Finite Group Databasebeta

← C3×#71170 #11778721

Subgroups — C3×#71170 #11778721

Order 1152.

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

normal subgroups only

This group has 473 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×#5602C211yesmaximal, characteristic
2C32×#481C211yesmaximal, characteristic
3C3×#4985C211yesmaximal, characteristic, complemented
4C3×#4970C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic
6C3×#4469C211yesmaximal, characteristic, complemented
7C3×#4467C211yesmaximal, characteristic, complemented
8C3×#1615—31nomaximal
9#71170C311yesmaximal, characteristic, direct product factor
10C32×#121C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C3×#935—21no—
13C3×#935—21no—
14C3×D4×Dic3—21no—
15C3×#924C2211yescharacteristic
16C2×C3×Dic3⋊C4C2211yescharacteristic
17C3×#889—21no—
18C3×#879—21no—
19C3×#878—21no—
20C32×#106—21no—
21C32×#102—21no—
22C32×C22⋊C8C2211yescharacteristic
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#810—21no—
28C3×#807—21no—
29C3×#539—31no—
30#5602C2×C311yescharacteristic
31C3×#484—31no—
32C3×#481—21no—
33C3×#481D311yescharacteristic
34C3×#481C2×C311yescharacteristic
35C3×#400—31no—
36#4985C2×C311yescharacteristic, complemented
37#4970C2×C311yescharacteristic, complemented
38C3×#328—31no—
39C3×#327—31no—
40C3×#324—31no—
41#4537C2×C311yescharacteristic
42#4469C2×C311yescharacteristic, complemented
43#4467C2×C311yescharacteristic, complemented
44C2×C32×D4—21no—
45C2×C32×D4D411yescharacteristic
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C2×C3×Dic6D411yescharacteristic
53C2×C32×C8—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58C3×#217—21no—
59C3×#217—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
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—31no—
77C3×C22⋊Q8—61no—
78C3×#121—21no—
79C3×#121C2×D311yescharacteristic
80C3×#121C22×C311yescharacteristic
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#935—21no—
87#935—21no—
88D4×Dic3—21no—
89#924C22×C311yescharacteristic
90C2×Dic3⋊C4C22×C311yescharacteristic
91#889—21no—
92#879—21no—
93#878—21no—
94C3×#107—61no—
95C3×#106—22no—
96C3×#106—21no—
97C3×#106—21no—
98C3×#103—61no—
99C3×#102—22no—
100C3×#102—21no—
101C3×#102—21no—
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#810—21no—
114#807—21no—
115C23×C32—21no—
116C23×C32C2×D411yescharacteristic
117C32×D4—41no—
118C32×D4—41no—
119C32×D4—41no—
120C2×C32×C4—21no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4—42no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3×Dic3—21no—
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—
136C2×C3×Dic3—81no—
137C3×Dic6—41no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140#539—31no—
141#484—31no—
142#481C3×D311yescharacteristic
143#400—31no—
144#328—31no—
145#327—31no—
146#324—31no—
147C2×C3×Q8—31no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—41no—
152C2×C3×D4#6711yescharacteristic
153C2×C3×D4C3×D411yescharacteristic
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—41no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C23×C311yescharacteristic
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3C3×D411yescharacteristic
167C22×Dic3C3×D411yescharacteristic
168C2×Dic6C3×D411yescharacteristic
169C2×C3×C8—22no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C2×C3×C8—61no—
173C3×C4⋊C4—22no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—31no—
180C3×C4⋊C4—41no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4#6711yescharacteristic
188C3×C4⋊C4C3×D411yescharacteristic
189C3×C22⋊C4—21no—
190C3×C22⋊C4—21no—
191C3×C22⋊C4—41no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C42—61no—
197#217—21no—
198#217—21no—
199#217—21no—
200#217—21no—
201C4⋊Dic3—21no—
202C4⋊Dic3C3×D411yescharacteristic
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208C4×Dic3—21no—
209C2×C3⋊C8—21no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—41no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32#12011yescharacteristic
216C22×C32#13511yescharacteristic
217C22×C32#13711yescharacteristic
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—41no—
221C32×C4—81no—
222C3×Dic3—41no—
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—31no—
232C22⋊Q8—61no—
233#121C2×C3×D311yescharacteristic
234C4×D4—61no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4C2×C3×D311yescharacteristic
237#107—61no—
238#106—21no—
239#103—61no—
240#102—21no—
241C22⋊C8—31no—
242C22⋊C8C2×C3×D311yescharacteristic
243#95—31no—
244#95—61no—
245#95—61no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—21no—
249C23×C3—41no—
250C23×C3D3×D411yescharacteristic
251C23×C3C2×C3×D411yescharacteristic
252C3×Q8—121no—
253C3×D4—41no—
254C3×D4—41no—
255C3×D4—42no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—81no—
261C3×D4—81no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4—42no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—82no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4—241no—
287C2×C3×C4D3×D411yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289C2×C3×C4C2×C3×D411yescharacteristic
290C2×C3×C4C2×C3×D411yescharacteristic
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—21no—
296C2×Dic3—21no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300C2×Dic3—41no—
301C2×Dic3—81no—
302Dic6—41no—
303C3×C8—42no—
304C3×C8—41no—
305C3×C8—41no—
306C3×C8—121no—
307C3⋊C8—41no—
308C2×C32—21no—
309C2×C32—21no—
310C2×C32—81no—
311C2×C32#45211yescharacteristic
312C2×C32#45411yescharacteristic
313C2×C32#45811yescharacteristic
314C2×Q8—31no—
315C2×D4—21no—
316C2×D4C3×#6711yescharacteristic
317C22×C4—21no—
318C22×C4—31no—
319C22×C4—31no—
320C22×C4—61no—
321C22×C4—61no—
322C22×C4C22×C3×D311yescharacteristic
323C2×C8—21no—
324C2×C8—61no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—31no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4C3×#6711yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—61no—
337C22⋊C4—61no—
338C22⋊C4—61no—
339C22⋊C4—61no—
340C42—61no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—81no—
357C22×C3—81no—
358C22×C3—81no—
359C22×C3#91511yescharacteristic
360C22×C3#91611yescharacteristic
361C22×C3#93711yescharacteristic
362C22×C3C3×#12011yescharacteristic
363C22×C3C3×#13511yescharacteristic
364C22×C3C3×#13711yescharacteristic
365C3×C4—22no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—41no—
371C3×C4—41no—
372C3×C4—41no—
373C3×C4—81no—
374C3×C4—82no—
375C3×C4—81no—
376C3×C4—81no—
377C3×C4—121no—
378C3×C4—121no—
379C3×C4—121no—
380C3×C4—121no—
381C3×C4—241no—
382Dic3—41no—
383Dic3—41no—
384Dic3—41no—
385Dic3—41no—
386Dic3—81no—
387C32#161511yescharacteristic, complemented, Sylow
388C23—21no—
389C23C3×D3×D411yescharacteristic
390Q8—121no—
391D4—41no—
392D4—41no—
393D4—41no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—241no—
409C2×C4C3×D3×D411yescharacteristic
410C2×C4C2×C3×#6711yescharacteristic
411C8—41no—
412C8—121no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—41no—
421C2×C3—41no—
422C2×C3—81no—
423C2×C3—81no—
424C2×C3—161no—
425C2×C3#505311yescharacteristic
426C2×C3#517311yescharacteristic
427C2×C3#520111yescharacteristic
428C2×C3C3×#45211yescharacteristic
429C2×C3C3×#45411yescharacteristic
430C2×C3C3×#45811yescharacteristic
431C22—21no—
432C22—21no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22C3×#91511yescharacteristic
437C22C3×#91611yescharacteristic
438C22C3×#93711yescharacteristic
439C4—21no—
440C4—21no—
441C4—41no—
442C4—81no—
443C4—121no—
444C4—121no—
445C4—121no—
446C4—121no—
447C4—241no—
448C3—21no—
449C3#7117011yescharacteristic, direct product factor
450C3C3×#161511yescharacteristic, complemented
451C2—21no—
452C2—21no—
453C2—81no—
454C2C3×#505311yescharacteristic
455C2C3×#517311yescharacteristic
456C2C3×#520111yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#481C2
socleC22×C32#120
prime radicalC32×#121C22
hypercenterC3×#481D3
hypocenterC3C3×#1615
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#481

Complements

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

NH ≅ G/Ntype
3. C3×#4985C2semidirect
4. C3×#4970C2semidirect
6. C3×#4469C2semidirect
7. C3×#4467C2semidirect
9. #71170C3direct (N × H)
36. #4985C2×C3semidirect
37. #4970C2×C3semidirect
42. #4469C2×C3semidirect
43. #4467C2×C3semidirect
387. C32#1615semidirect
449. C3#71170direct (N × H)
450. C3C3×#1615semidirect

Maximal subgroups

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

subgroupindex
C3×#56022
C32×#4812
C3×#49852
C3×#49702
C3×#45372
C3×#44692
C3×#44672
C3×#16153
#711703