect
41. #4540C2×C3semidirect
42. #4465C2×C3semidirect
43. #4464C2×C3semidirect
143. #489C3×D3semidirect
378. C32#1661semidirect
432. C3#71245direct (N × H)
433. C3C3×#1661semidirect

Maximal subgroups

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

subgroupindex
C3×#56842
C32×#4892
C3×#50862
C3×#50812
C3×#45402
C3×#44652
C3×#44642
C3×#16613
#712453