Finite Group Databasebeta

← C3×#68298 #11778733

Subgroups — C3×#68298 #11778733

Order 1152.

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

normal subgroups only

This group has 461 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
2C3×#5034C211yesmaximal, characteristic
3C3×#4722C211yesmaximal, characteristic, complemented
4C3×#4659C211yesmaximal, characteristic, complemented
5C32×#327C211yesmaximal, characteristic
6C3×#4469C211yesmaximal, characteristic, complemented
7C3×#4452C211yesmaximal, characteristic, complemented
8C3×#1615—31nomaximal
9#68298C311yesmaximal, characteristic, direct product factor
10C32×#121C2211yescharacteristic
11C3×#935—21no—
12C3×#935—21no—
13C3×D4×Dic3—21no—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C3×#924C2211yescharacteristic
16C2×C3×Dic3⋊C4C2211yescharacteristic
17C3×#889—21no—
18C3×#879—21no—
19C3×#878—21no—
20C32×C22⋊C8C2211yescharacteristic
21C32×#95C2211yescharacteristic
22C3×#832—21no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25C3×#830C2211yescharacteristic
26C3×#818—21no—
27C3×#816—21no—
28C3×#808—21no—
29C3×#539—31no—
30#5602C2×C311yescharacteristic
31C3×#484—31no—
32C3×#481—31no—
33C3×#400—31no—
34#5034C2×C311yescharacteristic
35#4722C2×C311yescharacteristic, complemented
36#4659C2×C311yescharacteristic, complemented
37C3×#328—31no—
38C3×#327—21no—
39C3×#327D311yescharacteristic
40C3×#327C2×C311yescharacteristic
41C3×#324—31no—
42#4469C2×C311yescharacteristic, complemented
43#4452C2×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⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C3×#217—21no—
57C3×#217—21no—
58C3×#217—21no—
59C3×#217—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—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—31no—
83C2×C3×C4⋊C4—31no—
84#935—21no—
85#935—21no—
86D4×Dic3—21no—
87C2×C4⋊Dic3C22×C311yescharacteristic
88#924C22×C311yescharacteristic
89C2×Dic3⋊C4C22×C311yescharacteristic
90#889—21no—
91#879—21no—
92#878—21no—
93C3×#107—61no—
94C3×#106—61no—
95C3×#103—61no—
96C3×#102—61no—
97C3×C22⋊C8—21no—
98C3×C22⋊C8—31no—
99C3×C22⋊C8C2×D311yescharacteristic
100C3×C22⋊C8C22×C311yescharacteristic
101C3×#95—21no—
102C3×#95—61no—
103C3×#95—61no—
104C3×#95C2×D311yescharacteristic
105C3×#95C22×C311yescharacteristic
106#832—21no—
107C3⋊#95—21no—
108C3⋊#95—21no—
109#830C22×C311yescharacteristic
110#818—21no—
111#816—21no—
112#808—21no—
113C23×C32—21no—
114C23×C32C2×D411yescharacteristic
115C32×D4—41no—
116C32×D4—41no—
117C32×D4—41no—
118C2×C32×C4—21no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—81no—
135C3×Dic6—41no—
136C32×C8—41no—
137C3×C3⋊C8—41no—
138#539—31no—
139#484—31no—
140#481—31no—
141#400—31no—
142#328—31no—
143#327C3×D311yescharacteristic
144#324—31no—
145C2×C3×Q8—31no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—41no—
150C2×C3×D4D1211yescharacteristic
151C2×C3×D4C3×D411yescharacteristic
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
162C22×Dic3—21no—
163C22×Dic3—21no—
164C22×Dic3C3×D411yescharacteristic
165C22×Dic3C3×D411yescharacteristic
166C2×Dic6C3×D411yescharacteristic
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—41no—
170C2×C3×C8—61no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4D1211yescharacteristic
182C3×C4⋊C4C3×D411yescharacteristic
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—41no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C42—61no—
191#217—21no—
192#217—21no—
193#217—21no—
194#217—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3C3×D411yescharacteristic
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—21no—
204C4×Dic3—21no—
205C2×C3⋊C8—21no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32—41no—
209C22×C32—41no—
210C22×C32—41no—
211C22×C32#12011yescharacteristic
212C22×C32#13511yescharacteristic
213C22×C32#13711yescharacteristic
214C32×C4—21no—
215C32×C4—21no—
216C32×C4—41no—
217C32×C4—81no—
218C3×Dic3—41no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—81no—
223#126—61no—
224#125—61no—
225#123—61no—
226#123—61no—
227C22⋊Q8—31no—
228C22⋊Q8—61no—
229#121C2×C3×D311yescharacteristic
230C4×D4—61no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—31no—
233#107—61no—
234#106—61no—
235#103—61no—
236#102—61no—
237C22⋊C8—31no—
238C22⋊C8C2×C3×D311yescharacteristic
239#95—61no—
240#95—61no—
241#95C2×C3×D311yescharacteristic
242C23×C3—21no—
243C23×C3—21no—
244C23×C3—21no—
245C23×C3—41no—
246C23×C3D3×D411yescharacteristic
247C23×C3C2×C3×D411yescharacteristic
248C3×Q8—121no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—41no—
252C3×D4—41no—
253C3×D4—41no—
254C3×D4—41no—
255C3×D4—81no—
256C3×D4—81no—
257C3×D4—81no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—42no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—81no—
279C2×C3×C4—81no—
280C2×C3×C4—81no—
281C2×C3×C4—121no—
282C2×C3×C4—122no—
283C2×C3×C4—121no—
284C2×C3×C4—241no—
285C2×C3×C4C2×D1211yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4C2×C3×D411yescharacteristic
288C2×C3×C4C2×C3×D411yescharacteristic
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—41no—
296C2×Dic3—42no—
297C2×Dic3—41no—
298C2×Dic3—81no—
299Dic6—41no—
300C3×C8—41no—
301C3×C8—41no—
302C3×C8—81no—
303C3×C8—121no—
304C3⋊C8—41no—
305C2×C32—21no—
306C2×C32—21no—
307C2×C32—81no—
308C2×C32#45211yescharacteristic
309C2×C32#45411yescharacteristic
310C2×C32#45811yescharacteristic
311C2×Q8—31no—
312C2×D4—21no—
313C2×D4C3×D1211yescharacteristic
314C22×C4—21no—
315C22×C4—31no—
316C22×C4—31no—
317C22×C4—61no—
318C22×C4—61no—
319C22×C4C22×C3×D311yescharacteristic
320C2×C8—21no—
321C2×C8—61no—
322C4⋊C4—31no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4C3×D1211yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—61no—
334C22⋊C4—61no—
335C22⋊C4—61no—
336C22⋊C4—61no—
337C42—61no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—81no—
354C22×C3—81no—
355C22×C3—81no—
356C22×C3#88211yescharacteristic
357C22×C3#91211yescharacteristic
358C22×C3#91511yescharacteristic
359C22×C3C3×#12011yescharacteristic
360C22×C3C3×#13511yescharacteristic
361C22×C3C3×#13711yescharacteristic
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—81no—
371C3×C4—81no—
372C3×C4—81no—
373C3×C4—82no—
374C3×C4—121no—
375C3×C4—121no—
376C3×C4—121no—
377C3×C4—121no—
378C3×C4—241no—
379Dic3—41no—
380Dic3—41no—
381Dic3—41no—
382Dic3—41no—
383Dic3—81no—
384C32#161511yescharacteristic, complemented, Sylow
385C23—21no—
386C23C3×D3×D411yescharacteristic
387Q8—121no—
388D4—41no—
389D4—41no—
390D4—41no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—121no—
403C2×C4—122no—
404C2×C4—121no—
405C2×C4—241no—
406C2×C4C2×C3×D1211yescharacteristic
407C2×C4C3×D3×D411yescharacteristic
408C8—41no—
409C8—121no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—41no—
418C2×C3—41no—
419C2×C3—81no—
420C2×C3—81no—
421C2×C3—161no—
422C2×C3#474211yescharacteristic
423C2×C3#478311yescharacteristic
424C2×C3#482711yescharacteristic
425C2×C3C3×#45211yescharacteristic
426C2×C3C3×#45411yescharacteristic
427C2×C3C3×#45811yescharacteristic
428C22—21no—
429C22—21no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22C3×#88211yescharacteristic
434C22C3×#91211yescharacteristic
435C22C3×#91511yescharacteristic
436C4—21no—
437C4—21no—
438C4—41no—
439C4—81no—
440C4—121no—
441C4—121no—
442C4—121no—
443C4—121no—
444C4—241no—
445C3—21no—
446C3#6829811yescharacteristic, direct product factor
447C3C3×#161511yescharacteristic, complemented
448C2—21no—
449C2—21no—
450C2—81no—
451C2C3×#474211yescharacteristic
452C2C3×#478311yescharacteristic
453C2C3×#482711yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#327C2
socleC22×C32#120
prime radicalC32×#121C22
hypercenterC3×#327D3
hypocenterC3C3×#1615
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#327

Complements

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

NH ≅ G/Ntype
3. C3×#4722C2semidirect
4. C3×#4659C2semidirect
6. C3×#4469C2semidirect
7. C3×#4452C2semidirect
9. #68298C3direct (N × H)
35. #4722C2×C3semidirect
36. #4659C2×C3semidirect
42. #4469C2×C3semidirect
43. #4452C2×C3semidirect
384. C32#1615semidirect
446. C3#68298direct (N × H)
447. C3C3×#1615semidirect

Maximal subgroups

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

subgroupindex
C3×#56022
C3×#50342
C3×#47222
C3×#46592
C32×#3272
C3×#44692
C3×#44522
C3×#16153
#682983