Finite Group Databasebeta

← C3×#71957 #11780741

Subgroups — C3×#71957 #11780741

Order 1152.

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

normal subgroups only

This group has 466 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
1C32×#563C211yesmaximal, characteristic
2C3×#5069C211yesmaximal, characteristic, complemented
3C3×#5064C211yesmaximal, characteristic, complemented
4C3×#5055C211yesmaximal, characteristic
5C3×#4543C211yesmaximal, characteristic, complemented
6C3×#4543C211yesmaximal, characteristic, complemented
7C3×#4540C211yesmaximal, characteristic
8C3×#1664—31nomaximal
9#71957C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8—21no—
11C32×#126—21no—
12C32×#126—21no—
13C32×#125C2211yescharacteristic
14C32×#125C2211yescharacteristic
15C32×#124C2211yescharacteristic
16C32×#123—21no—
17C32×C22⋊Q8—21no—
18C32×C22⋊Q8—21no—
19C3×#869C2211yescharacteristic
20C3×#835—21no—
21C3×#832—21no—
22C3×#810—21no—
23C3×#810—21no—
24C3×#808—21no—
25C3×#807—21no—
26C3×#803C2211yescharacteristic
27C3×#803C2211yescharacteristic
28C3×#803C2211yescharacteristic
29C3×#563—21no—
30C3×#563D311yescharacteristic
31C3×#563C2×C311yescharacteristic
32C3×#501—31no—
33C3×#491—31no—
34C3×#489—31no—
35#5069C2×C311yescharacteristic, complemented
36#5064C2×C311yescharacteristic, complemented
37#5055C2×C311yescharacteristic
38C3×#330—31no—
39C3×#330—31no—
40C3×#329—31no—
41#4543C2×C311yescharacteristic, complemented
42#4543C2×C311yescharacteristic, complemented
43#4540C2×C311yescharacteristic
44C2×C32×Q8—21no—
45C2×C32×Q8D411yescharacteristic
46C2×C32×D4D411yescharacteristic
47C22×C32×C4—21no—
48C2×C3×Dic6—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C4⋊C4D411yescharacteristic
58C32×C4⋊C4D411yescharacteristic
59C32×C22⋊C4—21no—
60C32×C22⋊C4—21no—
61C32×C22⋊C4—21no—
62C32×C22⋊C4—21no—
63C32×C22⋊C4—21no—
64C32×C42—21no—
65C32×C42C2311yescharacteristic
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#1664—31noSylow
72C3×C4⋊Q8—22no—
73C3×C4⋊Q8—21no—
74C3×C4⋊Q8—21no—
75C3×C4⋊Q8—31no—
76C3×#126—22no—
77C3×#126—22no—
78C3×#126—21no—
79C3×#126—21no—
80C3×#126—21no—
81C3×#126—21no—
82C3×#125—21no—
83C3×#125—21no—
84C3×#125C2×D311yescharacteristic
85C3×#125C2×D311yescharacteristic
86C3×#125C22×C311yescharacteristic
87C3×#125C22×C311yescharacteristic
88C3×#124—21no—
89C3×#124C2×D311yescharacteristic
90C3×#124C22×C311yescharacteristic
91C3×#123—22no—
92C3×#123—21no—
93C3×#123—21no—
94C3×C22⋊Q8—22no—
95C3×C22⋊Q8—22no—
96C3×C22⋊Q8—21no—
97C3×C22⋊Q8—21no—
98C3×C22⋊Q8—21no—
99C3×C22⋊Q8—21no—
100#869C22×C311yescharacteristic
101C3×#107—61no—
102C3×#106—61no—
103C3×#103—61no—
104C3×#103—61no—
105C3×#103—61no—
106C3×#102—61no—
107C3×#97—31no—
108C3×#97—31no—
109C3×#97—31no—
110#835—21no—
111#832—21no—
112#810—21no—
113#810—21no—
114#808—21no—
115#807—21no—
116#803C22×C311yescharacteristic
117#803C22×C311yescharacteristic
118#803C22×C311yescharacteristic
119C23×C32—21no—
120C32×Q8—41no—
121C32×Q8—81no—
122C32×D4—41no—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—81no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C3×Dic3—41no—
133C3×Dic6—42no—
134C3×C3⋊C8—22no—
135C3×C3⋊C8—41no—
136C3×C3⋊C8—41no—
137#563C3×D311yescharacteristic
138#501—31no—
139#491—31no—
140#489—31no—
141#330—31no—
142#330—31no—
143#329—31no—
144C2×C3×Q8—22no—
145C2×C3×Q8—21no—
146C2×C3×Q8—21no—
147C2×C3×Q8—21no—
148C2×C3×Q8—61no—
149C2×C3×Q8#6711yescharacteristic
150C2×C3×Q8C3×D411yescharacteristic
151C2×C3×D4—21no—
152C2×C3×D4#6711yescharacteristic
153C2×C3×D4C3×D411yescharacteristic
154C22×C3×C4—22no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C2×Dic6—21no—
158C2×C3×C8—61no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—22no—
163C3×C4⋊C4—22no—
164C3×C4⋊C4—22no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4#6711yescharacteristic
186C3×C4⋊C4#6711yescharacteristic
187C3×C4⋊C4#6711yescharacteristic
188C3×C4⋊C4#6711yescharacteristic
189C3×C4⋊C4C3×D411yescharacteristic
190C3×C4⋊C4C3×D411yescharacteristic
191C3×C4⋊C4C3×D411yescharacteristic
192C3×C4⋊C4C3×D411yescharacteristic
193C3×C22⋊C4—22no—
194C3×C22⋊C4—22no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4—21no—
198C3×C22⋊C4—21no—
199C3×C22⋊C4—22no—
200C3×C22⋊C4—22no—
201C3×C22⋊C4—22no—
202C3×C22⋊C4—21no—
203C3×C22⋊C4—21no—
204C3×C22⋊C4—21no—
205C3×C22⋊C4—21no—
206C3×C22⋊C4—21no—
207C3×C22⋊C4—21no—
208C3×C42—22no—
209C3×C42—21no—
210C3×C42—21no—
211C3×C42—21no—
212C3×C42C22×D311yescharacteristic
213C3×C42C23×C311yescharacteristic
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32—41no—
222C22×C32#12011yescharacteristic
223C32×C4—21no—
224C32×C4—21no—
225C32×C4—21no—
226C32×C4—41no—
227C32×C4—41no—
228C32×C4—41no—
229C32×C4—41no—
230C32×C4—41no—
231C3×Dic3—81no—
232C4⋊Q8—21no—
233C4⋊Q8—31no—
234#126—21no—
235#126—21no—
236#125C2×C3×D311yescharacteristic
237#125C2×C3×D311yescharacteristic
238#124C2×C3×D311yescharacteristic
239#123—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242#107—61no—
243#106—61no—
244#103—61no—
245#103—61no—
246#103—61no—
247#102—61no—
248#97—31no—
249#97—31no—
250#97—31no—
251C23×C3—22no—
252C23×C3—21no—
253C23×C3—21no—
254C3×Q8—41no—
255C3×Q8—41no—
256C3×Q8—81no—
257C3×Q8—82no—
258C3×Q8—81no—
259C3×Q8—81no—
260C3×Q8—122no—
261C3×D4—41no—
262C3×D4—41no—
263C3×D4—81no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—82no—
283C2×C3×C4—81no—
284C2×C3×C4—81no—
285C2×C3×C4—121no—
286C2×C3×C4C2×#6711yescharacteristic
287C2×C3×C4C2×#6711yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289C2×C3×C4C2×C3×D411yescharacteristic
290C2×C3×C4C2×C3×D411yescharacteristic
291C2×C3×C4C2×C3×D411yescharacteristic
292C2×Dic3—41no—
293Dic6—42no—
294C3×C8—62no—
295C3×C8—121no—
296C3×C8—121no—
297C3⋊C8—22no—
298C3⋊C8—41no—
299C3⋊C8—41no—
300C2×C32—81no—
301C2×C32#45411yescharacteristic
302C2×C32#45511yescharacteristic
303C2×C32#45611yescharacteristic
304C2×Q8—21no—
305C2×Q8—61no—
306C2×Q8C3×#6711yescharacteristic
307C2×D4C3×#6711yescharacteristic
308C22×C4—21no—
309C2×C8—61no—
310C2×C8—61no—
311C2×C8—61no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4C3×#6711yescharacteristic
321C4⋊C4C3×#6711yescharacteristic
322C4⋊C4C3×#6711yescharacteristic
323C4⋊C4C3×#6711yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C42—21no—
330C42C22×C3×D311yescharacteristic
331C22×C3—21no—
332C22×C3—42no—
333C22×C3—42no—
334C22×C3—42no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3#95311yescharacteristic
342C22×C3C3×#12011yescharacteristic
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—41no—
352C3×C4—42no—
353C3×C4—42no—
354C3×C4—42no—
355C3×C4—42no—
356C3×C4—42no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—41no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—241no—
368Dic3—81no—
369C32#166411yescharacteristic, complemented, Sylow
370C23—21no—
371Q8—41no—
372Q8—81no—
373Q8—122no—
374D4—41no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—81no—
381C2×C4—121no—
382C2×C4C2×C3×#6711yescharacteristic
383C2×C4C2×C3×#6711yescharacteristic
384C2×C4C2×C3×#6711yescharacteristic
385C8—62no—
386C8—121no—
387C8—121no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—82no—
392C2×C3—81no—
393C2×C3—81no—
394C2×C3#524211yescharacteristic
395C2×C3#524511yescharacteristic
396C2×C3#524611yescharacteristic
397C2×C3C3×#45411yescharacteristic
398C2×C3C3×#45511yescharacteristic
399C2×C3C3×#45611yescharacteristic
400C22—41no—
401C22—41no—
402C22—41no—
403C22C3×#95311yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—241no—
413C3—21no—
414C3#7195711yescharacteristic, direct product factor
415C3C3×#166411yescharacteristic, complemented
416C2—81no—
417C2C3×#524211yescharacteristic
418C2C3×#524511yescharacteristic
419C2C3×#524611yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#563C2
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC3×#563D3
hypocenterC3C3×#1664
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#563

Complements

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

NH ≅ G/Ntype
2. C3×#5069C2semidirect
3. C3×#5064C2semidirect
5. C3×#4543C2semidirect
6. C3×#4543C2semidirect
9. #71957C3direct (N × H)
35. #5069C2×C3semidirect
36. #5064C2×C3semidirect
41. #4543C2×C3semidirect
42. #4543C2×C3semidirect
369. C32#1664semidirect
414. C3#71957direct (N × H)
415. C3C3×#1664semidirect

Maximal subgroups

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

subgroupindex
C32×#5632
C3×#50692
C3×#50642
C3×#50552
C3×#45432
C3×#45402
C3×#16643
#719573