Finite Group Databasebeta

← C3×#71178 #11778727

Subgroups — C3×#71178 #11778727

Order 1152.

468 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 98 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×#5645C211yesmaximal, characteristic
2C32×#484C211yesmaximal, characteristic, complemented
3C3×#4985C211yesmaximal, characteristic, complemented
4C3×#4968C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic
7C3×#4469C211yesmaximal, characteristic, complemented
8C3×#1615—31nomaximal
9#71178C311yesmaximal, characteristic, direct product factor
10C32×C22⋊Q8C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C3×#946—21no—
13C3×#930C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15C3×#898—21no—
16C3×#894—21no—
17C3×#890—21no—
18C3×#886—21no—
19C3×#67⋊C4—21no—
20C32×#107—21no—
21C32×#103—21no—
22C32×C22⋊C8C2211yescharacteristic
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#809—21no—
28C3×#808—21no—
29C3×#539—31no—
30#5645C2×C311yescharacteristic
31C3×#484—21no—
32C3×#484D311yescharacteristic, complemented
33C3×#484C2×C311yescharacteristic, complemented
34C3×#481—31no—
35C3×#400—31no—
36#4985C2×C311yescharacteristic, complemented
37#4968C2×C311yescharacteristic
38C3×#328—31no—
39C3×#327—31no—
40C3×#324—31no—
41#4538C2×C311yescharacteristic, complemented
42#4470C2×C311yescharacteristic
43#4469C2×C311yescharacteristic, complemented
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C32×C8—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4D411yescharacteristic
58C32×C22⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71#1615—31noSylow
72C3×#126—61no—
73C3×#125—61no—
74C3×#123—61no—
75C3×#123—61no—
76C3×C22⋊Q8—21no—
77C3×C22⋊Q8—61no—
78C3×C22⋊Q8C2×D311yescharacteristic
79C3×C22⋊Q8C22×C311yescharacteristic
80C3×#121—31no—
81C3×C4×D4—61no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×C3×C4⋊C4C22×C311yescharacteristic
86#946—21no—
87#930C22×C311yescharacteristic
88C2×Dic3⋊C4C22×C311yescharacteristic
89#898—21no—
90#894—21no—
91#890—21no—
92#886—21no—
93#67⋊C4—21no—
94C3×#107—22no—
95C3×#107—21no—
96C3×#107—21no—
97C3×#106—61no—
98C3×#103—22no—
99C3×#103—21no—
100C3×#103—21no—
101C3×#102—61no—
102C3×C22⋊C8—21no—
103C3×C22⋊C8—31no—
104C3×C22⋊C8C2×D311yescharacteristic
105C3×C22⋊C8C22×C311yescharacteristic
106C3×#95—31no—
107C3×#95—61no—
108C3×#95—61no—
109C3⋊#95—21no—
110C3⋊#95—21no—
111C3⋊#95C22×C311yescharacteristic
112#830C22×C311yescharacteristic
113#809—21no—
114#808—21no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C32×Q8—41no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4—42no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C3×#67—41no—
126C3×#67—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C3×D12—41no—
137C3×C4×D3—81no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140#539—31no—
141#484C3×D311yescharacteristic, complemented
142#481—31no—
143#400—31no—
144#328—31no—
145#327—31no—
146#324—31no—
147C2×C3×Q8—21no—
148C2×C3×Q8#6711yescharacteristic
149C2×C3×Q8C3×D411yescharacteristic
150C2×C3×D4—31no—
151C2×C3×D4—61no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—41no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C23×C311yescharacteristic
162C2×#67—21no—
163C22×Dic3—21no—
164C22×Dic3C3×D411yescharacteristic
165C22×Dic3C3×D411yescharacteristic
166C2×D12C3×D411yescharacteristic
167C2×C4×D3—21no—
168C2×C3×C8—22no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—61no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—31no—
181C3×C4⋊C4—41no—
182C3×C4⋊C4—41no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4#6711yescharacteristic
189C3×C4⋊C4C3×D411yescharacteristic
190C3×C22⋊C4—21no—
191C3×C22⋊C4—21no—
192C3×C22⋊C4—41no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C42—61no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—21no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3C3×D411yescharacteristic
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208C4×Dic3—21no—
209C2×C3⋊C8—21no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32#12011yescharacteristic
213C22×C32#13511yescharacteristic
214C22×C32#13711yescharacteristic
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C2×C3×D3—41no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—41no—
221C32×C4—41no—
222C32×C4—81no—
223C3×Dic3—41no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—81no—
227#126—61no—
228#125—61no—
229#123—61no—
230#123—61no—
231C22⋊Q8—61no—
232C22⋊Q8C2×C3×D311yescharacteristic
233#121—31no—
234C4×D4—61no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4C2×C3×D311yescharacteristic
237#107—21no—
238#106—61no—
239#103—21no—
240#102—61no—
241C22⋊C8—31no—
242C22⋊C8C2×C3×D311yescharacteristic
243#95—31no—
244#95—61no—
245#95—61no—
246C23×C3—21no—
247C23×C3—61no—
248C23×C3D3×D411yescharacteristic
249C23×C3C2×C3×D411yescharacteristic
250C22×D3—21no—
251C3×Q8—41no—
252C3×Q8—41no—
253C3×Q8—42no—
254C3×D4—121no—
255C3×D4—121no—
256C3×D4—121no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—82no—
279C2×C3×C4—121no—
280C2×C3×C4—121no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4—241no—
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286C2×C3×C4C2×C3×D411yescharacteristic
287C2×C3×C4C2×C3×D411yescharacteristic
288#67—41no—
289#67—41no—
290C2×Dic3—21no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—41no—
296C2×Dic3—41no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299D12—41no—
300C4×D3—81no—
301C3×C8—42no—
302C3×C8—41no—
303C3×C8—41no—
304C3×C8—121no—
305C3⋊C8—41no—
306C2×C32—21no—
307C2×C32—21no—
308C2×C32#45211yescharacteristic
309C2×C32#45411yescharacteristic
310C2×C32#45811yescharacteristic
311C3×D3—81no—
312C2×Q8C3×#6711yescharacteristic
313C2×D4—31no—
314C2×D4—61no—
315C22×C4—21no—
316C22×C4—31no—
317C22×C4—31no—
318C22×C4—61no—
319C22×C4—61no—
320C22×C4C22×C3×D311yescharacteristic
321C2×C8—21no—
322C2×C8—61no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—31no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4C3×#6711yescharacteristic
333C22⋊C4—21no—
334C22⋊C4—61no—
335C22⋊C4—61no—
336C22⋊C4—61no—
337C22⋊C4—61no—
338C42—61no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—121no—
349C22×C3—121no—
350C22×C3—121no—
351C22×C3#91811yescharacteristic
352C22×C3#91911yescharacteristic
353C22×C3#93711yescharacteristic
354C22×C3C3×#12011yescharacteristic
355C22×C3C3×#13511yescharacteristic
356C22×C3C3×#13711yescharacteristic
357C2×D3—41no—
358C2×D3—41no—
359C2×D3—41no—
360C3×C4—22no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—81no—
371C3×C4—81no—
372C3×C4—82no—
373C3×C4—81no—
374C3×C4—81no—
375C3×C4—121no—
376C3×C4—121no—
377C3×C4—121no—
378C3×C4—241no—
379Dic3—41no—
380Dic3—41no—
381Dic3—41no—
382Dic3—81no—
383C32#161511yescharacteristic, complemented, Sylow
384C23—61no—
385C23C3×D3×D411yescharacteristic
386Q8—41no—
387D4—121no—
388D4—121no—
389D4—121no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—121no—
401C2×C4—121no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4—241no—
405C2×C4C3×D3×D411yescharacteristic
406C2×C4C2×C3×#6711yescharacteristic
407C8—41no—
408C8—121no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—41no—
417C2×C3—41no—
418C2×C3—241no—
419C2×C3#505311yescharacteristic
420C2×C3#518711yescharacteristic
421C2×C3#520111yescharacteristic
422C2×C3C3×#45211yescharacteristic
423C2×C3C3×#45411yescharacteristic
424C2×C3C3×#45811yescharacteristic
425D3—81no—
426C22—21no—
427C22—21no—
428C22—121no—
429C22—121no—
430C22—121no—
431C22C3×#91811yescharacteristic
432C22C3×#91911yescharacteristic
433C22C3×#93711yescharacteristic
434C4—21no—
435C4—21no—
436C4—41no—
437C4—41no—
438C4—81no—
439C4—121no—
440C4—121no—
441C4—121no—
442C4—241no—
443C3—21no—
444C3#7117811yescharacteristic, direct product factor
445C3C3×#161511yescharacteristic, complemented
446C2—21no—
447C2—21no—
448C2—241no—
449C2C3×#505311yescharacteristic
450C2C3×#518711yescharacteristic
451C2C3×#520111yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#484C2
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC3×#484D3
hypocenterC3C3×#1615
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#484

Complements

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

NH ≅ G/Ntype
2. C32×#484C2semidirect
3. C3×#4985C2semidirect
5. C3×#4538C2semidirect
7. C3×#4469C2semidirect
9. #71178C3direct (N × H)
32. C3×#484D3semidirect
33. C3×#484C2×C3semidirect
36. #4985C2×C3semidirect
41. #4538C2×C3semidirect
43. #4469C2×C3semidirect
141. #484C3×D3semidirect
383. C32#1615semidirect
444. C3#71178direct (N × H)
445. C3C3×#1615semidirect

Maximal subgroups

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

subgroupindex
C3×#56452
C32×#4842
C3×#49852
C3×#49682
C3×#45382
C3×#44702
C3×#44692
C3×#16153
#711783